Handbook of Supernovae 9783319218465, 9783319218458, 9783319218472

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Athem W. Alsabti Paul Murdin Editors

Handbook of Supernovae

Handbook of Supernovae

Athem W. Alsabti • Paul Murdin Editors

Handbook of Supernovae With 850 Figures and 60 Tables

123

Editors Athem W. Alsabti University College London Observatory University College London London, UK

Paul Murdin Institute of Astronomy University of Cambridge Cambridge, UK

ISBN 978-3-319-21845-8 ISBN 978-3-319-21846-5 (eBook) ISBN 978-3-319-21847-2 (print and electronic bundle) https://doi.org/10.1007/978-3-319-21846-5 Library of Congress Control Number: 2017943059 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To our host institutions for their tolerant hospitality: University College London Observatory and Institute of Astronomy, Cambridge

Preface

The term “supernovae” was first coined and used in 1931 to refer to eruptions of stars more powerful than novae. By 1938, the term “supernovae” was used to refer to a class of explosive stars discovered in many galaxies. Further studies revealed that our own Galaxy was a host of many such events recorded in history such as the Crab Nebula (SN1054 AD), Tycho’s Supernova (SN1572 AD), and Kepler’s Supernova (SN1604 AD), among many others discovered more recently with modern detection methods. With the advance of physics in the 1930s, the way stars synthesize elements beyond hydrogen and helium became increasingly understood; quantum mechanics gave rise to an understanding of white dwarf stars and the prediction of neutron stars and general relativity to black holes. In other words, the fate of the various types of stars was becoming clearer. However, there were still many issues relating to these problems that remained to be solved. Other landmarks related to supernovae worth mentioning include the lecture that Subrahmanyan Chandrasekhar gave in 1935 to the Royal Astronomical Society predicting theoretically the possible collapse of white dwarfs of a specific mass into a black hole. Another is the paper of 1957 known as B2 FH (referring to its authors, Margret Burbidge, Geoffrey Burbidge, William Fowler, and Fred Hoyle), where the road map was laid out for the mechanism of how stars manufacture the chemical elements. This paper, and subsequent research in explosive astrophysics, pushed our knowledge of how supernovae of a variety of types lead to the nucleosynthesis of heavy elements in the periodic table and in particular those with atomic number higher than iron. Indeed, we probably owe our existence in some way to supernovae for the processes which have influenced the creation and evolution of the solar system, planets, and life. On the observational side, Supernova 1987A, a relatively nearby supernova, even if in a neighbor galaxy, not our own, was close enough to be studied in detail, leading not only to an interest in neutrino astrophysics but also to a refined understanding of the supernova phenomenon, that is, the bright star that appears and fades. On one hand, the observation of neutrinos led to a focus on the crucial role that neutrinos play in supernovae. Additionally, focus on the explosion phenomenon in various types of supernova led to the discovery that the members of a particular class – the

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Type Ia supernovae – explode in such a way as to be considered a standard candle. The brightness of these objects, visible in galaxies at vast distances, means that they can be used to determine the size and the expansion rate of the Universe. These methods have recently been refined to such a high degree and applied to observations of such accuracy in programs of such statistical scope that they uncovered the accelerating nature of the cosmic expansion. A big influence on our own personal involvement in supernova studies took off in the 1960s when the first pulsar was discovered by Antony Hewish and his student Jocelyn Bell in 1967. At that time, both of us were students, one of us at Manchester University and the other at Oxford University. This event contributed to our choices of research topics as postgraduate students and postdoctoral fellows, at Manchester and at Rochester, NY, and Herstmonceux, respectively. One of us studied evolved supernova remnants (like the Monoceros Loop) and the other pulsars (the Crab and Vela pulsars) and black holes (like Cygnus X-1), all of them the outcome of corecollapse supernovae. Our personal fascination with supernova science has lasted ever since, even if now we get most of our satisfaction by observing what the young people are discovering than discovering new stuff ourselves. It has been a great pleasure to read the articles in this collection as they came in and learn what has happened since we retired from active research. We have been particularly drawn to an interest in a new branch of astronomy – astrochemistry – that indicated that complex molecules are created in space, many of them organic. Evidence has been found on the Earth, on the Moon, and in meteorites of radio isotopes indicative of an impact of direct radiation on the solar system and of the solar system passing through single and multiple remnants of expanding supernovae of various ages. An even newer branch of astronomy, the study of gravitational waves, has combined just one year of observation with a century of theory to add extra impact and relevance to research into supernovae and the black holes which they can create. Astronomy is about natural phenomena studied by whatever science is appropriate. Nowhere is this more true than in the field of supernova research. It encompasses several scientific fields, some of which seem not at first to be closely related. Supernovae and the phenomena associated with them bring together branches of physics and chemistry, even meteorology and biology, in connected multidisciplinary studies of interest to a wide variety of specialists. For all these reasons, and with our personal interest in supernova research, we set out to edit this major reference work. Our aim was to bring together the advanced work in the many fields connected to supernovae in such a way that one specialist viewing supernovae through the spectacles of his or her own expertise could find the expertise of a specialist in another area to help put together a more complete picture. Nothing would please us more than to learn in the future of a doctoral student finding a connection in this book between his or her own work and some other aspect of supernova research. There have already been published several excellent books about individual branches of this topic. Some are very advanced, while others less so. There are proceedings of conferences on specific elements of the topic. However, to our

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knowledge, this is the first inclusive didactic work on the complete range of supernova science published to date – as complete as we could make it. Both of us are active members of the International Astronomical Union (IAU). It was during IAU General Assembly meetings worldwide that the idea for undertaking this work emerged, encouraged by Maury Solomon, who also attended the IAU General Assembly meetings, tempting authors and editors to publish with Springer. Her direct encouragement to us as we speculated about the book and her subsequent visits to the UK gave us the “push” to go ahead. Once work started on this large reference work, Springer gave us all the support we needed, assembling a team led by Daniela Graf and Kerstin Beckert who took the responsibility of managing the large number of authors and scientific editors to deliver the final papers to production. This book consists of 12 parts. Each part has had a section editor who planned the detail of what was to be covered in each part, selected and contacted the authors to fit into our overall plan, and acted as referees for the contributions. We read and approved every paper ourselves, editing the presentation if necessary. Clearly, the section editors and the authors are the heroes of this work, and we thank them for the support of this project. London, UK Cambridge, UK

Athem W. Alsabti Paul Murdin

Contents

Volume 1 Part I Supernovae and Supernova Remnants . . . . . . . . . . . . . . . . . . . . 1

2

Supernovae and Supernova Remnants: The Big Picture in Low Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Athem W. Alsabti and Paul Murdin Discovery, Confirmation, and Designation of Supernovae . . . . . . . Hitoshi Yamaoka

Part II

1

3 29

Historical Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

3

Historical Supernovae in the Galaxy from AD 1006 . . . . . . . . . . . . David A. Green

37

4

Historical Records of Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Richard Stephenson

49

5

Supernova of 1006 (G327.6C14.6) . . . . . . . . . . . . . . . . . . . . . . . . . . . Satoru Katsuda

63

6

Supernova of 1054 and its Remnant, the Crab Nebula . . . . . . . . . . Roger Blandford and Rolf Bühler

83

7

Supernova of AD 1181 and its Remnant: 3C 58 . . . . . . . . . . . . . . . . Roland Kothes

97

8

Supernova of 1572, Tycho’s Supernova . . . . . . . . . . . . . . . . . . . . . . . Anne Decourchelle

117

9

Supernova 1604, Kepler’s Supernova, and its Remnant . . . . . . . . . Jacco Vink

139

10

Supernova Remnant Cassiopeia A . . . . . . . . . . . . . . . . . . . . . . . . . . . Bon-Chul Koo and Changbom Park

161

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11

Contents

Possible and Suggested Historical Supernovae in the Galaxy . . . . . David A. Green and F. Richard Stephenson

Part III

179

Types of Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

193

12

Observational and Physical Classification of Supernovae . . . . . . . . Avishay Gal-Yam

195

13

Hydrogen-Rich Core-Collapse Supernovae . . . . . . . . . . . . . . . . . . . . Iair Arcavi

239

14

Hydrogen-Poor Core-Collapse Supernovae . . . . . . . . . . . . . . . . . . . . Elena Pian and Paolo A. Mazzali

277

15

Type Ia Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kate Maguire

293

16

The Extremes of Thermonuclear Supernovae . . . . . . . . . . . . . . . . . . Stefan Taubenberger

317

17

Type Iax Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Saurabh W. Jha

375

18

Interacting Supernovae: Types IIn and Ibn . . . . . . . . . . . . . . . . . . . Nathan Smith

403

19

Superluminous Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Andrew Howell

431

Part IV

Supernovae and Stellar Evolution . . . . . . . . . . . . . . . . . . . . . . .

459

20

Low- and Intermediate-Mass Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . Amanda I. Karakas

461

21

Electron Capture Supernovae from Super Asymptotic Giant Branch Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ken’ichi Nomoto and Shing-Chi Leung

22

Supernovae from Massive Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marco Limongi

23

Very Massive and Supermassive Stars: Evolution and Fate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Raphael Hirschi

483 513

567

24

Supernovae from Rotating Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Georges Meynet and André Maeder

601

25

The Progenitor of SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Philipp Podsiadlowski

635

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26

Close Binary Stellar Evolution and Supernovae . . . . . . . . . . . . . . . . Omar G. Benvenuto and Melina C. Bersten

649

27

Population Synthesis of Massive Close Binary Evolution . . . . . . . . J. J. Eldridge

671

28

Supernova Progenitors Observed with HST . . . . . . . . . . . . . . . . . . . Schuyler D. Van Dyk

693

Volume 2 Part V

Light Curves and Spectra of Supernovae . . . . . . . . . . . . . . . . . .

721

29

Light Curves of Type I Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . Melina C. Bersten and Paolo A. Mazzali

723

30

Light Curves of Type II Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . Luca Zampieri

737

31

Spectra of Supernovae During the Photospheric Phase . . . . . . . . . Stuart A. Sim

769

32

Spectra of Supernovae in the Nebular Phase . . . . . . . . . . . . . . . . . . Anders Jerkstrand

795

33

Interacting Supernovae: Spectra and Light Curves . . . . . . . . . . . . . Sergei Blinnikov

843

34

Thermal and Non-thermal Emission from Circumstellar Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Roger A. Chevalier and Claes Fransson

875

35

Unusual Supernovae and Alternative Power Sources . . . . . . . . . . . Daniel Kasen

939

36

Shock Breakout Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eli Waxman and Boaz Katz

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37

Introduction to Supernova Polarimetry . . . . . . . . . . . . . . . . . . . . . . . 1017 Ferdinando Patat

Part VI

Explosion Mechanisms of Supernovae . . . . . . . . . . . . . . . . . . . 1051

38

Explosion Physics of Core-Collapse Supernovae . . . . . . . . . . . . . . . 1053 Thierry Foglizzo

39

Neutron Star Matter Equation of State . . . . . . . . . . . . . . . . . . . . . . . 1075 Jorge Piekarewicz

40

Neutrino-Driven Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095 Hans-Thomas Janka

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41

Explosion Physics of Thermonuclear Supernovae and Their Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1151 Peter Hoeflich

42

Combustion in Thermonuclear Supernova Explosions . . . . . . . . . . 1185 Friedrich K. Röpke

43

Evolution of Accreting White Dwarfs to the Thermonuclear Runaway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1211 Sumner Starrfield

44

Dynamical Mergers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1237 Enrique García–Berro and Pablo Lorén–Aguilar

45

Violent Mergers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1257 Rüdiger Pakmor

46

Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1275 Ken’ichi Nomoto and Shing-Chi Leung

Part VII

Stellar Remnants: Neutron Stars and Black Holes . . . . . . . . . . 1315

47

The Masses of Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317 Jorge E. Horvath and Rodolfo Valentim

48

Nuclear Matter in Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1331 Pawel Haensel and Julian L. Zdunik

49

Thermal Evolution of Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . 1353 Ulrich R. M. E. Geppert

50

Evolution of the Magnetic Field of Neutron Stars . . . . . . . . . . . . . . 1375 Chengmin M. Zhang

51

X-Ray Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385 Roland Walter and Carlo Ferrigno

52

Young Neutron Stars with Soft Gamma Ray Emission and Anomalous X-Ray Pulsars . . . . . . . . . . . . . . . . . . . . . . 1401 Gennady S. Bisnovatyi-Kogan

53

Strange Quark Matter Inside Neutron Stars . . . . . . . . . . . . . . . . . . 1423 Fridolin Weber

54

Neutron Stars as Probes for General Relativity and Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1447 Norbert Wex

55

Gamma Ray Pulsars: From Radio to Gamma Rays . . . . . . . . . . . . 1471 Jumpei Takata

Contents

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X-Ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1499 Jorge Casares, Peter Gustaaf Jonker, and Garik Israelian

57

Supernovae and the Evolution of Close Binary Systems . . . . . . . . . 1527 Edward P. J. van den Heuvel

58

The Core-Collapse Supernova-Black Hole Connection . . . . . . . . . . 1555 Evan O’Connor

Part VIII

Neutrinos, Gravitational Waves, and Cosmic Rays . . . . . . . . . 1573

59

Neutrino Emission from Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . 1575 Hans-Thomas Janka

60

Neutrino Signatures from Young Neutron Stars . . . . . . . . . . . . . . . . 1605 Luke F. Roberts and Sanjay Reddy

61

Diffuse Neutrino Flux from Supernovae . . . . . . . . . . . . . . . . . . . . . . 1637 Cecilia Lunardini

62

Neutrinos from Core-Collapse Supernovae and Their Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1655 Francis Halzen and Kate Scholberg

63

Gravitational Waves from Core-Collapse Supernovae . . . . . . . . . . 1671 Kei Kotake and Takami Kuroda

64

Detecting Gravitational Waves from Supernovae with Advanced LIGO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1699 Matthew Evans and Michele Zanolin

65

High-Energy Cosmic Rays from Supernovae . . . . . . . . . . . . . . . . . . 1711 Giovanni Morlino

66

High-Energy Gamma Rays from Supernova Remnants . . . . . . . . . 1737 Stefan Funk

Volume 3 Part IX Nucleosynthesis in Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . 1751 67

Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1753 Hideyuki Umeda and Takashi Yoshida

68

The Multidimensional Character of Nucleosynthesis in Core-Collapse Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1771 W. Raphael Hix and J. Austin Harris

69

Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Supernova Mechanism . . . . . . . . . . . . . . . . . . 1791 Sean M. Couch

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70

Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1805 Gabriel Martínez-Pinedo, Tobias Fischer, Karlheinz Langanke, Andreas Lohs, Andre Sieverding, and Meng-Ru Wu

71

Making the Heaviest Elements in a Rare Class of Supernovae . . . 1843 Friedrich-Karl Thielemann, Marius Eichler, Igor Panov, Marco Pignatari, and Benjamin Wehmeyer

72

Pre-supernova Evolution and Nucleosynthesis in Massive Stars and Their Stellar Wind Contribution . . . . . . . . . . . . 1879 Raphael Hirschi

73

Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1931 Ken’ichi Nomoto

74

Nucleosynthesis in Thermonuclear Supernovae . . . . . . . . . . . . . . . . 1955 Ivo Rolf Seitenzahl and Dean M. Townsley

Part X Evolution of Supernovae and the Interstellar Medium . . . . . . 1979 75

Dynamical Evolution and Radiative Processes of Supernova Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1981 Stephen P. Reynolds

76

Galactic and Extragalactic Samples of Supernova Remnants: How They Are Identified and What They Tell Us . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2005 Knox S. Long

77

Radio Emission from Supernova Remnants . . . . . . . . . . . . . . . . . . . 2041 Gloria Dubner

78

X-Ray Emission Properties of Supernova Remnants . . . . . . . . . . . . 2063 Jacco Vink

79

Ultraviolet and Optical Insights into Supernova Remnant Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2087 William P. Blair and John C. Raymond

80

Infrared Emission from Supernova Remnants: Formation and Destruction of Dust . . . . . . . . . . . . . . . . . . . . . . . . . . 2105 Brian J. Williams and Tea Temim

81

Dust and Molecular Formation in Supernovae . . . . . . . . . . . . . . . . . 2125 Mikako Matsuura

82

Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2159 Patrick Slane

Contents

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83

The Physics of Supernova 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2181 Richard McCray

84

The Supernova – Supernova Remnant Connection . . . . . . . . . . . . . 2211 Dan Milisavljevic and Robert A. Fesen

85

Supernova Remnants as Clues to Their Progenitors . . . . . . . . . . . . 2233 Daniel Patnaude and Carles Badenes

Part XI Supernovae and the Environment of the Solar System . . . . . . 2251 86

Effect of Supernovae on the Local Interstellar Material . . . . . . . . . 2253 Priscilla Frisch and Vikram V. Dwarkadas

87

Structures in the Interstellar Medium Caused by Supernovae: The Local Bubble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2287 Jonathan D. Slavin

88

Gould’s Belt: Local Large-Scale Structure in the Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2301 Jan Palouš and Soˇna Ehlerová

89

The Effects of Supernovae on the Dynamical Evolution of Binary Stars and Star Clusters . . . . . . . . . . . . . . . . . . . 2313 Richard J. Parker

90

Isotope Variations in the Solar System: Supernova Fingerprints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2331 Ulrich Ott

91

Impact of Supernovae on the Interstellar Medium and the Heliosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2359 D. Breitschwerdt, R. C. Tautz, and M. A. de Avillez

92

Determining Amino Acid Chirality in the Supernova Neutrino Processing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2383 Michael A. Famiano and Richard N. Boyd

93

Supernovae and the Formation of Planetary Systems . . . . . . . . . . . 2401 Alan P. Boss

94

Mass Extinctions and Supernova Explosions . . . . . . . . . . . . . . . . . . 2419 Gunther Korschinek

95

Galactic Winds and the Role Played by Massive Stars . . . . . . . . . . 2431 Timothy M. Heckman and Todd A. Thompson

96

Supernovae and the Chemical Evolution of Galaxies . . . . . . . . . . . 2455 Mike G. Edmunds

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Stardust from Supernovae and Its Isotopes . . . . . . . . . . . . . . . . . . . . 2473 Peter Hoppe

98

Supernovae, Our Solar System, and Life on Earth . . . . . . . . . . . . . 2489 Arnold Hanslmeier

99

The Moon as a Recorder of Nearby Supernovae . . . . . . . . . . . . . . . 2507 Ian A. Crawford

Part XII Cosmology from Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . 2523 100

History of Supernovae as Distance Indicators . . . . . . . . . . . . . . . . . 2525 Bruno Leibundgut

101

The Peak Luminosity–Decline Rate Relationship for Type Ia Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2543 Mark M. Phillips and Christopher R. Burns

102

Low-z Type Ia Supernova Calibration . . . . . . . . . . . . . . . . . . . . . . . . 2563 Mario Hamuy

103

The Hubble Constant from Supernovae . . . . . . . . . . . . . . . . . . . . . . . 2577 Abhijit Saha and Lucas M. Macri

104

The Infrared Hubble Diagram of Type Ia Supernovae . . . . . . . . . . 2593 Kevin Krisciunas

105

Discovery of Cosmic Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2605 Peter Garnavich

106

Confirming Cosmic Acceleration in the Decade That Followed from SNe Ia at z > 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2615 Adam G. Riess

107

Characterizing Dark Energy Through Supernovae . . . . . . . . . . . . . 2623 Tamara M. Davis and David Parkinson

108

Supernova Cosmology in the Big Data Era . . . . . . . . . . . . . . . . . . . . 2647 Richard Kessler

109

Cosmology with Type IIP Supernovae . . . . . . . . . . . . . . . . . . . . . . . . 2671 Peter Nugent and Mario Hamuy

Index of Supernovae, Supernova Remnants and Compact Stellar Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2689 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2697

About the Editors

Born in Iraq in 1945, Athem W. Alsabti moved to the UK on a scholarship to the University of Manchester. He obtained his BSc in mathematical physics in 1967, his MSc in 1968 (astrophysics, supernovae), and his PhD in 1970 (“Investigating very faint nebulosities associated with non-thermal galactic radio sources”). He now works at University College London, in the Department of Physics and Astronomy. Dr. Alsabti’s research interests are in the origin and evolution of supernovae and interstellar matter. Dr. Alsabti was also a professor of physics at Baghdad University and founded the Baghdad Planetarium and Iraqi National Observatory. He has been an active member of the International Astronomical Union (IAU) since 1973 and is a fellow of the Royal Astronomical Society (RAS). In the IAU, he is a member of the Advanced Development Projects Group. Dr. Alsabti is also a member of the World Space Observatory Committee and a consultant to the Cornwall Observatory and Planetarium Project. Educated at the Universities of Oxford and Rochester, NY, Paul Murdin has worked as an astronomer in the USA, Australia, England, Scotland, and Spain, where he led the operation of the Anglo-Dutch Isaac Newton Group of telescopes in the Canary Islands. He has been a research scientist (studying supernovae, neutron stars, and black holes – in 1972 Paul discovered the nature of the first black hole known in our galaxy, Cygnus X-1) and a science administrator for the UK government and the Royal Astronomical Society. He works at the Institute of Astronomy at the University of Cambridge, England, and is visiting professor at John Moores University, Liverpool. He has a secondary career as a broadcaster and commentator for the BBC and CNN, as well as a lecturer and writer on astronomy, including repeat appearances xix

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About the Editors

on BBC Radio 4’s In Our Time and at a number of literary and science festivals, like those at Hay-on-Wye and Edinburgh, and on the Cunard Liner Queen Elizabeth 2. His most recent books include Secrets of the Universe: How We Discovered the Universe (Thames and Hudson 2009), Mapping the Universe (Carlton 2011), and Are We Being Watched? The Search for Life in the Cosmos (Thames and Hudson 2013).

Contributors

Athem W. Alsabti University College London Observatory, University College London, London, UK Iair Arcavi Department of Physics, University of California, Santa Barbara, CA, USA Las Cumbres Observatory Global Telescope Network, Goleta, CA, USA Carles Badenes Department of Physics and Astronomy, Pittsburgh Particle Physics, Astrophysics, and Cosmology Center (PITT-PACC), University of Pittsburgh, Pittsburgh, PA, USA Omar G. Benvenuto Institute of Astrophysics La Plata (IALP), CCT-CONICETUNLP, La Plata, Argentina Faculty of Astronomical and Geophysical Sciences, National University of La Plata, La Plata, Argentina Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan Melina C. Bersten Member of the Carrera del Investigador Científico de la Comisión de Investigaciones Científicas de la Provincia de Buenos Aires (CIC), La Plata (Bs A), Argentina Institute of Astrophysics La Plata (IALP), CCT-CONICET-UNLP, La Plata, Argentina Faculty of Astronomical and Geophysical Sciences, National University of La Plata, La Plata, Argentina Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan Gennady S. Bisnovatyi-Kogan Space Research Institute of Russian Academy of Sciences, Moscow, Russia Moscow Engineering Physics Institute (MEPhI), National Research Nuclear University, Moscow, Russia xxi

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Contributors

William P. Blair Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA Roger Blandford Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, USA Sergei Blinnikov Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), Kashiwa, Chiba, Japan Alan P. Boss Department of Terrestrial Magnetism (DTM), Carnegie Institution for Science, Washington, DC, USA Richard N. Boyd Department of Physics, Department of Astronomy, Ohio State University (Emeritus), Columbus, OH, USA D. Breitschwerdt Department of Astronomy and Astrophysics, Berlin Institute of Technology, Berlin, Germany Rolf Bühler Deutsches Elektronen Synchrotron (DESY), Zeuthen, Germany Christopher R. Burns Carnegie Observatories, Pasadena, CA, USA Jorge Casares Instituto de Astrofísica de Canarias, La Laguna, Tenerife, Spain Departamento de Astrofísica, Universidad de La Laguna, La Laguna, Tenerife, Spain Department of Physics, Astrophysics, University of Oxford, Oxford, UK Roger A. Chevalier Department of Astronomy, University of Virginia, Charlottesville, VA, USA Sean M. Couch Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA Ian A. Crawford Department of Earth and Planetary Sciences, Birkbeck College, University of London, London, UK Tamara M. Davis ARC Centre of Excellence for All-sky Astrophysics (CAASTRO), Brisbane, QLD, Australia School of Mathematics and Physics, University of Queensland, Brisbane, QLD, Australia M. A. de Avillez Department of Mathematics, University of Évora, Évora, Portugal Anne Decourchelle Laboratoire AIM-Paris-Saclay (CEA/DRF/Irfu, CNRS/INSU, University Paris Diderot), CEA Saclay, Gif sur Yvette, Paris, France Gloria Dubner Institute of Astronomy and Space Physics (IAFE), CONICET, University of Buenos Aires, Buenos Aires, Argentina

Contributors

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Vikram V. Dwarkadas Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL, USA Mike G. Edmunds School of Physics and Astronomy, Cardiff University, Wales, UK ˇ Ehlerová Department of Galaxies and Planetary Systems, Astronomical Sona Institute, Czech Academy of Sciences, Prague, Czech Republic Marius Eichler Institute for Nuclear Physics, Technische Universität Darmstadt, Darmstadt, Germany J. J. Eldridge The Department of Physics, The University of Auckland, Auckland, New Zealand Matthew Evans Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA Michael A. Famiano Department of Physics, Western Michigan University, Kalamazoo, MI, USA Carlo Ferrigno ISDC, Geneva Observatory, University of Geneva, Versoix, Switzerland Robert A. Fesen Department of Physics and Astronomy, Dartmouth College, Hanover, NH, USA Tobias Fischer Institute for Theoretical Physics, University of Wrocław, Wrocław, Poland Thierry Foglizzo Laboratoire AIM (CEA/Irfu, CNRS/INSU, University Paris Diderot), CEA Saclay, Gif sur Yvette, Paris, France Claes Fransson Department of Astronomy and Oskar Klein Centre, Stockholm University, Stockholm, Sweden Priscilla Frisch Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL, USA Stefan Funk ECAP (Erlangen Centre for Astroparticle Physics), University Erlangen-Nürnberg, Erlangen, Germany Avishay Gal-Yam Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel Enrique García–Berro Departament de Física, Universitat Politècnica de Catalunya, Castelldefels, Spain Institute for Space Studies of Catalonia, Barcelona, Spain Peter Garnavich Physics Department, University of Notre Dame, Notre Dame, IN, USA

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Contributors

Ulrich R. M. E. Geppert Janusz Gil Institute of Astronomy, University of Zielona Góra, Zielona Góra, Poland Institute for Space Systems, German Aerospace Center (DLR), Bremen, Germany David A. Green Cavendish Laboratory, University of Cambridge, Cambridge, UK Pawel Haensel N. Copernicus Astronomical Center, Polish Academy of Sciences, Warszawa, Poland Francis Halzen Department of Physics, University of Wisconsin-Madison, Madison, WI, USA Mario Hamuy Astronomy Department, University of Chile, Santiago, Chile Millennium Institute of Astrophysics, Santiago, Chile Arnold Hanslmeier Institute of Physics, University of Graz, Graz, Austria J. Austin Harris Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA Timothy M. Heckman Department of Physics and Astronomy, and Center for Astrophysical Sciences, The Johns Hopkins University, Baltimore, MD, USA Raphael Hirschi Astrophysics Group, School of Chemical and Physical Sciences, Keele University, Staffordshire, UK Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba, Japan UK Network for Bridging Disciplines of Galactic Chemical Evolution (BRIDGCE), Staffordshire, UK W. Raphael Hix Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, USA Peter Hoeflich Department of Physics, Florida State University, Tallahassee, FL, USA Peter Hoppe Particle Chemistry Department, Max Planck Institute for Chemistry, Mainz, Germany Jorge E. Horvath Departmento de Astronomia, Universidade de São Paulo (USP), São Paulo, SP, Brazil Instituto de Astronomia, Geofísica e Ciências Atmosféricas USP, Cidade Universitária São Paulo, SP, Brazil D. Andrew Howell Las Cumbres Observatory, Goleta, CA, USA University of California, Santa Barbara, CA, USA

Contributors

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Garik Israelian Instituto de Astrofísica de Canarias, La Laguna, Tenerife, Spain Departamento de Astrofísica, Universidad de La Laguna, La Laguna, Tenerife, Spain Hans-Thomas Janka Max Planck Institute for Astrophysics, Garching, Germany Anders Jerkstrand Astrophysics Research Centre (ARC), Queen’s University Belfast, Belfast, UK Max-Planck Institute for Astrophysics, Garching, Germany Saurabh W. Jha Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ, USA Peter Gustaaf Jonker SRON, Netherlands Institute for Space Research, Utrecht, The Netherlands Department of Astrophysics/IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands Amanda I. Karakas School of Physics and Astronomy, Monash Centre for Astrophysics (MoCA), Monash University, Clayton, VIC, Australia Daniel Kasen Department of Astronomy, University of California, Berkeley, CA, USA Satoru Katsuda Faculty of Science and Engineering, Department of Physics, Chuo University, Bunkyo-ku, Tokyo, Japan Boaz Katz Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel Richard Kessler Department of Astronomy and Astrophysics, Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL, USA Bon-Chul Koo Department of Physics and Astronomy, Seoul National University, Seoul, South Korea Gunther Korschinek Physik-Department, Technische Universität München, Garching, Germany Kei Kotake Department of Applied Physics, Fukuoka University, Fukuoka, Japan Roland Kothes Dominion Radio Astrophysical Observatory, National Research Council Canada, Herzberg Programs in Astronomy and Astrophysics, Penticton, BC, Canada Kevin Krisciunas Department of Physics and Astronomy, George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX, USA Takami Kuroda Department of Physics, University of Basel, Basel, Switzerland

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Contributors

Karlheinz Langanke Institute for Nuclear Physics (Theory Center), Technische Universität Darmstadt, Darmstadt, Germany GSI Helmholtz Center for Heavy Ion Research, Darmstadt, Germany Bruno Leibundgut European Southern Observatory, Garching, Germany Excellence Cluster Universe, Technical University München, Garching, Germany Shing-Chi Leung Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan Marco Limongi INAF – Osservatorio Astronomico di Roma, Monteporzio Catone (Roma), Italy Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan Andreas Lohs Department of Physics, University of Basel, Basel, Switzerland Knox S. Long Space Telescope Science Institute, Baltimore, MD, USA Eureka Scientific, Inc., Oakland, CA, USA Pablo Lorén–Aguilar School of Physics, University of Exeter, Exeter, UK Cecilia Lunardini Department of Physics, Arizona State University, Tempe, AZ, USA Lucas M. Macri Department of Physics and Astronomy, Texas A&M University, College Station, TX, USA André Maeder Geneva Observatory of Geneva University, Versoix, Geneva, Switzerland Kate Maguire Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast, UK Gabriel Martínez-Pinedo Institute for Nuclear Physics (Theory Center), Technische Universität Darmstadt, Darmstadt, Germany GSI Helmholtz Center for Heavy Ion Research, Darmstadt, Germany Mikako Matsuura School of Physics and Astronomy, Cardiff University, Cardiff, UK Paolo A. Mazzali Astrophysics Research Institute, Liverpool John Moores University, Liverpool, UK Richard McCray Department of Astronomy, University of California, Berkeley, CA, USA Georges Meynet Geneva Observatory of Geneva University, Versoix, Geneva, Switzerland

Contributors

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Dan Milisavljevic High Energy Astrophysics, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA Giovanni Morlino Gran Sasso Science Institute, National Institute for Nuclear Physics (INFN), L’Aquila, Italy Paul Murdin Institute of Astronomy, University of Cambridge, Cambridge, UK Ken’ichi Nomoto Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan Peter Nugent Lawrence Berkeley National Laboratory and UC Berkeley Department of Astronomy, Berkeley, CA, USA Evan O’Connor Department of Physics, North Carolina State University, Raleigh, NC, USA Ulrich Ott Department of Natural Sciences, University of West Hungary, Szombathely, Hungary Max Planck Institute for Chemistry, Mainz, Germany Rüdiger Pakmor Theoretical Astrophysics Group, Heidelberg Institute for Theoretical Studies, Heidelberg, Germany Jan Palouš Department of Galaxies and Planetary Systems, Astronomical Institute, Czech Academy of Sciences, Prague, Czech Republic Igor Panov Institute for Theoretical and Experimental Physics of NRC Kurchatov Institute, National Research Center (NRC) Kurchatov Institute, Moscow, Russia Sternberg Astronomical Institute, M.V. Lomonosov State University, Moscow, Russia Changbom Park School of Physics, Korea Institute for Advanced Study, Seoul, South Korea Richard J. Parker Department of Physics and Astronomy, Royal Society Dorothy Hodgkin Fellow, The University of Sheffield, Sheffield, UK David Parkinson School of Mathematics and Physics, University of Queensland, Brisbane, QLD, Australia ARC Centre of Excellence for All-sky Astrophysics (CAASTRO), Brisbane, QLD, Australia Ferdinando Patat European Southern Observatory (ESO), Garching, Germany Daniel Patnaude High Energy Astrophysics, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA Mark M. Phillips Carnegie Observatories, Las Campanas Observatory, La Serena, Chile

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Contributors

Elena Pian Institute of Space Astrophysics and Cosmic Physics, INAF-IASF, Bologna, Italy Scuola Normale Superiore, Pisa, Italy Jorge Piekarewicz Department of Physics, Florida State University, Tallahassee, FL, USA Marco Pignatari Milne Center for Astrophysics, University of Hull, Hull, UK Philipp Podsiadlowski Department of Physics, University of Oxford, Oxford, UK John C. Raymond Smithsonian Astrophysical Observatory, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA Sanjay Reddy Institute for Nuclear Theory, University of Washington, Seattle, WA, USA Stephen P. Reynolds Department of Physics, North Carolina State University, Raleigh, NC, USA Adam G. Riess Space Telescope Science Institute, AURA, Johns Hopkins University, Baltimore, MD, USA Luke F. Roberts Theoretical AstroPhysics Including Relativity and Cosmology (TAPIR), California Institute of Technology, Pasadena, CA, USA Friedrich K. Röpke Heidelberg Institute for Theoretical Studies, Heidelberg, Germany Zentrum für Astronomie der Universität Heidelberg, Heidelberg, Germany Abhijit Saha Kitt Peak National Observatory, National Optical Astronomy Observatory (NOAO), Tucson, AZ, USA Kate Scholberg Department of Physics, Duke University, Durham, NC, USA Ivo Rolf Seitenzahl School of Physical, Environmental, and Mathematical Sciences, University of New South Wales (UNSW) Canberra, Australian Defense Force Academy, Canberra, ACT, Australia Andre Sieverding Institute for Nuclear Physics (Theory Center), Technische Universität Darmstadt, Darmstadt, Germany Stuart A. Sim School of Mathematics and Physics, Queen’s University Belfast, Belfast, UK Patrick Slane High Energy Astrophysics, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA Jonathan D. Slavin High Energy Astrophysics Division, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA Nathan Smith Steward Observatory, University of Arizona, Tucson, AZ, USA

Contributors

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Sumner Starrfield Earth and Space Exploration, Arizona State University (ASU), Tempe, AZ, USA F. Richard Stephenson Department of Physics, Durham University, Durham, UK Jumpei Takata School of Physics, Huazhong University of Science and Technology, Wuhan, China Stefan Taubenberger European Southern Observatory, Garching, Germany Max-Planck-Institut für Astrophysik, Garching, Germany R. C. Tautz Department of Astronomy and Astrophysics, Berlin Institute of Technology, Berlin, Germany Tea Temim Space Telescope Science Institute, Instruments Division, Baltimore, MD, USA Friedrich-Karl Thielemann Department of Physics, University of Basel, Basel, Switzerland Todd A. Thompson Department of Astronomy and Center for Cosmology and Astro-Particle Physics, The Ohio State University, Columbus, OH, USA Dean M. Townsley Department of Physics and Astronomy, The University of Alabama, Tuscaloosa, AL, USA Hideyuki Umeda Department of Astronomy, University of Tokyo, Tokyo, Japan Rodolfo Valentim Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo (UNIFESP), Diadema, SP, Brazil Edward P. J. van den Heuvel Anton Pannekoek Institute of Astronomy, University of Amsterdam, Amsterdam, The Netherlands Schuyler D. Van Dyk Infrared Processing and Analysis Center, California Institute of Technology Caltech/IPAC, Pasadena, CA, USA Jacco Vink Anton Pannekoek Institute and GRAPPA, University of Amsterdam, Amsterdam, The Netherlands Roland Walter ISDC, Geneva Observatory, University of Geneva, Versoix, Switzerland Eli Waxman Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel Fridolin Weber Department of Physics, San Diego State University, San Diego, CA, USA Center for Astrophysics and Space Sciences, University of California, San Diego, CA, USA

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Contributors

Benjamin Wehmeyer Department of Physics, University of Basel, Basel, Switzerland Norbert Wex Fundamental Physics in Radio Astronomy, Max Planck Institute for Radio Astronomy, Bonn, Germany Brian J. Williams CRESST/USRA and X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center (GSFC), Greenbelt, MD, USA Meng-Ru Wu Institute for Nuclear Physics (Theory Center), Technische Universität Darmstadt, Darmstadt, Germany Niels Bohr International Academy, Niels Bohr Institute, Copenhagen, Denmark Hitoshi Yamaoka Public Relations Center, National Astronomical Observatory of Japan, Tokyo, Japan Takashi Yoshida Department of Astronomy, University of Tokyo, Tokyo, Japan Luca Zampieri INAF-Astronomical Observatory of Padova, Padova, Italy Michele Zanolin Embry Riddle Aeronautical University, Prescott, AZ, USA Julian L. Zdunik N. Copernicus Astronomical Center, Polish Academy of Sciences, Warszawa, Poland Chengmin M. Zhang National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China Key Laboratory of Radio Astronomy, CAS, Beijing, China School of Physical Science, University of Chinese Academy of Sciences, Beijing, China

Part I Supernovae and Supernova Remnants

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Supernovae and Supernova Remnants: The Big Picture in Low Resolution Athem W. Alsabti and Paul Murdin

Abstract

A supernova is a star ending its life in a powerful explosion, nearly always leaving behind an expanding gaseous remnant, which has an influence on the surrounding circumstellar and interstellar medium, and possibly a compact stellar remnant. Multiple supernovae events, collectively, can have a strong influence on local galactic regions, the entire parent Galaxy, and the intergalactic medium. On average, supernovae occur at a rate of 2 per century per galaxy. The observational phenomena generated in and after each event show a rich variety of scientific properties. These are both photometric and spectroscopic (and covering the entire electromagnetic spectrum), but also include newer areas of observational astronomy, such as neutrino physics, cosmic rays and gravitational waves. Supernovae are the result of either of two distinct explosive mechanisms. Type Ia supernovae are explosions of white dwarfs pushed over the Chandrasekhar limit, typically with a peak luminosity 2  1043 erg s1 . They leave no stellar remnant. Type II, Type Ib and Type Ic supernovae are the results of the collapse of the core in supergiant progenitor stars of mass M > 8 solar masses, with a peak luminosity typically 1042 erg s1 . They leave a neutron star or black hole stellar remnant (or possibly none). Supernovae play an essential role in the synthesis of many elements in the periodic table, apart from the lightest (H, He and tiny amount of Be, B and Li, produced in the Big Bang). They distribute into the interstellar medium the

A.W. Alsabti () University College London Observatory, University College London, London, UK e-mail: [email protected] P. Murdin Institute of Astronomy, University of Cambridge, Cambridge, UK e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_1

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elements that they make and the elements made in, on and near to their progenitor stars by other processes. All these elements are injected into molecular clouds and provide the raw material from which stars and planetary systems form. Supernova explosions close to the Sun, say within 100 pc, continue to be an influence on the solar system, depositing identifiable isotopes like Fe60 on the Earth and Moon. Cosmic rays produced within the shells of supernova remnants influence climate and probably caused lasting effects on the evolution of life. Neutrinos produced by supernovae have an indirect effect on the chirality of amino acids.

Contents 1 2 3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Foundations of Supernova Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Progenitor Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 White Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Core-Collapse Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Pair-Instability Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 What Happens in a Typical Core-Collapse Supernova . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Circumstellar Material and Stellar Companions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Supernova Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Neutron Stars and Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Supernovae and the Environment of the Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Supernova Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

The study of supernovae connects us with almost all fields of research in astronomy and many in physics. No objects studied in astronomy have covered so many multidisciplinary topics as supernovae, as is shown by the scope and size of The Handbook of Supernovae, edited by the present authors (Springer 2016). The development of supernovae and their remnants takes place over a long time, and the association of historical supernovae, like the “Guest Star” of AD 1054, recorded by a number of oriental civilizations, and connected with explosive astrophysical objects now studied in great detail, such as the Crab Nebula, provides observational material to make connected studies of the evolution of supernovae over a millennium. The observations ongoing of recent supernovae, like SN 1987A in the Large Magellanic Cloud, repeatedly restart these studies, studied on timescales of decades. The investigation into the theoretical science of supernovae started on a path parallel to observational science in the 1930s. The observational path led to our understanding of brightness, light curves and spectra, as well as improving the methodology of their discovery on an industrial scale! On the other hand, the

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theoretical path taught us how stars advanced on their evolution to late stages of stellar structure and the ways in which they explode, resulting in different types and classes of supernovae. The interrelationships among all these observational data and theoretical possibilities are complex topics which remain matters for discussion up to the present day. The physics of the explosions remains at the cutting edge of research, in particular the way that the explosion in a supernova drives off the outer layers of its progenitor star and produces various remnants such as neutron stars and black holes. In the course of the explosion, new elements are formed by nucleosynthesis and the explosion scatters into interstellar space these elements and the other elements generated by nuclear burning and other processes in, on, and near the progenitor star. The role of remnants of supernovae as expanding shells pushing into the interstellar medium is also important, and the input of energy into the interstellar medium that supernovae generate affects the evolution of galaxies and the space around them. Beyond individual galaxies, intergalactic space can be measured using supernovae as standard candles. Coming back closer to home, the solar system can now be investigated from the point of view of the role of supernovae in creating its initial constituents and the formation from these constituents by supernova shocks of our Sun and its planetary system. The residue from the multiple supernovae explosions in the neighborhood of the Sun can be identified in interplanetary dust and on the Moon. In recent years, the planetary climate and space weather have also been found to have been affected by galactic cosmic rays originating from the expanding shells of supernova remnants. It has also been suggested that neutrinos originating from explosions of supernovae could have affected the molecular structure of amino acids in the solar system, thus affecting the emergence of life on Earth. The importance of supernovae in astrophysics can be judged by the list of Nobel Prizes awarded to scientists who have made significant advances in areas connected with supernova research: 2011: Saul Perlmutter, Brian P. Schmidt and Adam G. Riess “for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.” 2002: Riccardo Giacconi “for pioneering contributions to astrophysics, which have led to the discovery of cosmic X-ray sources.” 1993: Russell A. Hulse and Joseph H. Taylor Jr. “for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation.” 1983: Subrahmanyan Chandrasekhar “for his theoretical studies of the physical processes of importance to the structure and evolution of the stars.” 1983: William Alfred Fowler “for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe.” 1974: Antony Hewish “for his decisive role in the discovery of pulsars.”

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The Foundations of Supernova Astrophysics

The word “nova” in astronomy (plural “novae”) is an abbreviation of the Latin phrase “nova stella,” meaning “new star,” i.e., a bright star appears for a period of time at a place in the sky where there was no such bright star before. The occurrence of two such novae, in 1572 and 1604, was widely discussed in Europe because they were exhaustively studied by many influential astronomers, notably Tycho Brahe and Johannes Kepler, respectively. In that these two events focused attention on the intrinsic properties of stars, as distinct from their positions and motions, the two new stars can be said to have started astrophysics. In the early 1930s, following work by Knut Lundmark on the range of luminosities of novae in galaxies, Walter Baade and Fritz Zwicky identified a class of novae that were 10,000 times more powerful than others and gave currency to Lundmark’s word “supernova” (SN, plural SNe) to describe them. Large numbers of novae and supernovae have been discovered and observed over the centuries. Evidence has been uncovered of some novae and supernovae observed historically, prior to the time of modern science and recorded in contemporary accounts, usually with an astrological context. Historical evidence has been usually been correlated with the discovery of a “supernova remnant” (SNR), i.e., an expanding shell of material resulting from a supernova explosion, which draws attention to a locality in the sky and an epoch where a supernova has occurred. SN 1006, SN 1054 (the Crab Nebula), SN 1181 (3C58), Tycho’s SN 1572, and Kepler’s SN 1604 are examples of SNe/SNRs where the complete history over 500– 1000 years as well as a precise age is available to help us understand the astrophysics of these objects. In total, taking account of historical supernovae recorded with varying degrees of certainty over the last 2000 years, the number of supernovae that have been seen in our own Galaxy is a mere handful – fewer than 10. Most supernovae – hundreds and thousands of them – have been seen in external galaxies, such as M31, the Andromeda Galaxy, and the large numbers of galaxies at great distances, visible to us because the explosions are so powerful. Ordinary novae are relatively mild explosions on the surface of a white dwarf star. Baade and Zwicky’s brighter class of “supernovae” are, by contrast, disruptive explosions that result in the gravitational collapse of the progenitor star to a compact object such as a neutron star or black hole or even disrupt the entire progenitor. The material that does not end up in a compact stellar remnant is dispersed into the surrounding space, where it becomes a supernova remnant. The release of the gravitational binding energy of the core of the original star into kinetic energy amounts to approximately 1051 ergs; this is roughly 100 times the energy radiated by the Sun in its lifetime. The large amount of energy accounts for the powerful effects of a supernova and as a unit has been informally given the name FOE, some of the initials of words in the phrase “ten to the fifty-one ergs.” Most energy is released as neutrinos: 1053 ergs. The energy that is released heats the material of the collapsing core to temperatures of order 1010 K. The core collapses almost in free fall, in less

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than a second, so the energy release has a luminosity of 1054 erg s1 , roughly the same luminosity as the visible universe. The energy produced by a supernova explosion is spread into various forms including radiant energy, such as neutrinos, gravitational waves and the entire range of electromagnetic radiation, as well as the kinetic energy of outflowing material, high-energy cosmic rays, and nuclear energy. Radiant energy from the supernova phenomenon heats the body of the progenitor star, which shows as a photosphere with spectral lines of characteristic elements depending on the material’s composition and shapes depending on the distribution and motion of the material. The “new star” phenomenon is the manifestation of this large, hot, expanding photosphere. It starts abruptly, rising in brightness over a matter of hours, and is at its maximum brightness for a matter of days or weeks. Its brightness fades and its temperature falls with time so that the supernova becomes invisible over a matter of perhaps years, depending on the star’s distance. The rise and fall of the light output and temperature of the supernova constitute its light curve and its spectral evolution. These observational characteristics have properties that have been grouped into empirical classifications. As observed in SN 1987A and others, the shock waves produced by the supernova propagate into the circumstellar and interstellar medium surrounding the supernova and create effects and features within the parent galaxy. Supernovae take place only in certain kinds of stars at a particular stage of their lives, but, other than a general indication that a supernova is possible, there is little or no visible sign in the outer parts of the progenitor star that an explosion is imminent. Thus, supernovae are unannounced. Over most of astronomical history, supernovae have been discovered by chance, after one has happened and is noticed. They average around two per Galaxy per century, so it is necessary to scan at least hundreds, and better millions, of galaxies to find supernovae at a rate at which they can be studied at all intensively. The first systematic searches were by Fritz Zwicky, using the wide-field Schmidt telescopes of the Palomar Observatory. He repeatedly surveyed large numbers of galaxies, looking by eye on photographs for “new stars.” Follow-up observations were delayed by the time that the discovery process took, perhaps not made at all if it was not possible to change telescope schedules from their planned work and, if made, were made with an arbitrary set of equipment deployed for some unconnected purpose on whatever telescope was available. In the current era, a number of well-focused and coordinated supernova surveys are being executed, relying on automated gathering of large amounts of observational information, rapid computer processing of the blocs of “big data” to find candidate supernovae in a very short time, and follow-up observations that are prescheduled and appropriately equipped for well-targeted investigations in the certain knowledge that a number of supernovae would have been identified by the prior survey. These surveys have found hundreds of supernovae and made it possible to use them in statistically meaningful studies in cosmology and to provide large enough samples to discover rare types of supernova.

8

A.W. Alsabti and P. Murdin

It is worth mentioning that amateur astronomers carry out searches for supernovae, concentrating on the brighter galaxies distributed over the whole sky and thus providing early alerts to the nearer supernovae, which might be overlooked by professional searches that are concentrated in limited areas of the sky but which are material for potentially detailed study. The energy that is released by a supernova produces astronomical phenomena whose details depend on the kind of star that exploded, in particular its evolutionary state at the moment of explosion, and the star’s circumstellar and interstellar environment, including whether it has a binary companion or not. The range of circumstances of the explosions, the rapidity of the development of the explosions, the challenging physics, and the variety of significant dimensional scales in the various parts of the star all make the theoretical solution of the explosion difficult. It is even becoming clear that the simplifying assumption of spherical symmetry has to be abandoned because some supernovae are essentially asymmetric and some phenomena are the results of that. The drive to understand these explosions is strong because their consequences are far-reaching: supernovae have effects on the history of galaxies and planets, including the development of life on Earth.

3

Progenitor Stars

3.1

White Dwarfs

White dwarfs are stars whose hydrostatic equilibrium is supported by electrondegeneracy pressure. In 1930, Subrahmanyan Chandrasekhar showed that such a configuration was possible only if the star was less than a certain mass, up to what has become known as the Chandrasekhar limit, approximately 1.4 solar masses. Beyond this limit, a white dwarf star will collapse and appear as a supernova. The cause of the collapse is either the gradual accretion of matter from a nearby star, i.e., a companion in a binary system, or the merger of two white dwarf stars to produce a white dwarf star that is over the limit. This triggers a runaway thermonuclear explosion, with a subsonic (“deflagration”) flame that propagates through the body of the white dwarf. The composition of the white dwarf is commonly carbon and oxygen, possibly also silicon. Fusion of these nuclei releases energy and raises the temperature of the star’s material. Degeneracy pressure is independent of temperature, and a runaway thermonuclear reaction results, detonating the star. No compact remnant is left. The thermonuclear fusion process produced heavy elements in the iron group, like Co56 and Ni56 , whose radioactive decay powers the light curve of the supernova. The progenitor white dwarf star is the outcome of the evolution of a star, initially of up to 8 solar masses, in which its original hydrogen has been converted to heavier elements or lost into space in a stellar wind, so no hydrogen is visible in the supernova’s spectrum. Such a supernova spectrum is described as being of Type Ia. Super-chandra supernovae are rare Type Ia SNe that are particularly bright, conjectured to arise from white dwarfs that are up to twice the usual Chandrasekhar

1 Supernovae and Supernova Remnants: The Big Picture in Low Resolution

9

mass limit. The progenitor of such a supernova may result from the abrupt merger of two Chandrasekhar limit white dwarfs, or it may have been a single white dwarf partially supported by rapid rotation in addition to electron-degeneracy pressure.

3.2

Core-Collapse Supernovae

The evolution of most massive stars in general results in a core of heavy elements, typically iron but possibly, for the least massive stars in this range, a mixture of oxygen, neon, magnesium and silicon, O/Ne/Mg/Si. The core is electrondegenerate, essentially a white dwarf, but surrounded by an envelope of material that may well contain hydrogen but which has at least in part been nuclear-processed to elements heavier than hydrogen. The precise structure of the envelope depends on the initial mass of the progenitor star and its mass-loss history, which in turn depends on its metallicity and whether it is in a binary star system, and if so how close and massive was its companion during its evolution. Such a star, of initial mass above 8 solar masses but below 140 solar masses, produces a core-collapse supernova (CCSN). Often the spectrum of a CCSN shows hydrogen spectral lines, arising from residual hydrogen in the progenitor’s envelope, in which case it is designated through observations as a Type II. But if the pre-explosion evolutionary history of the progenitor (stellar winds, mass transfer in a binary system) has dispersed the hydrogen of its outer envelope into the circumstellar region and the core collapses inside an envelope primarily of helium, carbon, oxygen and silicon, no hydrogen is visible in the supernova’s spectrum, certainly not at first. The CCSN is then said to be of Type I, with suffixes in the classification label which identify compositional specifics such as the presence of helium or not (Type Ib or Type Ic, respectively), which make it different from a Type Ia. Other suffixes identify features of the light curve, such as a decline in brightness after maximum that is linear when expressed in astronomical magnitudes or is characterized by a standstill or plateau (Type II-L or Type II-P, respectively). Differences in the light curves are caused by differences in the density and compositional structure of the progenitors’ envelopes, and therefore the progression of opacity as the photospheres of the supernova material passes through the exploding body of their parent stars. The present supernova classification system is complex (Fig. 1) and grew incrementally. Many astronomers think that it is not fit for purpose and needs overhauling in the light of modern research. The energy released by a CCSN depends on the mass and structure of the progenitor star. Thus the luminosity of CCSNe is quite variable, because stars with masses >8 solar masses in an advanced evolutionary state have a variety of structures. Some extreme Type II-P supernovae are termed “ultra-faint SNe.” Some Type Ic SNe are “super-luminous (SL SNe),” while others are “broad-lined” (meaning high velocity of the ejecta) or “hyper-novae.” They may also be highenergy supernovae which are the origin of long-duration gamma-ray bursts.

10

A.W. Alsabti and P. Murdin

Fig. 1 A taxonomic map showing the classifications and interrelationships between supernova types (Figure supplied by Cosimo Inserra (Queen’s University Belfast))

3.3

Pair-Instability Supernovae

At the present time, now that the history of the universe has progressed via the elements generated and distributed by supernovae, and other processes, to produce an interstellar medium of approximately solar composition, the maximum mass of a star in hydrostatic equilibrium is about 120 solar masses. Otherwise the star exceeds the Eddington limit of luminosity at which radiation pressure overcomes gravitational attraction and disperses the star. The mass limit can be pushed to 150 solar masses or more for low metallicities, because the opacity of the stellar material is reduced. Even more massive stars may exist if they are not in equilibrium. Very massive stars of low metallicity, above 140 solar masses at the outset, do not get to form a stable iron core at the end of their evolution. Their central regions enter into an electron-positron pair-instability state during the oxygen burning stage. Collisions between nuclei and gamma rays in the core result in pair production, which reduces the thermal pressure in the oxygen core. The core collapses dynamically. This is a pair-instability supernova (PISN). The star is completely disrupted, leaving no stellar remnant behind. They may be manifested as SL SNe and/or SNe with abnormally long-duration light curves.

4

What Happens in a Typical Core-Collapse Supernova

The core of a CCSN collapses in less than 1 s to a compact stellar object, i.e., a neutron star if the initial mass of the progenitor is less than about 40 solar masses (there is a metallicity dependence; see Fig. 5) or black hole if more massive.

1 Supernovae and Supernova Remnants: The Big Picture in Low Resolution

11

The collapse heats the infalling material to a high temperature and releases most of the collapse energy in the form of neutrinos. The neutrinos also heat the envelope material and begin to launch it outwards to become supernova ejecta. Other neutrinos travel quickly out of the progenitor and radiate as the promptest indication to the outside universe that the core has collapsed and the supernova phenomenon is under way. It is possible in a nonspherical collapse that significant energy could be lost in the form of gravitational waves, and these also travel, undelayed, directly from the core and are equally prompt in announcing core collapse. At a later stage of the explosion, asphericity may result in detectable spectroscopic and polarization anomalies. If the collapse forms a neutron star, infalling material bounces on its hard surface, generating a shock wave that travels to the surface of the progenitor, taking about an hour. The shock heats the surrounding material, adding to breakouts from the surface, and heats it to a temperature of a million degrees. The sudden heating and brightening of the surface of the progenitor star and consequent ultraviolet photons, emitted in a flash lasting a few minutes, are the second signal to the outside universe that a supernova has occurred. The outer layers of the progenitor star start to expand, increasing its size by perhaps a factor of 10 or more in one day and its brightness by about a factor of 1000. It is in this third phase, about a day after the collapse of the core, that the star starts to exhibit to the rest of the universe the defining characteristic of a “new star.” It is an observational challenge to astronomy that the opportunity to study the onset of the supernova phenomenon is heralded by gravitational waves and neutrinos, the detection of which is intrinsically difficult so that detection techniques are in the early stages of development from their infancy, although the recent (2016) detection of gravitational waves from a binary black hole is an observational triumph that is encouraging. The calculation of the physics of the collapse is a complex problem involving thermodynamics, hydrodynamics, electromagnetism and gravitational theory, and atomic, nuclear, and particle physics. Numerical methods are challenging, with high-resolution steps required in both space and time. Additionally, the geometric model within which the calculation takes place may contain complicating factors such as rotation and asymmetry; indeed asphericity is a necessary complication to address some issues. The supernova continues to expand indefinitely, but its outer layers become more rarefied, and its photosphere eventually starts to contract, after a matter of weeks. It has reached its maximum brightness and begins to fade. If the collapse forms a black hole, there is no hard surface on which any infalling material can bounce. This means there is no outward shock. This reduces the energy deposited in the envelope. This can weaken the supernova, which is thus fainter than typical; it may weaken the supernova phenomenon so drastically that all the progenitor star’s material is swallowed by the black hole and no remnant is left at all. It is even possible that some supernovae take place by a sudden collapse of the entire star without any significant outflow at all, so that the star suddenly disappears. In the core collapse, the stellar material is heated to high temperatures and compressed to high densities. Nuclear reactions generate nickel-56, Ni56 , which

12

A.W. Alsabti and P. Murdin

with a half-life of 6 days decays to cobalt-56, Co56 , which itself is radioactive with a half-life of 77 days and decays to iron-56, Fe56 , which is stable. The Co56 decay emits a spectrum of gamma rays, including one with an energy of 847 MeV, as observed in SN 1987A. Expansion of the supernova material, especially since the material becomes lumpy, with transparent tunnels, allows gamma rays to exit from the supernova from a few weeks after the core collapse.

5

Nucleosynthesis

In an epoch-making paper in 1957, known by the initials of its authors as B2 FH, Margaret Burbidge, Geoffrey Burbidge, William Fowler and Fred Hoyle laid the foundation for the theory of the origin of the elements. The form of the study was to list a small number of nuclear processes that would produce the entire range of isotopes within the periodic table and calculate from principles of nuclear physics the cosmic abundances of the chemical elements. B2 FH also sought to identify astronomical sites where the processes occur. The nuclear physics led the astronomy. The nuclear processes that provide the energy to power stars are processes that build heavier elements from hydrogen. Supernova explosions distribute these elements into the interstellar medium (Figs. 2 and 3). In addition, the explosions themselves are nuclear processes that make further new elements (Fig. 4). One process on the B2 FH list was labeled the r-process. Its fundamental idea of nuclear physics was a succession of rapid neutron captures (hence the name r-process) by a heavy seed nucleus. The sites where this process occurred were identified as supernova explosions. B2 FH founded the physics of the origin of the elements, but the details of nucleosynthesis are more complex than they originally identified, with the astronomical circumstances playing a major role, as well as the nuclear physics. In present methodology, the yields of nuclides from supernova explosions are calculated starting from the astronomy. The calculation starts with a model for the supernova progenitor, models the SN explosion, and calculates the results of the explosive nucleosynthesis with laboratory-based nuclear reaction networks. The broad outcome is that supernovae are responsible for the creation of approximately half of the neutron-rich atomic nuclei heavier than iron, almost everything heavier than tin and everything heavier than lead. There are differences in the yields of the elements produced by CCSN and thermonuclear supernovae. The thermonuclear runaway in a carbon-oxygen white dwarf that produces a Type Ia supernova results in the explosive synthesis of irongroup elements, plus some others. SNe Ia are the main producer of iron in the universe. Type II/Ib/Ic core-collapse supernovae occur in evolved massive stars with a layered structure of alpha elements and result in the explosive nucleosynthesis of heavy elements near the core, with the outer layers expelled. Nuclear processing as the supernova shock wave propagates through the star produces “˛-products.” Carbon burning produces O, Ne, Mg, etc.; neon burning produces O, Mg, etc.; oxygen burning produces Si, S, Ar, Ca, etc.; and silicon burning produces Fe, Si, S, Ca, etc.

26

27

28

29

30

9

56

Ba

Barium

88

Ra

Radium

55

Cs

Cesium

87

Fr

Francium

Actinium

Ac

89

Lanthanum

La

57

Yttrium

Ti

41

42

Protactinium

Thorium

Uranium

U

92

91

Pa

Bh

107

Rhenium

Re

75

Technetium

Neptunium

Np

93

Promethium

Pm

61

60

Nd Neodymium

59

90

43

Tc

Bohrium

Pr

Th

Mn Manganese

Seaborgium

Sg

106

Tungsten

W

74

Molybdenum

Mo

Praseodymium

Dubnium

Db

105

Tantalum

Ta

73

Niobium

Nb

Cr Chromium

Ce

58

V Vanadium

Cerium

Ruthenium

Rf

104

Hafnium

Hf

72

Zirconium

Zr

40

Titanium

Plutonium

Pu

94

Samarium

Sm

62

Hassium

Hs

108

Osmium

Os

76

Ruthenium

Ru

44

Iron

Fe

Co

Americium

Am

95

Europium

Eu

63

Meitnerium

Mt

109

Iridium

Ir

77

Rhodium

Rh

45

Cobalt

Ni

Curium

Cm

96

Gadolinium

Gd

64

Darmstadtium

Ds

110

Platinum

Pt

78

Palladium

Pd

46

Nickel

Cu

Berkelium

Bk

97

Terbium

Tb

65

Roentgenium

Rg

111

Gold

Au

79

Silver

Ag

47

Copper

Californium

Cf

98

Dysprosium

Dy

66

Copernicium

Cn

112

Mercury

Hg

80

Cadmium

Cd

48

Zinc

Zn

31

Ga

Einsteinium

Es

99

Holmium

Ho

67

Uuntrium

Uut

113

Thallium

Tl

81

Indium

In

49

Gallium

32

Ge

Fermium

Fm

100

Erbium

Er

68

Flerovium

Fl

114

Lead

Pb

82

Tin

Sn

50

Germanium

P

Mendelevium

Md

101

Thulium

Tm

69

Uunpentium

Uup

115

Bismuth

Bi

83

Antimony

Sb

51

Arsenic

As

33

Phosphorus

Nobelium

No

102

Ytterbium

Yb

70

Livermorium

Lv

116

Polonium

Po

84

Tellurium

Te

52

Selenium

Se

34

Sulfur

S

16

Oxygen

Lawrencium

Lw

103

Lutetium

Lu

71

Uunseptium

Uus

117

Astatine

At

85

Iodine

I

53

Bromine

Br

35

Chlorine

Cl

17

Fluorine

F

Uunoctium

Uuo

118

Radon

Rn

86

Xenon

Xe

54

Krypton

Kr

36

Argon

A

18

Neon

Ne

Fig. 2 Elements made in less massive stars that are distributed into the interstellar medium principally by Type Ia supernova explosions (Heger et al. 2003)

Strontium

Rubidium

Y

39

38

Sr

37

Rb

21

Sc

Scandium

20

Ca

Calcium

K

19

Potassium

Si

15

14 Silicon

13

Al Aluminum

12

Mg

Magnesium

11

Na

Nitrogen

Carbon

Sodium

Boron

O

Beryllium

N

Lithium

C

10

B

Be

25

8

Li

24

7

Helium

23

6

3

22

5

4

Hydrogen

2

He

1

H

Solar type stars

1 Supernovae and Supernova Remnants: The Big Picture in Low Resolution 13

22

23

24

25

26

27

28

29

30

6

7

8

9

2

56

Ba

Barium

88

Ra

Radium

55

Cs

Cesium

87

Fr

Francium

Actinium

Ac

89

Lanthanum

La

57

Yttrium

Ti

V

Cr

Protactinium

Thorium

92

91

Pa

90

Th

Neodymium

Praseodymium

Cerium

60

Uranium

U

Nd

59

Pr

58

Seaborgium

Sg

106

Tungsten

W

74

Molybdenum

Mo

42

Chromium

Dubnium

Db

105

Tantalum

Ta

73

Niobium

Nb

41

Vanadium

Ce

Ruthenium

Rf

104

Hafnium

Hf

72

Zirconium

Zr

40

Titanium

Mn

Neptunium

Np

93

Promethium

Pm

61

Bohrium

Bh

107

Rhenium

Re

75

Technetium

Tc

43

Manganese

Plutonium

Pu

94

Samarium

Sm

62

Hassium

Hs

108

Osmium

Os

76

Ruthenium

Ru

44

Iron

Fe

Co

Americium

Am

95

Europium

Eu

63

Meitnerium

Mt

109

Iridium

Ir

77

Rhodium

Rh

45

Cobalt

Ni

Curium

Cm

96

Gadolinium

Gd

64

Darmstadtium

Ds

110

Platinum

Pt

78

Palladium

Pd

46

Nickel

Cu

Berkelium

Bk

97

Terbium

Tb

65

Roentgenium

Rg

111

Gold

Au

79

Silver

Ag

47

Copper

Californium

Cf

98

Dysprosium

Dy

66

Copernicium

Cn

112

Mercury

Hg

80

Cadmium

Cd

48

Zinc

Zn

Einsteinium

Es

99

Holmium

Ho

67

Uuntrium

Uut

113

Thallium

Tl

81

Indium

In

49

Gallium

Ga

31

Aluminum

Fermium

Fm

100

Erbium

Er

68

Flerovium

Fl

114

Lead

Pb

82

Tin

Sn

50

Germanium

Ge

32

Silicon

Fig. 3 Elements made in massive stars that are distributed into the interstellar medium by CCSN explosions

Strontium

Rubidium

Y

39

38

Sr

37

Rb

21

Sc

Scandium

20

Ca

Calcium

K

19

Potassium

Magnesium

Sodium

14

Si

13

Al

12

Mg

11

Na

Carbon

C

5

B Boron

4

Be

Beryllium

3

Li

Lithium

Mendelevium

Md

101

Thulium

Tm

69

Uunpentium

Uup

115

Bismuth

Bi

83

Antimony

Sb

51

Arsenic

As

33

Phosphorus

P

15

Nitrogen

N

Nobelium

No

102

Ytterbium

Yb

70

Livermorium

Lv

116

Polonium

Po

84

Tellurium

Te

52

Selenium

Se

34

Sulfur

S

16

Oxygen

O

Lawrencium

Lw

103

Lutetium

Lu

71

Uunseptium

Uus

117

Astatine

At

85

Iodine

I

53

Bromine

Br

35

Chlorine

Cl

17

Fluorine

F

Uunoctium

Uuo

118

Radon

Rn

86

Xenon

Xe

54

Krypton

Kr

36

Argon

A

18

Neon

Ne

10

He Helium

H

Hydrogen

1

Massive stars

14 A.W. Alsabti and P. Murdin

22

23

24

25

26

27

28

29

30

6

7

8

9

2

56

Ba

Barium

88

Ra

Radium

55

Cs

Cesium

87

Fr

Francium

Actinium

Ac

89

Lanthanum

La

57

Yttrium

Ti

V

Cr

Protactinium

Thorium

92

91

Pa

90

Th

Neodymium

Praseodymium

Cerium

60

Uranium

U

Nd

59

Pr

58

Seaborgium

Sg

106

Tungsten

W

74

Molybdenum

Mo

42

Chromium

Dubnium

Db

105

Tantalum

Ta

73

Niobium

Nb

41

Vanadium

Ce

Ruthenium

Rf

104

Hafnium

Hf

72

Zirconium

Zr

40

Titanium

Mn

Neptunium

Np

93

Promethium

Pm

61

Bohrium

Bh

107

Rhenium

Re

75

Technetium

Tc

43

Manganese

Fig. 4 Elements in the periodic table that are made in supernovae

Strontium

Rubidium

Y

39

38

Sr

37

Rb

21

Sc

Scandium

20

Ca

Calcium

K

19

Potassium

Magnesium

Plutonium

Pu

94

Samarium

Sm

62

Hassium

Hs

108

Osmium

Os

76

Ruthenium

Ru

44

Iron

Fe

Co

Americium

Am

95

Europium

Eu

63

Meitnerium

Mt

109

Iridium

Ir

77

Rhodium

Rh

45

Cobalt

Ni

Curium

Cm

96

Gadolinium

Gd

64

Darmstadtium

Ds

110

Platinum

Pt

78

Palladium

Pd

46

Nickel

Cu

Berkelium

Bk

97

Terbium

Tb

65

Roentgenium

Rg

111

Gold

Au

79

Silver

Ag

47

Copper

Californium

Cf

98

Dysprosium

Dy

66

Copernicium

Cn

112

Mercury

Hg

80

Cadmium

Cd

48

Zinc

Zn

Einsteinium

Es

99

Holmium

Ho

67

Uuntrium

Uut

113

Thallium

Tl

81

Indium

In

49

Gallium

Ga

31

Aluminum

Si

Sodium

14

13

Al

12

Mg

11

Na

Fermium

Fm

100

Erbium

Er

68

Flerovium

Fl

114

Lead

Pb

82

Tin

Sn

50

Germanium

Ge

32

Silicon

Carbon

C

5

B Boron

4

Be

Beryllium

3

Li

Lithium

Mendelevium

Md

101

Thulium

Tm

69

Uunpentium

Uup

115

Bismuth

Bi

83

Antimony

Sb

51

Arsenic

As

33

Phosphorus

P

15

Nitrogen

N

Nobelium

No

102

Ytterbium

Yb

70

Livermorium

Lv

116

Polonium

Po

84

Tellurium

Te

52

Selenium

Se

34

Sulfur

S

16

Oxygen

O

Lawrencium

Lw

103

Lutetium

Lu

71

Uunseptium

Uus

117

Astatine

At

85

Iodine

I

53

Bromine

Br

35

Chlorine

Cl

17

Fluorine

F

Uunoctium

Uuo

118

Radon

Rn

86

Xenon

Xe

54

Krypton

Kr

36

Argon

A

18

Neon

Ne

10

He Helium

H

Hydrogen

1

Supernovae

1 Supernovae and Supernova Remnants: The Big Picture in Low Resolution 15

16

A.W. Alsabti and P. Murdin

Because the progenitors of the white dwarfs have long life times, compared to the more massive stars which become core-collapse supernovae, iron-group elements and alpha-elements in stars of different ages trace different components of the history of our Galaxy.

6

Circumstellar Material and Stellar Companions

Some supernovae show narrow hydrogen emission lines in their spectra and are given a suffix to indicate the narrow lines, e.g., Type IIn. The underlying supernova may be of Type Ia or Type II, and the type may change as the supernova progresses through its various stages. Other rare supernovae show narrow helium emission lines, classified as Type Ibn. The hydrogen or helium emission probably arises from circumstellar material, which is swept up in the progressive expansion of the supernova. Ultraviolet light emitted by the supernova ionizes any circumstellar material, which in the case of a nearby supernova may then be visible as it recombines, to show a circumstellar nebula, as in the case of SN 1987A. When at a later time the material ejected from the supernova reaches the circumstellar material, it will be collisionally ionized. Binarity plays a role in the evolutionary build-up to the explosion of some supernovae. It is an essential feature of the double-degenerate model for Type Ia supernovae, which envisages the merger of two white dwarf stars, either gradually by a mass transfer process or more suddenly by wholesale merger. A companion star will stand in the way of a supernova explosion from the other star in its binary system. The sudden burst of radiated energy from the supernova will produce an X-ray and optical flash lasting minutes to days, and this affects the external layers of the companion star, with consequent spectral indications – which however are transient and easily overlooked. In some circumstances of proximity and mass ratios, a companion star may be liberated from its binary system and be ejected, essentially because the gravitational pull of the supernova progenitor has been switched off as the supernova material passes beyond the companion and there is no effective gravitational pull to hold the companion in orbit. The companion star continues at its orbital speed in a straight line and becomes a high-velocity star, moving at speed (>100 km s1 /, through the other stars of the Galaxy. Such stars are called “runaway stars.” In the intermediate case, the system survives intact but with an eccentric orbit, later circularized through tidal interactions. Supernovae that occur in star clusters may, to a small extent, affect the amount of gas that they contain. In the event that a Type II supernova occurs in a binary system, does not disrupt it, and leaves a stellar remnant (neutron star or black hole), the binary system may well evolve to show further interesting phenomena. X-ray binaries are pairs of stars in which the X-rays are generated as the companion star deposits material on the neutron star or black hole. The properties of such binary stars depend not only on the nature of the compact remnant and the separation of the stars but also the nature

1 Supernovae and Supernova Remnants: The Big Picture in Low Resolution

17

of the companion star, broadly whether it is a high-mass star (making a high-mass X-ray binary, HMXB) or low mass (LMXB). Associated phenomena include the mass transfer process, such as accretion disks, and outflows such as winds and jets (as in the star SS433). X-ray binaries may evolve further through a second supernova explosion to be a binary neutron star or a neutron star-white dwarf binary. The spin period of the first neutron star may be speeded up, and it may be released as a lone millisecond pulsar.

7

Supernova Remnants

The ejecta from a supernova are formed of the material of the progenitor star, including elements that have been processed in the course of the star’s evolution up to the moment of the supernova explosion and elements made from those elements by processing in the explosion itself. The ejecta are accelerated in the explosion to speed up to 30;000 km s1 . The outflow is spherical and homogeneous only to first order; there may be considerable irregularity and anisotropy not only because of the properties of the explosion but also because of proximate circumstellar material. Outside the circumstellar environment, after perhaps 10 years, the supernova blast wave encounters the interstellar medium, heating it to X-ray-emitting temperatures, manifest as a line-dominated spectrum with a bremsstrahlung continuum, and signaling the transition from SN to SNR. Nonthermal electrons produce synchrotron radiation: this is detected as radio emission from the SNR. A reverse shock propagates inward, reheating the ejecta. For hundreds to thousands of years, the expanding shell of material is in this “ejecta-driven” stage, during which the ejecta themselves can be identified as a hollow shell of outwardly moving filaments with abundances typical of the evolved progenitor star. A well-studied example is Cas A, the SNR from a supernova that exploded in about 1681. The energy radiated is small compared to the kinetic energy of the ejecta and the evolution of the supernova remnant is adiabatic, with the material cooled by expansion and progressively decelerated by interstellar material that is swept up. In an idealized formulation, there is an exact solution to the evolution of this phase formulated in the 1950s by Geoffrey Taylor and Leonid Sedov in the context of military explosions. The Taylor-Sedov phase of a supernova remnant lasts for perhaps 20,000 years. In some SNRs like the Crab Nebula, there is a central neutron star, which, if it is a pulsar, inflates a bubble of relativistic particles and a magnetic field to form a pulsar wind nebula (PWN) within the SNR, but the pulsar’s energy output does not usually alter the overall evolution of the SNR. The SNR expands and cools adiabatically until it reaches a temperature of about 1 million K. The ionized atoms of the SNR material capture free electrons and lose energy by radiation. Adiabatic expansion ceases, and the SNR enters the “radiative phase” or “snow plough phase” with more and more interstellar gas being swept up until it dominates over the ejected stellar material. This phase lasts perhaps 100,000 years, the shell breaking up and dispersing into the interstellar medium.

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The nuclear-processed material of the ejecta feed into the interstellar medium, enriching it with so-called metals, i.e., elements heavier than hydrogen or helium. As the supernova remnant cools, its gaseous elements progressively combine from ions to atoms to molecules and to solid grains. Infrared photometry and spectroscopy can be used to investigate the properties of the cooler stages. The first galaxies formed in the universe were under-abundant in heavy metals and thus generated lots of massive so-called Population III stars. They exploded as supernovae within a few million years and generated large amounts of carbon in the interstellar medium which condensed to dust. The “Dark Ages” is the period after the formation of the first galaxies during which dust obscures the visible light from the remaining stars in these galaxies and the abundant supernovae which they generate. Their visible-band radiant energy is absorbed and reradiated as infrared and millimeter wave radiation. The galaxies constitute high-redshift ultra-luminous infrared galaxies. Molecules in the ejecta of present-day supernovae feed into molecular clouds, with the dust, and the inorganic and organic molecules becoming the seed material of newly formed stars and planetary systems.

8

Neutron Stars and Black Holes

As the O/Ne/Mg core or iron core collapses in a CCSN, its temperature passes through 5  109 K. The iron nuclei photodisintegrate into alpha particles as a result of interaction with high-energy gamma rays and then protons and neutrons. At yet higher temperatures, the protons combine with electrons to form neutrons through the process of electron capture. At a density of 4  1026 g:cm3 , neutron degeneracy pressure halts the contraction, creating a neutron star, of mass around 2 solar masses. The mass distribution of neutron stars is tightly peaked but bimodal, representing possible formation mechanisms via two channels. If, in the course of its formation in a core-collapse supernova, the putative neutron star is more massive than the upper limit for such objects (as degeneracy-pressuresupported objects, neutron stars have maximum masses like white dwarfs), or if, depending on metallicity, it accretes material which, having begun to eject in the supernova explosion, stalls and falls back, the neutron star collapses further to a black hole (Fig. 5). A scheme that relates this underlying astrophysics to the observational types and classes of supernovae is shown in Fig. 6. The collapse of the core of a CCSN preserves to some extent its angular momentum, which is M k 2 ˝ (ignoring geometric and other factors of order 1), with the radius of gyration, k, decreasing by a factor of 100, so that its rotation frequency, ˝, increases by a factor of 104 . If the core rotated with a period of 1 day (as might be typical for a star), the neutron star now rotates with a period of about 1 s. The highly conductive material of the collapsing core traps magnetic field lines and throttles them into a smaller cross-sectional area, increasing the magnetic field strength by the same factor of 104 . The rapidly rotating neutron star becomes a pulsar, radiating in the radio region but perhaps over the entire electromagnetic spectrum.

1 Supernovae and Supernova Remnants: The Big Picture in Low Resolution

19

Fig. 5 Remnants of massive single stars as a function of initial metallicity (y-axis) and initial mass (x-axis). At low masses, the cores do not collapse, white dwarfs are made and supernovae do not occur (white strip at the very left). The thick green line separates the regimes where the stars keep their hydrogen envelope (left and lower right) from those where the hydrogen envelope is lost. The dashed blue line indicates the border of the regime of direct black hole formation (black). This domain is interrupted by a strip of pair-instability supernovae that leave no remnant (white). Outside the direct black hole regime, at lower mass and higher metallicity, follows the regime of BH formation by fallback (red cross-hatching and bordered by a black dot-dashed line). Outside of this, green cross-hatching indicates the formation of neutron stars. The lowest mass neutron stars may be made by O/Ne/Mg core collapse instead of iron core collapse (vertical dot-dashed lines at the left) (Figure from Fig. 1 of Heger et al. (2003), © American Astronomical Society, reproduced by permission)

Neutron stars with much higher than usual magnetic fields (giga-tesla) are called magnetars. A magnetar embedded within a supernova may generate sufficient power that the supernova is super-luminous.

9

Supernovae and the Environment of the Solar System

The local interstellar medium is a region that surrounds the solar system out to a few hundred parsecs. This region contains several structures. Among the largest is Gould’s Belt, a flat, young, massive, elliptical star system about 350  250  50 pc in

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Fig. 6 Supernovae types of nonrotating massive single stars. The diagram is divided in the same way as Fig. 5. Green horizontal hatching indicates the domain where Type II-P supernovae occur. At the upper right-hand edge of the SN Type II regime, close to the green line across which the hydrogen envelope is lost, Type II-L/b supernovae are made (purple cross-hatching). In the upper right-hand quarter of the figure, above both the lines of hydrogen envelope loss and direct black hole formation, Type Ib/c supernovae occur. In the direct black hole regime, no “normal” supernovae occur since no SN shock is launched. Pair-instability supernovae (red cross-hatching) make no remnant, except very high-mass supernovae that launch their ejection before the core collapses (lower right-hand corner; brown diagonal hatching) (Figure from Fig. 2 of Heger et al. (2003), © American Astronomical Society, reproduced by permission)

dimension (Fig. 7). It consists of OB stars, molecular clouds, and neutral hydrogen as well as high-temperature coronal gas and dust. Gould’s Belt contains many young stellar associations, the bright stars in many constellations including (in order going more or less eastward) Cepheus, Lacerta, Perseus, Orion, Canis Major, Puppis, Vela, Carina, Crux (the Southern Cross), Centaurus, Lupus, and Scorpius (including the Scorpius-Centaurus Association). Many of these stars will explode as core-collapse supernovae and some of their sisters already have. These supernovae have left their mark on the local structures. For example, a supernova that exploded near the Orion Nebula in the Orion Association about 2 million years ago created a set of runaway stars, namely, AE Aurigae, 53 Arietis, and  Columbae.  Ophiuchi is a similar example, running away from a location in the Scorpius-Centaurus Association (Sco-Cen). Gould’s Belt also contains interstellar clouds and has been long associated with an expanding

1 Supernovae and Supernova Remnants: The Big Picture in Low Resolution

US

200 Cep OB6

Z (pc)

100 0

UCL LCC

Sun

Tr 10

α Per Lac OB1

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Geminga

vela OB2

Vela

On OB 1a

100

Per OB2

re

Ori OB 1b

200 500

ic

ct

Ori OB 1c

a al

t en

c

G

0 500

400

400 200

0 200 X (pc)

Y (pc)

Fig. 7 3D view of the present Gould’s Belt and its velocity field with respect to the local standard of rest. The local OB associations are marked as spheres. The diamond notes the location of the Belt center and the star that of the Sun. Local associations include the Scorpius-Centaurus Association thought to be the major source of supernovae in the neighborhood of the Sun (Figure by I.A.Grenier.)

HI Ring 28. The fact that dark clouds participate to the expansion was recognized 20 years. H2 complexes, such as Orion, Ophiuchus, and Lupus, have long been related to the Belt, but more recently mapped complexes, such as Aquila Rift, Cepheus, Cassiopeia, Perseus, and Vela, appear to be part of the expanding shell as well (Fig. 8). Sco-Cen is believed to be the cradle of several young massive OB stars that exploded in the past 15 million years creating a high-temperature low-density cavity in a network of expanding gas called a super-bubble. Part of this structure is the local bubble, believed to be a result of shock waves caused by multiple supernova explosions in the local interstellar medium. Its electron density is 0:07 atoms cm3 , which is about one order of magnitude less dense than the local interstellar medium. This region is 200 pc in diameter, and its age is 10 million years. The solar system is only 10–20 pc from the edge of the local bubble. The local bubble is not a perfect structure but has also got small structures that seem out of place. These include parsec-sized clouds of temperature 8000 K, with other smaller clouds in the neighborhood of the solar system (very local interstellar medium). The Sun appears to be located in such local cloud with a relative velocity 19 km s1 . The flow comes from direction of gas and dust where an SNR (Loop 1) merges with the local bubble. Supernovae in the neighborhood of the Sun have influence on scales of the order 100 pc. The influence on the heliosphere of the solar system is very evident. Such influence includes the formation of structures at the heliosphere’s boundary with the interstellar medium such as filaments.

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to

Gum Nebula

Scorpius-Centaurus Association ga

lac

Aquila Rift

tic

ce

nt

Vela SNR

er

Scorpius–Centaurus Shells

direction

ovement

of sun’s m

sun

The Local Bubble

Orion Association

M

Orion Shell

R A

N O R I O

S P

I R

A

L

Fig. 8 Local interstellar medium in solar neighborhood, showing the Sun’s position with respect to the Scorpius-Centaurus Association, where nearby supernovae are thought to have originated (Figure by P. Frisch.)

External influences on the solar system include supernovae, supernova remnants and galactic cosmic rays, as well as cosmic dust and the interstellar medium, including neutral atoms and ions. The region dominated by solar influences extends for around 100 AU is created by the solar wind and is called the heliosphere (Fig. 9). Separating the two regions, where the influences balance, is the termination shock. In the inner heliosphere, solar cosmic rays (SCR) with MeV to GeV energies are a major concern. However, galactic cosmic rays (GCR) (MeV to TeV) and anomalous cosmic rays (ACR) (1  Cosmology with Type IIP Supernovae  Detecting Gravitational Waves from Supernovae with Advanced LIGO  Determining Amino Acid Chirality in the Supernova Neutrino Processing Model  Discovery of Cosmic Acceleration  Discovery, Confirmation, and Designation of Supernovae  Dust and Molecular Formation in Supernovae  Dynamical Evolution and Radiative Processes of Supernova Remnants  Dynamical Mergers  Effect of Supernovae on the Local Interstellar Material  Electron Capture Supernovae from Super Asymptotic Giant Branch Stars  Evolution of Accreting White Dwarfs to the Thermonuclear Runaway  Evolution of the Magnetic Field of Neutron Stars

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 Explosion Physics of Core-Collapse Supernovae  Explosion Physics of Thermonuclear Supernovae and their Signatures  Galactic Winds and the Role Played by Massive Stars  Gamma Ray Pulsars: From Radio to Gamma Rays  Gould’s Belt: Local Large-Scale Structure in the Milky Way  Gravitational Waves from Core-Collapse Supernovae  High-Energy Gamma Rays from Supernova Remnants  Historical Records of Supernovae  Historical Supernovae in the Galaxy from AD 1006  History of Supernovae as Distance Indicators  Hydrogen-Poor Core-Collapse Supernovae  Hydrogen-Rich Core-Collapse Supernovae  Impact of Supernovae on the Interstellar Medium and the Heliosphere  Influence of Non-spherical Initial Stellar Structure on the Core-Collapse

Supernova Mechanism  Infrared Emission from Supernova Remnants: Formation and Destruction of Dust  Interacting Supernovae: Spectra and Light Curves  Interacting Supernovae: Types IIn and Ibn  Introduction to Supernova Polarimetry  Isotope Variations in the Solar System: Supernova Fingerprints  Light Curves of Type I Supernovae  Light Curves of Type II Supernovae  Low- and Intermediate-Mass Stars  Low-z Type Ia Supernova Calibration  Making the Heaviest Elements in a Rare Class of Supernovae  Mass Extinctions and Supernova Explosions  Neutrino-Driven Explosions  Neutrino Emission from Supernovae  Neutrino Signatures from Young Neutron Stars  Neutrinos from Core-Collapse Supernovae and Their Detection  Neutron Star Matter Equation of State  Neutron Stars as Probes for General Relativity and Gravitational Waves  Nuclear Matter in Neutron Stars  Nucleosynthesis in Hypernovae Associated with Gamma Ray Bursts  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Nucleosynthesis in Thermonuclear Supernovae  Observational and Physical Classification of Supernovae  Population Synthesis of Massive Close Binary Evolution  Possible and Suggested Historical Supernovae in the Galaxy  Pre-supernova Evolution and Nucleosynthesis in Massive Stars and their Stellar

Wind Contribution  Pulsar Wind Nebulae  Shock Breakout Theory  Spectra of Supernovae During the Photospheric Phase  Spectra of Supernovae in the Nebular Phase

1 Supernovae and Supernova Remnants: The Big Picture in Low Resolution

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 Stardust from Supernovae and Its Isotopes  Strange Quark Matter Inside Neutron Stars  Structures in the Interstellar Medium Caused by Supernovae: The Local Bubble  Superluminous Supernovae  Supernova 1604, Kepler’s Supernova, and its Remnant  Supernova Cosmology in the Big Data Era  Supernova of 1006 (G327.6+14.6)  Supernova of 1054 and its Remnant, the Crab Nebula  Supernova of AD 1181 and its Remnant: 3C 58  Supernova Progenitors Observed with HST  Supernova Remnant Cassiopeia A  Supernova Remnants as Clues to Their Progenitors  Supernovae and the Chemical Evolution of Galaxies  Supernovae and the Evolution of Close Binary Systems  Supernovae and the Formation of Planetary Systems  Supernovae from Massive Stars  Supernovae from Rotating Stars  Supernovae, Our Solar System, and Life on Earth  The Core-Collapse Supernova-Black Hole Connection  The Effects of Supernovae on the Dynamical Evolution of Binary Stars and Star

Clusters  The Extremes of Thermonuclear Supernovae  The Hubble Constant from Supernovae  The Infrared Hubble Diagram of Type Ia Supernovae  The Masses of Neutron Stars  The Multidimensional Character of Nucleosynthesis in Core-Collapse Super-

novae  The Peak Luminosity-Decline Rate Relationship for Type Ia Supernovae  The Physics of Supernova 1987A  The Progenitor of SN 1987A  The Supernova – Supernova Remnant Connection  Thermal and Non-thermal Emission from Circumstellar Interaction  Thermal Evolution of Neutron Stars  Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs  Type Iax Supernovae  Ultraviolet and Optical Insights into Supernova Remnant Shocks  Unusual Supernovae and Alternative Power Sources  Very Massive and Supermassive Stars: Evolution and Fate  Violent Mergers  X-ray Binaries  X-ray Emission Properties of Supernova Remnants  X-ray Pulsars  Young Neutron Stars with Soft Gamma Ray Emission and Anomalous X-ray

Pulsars

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References Heger A, Fryer CL, Woosley SE, Langer N, Hartmann DH (2003) How Massive Single Stars End Their Life. The Astrophysical Journal v.591, No.1, pp. 288–300

2

Discovery, Confirmation, and Designation of Supernovae Hitoshi Yamaoka

Abstract

Supernovae are unpredictable events. Quick distribution of a report of the discovery and confirmation of a supernova is especially important to understand such events. This chapter summarizes the recent status of the notification of supernovae discoveries. The system introduced by the International Astronomical Union (IAU) in the 1990s was able to cope with the rate of discoveries at that time, namely, tens per year, but has been rendered obsolescent by the flood of discoveries from new surveys.

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Discoveries of Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Confirmation of Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Designation of Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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29 30 31 31 32 32 32

Introduction

Supernovae (SNe) are rare events in a given galaxy. The supernova (SN) rate is estimated to be one per several dozen years per galaxy (or 1011 Msol /. The last SN observed in the Milky Way Galaxy occurred in 1604 AD. Research about SNe is, therefore, based on extragalactic SNe, and there are many galaxies in the Universe.

H. Yamaoka () Public Relations Center, National Astronomical Observatory of Japan, Tokyo, Japan e-mail: [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_128

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Not only are supernova explosions interesting in their own right, but they are also important events in the dynamical and chemical evolution of the Universe. Because they are bright, they can be detected from far away and are very powerful tools for distance measurements.

2

Discoveries of Supernovae

After the outbreak of the nearby SN 1987A in the Large Magellanic Cloud, attention on SNe has greatly increased, and many more supernovae are now discovered than used to be the case. Digital imaging and enlargement of telescope aperture has led to the discovery of fainter and fainter SNe. In recent years, the number of SNe discovered has increased from approximately 200 per year in 2000–3400 in 2015 (Table 1). Basically SNe are hunted and discovered by two strategies. One is monitoring a number of individual galaxies. The observer images individual galaxies (more than 1000 galaxies per night), and compares the new images with images previously taken, to seek out a new bright dot in the image. Many amateur astronomers adopt this method, as well as the Lick Observatory Supernova Search (LOSS) team using the Katzman Automatic Imaging Telescope (KAIT) (Filippenko et al. 2001). The second strategy is to make a large-area survey with a mosaic of CCDs covering a wide area. This strategy can detect field SNe (those not associated with a bright host galaxy). The intermediate Palomar Transient Factory (iPTF) (Kulkarni 2013) and the All-Sky Automated Survey for Supernovae (ASAS-SN) (http://www.astronomy.ohio-state.edu/~assassin/index.shtml) are examples. Images taken by large-area surveys for other objectives (such as the Near-Earth Asteroid Survey) are also used for SNe discoveries. The Panoramic Survey Telescope & Rapid Response System (Pan-STARRS) (http://pan-starrs.ifa.hawaii.edu/public/ home.html) is a typical example.

Table 1 Yearly numbers of reported SN discoveries. Numbers in parentheses are that of confirmed and announced SNe on IAUCs/CBETs Year 1981 1982 1983 1984 1985 1986 1987 1988

Discovery 11 27 28 22 21 16 20 35

1989 1990 1991 1992 1993 1994 1995 1996 1997

32 38 64 73 38 41 58 96 163

1998 1999 2000 2001 2002 2003 2004 2005 2006

163(162) 206(201) 185(184) 307(305) 338(334) 426(335) 373(251) 377(367) 554(551)

2007 2008 2009 2010 2011 2012 2013 2014 2015

607(572) 520(261) 475(390) 586(337) 902(298) 1045(322) 1457(228) 1632(136) 3412(61)

2 Discovery, Confirmation, and Designation of Supernovae

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Confirmation of Supernovae

Confirmation on whether the object that has been discovered is a genuine SN is based on follow-up observations, especially by spectroscopy. SNe are explosive objects, so the spectra of SNe are characterized by broad lines (about 3000– 10,000 km/s) with P Cygni profiles, typically in absorption. Low-resolution spectra (R about 1000) are good enough for classification. SNe are classified into types by spectroscopic features and light curves. Since the spectrum of a supernova changes with time (days after explosion), spectroscopy tells us both the type and the age of the supernova. The main classification is made by the existence of hydrogen features; if the Balmer lines are absent, it is classified as a type I SN. Type II SNe are characterized by strong Balmer lines, especially H˛ with a P Cygni profile. Many subclasses are defined by secondary spectral features and characteristics light curves. Such a classification is nowadays made computationally by the SNID code (Blondin and Tonry 2007) which is a leading software package. Another famous software package is GELATO, which is provided on the Web (https://gelato.tng.iac. es/). These packages compare the observed spectrum with many archived spectra of SNe of every type and age and identify the spectrum that most resembles it.

4

Designation of Supernovae

Discoveries and spectroscopic confirmations are used to be all reported to the Central Bureau for Astronomical Telegrams (CBAT) of the International Astronomical Union (IAU). CBAT announces new supernovae by issuing an IAU Circular (IAUC) or the Central Bureau Electronic Telegrams (CBET). The new discovery information announced in this way is well reviewed and refereed. When a supernova appears via these publications, it gets a unique designation. The format of the designation, like SN 2015bf, was originally adopted from the Asiago Supernova Catalogue (Barbon et al. 1999) where “2015” is the year of object appearance and “bf” is the order of the announcement. The designation follows the following format: “A” is the first SN of the year, “B” is the second,“Z” is the 26th, “aa” is the 27th, “ab” is the 28th, and so on. We can designate with this system up to 702 SNe. The designation system for the 703rd SN and beyond has not been defined. In recent years, many SN researchers do not report their discoveries and confirmations to the CBAT (Table 1). They distinguish their discoveries with their own provisional designation. Some groups announce them as Astronomer’s Telegrams (http://www.astronomerstelegram.org/), which is an unrefereed mailing list. Other groups announce them only on their own Web page or in the research paper only.

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The present situation suffers from many disadvantages. A definitive list of discovered supernova does not exist. Maintenance of the lists depends on voluntary effort. (http://www.rochesterastronomy.org/snimages/index.html). Provisional designations may be duplicated, although cross identification of objects is possible using a database such as the NASA Extragalactic Database (NED) (http://ned.ipac. caltech.edu/). After the beginning of 2016, the Transient Name Server (TNS) was established which treats the discoveries and spectroscopic confirmations of supernovae (https:// wis-tns.weizmann.ac.il/). It has approved formally by the IAU. It supplies AT 2016xxx designations immediately after the report and gives SN 2016xxx designations after spectroscopic confirmation. Beyond the 703rd SN, it uses three-letter designations, which has not been stipulated by IAU. There remain, however, many discoveries which have not been reported on TNS but only on the Web pages of the discoverer’s team. We have to keep eyes on the status of SN reports.

5

Conclusions

There is very confusing situation around the report and announcement of supernova discoveries, with a need for greater coherence and systematization. SN researchers themselves are in the best position to resolve the issue.

6

Cross-References

 Hydrogen-Poor Core-Collapse Supernovae  Hydrogen-Rich Core-Collapse Supernovae  Interacting Supernovae: Types IIn and Ibn  Observational and Physical Classification of Supernovae  Superluminous Supernovae  The Extremes of Thermonuclear Supernovae  Type Ia Supernovae  Type Iax Supernovae Acknowledgements I would like to thank T. Mistry for his kind review of the manuscript.

References Barbon R, Buondi V, Cappellaro E, Turatto M (1999) The Asiago Supernova Catalogue (Dynamic Version). Astron Astrophys Suppl Ser 139:531–536 Blondin S, Tonry JL (2007) Determining the Type, Redshift, and Age of a Supernova Spectrum. Astrophys J 666:1024–1047

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Filippenko AV, Li WD, Treffers RR, Modjaz M (2001) The Lick Observatory Supernova Search with the Katzman Automatic Imaging Telescope. In: Chen WP, Lemme C, Paczynski B (eds) Small-Telescope Astronomy on Global Scales. Astronomical Society of the Pacific conference series, vol 246. San Francisco, pp 121–130 Kulkarni SR (2013) vol 4807. http://www.astronomerstelegram.org/?read=4807

Part II Historical Supernovae

3

Historical Supernovae in the Galaxy from AD 1006 David A. Green

Abstract

The end points of evolution for some stars are supernova explosions, which release large amounts of energy and material into the surrounding interstellar medium. This energy and material then produces a supernova remnant, of which nearly three hundred have been identified in our Galaxy. The expected rate of supernovae in our Galaxy is approximately two per century, although most will be too far away to be have been observed optically, due to obscuration along the line-of-sight through the Galactic disk. However, supernovae which are relatively nearby are expected to be visible optically, even with the naked eye. Over the last 1000 years or so there are definite historical records of five supernovae in our Galaxy – in AD 1006, 1054, 1181, 1572 and 1604 – that have been observed, all in the pre-telescopic era. The majority of the historical records of these supernovae are from East Asia (i.e., China, Japan and Korea). In addition, detailed European records are available for the most recent two supernovae, and there are also a variety of Arabic records available for some of these events. The records of these five “historical” supernovae are reviewed here, along with a brief discussion of the supernova remnants produced by them. The historical observations of these five supernova allow quantitative astrophysical studies of their remnants, since their ages are known precisely. Also discussed briefly are observations from AD 1680 which have been proposed as being from the supernova that produced the well-known and young supernova remnant Cassiopeia A.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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D.A. Green () Cavendish Laboratory, University of Cambridge, Cambridge, UK e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_2

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3

The Historical Galactic Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Bright Supernova of AD 1006 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 AD 1054 – The Crab Nebula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 AD 1181 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 AD 1572 – Tycho’s SN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 AD 1604 – Kepler’s SN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Cassiopeia A – The Remnant of a Late 17th Supernova? . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

In the 1920s it was first recognized that some optical nebulae were not within our Galaxy, but are in fact distant galaxies. This means that transient or new stars – or “novae” from Latin – seen in these distant galaxies must be intrinsically very much more luminous than any novae seen in our Galaxy, which must be much closer, hence the term “supernova” (SN) for these new stars seen in distant galaxies (e.g., Baade and Zwicky 1934). Supernovae interact with their surroundings to produce extended supernova remnants (SNRs). The expected rate of SNe in our Galaxy is about two per century, although most will not have been easily detected, due to obscuration. However, there are historical records of several relatively nearby Galactic supernovae over the last millennium or so. The records of the five “historical” supernovae – from AD 1006, 1054, 1181, 1572, and 1604 (all in the pre-telescopic era) – are reviewed below, along with a brief discussion of other observations from AD 1680 which have been proposed as being from the supernova that produced the well-known, young supernova remnant Cassiopeia A. Note that dates provided below are in the Julian calendar, except for the supernova of AD 1604 (Kepler’s SN) in Sect. 3.5, which are in the Gregorian calendar.

2

Background

Supernovae are of astrophysical interest for a variety of reasons, in particular a subset of them are used as “standard candles,” of consistent intrinsic luminosity, in cosmological studies. They are also important for the injection of energy and heavy elements into their surrounding interstellar medium. Up to 2015, over 6500 SNe have been identified in external galaxies (IAU Central Bureau for Astronomical Telegrams 2015), with up to about three hundred detected a year recently. (The closest supernova seen in the modern era is SN 1987A in the Large Magellanic Cloud, a small companion Galaxy to our own, which is about 55 kpc away.) Supernovae are classified into various types, on the basis of their optical spectra. The original classification (e.g., see Minkowski 1941) is that “type I” SNe do not show hydrogen lines in their spectra, whereas “type II” do. This is, basically,

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consistent with the idea that “type II” SNe are from more massive stars and that “type I” SNe are observed in both spiral and elliptical galaxies, while “type II” SNe are seen only in spiral galaxies (which, unlike ellipticals, have significant current star forming activity, which produces short-lived, high-mass stars). (The “light curves” of supernovae – i.e., the evolution of their optical brightness with time – vary with their type. However, even with high-quality observations, it is difficult to classify the type of a SN on the basis of a light curve alone.) More recently, “type I” SNe have been further subdivided into the “type Ia’s” – which are classic supernovae from low-mass progenitors and are used as “standard candles” in cosmology – and “type Ib’s” and “type Ic’s,” which, although lacking hydrogen in the spectra, are from high-mass stars which have lost their outer, hydrogen-rich layers (unlike “type Ia’s,” they do have Si in their optical spectra). Supernovae release a large amount of mass and energy into the interstellar medium (ISM), of the order of a solar mass or more and 1044 J, respectively – with initial expansion speeds of the order of 104 km s1 – which interact with their surroundings to produce extended supernova remnants. Another distinction between the “type Ia” and other supernovae is that the former are not expected to leave behind a compact remnant, whereas the latter may leave behind a fast rotating, compact neutron star. Such neutron stars may be observable – usually at radio wavelengths – as a “pulsar,” showing regular pulses of emission, as the beams they produce sweep past the Earth. In our Galaxy there are currently nearly three hundred supernova remnants identified (Green 2014). These range in angular size from several arc minutes to several degrees and have estimated ages of usually several thousands to several tens of thousands of years. The current catalogues of Galactic SNRs are incomplete due to observational selection effects (e.g., Green 2005). Older, large remnants are difficult to identify due to their intrinsic faintness. Also, young but distant SNRs are difficult to identify, as higher-resolution observations are required to recognize their nature. Almost all Galactic SNRs are detected at radio wavelengths, due to their synchrotron emission. About 40 about 30 SNRs are generally classified into three types. Most (80 %) are “shell” type, showing more or less complete limb-brightened rings of emission at radio wavelengths. These shells decelerate as they sweep up appreciable mass from their surroundings. There is a small fraction ( 5 %) which are “filled center” (or “plerions”) – like the Crab Nebula (see Sect. 3.2) – showing centrally brightened emission, due to having central pulsars. The remainder are “composite” types, showing some properties of both “shell” and “filled-center” remnants at radio wavelengths. (In addition, there are some objects that are conventionally considered as SNRs, but which do not readily fit into the three categories above.) The expected rate of supernovae in our Galaxy is approximately two per century. Supernovae which are relatively nearby are expected to be visible optically, even with the naked eye. Historically, most supernovae in our Galaxy will have been too far away to have been observed optically, due to obscuration along the line of

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Table 1 Historical supernovae in our Galaxy since AD 1006

Date AD 1006 AD 1054 AD 1181 AD 1572

Duration of visibility 3 years 21 months 6 months 18 months

1604

12 months

AD

Name of supernova remnant G3276+145 Crab Nebula 3C58 Tycho’s supernova remnant Kepler’s supernova remnant

Historical records East Asian Chinese Korean Y Y Y Y Y Y

Y

Japanese European Arabic Y Y Y Y Y Y Y Y

sight through the Galactic disk. However, there are historical records from the last millennium or so of naked eye observations of apparently “new” stars in our Galaxy, some of which were supernovae (Stephenson and Green 2002). Most of the available records of these supernovae are from East Asia (i.e., mostly from China, but also from Japan and Korea). Chinese royal courts employed astronomers/astrologers who recorded a wide range of astronomical phenomena, and printed records of these have been preserved, albeit often only in summary form for the older records. There are extensive European records available for the most recent two supernovae, and there are a variety of Arabic records also available for some of these events. The various sources for the available records of the five “historical” supernovae in the last millennium or so (i.e., those from AD 1006, 1054, 1181, 1572, and 1604) are summarized in Table 1. From modern observations, it is known that the remnants of these five “historical” supernovae are relatively nearby in the Galaxy (less than few kpc away, whereas the Sun is 8.5 kpc from the center of our Galaxy). This is as expected, for their supernovae to have been visible optically to the naked eye. So, although the observed rate of “historical” supernovae is about one every two centuries in the last millennium, this is consistent with the expected total rate of around two per century, given both (i) the large uncertainties due to small number statistics and (ii) the selection effect that distant Galactic supernovae would be missed. Distances are available for some supernova remnants in our Galaxy from various observational techniques or else can be estimated approximately from the observed statistical properties of SNRs. Combining a distance with the observed angular size provides a physical diameter for a particular remnant, from which the SNR’s age can be estimated. This requires a model for the dynamical evolution of SNRs, which in turn relies on an assumed energy for the SN explosion and an average density for the surrounding interstellar medium. Consequently, the age estimates available for most Galactic SNRs are imprecise. However, for the remnants of five historical supernovae, definite ages are available, which are very useful for quantitative astrophysical studies of them.

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3

The Historical Galactic Supernovae

3.1

The Bright Supernova of AD 1006

The supernova seen in AD 1006 was the brightest of the historical supernovae, and consequently there are extensive records of it available from a range of sources. There are records from China and Japan – where it was first seen on AD 1006 May 1 – of various Arabic sources, and there are also a few European records. At its brightest it had an apparent magnitude perhaps as bright as 7 (Stephenson and Green 2002), meaning it was visible in daylight. Clearly this was a striking new star in the sky, as is shown by this Chinese report of it in the Wenxian Tongkao: Jingde reign period, third year, [DAD 1006–1007], there was a huge (ju) star seen in the sky at the west of Di (lunar lodge). Its bright rays were like a golden disc. No-one could determine its significance. Zhou Keming, the chief official of the Spring Agency reported that according to the (star manuals) Tianwen Lu and the Jingzhou Zhan, the star was a Zhoubo. Its form was like the half Moon and it had pointed rays. It was so brilliant (huang huang) that one could really see things clearly (ran ke yi jian wu) (by its light). (from Stephenson and Green 2002)

A “lunar lodge” is one of 28 regions used in Chinese astronomy, which effectively define a range of right ascension. The star was visible for 3 years, to AD 1009. The diverse observations of this SN constrain its distance within a few degrees in different coordinates: (i) the Chinese observations give a range in right ascension, (ii) Arabic records provide an ecliptic longitude range, and (iii) from observations made at the St Gallen Monastery in Switzerland – where the new star was just visible – a lower limit to its declination. Close to this position is a large (30 arcmin diameter) limb-brightened shell of radio emission (PKS 145941, DG327:6C14:5) (e.g., Reynoso et al. 2013) which was identified as the remnant of this supernova by Gardner and Milne (1965). Subsequent observations of this SNR have also detected extended X-ray emission from it and optical filaments in the northwest (Allen et al. 2001; Raymond et al. 2007).

3.2

AD 1054 – The Crab Nebula

In China this supernova was first observed on AD 1054 July 4, and there are extensive records covering observations of it for nearly 2 years. In addition, there are two records from Japan and a brief Arabic record of its visibility in Constantinople (Brecher 1978). There have been claims of European reports of this supernova, but none of these proposed records are completely convincing (see further discussion in Stephenson and Green 2003). Also, pictographs/drawings of a star close to a crescent Moon in the southwestern USA have been suggested as a possible record of this supernova (e.g., Miller 1955), as the Moon would be close to the supernova on AD 1054 July 5th. However, no specific dating evidence is available for these pictographs/drawings, and the interpretation of these as records of the supernova is speculative.

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The following Chinese record, from the Songshi (Annals, Chapter 12), reports the end of the visibility of supernova, AD 1056 April 6th: Jiayou reign period, first year, third lunar month, (day) xinwei [8] [DAD 1056 April 6th]. The Director of the Astronomical Bureau reported that since the first year of the Zhihe reign period, fifth lunar month, a guest star had appeared (chu) at daybreak (chen) at the east, guarding (shou) Tianguan. Now it has vanished (mo). (from Stephenson and Green 2002)

Tianguan is a Chinese asterism consisting of a single star,  Tau. The remnant of this supernova is the very well-known “Crab Nebula.” This unusual optical nebulosity, several arcmin in extent, was noted by Messier in the eighteenth century and is included as the first object in his catalogue of known optical nebulae (which was compiled to avoid rediscovering known nebulae, when searching for new comets). The Crab Nebula was first proposed as the remnant of this SN in the 1920s (Hubble 1928; Lundmark 1921), which has generally been accepted since the 1940s (Duyvendak 1942a,b; Oort 1942). Optically, the Crab Nebula consists of both polarized synchrotron emission and thermal filaments, which are expanding (e.g., Bietenholz and Nugent 2015; Charlebois et al. 2010). The Crab Nebula is one of the brightest sources in the sky at radio, X-ray, and  -ray wavelengths (e.g., Aharonian et al. 2006; Hester et al. 2002). The radio source is Taurus A (D3C144, DG184:65:8), which has an expanding “filled-center” morphology 75 arcmin2 in extent (e.g., Bietenholz and Nugent 2015), which was first identified as the radio remnant of the supernova of AD 1054 by Bolton and Stanley (1949). The Crab Nebula contains a pulsar which was first identified in the radio by Staelin and Reifenstein (1968), but which has also been detected over a wide range of wavelengths, up to  -rays.

3.3

AD 1181

There are three Chinese and five Japanese records of this supernova, but only limited details are provided. At this time there were two separate Chinese empires, and these provide independent records. The supernova was first seen on AD 1181 August 6th, in southern China, and the last report of its visibility – again in southern China – was AD 1182 February 6th, as shown in this record from the Wenxian Tongkao: Ninth year first month, day guihai [60] [DAD 1182 February 6th]: the guest star was no longer seen (bujian). From the previous year, sixth month, day jisi [6] [DAD 1181 August 6th] until this time was a total of 185 days; then it faded and hid itself (shaofu). (from Stephenson and Green 2002)

The available historical records do not constrain the position of the supernova well, and it was not until 1971 that the identification of the remnant of this supernova was made by Stephenson (1971). The remnant is the bright radio source 3C58 (DG130:7 C 3:1), which is 5  10 arcmin2 in extent and is centrally brightened, being a “filled-center” SNR (e.g., Bietenholz et al. 2001). This remnant has faint optical filaments and also shows centrally brightened X-ray structure (e.g., Fesen

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et al. 2008; Slane et al. 2004). Although the morphology of 3C58 has long suggested that it contains a pulsar, this was not detected until 2002 (Camilo et al. 2002).

3.4

AD 1572 – Tycho’s SN

This supernova is usually called Tycho’s SN, as Tycho Brahe made a detailed study of it. This supernova was first reported in both Europe and Korea on AD 1572 November 6th and in China 2 days later. Due to bad weather, Tycho Brahe did not first see it until November 11th, and it clearly made a strong impression on him, as shown by this report on his first sighting of it: . . . Behold, directly overhead, a certain strange star was suddenly seen, flashing its light with a radiant gleam and it struck my eyes. Amazed, and as if astonished and stupefied, I stood still, gazing for a certain length of time with my eyes fixed intently on it and noticing that same star placed close to the stars which antiquity attributed to Cassiopeia. When I had satisfied myself that no star of that kind had ever shone forth before, I was led into such perplexity by the unbelievability of the thing that I began to doubt the faith of my own eyes . . . (Progymnasmata, chapter 3). (from Stephenson and Green 2002)

This new star appeared in the constellation of Cassiopeia, which is an easily recognized “W” shape; see Fig. 1. The supernova had a peak apparent magnitude of about 4. The supernova was observed until AD 1574 March by Tycho Brahe and slightly longer in China (until sometime in AD 1574 April or May). Tycho Brahe subsequently wrote a treatise Progymnasmata, in which he discussed the observations of this “new” star in the context of the then conventional views of the Universe. These views, dating back to Aristotle, were that the heavens consisted of multiple celestial spheres. The inner spheres – which move – correspond to atmospheric phenomena, the Sun, the Moon, and the planets, with the “fixed” stars in the most distant, eighth sphere. Tycho’s careful positional measurements convinced him that the “new” star had a fixed position and hence was in the most distant, eighth sphere, with the “fixed” stars. This showed that changes in the eighth sphere of the “fixed” stars were possible, which was inconsistent with the then widely accepted view that changes were only possible in regions closer than the Moon. The position of the SN was defined within a few arcmin by Tycho’s observations, and the identification of the remnant as a bright radio source (3C10, DG120:1 C 1:4) was first suggested by Hanbury Brown and Hazard (1952), which was soon confirmed by other observations. This remnant is 8 arcmin in diameter and shows a limb-brightened expanding shell of emission in the radio and in X-rays (e.g., Katsuda et al. 2010; Reynoso et al. 1997). In the optical there are several filaments and knots seen around its rim (e.g., Ghavamian et al. 2001). Remarkably, it is possible to detect the “light echo” from the SNe, i.e., light which has been reflected from interstellar clouds, and is only now arriving, so is accessible by modern large optical telescopes. Spectroscopic analysis of this light echo shows that Tycho’s SN was of a “type Ia” (Krause et al. 2008).

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Fig. 1 From Tycho Brahe De nova stella, showing the position of the “new” star observed in AD 1572 – labeled “I,” toward the top – in relation to the stars in the constellation of Cassiopeia

3.5

AD 1604 – Kepler’s SN

This supernova is usually called Kepler’s SN, as Johannes Kepler made extensive observations of it from Prague. However, he was not the first to observe it, due to poor weather. It was first reported in Europe on AD 1604 October 9th, from two independent Italian observers, but Kepler himself did not observe it until October

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17th. Also, it was not visible on October 8th, as several European astronomers made no mention of this “new” star when observing a nearby conjunction of Mars and Jupiter on that date. There are two records of this supernova from China, where it was first observed on AD 1604 October 10th. It was also observed in Korea from October 13th, and records of observations made on most days in the first 6 months of the supernova exist, often giving brightness comparisons with planets or particular stars. The following is a Korean record of this supernova from the Sonjo Sillok (Chapter 178): King Sonjo, 37th year, ninth lunar month, (day) wuchen [5] [DAD 1604 Oct 13]. In the first watch of the night, there was a guest star; it was 10 du in Wei lunar lodge and its distance from the (north) pole (qiuji) was 110 du. Its form (xingti) was smaller than Jupiter and its colour was orange (lit. yellowish-red). It was scintillating (dongyao). (from Stephenson and Green 2002)

Here du is a Chinese astronomical degree – with 365¼ du in a full circle – i.e., the apparent mean motion of the Sun with respect to the stars in 1 day. The supernova increased in brightness for about 3 weeks after it was first detected and reached a peak brightness of approximately 2 or 3 in apparent magnitude. The European and Korean brightness comparisons are in good agreement and allow a “light curve” – i.e., a plot showing the brightness evolution with the time – for the supernova to be produced (see Clark and Stephenson 1977). Although this is consistent with the new star being a supernova, it does not reliably distinguish which type of SN it was. Kepler’s observations of the distance of the SN from nearby stars define its position to better than 1 arcmin. This accurate position allowed Baade (1943) to identify a faint optical nebulosity as the remnant of this supernova (G4.5 C 6.8), (see also, e.g., Sankrit et al. 2008) which has subsequently also been detected at radio and X-ray wavelengths, where it has a limb-brightened shell morphology, 3 arcmin in diameter (e.g., DeLaney et al. 2002; Vink 2008).

4

Cassiopeia A – The Remnant of a Late 17th Supernova?

One of the brightest radio sources in the sky is Cassiopeia A (Cas A, D G111.7  2.1), which is clearly a young supernova remnant that is relatively nearby in the Galaxy. In the radio and in X-rays, Cas A shows bright, expanding shell of emission, with many compact knots (e.g., Anderson and Rudnick 1995; Patnaude and Fesen 2009). Optically, it has a complex mixture of filaments, fast expanding knots, and “quasi-stationary flocculi” (e.g., Milisavljevic and Fesen 2013). Expansion studies show that Cas A is around 300 years old (Fesen et al. 2006), and consequently historical observations of the supernova that produced Cas A might be expected. In fact, it has been possible to detect a “light echo” from the SN that produced Cas A (Rest et al. 2008). With regard to possible historical records, Ashworth (1980) proposed that while engaged in charting the stars of Cassiopeia in AD 1680, John Flamsteed had

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observed Cas A’s supernova. Ashworth (1980) noted that Flamsteed’s catalogue includes a faint (sixth magnitude) star “3 Cas” which is close to the position of Cas A. Modern observations reveal no known star at this location, and Ashworth suggested that “3 Cas” represented an outburst of the supernova itself. The position of “3 Cas” was determined by Flamsteed from his measurements of its angular distance from two other stars (ˇ Peg and ˇ Per). However, the positional offset between “3 Cas” and Cas A of 10 arcmin is much larger than Flamsteed’s typical measurement error of about 1 arcmin. Instead, Broughton (1979) and Kamper (1980) proposed that the apparent position of the catalogued “3 Cas” is due to Flamsteed accidentally compounding his measured angular distances from the reference stars (ˇ Peg and ˇ Per) to two separate faint stars (SAO 35386 and AR Cas), as though they corresponded to a single star. Neither SAO 3586 nor AR Cas is actually included in Flamsteed’s catalogue, but their respective angular distances from ˇ Peg and ˇ Per are consistent with the angular distances of “3 Cas” within Flamsteed’s typical measurement error. Thus, it seems Flamsteed did not observe the outburst of the star which produced Cas A.

5

Conclusions

For the nearly three hundred SNRs that have been identified in our Galaxy, in almost all cases, only estimates of their ages can be made, which are not precise. These are obtained from their physical size, deduced from their observed angular size, and their distance, using a model for their dynamical evolution. However, distances are often not well known, and there are also uncertainties in the dynamical models (e.g., assumptions for the supernova energy and density of the surroundings). This lack of accurate ages therefore limits the accuracy of most quantitative studies of these SNRs. However, there are definite known ages of the five remnants of the historical supernovae listed in Table 1, discussed above, which allows more quantitative astrophysical studies of these particular Galactic supernova remnants to be made.

6

Cross-References

 Historical Records of Supernovae  Possible and Suggested Historical Supernovae in the Galaxy  Supernova 1604, Kepler’s Supernova, and its Remnant  Supernova of 1006 (G327.6+14.6)  Supernova of 1054 and its Remnant, the Crab Nebula  Supernova of 1572, Tycho’s Supernova  Supernova of AD 1181 and its Remnant: 3C 58  Supernova Remnant Cassiopeia A

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References Aharonian F, Akhperjanian AG, Bazer-Bachi AR et al (2006) Observations of the Crab nebula with HESS. Astron Astrophys 457:899–915 Allen GE, Petre R, Gotthelf EV (2001) X-ray synchrotron emission from 10–100 TeV cosmic-ray electrons in the supernova remnant SN 1006. Astrophys J 558:739–752 Anderson MC, Rudnick L (1995) The deceleration powering of synchrotron emission from ejecta components in supernova remnant Cassiopeia A. Astrophys J 441:307–333 Ashworth WB Jr (1980) A probable Flamsteed observations of the Cassiopeia A supernova. J Hist Astron 11:1–9 Baade W (1943) Nova Ophiuchi of 1604 as a supernova. Astrophys J 97:119–127 Baade W, Zwicky F (1934) On super-novae. Proc Natl Acad Sci 20:254–259 Bietenholz MF, Nugent RL (2015) New expansion rate measurements of the Crab nebula in radio and optical. Mon Not R Astron Soc 454:2416–2422 Bietenholz MF, Kassim NE, Weiler KW (2001) The radio spectral index and expansion of 3C 58. Astrophys J 560:772–778 Bolton JG, Stanley GJ (1949) The position and probable identification of the source of the Galactic radio-frequency radiation Taurus-A. Aust J Sci Res A Phys Sci 2:139–148 Brecher K (1978) A near-eastern sighting of the supernova explosion of 1054. Nature 273:728–730 Broughton RP (1979) Flamsteed’s 3 Cassiopeia D Ar-Cassiopeia C SAO35386. J R Astron Soc Canad 73:381–383 Camilo F, Stairs IH, Lorimer DR, Backer DC, Ransom SM, Klein B, Wielebinski R, Kramer M, McLaughlin MA, Arzoumanian Z, Müller P (2002) Discovery of radio pulsations from the Xray pulsar J0205+6449 in supernova remnant 3C 58 with the Green Bank Telescope. Astrophys J 571:L41–L44 Charlebois M, Drissen L, Bernier A-P, Grandmont F, Binette L (2010) A hyperspectral view of the Crab nebula. Astron J 139:2083–2096 Clark DH, Stephenson FR (1977) The historical supernovae. Pergamon Press, Oxford DeLaney T, Koralesky B, Rudnick L, Dickel JR (2002) Radio spectral index variations and physical conditions in Kepler’s supernova remnant. Astrophys J 580:914–927 Duyvendak JJL (1942a) Further data bearing on the identification of the Crab nebula with the supernova of 1054 A.D. Part I. The ancient oriental chronicles. Publ Astron Soc Pac 54:91–94 Duyvendak JJL (1942b) The ‘guest-star’ of 1054. T’oung Pao 36:174–178 Fesen RA, Hammell MC, Morse J, Chevalier RA, Borkowski KJ, Dopita MA, Gerardy CL, Lawrence SS, Raymond JC, van den Bergh S (2006) The expansion asymmetry and age of the Cassiopeia A supernova remnant. Astrophys J 645:283–292 Fesen R, Rudie G, Hurford A, Soto A (2008) Optical imaging and spectroscopy of the Galactic supernova remnant 3C 58 (G130.7+3.1). Astrophys J Suppl Ser 174:379–395 Gardner FF, Milne DK (1965) The supernova of A.D. 1006. Astron J 70:754 Ghavamian P, Raymond J, Smith RC, Hartigan P (2001) Balmer-dominated spectra of nonradiative shocks in the Cygnus loop, RCW 86, and Tycho supernova remnants. Astrophys J 547:995–1009 Green DA (2005) Some statistics of Galactic SNRs. Memorie della Soc Astron Ital 76:534–541 Green DA (2014) A catalogue of 294 Galactic supernova remnants. Bull Astron Soc India 42:47– 58. See also http://www.mrao.cam.ac.uk/surveys/snrs/. Accessed 1 Nov 2015. Hanbury BR, Hazard C (1952) Radio-frequency radiation from Tycho Brahe’s supernova (A.D. 1572). Nature 170:364–365 Hester JJ, Mori K, Burrows D, Gallagher JS, Graham JR, Halverson M, Kader A, Michel FC, Scowen P (2002) Hubble space telescope and Chandra monitoring of the Crab synchrotron nebula. Astrophys J 577:L49–L52 Hubble EP (1928) Novae or temporary stars. Leaflet Astron Soc Pac 1:55–58 IAU Central Bureau for Astronomical Telegrams (2015) List of supernovae. http://www.cbat.eps. harvard.edu/lists/Supernovae.html. Accessed 1 Nov 2015.

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Kamper KW (1980) Are there historical records of the Cas A supernova? The Observatory 100:3–4 Katsuda S, Petre R, Hughes JP, Hwang U, Yamaguchi H, Hayato A, Mori K, Tsunemi H (2010) X-ray measured dynamics of Tycho’s supernova remnant. Astrophys J 709:1387–1395 Krause O, Tanaka M, Usuda T, Hattori T, Goto M, Birkmann S, Nomoto K (2008) Tycho Brahe’s 1572 supernova as a standard type Ia as revealed by its light-echo spectrum. Nature 456: 617–619 Lundmark K (1921) Suspected new stars recorded in old chronicles and among recent meridian observations. Publ Astron Soc Pac 33:225–238 Milisavljevic D, Fesen RA (2013) A detailed kinematic map of Cassiopeia A’s optical main shell and outer high-velocity ejecta. Astrophys J 772:134 (15pp) Miller WC (1955) Two prehistoric drawings of possible astronomical significance. Leaflet Astron Soc Pac 7:105–112 Minkowski R (1941) Spectra of supernovae. Publ Astron Soc Pac 53:224–225 Oort JH (1942) Note on the supernova of 1054. T’oung Pao 36:179–180 Patnaude DJ, Fesen RA (2009) Proper motions and brightness variations of nonthermal X-ray filaments in the Cassiopeia A supernova remnant. Astrophys J 697:535–543 Rest A, Welch DL, Suntzeff NB, Oaster L, Lanning H, Olsen K, Smith RC, Becker AC, Bergmann M, Challis P, Clocchiatti A, Cook KH, Damke G, Garg A, Huber ME, Matheson T, Minniti D, Prieto JL, Wood-Vasey WM (2008) Scattered-light echoes from the historical Galactic supernovae Cassiopeia A and Tycho (SN 1572). Astrophys J 681:L81–L84 Raymond JC, Korreck KE, Sedlacek QC, Blair WP, Ghavamian P, Sankrit R (2007) The preshock gas of SN 1006 from Hubble Space Telescope Advanced Camera for Surveys observations. Astrophys J 659:1257–1264 Reynoso EM, Moffett DA, Goss WM, Dubner GM, Dickel JR, Reynolds SP, Giacani EB (1997) A VLA study of the expansion of Tycho’s supernova remnant. Astrophys J 491:816–828 Reynoso EM, Hughes JP, Moffett DA (2013) On the radio polarization signature of efficient and inefficient particle acceleration in supernova remnant SN 1006. Astron J 145:104 (9pp) Sankrit R, Blair WP, Frattare LM, Rudnick L, DeLaney T, Harrus IM, Ennis JA (2008) Hubble Space Telescope/Advanced Camera for Surveys narrowband imaging of the Kepler supernova remnant. Astron J 135:538–547 Slane P, Helfand DJ, van der Swaluw E, Murray SS (2004) New constraints on the structure and evolution of the Pulsar wind nebula 3C 58. Astrophys J 616:403–413 Staelin DH, Reifenstein EC III (1968) Pulsating radio sources near the Crab nebula. Science 162:1481–1483 Stephenson FR (1971) Suspected supernova in A.D. 1181. Q J R Astron Soc 12:10–38 Stephenson FR, Green DA (2002) Historical supernovae and their remnants. Oxford University Press, Oxford/New York Stephenson FR, Green DA (2003) Was the supernova of AD 1054 reported in European history? J Astron Hist Herit 6:46–52 Vink J (2008) The kinematics of Kepler’s supernova remnant as revealed by Chandra. Astrophys J 689:231–241

4

Historical Records of Supernovae F. Richard Stephenson

Abstract

The absence of any definite sightings of supernovae in our own galaxy in the telescopic era heightens the importance of historical accounts of these events. However, early records cite a wide variety of “new stars”: some moving, others stationary; some of large angular size, others starlike; some of unknown or very short duration, others visible for many months. Hence, in attempting to identify potential supernovae among such a miscellany of temporary stars, a priority is to define a set of selection criteria. On this basis, only five new stars (appearing in AD 1006, 1054, 1181, 1572, and 1604), can be confidently rated as supernovae. In each case, there is a wide variety of convincing evidence which can be utilized to establish the supernova nature of these objects and reliably identify their presentday remnants. Historical sources of pre-telescopic astronomical observations are diverse: these largely originate from Babylon, East Asia (mainly China, but also Japan and Korea), the Arab regions, and Europe. East Asian history is replete with reports of a wide variety of celestial phenomena, and they are the main source of observations of Galactic supernovae. In general, Arab astronomers appear to have had little interest in new stars and were more concerned with eclipses and other cyclical phenomena. However, several Arab chroniclers gave vivid accounts of the brilliant supernova of AD 1006. Not until the Renaissance do we find much European interest in stellar outbursts, but the appearance of the bright supernovae of AD 1572 and 1604 inspired astronomers such as Tycho Brahe and Kepler to make extensive observations of these stars with unparalleled accuracy.

F.R. Stephenson () Department of Physics, Durham University, Durham, UK e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_44

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Contents 1 2 3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Categories of Historical “New Stars” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Possible Sources of Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Babylon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Ancient and Medieval China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Korea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Arab World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Ancient Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Medieval Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 European Renaissance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Other Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Observations of supernovae in external galaxies suggest that in a galaxy the size of the Milky Way an average frequency of about two supernovae per century might be expected. However, since the solar system lies very close to the plane of the Milky Way, obscuring interstellar dust prevents detection of most of the supernova events occurring in our own Galaxy. Possibly because of this factor, no supernovae have definitely been detected in the Milky Way in recent centuries. The most recent Galactic supernova for which we have reliable records was sighted (by Johannes Kepler and others) as long ago as AD 1604; this was several years before the advent of telescopic astronomy.

2

Categories of Historical “New Stars”

Ancient and medieval observers from a wide variety of cultures have left us numerous records of unusual celestial occurrences. These include cyclical phenomena such as solar and lunar eclipses and lunar and planetary movements – as well as events occurring intermittently such as meteors, comets, and stellar outbursts. Many of the observers were astronomers, who carefully and systematically watched the skies for unusual phenomena. Others were people such as chroniclers who had no particular interest in astronomy but wished to place on record their impressions of remarkable celestial events. As a result of these various efforts, many reports of temporary stars have come down to us. In addition to meteors (characterized by their rapid movements), these objects were probably a mixture of comets, novae, and a few supernovae – perhaps along with occasional variable stars. Some of these temporary stars were described as moving from day to day, while others were said to remain stationary, thus providing a direct indication of their stellar nature. However,

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many records are quite brief, giving few descriptive details. Hence it often proves difficult to determine the precise nature of a temporary star noted in ancient or medieval history. It should be emphasized that until the pioneering work of Tycho Brahe and his contemporaries in the late sixteenth century, observers – whether astronomers or not – had no real concept of the nature of the stars which they described. Tycho, Thomas Digges, and others were able to show that the brilliant star which appeared in Cassiopeia in AD 1572 had no detectable parallax and thus was located far beyond the orbit of Saturn and among the fixed stars. However, this discovery took a while to circulate – especially outside Europe. In attempting to identify potential supernova candidates among the medley of temporary stars recorded in history, it is necessary for us to establish a series of selection criteria (e.g., Stephenson and Green 2005). With this in mind, David Green and I have drawn up a set of six criteria. These may be listed as follows: (i) long duration of visibility (preferably at least 3 months); (ii) fixed location, carefully described (preferably with a direct indication that the position did not change); (iii) low Galactic latitude (usually less than about 10 deg); (iv) small angular size (in particular, no evidence of a tail); (v) unusual brilliance (e.g., daylight visibility); and (vi) several independent reports (giving corroborative information). If a temporary star satisfies these various conditions, it would seem well worth matching with a known supernova remnant (SNR). In recent decades, some three hundred SNRs have been detected in our galaxy, largely as the result of surveys at radio wavelengths. However, in practice such matching can only rarely be achieved, partly because of the mediocre quality of most early records. To date, only five Galactic supernovae – observed in AD 1006, 1054, 1181, 1572, and 1604 – have been confidently identified and linked with SNRs. These stars were widely observed and the celestial locations are carefully described. Earlier possible supernovae were observed in China in AD 185, 386, and 393. However, although each of these three stars was seen for several months (probably for as long as 20 months in AD 185), the records are brief and they are not supported by observations made in other parts of the world. In the author’s opinion, when investigating historical supernovae it is not advisable to commence with one of the many known SNRs and then to search for historical records of the original outbursts. In particular, it is usually only possible to determine the approximate age of a SNR based on radio and optical data. An apparent agreement in position between a SNR and a temporary star recorded in history may seem attractive, but unless the records of the star satisfy a wide variety of conditions, the accord in position may well be spurious. Historical records of the few potential supernovae which satisfy the six criteria outlined above have all been studied in detail (cf. Stephenson and Green 2002). For instance, as many as 30 separate reports of the brilliant supernova of AD 1006 (which remained visible for some 3 years) have been identified. These originate from a wide variety of sites in East Asia, the Arab world, and Europe. In the case of the event in AD 1054 (which remained visible for 21 months and was responsible for the production of the Crab nebula), nine records are preserved. The corresponding figures for the supernova of

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AD 1181 are 6 months and eight separate records. Both the supernovae of AD 1572

and 1604 were widely observed for many months in Europe, as well as in China and Korea. As a result, numerous detailed reports of these events are preserved.

3

Possible Sources of Observations

Observations of celestial events may be found in the records of a variety of cultures. Regrettably, these records are often far from complete. Unfavorable weather has been a major factor in limiting observation at all periods. Further, much depends on human factors such as what the observers’ particular interests were, what information they decided to place on record, and what remains of their reports today. Literary disasters – both accidental and deliberate (as in times of war) – have led to the loss of much original material from many parts of the world. As will be discussed below, in several early civilizations (notably in ancient Babylon and the medieval Arab world), astronomers were mainly interested in observing cyclical phenomena in order to assist prediction of similar events. Hence, reports of sporadic events such as comets and stellar outbursts are rare. By contrast, East Asian astronomers took notice of almost every type of celestial event which was visible to the unaided eye.

3.1

Babylon

Many of the earliest astronomical records which still survive today originate from Babylon. These records, inscribed on clay tablets, were accidentally discovered in the ruins of the city of Babylon during the 1870s by the inhabitants of the surrounding villages. Many of the tablets were acquired by the British Museum, where they can be viewed today. Unfortunately, only a few tablets were excavated by archaeologists. Some 2000 Babylonian texts devoted to astronomy are now extant. Most are in a fragmentary condition, and it may be conservatively estimated that less than 10 % of what was originally a vast archive now survive. The Babylonian scribes used a cuneiform (wedge-shaped) script. After completion, the tablets were either baked or Sun-dried. The script which they used was syllabic in nature and, thanks to the work of scholars over the past century or so, is now well understood – as is the operation of the Babylonian lunisolar calendar. Detailed transliterations and translations of the Babylonian astronomical texts have been published by Sachs and Hunger (1988, and subsequent volumes). Celestial observations were undertaken by official astronomers in Babylon over many centuries. Probably astrology provided the main motivation for skywatching. The date range covered by the extant astronomical records extends from around 720 BC to AD 75, although most of the surviving texts were composed between about 450 BC and 50 BC. Babylonian observational texts fall into two main groups: astronomical diaries and compilations of specific data which the Babylonian astronomers subsequently

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extracted from the diaries, for example, to assist predicting future astronomical events. Most recorded observations are of cyclical phenomena: lunar and solar eclipses, lunar and planetary movements, and so on. Babylonian eclipse observations have proved of considerable importance in studies of Earth’s past rotation (Stephenson 1997). By comparison, reports of sporadic events are rare. Several records of comets (termed sallummu) occur in the texts; these can be recognized by their motion over a period of time. In particular, observations of Halley’s Comet in both 164 and 87 BC have been identified (Stephenson et al. 1985). However, there are no known Babylonian reports of unusual starlike objects which might be interpreted as novae or supernovae.

3.2

Ancient and Medieval China

Commencing around 700 BC, Chinese historical text have proved to be a prolific source of astronomical records. The study of astrology was very important, and from an early period official astronomers were employed at the Chinese court. Their duty was to maintain a regular watch of the sky, both night and day, and to note any unusual celestial phenomena: both cyclical and intermittent. What are probably the oldest reliable astronomical records from China occur in the Chunqiu (“Spring and Autumn Annals”). This chronicle covers the period from 722 to 481 BC. It contains many accurately dated reports of solar eclipses, as well as occasional brief records of comets – identified as xingbo (“bushy stars”). However, no recognizable accounts of stellar events are known to be preserved in Chinese history until the Han dynasty (206 BC–AD 220). From then onward, until the end of the last dynasty in 1911, vast numbers of astronomical records of all kinds – following very much a traditional style – are preserved in a wide variety of sources. Over many centuries, Chinese writing gradually developed from simple pictograms to an advanced form of ideographic script. However, commencing in the first century AD , a standardized script was adopted. This script remained essentially unchanged until the mid-twentieth century when the more complex characters were simplified by scholars in the People’s Republic. However, in general, this revision has not found favor elsewhere. The traditional Chinese lunisolar calendar has been extensively studied. Most years had 12 lunar months, totaling about 354 days. Every 30 months or so an additional 13th (intercalary) month was inserted to keep the calendar in step with the seasons. An independent 60-day cycle was also in operation. Lists of emperors giving the corresponding BC or AD year of accession are widely available, and various tables have been published enabling dates to be converted to the Julian or Gregorian calendar. The author has devised a computer program based on the tables of Hsueh and Ou-yang (1956) to expedite date conversion. The invention of block printing in China (eighth century AD) gradually led to the printing and reprinting of many early texts. As a result, numerous older manuscripts have been lost and those that remain are now relatively rare. Reprints of the various official histories and other major historical compilations are currently available in libraries worldwide.

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The principal sources of observations in Chinese history are the 25 dynastic histories (Zhengshi). Most of these extensive compilations contain a section in one or more chapters devoted to astronomy and, in particular, give details of the individual astronomical observations made during the appropriate dynasty; this section of the history is usually entitled Tianwenzhi (“Reports on astronomy”). Celestial observations are also frequently cited in the basic annals (Benji) of these same histories – although often in less detail than in the Tianwenzhi. A further valuable source of ancient and medieval Chinese astronomical records is the Wenxian Tongkao (“Comprehensive Study of Documents and Records”), edited by Ma Duanlin. This work, which was completed in AD 1307, contains an extensive section (chapters 282–294) devoted to astronomy. Chronicles, such as the Ming Shilu (“Veritable records of the Ming dynasty”), covering most of the Ming dynasty (AD 1368–1644), also cite many astronomical observations. The number of additional sources (including provincial histories) is very large. Relatively recently, an important compilation of Chinese astronomical records of various kinds was published in a single volume by Beijing Observatory (1988). This compendium, which is entitled Zhongguo Gudai Tianxiang Jilu Zongji (“A Union Table of Ancient Chinese Records of Celestial Phenomena”), cites numerous observations from ancient times to the early twentieth century. The astronomical observations are grouped by category and the Julian or Gregorian date of each report is given. In the various historical sources, comets are usually identified using the descriptive terms xingbo (“bushy stars”) or huixing (“broom stars”). A less common alternative is zhangxing (“long stars”). The term kexing (“guest star”) is the most frequently used expression to identify a fixed starlike object (Stephenson and Green 2009). One of the accounts of the guest star of AD 1181 (an established supernova) emphasizes the perceived astrological significance of this star. The text, in the Wenxian Tongkao, asserts that the occurrence of the guest star warned of the arrival of an unwelcome guest at the Song dynasty court: an ambassador from the Jin dynasty in North China. When the star was lost to view 6 months later, it signaled the departure of the ambassador. However, the use of the term guest star is by no means exclusively applied to stellar objects. Several Chinese accounts describe moving guest stars, which are clearly of cometary nature. In common with the supernova of AD 1181, the supernovae of AD 1054, 1572 and 1604 were also widely described as guest stars in Chinese history. Uniquely, because of its extreme brilliance and remarkable yellow color, the supernova of AD 1006 was termed a Zhoubo (“Earl of Zhou”) star instead. It is almost routine to find Chinese records of one or more star groups in or near which a temporary star (whether stationary or moving) appeared. Possibly as early as the Zhanguo or “Warring States Period” (481–221 BC), Chinese astronomers divided the visible stars (north of about declination 55 deg) into some 280 groups. On average each asterism contained only about six stars, although individual totals ranged from only one to as many as 30 stars. Most Chinese asterisms bear little or no relation to the standard occidental constellations – which are usually much larger. Several Chinese star maps survive from the ancient world, sometimes engraved on

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the ceilings of tombs. However, these early artifacts are often fairly crude. The oldest extant Chinese star chart which is carefully executed dates from AD 1247; engraved on stone, this is preserved in Suzhou Museum. Late copies of the oldest printed star chart, first produced around AD 1090 by Su Song, are available, but their reliability is uncertain, as the originals are lost. For details of these and other Chinese star charts, see, for example, Stephenson (1994). In recent years, much effort has gone into the identification of the constituents of star groups near which suspected supernovae occurred. This process is often tedious, and its difficulty has been compounded by the fact that Chinese star maps tend to represent all stars by symbols of uniform size, regardless of brightness. Chinese astrography was equatorial in character, unlike its occidental counterpart which until the nineteenth century was ecliptical in character. A series of 28 xiu (“lunar lodges”) – constellations circling the sky in the general region of the celestial equator – were used as right ascension markers. A selected star in each of these star groups was used to define the western boundary of each zone of R.A. The R.A. of a particular star would be described as so many degrees in a particular lunar lodge. Curiously, although the average angular extent of a lunar lodge was about 13 deg, the actual width ranged from less than 1 deg (for the division named Zuixi) to 33 deg (in the case of Dongjing). So far no satisfactory explanation has been offered for this marked variation. North polar distance, measured from the north celestial pole, was the Chinese counterpart of declination. Angles were measured in du (“degrees”), the apparent mean motion of the Sun in 1 day, and thus equal to 0.9856 deg. Chinese astronomical records, although often impressive in comparison with other early cultures, are nevertheless by no means complete. There are numerous lacunae in the records, notably between about AD 550 and 750. Although detailed Chinese reports of the supernovae of AD 1006, 1054, 1181, 1572, and 1604 are available, records of earlier proposed supernovae (as in AD 185, 386, and 393) are remarkably brief, rendering identification of possible remnants uncertain.

3.3

Korea

Korean astronomy and celestial mapping owed their origin to China. Dates in Korean history (down to the Japanese annexation in 1910) follow the traditional Chinese lunisolar calendar, except that years are numbered in terms of the reigns of Korean kings and queens. Lists of Korean rulers, giving the appropriate BC or AD year of accession, are readily available, and conversion of dates to the Julian or Gregorian calendar is usually straightforward. All major Korean historical works composed before the twentieth century were written in Classical Chinese; use of the Korean alphabet (Hangul), which was devised in the fifteenth century, only became widespread in modern times. The oldest detailed history of Korea is the Samguk sagi (“History of the Three Kingdoms,” which was composed in AD 1145 by Kim Pusik). This history, which covers the period from the first century BC to AD 935, contains numerous astronomical records. However, until the late seventh century AD, many reports of celestial

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phenomena in the Samguk sagi are copied from Chinese history and there are few original observations (Stephenson 2013). Later astronomical records in the Samguk sagi are more original but there are no reports which assert that a temporary star remained fixed for any length of time; only the date of discovery is given. During the subsequent Koryo dynasty (AD 936–1392), several observations of new stars, usually identified as “guest stars”, are found in the Koryo-sa (“History of Koryo”), which is modeled on a typical Chinese dynastic history. However, once again no durations of visibility are quoted. The supernovae of AD 1054 and 1181 are both overlooked in the Koryo-sa; although there is a single brief report in this history that “a broom star was seen” at some time during the year AD 1006, no descriptive details are given. During the following Yi or Choson dynasty (AD 1392–1863), numerous astronomical records are cited in the Choson Wangjo Sillok (“Veritable records of the Choson dynasty”). This extensive chronicle is now available on CD-ROM. An even more detailed chronicle than the Choson Wangjo Sillok is the Sungjongwon Ilgi (“Daily Records of the Office of the Royal Secretaries”). It is regrettable that mainly as a result of literary losses which occurred during the Japanese invasion of Korea in AD 1592, this work – which originally commenced in AD 1392 – now only extends from AD 1623 to 1894. There appear to be no reports of potential supernovae in this extensive compilation. An additional (secondary) source for Korean history is the Chungbo Munhon Bigo (“Revised Encyclopedia”); although published as late as 1907, this is a revision of a work produced in AD 1770. The Chungbo Munhon Bigo should be used with caution; it is by no means complete and contains several serious errors. For instance, in this work guest stars were said to occur in the years corresponding to AD 1600 and 1664. However, both reports actually relate to the supernova of AD 1604, as is clear from comparison with the detailed accounts in the Choson Wangjo Sillok. Only a very brief report of the brilliant supernova of AD 1572 is preserved in the Choson Wangjo Sillok. This gives the date of first sighting but the period of visibility is not specified. The record merely asserts that “a guest star appeared beside Cexing (D  Cas); it was as bright as Venus.” Not until as late as AD 1592 do we find Korean records which indicate that any temporary star remained fixed for an appreciable length of time. In that year the Choson Wangjo Sillok relates that as many as four guest stars were observed over intervals from several weeks to several months. By far the most interesting and important accounts of a new star in Korean history relate to the supernova of AD 1604. Although the celestial position of this object is only estimated to the nearest degree in the Sillok – in comparison with the accurate measurements by European observers such as Kepler and Fabricius – the light variation is reported in detail over several months, using comparisons with nearby stars and planets (as independently undertaken in Europe). There is no other comparable example throughout East Asian history. By combining European and Korean brightness estimates, it is possible to construct a well-defined light curve for the star, the regular pattern of which is characteristic of a supernova, although whether of type I or type II is uncertain.

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Japan

As in the case of Korea, Japanese astronomy (including terminology) and astrography are of Chinese origin. The Chinese lunisolar calendar was adopted in Japan at an early period, but with years expressed in terms of the reigns of Japanese emperors. The earliest reliable Japanese astronomical records – few in number – date from the seventh century AD. They are to be found in the Nihon Shoki (“Chronicles of Japan”), which covers the period from earliest (mythical) times to AD 697. The text of the Nihon Shoki, which was composed in AD 720, is in Classical Chinese, as is true of most later Japanese histories. In general, Japanese historical sources tend to be more diverse than their Chinese or Korean counterparts. The most extensive history is the Dainihonshi (“History of Great Japan”), which was compiled as late as AD 1715. However, privately compiled histories, diaries, and temple records also provide valuable sources of astronomical records. In particular, the diary of the poetcourtier Fujiwara Sadaie (who lived between AD 1163 and 1241) is a major source of Japanese observations of supernovae. This important work is entitled Meigetsuki (“Diary of the Full Moon”). In AD 1230, following the appearance of a “guest star” (which, as reports of the event in Chinese histories demonstrate, was actually a comet), Fujiwara began making a list of temporary stars recorded in previous Japanese sources. In all, he assembled records of eight new stars, ranging in date from AD 642 to 1181. All of these objects are found in his diary entry for a single day (corresponding to AD 1230 Dec 13). What is especially notable is that three of these stars prove to be supernovae: those appearing in AD 1006, 1054, and 1181. What is also remarkable is that the records of these three supernovae in the Meigetsuki contain more positional details than any other Japanese source. An extensive secondary compilation of Japanese astronomical records down to AD 1600 was composed by Kanda Shigeru (1935). Based on Kanda’s work and that of Ohsaki Shyoji (1994), which continues from AD 1600 to AD 1868 (the beginning of the Meiji era), it is apparent that there are no known Japanese reports of either the supernovae of AD 1572 or 1604. Nevertheless, Japanese accounts of the supernovae of AD 1006, 1054, and 1181 – each described as “guest stars” – provide a valuable supplement to the data in Chinese history.

3.5

Arab World

Few Arab records of celestial phenomena are preserved prior to AD 800, partly because the study of astronomy was opposed following directives in the Qu’ran. This situation was only relaxed toward the end of the eighth century AD, when ancient Greek works on astronomy began to be purchased from the Byzantine empire and translated into Arabic. Several important Arab astronomical treatises – such as those by ibn Yunus (d. AD 1009), al-Battani (AD 850–929), and alBiruni (AD 973–1048) – are preserved. However, the main concerns of these works are eclipses and other cyclic phenomena: both observations and predictions.

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Little interest in sporadic phenomena was shown by Arab astronomers, probably because of the restrictive views of Aristotle, who believed that the celestial vault was immutable (see Sect. 3.6). Hence for Arab reports of temporary stars it is necessary to rely on works other than astronomical treatises, such as chronicles. The Muslim calendar numbers years from al-Hijrah, the migration of the Prophet Muhammad from Mecca to Medina in AD 622. Each year contains of 12 lunar months – a total of about 354 days. As there are no intercalary months, the start of the year regresses through the seasons every 33 years or so. Tables for to conversion of dates to the Western calendar have been published by Freeman-Grenville (1995). Arab chronicles mainly cover the period from AD 800 to 1500. Unfortunately, relatively few chronicles have so far been published; many are still only available in manuscript form. Although several medieval Arab reports of comets are preserved, accounts of stellar events are rare and relate mainly to the brilliant supernova which appeared in AD 1006 (D AH 396). The research of Goldstein (1965) was especially productive in uncovering Arab observations of this supernova and at least five independent Arab accounts of the star are known; four of them in chronicles. The most detailed of these records – from Egypt – gives careful measurements of its position as well as emphasizing its extreme brilliance. Its author, ibn Ridwan, who was a physician, described the star in his commentary on Ptolemy’s treatise on astrology – the Tetrabiblos. Ibn Ridwan termed the star as a “spectacle” (athar or nayzak), comparing its light with that of the Moon. He also carefully described its location. The only other known Arab report of a supernova is a brief reference to the supernova of AD 1054 by Ibn Butlan, a Christian physician living in Constantinople. This tells us very little except that the star appeared in the zodiacal sign of Gemini.

3.6

Ancient Europe

Various ancient Greek and Latin texts (which mainly cover the period from about 700 BC to AD 500) cite several references to temporary stars. It is clear from the descriptions that most of these objects were probably comets (cf. Kronk 2000). Aristotle, in his Meteorology, considered the nature of comets in some detail, concluding that they were merely phenomena occurring in the terrestrial atmosphere. He was also of the opinion that physical change could only take place in the sub-lunar zone; in his view the region beyond the Moon was changeless. These notions were to influence Arab and late medieval European ideas regarding comets and presumably stellar outbursts. The Mathematike Syntaxis (later known as the Almagest), composed by Claudius Ptolemy around AD 150, makes no mention of temporary stars. However, this work is a textbook on mathematical astronomy and is not concerned with sightings of sporadic phenomena. Possibly the only ancient European mention of a new star which might have been of stellar nature is that mentioned by Pliny is his Historia Naturalis. Pliny asserted that the appearance of

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a “new star” inspired Hipparchus of Rhodes in 129 BC to compile his great star catalogue. However, no details of the position of the new star are given by Pliny. Hence we can only speculate on its nature.

3.7

Medieval Europe

After the close of the Classical Age (ca. AD 500), there were scarcely any astronomers of note in Europe for fully 1,000 years: until as late as AD 1450. Astronomical records are rare in medieval European literature until around AD 800. However, the subsequent growth of monastic and town annals throughout much of Europe was to have a remarkable outcome. Although most chroniclers had little interest in astronomy, they often set on record their impressions of spectacular celestial events. Unlike so many other parts of the world, astrology was not a significant factor in this process. Chronicles prove to be the main source of medieval European reports of astronomical phenomena. Celestial events which were noted include large solar eclipses, lunar eclipses, comets, meteors, and auroral displays, as well as occasional sightings of “new stars.” Vast numbers of chronicles are preserved today, often still only in manuscript form. Fortunately, numerous chronicles have been published in their original language (mainly Latin) in extensive compilations such as Scriptores Rerum Italicarum and Monumenta Germaniae Historica. These publications are available in major libraries. Accounts of celestial phenomena in medieval European annals tend to be qualitative, but often descriptions are in vivid detail. In particular, accounts of total solar eclipses have yielded important information on long-term variations in the length of the day (cf. Stephenson 1997). The brilliant supernova of AD 1006, which appeared in the southern constellation of Lupus, attracted some attention in Europe (notably in the monastery of St. Gallen in Switzerland). However, this event was exceptional. Apart from a brief Arabic reference in a Constantinople source (see Sect. 3.5), there are no known European accounts of the supernova of AD 1054. Although this star was well placed for northern observers, it was no brighter than the planet Venus. It does seem that potential medieval European observers – like so many nonastronomers in our modern world today – simply were unable to recognize a new star. For instance, chroniclers occasionally record conjunctions of the Moon with unidentified bright stars on specific dates. Retrospective computations demonstrate that in each case the “star” was indeed a planet: especially Venus (Stephenson and Green 2002). It should be emphasized that the apparent negligence in recording the supernova of AD 1054 was not – as might be supposed – due to uncritical acceptance of the Aristotelian concept of an unchanging celestial vault. The works of Aristotle were largely unknown in medieval (Latin) Europe until well after AD 1100 – following the capture of Toledo, a major Muslim centre of learning, by Christians in AD 1085. This event gradually led to widespread studies of the ancient Greek

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texts, copies of which had been carefully preserved by the Arabs. Unfortunately, no further potential accounts of supernovae (including that of AD 1181) are to be found in European history until the Renaissance.

3.8

European Renaissance

Not until around AD 1450 did European astronomers commence making regular celestial observations. Active observers at this period included both Johannes Muller (Regiomontanus) and Bernard Walther at Munich and Paolo de Pozzo Toscanelli at Florence. Toscanelli is especially noted for making the first careful European observations of Halley’s Comet in AD 1456. However, not until more than a century afterward did European astronomers witness a stellar outburst: the supernova of AD 1572. Whereas the locations of the supernovae of AD 1006, 1054, and 1181 had only been estimated to the nearest degree or so, the vast improvement in instrument design which had been achieved by the late sixteenth century enabled the position of the star of AD 1572 to be determined with remarkable precision. Both Tycho Brahe (observing from his uncle’s home in Scania – a Danish province in what is now Southern Sweden) and Thomas Digges (in Cambridge) measured the position of the new star to the nearest arcmin or so. Tycho also systematically compared the changing brightness of the supernova with both Venus and Jupiter as well as with several stars. Using these various estimates, it is possible to delineate a useful light curve of the star. This shows a smooth decline in brightness over the 18 months or so of observation. In its general form, this light curve is characteristic of a supernova, although it is not possible to determine the type of supernova from Tycho’s observations. Regrettably, the various observations of earlier supernovae – such as those occurring in AD 1006, 1054, and 1181 – give little information on the changes in brightness of these stars. Only about three decades were to elapse before the next supernova was sighted: in AD 1604. Two years before that date, Tycho had died, but now his former student at Prague, Johannes Kepler, emulated Tycho’s observations of the previous event. Kepler (and also David Fabricius, at Osteel) measured the position of the supernova of AD 1604, which appeared in Ophiuchus, to the nearest arcmin. Kepler systematically compared the changing brightness of the new star with a variety of planets and stars (see also Section 3.3).

3.9

Other Sources

Other possible supernova sightings have been proposed – e.g., by native Americans. Several cave paintings/petroglyphs in the southwest of the USA depict a crescent near a star symbol. It has been suggested (cf. Brandt and Williamson 1979) that these might possibly represent a conjunction between the Moon and the supernova of AD 1054 – which produced the Crab nebula supernova remnant – on July 5, the day after the discovery in China. However, the date of the paintings/petroglyphs can

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only be roughly determined from historical considerations – to between the tenth and twelfth centuries. Quite possibly the artifacts might represent a conjunction of the Moon with the planet Venus instead. By contrast, it is indeed fortunate that so many detailed observations of supernovae are preserved from East Asia, the Arab regions, and Europe.

4

Conclusions

Studies of historical records have brought to light many important early records of supernovae. As a result of these researches, it has been possible to confidently recognize observations of five supernovae (occurring in AD 1006, 1054, 1181, 1572, and 1604), leading to the identification of their remnants. As a result, we know the exact length of time over which these remnants have been expanding, thus providing helpful information in modeling the supernova process. Three other new stars (seen in AD 185, 386, and 393) may well have been supernovae, but the brief records which survive are not adequate to identify the present remnants with certainty. With regard to future developments, it seems that further progress in discovering additional East Asian observations of supernovae is unlikely. The various sources have been thoroughly searched. However, it seems possible that further investigation of medieval Arab and European sources – especially unpublished manuscripts – might be fruitful. However, this would probably require a vast amount of work with little definite prospect of progress.

5

Cross-References

 Historical Supernovae in the Galaxy from AD 1006  Possible and Suggested Historical Supernovae in the Galaxy  Supernova 1604, Kepler’s Supernova, and its Remnant  Supernova of 1006 (G327.6C14.6)  Supernova of 1054 and its Remnant, the Crab Nebula  Supernova of 1572, Tycho’s Supernova  Supernova of AD 1181 and its Remnant: 3C 58  Supernova Remnant Cassiopeia A

References Beijing Observatory (1988) Zhongguo Gudai Tianxiang Jilu Zongji (A Union Table of Ancient Chinese Records of Celestial Phenomena). Kexue Jishi Chubanshe, Kiangxu Brandt JC, Williamson RA (1979) The 1054 supernova and native American rock art. J Hist Astron Archaeoastron Suppl 10:S1–S38 Hsueh Chung-san, Ou-yang I (1956) A Sino-Western calender for two thousand years AD 1–2000. Peking

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Freeman-Grenville GSP (1995) The Islamic and Christian calendars, AD 622–2222 (AH 1–1650). Garnet, Reading Goldstein BR (1965) Evidence for a supernova of A.D. 1006. Astron J 70:105–114 Kronk GW (2000) Cometography. A catalogue of comets, vol 1, Ancient–1799. Cambridge University Press Sachs AJ, Hunger H (1988) Astronomical diaries and related texts from Babylonia, vol I. Austrian Academy of Sciences Press, Vienna Kanda Shigeru (1935) Nihon Temmon Shiryo (Japanese Historical Astronomical Data). Koseisha, Tokyo Ohsaki Shyoji (1994) Kinsei Nihon Temmon Shiryo (Pre-modern Japanese historical astronomical data). Hara Shobo, Tokyo Stephenson FR (1994) Chinese and Korean star maps and catalogs. In: Harley JB, Woodward D (eds) A history of cartography, vol II, part 2. University of Chicago Press, pp 511–578 Stephenson FR (1997) Historical eclipses and Earth’s rotation. Cambridge University Press Stephenson FR (2013) Astronomical records in the Samguk Sagi during the Three Kingdoms Period: Earliest Times to A.D. 668. Korean Stud 37:174–224 Stephenson FR, Green DA (2002) Historical supernovae and their remnants. Oxford University Press Stephenson FR, Green DA (2005) A reappraisal of some proposed historical supernovae. J Hist Astron 36:217–229 Stephenson FR, Green DA (2009) A catalogue of ‘Guest Stars’ recorded in East Asian history from earliest times to A.D. 1600. J Hist Astron 40:31–54 Stephenson FR, Yau KKC, Hunger H (1985) Records of Halley’s comet on Babylonian tablets. Nature 314:587–592

5

Supernova of 1006 (G327.6C14.6) Satoru Katsuda

Abstract

SN 1006 (G327:6 C 14:6) was the brightest supernova (SN) witnessed in human history. As of 1000 years later, it stands out as an ideal laboratory to study Type Ia SNe and shocks in supernova remnants (SNRs). The present state of knowledge about SN 1006 is reviewed in this article. No star consistent with a surviving companion expected in the traditional single-degenerate scenario has been found, which favors a double-degenerate scenario for the progenitor of SN 1006. Both unshocked and shocked SN ejecta have been probed through absorption lines in ultraviolet spectra of a few background sources and thermal X-ray emission, respectively. The absorption studies suggest that the amount of iron is 0:35, (following the notation of Silverman et al. 2012; Fig. 1). They also show prominent S II absorption lines that are not seen in other SN classes (Fig. 2). The common Type Ia SN 1991bg-like subclass shares these spectral charateristics. There is strong evidence (Table 1) that both normal and SN 1991bg-like SNe Ia result from white dwarf explosions.

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×10-12 SN 2011fe,peak -2.9d SN 1991T, peak +7 SN 1991bg, peak

Si II S II

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0 4000

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Fig. 2 A spectrum of SN 2011fe (top), a normal Type Ia supernova, obtained 2.9 days prior to peak B-band magnitude. This Hubble Space Telescope spectrum from Mazzali et al. (2014) extends further into both the UV and the IR than shown and is not compromised by telluric absorption correction residuals. The spectrum is dominated by absorption lines from intermediatemass elements; major features are marked. Additional absorption features are due to iron-group elements; for additional details see Mazzali et al. (2014). Events belonging to the SN 1991T-like subclass have similar spectra to normal events after peak (middle spectrum from Filippenko et al. 1992a) but show very distinctive features earlier (Fig. 3). Members of the SN 1991bg-like class (bottom spectrum from Filippenko et al. 1992b) are also quite similar but show a distinctive broad absorption trough (due to blends of Fe-group elements, e.g., Mazzali et al. 1997) spanning 4000– 4500 Å at peak

SNe Ib are defined by displaying prominent He I 5876Å 6678Å 7065Å absorption lines in near-peak spectra (Fig. 6), as well as a relatively shallow OI 7774Å line (Fig. 1; see e.g., Liu et al. 2016; Matheson et al. 2001). These events also show an absorption line near 6150Å whose nature is debated. Following Parrent et al. (2016) and Liu et al. (2016), it seems like the evidence prefers associating this line with hydrogen H˛ over Si II (contrary to, e.g., Filippenko 1997). There is strong evidence (Table 1) connecting this class with massive star progenitors, which seem to have all retained only a very small (but nonzero) fraction of their original hydrogen envelope. Normal SNe Ic are overall similar to SNe Ib (Fig. 6) but (by definition) do not show the three characteristic He I features near peak. However, they often do show a prominent 6150Å feature that we associate with Si II (rather than with

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Fig. 3 Early spectra of SNe Ia. The normal SN 2011fe was discovered very shortly after explosion; a spectrum at 16d prior to peak from Nugent et al. (2011; top) is shown. Spectra of SN 1991T prior to peak (a spectrum at 10d from Filippenko et al. 1992a is shown) lack strong Si II features due to its high photospheric temperature; instead, prominent Fe III lines are seen. The earliest spectrum of SN 2002cx (at 4d, from Li et al. 2003) has similar Fe III features but at much lower velocities. An early spectrum of the “Super-Chandra” event SN 2009dc (9.4d, from Taubenberger et al. 2011) shows weak and low-velocity Si II and prominent CII

hydrogen, but see below), as well as a strong OI 7774Å . As shown in Fig. 1, the location of these events in the line depth ratio diagram allows one to differentiate SNe Ic from both SNe Ia (a(6150)120

plateau photosphere (in ejecta)

R ~ 100 AU

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After plateau/Late CSM interaction

forward shock sources of late-time H-alpha

R ~ 1000 AU R ~ 200 AU

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Fig. 2 Sketch of the more complicated interaction when the CSM is highly asymmetric; in this example a disklike distribution surrounds the progenitor. (a) The initial pre-explosion state is a progenitor with a wind, as well as a dense disk at radii of 10 AU. (b) Immediately after explosion, narrow lines may arise either from a photoionized dense wind or from the disk. Strong CSM interaction with the disk occurs immediately and enhances the early luminosity, but the emergent spectrum may be dominated by narrow lines with Lorentzian wings. (c) CSM interaction with the disk has slowed the forward shock in the equatorial plane, but the SN ejecta expand relatively unimpeded in the less dense polar regions. After a few days, the normal SN ejecta photosphere may expand so much that it completely envelopes the CSM interaction occurring in the disk. The enveloped CSM interaction can now heat the optically thick ejecta from the inside and contribute significantly to the total visible luminosity, even if no narrow lines are seen, and may cause the photosphere to be asymmetric. (d) At late times, the SN ejecta photosphere recedes. At this time, the CSM interaction in the disk is exposed again (now with larger radial velocities because it has been accelerated), and intermediate-width and possibly doubled-peaked lines may be seen from the ongoing interaction. This sketch was originally invoked to explain the observed evolution of PTF11iqb (Smith et al. 2015)

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thick SN ejecta can completely envelope the equatorial CSM interaction, hiding some or all of the narrow and intermediate-width lines that arise due to CSM interaction. The extra radiated energy generated by the equatorial CSM interaction is now unable to escape freely because it has been swallowed by the opaque fast ejecta, and this radiative energy is instead deposited in the interior of the optically thick SN ejecta and must diffuse out. It will therefore add extra heat to the outer envelope, perhaps mimicking extra deposition of radioactive decay energy. The asymmetric injection of heat in this way will likely make the photosphere asymmetric. Viewed from the outside at a time of roughly a month after explosion, one might then observe a broad-lined SN photosphere with enhanced luminosity and perhaps a longer than normal duration, unusual line profiles, or significant polarization. At this stage, it would be difficult to tell the difference between some small extra amount of radioactive heating or buried CSM interaction. All hope is not lost, though, because an observer might then be able to deduce that CSM interaction was contributing to the main light curve all along by watching until late times. After the SN recombination photosphere recedes, the enveloped CSM interaction region is exposed once again. When this happens, the dense CSM disk that has been swept up into a cold dense shell (or cold dense torus) and accelerated to a few thousand km s1 may now be seen again via strong intermediate-width line emission. Prominent examples of this are SN 1998S, PTF 11iqb, SN 2009ip, and even the SN IIb 1993J (Leonard et al. 2000; Matheson et al. 2000; Mauerhan et al. 2014; Pozzo et al. 2004; Smith et al. 2014, 2015). This line emission can be much stronger than the nebular emission from the optically thin inner ejecta heated by the dwindling radioactive decay. Moreover, the ongoing CSM interaction can emit strong X-rays that propagate back into the SN ejecta, potentially changing the emergent nebular spectrum. Perhaps the most important thing to realize is that we now have two different physical explanations for the wide diversity in peak luminosity of SNe IIn, even if all explosions have the same 1051 ergs of kinetic energy. The range of luminosity from the strongest CSM interaction in superluminous SNe down to cases with minimal extra luminosity provided by CSM interaction can be explained either by ramping down the density of the progenitor’s wind or by increasing the degree of asymmetry in dense CSM. The strongest clues that significant CSM asymmetry is present are from (1) spectropolarimetry (e.g., Mauerhan et al. 2014), (2) asymmetric line profile shapes (although some asymmetry can also be caused by dust or occultation by the SN photosphere itself), or (3) the time evolution of velocities (e.g., seeing very fast speeds in the SN ejecta that persist after the strongest CSM interaction has subsided; Smith et al. 2014). The last point confirms unequivocally that not all the fast SN ejecta participated in the CSM interaction. There may also be some special observed signatures of asymmetry at certain viewing angles (e.g., edge-on) and specific times. If one does recognize such signatures of asymmetry, one must realize that the progenitor mass-loss rate inferred from equation (2) as well as the SN explosion energy are not just lower limits, but likely underestimates by a factor of 10. Of course, one can also invoke differences in explosion energy, explosion mechanism, SN ejecta mass, and radioactive yield to also contribute to the observed diversity.

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413

Observed Subtypes

The main physical parameters that determine the observed properties of a typical core-collapse SN are the mass of ejecta, kinetic energy of the explosion (as well as the mass of synthesized radioactive material), and the composition and structure of the star’s envelope at the time of explosion. This leads to the wide diversity in observed types of normal ejecta-dominated core-collapse SNe and thermonuclear SNe (II-P, II-L, IIb, Ib, Ic, Ia). For interacting SNe, we have all these same free parameters of the underlying explosion—as well as the possibility of SNe with low or no radioactive yield and a wider potential range of explosion energy—but to these, we must also add the variable parameters associated with the CSM into which the SN ejecta crash: CSM mass and/or mass-loss rate, radial distribution (speed and ejection time before explosion), CSM composition, and CSM geometry. Given these parameters, it may not be surprising that the class of interacting SNe is extremely diverse and observations are continually uncovering new or apparently unique characteristics. Moreover, a SN can change type depending on when it is seen. An object that looks like a SN IIn in the first few days can morph into a normal SN II-L or SN IIb if it undergoes enveloped/asymmetric CSM interaction and may then return to being a Type IIn at late times, as discussed in the previous section. There are, however, some emerging trends among interacting SNe. The list below attempts to capture some of these emerging subtypes among interacting SNe that appear to share some common and distinct traits. The reader should be advised, however, that this is still a rapidly developing field, so this is neither a definitive nor a complete list, and moreover, there are observed events that seem to skirt boundaries or overlap fully between different subtypes. Further subdivisions are likely to be clarified with time. The list below includes a descriptive name and some prototypical or representative observed examples that are often mentioned (again, not a complete list). Superluminous IIn; compact shell (SN 2006gy). SN 2006gy was the first superluminous SN to be discovered, and it remains extremely unusual even though several other SLSNe IIn have since been found (see Ofek et al. 2007; Smith et al. 2007, 2010a; Woosley et al. 2007). It had a slow rise to peak (70 days) and faded within another 150 days or so, which is unlike the other SLSNe IIn that seem to fade very slowly and steadily from peak. Also unusual was that it had strong intermediatewidth P Cygni absorption features in its spectra, strong line-blanketing absorption in the blue, and narrow P Cygni features from the CSM. It is thought to have arisen from a relatively compact and opaque CSM shell, where CSM interaction mostly subsided within a year. In this case, the CSM is thought to have arisen from a single eruption that ejected 20 Mˇ about 8 years prior to core-collapse (Smith et al. 2010a). SN 2006gy is one of the best observed SNe IIn and is often discussed, but readers should be aware that it is not at all typical.

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Superluminous IIn; extended shell (SN 2006tf, SN 2010jl, SN 2003ma). These are basically the superluminous version of the SN 1988Z-like subclass, discussed next. Unlike SN 2006gy, they show strong, smooth blue continua without much line blanketing and little or no P Cygni absorption in their intermediate-width lines. They also tend to fade slowly and steadily, in some cases remaining bright for several years as the shock runs through an extended dense shell (e.g., Fransson et al. 2014; Rest et al. 2011; Smith et al. 2008a). Enduring IIn (SN 1988Z, SN 2005ip). These SNe IIn show a smooth blue continuum superposed with strong narrow and intermediate-width H lines and in some cases even broad components (Aretxaga et al. 1999; Chugai and Danziger 1994; Smith et al. 2009). Some cases, such as SN 2005ip, have strong narrow coronal emission lines (Smith et al. 2009), implying photoionization of dense clumpy CSM by X-rays generated in the shock. They tend to be more luminous than SNe II-P, but not as bright as SLSNe. These objects tend to fade very slowly and show signs of strong CSM interaction for years or even decades after discovery; SN 1988Z is still going strong. One can picture these as a stretched-out version of the SLSNe IIn, in the sense that they have somewhat lower luminosities at peak, but they last longer, eventually sweeping through similar amounts of total CSM mass (of order several to 20 Mˇ ). While SLSNe have CSM that is so dense that it requires eruptive LBV-like mass loss in the years or decades before explosion, these enduring SNe IIn like SN 1988Z and SN 2005ip can potentially be explained by extreme RSG winds blowing for centuries before core-collapse. If there is such a thing as a “standard” SN IIn, this is probably what most IIn enthusiasts have in mind. Transitional IIn (SN 1998S, PTF11iqb, SN 2013cu). This class of SNe IIn only shows fleeting signatures of CSM interaction that disappear quickly and may be entirely missed if the SN is not discovered early after explosion. SN 1998S was one of the nearest and best studied SNe IIn that helped shape our understanding of SNe IIn, and so it has often been referred to as “prototypical”—but it really is not. SN 1998S was not very luminous, and its spectral signatures of CSM interaction disappeared pretty quickly, transitioning into a broad-lined ejectadominated photosphere within a couple weeks (Leonard et al. 2000; Shivvers et al. 2015). This indicated that the total mass of CSM was actually quite modest (of order 0.1 Mˇ or so), substantially different from the types noted above. If it had not been caught so early, SN 1998S might not have been classified as a Type IIn at all. An older example of this was SN 1983K (Niemela et al. 1985). More recently, a few other related objects have been found (SN 2013cu & PTF11iqb; Gal-Yam et al. 2014; Smith et al. 2015), which only showed a Type IIn spectrum for the first few days after discovery (and these cases were thought to have been discovered very early, within 1 day or so of explosion). PTF11iqb and SN 2013cu then morphed into broad-lined SNe with spectra similar to SNe II-L or SNe IIb, respectively. At late times, PTF11iqb showed strong CSM interaction again, very similar to SN 1998S and the Type IIb SN 1993J. We do not know how common these are. While SNe IIn

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represent roughly 8–9 % of core-collapse SNe (Smith et al. 2011a), this statistic does not include SNe that only exhibit Type IIn characteristics for a brief window of time and then morph into other types after a few days; thus, early strong CSM interaction with dense inner winds might be fairly common among the larger population of ccSNe. The corresponding (potentially very important) implication is that many core-collapse SNe may suffer a brief pulse of episodic mass loss shortly before core-collapse. The reason for this is not yet known but is probably related to the final nuclear burning stages and may have important implications for models of core-collapse. Late-time interaction in otherwise normal SNe (SN 1993J, SN 1986J). The overlap with the previous subclass is probably considerable, but it is worth mentioning that some otherwise normal SNe (perhaps appearing normal simply because we missed the early IIn signatures in the first day or so) show particularly strong CSM interaction at late times. Some of the more common cases are SNe IIb and SNe II-L, for which there are well-studied and famous nearby examples like SN 1993J and SN 1986J (Matheson et al. 2000; Milisavljevic and Fesen 2013). For these, the transition from a SN into a SN remnant is somewhat blurry, and some of these are well-known nearby aging SNe. Because this interaction is most apparent when the SNe have faded after the first year, this phenomenon can only be studied in nearby galaxies. These may be caused by strong RSG winds or by equatorial CSM deposited by binary interaction in objects like SNe IIb that are more clearly associated with the end products of binary evolution. The reason why this CSM still resides close to the star at the time of death is still unclear and (as for the previous subclass) may hint at some rapid and dramatic changes in the final nuclear burning sequences in a wider fraction of SN progenitors than just standard SNe IIn. Delayed onset, slow rise, multi-peaked (SN 2009ip, SN 2010mc, SN 2008iy, SN 1961V, SN 2014C). In contrast to the previous subclass, some SNe IIn show little or no signs of CSM interaction at first but then rise to the peak of CSM interaction after a delay of months or years. This delay is presumably due to the time it takes for the fastest SN ejecta to catch up to a CSM shell that was ejected a year or more before core-collapse. The underlying SN ejecta photosphere could be relatively faint at first if the progenitor was a more compact BSG, like SN 1987A, or an LBV; the faintness of the initial SN might cause the initial transient to be missed altogether or mistaken as a pre-SN eruption rather than the actual SN, since it might precede the delayed onset of peak luminosity that actually arises when the ejecta overtake the CSM. It must be admitted, however, that from the time of peak onward, these tend to appear as relatively normal SNe IIn; as such, the distinction between this “delayed onset” subclass and other SNe IIn might be artificial and only distinguishable in cases with fortuitous prediscovery or pre-peak data. The amount of delay in the onset of CSM interaction bears important physical information about the elapsed time between the pre-SN eruption and core-collapse. In the case of SN 2009ip, the delay of 40 days made sense, as fast SN ejecta caught up to CSM moving at 10 % the speed, associated with eruptions that were actually observed a

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year or so before the SN (Mauerhan et al. 2013a, 2014; Smith et al. 2014). SN 1961V had a light curve consistent with a normal SN II-P for the first 100 days, followed by a brighter peak (Smith et al. 2011b). In SN 2014C, the delayed onset had different chemical properties, where a H-poor stripped-envelope SN crashed into a H-rich shell after a year (Milisavljevic et al. 2015). In some cases, however, the delayed onset is rather extreme and the CSM interaction strong; SN 2008iy appeared to be a relatively normal core-collapse SN in terms of luminosity, which rose to very luminous peak as a Type IIn after 400 days (Miller et al. 2010). SN 1987A might be thought of as an even more extended version of this, where the onset of CSM interaction was delayed for 10 years as the SN ejecta caught up to CSM ejected 104 yr earlier. We do not know what fraction of normal SNe have a delayed onset of CSM interaction, since most SNe are not monitored continuously with large telescopes for years or decades after they fade. Type IIn-P (SN 1994W, SN 2011ht, the Crab). This is a distinct subclass of SNe IIn that exhibit IIn spectra throughout their evolution but have light curves with a well-defined plateau drop (Mauerhan et al. 2013b). They are not to be confused with “transitional” SNe IIn/II-P that may have narrow lines at early times and evolve into an otherwise normal SN II-P. In SNe IIn-P, the narrow H lines with strong narrow P Cygni profiles are seen for the duration of their bright phase. The drop from the plateau is quite extreme (several magnitudes), and the latetime luminosities suggest low yields of 56 Ni. These may be the result of 1050 erg electron capture SN explosions with strong CSM interaction (Mauerhan et al. 2013b; Smith 2013). It has been proposed that the Crab Nebula may be the remnant of this type of event, although this remains uncertain (Smith 2013). SN IIn impostors (LBVs, SN 2008S-like, etc.). These transients have narrow H lines in their spectra similar to SNe IIn but are subluminous (fainter than MR ' 15.5 mag) and have slower velocities than normal SNe IIn (see Smith et al. 2011b and references therein). One may argue that the luminosity cut is arbitrary, but the narrow lines without any broad wings do seem distinct from other SNe IIn (most of the time). Some are certainly nonterminal transients akin to LBVs (because they repeat or the star survives), but some cases are not so clear. Although they may not be SNe, they are included here because we are not sure yet—some objects thrown into this bin could be underluminous because they are interacting transients that arise from “failed” SNe (fallback to a black hole), pulsational pair instability SNe, ecSNe, SNe from compact BSG progenitors with low radioactive yield, mergers with compact object companions, or other terminal events. Type Ia/Type IIn or Ia-CSM (SN 2002ic, SN 2005gj, PTF11kx). These are transients that show spectral features indicative of an underlying SN Ia ejecta photosphere, but with strong superposed narrow H lines and additional continuum luminosity (Silverman et al. 2013). Cases with stronger CSM interaction tend to obscure the Type Ia signatures, leading to ongoing controversy about their potential core-collapse or thermonuclear nature (Benetti et al. 2006). Cases with weaker

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CSM interaction (PTF11kx) reveal the Type Ia signatures more clearly, allowing them to be identified unambiguously as thermonuclear events. The relatively rare evolutionary circumstance that leads a thermonuclear SN to have a large mass of H-rich CSM is still unclear. Type Ibn (SN 2006jc). These are similar to SNe IIn, except that H lines are weak or absent, so that narrow or intermediate-width He I lines dominate the spectrum (H˛ is weaker than He I 5876). Without the assistance of H opacity, these objects tend to fade more quickly than most SNe IIn. The class is quite diverse and includes a range of H line strengths and CSM speeds, including transitional IIn/Ibn cases (SN 2011hw) where H and He I lines have similar strength (Pastorello et al. 2008, 2015; Smith et al. 2012a). It has been hypothesized that the likely progenitors may be Wolf-Rayet stars or LBVs in transition to a WR-like state (Foley et al. 2007; Pastorello et al. 2007; Smith et al. 2012a). Type Icn (hypothetical). A discovery of this class has not yet been reported (as far as the author is aware), but as transient searches continue, there may be cases where a SN interacts with a dense shell of CSM that is both H and He depleted, yielding narrow or intermediate-width lines of CNO elements, for example. With sufficient creativity, one can imagine stellar evolution pathways that might create this; such SNe are clearly rare, and if they never turn up, their absence will provide interesting physical constraints for some binary models.

5

Dust Formation in CSM Interaction

The formation of dust by SNe may be essential to explain the amount of dust inferred in high-redshift galaxies. SNe with strong CSM interaction provide an avenue for dust formation that is different from normal SNe and possibly much more efficient. In normal SNe, dust forms in the freely expanding ejecta where there is a competition between cooling and low enough temperatures, while the ejecta are also rapidly expanding and achieving lower and lower densities. Even if dust forms efficiently, this ejecta dust might get destroyed when it crosses the reverse shock. In interacting SNe, by contrast, evidence suggests that dust can form very rapidly in the extremely dense, post-shock cooling layers (Zones 2 and 3 in Fig. 1). Moreover, this dust is already behind the shock and may therefore stand a better chance of surviving and contributing to the ISM dust budget. The first well-studied case of post-shock dust formation was in SN 2006jc, which was a Type Ibn. The classic signs of dust formation were seen starting at only 50 days post-discovery, in an increase in the rate of fading, excess IR emission, and an increasing blueshifted asymmetry in emission-line profiles (Smith et al. 2008b). The last point strongly favored post-shock dust formation, since this was seen in the intermediate-width lines that were emitted from the post-shock zones. The Type Ibn event may have been the result of a Type Ic explosion crashing into a He-rich shell. In this case, one might think that the C-rich ejecta were important in assisting the

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efficient formation of dust, as is seen for the post-shock dust formation in collidingwind WC+O binaries (Gehrz and Hackwell 1974; Williams et al. 1990). However, similar evidence for this same mode of post-shock dust formation has also been seen in several Type IIn events, such as SN 2005ip, SN 1998S, SN 2006tf, SN 2010jl, and others (Fox et al. 2009; Gall et al. 2014; Pozzo et al. 2004; Smith et al. 2008a, 2009, 2012b). It may therefore be the case that enhanced post-shock dust formation is a common outcome of strong CSM interaction, where efficient post-shock cooling causes the forward shock to collapse and become very dense.

6

Progenitors and Pre-SN Mass Loss

Basic considerations about powering SNe IIn with CSM interaction, noted above, argue that extremely strong pre-SN mass loss is required. What sorts of progenitor stars can give rise to this dense CSM?

6.1

CSM Properties

The first thing to do is to look around us in the nearby universe and ask what sort of observed classes of stars might fit the bill. Figure 3 makes this comparison by plotting the diversity in wind density of interacting SNe, deduced from the preshock wind (or shell) expansion speed and the inferred mass-loss rate, as compared to expected mass loss from known types of stars. The shaded and colored regions in this figure show rough parameters for different classes of evolved massive stars that are potential SN progenitors with strong winds. These are taken from the recent review by Smith (2014); see the caption for definitions. In this plot, a given wind density parameter (required for a particular value of a CSM interaction luminosity via Eq. 1) has a diagonal line increasing to the upper right. The solid line shows a typical value for a moderate-luminosity SN IIn, and the dashed line is a typical lower bound for wind densities required to make a SN IIn (although an object can be slightly below this line and still make a Type IIn spectrum if the wind is clumpy or asymmetric). We can see immediately that the normal classes of evolved stars with strong but relatively steady winds (WR stars, LBV winds, normal YSGs and RSGs, AGB stars; see caption to Fig. 3 for the key to the abbreviations) do not match up to the wind density required for SNe IIn. These could potentially produce SNe that have strong X-ray or radio emission from CSM interaction, but they are not dense enough to slow the forward shock and to cause the forward shock to cool radiatively and collapse into the cool dense shell that is required for intermediate-width H˛. The only observed classes of stars that have the high wind densities required are the giant eruptions of LBVs and the most extreme cool hypergiants (the slower winds of extreme RSGs and YHG make their winds have density comparable to the shells in LBV giant eruptions, even though the mass-loss rates are lower). Both classes of stars are not steady winds, but rather, they are dominated by relatively short-lived

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Fig. 3 Plot of mass-loss rate as a function of wind velocity, comparing values for interacting SNe to those of known types of stars. The solid-colored regions correspond to values for various types of evolved massive stars taken from the review about mass loss by Smith (2014), corresponding to AGB and super-AGB stars, red supergiants (RSGs) and extreme RSGS (eRSG), yellow supergiants (YSG), yellow hypergiants (YHG), LBV winds and LBV giant eruptions, binary Roche-lobe overflow (RLOF), luminous WN stars with hydrogen (WNH), and H-free WN and WC WolfRayet (WR) stars. A few individual stars with well-determined very high mass-loss rates are shown with circles (VY CMa, IRC+10420,  Car’s eruptions, and P Cyg’s eruption). Also shown with X’s are some representative examples of SNe IIn (and one SN Ibn) that have observational estimates of the pre-shock CSM speed from the narrow emission component as measured in moderately high-resolution spectra as well as estimates of the progenitor mass-loss required, taken from the literature. The diagonal lines are wind density parameters (w=MP =VCSM ) of 51016 and 51015 g cm1 , which are typically the lowest wind densities required to make a SN IIn. Values are taken from the literature; this figure is from a paper in prep. by the author. Note that in some cases, an observationally derived value for the mass of the CSM has been converted to a mass-loss rate with a rough estimate of the time elapsed since ejection

phases of eruptive or episodic mass loss or extremely dense and clumpy winds. In the case of LBVs, these are eruptions that last a few months to a decade. For extreme RSGs and YHGs, these are phases of enhanced mass loss that may persist for centuries to a few thousand years.

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From the point of view of their mass loss, LBVs (and to a lesser extent the most extreme cool hypergiants) are good candidates for the progenitors of SNe IIn. This does not, however, mean that these stars are necessarily all poised to explode in the next couple years, nor does it mean that they are the only possible IIn progenitors. The caveat is that the progenitors of SNe IIn undergo strong eruptive or episodic mass loss immediately before core-collapse and may therefore experience significant changes in their internal structure. The stars may have looked very different in the time period before their pre-SN eruptions began. Hence, these stars in their immediate pre-SN state may not actually exist among nearby populations of stars in the Milky Way and Magellanic Clouds right now. Also note that this is a mass-loss rate, not total mass, and note that these are usually lower limits to the required mass-loss rate (the high rate makes high optical depths and, hence, makes an observational determination difficult). In cases where we have estimates of the total mass ejected, one must divide by an assumed timescale to derive a mass-loss rate; for SNe IIn, this timescale is inferred from the relative velocities of the CSM and CDS. Since we are essentially plotting a wind density, it is important to recognize that two different SNe with the same inferred progenitor mass-loss rate might have had that high mass loss lasting for very different amounts of time and, hence, may have very different amounts of total mass ejected shortly before the SN. In some cases, the total mass can be more constrainting than the rate. For example, the total mass of 20 Mˇ required for some superluminous SNe IIn rules out any progenitor stars with initial masses below about 30–40 Mˇ , because we need a comparable mass of SN ejecta to provide enough momentum for a long-lasting interaction phase (not to mention mass loss due to winds throughout the life of the star). Also, there are cases like SN 2005ip where the inferred mass-loss rate is on the low end, but this SN had remarkably long-lasting CSM interaction that suggests a total mass of order 15 Mˇ of H-rich material (e.g., Smith et al. 2009; Stritzinger et al. 2012), which rules out lower-mass RSGs and super-AGB stars for its progenitor.

Warning 3. One must be somewhat cautious in drawing conclusions about the progenitor based on only the observed pre-shock CSM speed. We generally think of the outflow speed being proportional to the star’s escape velocity, so we expect slower outflows from RSGs and YHGs, somewhat faster speeds for LBVs and BSGs (few 102 km s1 ), and very fast outflows for WR stars (few 103 km s1 ). This is a good guide if the outflow is a relatively steady radiationdriven wind. However, remember that the observed CSM may be the result of eruptive or explosive mass loss driven by a shock wave. If so, it is possible to get a relatively fast outflow even from a bloated RSG; eruption speeds need not match steady wind speeds for various types of stars in Fig. 3. Moreover, the high luminosity of the SN itself can potentially accelerate the pre-shock CSM (essentially a radiatively driven wind from a temporarily much more (continued)

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luminous star), which could also lead to a faster pre-shock CSM speed than expected for a certain type of star, or multiple velocity components in the CSM.

6.2

Direct Detections

The types of inferences described above are all still based on rather indirect and circumstantial evidence. A potentially more direct way to link SNe to their progenitors is to detect the progenitor star in pre-explosion imaging data, usually with the Hubble Space Telescope, although ground-based imaging has been used for some very nearby cases (see review by Smartt 2009). This method has been used successfully for some other types of SNe, especially SNe II-P, SNe IIb, and one particularly famous II-pec event that occurred 20 years ago. The progenitor identification can be confirmed after the SN fades, to verify that the progenitor star is gone (as opposed to being a chance alignment, a host cluster, or a companion star). For interacting SNe, however, the interpretation of pre-SN direct detections can be a little tricky. First, the “direct” detection of the progenitor might actually be a direct detection of a pre-SN eruption and not the quiescent star. This source might indeed fade after the SN, but it is hard to tell if the star is really dead or if the eruption has just subsided and the star returned to its quiescent state. Inferring an initial mass by comparison with stellar evolution tracks is also complicated if the progenitor might be in an outburst rather than in its quiescent state (we do not have much choice here and are lucky if there is even one HST image in the archive, but one just needs to be aware of the caveat). A second complication is that some SNe IIn have persistent CSM interaction for years or decades after the SN, and so one might need to wait a very long time before the SN has faded enough to be fainter than the progenitor. Third, a faint progenitor or even a faint upper limit to a progenitor is very inconclusive in terms of its implication for the mass of the star. This is because with interacting SNe, there is, by definition, a large mass of CSM. Thus, we certainly expect some cases where the progenitor was surrounded by a massive dust shell that should obscure the progenitor star’s visible light output. This makes it difficult to place a progenitor detection (or upper limit) on an HR diagram and infer an initial mass if one has only an optical filter. Despite this ambiguity, there have been a few lucky and important cases that guide our intuition about the progenitors of SNe IIn and SNe Ibn. SN 2005gl: This was a SN IIn where a very luminous progenitor consistent with an LBV star like P Cygni was detected in HST imaging, and the SN had an implied mass-loss rate of 0.01 Mˇ yr1 (Gal-Yam et al. 2007), and this source then faded after the SN (Gal-Yam and Leonard 2009). Moreover, the pre-shock CSM speed of 420 km s1 inferred from narrow H lines was suggestive of the fast outflow from an

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LBV (Smith et al. 2010a). As noted above, there is some ambiguity as to whether the pre-SN detection was a massive quiescent LBV-like star or a pre-SN eruption caught by the HST image. In either case an eruptive LBV-like star is likely, although the implied initial mass may be different. Based on its spectral evolution, SN 2005gl fits into the subclass of “transitional” SNe IIn like SN 1998S and PTF11iqb, which show a Type IIn spectrum at first but later show broad P Cygni lines indicative of a SN photosphere, so this can be taken as an argument that it was most likely a core-collapse SN event. SN 1961V: Long considered an extreme LBV or SN impostor event, recent arguments favor an actual core-collapse SN for the 1961 transient (Kochanek et al. 2011; Smith et al. 2011a). If this was a SN, then it has one of the best documented progenitor detections and progenitor variability among SNe, and it holds the record for the most massive directly detected SN progenitor. The pre-1961 variability suggests a very massive 100 Mˇ blue LBV-like progenitor that was variable before the SN. The source at the SN position is now more than 5.5 mag fainter than this progenitor (a much more dramatic drop than in the case of SN 2005gl), and there is no IR source with a luminosity comparable to the progenitor (Kochanek et al. 2011), so the extremely massive star is likely dead. SN 2006jc: An eruption in 2004 was noted as a possible LBV or SN impostor, and then a SN occurred at the same position 2 years later. The pre-SN outburst had a peak luminosity similar to SN impostors (Pastorello et al. 2007). The SN explosion 2 years later was of Type Ibn with strong narrow He I emission lines (Foley et al. 2007; Pastorello et al. 2007). There is no detection of the quiescent progenitor, but this unusual case implies an LBV-like eruption that occurred in a WR-like progenitor star that was clearly H depleted. The CSM speed was of order 1000 km s1 , which is consistent with WR stars, and faster than typical LBVs. SN 2011ht: This belongs to the subclass of SNe IIn-P, which are thought to arise from lower-energy explosions that may be linked to electron capture SNe in 8–10 Mˇ super-AGB stars (Mauerhan et al. 2013b; Smith 2013). There is no detection of the quiescent progenitor, although deep upper limits seem to rule out a luminous, blue quiescent star (Mauerhan et al. 2013b; Roming et al. 2012). However, Fraser et al. (2013b) reported the detection of pre-SN eruption activity in archival data. This may be an important demonstration that non-LBVs can have violent pre-SN eruptions as well. SN 2010jl: This was a SLSN IIn with roughly 10 Mˇ or more of CSM. Smith et al. (2011c) identified a candidate source at the location of the SN in pre-explosion HST images that suggested either an extremely massive progenitor star or a very young massive-star cluster; in either case it seems likely that the progenitor had an initial mass above 30 Mˇ . We are still waiting for this SN to fade to see if the progenitor candidate was actually the progenitor or a massive young cluster/association. SN 2009ip: This source was initially discovered as an LBV-like outburst in 2009 (its namesake) before finally exploding as a much brighter SN in 2012. A quiescent progenitor star was detected in archival HST data, indicating a very massive 50–80 Mˇ progenitor (Foley et al. 2011; Smith et al. 2011b). In this case, the

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HST detection may well have been the quiescent progenitor, rather than an outburst, because much brighter outbursts came later. It showed slow variability consistent with an S Dor LBV-like episode (Smith et al. 2010b), followed by a series of brief LBV-like giant eruptions (Mauerhan et al. 2013a; Pastorello et al. 2013; Smith et al. 2010b). Unlike any other object, we also have detailed, high-quality spectra of the pre-SN eruptions (Foley et al. 2011; Smith et al. 2010b). The presumably final SN explosion of SN 2009ip in 2012 would fall into the “delayed onset” subclass, since at first the fainter transient showed very broad lines indicative of a SN photosphere. Reaching peak, however, it looked like a normal SN IIn, as the fast ejecta crashed into the slow material ejected 1–3 years earlier (Mauerhan et al. 2013a; Smith et al. 2014). A number of detailed studies of the bright 2012 transient have now been published, although there has been some controversy about whether the 2012 event was a core-collapse SN (Mauerhan et al. 2013a; Ofek et al. 2013; Prieto et al. 2013; Smith et al. 2014) or some type of extremely bright nonterminal event (Fraser et al. 2013a; Margutti et al. 2014; Pastorello et al. 2013). More recently, Smith et al. (2014) showed that the object continues to fade, and its late-time emission is consistent with late-time CSM interaction in normal SNe IIn. If SN 2009ip was indeed a SN, it provides a strong case that very massive stars above 30 Mˇ may in fact experience core-collapse and explode and that LBV-like stars are linked to some SNe IIn.

6.3

Links to Progenitor Types

We will undoubtedly find more examples of direct detections and pre-SN outbursts in the future. One must bear in mind, though, that LBVs and eruptive precursors are relatively easy to detect because they are brighter than any quiescent stars, so these cases do not rule out alternatives such as dust-enshrouded RSGs or faint and hot quiescent stars. From various clues described above such as the CSM mass and mass-loss rate, CSM expansion speed, H-rich composition, and direct detections of progenitors or environments, we can attempt to link certain subclasses of interacting SNe to different possible progenitors. Some associations are more likely than others. SLSN IIn (compact and extended shell; SN 2006gy or SN 2010jl-like): Based on the extreme required masses of (10–20 Mˇ ) of H-rich CSM, typically expanding at a few hundred km s1 , it seems very likely that the progenitors of SLSNe IIn are very massive, eruptive LBV-like stars (see review by Smith 2014). If they are not truly LBVs, then they do a very good impersonation. The simple fact that very massive stars above 40 Mˇ are exploding as H-rich SNe is a challenge to understand, since stellar evolution models predict all those stars to shed their H envelopes at roughly solar metallicity. Most of these have huge mass ejections occurring just a few years or decades before the SN, so the connection to nearby LBVs—some of which have shells that are hundreds or thousands of years old—is not yet clear. LBVlike progenitors are even likely in cases where the progenitor is optically faint, if a pre-SN eruption has obscured the star with a dust cocoon (as is likely to be the case, given the consequent CSM interaction). Since the progenitors must be very massive

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stars simply because of the mass budget, the physical mechanism of pulsational pair instability eruptions is a viable candidate for the pre-SN outbursts (Woosley et al. 2007). This is not the case for the remainder of SNe IIn, because they are too common (Smith et al. 2014). Normal, enduring SNe IIn (SN 1988Z-like): Likely progenitor types are LBVs or extreme cool hypergiants (YHGs/eRSGs), based mostly on the required massloss rates and observed CSM speeds. For these enduring cases, we require either strong mass loss in several centuries preceding the SN or a large bipolar shell ejected shortly before the SN with a range of ejection speeds (to accommodate CSM interaction over a large range of radii, lasting for a long time). Total CSM masses that exceed 10 Mˇ in some cases and integrated radiated energies that exceed 1051 ergs (over years) point to relatively massive progenitor stars. Enhanced late-phase RSG mass loss (Yoon and Cantiello 2010) or instabilities in late nuclear burning sequences (Quataert and Shiode 2012; Smith and Arnett 2014) are good candidates for the episodic mass loss. Transitional or fleeting SNe IIn (SN 1998S-like): Likely progenitors are RSGs, YHGs, or BSG/LBVs with less extreme pre-SN bursts of mass loss, confined to a relatively short-duration event preceding core-collapse (i.e., within a few years preceding the SN). These objects also seem to require highly asymmetric CSM interaction, to allow the expanding SN photosphere to completely or mostly envelope the disk of CSM interaction that emits narrow lines (as discussed in Sect. 3). For this reason, there is a strong suspicion that close binary interaction plays a role in their pre-SN episodic mass loss, although it must still be linked somehow to the final nuclear burning sequences (see Smith and Arnett 2014 regarding the role of close binaries in this scenario). SNe IIn-P (SN 2011ht-like): The favored scenario for these events involves an intermediate-mass progenitor in a super-AGB phase that suffers a sub-energetic (1050 erg) electron-capture SN. This is based on the low 56 Ni yield, the deep absorption features that imply more-or-less spherical symmetry, and the energy/mass budgets inferred (Mauerhan et al. 2013b; Smith 2013). However, observations cannot yet confidently rule out a more massive progenitor that suffers fallback to a black hole, yielding a smaller ejecta mass and very low 56 Ni yield (although in the case of SN 2011ht, progenitor upper limits seem to argue against this highermass interpretation). This type of SN also fits the bill for SN 1054 and the Crab Nebula (Smith 2013), whose abundances and kinetic energy seem to point to an electron capture SN from an intermediate-mass star (Nomoto et al. 1982). If these are ecSNe, then the pre-SN episodic mass loss might be related to nuclear flashes in the advanced degenerate core-burning sequences. SN IIn impostors: This group of putatively non-SN transients may be quite diverse, and it may include transients that have narrow lines because they are powered largely by CSM interaction (and weaker explosions than core-collapse SNe) and other transients that have narrow lines because they have slow winds/outflows. This may include LBVs, super AGB stars, binaries with a compact object, stellar mergers, pre-SN nuclear burning instabilities, failed SNe, or all of the above. Any massive supergiant star enshrouded in dust or with strong binary interaction that

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suffers an instability is a viable candidate. The theoretical mechanisms for this class of outbursts are still very poorly understood, and there is probably considerable overlap with pre-SN outbursts that lead to SNe IIn and Ibn. SNe Ibn: The most likely progenitors are massive WR stars that for unknown reasons undergo pre-SN outbursts. This is interesting, because there is no known precedent for an observed eruption in a H-deficient massive star. SNe Ia/IIn or Ia-CSM: If these really are thermonuclear SNe Ia (some cases seem clear; others are still debated in the literature), then the exploding progenitors are white dwarfs that have arisen from initial masses below roughly 8 Mˇ . In this case, a single degenerate system is clearly required to supply the large mass of Hrich CSM (several Mˇ in some cases). There is, as yet, no viable explanation for the sudden ejection of a large mass of H (by the companion) shortly preceding the thermonuclear explosion of the WD.

7

Closing Comments

Observations of interacting SNe present one of the most interesting challenges to our understanding of the end phases of evolution for massive stars. What makes these stars explode before they explode? Computational resources are only beginning to meet the needs of the complex problem of simulating convection and nuclear burning coupled with stellar structure and turbulence in these final phases (Arnett and Meakin 2011; Meakin and Arnett 2007). The fact that 10 % of core-collapse events are preceded by some major reorganization of the stellar structure and energy budget tells us that we have been missing something important, which might be a key ingredient for understanding core-collapse SNe more generally. It will be important to try and understand if this 10 % corresponds to the most extreme manifestation of a wider instability (e.g., if all stars undergo some instability in the final burning sequences, only the most extreme cases lead to detectably violent mass loss and SNe IIn) or if SNe IIn are the outcome of special circumstances in a particular evolution channel (i.e., interacting binaries within a certain mass and orbital period range). There is still very little information available on any trends with metallicity, although this is always good to investigate when mass loss plays a critical role. Recent years have seen something of a paradigm shift in massive star studies. Formerly standard or straightforward assumptions about the simplicity of single-star evolution are giving way to more complicated scenarios as astronomers grudgingly admit that binary stars not only exist but are common and influential (e.g., Sana et al. 2012). This may be especially true among transient sources and stellar deaths that seem otherwise peculiar or difficult to understand. Given the very high multiplicity fraction among massive stars, binary interaction should probably not be considered a last resort or the refuge for an uncreative theorist but, rather, a default assumption. Whether they are binaries or not, all SNe IIn require some major shift in stellar structure and mass loss before the SN. The synchronization with core-collapse gives a strong implication that something wild is happening in the latest sequences of

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nuclear burning. Those cases where a star changes its structure as a result of these nuclear burning instabilities (i.e., an inflated envelope) in a close binary system seem promising for inducing sudden eruptive behavior for various reasons (Smith and Arnett 2014). Single stars may also be able to induce their own violent mass loss in the couple years preceding core-collapse due to energy transported to the envelope from Ne and O burning zones (Quataert and Shiode 2012). However, we do not yet have a good explanation in single-star evolution for the strong mass loss that leads to the “enduring” class of SNe IIn or some of the more extreme cases of “delayed onset” of CSM interaction, where the strong interaction that lasts for years after explosion suggests very strong mass loss for decades or centuries before corecollapse. If binary interaction is an important ingredient, then this sort of interaction before a SN might make asymmetric CSM very common, suggesting that we should be paying close attention to possible observed signatures of asymmetry.

8

Cross-References

 Dust and Molecular Formation in Supernovae  Electron Capture Supernovae from Super Asymptotic Giant Branch Stars  Interacting Supernovae: Spectra and Light Curves  Observational and Physical Classification of Supernovae  Supernovae from Massive Stars  Supernova of 1054 and its Remnant, the Crab Nebula  Supernova Progenitors Observed with HST  The Physics of Supernova 1987A  The Progenitor of SN 1987A  Thermal and Non-thermal Emission from Circumstellar Interaction  The Supernova – Supernova Remnant Connection Acknowledgements My attempt to understand interacting SNe and their connections to massive stars has benefitted greatly from conversations with numerous people but especially Dave Arnett, Matteo Cantiello, Nick Chugai, Selma de Mink, Ori Fox, Morgan Fraser, Dan Kasen, Jon Mauerhan, Stan Owocki, Jose Prieto, Eliot Quataert, Jorick Vink, and Stan Woosley. While drafting this chapter, I received support from NSF grants AST-1312221 and AST-1515559.

References Aretxaga I, Benetti S, Terlevich RJ, Fabian AC, Cappellaro E, Turatto M et al (1999) SN 1988Z: spectro-photometric catalogue and energy estimates. MNRAS 309:343 Arnett WD, Meakin C (2011) Turbulent cells in stars: fluctuations in kinetic energy and luminosity. ApJ 741:33 Benetti S, Cappellaro E, Turatto M, Tautenberger S, Haratyunyan A, Valenti S (2006) Supernova 2002ic: the collapse of a stripped-envelope, massive star in a dense medium? ApJ 653:L129 Chugai NN (1997) Supernovae in dense winds. Ap&SS 252:225 Chugai NN (2001) Broad emission lines from the opaque electron-scattering environment of SN 1998S. MNRAS 326:1448

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Chugai NN, Danziger IJ (1994) SN 1988Z: low-mass ejecta colliding with the clumpy wind? MNRAS 268:173 Chugai NN, Blinnikov SI, Cumming RJ, Lundqvist P, Bragaglia A, Filippenko AV et al (2004) The Type IIn supernova 1994W: evidence for the explosive ejection of a circumstellar envelope. MNRAS 352:1213 Dessart L, Audi E, Hillier DJ (2015) Numerical simulations of superluminous supernovae of Type IIn. MNRAS 449:4304 Filippenko AV (1997) Optical spectra of supernovae. Annu Rev Astron Astrophys 35:309 Foley RJ, Smith N, Ganeshalingam M, Li W, Chornock R, Filippenko AV (2007) SN 2006jc: A Wolf-Rayet star exploding in a dense He-rich circumstellar medium. ApJL 657:L105 Foley RJ, Berger E, Fox O, Levesque EM, Challis PJ, Ivans II et al (2011) The diversity of massive star outbursts. I. Observations of SN 2009ip, UGC 2773 OT2009-1, and their progenitors. ApJ 732:32 Fox O, Skrutskie MF, Chevalier RA, Kanneganti S, Park C, Wilson J et al (2009) Near-infrared photometry of the Type IIn SN 2005ip: the case for dust condensation. ApJ 691:650 Fransson C, Ergon M, Challis PJ, Chevalier RA, France K, Kirshner RP et al (2014) Highdensity circumstellar interaction in the luminous Type IIn SN 2010jl: the first 1100 days. ApJ 797:118 Fraser M, Inserra C, Jerkstrand A, Kotak R, Pignata G, Benetti S et al (2013a) SN 2009ip à la PESSTO: no evidence for core collapse yet. MNRAS 433:1312 Fraser M, Magee M, Kotak R, Smartt SJ, Smith KW, Polshaw J et al (2013b) Detection of an outburst one year prior to the explosion of SN 2011ht. ApJ 779:L8 Gall C, Hjorth J, Watson D, Dwek E, Maund JR, Fox O et al (2014) Rapid formation of large dust grains in the luminous supernova 2010jl. Nature 511:326 Gal-Yam A, Leonard DC (2009) A massive hypergiant star as the progenitor of the supernova SN 2005gl. Nature 458:865 Gal-Yam A, Leonard DC, Fox DB, Cenko SB, Soderberg AM, Moon DS et al (2007) On the progenitor of SN 2005gl and the nature of Type IIn supernovae. ApJ 656:372 Gal-Yam A, Arcavi I, Ofek EO, Ben-Ami S, Cenko SB, Kasliwal MM et al (2014) A Wolf-Rayetlike progenitor of SN? 2013cu from spectral observations of a stellar wind. Nature 509:471 Gehrz RD, Hackwell JA (1974) Circumstellar dust emission from WC9 stars. ApJ 194:619 Kochanek CS, Szczygiel DM, Stanek KZ (2011) The supernova impostor impostor SN 1961V: Spitzer shows that Zwicky was right (again). ApJ 737:76 Leonard DC, Filippenko AV, Barth AJ, Matheson T (2000) Evidence for asphericity in the Type IIN supernova SN 1998S. ApJ 536:239 Margutti R, Milisavljevic D, Soderberg AM (2014) A Panchromatic view of the restless SN 2009ip reveals the explosive ejection of a massive star envelope. ApJ 780:21 Matheson T, Filippenko AV, Barth AJ, Ho LC, Leonard DC, Bershady MA et al (2000) Optical spectroscopy of supernova 1993J during its first 2500 days. AJ 120:1487 Mauerhan JC, Smith N, Filippenko AV, Blanchard KB, Blanchard PK, Casper CFE et al (2013a) The unprecedented 2012 outburst of SN 2009ip: a luminous blue variable star becomes a true supernova. MNRAS 430:1801 Mauerhan JC, Smith N, Silverman JM, Filippenko AV, Morgan AN, Cenko SB et al (2013b) SN 2011ht: confirming a class of interacting supernovae with plateau light curves (Type IIn-P). MNRAS 431:2599 Mauerhan JC, Williams GG, Smith N, Smith PS, Filippenko AV, Hoffman JL et al (2014) Multiepoch spectropolarimetry of SN 2009ip: direct evidence for aspherical circumstellar material. MNRAS 442:1166 Meakin C, Arnett WD (2007) Turbulent convection in stellar interiors. I. Hydrodynamic simulation. ApJ 667:448 Milisavljevic D, Fesen RA (2013) A detailed kinematic map of cassiopeia A’s optical main shell and outer high-velocity ejecta. ApJ 772:134

428

N. Smith

Miller A, Silverman JM, Butler NR, Bloom JS, Chornock R, Filippenko AV et al (2010) SN 2008iy: an unusual Type IIn supernova with an enduring 400-d rise time. MNRAS 404:305 Niemela VS, Ruiz MT, Phillips MM (1985) The supernova 1983k in NGC 4699 – Clues to the nature of Type II progenitors. ApJ 289:52 Nomoto K, Sugimoto D, Sparks WM, Fesen RA, Gull TR, Miyaji S (1982) The Crab Nebula’s progenitor. Nature 299:803 Ofek EO, Cameron PB, Kasliwal MM, Gal-Yam A, Rau A, Kulkarni SR et al (2007) SN 2006gy: an extremely luminous supernova in the galaxy NGC 1260. ApJ 659:L13 Ofek EO, Lin L, Kouveliotou C, Younes G, Gogus E, Kasliwal MM, Cao Y (2013) SN 2009ip: constraints on the progenitor mass-loss rate. ApJ 768:47 Pastorello A, Smartt SJ, Mattila S, Eldridge JJ, Young D, Itagaki K et al (2007) A giant outburst two years before the core-collapse of a massive star. Nature 447:829 Pastorello A, Mattila S, Zampieri L, Della Valle M, Smartt SJ, Valenti S, Agnoletto I et al (2008) Massive stars exploding in a He-rich circumstellar medium – I. Type Ibn (SN 2006jc-like) events. MNRAS 389:113 Pastorello A, Cappellaro E, Inserra C, Smartt SJ, Pignata G, Benetti S et al (2013) Interacting supernovae and supernova impostors: SN 2009ip, is this the end? ApJ 767:1 Pastorello A, Benetti S, Brown PJ, Tsvetkov DY, Inserra C, Taubenberger S et al (2015) Massive stars exploding in a He-rich circumstellar medium – IV. Transitional Type Ibn supernovae. MNRAS 449:1921 Pozzo M, Meikle WPS, Fassia A, Geballe T, Lundqvist P, Chugai NN et al (2004) On the source of the late-time infrared luminosity of SN 1998S and other Type II supernovae. MNRAS 352:457 Prieto JL, Brimacombe J, Drake AJ, Howerton S (2013) The 2012 rise of the remarkable Type IIn SN 2009ip. ApJL 763:L27 Quataert E, Shiode J (2012) Wave-driven mass loss in the last year of stellar evolution: setting the stage for the most luminous core-collapse supernovae. MNRAS 423:L92 Rest A, Foley RJ, Gezari S, Narayan G, Draine B, Olsen K et al (2011) Pushing the boundaries of conventional core-collapse supernovae: the extremely energetic supernova SN 2003 ma. ApJ 729:88 Roming PWA, Pritchard TA, Prieto JL, Kochanek CS, Fryer CL, Davidson K et al (2012) The unusual temporal and spectral evolution of the TYPE IIn supernova 2011ht. ApJ 751:92 Sana H, de Mink SE, de Koter A, Langer N, Evans CJ, Gieles M et al (2012) Binary interaction dominates the evolution of massive stars. Science 337:444 Schlegel EM (1990) A new subclass of Type II supernovae? MNRAS 244:269 Shivvers I, Mauerhan JC, Leonard DC, Filippenko AV, Fox OD (2015) Early emission from the Type IIn supernova 1998s at high resolution. ApJ 806:213 Silverman JM, Nugent PE, Gal-Yam A, Sullivan M, Howell DA et al (2013) Type Ia supernovae strongly interacting with their circumstellar medium. ApJ Suppl 207:3 Smartt SJ (2009) Progenitors of core-collapse supernovae. ARA&A 47:63 Smith N (2013) The Crab Nebula and the class of Type IIn-P supernovae caused by sub-energetic electron-capture explosions. MNRAS 434:102 Smith N (2014) Mass loss: its effect on the evolution and fate of high-mass stars. ARA&A 52:487 Smith N, Arnett WD (2014) Preparing for an explosion: hydrodynamic instabilities and turbulence in presupernovae. ApJ 785:82 Smith N, Li W, Foley RJ, Wheeler JC, Pooley D, Chornock R et al (2007) SN 2006gy: Discovery of the most luminous supernova ever recorded, powered by the death of an extremely massive star like  carinae. ApJ 666:1116 Smith N, Chornock R, Li W, Ganeshalingam M, Silverman JM, Foley RJ et al (2008a) SN 2006tf: Precursor eruptions and the optically thick regime of extremely luminous Type IIn supernovae. ApJ 686:467 Smith N, Foley RJ, Filippenko AV (2008b) Dust formation and He II 4686 emission in the dense shell of the peculiar Type Ib supernova 2006jc. ApJ 680:568

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Smith N, Silverman JM, Chornock R, Filippenko AV, Wang X et al (2009) Coronal lines and dust formation in SN 2005ip: not the brightest, but the hottest Type IIn supernova. ApJ 695:1334 Smith N, Chornock R, Silverman JM, Filippenko AV, Foley RJ (2010a) Spectral evolution of the extraordinary Type IIn supernova 2006gy. ApJ 709:856 Smith N, Miller A, Li W, Filippenko AV, Silverman JM, Howard AW et al (2010b) Discovery of precursor luminous blue variable outbursts in two recent optical transients: the fitfully variable missing links UGC 2773-OT and SN 2009ip. AJ 139:1451 Smith N, Li W, Filippenko AV, Chornock R (2011a) Observed fractions of core-collapse supernova types and initial masses of their single and binary progenitor stars. MNRAS 412:1522 Smith N, Li W, Silverman JM, Ganeshalingam M, Filippenko AV (2011b) Luminous blue variable eruptions and related transients: diversity of progenitors and outburst properties. MNRAS 415:733 Smith N, Mauerhan JC, Silverman JM, Ganeshalingam M, Filippenko AV, Cenko SB et al (2012a) SN 2011hw: helium-rich circumstellar gas and the luminous blue variable to Wolf-Rayet transition in supernova progenitors. MNRAS 426:1905 Smith N, Silverman JM, Filippenko AV, Cooper MC, Matheson T, Bian F et al (2012b) Systematic blueshift of line profiles in the Type IIn supernova 2010jl: evidence for post-Shock dust formation? AJ 143:17 Smith N, Mauerhan JC, Prieto JL (2014) SN 2009ip and SN 2010mc: core-collapse Type IIn supernovae arising from blue supergiants. MNRAS 438:1191 Smith N, Mauerhan JC, Cenko SB, Kasliwal MM, Silverman JM, Filippenko AV et al (2015) PTF11iqb: cool supergiant mass-loss that bridges the gap between Type IIn and normal supernovae. MNRAS 449:1876 Stritzinger M, Taddia F, Fransson C, Fox OD, Morrell N, Phillips MM et al (2012) Multiwavelength observations of the enduring Type IIn supernovae 2005ip and 2006jd. ApJ 756:173 van Marle AJ, Smith N, Owocki SP, van Veelen B (2010) Numerical models of collisions between core-collapse supernovae and circumstellar shells. MNRAS 407:2305 Williams PM, van der Hucht KA, Pollock AMT, Florkowski DR, van der Woerd H, Wamsteker WM (1990) Multi-frequency variations of the Wolf-Rayet system HD 193793. I – infrared, X-ray and radio observations. MNRAS 243:662 Woosley SE, Blinnikov S, Heger A (2007) Pulsational pair instability as an explanation for the most luminous supernovae. Nature 450:390 Yoon SC, Cantiello M (2010) Evolution of massive stars with pulsation-driven superwinds during the red supergiant phase. ApJ 717:L62

Superluminous Supernovae

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D. Andrew Howell

Abstract

Superluminous supernovae are hydrogen-rich (SLSNe-II), or hydrogen-poor (SLSNe-I), explosions so bright that they require a power source beyond that of traditional supernovae. SLSNe-I rise to a peak over 20–90 days and then decline over a timescale roughly twice as long. At early times they have a blue continuum, peaking in the ultraviolet, have temperatures in excess of 14,000 K, and show ionized lines of carbon and oxygen out of thermodynamic equilibrium. As the supernovae cool, their spectra start to resemble SNe Ic, though with a time delay. They also favor environments with metallicities half solar or lower. Modeling indicates that they are explosions of stripped carbon-oxygen stellar cores, similar to but sometimes more massive than the progenitors of SNe Ic. SLSNe-I similar to SN 2007bi have broader light curves and seemingly more massive progenitors. Some have proposed that these are pair-instability supernovae, but in general the supernovae rise too quickly for this model. Most SLSNe-I show no signs of interaction and instead seem to be powered by a central engine. The magnetar spin-down model has been the most successful at reproducing the light curves and peak luminosity of SLSNe, though it may not be unique. Most SLSNe-II seem to be powered by interaction of these SNe with circumstellar material, as in SNe IIn. However, there are a handful of hybrid cases, or SLSNe-II, with weak or little interaction, which may be related to SLSNe-I.

D.A. Howell () Las Cumbres Observatory, Goleta, CA, USA University of California, Santa Barbara, CA, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_41

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Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hydrogen Poor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Light Curve Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Precursor Peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Ejecta Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Theoretical Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 SN 2007bi-Likes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Hydrogen Rich . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Intermediate Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 SLSNe as Cosmological Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Host Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Superluminous supernovae (SLSNe), as the name attests, are supernovae that are brighter than usual. As a result of the overly broad name, the category is a catchall describing several classes of supernovae – some with hydrogen, some without, some interacting, and some probably not. A few authors have defined SLSNe as those brighter than M D 21 at peak, though this arbitrary cut could leave out related physical phenomena. Instead, I define SLSNe as luminous SNe which cannot be explained by the power sources fueling traditional (Types I and II) supernovae: radioactive decay from a moderate amount of elements synthesized in the explosion, the energy deposited by a shock unbinding the star, or interaction with moderate but obvious amounts of circumstellar material (CSM) previously lost by the supernova progenitor or a companion. This last point creates a gray area. Should Type IIn supernovae count as SLSNe? Type IIn supernovae are those with a strong blue continuum at early times and narrow and intermediate width hydrogen emission lines at some points in their spectroscopic evolution. They are thought to be the collapse of massive stars whose ejecta shock CSM. On the one hand, they have been recognized as a class since the 1980s, a large and diverse one, and the source of their luminosity is not a mystery. On the other, some SNe IIn are so bright that they have been considered SLSNe [e.g., SN 2006gy (Ofek et al. 2007; Smith et al. 2007), which reached a peak absolute magnitude of 22]. A complicating factor is that interaction should be considered as a possible power source for SLSNe, whether or not the spectra show narrow lines. Here I compromise – I will generally not include clear SNe IIn, as their power source is not a mystery. However, I will mention a few extraordinary cases where appropriate and discuss interaction as a possible power source. In the late 1990s, a few unusually luminous supernovae were discovered – SN 1997cy (Germany et al. 2000, M D 20) was interacting, SN 1999as Knop

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et al. (1999) was a Type Ic supernova which peaked well above the typical absolute magnitude, and 1999bd (Nugent et al. 1999) was an early and relatively unrecognized SLSN-II. However these events were largely explained away as either something possibly related to hypernovae (in the case of SN 1999as) or a SN IIn (SN 1997cy and SN 1999bd). The history of SLSNe starts in earnest with two discoveries by Robert Quimby and the Texas Supernova Search who first established SNe with individual luminosities so extreme that they clearly represented a crisis to typical models. SN 2006gy (Smith et al. 2007), a SN IIn, was brighter than M D 21 for about 100 days and radiated more than 1051 ergs. SN 2005ap (discovered first but published second in Quimby et al. 2007) was what we now call a SLSN-I, discovered at z D 0:283. It peaked at an unfiltered absolute magnitude of 22, unheard-of at the time, and showed a band of five O II features, which is today recognized as a signature of the class. This was followed by SN 2008es, another superluminous Type II discovered by ROTSE-IIIb in a dwarf galaxy at z D 0:205 (Gezari et al. 2008; Miller et al. 2008). It had a light curve similar to a SN II with a linear decline (SN II-L) but was more than an order of magnitude more luminous, reaching MV D 22:2. Meanwhile, Barbary et al. (2008) described SCP06F6, a transient in the Supernova Cosmology Project’s cluster supernova search, which had an unknown redshift, three mysterious absorption lines, an extraordinarily long rise and decline, and slowly evolving spectra. The Supernova Legacy Survey identified two similar supernovae, which were talked about at conferences, but unpublished until their status as SLSNe was determined (Howell et al. 2013). The status of all these events was made clear with the discovery by Quimby et al. (2011) of events in the Palomar Transient Factory (PTF) sample that had O II lines like SN 2005ap yet a redshift high enough to reveal restframe UV lines like the SCP06F6 and SNLS events. They also found weak host galaxy Mg II lines in an SCP06F6 spectrum placing it at z D 1:189, thereby cementing its status as a SLSN. After people knew what to look for, SLSNe were found in many surveys. Pastorello et al. (2010) presented SN 2010gx from Pan-STARRS1 (PS1; aka CSS100313: 112547-084941, and PTF10cwr). They established that these hydrogen-poor SLSNe started to look like SNe Ic at later times, albeit with a time delay. More were found in PS1 (e.g., Berger et al. 2012; Chomiuk et al. 2011). And a SN from SDSS-II established the first solid evidence for a bump in the light curve at early times (Leloudas et al. 2012). Parallel to this, SN 2007bi was discovered (Gal-Yam et al. 2009), a superluminous supernova with a long, slow decline matching the decay of 56 Co and a nebular spectrum interpreted as showing evidence for a large synthesized mass of 56 Ni. Thus the SN was interpreted as the first evidence for a pair-instability supernova (PISN; Barkat et al. 1967; Rakavy and Shaviv 1967). This early work was reviewed by Gal-Yam (2012), who divided SLSNe into three classes: SLSNe-I (those without hydrogen; Sect. 2), SLSNe-II (those with hydrogen; Sect. 4), and SLSNe-R (where R stands for radioactive, i.e., those like SN 2007bi). I keep all three classes, but rather than use the “R” category (which relies on possibly

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incorrect theoretical interpretation), I call the latter SN 2007bi-likes (Sect. 3). In addition, I will mention intermediate events, including a new class of fast-rising luminous transients (Sect. 5).

2

Hydrogen Poor

Strictly speaking, one might classify something as a hydrogen-poor superluminous supernova (SLSN-I), if it meets the two criteria in the name – it reaches an absolute magnitude brighter than some threshold, e.g., M < 21, in some band, and it does not have hydrogen in the spectrum. But here I have relaxed the first criterion, and there are cases of SLSNe which seem similar to SLSNe-I but have a small amount of hydrogen. Furthermore, there are times when we will want to classify SLSNe based solely on a single light curve or spectrum. So it is instructive to consider additional criteria which almost all members of the class seem to possess. In general SLSNe-I: – Reach a peak absolute magnitude above that of typical SNe. – Have little or no hydrogen in their spectra. – Rise in brightness over 20–90 days in the restframe and decline over timescale longer than, but proportional to, the rise. – Have blue spectra for of order a week, indicative of blackbody temperatures of 14,000 K or higher, then declining over time. – Are brighter in the ultraviolet than typical SNe. – Have spectra that resemble SNe Ic but delayed by tens of days relative to normal SNe Ic. – Have a characteristic pattern of O II lines in the optical near maximum light. – Have a series of broad absorption lines in the UV dominated by C, Mg, and Fe. – Have velocities near maximum light of order 10,000 km s1 , comparable to normal SNe Ic. – Prefer low-metallicity, star-forming environments. These properties will be characterized in detail in the following sections, and the implications for their progenitors will be explored. Note that SLSNe-I are distinct from the gamma ray burst associated broad-line SNe Ic (Ic-BL, sometimes called hypernovae) in that the latter are redder, do not achieve the same luminosities, have higher velocity lines, and seem to be powered by the decay of 56 Ni.

2.1

Light Curve Evolution

SLSNe-I start with a hot, blue continuum that peaks in the restframe ultraviolet and have broadband colors consistent with a blackbody above 14,000 K, though often as high or higher than 20,000 K. During these first few days or weeks, the light curve may even rise and fall with a precursor peak before the main peak (see Sect. 2.3).

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Fig. 1 Representative light curves and ranges of SLSNe and normal SNe Ic from Nicholl et al. (2015b). The dark blue represents the range of SLSNe, while the light gray represents the range of SNe Ic. If the Taddia et al. (2015) template and gray range are scaled up in brightness by a factor of 3.5 and stretched in time by a factor of 3, they produce the upper black line and surrounding light blue region, which is well matched to the range of SLSNe. The broad-lined SNe Ic SN 2006nx, 2012bz, and 1998bw lie in the gap but have narrower light curves than SLSNe. SN 2011bm (Valenti et al. 2012) had a light curve width comparable to SLSNe, though at lower luminosity and with normal SNe Ic spectra

Besides the precursor peak, the light curves of SLSNe-I are similar to those of SNe Ic but are brighter and more stretched out in time. Nicholl et al. (2015a) studied a sample of 24 SLSNe-I and found that their light curves were on average 3.5 mag brighter and three times broader than SNe Ic (Fig. 1). Their rise time was also proportional to their decline time, with the decline being about a factor of two longer on average. Compare this to the light curves of SNe IIn, which range in luminosity over a factor of more than 100, and have a diverse range of rise times, fall times, and even bumps (Kiewe et al. 2011). Most SLSNe-I have relatively smooth light curves, but some do show undulations, notably SN 2015bn (Nicholl et al. 2016a). SLSNe-I produce significant output the in the restframe ultraviolet, making difficult-to-obtain short wavelength coverage important for fully characterizing them. In general, the UV bands peak earlier than they do in restframe U (Howell et al. 2013). SLSNe-I reach a peak bolometric luminosity of order 1044 ergs s1 . Thus they achieve a peak brightness higher than typical SNe Ic by a factor of 10–100. After integrating their complete light curve, SLSNe-I radiate of order 1051 erg, comparable to the total kinetic energy of a typical core-collapse supernova, and two orders of magnitude more energy than radiated by normal events.

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2007bi-like SLSNe have broader light curves than “normal” SLSNe. One way to answer whether they belong in a separate category is whether there is a continuum of decline rates from normal SLSNe to 2007bi-likes. I consider this in Sect. 3. Late-time (>100 day) light curves of SLSNe can help distinguish between theoretical scenarios, but observations are difficult to obtain. When temperatures fall below 10,000 K, IR observations become important, but these are even more scarce than optical observations (Inserra et al. 2013).

2.2

Spectroscopy

SLSN-I spectra are dominated by absorption lines of mostly intermediate mass and a few iron-peak elements, some of which are not seen in typical SNe. Representative high signal-to-noise spectra have been used to show characteristic evolution in Fig. 2, reproduced from Nicholl et al. (2015b). At the earliest times, the most obvious feature in the optical is a series of five lines of O II, which may persist until shortly after maximum light. These lines come from excited lower levels of oxygen, requiring departures from local thermodynamic equilibrium (LTE; Mazzali et al. 2016). Simultaneously, singly and doubly ionized lines of carbon (along with Fe III and Mg II) dominate the UV spectra. Howell et al. (2013) found that LTE codes were inadequate to correctly identify certain lines, but radiative transfer through several solar masses of carbon and oxygen, with a solar composition of heaver elements, was sufficient to correctly reproduce spectra up to maximum light (Fig. 3). After maximum light, temperatures cool enough for oxygen to recombine (around 15,000 K), and this distinctive complex of O II features disappears (this and other features of spectroscopic evolution may be delayed in the SN 2007bilikes). They are replaced by Ca II H&K, Mg II, Si II, and Fe II. A few weeks after maximum, SLSNe-I start to resemble SNe Ic at maximum light, though bluer (Nicholl et al. 2015b; Pastorello et al. 2010). Between 1 and 2 months after maximum, Ca II and Mg I go into emission in the blue part of the spectrum, while O I and the Ca IR triplet dominate the red in absorption. Forbidden lines start appearing at about 100 days after maximum and over the next hundred days become stronger, more emission dominated, and eventually nebular. This is similar to but significantly delayed from normal SNe Ic. Spectra obtained at very late times for the nearby SLSN 2015bn (a 2007bi-like) showed that these objects can take over 300 days to become fully nebular. At this phase, the spectra are nearly identical to very energetic and/or GRB-related SNe Ic such as SNe 1998bw, 1997dq, and 2012au (Jerkstrand et al. 2016; Nicholl et al. 2016b). Velocities measured from the spectra of SLSNe-I are comparable to normal SNe Ic, although they decline much more slowly. This was both a clue and a mystery in SCP06F6 before it was recognized as a SLSN (Barbary et al. 2008). It had velocities comparable to those of SNe, yet they did not seem to evolve redward with time as SN lines do when they track a photosphere receding inward in mass coordinates as

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Fig. 2 Figure from Nicholl et al. (2015b) showing the spectroscopic evolution of SLSNe-I. High signal-to-noise, representative spectra were chosen from a variety of events. Gray lines are blackbody fits. Dates are shown relative to maximum light. Note the early, UV-bright spectra with O II lines, characteristic of the class. In this figure, the three most prominent early UV lines are identified as C II, Si III, and Mg II. However, these were identified by a parameterized code which treats lines in LTE. More reliable determinations of these lines are presented in Fig. 3, which used a non-LTE radiative transfer code to make the identifications

the SN expands and cools. Nicholl et al. (2015b) measured the minimum of the FeII 5169 line 20–30 days after maximum in a sample of 24 SLSNe-I and 15 SNe Ibc and found a median velocity and standard deviation of 10;500 ˙ 3100 km s1 for SLSNe and 9800 ˙ 2500 km s1 for SNe Ibc. Velocities measured from the width of late-time nebular emission features are consistent with this (Inserra et al. 2013; Nicholl et al. 2013). While SNe Ic velocities drop by 4000–8000 km s1 over the first month after maximum light (Valenti et al. 2012), SLSNe-I velocities decline by at most 2000 km s1 , though many show no perceptible decline.

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Fig. 3 Figure from Howell et al. (2013) showing premaximum restframe UV spectra of SLSNe-I, SCP06F6, and SNLS-06D4eu. Middle lines show theoretical spectra generated by shining different luminosities through a homologously expanding sphere of 5 Mˇ of a C+O+solar composition. The figure shows that the two apparently different spectra can be obtained with a similar underlying progenitor. Note that these lines have been attributed to other elements by authors using less sophisticated parameterized LTE codes

2.3

Precursor Peaks

With SN 2006oz, Leloudas et al. (2012) discovered that some SLSNe have a peak prior to maximum light. They found a bump in the ugriz light curve 30 days before maximum. Howell et al. (2013) also noticed that the couple of points of the restframe UV light curve of SNLS-06D4eu were flat before the SN began to rise. Then Nicholl et al. (2015b) observed a well-resolved precursor bump lasting about 2 weeks in the restframe in the g-band in LSQ14dbq, and Smith et al. (2016) observed a multicolor precursor decline in DES14X3taz. A study by Nicholl and Smartt (2016) found that these precursor peaks may be ubiquitous in SLSNe-I (see Fig. 4, reproduced from their paper). Out of 14 SLSNe-I with early data, eight had at least some indication of a precursor peak, and the rest had data too poor to rule them out. This study claims that the data are consistent with all SLSNe-I having an early peak prior to maximum light, though compelling cases of weak or nonexistent precursor peaks have come to light since. In fact many normal core-collapse supernovae show a precursor peak soon after explosion. It was theoretically expected that the shock breakout from a massive star would produce an initial burst of radiation, which would decline over the first

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LSQ14bdq (g - 4.5 mag) PTF09cnd (g - 3)

iPTF13ajg (u + 0.5)

SN1000+0216 (1600 Å)

PS1-10pm (2840Å + 1.8) SN 2006oz (g + 3.5)

PS1-10ahf (2900Å - 1.7)

−26

SNLS 06D4eu (2420Å + 1)

Absolute magnitude + constant

−24

−22

−20

−18

−16

−14 0

10

20

60 50 40 30 Rest-frame days

70

80

90

Fig. 4 Figure from Nicholl and Smartt (2016) showing precursor peaks in eight supernovae. The black line shows data from LSQ14bdg (black circles), and it is shown scaled in amplitude and stretched in time, fit to the other SNe. Thin colored lines show fits to the main peak of each supernova. Precursor bumps can last for a few days to two weeks and are one to several magnitudes fainter than maximum light

few minutes to hours before radioactive decay or the geometric expansion of the supernova got bright enough to give rise to the main light curve (Falk 1978; Klein and Chevalier 1978). This was observed in SN 1987A and SN 1993J. A similar phenomenon has been seen, though with an initial decay over a longer timescale, in both SNe II-P (Gezari et al. 2015; Schawinski et al. 2008) and stripped-envelope supernovae (Soderberg et al. 2008). It is often attributed to shock breakout in a wind. But in the optical, Type IIb supernovae (those that have some, but not a lot of hydrogen) frequently show a many-day long precursor peak in the optical (e.g., Arcavi et al. 2011). This is attributed to cooling after shock breakout (Rabinak and Waxman 2011). Given that some SLSNe-I had such a bright and long precursor peak, if it is due to postshock cooling, it would have to be cooling not of the star but of an extended circumstellar envelope (Nicholl et al. 2015b; Piro 2015; Smith et al. 2016). Another possibility is to get a dip in the initial rise and ultimate maximum via an increased electron-scattering opacity caused by interaction with a dense circumstellar shell at some distance from the progenitor (Moriya and Maeda 2012). However, that seems

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somewhat disfavored if every SLSN-I is required to have such an arrangement. It also requires that the SLSN itself is powered by interaction. Another possibility is the shock breakout from the already-expanded supernova ejecta of a bubble inflated by a magnetar (Kasen et al. 2016). However, this requires suppressing the thermal energy of the magnetar to get the correct shape. Smith et al. (2016) were able to measure colors (and temperature) during a precursor bump, finding T > 20; 000 K and rapid cooling, consistent with a shock in extended material.

2.4

Ejecta Masses

Independent of the mechanism of powering superluminous supernovae, if we can get estimates of the mass of the ejecta, we can get clues to their progenitors. There are several techniques for doing so – estimating the mass using the light curve width as an indicator of the diffusion time through the ejecta (e.g., Nicholl et al. 2015b), estimating the oxygen mass through nebular spectra and scaling to the mass of the whole SN accordingly (e.g., Gal-Yam et al. 2009), or direct modeling with radiative transfer (Dessart et al. 2012; Howell et al. 2013). Using a parameterized model, Howell et al. (2013) used radiative transfer to calculate the effect of putting various luminosities through expanding balls of gas of different compositions, masses, and velocities (Fig. 3). They determined that (a) the spectra of SLSNe-I were best reproduced with a carbon-oxygen atmosphere, (b) varying only the luminosity could account for the variations seen in spectra for different events, and (c) the spectra of SNLS-06D4eu, one of the most luminous events seen, could be reproduced with 5 Mˇ of ejecta. This model was not dependent on the magnetar scenario explicitly but did assume a central source of luminosity. In a separate test, the authors reproduced the light curve of SNLS06D4eu with the spin-down of a magnetar with 3 Mˇ of ejecta. It is possible to estimate ejecta masses using a formula adapted from Kasen and Bildsten (2010) and Inserra et al. (2013): 

 Mej D 0:77 0:1 cm2 g 1

1 

v 10;000 km s1



m 2 10 d

(1)

where m is the diffusion time,  is the opacity, Mej is ejecta mass, and v is the ejecta scale velocity from Arnett (1982). In the absence of any good way to determine the scale velocity, Nicholl et al. (2015b) substitute photospheric velocities as measured by Fe II features. These were found to be similar to normal SNe Ic, around 10,000 km s1 . This implies that differences in the diffusion time between SLSNe-I and SNe Ic are dominated by either ejecta mass or opacity differences. If SLSNe-I and SNe Ibc also have similar opacities, then the longer diffusion time (i.e., longer rise and fall of the light curve) of SLSNe-I implies that they have larger ejecta masses. But what is the relevant opacity?  D 0:1 cm2 g 1 is appropriate for an electron-scattering atmosphere with ionization states typically seen in normal SNe. However a fully ionized gas should have  D 0:2 cm2 g 1 . Nicholl et al.

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bj

SLSN =

Ej

M

Ej

M

bj

SLSN =

Fig. 5 Figure from Nicholl et al. (2015b) showing ejecta mass distributions for both SLSNe and SNe Ibc under different assumptions. The top panel assumes an opacity of  D 0:1 cm2 g1 for the SLSNe, while the bottom assumes 0.2. The former, matched to assumptions used for SNe Ibc, would indicate that SLSNe have ejecta twice as high as SNe Ibc on average. But the lower panel shows that if the opacity is twice as high in SLSNe as in SNe Ibc, then their ejecta masses could be comparable. This could be possible if SLSNe are more ionized, e.g., by a magnetar

(2015b) point out that the gas well below the photosphere should be fully ionized right after explosion, but it quickly cools. Even though SLSNe are hotter for longer than normal SNe Ic, Inserra et al. (2013) showed that  D 0:1 cm2 g 1 is a reasonable approximation for the conditions in SLSNe-I. However, Nicholl et al. calculate ejected masses using  D 0:1 cm2 g 1 and then a lower limit (half the mass) using  D 0:2 cm2 g 1 . Their derived ejecta masses are shown in Fig. 5. SLSNe have a range of ejecta masses of 3–30 Mˇ , with a mean of 10 Mˇ , a standard

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deviation of 9 Mˇ , and a median of 6 Mˇ . These are a factor of a few higher than normal SNe Ic, for which they derive a mean of 3.1 Mˇ , a standard deviation of 2.9 Mˇ , and a median of 2.5 Mˇ . For broad-line SNe Ic, the mean, standard deviation, and median are 3.1, 1.3, and 2.9 Mˇ .

2.5

Theoretical Implications

SLSNe require an additional luminosity source over and above the core-collapse shock-deposited energy or the hundredths-to-tenths of solar masses of radioactive 56 Ni synthesized in the explosion. There are three main contenders: (1) much more 56 Ni, as would be generated in a pair-instability supernova; (2) interaction with circumstellar material, perhaps optically thick H-poor CSM (e.g., Chatzopoulos and Wheeler 2012; Chevalier and Irwin 2011; Ginzburg and Balberg 2012); and (3) a central engine, such as the spin-down of newly created magnetar (Kasen and Bildsten 2010; Woosley 2010) or jets generated from late accretion onto a newly formed black hole (Dexter and Kasen 2013). Some models combine two or more sources, such as pulsational pair-instability SNe, where the star pulsates several times, ejecting shells of matter, which collide, before finally exploding (Woosley et al. 2007). There is universal agreement (see discussions in, e.g., Chomiuk et al. 2011; Howell et al. 2013; Nicholl et al. 2015b; Pastorello et al. 2010; Quimby et al. 2011) that the synthesis of several to tens of solar masses of radioactive 56 Ni cannot explain the extreme luminosities of normal (i.e., non-2007bi-like) SLSNe-I. Large ejecta masses are required, producing large diffusion times, which do not match their light curves. For normal (faster-declining) SLSNe-I, interaction power has been invoked by some authors to explain their light curves, (e.g., Chatzopoulos et al. 2013b; Sorokina et al. 2016). In normal SNe IIn, there are narrow-to-intermediate velocity lines of hydrogen indicative of interaction with a circumstellar shell of material. At early times, they also have a blue continuum with no absorption lines, indicating that the interaction forms a photosphere above where hydrogen absorption lines are usually formed. Such material may also be clumpy or grouped into shells, causing bumps in the light curve and associated changes in narrow spectroscopic lines (e.g., Graham et al. 2014). This is a possible explanation for the bumps seen in the light curves of some SLSNe (Nicholl and Smartt 2016). However, it is not trivial to hide the narrow lines – SNe interacting with hydrogen-poor but helium-rich CSM also show narrow lines of helium (SNe Ibn; e.g., Hosseinzadeh et al. 2016; Pastorello et al. 2015). And Type Ia supernovae, which do not have hydrogen in their spectra, sometimes show narrow hydrogen lines when they interact with circumstellar material (Silverman et al. 2013). Furthermore, circumstellar material may be illuminated and ionized by the shock breakout at early times, producing narrow high-ionization lines as seen in some SNe II (e.g., Gal-Yam et al. 2014; Khazov et al. 2016). None of these signatures are seen in SLSNe-I, so any interaction must by physically different (though the latter “flash spectroscopy” idea has not been tested in SLSNe). Some

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have proposed hydrogen-poor CSM moving at high velocity to explain the lack of narrow lines (e.g., Chatzopoulos et al. 2013b). Aside from the lack of narrow lines, there are other indications that interaction may not be the power source for SLSNe-I. Interaction with hydrogen-free material has been seen before in SN 2010mb, a SN Ic with a very slowly declining light curve (600 d), though it did not achieve an excessive luminosity (Ben-Ami et al. 2014). The fact that it showed oxygen line emission from interaction even at lower luminosities would seem to indicate that such evidence is hard to hide. As a rule of thumb, to achieve sufficient conversion of kinetic energy into radiation, the CSM mass ought to be comparable to the ejecta mass (MCSM & Mej =2) (e.g., Nicholl et al. 2015b). Since interaction happens on the outside of the ejecta, anything that substantially affects the light curve (e.g., brightening it by a factor of 100) ought to comparably affect the spectra. This is not what is seen in SLSNe, since they have absorption lines which are not covered by a continuum even at early times (Fig. 2). SNe IIn also have a wide array of luminosities, plateaus, and decline rates, owing to the great diversity in CSM properties (Kiewe et al. 2011; Taddia et al. 2013), though SLSNe do not (Fig. 1). And finally, the rise time of SLSNe is proportional to the decline time, which is true of SNe powered by a central source, but should not necessarily be true of interacting SNe. The most commonly invoked scenario to provide the energy source for SLSNe-I is power by a central engine. Since energy is injected after the supernova has reached a larger radius, less is lost to expansion. The magnetar spin-down model (Kasen and Bildsten 2010; Woosley 2010) works by transferring some of the energy from a strongly magnetized, rapidly spinning neutron star to the expanding ejecta. It has provided a good fit to the peak luminosity, light curve rise and decline, and tail rate of decline for almost all SLSNe-I (including SN 2007bi-likes) using a reasonable range of magnetic fields, initial spin periods, and magnetar masses (see, e.g., compilations in Inserra et al. 2013; Nicholl et al. 2015b). Admittedly, having three tunable parameters makes the model quite flexible. Aside from doing a good job of fitting the light curves, the magnetar spin-down model makes several testable predictions. It predicts a high temperature at early times, for example. This is a universal feature of SLSNe, though this is expected in the CSM interaction model as well (e.g., Nicholl et al. 2015b). A more unique prediction is that the magnetar should ionize a bubble inside the SN, piling up a shell of material (Chen et al. 2016a; Kasen and Bildsten 2010; Woosley 2010). This ought to lead to nearly constant velocities for a time in the spectroscopic evolution of SLSNe, which is also seen in most SLSNe (e.g., Nicholl et al. 2015b). One might also expect the late emission of high-energy radiation if this pulsar wind nebula bubble breaks through the photosphere (Metzger et al. 2014). This could explain the late X-rays seen in SCP06F6 (Gänsicke et al. 2009; Levan et al. 2013). An ionized bubble increases the electron-scattering opacity and decreases the line opacity. As such a bubble makes its way through the photosphere, it may explain the post-peak bumps in some light curves. Finally, at late times, in the simplest version of the model, light curves should drop off as t 2 (Kasen and Bildsten 2010). Though latetime data is scarce, many SLSNe seem to behave this way (Inserra et al. 2013).

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Not all do. Models adjusted to take into account late-time leakage of hard radiation from the scenario outlined above can accommodate this, at the cost of another free parameter (Chen et al. 2015; Lunnan et al. 2016; Wang et al. 2015). While the magnetar spin-down model provides good fits to most SLSNe, it is not clear the extent to which this is physically what is happening or whether it just a proxy for a central engine. Late accretion onto a black hole may ultimately achieve the same result, though theoretically this has not yet been shown for a wide variety of SLSNe-I (Dexter and Kasen 2013). Jets may be involved in either powering via black hole accretion or even in the magnetar spin-down case (Gilkis et al. 2016; Soker 2016). Published models involving jets have not been as successful as the magnetar spin-down, but this may be because it is not easy to capture the threedimensional complexity in a neatly parameterized 1D model. One way to observationally probe for jets is to find asymmetry in the ejecta, possibly at late times after the inner layers are uncovered. Normal core-collapse supernovae show increasing polarization as the core is revealed (Leonard et al. 2006), thought to be evidence for asymmetry. For SLSNe, SN 2015bn did show a change in spectropolarimetry over two epochs (Inserra et al. 2016a). LSQ14mo showed no change in polarization over 26 days (Leloudas et al. 2015a), though the data may not have been sensitive to subtle asymmetries.

3

SN 2007bi-Likes

There are now a handful of hydrogen-poor superluminous supernovae known whose light curves decline about twice as slowly as typical SLSNe-I. SN 2007bi, the prototype of these, had a peak absolute magnitude of 21.3 and a total radiated energy of >1051 ergs which, if powered by radioactive decay, indicates 5Mˇ of 56 Ni (Gal-Yam et al. 2009). The decline rate was broadly consistent with the decay of 56 Co, 0.0098 mag per day, over 500 days. From analysis of nebular oxygen lines, Gal-Yam et al. (2009) inferred 8–15 Mˇ of oxygen, used this to argue for a total ejecta mass of 100Mˇ , and claimed lower limit of 50 Mˇ . With such high mass ejecta, the total kinetic energy would be approximately 1053 erg. Gal-Yam (2012) added other SNe to the class, including SN 1999as, SN 2010hy, and PTF10nmn. Spectroscopically, SN 2007bi-like SNe resemble normal SLSNe-I, though they may evolve on a slower timescale. They also start to look like SNe Ic at late times (Nicholl et al. 2013). Gal-Yam et al. (2009) interpret SN 2007bi as a pair-instability SN. These SNe have been theorized to be the endpoints of massive stars ('140Mˇ ) with massive oxygen cores (65–130Mˇ ), where temperatures get so high that electron-positron pair production occurs (Barkat et al. 1967; Kasen et al. 2011; Rakavy and Shaviv 1967). This weakens their pressure support, causing the core to contract, ignite oxygen burning, and blow the star apart in a thermonuclear explosion. In the process, the stars should synthesize many solar masses of 56 Ni. These stars were expected to exist in the metal-poor early universe – their discovery at low redshifts (SN 2007bi is at z D 0:127/ would be a surprise.

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Fig. 6 Figure from Nicholl et al. (2015b) showing the decline timescale for SLSNe-I and SLSNe-II. They find no statistically significant evidence for a bimodal distribution between the long-declining SN 2007bi-likes and faster-declining SLSNe-I

Nicholl et al. (2015b) note that normal SLSNe-I and SN 2007bi-likes are similar in most properties, except that 2007bi-likes take longer to evolve. They therefore group 2007bi-likes into the same category as SLSNe-I but plot the distribution of decline timescale of all SLSNe-I to see if there is evidence for a bimodal distribution. From Fig. 6, it looks at first glance like the distribution groups into two categories – those with a 20–40 day decline and those with a 60–90 day decline. However they analyze the two data sets using a variety of statistics and find no significant evidence for two distinct groups based on decline rate alone or related proxies. SN 2007bi was discovered near maximum light so its rise time could not be accurately measured. Pair-instability models require a rise time of 100 days, as it takes photons this long to diffuse through the massive ejecta. Nicholl et al. (2013) presented two similar supernovae, PTF12dam and PS1-11ap, which rose a factor of two faster, in conflict with the PISN models (see also Chen et al. 2015; McCrum et al. 2014). These also had early spectra similar to those of SLSNe, which are bluer than PISN UV line-blanketed models (Dessart et al. 2012). Nicholl et al. (2013) also argue that the late-time oxygen fits are not unique and these SNe can be fit with as little as 10–16 Mˇ of total ejecta. Moriya et al. (2010) also fit the data from SN 2007bi to a theoretical model of the core-collapse SNe, although in their case it was a 43Mˇ core of a star which was originally 100 Mˇ . Dessart et al. (2012) and Nicholl et al. (2013) ultimately showed that SNe like SN 2007bi can be fit with a magnetar spin-down model like SLSNe-I. The similar PTF12dam can be fit with a CSM interaction model, though it requires an extreme 13Mˇ of hydrogen-free CSM (Chen et al. 2015).

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However, there is at least one relatively nearby SN 2007bi-like supernova with a long (& 125 day) rise: PS1-14bj (Lunnan et al. 2016). It is similar to SN 2007bi spectroscopically and has a similar (though somewhat lower) peak luminosity. But it has other novel features like a flatter peak, a constant color temperature for 200 days after maximum, and a late-time spectra with 3400 km s1 wide emission lines of [O III]. This requires late-time heating inconsistent with either the PISN model or the simplest version of the magnetar model, where the energy input monotonically declines. Lunnan et al. (2016) argue that either interaction or a modified magnetar model with late leakage from a pulsar wind nebula could explain the observations. Another possibility is a rotational model of a PISN (Chatzopoulos et al. 2013a) Two other pair-instability supernova candidates have been found in CFHT Legacy Survey data at z D 2–4 by targeting filter dropouts of their hosts due to the Lyman break (Cooke et al. 2012). They have long rise and fall times, appear to match model predictions, and are from the early universe. However due to their extreme distances, they are seen in the restframe UV and are distant enough that the data is sparse or noisy.

4

Hydrogen Rich

Type IIn supernovae, those with narrow lines of hydrogen indicating a supernova interacting with circumstellar material, can be superluminous (e.g., SN 2006gy; Smith et al. 2007). However, here we focus on the much more rare, and more poorly understood, class of SLSNe-II, i.e., those with hydrogen but no obvious narrow lines (Fig. 7). Only a few are known. The first such supernova was the aforementioned SN 2008es (Gezari et al. 2008; Miller et al. 2008). It rose to maximum over 23˙1 days, followed by a linearly declining light curve, not unlike the Type II linear (II-L) SNe 1979C and 1980K. However, SN 2008es was more than an order of magnitude more luminous, reaching MV D 22:2 and ultimately radiated nearly 1051 ergs. Since the expansion velocities were typical of a supernova, 10,000 km s1 (albeit on the high side for SNe II), this implies a high efficiency of conversion to kinetic to radiated energy (or a high mass). As in hydrogen-deficient SLSNe, early spectra were blue, consistent with a blackbody at 14,000 K. Interaction with either a dense circumstellar shell ejected by a previous explosive event, or with a stellar wind, was invoked to explain the excess luminosity, though it is not clear how other signs of interaction can be hidden. These papers were also published before the magnetar spin-down model. A new potential clue to the origins of SLSNe-II came with CSS121015: 004244+13287 (hereafter CSS121015; Benetti et al. 2014), a possible hybrid event. Discovered early at z D 0:2868, it was the subject of an intensive PESSTO monitoring campaign from 30 days to more than 200 days after maximum light in the restframe. It was exceedingly luminous, rising to a peak absolute magnitude of 22:5 before beginning a linear light curve decline. It did have narrow hydrogen features, a sure sign of interaction, although they were relatively weak. Early spectra were of a hot blue continuum, eventually giving way to a spectrum that variously

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Fig. 7 Figure from Inserra et al. (2016b) showing spectra of SLSNe-II at 20 days (upper) and 40 days (lower) from maximum light, along with comparison SNe. Dashed lines mark the position of hydrogen features. The top panel shows that all SNe in this category have hydrogen, except SN 2011ke, a SLSN-I shown for comparison. The bottom panel shows a comparison to SN 1980K, a IIL, demonstrating that SLSNe-II can follow the spectroscopic evolution of their less luminous counterparts, though delayed in time

resembled SLSNe-II, SLSNe-I, and SN 2005gj, which is thought to be a Type Ia interacting with circumstellar material (Aldering et al. 2006). This latter fact is not as surprising as it first sounds, since a few weeks after maximum light, many SN subtypes can look similar. The spectra clearly are indicative of interaction in this case, and it does raise the question whether slightly less intense interaction could be enough to drive an extreme luminosity but be relatively hidden in the spectrum. Benetti et al. (2014) also point out that an additional source of luminosity such as a magnetar cannot be ruled out. Finally, the picture was enlarged again with SN 2013hx and PS15br (Inserra et al. 2016b). Both are bright SLSNe-II with broad hydrogen lines and no signs of interaction during the photospheric phase. SN 2013hx had a 37 day rise, reaching

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Mg D 21:7, while PS15br’s rise time may have been similar, but it only reached a peak of Mg D 20:2. Both SNe had hot blue continua for the first few weeks, and spectra several weeks after maximum resemble SNe II-L from an earlier phase (Fig. 7). The two supernovae are not identical, however. Spectra of PS15br from 32 to 102 days show the development of a broad, asymmetric H˛ emission feature, along with a narrower component, indicative of interaction. Its light curve also has a shallower late decline and is slightly bumpier, also pointing to interaction. Yet again, this raises as many questions as it answers. Clearly whatever caused the hot blue continuum and high peak luminosity happened early. Why then was the interaction only seen late? And why is it only seen in some SLSNe-II? A model invoking a magnetar spin-down to explain the luminosity also works well. Is the interaction just a red herring?

5

Intermediate Events

Finding SNe in between various classes of SLSNe or between SLSN and normal SNe can help elucidate their progenitors. For example, the PISN model would predict a sharp division between those and normal SNe, since they are physically distinct phenomena, while the magnetar spin-down model may predict a continuum. Indeed, there have been several cases of SNe intermediate in some properties between normal and SLSNe. Inserra et al. (2013) point out that PTF10hgi and PTF11rks have peak absolute magnitudes fainter than Mg D 21. PTF11rks also evolves spectroscopically faster than other SLSNe. Valenti et al. (2012) presented SN 2011bm, which had a light curve width similar to SLSNe-I (Fig. 1), though only a slightly higher luminosity than normal SNe Ibc. It also had a spectroscopic evolution similar to SNe Ibc, though more spread out in time. SN 2012aa was also a supernova which showed the spectral evolution of a SN Ibc but a rise time of 34 days and a decline of 54 days, more similar to SLSNe (Roy et al. 2016). It also had a peak luminosity of 1:6  1043 erg s1 (Mbol  20), intermediate between the two. Even more curiously, it had a second peak in the light curve in all bands between 40 and 55 days after maximum, which may indicate interaction with circumstellar material. It did not show narrow lines of hydrogen or helium as seen in SNe IIn or SNe Ibn, but it did show an emission line at restframe 6500 Å, which could be H˛ blueshifted by 3000 km s1 . The host galaxy was a star-forming spiral galaxy consistent with solar metallicity. SN 2012au was a SN Ib with high velocity lines (up to 20,000 km s1 ), which reached a peak absolute magnitude of MB D 18:1 (Milisavljevic et al. 2013). It had a total kinetic energy of 1052 erg. There were also two velocity components in the spectra, with some lines .2000 km s1 . The late-time spectra were similar to the slow hypernovae SN 1997dq and SN 1997ef but also somewhat similar to SN 2007bi. There are also cases of SLSNe-I with signs of H or He. Inserra et al. (2013) find that SN 2012il had a broad He 10830 line at +52 days. And Yan et al. (2015) find broad H˛ in the late-time spectrum of the 2007bi-like iPTF13ehe. Mazzali

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et al. (2016) make the case that high-ionization conditions at early times can hide hydrogen or helium so that they do not become visible until the supernova cools. An alternative explanation for the hydrogen in iPTF13ehe is stripping from a binary companion as the supernova collides with it (Moriya et al. 2015). Finally, Arcavi et al. (2016) reported four supernovae – one from PTF and three from SNLS – which had a fast ( C1 and ŒFe=H < 1. There are CEMP-r and CEMP-s stars, enriched in r- or s-elements. CEMP-no stars show no significant s-enhancement. CEMP-no stars have [Fe/H] between 2:5 and about 7 and with excesses of the [C/Fe] ratios up to 4 dex. Spinstars are low Z massive stars with fast rotation, strong mixing, and high mass loss (Meynet et al. 2010). The interpretation in terms of spinstars of the huge abundance anomalies of the CEMP-no stars, which are the objects with the lowest known [Fe/H], supports the view that there are high rotational effects for the stars with the lowest metallicities. Models of massive stars with Z D 0 and an initial rotation velocity equal to about half the critical value have been calculated by Ekström et al. (2008b). Other models have been calculated with Z D 108 , 105 (Hirschi 2007; Meynet et al. 2006), 2  103 (Georgy et al. 2013). In stars of low Z, the effects of rotation, in particular internal mixing and mass loss, may be even stronger than at solar metallicity, thus favoring the formation of objects like spinstars. The stars are much more compact than at solar Z, because the opacity is weaker and thus radiation inflates the radii of the stars less. In the extreme case of stars with Z D 0, the pp-chains are insufficient to sustain the luminosity and the stars further contract. For a given mass, their radii are about

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3.5 times smaller than at solar metallicity. These smaller radii favor internal mixing since the mixing timescale goes like R2 =D, where D is the diffusion coefficient. Moreover the internal -gradients are higher and favor strong shear mixing, which has many consequences in the course of evolution. Let us examine the evolution of spinstars. During the main sequence (MS) phase, the stellar cores are refueled by internal mixing which brings fresh hydrogen. Thus, fast rotation makes the stellar cores bigger and the star more luminous. Such an effect is smaller in further stages, because the high gradient of mean molecular weight  at the edge of the core tends to prevent strong mixing. Nevertheless, the core is initially larger and remains larger all the way up to the supernova stage. Another feature of the Z D 0 and low Z models (present even at Z D 0:002) is that the stars easily reach the break-up limit during their MS phase, even if their initial rotation velocity is moderate. Some mass is lost at this stage, but this remains of the order of a few percent of the total stellar mass. The mixing in spinstars brings CNO products (mainly 14 N and 13 C) at the stellar surface. Also, C and O produced by core He burning may be brought to the H-burning shell, thus producing primary 14 N and 13 C, further reactions involving the Ne-Na and Mg-Al cycle may also intervene. Primary 14 N means nitrogen not made from the initial C and O (it would then be a secondary element) but from C and O produced in the star itself from the initial H and He elements. The surface enrichments in heavy elements like C increase the opacity in the outer layers and thus drive significant stellar winds (Hirschi 2007; Meynet et al. 2006). The mass loss by these winds can be very large particularly in the red supergiant stage, with the effect of reducing the final stellar mass and contributing to the chemical yields. Ejecta from stellar winds have much lower velocities than the ejecta from supernovae; thus they are more likely to contribute to the local chemical enrichments. In the models at Z D 0, the model with 150 MSun , a magnetic field and an initial velocity equal to half the critical value show some interesting properties (Ekström et al. 2008a). The model rapidly reaches the critical velocity (the socalled -limit if one takes into account the radiation pressure effect). The star model loses very little mass during the MS phase but a lot in the red supergiant phase due to the chemical enrichment and keeping at the -limit. It enters the WR stage, characterized by further heavy mass loss. At the end of core He burning, only 58 MSun are remaining and this mass is lower than the minimum limit for a pair creation supernova (PCSN), which is 64 MSun (Heger and Woosley 2002). Thus, rotation may allow the most massive stars to avoid the PCSN event. We note that the predicted nucleosynthetic signature of PCSN has not been observed up to now. There is an impressive series of six recent kinds of observations which give support to the concept of spinstars in the early generations of massive stars (Chiappini 2013). These are: (i) The evidences in the study of galactic chemical evolution for a production of primary nitrogen in stars with Z < 0:001.

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(ii) In similar studies, the increase of the C/O ratios at low [Fe/H] also implies an injection of C by heavy mass loss. (iii) The same trend is further supported by the low 12 C/13 C observed in metal poor giants of the galactic halo (Chiappini et al. 2008). (iv) Another, however less direct, argument is based on the behavior of the beryllium and boron [Be/H] ratios with respect to [O/H]. (v) The s-elements generally are accounted for by mass transfer in binary containing an AGB star. Such objects produce s-elements mainly of the second (Ba) and third (Pb) peaks, with very little elements of the first peak (Sr). The problem is that the observations of low Z stars show a large fraction of stars with a [Sr/Ba]>1, which cannot be produced by AGB stars. Most interestingly, spinstar models (Frischknecht et al. 2016) show that the internal mixing in rotating massive stars produces significant amounts of s-elements, with much more from the first peak than the second or third one. Another possible indication may come from the observations of a double sequence for many globular clusters (Piotto et al. 2005). This indicates that the relative helium to heavy elements enrichments Y=Z is above 70, while supernovae only produce a ratio of about 4. A contribution from the winds of massive stars is one of the possibilities to explain such high Y=Z ratios. On top of these indications, the model of spinstars is well supported by the study of CEMP-no stars (Maeder et al. 2015). CEMP-no stars have not only low [Fe/H] ratios and large excesses in the [C/Fe] ratios but also present a wide variety in the [C/Fe], [N/Fe], [O/Fe], [Na/Fe], [Mg/Fe], [Al/Fe], and [Sr/Fe] ratios. Back-andforth motions with partial mixing between the He and H regions may account for this variety in the products of the CNO, Ne-Na, and Mg-Al cycles. Some s-elements of the first peak may even be produced by these processes in a small fraction of the CEMP-no stars. Neither the yields of AGB stars (in binaries or not) nor the yields of classic supernovae can fully account for the observed abundance ratios in CEMPno stars. Better agreement is obtained once the chemical contribution by stellar winds of fast-rotating massive stars is taken into account, where partial mixing takes place, leading to various amounts of CNO being ejected. These events occur before the corresponding supernova explosion, which will bring its contribution in heavy elements. However, the anomalous abundance ratios mentioned above appear to result from spinstar evolution before the supernova explosion. Thus, as a whole, there are really a number of facts in support of a strong rotational mixing in the early stellar generations at very low metallicities. The mass loss from these stars produces a significant nucleosynthetic contribution before the supernova explosions. These enrichments are particularly rich in products from the CNO burning, from the Ne-Na and Mg-Al cycles, and from neutron captures producing s-elements of the first peak. All these effects imply that the role of rotation in the evolution of the first stars, and more generally among low metallicity stars, is very important and considerably influences the properties of the supernova progenitors, along the lines indicated in the above Sects. 3 and 4.

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Cross-References

 Close Binary Stellar Evolution and Supernovae  Evolution of the Magnetic Field of Neutron Stars  Hydrogen-Rich Core-Collapse Supernovae  Hydrogen-Poor Core-Collapse Supernovae  Interacting Supernovae: Types IIn and Ibn  Light Curves of Type II Supernovae  Nucleosynthesis in Hypernovae Associated with Gamma Ray Bursts  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Observational and Physical Classification of Supernovae  Population Synthesis of Massive Close Binary Evolution  Pre-supernova Evolution and Nucleosynthesis in Massive Stars and their Stellar

Wind Contribution  Superluminous Supernovae  Supernovae and Supernova Remnants: The Big Picture in Low Resolution  Supernovae and the Evolution of Close Binary Systems  Supernovae from Massive Stars  Supernova Progenitors Observed with HST  Supernova Remnants as Clues to Their Progenitors  The Masses of Neutron Stars  The Progenitor of SN 1987A  Very Massive and Supermassive Stars: Evolution and Fate

References Abbott BP, 974 Colleagues (2016) Binary Black Hole Mergers in the first advanced LIGO observing run. Phys Rev X 6:041015 Bersten MC, Benvenuto OG, Folatelli G et al (2014) iPTF13bvn: the first evidence of a binary progenitor for a Type Ib supernova. Astron J 148:68 Cao Y, Kasliwal MM, Arcavi I et al (2013) Discovery, progenitor and early evolution of a stripped envelope supernova iPTF13bvn. ApJL 775:L7 Chiappini C (2013) First stars and reionization: spinstars. Astron Nachr 334:595 Chiappini C, Ekström S, Meynet G et al (2008) A new imprint of fast rotators: low12 C/13 C ratios in extremely metal-poor halo stars. A&A 479:L9 Crowther PA (2007) Physical properties of Wolf-Rayet stars. Ann Rev Astron Astrophys 45:177 De Mink SE, Cantiello M, Langer N et al (2009) Rotational mixing in massive binaries. Detached short-period systems. A&A 497:243 Doherty CL, Gil-Pons P, Siess L, Lattanzio JC, Lau H (2015) Super- and massive AGB stars – IV. Final fates – initial-to-final mass relation. MNRAS 446:2599 Drout MR, Soderberg AM, Gal-Yam A et al (2011) The first systematic study of Type Ibc supernova multi-band light curves. ApJ 741:97 Ekström S, Meynet G, Maeder A (2008a) Can very massive stars avoid pair-instability supernovae? IAU Symposium, vol 250, pp 209–216

632

G. Meynet and A. Maeder

Ekström S, Meynet G, Chiappini C, Hirschi R, Maeder A (2008b) Effects of rotation on the evolution of primordial stars. A&A 489:685 Ekström S, Georgy C, Eggenberger P (2012) Grids of stellar models with rotation. I. Models from 0.8 to 120 M at solar metallicity (Z = 0.014). A&A 537:A146 Eldridge JJ, Fraser M, Smartt SJ, Maund JR, Crockett RM (2013) Thedeath of massive stars – II. Observational constraints on the progenitors of Type Ibc supernovae. MNRAS 436:774 Eldridge JJ, Fraser M, Maund JR, Smartt SJ (2015) Possible binary progenitors for the Type Ib supernova iPTF13bvn. MNRAS 446:2689 Filippenko AV (1997) Optical spectra of supernovae. Ann Rev Astron Astrophys 35:309 Frischknecht U, Hirschi R, Pignatari M et al (2016) s-process production in rotating massive stars at solar and low metallicities. MNRAS 456:1803 Fremling C, Sollerman J, Taddia F et al (2014) The rise and fall of the Type Ib supernova iPTF13bvn. Not a massive Wolf-Rayet star. A&A 565:114 Gal-Yam A (2012) Luminous Supernovae. Science 337:927 Georgy C (2012) Yellow supergiants as supernova progenitors: an indication of strong mass loss for red supergiants? A&A 538:L8 Georgy C, Ekström S, Meynet G et al (2012) Grids of stellar models with rotation. II. WR populations and supernovae/GRB progenitors at Z = 0.014. A&A 542:A29 Georgy C, Ekström S, Eggenberger P et al (2013) Grids of stellar models with rotation. III. Models from 0.8 to 120 M at a metallicity Z = 0.002. A&A 558:A103 Gordon MS, Humphreys RM, Jones TJ (2016) Luminous and variable stars in M31 and M33. III. The yellow and red supergiants and post-red supergiant evolution. arXiv:1603.08003 Groh JH, Meynet G, Ekström S (2013a) Massive star evolution: luminous blue variables as unexpected supernova progenitors. A&A 550:L7 Groh JH, Georgy C, Ekström S (2013b) Progenitors of supernova Ibc: a single Wolf-Rayet star as the possible progenitor of the SN Ib iPTF13bvn. A&A 558:L1 Groh JH, Meynet G, Georgy C, Ekström S (2013c) Fundamental properties of core-collapse supernova and GRB progenitors: predicting the look of massive stars before death. A&A 558:A131 Heger A, Woosley SE (2002) The nucleosynthetic signature of population III. ApJ 567:532 Heger A, Langer N, Woosley SE (2000) Presupernova evolution of rotating massive stars. I. Numerical method and evolution of the internal stellar structure. ApJ 528:368 Heger A, Woosley SE, Spruit HC (2005) Presupernova evolution of differentially rotating massive stars including magnetic fields. ApJ 626:350 Hirschi R (2007) Very low-metallicity massive stars: pre-SN evolution models and primary nitrogen production. A&A 461:571 Hirschi R, Meynet G, Maeder A (2004) Stellar evolution with rotation. XII. Pre-supernova models. A&A 425:649 Hirschi R, Meynet G, Maeder A (2005a) Yields of rotating stars at solar metallicity. A&A 433:1013 Hirschi R, Meynet G, Maeder A (2005b) Stellar evolution with rotation. XIII. Predicted GRB rates at various Z. A&A 443:581 Humphreys RM, Martin JC (2012) Eta carinae: from 1600 to the present. Astrophys Space Science Libr 384:1 Karlsson T, Johnson JL, Bromm V (2008) Uncovering the chemical signature of the first stars in the universe. ApJ 679:6 Krause O, Tanaka M, Usuda T et al (2008) Tycho Brahe’s 1572 supernova as a standard type Ia as revealed by its light-echo spectrum. Nature 456:617 Maeder A (2009) Physics, formation and evolution of rotating stars. Springer, Berlin 829 p Maeder A, Meynet G (2012) Rotating massive stars: from first stars to gamma ray bursts. Rev Mod Phys 84:25 Maeder A, Georgy C, Meynet G, Ekström S (2012) On the Eddington limit and Wolf-Rayet stars. A&A 539:A110

24 Supernovae from Rotating Stars

633

Maeder A, Grebel EK, Mermilliod J-C (1999) Differences in the fractions of Be stars in galaxies. A&A 346:459 Maeder A, Meynet G, Chiappini C (2015) The first stars: CEMP-no stars and signatures of spinstars. A&A 576:A56 Mandel I, de Mink SE (2016) Merging binary black holes formed through chemically homogeneous evolution in short-period stellar binaries. MNRAS 458:2634 Marchant P, Langer N, Podsiadlowski P, Tauris TM, Moriya TJ (2016) A new route towards merging massive black holes. A&A 588:A50 Martayan C, Floquet M, Hubert AM et al (2007) Be stars and binaries in the field of the SMC open cluster NGC 330 with VLT-FLAMES. A&A 472:577 Martins F, Hervé A, Bouret J-C et al (2015) The MiMeS survey of magnetism in massive stars: CNO surface abundances of Galactic O stars. A&A 575:A34 Meynet G, Maeder A (1997) Stellar evolution with rotation. I. The computational method and the inhibiting effect of the -gradient. A&A 321:465 Meynet G, Maeder A (2002) The origin of primary nitrogen in galaxies. A&A 381:L25 Meynet G, Ekström S, Maeder A (2006) The early star generations: the dominant effect of rotation on the CNO yields. A&A 447:623 Meynet G, Hirschi R, Ekstrom S et al (2010) Are C-rich ultra iron-poor stars also He-rich? A&A 521:A30 Meynet G, Eggenberger P, Maeder A (2011) Massive star models with magnetic braking. A&A 525:L11 Meynet G, Chomienne V, Ekström S et al (2015) Impact of mass-loss on the evolution and presupernova properties of red supergiants. A&A 575:A60 Moriya T, Groh JH, Meynet G (2013) Episodic modulations in supernova radio light curves from luminous blue variable supernova progenitor models, A&A 557:L2 Moffat AFJ (2008) A Global Assessment of Wolf-Rayet Binaries in the Magellanic Clouds. Revista Mexicana de Astronomía y Astrofísica 33:95 Piotto G, Villanova S, Bedin LR et al (2005) Metallicities on the Double Main Sequence of ¨ Centauri Imply Large Helium Enhancement. ApJ 621:777 Przybilla N, Firnstein M, Nieva MF et al (2010) Mixing of CNO-cycled matter in massive stars. A&A 517:A38 Smartt SJ (2009) Progenitors of core-collapse supernovae. Ann Rev Astron Astrophys 47:63 Smartt SJ (2015) Observational constraints on the progenitors of core-collapse supernovae: the case for missing high-mass stars. Publ Astron Soc Aust 32:e016 Smith N (2014) Mass loss: its effect on the evolution and fate of high-mass stars. Ann Rev Astron Astrophys 52:487 Song HF, Maeder A Meynet G et al (2013) Close-binary evolution. I. Tidally induced shear mixing in rotating binaries. A&A 556:A100 Song HF, Meynet G, Maeder A et al (2016) Massive star evolution in close binaries. Conditions for homogeneous chemical evolution. A&A 585:A120 Stacy A, Bromm V, Loeb A (2011) Rotation speed of the first stars. MNRAS 413:543 Tinyanont S, Kasliwal MM, Fox OD et al (2016) A systematic study of mid-infrared emission from core-collapse supernovae with SPIRITS. arXiv:1601.03440 Vink JS, de Koter A (2005) On the metallicity dependence of Wolf-Rayet winds. A&A 442:587 Von Zeipel H (1924) Radiative equilibrium of a double-star system with nearly spherical components. MNRAS 84:665 Woosley SE (1993) Gamma-ray bursts from stellar mass accretion disks around black holes. ApJ 405:273 Woosley SE, Bloom JS (2006) The supernova gamma-ray burst connection. Ann Rev Astron Astrophys 44:507 Woosley SE, Blinnikov S, Heger A (2007) Pulsational pair instability as an explanation for the most luminous supernovae. Nature 450:390

634

G. Meynet and A. Maeder

Yoon S-C, Langer N (2005) Evolution of rapidly rotating metal-poor massive stars towards gammaray bursts. A&A 443:643 Yoshida T, Umeda H (2011) A progenitor for the extremely luminous Type Ic supernova 2007bi. MNRAS 412:L78 Yusof N, Hirschi R, Meynet G et al (2013) Evolution and fate of very massive stars. MNRAS 433:1114 Zahn J-P (1992) Circulation and turbulence in rotating stars. A&A 265:115

The Progenitor of SN 1987A

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Abstract

Supernova 1987A in the Large Magellanic Cloud was the first naked-eye supernova since Kepler’s supernova in 1604. Neutrino detections from the event dramatically confirmed the long-held belief that this type of supernova is triggered by the final collapse of the core of a massive star, but in many other respects it was a very unusual, even anomalous event. The progenitor was a blue supergiant instead of a red supergiant, as had been predicted theoretically, and the system was surrounded by a spectacular triple-ring nebula that consists of material that was ejected only 20,000 years before the explosion. This chapter will discuss the mystery of the supernova progenitor and how all the evidence points toward a dramatic event that occurred some 20,000 years ago, the merger of two massive stars and how future observations will further help to prove or refute the current picture.

Contents 1 2 3 4 5 6 7

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Neutrino Burst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Mystery of the Progenitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Early Progenitor Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Triple-Ring Nebula and the Chemical Anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . The Importance of Binary Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Merger Model for SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Formation of the Triple-Ring Nebula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alternative Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Ph. Podsiadlowski () Department of Physics, University of Oxford, Oxford, UK e-mail: [email protected]; [email protected]

© Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_123

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Future Tests and Unsolved Mysteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 The Complex Outer Circumstellar Nebula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 The Missing Compact Remnant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Supernova 1987A (SN 87A) was first detected on February 23, 1987. It was the first naked-eye supernova since Kepler’s supernova in 1604, an event astronomers had long been waiting for. It occurred in the Large Magellanic Cloud (LMC), a satellite galaxy of the Milky Way in the outskirts of the Tarantula Nebula (30 Doradus), a very active region of massive star formation, in fact the closest mini-starburst we know of. At its peak, it reached a visual magnitude of 3 and could clearly be seen with the naked eye from the Southern hemisphere. The discovery of neutrinos from the supernova confirmed in a spectacular way that supernovae of this type are caused by the collapse of a massive star to a neutron star, as was first speculated by Fritz Zwicky and his colleagues in the 1930s. While this has been one of the major successes in modern theoretical astrophysics, in many other respects the supernova was quite different from what had been expected. While stellar evolution theory firmly predicted that massive hydrogen-rich stars explode as red supergiants, the progenitor, which in this case could be identified on old plates taken before the supernova, was a blue supergiant (the arrow in Fig. 1 points to it), a star that did not appear to be even close to the end of its life. Why this star exploded as a blue supergiant has remained one of the most enduring puzzles of this spectacular event and will be the topic of this chapter. As in any good mystery story, there have been many false leads and unexpected turns, but a consistent picture has emerged over the years that can describe the unusual evolution of the progenitor up to its final surprising demise. Detailed reviews on all aspects of SN 1987A can be found in Arnett et al. (1989), McCray (1993), and McCray and Fransson (2016), reviews specifically on the question of the progenitor (including all relevant references) in Podsiadlowski (1992) and Podsiadlowski et al. (2007). In this chapter, I will start by discussing the importance of the supernova neutrino burst (Sect. 2) and explain the mystery of the progenitor (Sect. 3). In Sect. 4, I will summarize the key observational clues that were essential for helping to unravel the mystery and strongly point to a binary origin for the progenitor, followed by a general discussion of binary evolution effects in Sect. 5 that are important for understanding the diversity of observed supernova events. In Sect. 6 I will discuss in detail the presently best model that can explain all the aspects of this event and in Sect. 7 possible alternative ideas as far as they exist. In Sect. 8 I will look at how future observations should be able to ultimately either prove or refute our working model and discuss some unresolved open questions, followed with some brief conclusions in Sect. 9.

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Fig. 1 Before (right) and after (left) images, taken with the AAT, of the region where SN 1987A occurred. The arrow in the left panel points at SK 69ı 202, a system of stars that contained the progenitor of the supernova, a blue supergiant

2

The Neutrino Burst

The discovery of neutrinos from the supernova proved to be one of the most spectacular successes of modern theoretical astrophysics. The two main neutrino detectors that were operating at the time discovered a total of 18 neutrinos, 11 from the Kamiokande II detector in Japan and 7 from the IMB detector in Ohio. The two detectors were two huge water detectors that discovered most of the neutrinos by the Cherenkov radiation caused by the recoil of positrons produced in the absorption of electron anti-neutrinos on the free protons in the water molecules (for more details, see Arnett et al. 1989). The neutrinos, with a typical energy of about 4 Mev, reached the detectors some 3 h before the first light could have been seen from the supernova. The reason for the delay is that, because of the weak interactions of neutrinos with matter, they can travel essentially unimpededly from outside the core to the observer, while it took some 3 h for the supernova shock triggered by the collapse to reach the surface of the progenitor, which initiates the observable supernova display. Even though there were only 18 neutrinos discovered, their cross sections with matter are sufficiently well known that it allowed astronomers to estimate the energy in the neutrino burst: assuming that there are 3 light neutrino species, the energy has

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been estimated to be E D 2:5 ˙ 1:5  1046 J, an energy that is remarkably close to the gravitational binding energy of a neutron star, roughly 10 % of its rest mass for a 1:4 Mˇ neutron star. This proved that indeed most of the energy released in the collapse of the progenitor’s core escaped in the form of neutrinos, and it remains one of the lasting theoretical problems how a fraction of this neutrino energy can be trapped by the infalling envelope to eject the rest of the star and drive an explosion, i.e., produce an observable supernova. Moreover, the neutrinos were observed over a period of 12 s, much longer than the actual collapse phase (60 Mˇ ) can only be inferred from the single-band luminosity (Foley et al. 2011; Margutti et al. 2014). A test will be done if the precursor has indeed vanished; a recent announcement seems to indicate that SN 2009ip is now at a level fainter than the star (Thöne et al. 2015); however, additional follow-up is required. More discussion

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Fig. 6 (a) A portion of a HST F547M image of the SN 2005gl site 8 years prior to explosion. Within the white circle is an object at MV  10:3 mag (L  106:0 Lˇ ), a luminosity inconsistent with a normal star. (b) An AO-assisted NIRC2 image of the SN obtained at the Keck-II telescope. (c) A portion of the same field, imaged in 2007 in F547M. The object seen 10 years earlier has vanished or faded away. The red and green circles indicate some of the fiducial objects used to register the three images (Reprinted by permission from Macmillan Publishers Ltd: Gal-Yam and Leonard 2009)

of vanishing progenitors is presented below. A similar example may be SNHunt 275 (Elias-Rosa et al. 2015). I note that the luminous blue progenitor candidate for SN 2010jl (Smith et al. 2011a) remains to be confirmed.

5.2.5 Type Ib SN Progenitors The search for SN Ib progenitors in HST data has been relatively fruitless, as seen in Table 2. SNe Ib, like SNe Ic, are thought to arise either from single, high-mass WR stars or interactive binaries with lower-mass components. The limits so far tend to discount WR stars as progenitors (Eldridge et al. 2013), unless WR stars become less luminous optically some time before they explode (Yoon et al. 2012) or the extinction to these SNe, and, therefore, their progenitors, has been underestimated (Eldridge et al. 2013). As Eldridge et al. (2013) have pointed out, binary interaction alone will not strip away all of a star’s H envelope. Below 15 Mˇ , stars must first evolve to a He giant phase to lose the rest of the mass (for stars above this limit, the mass loss is strong enough during He burning), so, in many cases, these are the stars that we would be seeking to detect. One truly exceptional case may be the possible identification of the progenitor of iPTF13bvn (Cao et al. 2013). See Fig. 7. The identified object was initially shown to have MB  5:5, MV  5:5, and MI  5:8 mag. If single, it would be consistent with the expected luminosities of WN and WC WR stars, possibly in the initial mass range of 31–35 Mˇ (Groh et al. 2013), although an interacting binary system would also be possible (Bersten et al. 2014). Eldridge et al. (2015) found that the original DOLPHOT measurements (Cao et al. 2013) were actually 0.7 to 0.2 mag too faint (from F435W to F814W), and the object is likely too luminous to be a single WR. It was proposed that a suite of binary models with masses between 10 and 20 Mˇ provided better fits to the newly measured data points (Eldridge et al. 2015). It is evident from Fig. 7 that the progenitor may sit

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Fig. 7 A portion of the HST F555W image of the iPTF13bvn site 8 years prior to explosion. The SN position, based on a HST image of the SN, is indicated by the white circle and is possibly coincident with a point source in the pre-SN image (This figure is similar to that shown in Cao et al. (2013), their Fig. 1.) North is up, and east is to the left

among a complex background. So, imaging at late times, when the SN has faded, is essential for determining whether the first SN Ib progenitor has been detected and what is its nature.

5.2.6 Type Ic SN Progenitors No progenitor, not even a candidate, has been identified for SNe Ic. SN Ic progenitors, therefore, are the current “Holy Grail” of progenitor searches. Many of the reasons that SN Ic progenitors are difficult to detect are the same as for SN Ib progenitors discussed above. However, additionally complicating the search, as shown by a number of the non-detections so far - see Table 2 - is that SNe Ic tend to occur near complex, crowded environments. Also, even when away from a crowded location, SNe Ic tend to be extinguished by, likely, interstellar dust: the reddening to a sample of SNe Ic was E.B  V / & 0:4 mag (Drout et al. 2011). This is not entirely surprising, since we expect their progenitors to be massive and relatively young, i.e., not far from their dusty natal clouds.

6

After the SN Has Faded Away

I have been referring to the “progenitor” throughout, so far, as the progenitor; however, in fact, it is still only a progenitor candidate, until very late-time imaging can be obtained to determine if the progenitor has indeed vanished. This has been accomplished for SN 1987A (Chevalier 1992), SN 1993J and SN 2003gd (Maund and Smartt 2009), SN 1997bs (Adams and Kochanek 2015), SN 2004A (Maund

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Table 3 Some SN progenitor identifications revisited SN 1999ev 2006my

Type II-P II-P

Revision Not detected Not detected?

2006ov 2008cn 2009kr 2009md

II-P II-P IIL? II-P

Not detected RSG, not YSG Not detected Not detected

Reference Maund et al. (2014a) Leonard et al. (2008), Crockett et al. (2011), and Maund et al. (2014a) Crockett et al. (2011) Maund et al. (2015a) Maund et al. (2015a) Maund et al. (2015a)

et al. 2014a), SN 2004et (Crockett et al. 2011), SN 2005cs (Maund et al. 2014a), SN 2005gl (Gal-Yam and Leonard 2009), SN 2006my (Maund et al. 2014a), SN 2008ax (Folatelli et al. 2015), SN 2008bk (Maund et al. 2014b; Van Dyk 2013) SN 2011dh (Van Dyk et al. 2013), and SN 2012aw (Fraser 2016; Van Dyk et al. 2015b). For SNe 1993J (Fox et al. 2014; Maund and Smartt 2009; Maund et al. 2004; Van Dyk et al. 2002), 2004et (Crockett et al. 2011), and 2008bk (Maund et al. 2014b; Van Dyk 2013), follow-up with HST has revealed the presence of fainter stars in the SN environment, within the seeing disks of the ground-based progenitor detections. Careful removal of the fluxes of these stars from that of the original progenitor detection, in principle, should result in the true progenitor brightness.

6.1

Revisiting Previous Detections

In a few cases, revisiting the site with HST after the SN has disappeared has led to some surprises and subsequent revisions in the original progenitor detections. These are summarized in Table 3. Notably, SNe 1999ev, 2006ov, 2009kr, and 2009md have been rendered to be non-detections after all. Crockett et al. (2011) had eliminated the SN 2006my progenitor from consideration; however, Maund et al. (2014a) added it back in through late-time HST imaging. Maund et al. (2015a) found a blue star at the position of SN 2008cn, making it now more likely that the reported yellow color for the progenitor (Elias-Rosa et al. 2009) was actually a blend of the light from the blue star with that of a RSG which has vanished. Maund et al. (2014a) re-estimated the initial masses of the SN II-P 2003gd, 2004A, 2005cs, and 2006my progenitors, based on their very late-time imaging.

6.2

Searching for a Binary Companion

As a result of very late-time imaging of stripped-envelope SN sites, one can search for the surviving companion of a putative progenitor interacting binary system. It is then possible, either accidentally or intentionally, to detect it. For the former, this may be the case for SN 1993J (Fox et al. 2014). Also, in blue and ultraviolet HST images of SN 2011dh, Folatelli et al. (2014) found a point source that may

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be consistent with predictions made by interacting binary models, although Maund et al. (2015b) offer a cautionary note. For the latter, Van Dyk et al. (2016) searched for, but did not detect, a binary companion to the SN 1994I progenitor. Additionally, in their reanalysis of the SN 2008ax progenitor, Folatelli et al. (2015) attempted to constrain the properties of an undetected companion using their theoretical binary models.

7

Conclusions

Despite a substantial amount of work exerted over more than a decade or so, the overall number of identified SN progenitors is actually yet quite small, and reaching overarching conclusions about massive stellar evolution, based on this small lot, is likely still quite premature. It is strikingly evident that we need to increase the sample greatly. However, we need nature to cooperate and provide us with a number of new, nearby examples. Happy progenitor hunting!

8

Cross-References

 Close Binary Stellar Evolution and Supernovae  Discovery, Confirmation, and Designation of Supernovae  Electron Capture Supernovae from Super Asymptotic Giant Branch Stars  Evolution of Accreting White Dwarfs to the Thermonuclear Runaway  Interacting Supernovae: Types IIn and Ibn  Spectra of Supernovae in the Nebular Phase  Observational and Physical Classification of Supernovae  Spectra of Supernovae During the Photospheric Phase  Supernovae from Massive Stars  Supernovae from Rotating Stars  Very Massive and Supermassive Stars: Evolution and Fate  Violent Mergers

References Adams SM, Kochanek CS (2015) LOSS’s first supernova? New limits on the ‘impostor’ SN 1997bs. Mon Not R Astron Soc 452:2195–2207 Aldering G, Humphreys RM, Richmond M (1994) SN 1993J: the optical properties of its progenitor. Astron J 107:662–672 Anderson J, King IR (2006) PSFs, photometry, and astronomy for the ACS/WFC. Instrument Science report ACS 2006-01, 34pp Anderson JP, Habergham SM, James PA, Hamuy M (2012) Progenitor mass constraints for corecollapse supernovae from correlations with host galaxy star formation. Mon Not R Astron Soc 424:1372–1391 Anderson JP, González-Gaitán S, Hamuy M et al (2014) Characterizing the V-band light-curves of hydrogen-rich Type II supernovae. Astrophys J 786(id.67):35

28 Supernova Progenitors Observed with HST

713

Asplund M, Grevesse N, Sauval AJ, Scott P (2009) The chemical composition of the sun. Annu Rev Astron Astrophys 47:481–522 Barbon R, Ciatti F, Rosino L (1979) Photometric properties of Type II supernovae. Astron Astrophys 72:287–292 Barth AJ, Van Dyk SD, Filippenko AV et al (1996) The environments of supernovae in archival hubble space telescope images. Astron J 111:2047–2058 Bersten MC, Benvenuto O, Hamuy M (2011) Hydrodynamical models of Type II plateau supernovae. Astrophys J 729(id.61):19 Bersten MC, Benvenuto O, Folatelli G et al (2014) iPTF13bvn: the first evidence of a binary progenitor for a Type Ib supernova. Astron J 148(id.68):6 Bose S, Sutaria F, Kumar B et al (2015) SN 2013ej: a Type IIL supernova with weak signs of interaction. Astrophys J 806(id.160):18 Cao Y, Kasliwal MM, Arcavi I et al (2013) Discovery, progenitor and early evolution of a stripped envelope supernova iPTF13bvn. Astrophys J 775(id.L7):7 Cardelli JA, Clayton GC, Mathis JS (1989) The relationship between infrared, optical, and ultraviolet extinction. Astrophys J 345:245–256 Castelli F, Kurucz RL (2003) New grids of ATLAS9 model atmospheres. In: Piskunov N, Weiss WW, Gray DF (eds) Modelling of stellar atmospheres. ASP, San Francisco, p A20 Chen Y, Bressan A, Girardi L et al (2015) PARSEC evolutionary tracks of massive stars up to 350 Mˇ at metallicities 0:0001 Z 0:04. Mon Not R Astron Soc 452:1068–1080 Chevalier RA (1992) Supernova 1987A at five years of age. Nature 355:691–696 Chevalier RA, Soderberg AM (2010) Type IIb supernovae with compact and extended progenitors. Astrophys J 711:L40–L43 Cohen JG, Darling J, Porter A (1995) The nonvariability of the progenitor of supernova 1993J in M81. Astron J 110:308–311 Crockett RM, Smartt SJ, Eldridge JJ et al (2007) A deeper search for the progenitor of the Type Ic supernova 2002ap. Mon Not R Astron Soc 381:835–850 Crockett RM, Maund JM, Smartt SJ et al (2008a) The birth place of the Type Ic supernova 2007gr. Astrophys J 672:L99–L102 Crockett RM, Eldridge JJ, Smartt SJ et al (2008b) The Type IIb SN 2008ax: the nature of the progenitor. Mon Not R Astron Soc 391:L5–L9 Crockett RM, Smartt SJ, Pastorello A et al (2011) On the nature of the progenitors of three Type II-P supernovae: 2004et, 2006my and 2006ov. Mon Not R Astron Soc 410:2767–2786 Dalcanton JJ, Williams BF, Seth AC et al (2009) The ACS nearby galaxy survey treasury. Astrophys J Supp 183:67–108 Dall’Ora M, Botticella MT, Pumo ML et al (2014) The Type IIP supernova 2012aw in M95: hydrodynamical modeling of the photospheric phase from accurate spectrophotometric monitoring. Astrophys J 787(id.139):18 de Jaeger T, González-Gaitán S, Anderson JP et al (2015) A hubble diagram from Type II supernovae based solely on photometry: the photometric color method. Astrophys J 815(id.121):13 Dolphin AE (2000a) WFPC2 stellar photometry with HSTPHOT. Publ Astron Soc Pac 112:1383– 1396 Dolphin AE (2000b) The charge-transfer efficiency and calibration of WFPC2. Publ Astron Soc Pac 112:1397–1410 Drout MR, Soderberg AM, Gal-Yam A et al (2011) The first systematic study of Type Ibc supernova multi-band light curves. Astrophys J 741(id.97):20 Eggleton PP (1971) The evolution of low mass stars. Mon Not R Astron Soc 151:351–364 Ekstöm S, Georgy C, Eggenberger P et al (2012) Grids of stellar models with rotation. I. models from 0.8 to 120 Mˇ at solar metallicity (Z = 0.014). Astron Astrophys 537(id.A146):18 Eldridge JJ, Fraser M, Smartt SJ et al (2013) The death of massive stars – II. observational constraints on the progenitors of Type Ibc supernovae. Mon Not R Astron Soc 436:774–795 Eldridge JJ, Fraser M, Maund JR, Smartt SJ (2015) Possible binary progenitors for the Type Ib supernova iPTF13bvn. Mon Not R Astron Soc 446:2689–2695

714

S.D. Van Dyk

Elias-Rosa N, Van Dyk SD, Li W et al (2009) On the progenitor of the Type II-Plateau SN 2008cn in NGC 4603. Astrophys J 706:1174–1183 [Erratum: Astrophys. J. 711, 1343 (2010)] Elias-Rosa N, Van Dyk SD, Li W et al (2010) The massive progenitor of the Type II-linear supernova 2009kr. Astrophys J 714:L254–L259 Elias-Rosa N, Van Dyk SD, Li W et al (2011) The massive progenitor of the possible Type II-linear supernova 2009hd in Messier 66. Astrophys J 742(id.6):11 Elias-Rosa N (2013) The progenitors of stripped-envelope supernovae. In: Guirado JC, Lara LM, Quilis V, Gorgas J (eds) Highlights of Spanish astrophysics VII. Spanish Astronomical Society, Valencia, pp 649–649 Elias-Rosa N, Pastorello A, Maund JR et al (2013) On the progenitor of the Type Ic SN 2013dk in the Antennae galaxies. Mon Not R Astron Soc 436:L109–L113 Elias-Rosa N, Benetti S, Tomasella L et al (2015) Asiago spectroscopic classification of the SN impostor SNhunt275. Astron Telegram No. 7042 Faran T, Poznanski D, Filippenko AV et al (2014) A sample of Type II-L supernovae. Mon Not R Astron Soc 445:554–569 Filippenko AV (1997) Optical spectra of supernovae. Annu Rev Astron Astrophys 35:309–355 Filippenko AV, Barth AJ, Bower GC et al (1995) Was Fritz Zwicky’s “Type V” SN 1961V a Genuine Supernova? Astron J 110:2261–2273 Flower PJ (1996) Transformations from theoretical Hertzsprung-Russell diagrams to colormagnitude diagrams: effective temperatures, B-V colors, and bolometric corrections. Astrophys J 469:355–365 Folatelli G, Bersten MC, Benvenuto OG et al (2014) A blue point source at the location of supernova 2011dh. Astrophys J 793(id.L22):5 Folatelli G, Bersten MC, Kuncarayakti H et al (2015) The progenitor of the Type IIb SN 2008ax revisited. Astrophys J 811(id.147):13 Foley RJ, Berger E, Fox O et al (2011) The diversity of massive star outbursts. I. observations of SN 2009ip, UGC 2773 OT2009-1, and their progenitors. Astrophys J 732(id.32):13 Foley RJ, Van Dyk SD, Jha SW et al (2015) On the progenitor system of the Type Iax supernova 2014dt in M61. Astrophys J 798(id.L37):4 Fox OD, Bostroem KA, Van Dyk SD et al (2014) Uncovering the putative B-star binary companion of the SN 1993J progenitor. Astrophys J 790(id.17):13 Fraser M (2016) The disappearance of the progenitor of SN 2012aw in late-time imaging. Mon Not R Astron Soc 456:L16–L19 Fraser M, Takáts K, Pastorello A et al (2010) On the progenitor and early evolution of the Type II supernova 2009kr. Astrophys J 714:L280–L284 Fraser M, Ergon M, Eldridge JJ et al (2011) SN 2009md: another faint supernova from a low-mass progenitor. Mon Not R Astron Soc 417:1417–1433 Fraser M, Maund JR, Smartt SJ et al (2012) Red and dead: the progenitor of SN 2012aw in M95. Astrophys J 759(id.L13):5 Fraser M, Inserra C, Jerkstrand A et al (2013a) SN 2009ip à la PESSTO: no evidence for core collapse yet. Mon Not R Astron Soc 433:1312–1337 Fraser M, Magee M, Kotak R et al (2013b) Detection of an outburst one year prior to the explosion of SN 2011ht. Astrophys J 779(id.L8):6 Fraser M, Maund JR, Smartt SJ et al (2014) On the progenitor of the Type IIP SN 2013ej in M74. Mon Not R Astron Soc 439:L56–L60 Fraser M, Kotak R, Pastorello A et al (2015) SN 2009ip at late times – an interacting transient at +2 years. Mon Not R Astron Soc 453:3886–3905 Freedman WL, Madore BF, Mould JR et al (1994) Distance to the Virgo cluster galaxy M100 from Hubble Space Telescope observations of Cepheids. Nature 371:757–762 Fruchter AS, Hack W, Dencheva N et al (2010) BetaDrizzle: a redesign of the multiDrizzle package. In: Deustua S, Oliveira C (eds) Space telescope science institute calibration workshop proceedings, STScI, Baltimore, pp 376–381 Gall EEE, Polshaw J, Kotak R et al (2015) A comparative study of Type II-P and II-L supernova rise times as exemplified by the case of LSQ13cuw. Astron Astrophys 582(id.A3):19

28 Supernova Progenitors Observed with HST

715

Gal-Yam A, Leonard DC (2009) A massive hypergiant star as the progenitor of the supernova SN 2005gl. Nature 458:865–867 Gal-Yam A, Fox DB, Kulkarni SR et al (2005) A high angular resolution search for the progenitor of the Type Ic Supernova 2004gt. Astrophys J 630:L29–L32 Gal-Yam A, Leonard DC, Fox DB et al (2007) On the progenitor of SN 2005gl and the nature of Type IIn Supernovae. Astrophys J 656:372–381 Georgy C (2012) Yellow supergiants as supernova progenitors: an indication of strong mass loss for red supergiants? Astron Astrophys 538(id.L8):5 Gilmozzi R, Cassatella A, Clavel J et al (1987) The progenitor of SN 1987A. Nature 328:318–320 Gonzaga S, Hack W, Fruchter A, Mack J (eds) (2012) The DrizzlePac handbook. STScI, Baltimore Graham ML, Sand DJ, Valenti S et al (2014) Clues to the nature of SN 2009ip from photometric and spectroscopic evolution to late times. Astroph J 787(id.163):16 Graur O, Maoz D, Shara MM (2014) Progenitor constraints on the Type-Ia supernova SN 2011fe from pre-explosion Hubble Space Telescope He II narrow-band observations. Mon Not R Astron Soc 442:L28–L32 Groh JH, Georgy C, Ekström S (2013) Progenitors of supernova Ibc: a single Wolf-Rayet star as the possible progenitor of the SN Ib iPTF13bvn. Astron Astrophys 558(id.L1):4 Gustafsson B, Edvardsson B, Eriksson K et al (2008) A grid of MARCS model atmospheres for late-type stars. I. Methods and general properties. Astron Astrophys 486:951–970 Hendry MA, Smartt SJ, Maund JR et al (2005) A study of the Type II-P supernova 2003gd in M74. Mon Not R Astron Soc 359:906–926 Hendry MA, Smartt SJ, Crockett RM et al (2006) SN 2004A: another Type II-P supernova with a red supergiant progenitor. Mon Not R Astron Soc 369:1303–1320 Holtzman JA, Hester JJ, Casertano S et al (1995) The performance and calibration of WFPC2 on the Hubble Space Telescope. Publ Astron Soc Pac 107:156–178 Huang F, Wang X, Zhang J et al (2015) SN 2013ej in M74: a luminous and fast-declining Type II-P Supernova. Astroph J 807(id.59):12 Humphreys EML, Reid MJ, Moran JM et al (2013) Toward a new geometric distance to the active galaxy NGC 4258. III. Final results and the Hubble constant. Astroph J 775(id.13):10 Isserstedt J (1975) Photoelectric photometry of supergiants in the Large Magellanic Cloud. Astron Astrophys Suppl 19:259–269 Jerkstrand A, Fransson C, Maguire K et al (2012) The progenitor mass of the Type IIP supernova SN 2004et from late-time spectral modeling. Astron Astrophys 546(id.A28):21 Kankare E, Mattila S, Ryder S et al (2014) The nature of supernovae 2010O and 2010P in Arp 299 – I. Near-infrared and optical evolution. Mon Not R Astron Soc 440:1052–1066 Kelly PL, Kirshner RP, Pahre M (2008) Long -ray bursts and Type Ic core-collapse supernovae have similar locations in hosts. Astroph J 687:1201–1207 Kelly PL, Fox OD, Filippenko AV et al (2014) Constraints on the progenitor system of the Type Ia Supernova 2014J from pre-explosion Hubble Space Telescope Imaging. Astroph J 790(id.3):9 Kewley LJ, Ellison SL (2008) Metallicity calibrations and the mass-metallicity relation for starforming galaxies. Astroph J 681:1183–1204 Kochanek CS, Szczygiel DM, Stanek KZ (2011) The Supernova Impostor Impostor SN 1961V: spitzer shows that Zwicky was right (again). Astroph J 737(id.76):11 Kochanek CS, Khan R, Dai X (2012) On absorption by circumstellar dust, with the progenitor of SN 2012aw as a case study. Astroph J 759(id.20):10 Kuncarayakti H, Maeda K, Bersten MC et al (2015) Nebular phase observations of the Type-Ib supernova iPTF13bvn favour a binary progenitor. Astron Astrophys 579(id.A95):9 Kurucz R (1993) ATLAS9 stellar atmosphere programs and 2 km/s grid. Kurucz CD-ROM, No. 13. Smithsonian Astrophysical Observatory, Cambridge Lee MG, Freedman WL, Madore BF (1993) The tip of the red giant branch as a distance indicator for resolved galaxies. Astrophys J 417:553–559 Leonard DC, Gal-Yam A, Fox DB et al (2008) An upper mass limit on a red supergiant progenitor for the Type II-Plateau Supernova SN 2006my. Publ Astron Soc Pac 120:1259–1266

716

S.D. Van Dyk

Levesque EM, Massey P, Olsen KAG et al (2005) The effective temperature scale of galactic red supergiants: cool, but not as cool as we thought. Astrophys J 628:973–985 Li W, Van Dyk SD, Filippenko AV, Cuillandre J-C (2005) On the progenitor of the Type II Supernova 2004et in NGC 6946. Publ Astron Soc Pac 117:121–131 Li W, Van Dyk SD, Filippenko AV et al (2006) Identification of the red supergiant progenitor of Supernova 2005cs: do the progenitors of Type II-P supernovae have low mass? Astrophys J 641:1060–1070 Li W, Wang X, Van Dyk SD et al (2007) On the progenitors of two Type II-P Supernovae in the Virgo cluster. Astrophys J 661:1013–1024 Li W, Bloom JS, Podsiadlowski P et al (2011) Exclusion of a luminous red giant as a companion star to the progenitor of supernova SN 2011fe. Nature 480:348–350 Maíz-Apellániz J, Bond HE, Siegel MH et al (2004) The progenitor of the Type II-P SN 2004dj in NGC 2403. Astrophys J 615:L113–L116 Mamajek EE, Torres G, Prsa A et al (2015) IAU 2015 resolution B2 on recommended zero points for the absolute and apparent bolometric magnitude scales. eprint arXiv:1510.06262 Maoz D, Mannucci F (2008) A search for the progenitors of two Type Ia Supernovae in NGC 1316. Mon Not R Astron Soc 388:421–428 Maoz D, Mannucci F, Nelemans G (2014) Observational clues to the progenitors of Type Ia Supernovae. Annu Rev Astron Astrophys 52:107–170 Margutti R, Miliisavljevic D, Soderberg AM et al (2014) A panchromatic view of the restless SN 2009ip reveals the explosive ejection of a massive star envelope. Astrophys J 780(id.21):38 Mattila S, Smartt SJ, Eldridge JJ et al (2008) VLT detection of a red supergiant progenitor of the Type II-P Supernova 2008bk. Astrophys J 688:L91–L94 Mauerhan JC, Smith N, Filippenko AV et al (2013) The unprecedented 2012 outburst of SN 2009ip: a luminous blue variable star becomes a true supernova. Mon Not R Astron Soc 430:1801–1810 Mauerhan J, Williams GG, Smith N et al (2014) Multi-epoch spectropolarimetry of SN 2009ip: direct evidence for aspherical circumstellar material. Mon Not R Astron Soc 442:1166–1180 Maund JR, Smartt SJ (2005) Hubble Space Telescope imaging of the progenitor sites of six nearby core-collapse supernovae. Mon Not R Astron Soc 360:288–304 Maund JR, Smartt SJ (2009) The disappearance of the progenitors of supernovae 1993J and 2003gd. Science 324:486–488 Maund JR, Smartt SJ, Kudritzki RP et al (2004) The massive binary companion star to the progenitor of supernova 1993J. Nature 427:129–131 Maund JR, Smartt SJ, Schweizer F (2005a) Luminosity and mass limits for the progenitor of the Type Ic Supernova 2004gt in NGC 4038. Astrophys J 630:L33–L36 Maund JR, Smartt SJ, Danziger IJ (2005b) The progenitor of SN 2005cs in the Whirlpool Galaxy. Mon Not R Astron Soc 364:L33–L37 Maund JR, Fraser M, Ergon M et al (2011) The yellow supergiant progenitor of the Type II Supernova 2011dh in M51. Astrophys J 739(id.L37):5 Maund JR, Fraser M, Smartt SJ et al (2013) Supernova 2012ec: identification of the progenitor and early monitoring with PESSTO. Mon Not R Astron Soc 431:L102–L106 Maund JR, Reilly E, Mattila S (2014a) A late-time view of the progenitors of five Type IIP supernovae. Mon Not R Astron Soc 438:938–958 Maund JR, Mattila S, Ramirez-Ruiz E, Eldridge JJ (2014b) A new precise mass for the progenitor of the Type IIP SN 2008bk. Mon Not R Astron Soc 438:1577–1592 Maund JR, Fraser M, Reilly E et al (2015a) Whatever happened to the progenitors of supernovae 2008cn, 2009kr and 2009md? Mon Not R Astron Soc 447:3207–3217 Maund JR, Arcavi I, Ergon M et al (2015b) Did the progenitor of SN 2011dh have a binary companion? Mon Not R Astron Soc 454:2580–2585 McCully C, Jha SW, Foley RJ et al (2014) A luminous, blue progenitor system for the Type Iax supernova 2012Z. Nature 512:54–56 Milisavljevic D, Fesen RA, Chevalier RA et al (2012) Late-time optical emission from corecollapse supernovae. Astrophys J 751(id.25):14

28 Supernova Progenitors Observed with HST

717

Nakano S, Itagaki K, Puckett T (2006) Possible Supernova in UGC 4904, vol 666. Central Bureau Electronic Telegrams, Cambridge, MA, USA Ofek EO, Sullivan M, Cenko SB et al (2013) An outburst from a massive star 40 days before a supernova explosion. Nature 494:65–67 Felipe Olivares E, Hamuy M, Pignata G et al (2010) The standardized candle method for Type II Plateau Supernovae. Astrophys J 715:833–853 Pastorello A, Crockett RM, Martin R et al (2009) SN 1999ga: a low-luminosity linear Type II supernova? Astron Astrophys 500:1013–1023 Pastorello A, Cappellaro E, Inserra C et al (2013) Interacting supernovae and supernova impostors: SN 2009ip, is this the End? Astrophys J 767(id.1):19 Phillips MM, Simon JD, Morrell N et al (2013) On the source of the dust extinction in Type Ia Supernovae and the discovery of anomalously strong Na I absorption. Astrophys J 779(id.38):21 Pilyugin LS, Vlchez JM, Thuan TX (2010) New improved calibration relations for the determination of electron temperatures and oxygen and nitrogen abundances in H II regions. Astrophys J 720:1738–1751 Poznanski D, Butler N, Filippenko AV et al (2009) Improved standardization of Type II-P Supernovae: application to an expanded sample. Astrophys J 694:1067–1079 Poznanski D, Prochaska JX, Bloom JS (2012) An empirical relation between sodium absorption and dust extinction. Mon Not R Astron Soc 426:1465–1474 Prieto JL, Kistler MD, Thompson TA et al (2008) Discovery of the dust-enshrouded progenitor of SN 2008S with Spitzer. Astrophys J 681:L9–L12 Prieto JL, Osip D, Palunas P (2012) Candidate progenitor of the Type II SN 2012A in the Near-IR. Astron Telegram No. 3863 Prieto JL, Brimacombe J, Drake AJ, Howerton S (2013) The 2012 rise of the remarkable Type IIn SN 2009ip. Astrophys J 763(id.L27):5 Radburn-Smith DJ, Dalcanton JJ, De Jong RS, Streich D, Vlajic M, Seth AC et al (2011) The GHOSTS survey. I. Hubble Space Telescope advanced camera for surveys data. Astrophys J Supp 195(id.18):22 Rousseau J, Martin N, Prévot L et al (1978) Studies of the Large Magellanic Cloud stellar content: III. spectral types and V magnitudes of 1822 members. Astron Astrophys Suppl 31:243–260 Ryder S, Staveley-Smith L, Dopita M et al (1993) SN 1978K: an extraordinary supernova in the nearby galaxy NGC 1313. Astrophys J 416:167–181 Sana H, de Mink SE, de Koter A et al (2012) Binary interaction dominates the evolution of massive stars. Science 337:444–446 Sanders NE, Soderberg AM, Gezari S et al (2015) Toward characterization of the Type IIP supernova progenitor population: a statistical sample of Light Curves from Pan-STARRS1. Astrophys J 799(id.208):23 Schlafly EF, Finkbeiner DP (2011) Measuring reddening with sloan digital sky survey stellar spectra and recalibrating SFD. Astrophys J 737(id.103):13 Schlafly EF, Green G, Finkbeiner DP et al (2014) A map of dust reddening to 4.5 kpc from PanSTARRS1. Astrophys J 789(id.15):9 Schmidt BP, Kirshner RP, Eastman RG (1992) Expanding photospheres of Type II supernovae and the extragalactic distance scale. Astrophys J 395:366–386 Sirianni M, Jee MJ, Benítez N et al (2005) The photometric performance and calibration of the Hubble Space Telescope Advanced Camera for Surveys. Publ Astron Soc Pac 117:1049–1112 Smartt SJ, Gilmore GF, Trentham N et al (2001) An upper mass limit for the progenitor of the Type II-P supernova SN 1999gi. Astrophys J 556:L29–L32 Smartt SJ, Gilmore GF, Tout CA, Hodgkin ST (2002a) The nature of the progenitor of the Type II-P Supernova 1999em. Astrophys J 565:1089–1100 Smartt SJ, Vreeswijk PM, Ramirez-Ruiz E et al (2002b) On the progenitor of the Type Ic supernova 2002ap. Astrophys J 572:L147–L151 Smartt SJ, Maund JR, Gilmore GF et al (2003) Mass limits for the progenitor star of supernova 2001du and other Type II-P supernovae. Mon Not R Astron Soc 343:735–749

718

S.D. Van Dyk

Smartt SJ, Maund JR, Hendry MA et al (2004) Detection of a red supergiant progenitor star of a Type II-Plateau supernova. Science 303:499–503 Smartt SJ, Eldridge JJ, Crockett RM, Maund JR (2009) The death of massive stars I. Observational constraints on the progenitors of Type II-P supernovae. Mon Not R Astron Soc 395:1409–1437 Smartt SJ (2015) Observational constraints on the progenitors of core-collapse supernovae: the case for missing high-mass stars. Publ Astron Soc Austr 32(id.e016):22 Smith N, Miller A, Li W et al (2010) Discovery of precursor luminous blue variable outbursts in two recent optical transients: the fitfully variable missing links UGC 2773-OT and SN 2009ip. Astron J 139:1451–1467 Smith N, Li W, Miller AA et al (2011a) A massive progenitor of the luminous Type IIn Supernova 2010jl. Astrophys J 732(id.63):6 Smith N, Li W, Silverman JM et al (2011b) Luminous blue variable eruptions and related transients: diversity of progenitors and outburst properties. Mon Not R Astron Soc 415:773–810 Sonneborn G, Altner B, Kirshner RP (1987) The progenitor of SN 1987A – spatially resolved ultraviolet spectroscopy of the supernova field. Astrophys J 323:L35–L39 Stancliffe RJ, Eldridge JJ (2009) Modelling the binary progenitor of Supernova 1993J. Mon Not R Astron Soc 396:1699–1708 Stetson PB (1987) DAOPHOT – a computer program for crowded-field stellar photometry. Publ Astron Soc Pac 99:191–222 Takáts K, Pignata G, Pumo ML et al (2015) SN 2009ib: a Type II-P supernova with an unusually long plateau. Mon Not R Astron Soc 450:3137–3154 Thöne C, de Ugarte Postigo A, Leloudas G et al (2015) SN 2009ip is now below the proposed progenitor level observed in 1999. Astron Telegram No. 8417 Tomasella L, Cappellaro E, Fraser M et al (2013) Comparison of progenitor mass estimates for the Type IIP SN 2012A. Mon Not R Astron Soc 434:1636–1657 Torres G (2010) On the use of empirical bolometric corrections for stars. Astron J 140:1158–1162 Valenti S, Sand D, Stritzinger M et al (2015) Supernova 2013by: a Type IIL supernova with a IIP-like light-curve drop. Mon Not R Astron Soc 448:2608–2616 Van Dyk SD (2013) An echo of supernova 2008bk. Astron J 146(id.24):6 Van Dyk SD, Matheson T (2012) It’s Alive! The supernova impostor 1961V. Astrophys J 746(id.179):10 Van Dyk SD, Peng CY, Barth AJ, Filippenko AV (1999) The environments of supernovae in postrefurbishment Hubble Space Telescope Images. Astron J 118:2331–2349 Van Dyk SD, Garnavich PM, Filippenko AV et al (2002) The progenitor of supernova 1993J revisited. Publ Astron Soc Pac 114:1322–1332 Van Dyk SD, Li W, Filippenko AV (2003a) A search for core-collapse supernova progenitors in Hubble Space Telescope Images. Publ Astron Soc Pac 115:1–20 Van Dyk SD, Li W, Filippenko AV (2003b) On the progenitor of supernova 2001du in NGC 1365. Publ Astron Soc Pac 115:448–452 Van Dyk SD, Li W, Filippenko AV (2003c) On the progenitor of the Type II-Plateau supernova 2003gd in M74. Publ Astron Soc Pac 115:1289–1295 Van Dyk SD, Li W, Cenko SB et al (2011) The progenitor of supernova 2011dh/PTF11eon in Messier 51. Astrophys J 741(id.L28):5 Van Dyk SD, Davidge TJ, Elias-Rosa N et al (2012a) Supernova 2008bk and its red supergiant progenitor. Astron J 143(id.19):12 Van Dyk SD, Cenko SB, Poznanski D et al (2012b) The red supergiant progenitor of supernova 2012aw (PTF12bvh) in Messier 95. Astrophys J 756(id.131):9 Van Dyk SD, Zheng W, Clubb KI et al (2013) The progenitor of supernova 2011dh has vanished. Astrophys J 772(id.L32):5 Van Dyk SD, Zheng WK, Fox OD et al (2014) The Type IIb supernova 2013df and its cool supergiant progenitor. Astron J 147(id.37):9 Van Dyk SD, Lee JC, Sabbi E et al (2015a) Supernova progenitors and a light echo in LEGUS galaxies. In: AAS meeting of the American Astronomical Society, Seattle, vol 225, Id.140.25

28 Supernova Progenitors Observed with HST

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Van Dyk SD, Lee JC, Anderson J et al (2015b) LEGUS discovery of a light echo around supernova 2012aw. Astrophys J 806(id.195):9 Van Dyk SD, de Mink SE, Zapartas E (2016) Constraints on the binary companion to the SN Ic 1994I progenitor. Astroph J 818:75 Walborn NR, Prevot ML, Prevot L et al (1989) The spectrograms of Sanduleak -69.202 deg, precursor to supernova 1987A in the Large Magellanic Cloud. Astron Astrophys 219:229–236 Weaver TA, Zimmerman GB, Woosley SE (1978) Presupernova evolution of massive stars. Astroph J 225:1021–1029 White GL, Malin DF (1987) Possible binary star progenitor for SN 1987A. Nature 327:36–38 Williams BF, Peterson S, Murphy J et al (2014a) Constraints for the progenitor masses of 17 Historic core-collapse supernovae. Astroph J 791(id.105):9 Williams BF, Lang D, Dalcanton JJ et al (2014b) The panchromatic hubble andromeda treasury. X. Ultraviolet to infrared photometry of 117 million equidistant stars. Astrophys J Suppl 215(id.9):34 Woosley SE, Weaver TA (1986) The physics of supernova explosions. Annu Rev Astron Astrophys 24:205–253 Yoon S-C, Cantiello M (2010) Evolution of massive stars with pulsation-driven superwinds during the red supergiant phase. Astrophys J 717:L62–L65 Yoon S-C, Gräfener G, Vink JS et al (2012) On the nature and detectability of type Ib/c supernova progenitors. Astron Astrophys 544(id.L11):5 Zwicky F (1964) NGC 1058 and its supernova 1961. Astrophys J 139:514–519

Part V Light Curves and Spectra of Supernovae

Light Curves of Type I Supernovae

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Melina C. Bersten and Paolo A. Mazzali

Abstract

The light curve of Type I supernovae (SNe I), i.e. the explosion of H-deficient stars, is mainly powered by radioactive decay. Despite their different physical origin, thermonuclear explosions of white dwarfs (SNe Ia) and core-collapse explosions of massive stars with H-free envelopes (SNe Ib/c) can be understood in the same framework. The overall morphology of the light curves is similar for all SNe I. The small radius of the progenitor is responsible for the rapid degrading of the shock energy, leading to a fast initial peak that is usually unobserved. Thereafter, the luminosity of the SN and the shape of its light curve are determined by the radioactive energy input (56 Ni and 56 Co are the primary radioactive isotopes that power the light curve) and by the mass of the ejecta and the energy of the explosion. The energy of the explosion sets the expansion velocity which then critically determines the density and opacity of the gas. Physical parameters of the progenitor star and the explosion itself can be estimated from the shape of the light curve or derived more accurately by modeling the evolution of the light curve and the spectra simultaneously.

M.C. Bersten () Member of the Carrera del Investigador Científico de la Comisión de Investigaciones Científicas de la Provincia de Buenos Aires (CIC), La Plata (Bs A), Argentina Institute of Astrophysics La Plata (IALP), CCT-CONICET-UNLP, La Plata, Argentina Faculty of Astronomical and Geophysical Sciences, National University of La Plata, La Plata, Argentina Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan e-mail: [email protected]; [email protected] P.A. Mazzali Astrophysics Research Institute, Liverpool John Moores University, Liverpool, UK e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_25

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Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Light-Curve Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Characteristic Phases: Heating and Cooling Processes . . . . . . . . . . . . . . . . . . . . . 2.2 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Numerical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Analytic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Physical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Observed Properties of SN I Light Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

The evolution of the supernova luminosity – its light curve (LC) – provides valuable information about the explosion, and it can be understood in terms of the heating and cooling processes that take place. Before analyzing these processes, we discuss some important basic concepts of SN events. Typically, a SN has a luminosity of 108 –109 Lˇ for a period of weeks to months, which is comparable to the luminosity of the host galaxy. This radiative energy corresponds to only 1 % of their typical kinetic energy, which is 1051 erg (a quantity commonly known as 1 foe or, more recently, as 1 Bethe). The characteristic broad P-Cygni profiles in SN spectra, with mean expansion velocities of the order of 104 km s1 , are an indication of a rapidly expanding atmosphere. In addition, the observed temperatures near maximum brightness are 1–2 Tˇ , (where Tˇ stands for the effective temperature of the Sun), which implies radii of 105 Rˇ , assuming spherical symmetry and that the SN radiates as a black body. This means that SNe are necessarily objects with large surface areas. In the case of CCSNe, the kinetic energy represents only 1% of the energy released during the explosion. The remaining 99% (1053 erg) is carried away by neutrinos created during the collapse of the core. An important point to consider in any analysis of SN LCs is that due to the difficulty of modeling the explosion from first principles, the SN problem is usually decoupled into two independent parts: the explosion trigger and the ejection of the stellar mass. This is because of the difference in energetic and timescales between the two processes (seconds for the explosion itself and days for the ejected envelope). The energy transferred to the envelope (which we call explosion energy) plays the role of a coupling parameter between the internal and external parts of the problem. In addition, the processes that control the envelope ejection and the supernova radiation do not depend on how the energy is transferred to the envelope as long as this process occurs in a short enough time. The explosion trigger of course can have a significant effect on the light curve through the amount of 56 Ni created in the first few seconds. Based on the propagation of the explosion through the envelope, independently of how it is triggered, it is possible to study the observational outcome of the explosion, such as LCs and spectra.

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In a very simplistic view, a SN can be thought as a star where a large amount of energy is suddenly released. This energy produces a powerful shock wave that heats and accelerates the matter leading to expansion and radiation. During the explosion violent nuclear burning occurs transforming some of the ejecta matter into heavier elements. First the star is opaque to its thermal energy until it expands enough to allow the photons to diffuse away. The efficiency of the conversion of the conversion of internal energy into kinetic energy depends on the structure of the progenitor star. This conversion reduces the amount of thermal energy available to be radiated. In compact stars, as in the case of SNe I, most of the thermal energy is used during the initial expansion, and by the moment that photons can easily escape, the ejecta have cooled substantially. This process alone would thus produce a rapid decrease in the LC of the SN, which would become quite faint within just a few days after the explosion. Therefore, an additional source of heating is required to sustain the luminosity increase to maximum light and the later long-term exponential tail. This extra source is the decay of radioactive isotopes produced during explosive burning. This decay produces energetic photons and positrons that become trapped in the SN ejecta thus heating the material. Radioactive decay is not affected by the expansion of the ejecta, and it provides the extra source of heating to power the luminosity by the time that the SN has expanded enough (Colgate and White 1966). In summary, the SN LC will be determined by the size and mass of the progenitor, the energy of the explosion, and the amount of radioactive material produced in the ejecta. The speed of the expansion regulates the decrease of the opacity and hence the release of the radiation that is trapped in the ejecta, thus contributing in a substantial way to the shape and intensity of the light curve.

2

Light-Curve Physics

2.1

Characteristic Phases: Heating and Cooling Processes

The LC of a normal SN is powered by the shock energy (or explosion energy) and the radioactive decay mainly of 56 Ni that is synthesized during the explosion. Cooling is dominated by the loss of photons (“diffusion cooling”) and the expansion of the ejecta (“adiabatic cooling”). LC phases can be defined in terms of the dominant heating or cooling process at each moment. Figure 1 shows typical bolometric LCs of a SN I where different phases can be identified. The main features of the LC can be understood in terms of the following processes: shock emergence, expansion and radiative diffusion, recombination, and heating by radioactive decay. The latter process depends strongly on the composition of the SN ejecta. For SNe II, large amounts of H produce a strong recombination effect that drives the “plateau” phase. Before electromagnetic emission emerges, a shock wave (SW) propagates through the envelope of the star. The velocities acquired by the matter are so high that they exceed the local speed of sound, leading to the formation of a SW. The

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Fig. 1 Bolometric light curve of Type I supernovae calculated using a hydrodynamical code (Bersten et al. 2011). The different phases during the luminosity evolution (see Sect. 2.1) are indicated in the plot. Actually, the model presented here corresponds to the explosion of a compact object to which an extended thin envelope was attached. This envelope was included to more clearly show the cooling phase. However, we note that the duration of this phase for typical Type I progenitors is very short ( 1 hr), and it has never been observed for type Ia or Ic objects. For type Ib SNe, there are very few cases where some early emission was detected probably associated to this cooling phase

SW heats and accelerates the matter depositing mechanical and thermal energy into successive layers of the envelope until it reaches the surface, where photon diffusion dominates, and energy begins to be radiated away (Grasberg et al. 1971; Weaver 1976). The SW propagation is a complex problem that needs to be treated numerically. After the shock passes, the gas becomes radiation dominated, and the energy is more or less equally divided between kinetic and internal energy. When the shock arrives at regions where the optical depth falls to ' vSW =c (where vSW is the shock wave velocity), photons can escape, and the SN produces the first electromagnetic signature of the explosion. This is usually called “shock breakout.” The effective temperature and bolometric luminosity suddenly rise and reach their maximum values a few hours after breakout. Because of the high temperature, shock breakout emission is in the UV/X-ray or even gamma ray regime depending on the progenitor properties. Soon after shock emergence, acceleration of the material ends, and the expansion becomes nearly homologous (see e.g. Falk and Arnett 1977) The breakout is followed by a violent expansion, resulting in the cooling of the outermost layers and an increase in photospheric radius. The bolometric luminosity abruptly decreases, but, because of the decrease in effective temperature and the consequent shift of the emission peak to longer wavelengths, the luminosity in the optical range increases. During the expansion only a small fraction of the photon energy can diffuse into the surroundings. Therefore, it is possible to consider the cooling process to be approximately adiabatic, and this approximation remains

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valid, while the timescale for radiation diffusion is much longer than the expansion timescale. Note that the expansion timescale, h D R=v, increases with time, while the diffusion timescale, d D R2 =c, decreases because  / R3 . Thus, there is a time after which the condition for this approximation breaks down. The bolometric luminosity and the temperature of the ejecta decrease during the expansion, and the photosphere moves inward (in mass) into the ejecta. In the case of a core-collapse SN of type I (SN Ib/c), if a He shell was retained by the progenitor (SNe Ib or IIb), then when the temperature drops to values close to the recombination temperature of He, a recombination wave may form causing a brief “plateau” at low luminosity during a few days (Dessart et al. 2011). The existence of this plateau phase is suggested by theoretical models, but it has not been clearly observed. The predicted duration of the recombination plateau depends on the degree of mixing of radioactive material. If mixing extends to very outer layers, the phenomenon may completely disappear. The low luminosity, early occurrence, and short duration predicted for this phenomenon make it difficult to observe even for modern surveys. Independently of the existence of the initial plateau, models predict that the luminosity will decrease a few days after explosion unless there is an extra source of energy (see dashed line in Fig. 1). This extra heating is provided by the decay of radioactive material. The main part of the LC is in fact regulated and defined by this source of energy. Without radioactive material, SNe I would be extremely fast transients, and their mere detection would be challenging. The following section describes the radioactivity-dominated phase.

2.2

Radioactivity

During the SN event, explosive nucleosynthesis occurs, and part of the progenitor’s material is burned into various elements. Among these products, unstable isotopes of iron group elements are formed (Bodansky et al. 1968; Truran et al. 1967). The decay of these isotopes and subsequent thermalization of the decay products generate extra energy that is essential to power the LC during its main peak and beyond (Colgate and McKee 1969). The most abundantly produced radioactive isotope is 56 Ni which decays with a 6.1-day half-life to 56 Co, which in turn decays with a 77.7-day half-life to stable 56 Fe. The timescale of the decay is crucial. Too fast a decay would release all the energy early on, and the energy would be spent during the initial expansion. Too long a decay would release most of the energy at times when the ejecta become dilute. The ejecta may then be optically thin to high-energy photon which would escape without depositing their energy to power the LC. Initially, the decays produce energetic  -rays and positrons which are thermalized in the ejecta to provide the thermal luminosity of the SN. Thus, it is necessary to determine a local heating rate which generally is not the same as the simple radioactive decay rate. Instead, the decay rate should be modified by the probability of thermalization determined by the rate at which  -rays and positrons deposit

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energy at various points in the gas as they travel through the ejecta. The individual  -rays undergo several scattering events with matter, predominantly by compton scattering. During this process the  -rays transfer their energy to the electrons resulting in the emission of “optical” photons (this means photons roughly in thermal equilibrium with the temperature of the gas). This problem is complicated if tackled from first principles. A set of  -ray transfer equations must be solved simultaneously with the hydrodynamic equations, which requires a multiple energy group calculation (Swartz et al. 1995). However, if the ejecta are optically thick to  -rays, it is possible to assume that the  -rays deposit their energy locally. The rate of energy released per gram of material by the Ni–Co–Fe decay chain is "rad D 3:91010 exp.t = Ni /C 6:78109 Œexp.t = Co /exp.t = Ni /I erg g1 s1 ; (1) where Ni D 8:8 days, and Co D 113:6 days are the exponential decay times of the radioactive isotopes. The amount of energy deposited at each point is given by the solution of the  -ray transfer multiplied by the previous expression. Assuming a complete local deposition of the decay energy, the total luminosity of the radioactive energy can be approximated as L D MNi "rad :

(2)

In this case, the luminosity is a direct measure of the 56 Ni mass synthesized in the explosion. Complete deposition of the  -rays only occurs in SNe II, which have a thick H envelope, or in SNe I at very early phases, when the density is sufficiently high. When densities are too small, only some of the energy will be deposited. A reasonable approximation for the light curve requires that  -ray deposition is solved for numerically.

2.3

Numerical Treatment

Solving the problem of the SN explosion and subsequent radiative emission is a very complicated task that can only be handled under several simplifications. As it was mentioned in Sect. 2, the explosion itself is treated as a separate problem from the expansion and radiation. Models of the spectra and the LC in some cases start from a post-explosion density and abundance distribution and study the propagation of the radiation through the envelope. There are different approaches usually employed to compute SN LC. A common approach assumes spherical symmetry to solve the hydrodynamic equations coupled to radiation transport in one dimension. The simplest way to do this is to use the diffusion approximation for the transport, i.e., assuming that matter and radiation are in equilibrium, and to use the Rosseland mean opacity. This is usually called the “one-group approximation.” The calculation is able to produce the bolometric luminosity, which can be converted into broadband LCs by assuming, for example, back-body emission.

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A more physically accurate approach is to solve the full set of frequencydependent radiation transfer equations (the “multigroup method”). In this case, multiband LCs can be obtained provided that accurate monochromatic opacities are incorporated. Because of the dominant role played by line opacity in SNe I, mean opacities are never very accurate. Because of its high computational cost, this method is usually applied in one dimension. A popular approach is to solve for  -ray and positron diffusion and thermalization using a Monte Carlo technique (see, e.g., Ambwani and Sutherland 1988; Lucy 1999). The same can then be applied to compute spectra. Broadband LCs can then be obtained from the spectra. Monte Carlo methods are well suited for multidimensional studies, but these require the availability of multidimensional explosion models. The Monte Carlo technique is probably the most efficient way to model the SN during phases where hydrodynamic effects can be neglected, a condition which usually is verified soon after shock breakout.

2.4

Analytic Approach

Models of SN I LCs based on analytical formulations have been used for several decades as a simple way to understand the main physical processes underlying SN light curves and the parameters that regulate them. One of the most extensively used models is that developed by Arnett in 1982. It is useful to describe the LC during phases where radioactivity is dominant. The model involves several important assumptions, so it can only be considered as a rough approximation of the real problem. However it is a useful educational and intuitive tool for understanding the basic physics that govern supernova light curves. It assumes homologous expansion of the ejecta, with a gas dominated by radiation energy in spherical symmetry, which are reasonable assumptions. It also assumes that all radioactive 56 Ni is located at the center of the progenitor. While this is a good approximation for SNe IIP, where the ejected mass is much larger than the 56 Ni mass, it is clearly not if the star is compact as are the progenitors of SNe I, because the inner 56 Ni sphere may not be very small compared to the entire star. Additionally, radioactive material is often mixed out to high velocities, which affects the rise of the light curve. A constant value for the optical opacity and the diffusion approximation for photons are also assumed. These latter two hypotheses are also not ideal in the case of SNe I. In the Arnett model, the thermal evolution of matter is governed by the first law of thermodynamics: @L EP C P VP D "rad  ; @m

(3)

ac @T 4 ; 3 @m

(4)

where L D .4 r 2 /2

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assuming the diffusion approximation. Here, V is the specific volume, P is the total pressure, and E is the total internal energy per unit mass. Note that the gas components of P and E are neglected for a gas dominated by radiation. Finally, "rad is the rate of energy released by the radioactive decay per unit mass as defined in Eq. (1). Equation (3) is solved assuming the “one-zone” approximation, i.e., separating the space and time variables. A complete description of the resolution can be found in Arnett (1982). The solution for the luminosity evolution is Lbol .t / D MNi e

x 2

 Z ."Ni  "Co /

Z

x

u.z/d z C 0

2

x

w.z/d z ;

(5)

0 2

with u.z/ D 2ze .2zyCz / , w.z/ D 2ze .2zyC2zrCz / , x D t = m , y D m =.2 Ni /, and r D Πm . Co  Ni /=.2 Co Ni /. The energy rates per gram of 56 Ni and 56 Co are Ni D 3:9  1010 erg g1 s1 and Co D 6:78  109 erg g1 s1 . And Ni and Co are the exponential decay times of 56 Ni and 56 Co, while m is the timesale of the LC which can be written as 2 D

2opt Mej ˇcvsc

(6)

assuming a homogeneous density. opt is the optical opacity, c is the speed of light, ˇ  13:8 is a constant of integration (Arnett 1982), and vsc is the scale velocity of the SN. Usually, vsc is associated to the observed photospheric velocity at maximum light and to the width of the light. In practice, the photospheric velocity (vph ) is affected by the distribution of density and opacity and therefore may not accurately represent by a scale velocity. The kinetic energy can be estimated from vsc (or vph ), Ek D

3 2 Mej vph 10

(7)

This relation was obtained assuming a constant density sphere in homologous expansion (Arnett 1982). Using the Eq. (5), an estimation for the 56 Ni mass and can be derived from the observed LC. While the estimate of the 56 Ni mass may be reasonable, barring mixing out of 56 Ni or the presence of high-density radioactive cores, the estimate of the total mass and the kinetic energy is only approximate, as the photospheric velocity is by definition a time-dependent quantity, as is the opacity. The essential relation that can be obtained is 3=4

/

 1=2 Mej 1=4

Ek

(8)

This simple analytic treatment of the explosion physics necessarily prevents the use of this relation to derive absolute and reliable values of mass and energy.

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However it is useful when rescaling the properties of SNe that have similar light curves and/or spectra and have been properly modeled (see e.g., Mazzali et al. 2013).

3

Physical Parameters

We have thus shown, with simple physics, that the LC of SN depends on physical parameters of the progenitor star such as its mass, radius, and chemical composition and also on the explosion energy and the amount of radioactive material (mainly 56 Ni) produced during the explosion. By modeling the light curve, it is possible to put constraints on these parameters. That is, the LC provides a useful tool to test models of stellar evolution as it unveils the internal structure (chemical composition, mixing, and mass distribution) of the progenitor object. In practice the situation is more complex, since there is degeneracy between some parameters. Adding spectral models is usually advised to break the degeneracy. A point to consider is that not all the phases of the LC depend in the same way on different physical parameters. Hence, when compared with observations, it is important to know in which phase the SN is. At early times, before the radioactive phase, the LC depends mainly on the progenitor radius and to some extent on the radioactive mixing, while on the main peak, the 56 Ni mass is the dominant parameter followed by the ejecta mass and explosion energy. 56 Ni mass is the dominant parameter on the radioactive tail (see e.g., Bersten et al. 2012). Observing a SN I before the radioactivity-dominated phase is extremely difficult owing to the short duration of the breakout and the following cooling phase. The more compact the progenitor star, the shorter and more difficult to observe this phase will be. Therefore, in most of the cases, the information on the progenitor radius is lost.

4

Observed Properties of SN I Light Curves

The Type I supernova classification is primarily a spectroscopic one – SNe that do not show H in their spectra. The absence of H means that, although SNe I includes very different phenomena (thermonuclear SNe Ia and core-collapse, envelope-free SNe Ib/c), their LCs are similar. They are dominated by the contribution of 56 Ni heating, and they all share a late exponential phase – the radioactive tail. Shock heating and cooling is predicted but seldom observed because of the small size of the progenitor star and the consequent brief duration of this phenomenon. Type Ia SNe are remarkable for their homogeneity. Their light curves are rather bright – the average 56 Ni production is 0:5 Mˇ . They have long been proposed as standard candles for cosmology, and although this turned out to be too simple, they are good “standardizable” candles (Phillips 1993). They rise in 17–21 days and decline over a similar timescale. Importantly, the rate of decline and the luminosity are rather closely related (although there are exceptions), which makes it possible to use a distance-independent measurement such as light curve shape as a proxy for luminosity and hence to infer the distance to the SN. This method

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was at the heart of the use of SNe Ia to discover Dark Energy, the accelerated expansion of the Universe. SNe Ia are – roughly – Chandrasekhar-mass CO white dwarfs that burn explosively. They produce different amounts of 56 Ni, and hence they reach different peak luminosity, but the exact reason for this is not yet well understood. Studying their spectra has shown that SNe Ia that produce more 56 Ni correspondingly underproduce intermediate-mass elements (e.g., Si, S; IME), which is the other main product of the explosion (Mazzali et al. 2007). This indicates that most of the white dwarf is burned in the explosion and nuclearly processed. The relation between LC width and luminosity can then be simply understood as an opacity effect: 56 Ni, its decay products 56 Co and 56 Fe, and other Fe-group elements that are produced in the explosion are rich in spectral lines. In the conditions of SN Ia ejecta – high mean molecular weight – the electron density is low because a typical ion contributes only 1–2 electrons to the free electron gas, and line opacity is the dominant opacity. IME have much lower line opacity because their ions have fewer possible available states. Hence SNe which produce more 56 Ni are not only more luminous and slightly more energetic (the kinetic energy yield from burning to Fegroup is larger than it is from burning only to IME (Woosley and Weaver 1986)) but have also higher opacity. The longer photon diffusion time that this causes results in broader light curves. This trend exist in the bolometric LC and is dominant in the bluer bands, which are most affected by line opacity. It is also present, but less strong, in the redder bands. In the NIR, many SNe Ia even show a double peak, which is understood to be the effect of the cooling of the ejecta and the increasing occupation of low-lying levels of Fe (mostly FeII). It has even been suggested that SNe Ia may be good standard (as opposed to standardizable) candles in the near infrared (Krisciunas et al. 2011). The case of SNe Ib/c is slightly different. In this case the SN material is the CO core of a massive star which has lost its H/He envelopes before collapsing. The ejected mass may be highly variable from less than 1 to (at least) more than 10 Mˇ . Only a fraction of this mass is converted to 56 Ni. The LCs of SNe Ib/c are usually not as luminous as those of SNe Ia, although in some cases (GRB/SNe), they can reach similar luminosities. The variety of ejected masses is compounded by a variety of explosion energies, resulting in light curves that span a large range of rise times, peak luminosities, and duration. The LCs of SNe Ic appear to be more diverse than those of SNe Ib, possibly because the pre-explosion conditions of SNe Ic are themselves more diverse; SNe Ic are almost certainly the outcome of the explosions of stars that underwent major episodes of interaction with a binary companion. If we adopt a simplistic approach (see above), the shape of the LC depends on ejected mass, kinetic energy, and opacity. This means that, if both mass and energy are variable (opacity almost certainly is as well, not only between different SNe but also in a single SN as a function of depth and time, and it can only be estimated by performing accurate radiative transfer calculations), it is not possible to infer M and E from the LC shape because of the degeneracy implicit in the problem. This degeneracy may be broken if one of the two values can be inferred from other data. The mass may be inferred from the analysis of late-time spectra, when the SN ejecta behave like a nebula, are mostly transparent to radiation, and can therefore be

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modeled. This method is good but to no better than a factor of 2, because the mass at the higher velocity is easily fully transparent because of low densities and does not show up in nebular line emission. Also, it is important that both the optical and the NIR are available, as many elements only radiate in the NIR (Mazzali et al. 2010). Estimating Ek is even more uncertain. A velocity at maximum may represent the mean velocity of the ejecta, and it may be useful to infer the bulk of the mass, but does not capture the highest velocity ejecta, which carry the bulk of the Ek . Estimates based on a typical velocity near maximum may fall short by factors of several (e.g., Lyman et al. 2016). Only accurate spectral modeling of a time series of spectra can reliably yield both the mass and the energy. The LCs of SNe Ib/c are less dominated by line opacity, because the mean molecular weight is lower, and therefore the electron density is higher as compared to the ion density. Rescaling arguments can then be used to derive the properties of photometric and spectroscopic nearest neighbors. Despite all this, some basic correlations have been found among SNe Ib/c: SNe that reach a higher luminosity (hence produced more 56Ni) tend also to have higher Ek ’s. This is shown by the fact that their spectra show broader lines. The case of the extremely broad-lined GRB/SNe is an extreme example, but a correlation is found at practically all luminosities (e.g., Mazzali et al. 2013). Additionally, the more energetic and more luminous SNe tend also to be the ones with the larger ejected mass. This seems to indicate a correlation between progenitor mass and energy of the explosion (energy is necessary also to stimulate nuclear burning and thus to produce 56 Ni), but much work is still needed to confirm these trends and associate them with the properties and the evolutionary history of the progenitor stars). One further twist is that SNe Ib/c are aspherical to some degree (GRB/SNe probably being the most aspherical), so the LCs may be viewing-angle dependent.

5

Conclusions

We have analyzed the main physical processes that are relevant to understand the different phases of of the I supernovae light curves. We emphasize the role of radioactivity as the main power source in most of the LC evolution, independently of the physical origin of the explosion (thermonuclear vs. core collapse). This is mainly due to the compact structure of the progenitors. In spite of being all dominated by radioactivity, there is a variety in LC shapes as a consequence of the progenitor properties. We have discussed different approaches to estimate physical parameters of the SN progenitors from the LC. We have also pointed out the caveats to be taken into account when simple prescriptions are employed, such as analytic modeling. Although the overall morphology of the LC is similar for all SNe I, there is a wide range of observed properties among different subtypes, such as peak luminosities, rise and decline times, and tail luminosities. These differences are also present within the subgroups. For normal SN Ia, a standardization is possible that is the base

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of their use as distance indicators. But for other SN I subtypes, such standardization is not possible. This is related to the much more diverse properties among massive stars as opposed to those of Chandrasekhar mass white dwarf stars, which have relatively uniform masses and radii.

6

Cross-References

 Discovery of Cosmic Acceleration  Evolution of Accreting White Dwarfs to the Thermonuclear Runaway  Explosion Physics of Core-Collapse Supernovae  Hydrogen-Poor Core-Collapse Supernovae  Light Curves of Type II Supernovae  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Nucleosynthesis in Thermonuclear Supernovae  Observational and Physical Classification of Supernovae  Shock Breakout Theory  The Peak Luminosity-Decline Rate Relationship for Type Ia Supernovae  Type Ia Supernovae

References Ambwani K, Sutherland P (1988) Gamma-ray spectra and energy deposition for type IA supernovae. ApJ 325:820 Arnett WD (1982) Type I supernovae. I – analytic solutions for the early part of the light curve. ApJ 253:785 Bersten MC, Benvenuto O, Hamuy M (2011) Hydrodynamical models of Type II plateau supernovae. ApJ 729:61 Bersten MC, Benvenuto OG, Nomoto K et al (2012) The Type IIb supernova 2011dh from a supergiant progenitor. Astrophys J 757:31 Bodansky D, Clayton DD, Fowler WA (1968) Nuclear quasi-equilibrium during silicon burning. ApJ Supp 16:299 Colgate SA, McKee C (1969) Early supernova luminosity. ApJ 157:623 Colgate SA, White RH (1966) The hydrodynamic behavior of supernovae explosions. ApJ 143:626 Dessart L, Hillier DJ, Livne E et al (2011) Core-collapse explosions of Wolf-Rayet stars and the connection to Type IIb/Ib/Ic supernovae. MNRAS 414:2985 Falk SW, Arnett WD (1977) Radiation dynamics, envelope ejection, and supernova light curves. ApJ Supp 33:515 Grasberg EK, Imshenik VS, Nadyozhin DK (1971) On the theory of the light curves of supernovate. Ap & Space Sci 10:3 Krisciunas K, Li W, Matheson T et al (2011) The most slowly declining Type Ia supernova 2001ay. Astron J 142:74 Lucy LB (1999) Computing radiative equilibria with Monte Carlo techniques. Astron Astrophys 344:282 Lyman JD, Bersier D, James PA et al (2016) Bolometric light curves and explosion parameters of 38. MNRAS 457:328 Mazzali PA, Röpke FK, Benetti S, Hillebrandt W (2007) A common explosion mechanism for Type Ia supernovae. Science 315:825

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Mazzali PA, Maurer I, Valenti S, Kotak R, Hunter D (2010) The Type Ic SN 2007gr: a census of the ejecta from late-time optical-infrared spectra. MNRAS 408:87 Mazzali PA, Walker ES, Pian E et al (2013) The very energetic, broad-lined Type Ic supernova 2010ah (PTF10bzf) in the context of GRB/SNe. MNRAS 432:2463 Phillips MM (1993) The absolute magnitudes of Type IA supernovae. MNRAS 413:L105 Swartz DA, Sutherland PG, Harkness RP (1995) Gamma ray transfer and energy deposition in supernovae. ApJ 446:766 Truran JW, Arnett WD, Cameron AGW (1967) Nucleosynthesis in supernova shock waves. Can J Phys 45:2315 Weaver TA (1976) The structure of supernova shock waves. ApJ Suppl 32:233 Woosley SE, Weaver TA (1986) The physics of supernova explosions. ARA&A 24:205

Light Curves of Type II Supernovae

30

Luca Zampieri

Abstract

The observed light curves of Type II supernovae are rather heterogeneous. Understanding the origin of this diversity requires understanding the physical evolution of their ejecta. This is accomplished through the implementation of different radiation hydrodynamics approaches, some of which are summarized in this chapter. We first review an approximate semi-analytic treatment of the evolution of the ejecta that has been developed by several authors in the last two decades and is adequate to obtain a solid physical understanding of several basic processes. We then describe in detail the full radiation-hydrodynamics approach in spherical symmetry, discussing the evolution of the supernova internal structure and describing the physical effects of the ejecta properties on the light curve. These treatments are used to illustrate how to model observables of Type II supernovae (not only the light curves but also the evolution of the photospheric properties), to estimate the physical parameters of the ejecta, and to constrain their progenitors. Finally, we shortly address also the implications of these studies for understanding the use of Type II supernovae as cosmological distance indicators.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observed Light Curves of Type II Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 What a (Noninteracting) Type II Supernova Looks Like . . . . . . . . . . . . . . . . . . . . 2.2 The Famous (Peculiar) Light Curve of SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Two More Observables: Photospheric Velocity and Temperature . . . . . . . . . . . . .

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L. Zampieri () INAF-Astronomical Observatory of Padova, Padova, Italy e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_26

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2.4 From Faint to Luminous Events: The Variety of Type IIP Supernovae . . . . . . . . 2.5 Measuring Cosmological Distances with Type IIP Supernova Light Curves and Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Physics of an Expanding, Shocked Stellar Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Diffusion of Radiation in a Hot, Ionized Expanding Medium . . . . . . . . . . . . . . . . 3.2 Radiative Recombination and Recombination Wavefronts . . . . . . . . . . . . . . . . . . 3.3 Ongoing Internal Power from Unstable Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Radiation-Hydrodynamics Modeling of Supernova Ejecta . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Full Radiation-Hydrodynamics Approach in Spherical Symmetry . . . . . . . . 4.2 Evolution of the Ejecta Internal Structure and Fallback . . . . . . . . . . . . . . . . . . . . 4.3 Effects of Physical Parameters of the Ejecta on the Light Curve . . . . . . . . . . . . . 5 Interpreting Type II Supernova Observables and Constraining the Progenitor . . . . . . . 5.1 The Emergence of the Supernova Shock Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The Three Canonical Evolutionary Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Modeling Observables and Estimating Physical Parameters of the Ejecta and Progenitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Correlation of Observational Parameters and Their Physical Interpretation . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Core-collapse supernovae (SNe) are the endpoint of the evolution of stars having main sequence masses larger than 8 Mˇ . They are produced by the collapse of their core when it becomes mostly comprised of Fe, and no further nuclear burning can support it against its own weight. The core collapses until nuclear forces halt it, releasing a huge amount of gravitational binding energy and launching a shock wave that in many cases propagates through the star and unbinds all or part of it. The core survives the explosion and becomes a neutron star or, if the pre-SN star is sufficiently massive (above 20–25 Mˇ ), a black hole. During its pre-SN evolution, the star can undergo significant mass loss episodes and lose part of its envelope. If, at the time of the explosion, the star still retains a significant amount of hydrogen, it appears spectroscopically as a Type II SN (Turatto 2003). Many of these hydrogen-rich core-collapse SNe have a number of common distinctive features in their observed light curves that were recognized since the early systematic photometric studies of these events (Barbon 1979).

2

Observed Light Curves of Type II Supernovae

2.1

What a (Noninteracting) Type II Supernova Looks Like

The majority of Type II SNe exhibit a light curve with a characteristic plateau from a few tens of days after explosion up to 100 days. This dominant feature makes a transition to a sharp decline at later phases that is then followed by an exponential decay continuing until the SN fades below detectability. As discussed later, this

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Fig. 1 Bolometric light curves of some representative Type II plateau (IIP) SNe and SN 1987A

late-time decline is powered by the radioactive decay of 56 Co – end product of the decay of 56 Ni synthethized during the explosion – into 56 Fe. The decay chain 56 Ni ! 56 Co ! 56 Fe is an important energy source for normal Type II SNe, and its contribution is mostly visible at late stages. The typical behavior of a Type II SN is well illustrated by the evolution of the well-sampled bolometric light curves of SN 1999em (Leonard et al. 2003), SN 2009ib (Takáts et al. 2015), SN 20012ec (Barbarino et al. 2015), and SN 2013ej (Huang et al. 2015) in Fig. 1. In fact, this apparent similarity of Type II plateau (IIP) SNe hides rather significant diversities, both in the detailed trend of the plateau and in the ranges of plateau and tail luminosities, as already apparent in Fig. 1. These diversities can be even more evident comparing light curves in single photometric bands. A smaller subgroup of Type II SNe looks different. These SNe share a similar quasi-linear decline of the (logarithm of the) luminosity from a few tens of days after explosion onward. Representative cases of this group, called Type II linear (IIL) SNe, are SN 1990K (Cappellaro et al. 1995; Fig. 2) and SN 2009 kr (Elias-rosa et al. 2010). This group is as heterogeneous as (or even more than) the other one, with some SNe revealing a hint of a plateau during a predominantly linear decline. In this respect, SN 2013ej, which is classified as a IIP SN, can in fact be considered phenomenologically somewhat intermediate between a Type IIP and IIL SN.

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Fig. 2 Bolometric light curves of Type II linear (IIL) and IIb SNe, compared with that of the Type IIP SN 2013ej

A predominantly linear decline in the light curve, after a peak at 20 days, is typical of another subgroup of Type II SNe. They are characterized also by significant spectral evolution, with helium lines becoming progressively more significant in their spectra, that resemble more and more those of Type Ib SNe as the SN evolves (Turatto 2003). For this reason, they are dubbed Type IIb SNe. Two events belonging to this group are SN 1993J (one of the closest and best studied SNe, e.g., Benson et al. 1994) and SN 2008ax (Pastorello et al. 2008; Taubenberger et al. 2011; Fig. 2). They are considered transitional objects between hydrogen-rich Type II SNe and hydrogen stripped, helium-rich Type I SNe. Spectral peculiarities in the form of narrow hydrogen emission lines are also observed in otherwise normal Type II SNe. These objects are called Type IIn SNe. Emission lines are believed to originate from the interaction of the SN ejecta with a dense optically thin circumstellar medium lost by the pre-SN star in a previous evolutionary phase. Luminous Blue Variables can produce significant mass ejections of this type. Some events resembling faint Type IIn SNe are in fact giant eruptions of Luminous Blue Variable stars and do not lead to the explosion of the star. They are also dubbed SN impostors. In a few cases, observations show a Luminous Blue Variable outburst few weeks before the final explosion of the SN (e.g., Tartaglia et al. 2016). SNe interacting with the circumstellar medium are not treated in detail here.

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In the past decade, a new class of “super-luminous” SNe was discovered, with luminosity up to hundreds of times that of typical SNe (Gal-Yam 2012). Some of them are hydrogen rich as they do show hydrogen lines in their spectra and are then phenomenologically classified as Type II super-luminous SNe. The origin and energy source of these astonishing events are currently debated and may involve power sources alternative to the shock wave and radioactive decay. This class of objects is not covered here.

2.2

The Famous (Peculiar) Light Curve of SN 1987A

SN 1987A stands out among Type II SNe, in fact among all core-collapse SNe. This SN exploded in the nearby Large Magellanic Cloud galaxy, only 50 kpc away, on February 23, 1987. Because of its proximity, it is the brightest supernova after that recorded by Kepler in our Galaxy in 1604 (SN 1604). It is also the first supernova to be observed in every band of the electromagnetic spectrum (from radio to gamma rays) and the first detected through its initial burst of neutrinos. The light curve of SN 1987A is definitely peculiar (Hamuy et al. 1988; Fig. 1). There is no plateau, which is instead replaced by a broad peak reaching a maximum at 60 days since explosion. After that, the light curve settles on an exponential decay typical of a Type IIP SN, from which an amount of ' 0:07 Mˇ of 56 Ni is inferred to have been ejected. A small fraction of Type II events show a similar photometric evolution and are broadly classified as SN 1987A-like SNe.

2.3

Two More Observables: Photospheric Velocity and Temperature

Besides the light curve, crucial information on a SN comes from its spectrum. In addition to the spectral classification and an assessment of the chemical composition, the observed spectrum provides also information on the physical conditions of the ejecta at the photosphere and on their evolution with time. Even without undertaking a detailed spectral synthesis calculation, the velocity of the ejecta vph and the temperature of the continuum Tph at the photosphere can be almost directly inferred from observations of the spectral lines and the shape of the spectrum. The evolution of these two observables for SN 1987A, SN 1999em, and SN 2013ej is shown in Fig. 3. The ejecta are initially very hot and then cool down because of expansion and emission of radiation. When the temperature becomes equal to the hydrogen recombination temperature (4000–6000 K), the bulk of the SN ejecta starts recombining, and the emission is dominated by the sudden release of energy caused by the receding motion of the wavefront through the envelope. During this state transition, the temperature levels off at the hydrogen recombination temperature. The velocity inferred from the metal lines is 3000–6000 km/s at 30 days since explosion. It then gradually decreases as the ejecta evolve. This is a consequence

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Fig. 3 Evolution of photospheric velocity (from Fe II  4924, 5018, 5169) and photospheric temperature of Type II SNe

of the fact that, as the plasma recombines, the photosphere recedes through the envelope from the outer high-velocity mass shells to the inner low-velocity ones. As we will see later, together with the light curve, the evolution of vph and Tph can be used to put crucial constraints on the radiation-hydrodynamics modeling of the ejecta. Type IIL SNe tend to have higher ejecta velocities than Type IIP SNe, while SN 1987A-like events tend to be slower and cool down more quickly.

2.4

From Faint to Luminous Events: The Variety of Type IIP Supernovae

As mentioned above, while the majority of Type IIP SNe have luminosities in the range shown in Fig. 1, they display large variations in their observational properties. Not only the emitted luminosity but also the expansion velocity and the photospheric temperature span a wide range of values, going from faint, low-velocity events, such as SN 2003gd (Hendry et al. 2005) or SN 2005cs (Pastorello et al. 2009), to very luminous and rapidly expanding ones such as SN 1992am (Schmidt et al. 1994) or SN 2009kf (Botticella et al. 2010; Fig. 4). The difference in luminosity may be very large, even two orders of magnitude. At the same time, SNe that have similar

30 Light Curves of Type II Supernovae

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Fig. 4 From faint to luminous Type II SNe

luminosities during the plateau phase may show significant differences at later epochs when the light curve is dominated by the radioactive decay of 56 Co into 56 Fe. However, even the brightest ones are less luminous than the super-luminous SNe mentioned above. A few very luminous Type IIP events exist (L  1043 erg/s) that show significant near-ultraviolet emission during the early evolutionary phases and high photospheric velocities and temperatures. At the other extreme, faint Type IIP SNe have a lowluminosity plateau (L  1041 erg/s) lasting about 100 days, an underluminous late-time exponential tail, intrinsic colors that are unusually red, and spectra showing prominent and narrow P Cygni line profiles (Spiro et al. 2014). The velocity of the ejecta inferred from measurements at the end of the plateau is 1000 km/s. Also the 56 Ni mass ejected in the explosion is very small (< 0:01 Mˇ ).

2.5

Measuring Cosmological Distances with Type IIP Supernova Light Curves and Velocities

The interest toward Type II SNe has grown also because a number of works have convincingly shown that Type IIP SNe can provide a tool for probing cosmological distances at intermediate redshifts, independent of Type Ia SNe (Hamuy 2003; Nugent et al. 2006; Olivares et al. 2010). The possibility of building Hubble diagrams for hydrogen-rich core-collapse SNe is strictly related to the capability of calibrating them and, consequently, to turn them into usable distance indicators.

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As summarized in Pumo and Zampieri (2013), a careful analysis of the foundations of the different calibration methods is important to put them on solid ground. Two different approaches are used to derive distance measurements for corecollapse SNe: The first is based on theoretical spectral modeling like the expanding photosphere method (Eastman et al. 1996) or the ensuing spectral expanding atmosphere method (Baron et al. 2004), while the second relies on more empirical techniques as the standardized candle method, based on an observational correlation between the luminosity of a SN and its expansion velocity (Hamuy 2003), or the method based on the steepness of the light curve at the end of the plateau (Elmhamdi et al. 2003). Nugent et al. (2006) applied the standardized candle method to a sample of local and z D 0:3 Type IIP SNe and derived a Hubble diagram that has a scatter of only 0.26 mag. Understanding the physical evolution of Type II SN ejecta and assessing the physical origin of their diversity (including the existence of correlations among their observables) requires to be able to understand and reproduce the properties of their observed light curves and the evolution of their photospheric velocity/temperature curves. This is accomplished through the implementation of different radiationhydrodynamics approaches, some of which are described in the next sections.

3

Physics of an Expanding, Shocked Stellar Envelope

The dynamical evolution of an expanding, shocked stellar envelope of a massive star during and after the SN shock passage is quite complex. The propagation of the shock determines how the explosion energy is distributed in the envelope of the progenitor star. The star mixes but does not homogenize. The actual velocity, density, and heavy element distributions of the post-shock material affect the light curve and estimation of the envelope mass in a major way. The outer part of the star (typically involving only 1% by mass of the envelope) develops a steep power-law density structure that affects the light curve at shock breakout and during the first 10–20 days after it. To reach a basic physical understanding of the gross evolution of the SN ejecta following a few tens of days after shock passage, we can neglect this complex phase and rather assume idealized initial conditions that provide an approximate description of the ejected material, as derived from hydrodynamical calculations (see Zampieri et al. 2003). In realistic explosion calculations, a few days after shock passage, most of the ejected envelope has an approximately homologous velocity profile and uniform density. The velocity distribution results from the innermost layers having to push the overlying layers and transferring to them most of their kinetic energy and momentum. Within these approximations, it is possible to model the ejecta in spherical symmetry, as a hot freely expanding ionized envelope with initial radius R0 and density 0 D .3=4 /M =R03 , where M is the total envelope mass. The velocity v of each shell of the envelope is approximately constant in time and proportional to its position within the envelope (homologous expansion). At t0 it is: v D V0 .r.t0 /=R0 /;

(1)

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where V0 is the (constant) velocity of the outermost shell of the envelope initially at R0 . The radius of each gas shell increases linearly with time as: r.t / D r.t0 / C v.t  t0 / ' v.t  t0 /

at t  t0 >> td;0 ;

(2)

where td;0 D R0 =V0 is the initial expansion timescale of the envelope. For the outermost shell: R.t / D R0 CV0 .t t0 / ' V0 .t t0 /. Mass conservation then gives: 3 .t / D 0 .R0 =R.t //3 ' 0 td;0 =.t  t0 /3 :

(3)

The total energy of the ejecta, Eexp , can be written as the sum of their kinetic (Ek ) and thermal (Eth ) energies. Using Eq. (1) and d m D 4 r 2 dr, at t0 it is: 1 Ek D 2 Z Eth D

Z

M

3 M V02 10 Z R0 "d m D 4 aR T 4 .t0 ; r/r 2 dr v2d m D

0 M

0

Eexp D Ek C Eth ;

(4) (5)

0

(6)

where " D aR T 4 .t0 ; r/=0 is the initial specific energy density for a radiationdominated gas (aR D 4=c is the radiation constant and  the Stefan-Boltzmann constant) and T is its temperature. As shown in realistic explosion calculations, energy equipartition is often realized at t0 (Ek ' Eth ). This is expected for a strong radiation-dominated shock that, after its passage, roughly deposits equal amounts of thermal and kinetic in the ejecta. During evolution, the internal thermal energy is eventually spent in expanding the ejecta and emitting radiation. Concerning the ejecta chemical composition, the actual elemental distribution depends on several factors, including the explosion energy, explosion dynamics, and degree of mixing. As mentioned above, the star mixes, but the final composition has a rather complex three-dimensional filamentary structure, as shown also by observations of SN remnants. Again, to get a general understanding of the physical evolution of the ejecta and obtain an approximate but reliable estimate of their light curve, we can adopt the approximation that elements are completely mixed throughout the envelope and that their distribution depends only on r. In particular, we can approximately assume that the most abundant elements in the ejecta (hydrogen, helium, and oxygen) are uniformly distributed, whereas the most relevant radioactive isotope that powers the late-time light curve (56 Co, decay product of 56 Ni) is centrally peaked (being produced in large amounts during the explosive nucleosynthesis in the innermost part of the ejecta). The approximate semi-analytic treatment adopted in following part of this section is based on that originally introduced by Arnett (1996) and Popov (1993) and later developed by Zampieri et al. (2003).

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Diffusion of Radiation in a Hot, Ionized Expanding Medium

Besides transferring kinetic energy and momentum to the ejecta, the shock wave deposits also a large amount of thermal energy into them. Then, after shock breakout, the ejecta are hot, largely ionized, and free coasting. In these conditions, the thermal balance in the ejecta is governed by the competition among the P d V work needed to expand the plasma, the energy losses through radiative diffusion, and the energy input from the radioactive decay of unstable isotopes synthetized during the explosion. Assuming that radiation is in local thermodynamics equilibrium (LTE) with the gas throughout the envelope, the energy balance equation becomes a second-order partial differential equation for the temperature T . Arnett (1996) has shown that, under ad hoc assumptions on the radial distribution of 56 Ni and appropriate boundary conditions, the energy equation can be solved by separation of variables. The final solution has the form: 4 T 4 .t; r/ D T04 .R0 =R/4 .r=R/.t / ' T04 .r=R/.t / td;0 =.t  t0 /4 ;

(7)

where .r=R/ and .t / are two functions describing the spatial and time dependence. The term .R0 =R/4 accounts for the decrease in temperature caused by expansion. If  is the plasma opacity, in the limit 1=./ ! 0 (zero mean free path), the spatial dependence is given by (Arnett’s “radiative zero” solution): .r=R/ D sin. r=R/=. r=R/:

(8)

Neglecting radioactive energy input, the time-dependent part of the solution is: .t / D e t=td iff;0 t

2 =.2t d;0 td iff;0 /

;

(9)

where td iff;0 D 30 R02 =. 2 c/ is the initial radiation diffusion timescale. After a few expansion timescales (t > 2td;0 ), the second term in the argument of the exponential in Eq. (9) dominates the decay. Thepdecrease in T caused by radiative diffusion is “accelerated” by expansion. At t > 2td;0 td iff;0 the light curve falls as a Gaussian, faster than a simple exponential. In certain cases, the radioactive heating power is not negligible during the diffusion phase. Under specific assumptions on the radial distribution of 56 Ni (i.e., that it is proportional to T .r/4 ), the spatial part of the solution is again given by Eq. (8), but the time-dependent part is no longer expressed by Eq. (9). The energy equation contains additional functions decaying as e t= , where is the radioactive decay time (see below) and can be solved either analytically (Arnett 1996) or numerically (Zampieri et al. 2003) to determine .t /. For long time after explosion, the envelope is optically thick to radiation, and the diffusion approximation holds. The radiative luminosity L is then given by: 4 R2 c LD 3



@w0 @r

 D R

4 caR T04 R0 .t / D L0 .t /; 30

(10)

30 Light Curves of Type II Supernovae

747

where the radiation energy density w0 D aR T 4 (LTE) and L0 D

4  4  c.R0 =/.Eth =M / D c.R0 =/V02 : 9 I 30 I

(11)

Here  D Πddy yD1 and y D r.t0 /=R0 . We assumed energy equipartition and RR made use of Eqs. (4) and (5), with 4 aR 0 0 T 4 r 2 dr D .4 aR T04 R03 /I and I D R1 .y/y 2 dy. From Eq. (10) it can be seen that, at the beginning of the evolution 0 when  ' 1, the luminosity is equal to L0 . The reason for this early constant value of the luminosity is that the decrease of the radiation energy density gradient (@w0 =@r) is exactly compensated by the increase in both the photon mean free path (1=) p and the envelope radius (R). On the other hand, as mentioned above, at t > 2td;0 td iff;0 , the internal energy is being rapidly exhausted, and the luminosity falls off as a Gaussian. Equation (11) shows also that, for a given thermal energy and initial radius, at the beginning of the evolution, stars with less massive envelopes are brighter than stars with more massive ejecta (the mean free path is larger). Conversely, for a given thermal energy and ejecta mass, more extended ejecta are brighter than smaller ones (they suffer less degradation of internal energy through expansion).

3.2

Radiative Recombination and Recombination Wavefronts

Because of expansion and radiative diffusion, the temperature of the envelope decreases up to the point at which it becomes equal to the recombination temperature Trec of the plasma. As the temperature is lower in the external layers, recombination occurs first in the outer envelope but then propagates quickly inward through it. Denoting the position of the recombination wavefront with ri .t /, at any given time, the portion of the envelope below ri remains in LTE with radiation, whereas that above it recombines and becomes transparent to optical photons. During this phase, we can then approximately describe the ejecta as composed of two physically distinct regions, one above (A) and the other below (B) the recombination wavefront. In these assumptions, the recombination wavefront essentially coincides with the photosphere of the ejecta. Following Arnett (1996), we assume that in region (B), radiative diffusion can effectively readjust the radial temperature distribution to the changing position of the outer boundary at ri (the so called “slow approximation”). This is appropriate for ejecta in which the timescale for the motion of the recombination front is longer than the thermal timescale of the envelope below ri , i.e., if the wavefront is not moving too fast (although the behavior of the light curve is not crucially dependent on this assumption, Arnett 1996). In this approximation, in region (B), the basic assumptions stated above remain valid, and the solution can still be obtained by separation of variables. The spatial dependence of T .r/ is given by Arnett’s “radiative zero” solution (Eq. (8)) with the outer boundary R replaced by ri . However, the time-dependent part of the solution is no longer expressed by Eq. (9),

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L. Zampieri

because the energy equation contains an additional unknown function of time, ri .t /. If radioactive heating is included, the equation will contain also additional exponentially decaying functions of time. Following Popov (1993), an approximate solution for the time-dependent equation can be found setting the diffusion luminosity at ri equal to the luminosity emitted by a blackbody at the effective temperature Teff : 

4 ri .t /2 c 3



@w0 @r



4 D 4 ri .t /2  Teff ;

(12)

ri

which gives (Zampieri et al. 2003) 3 .t / D  1 0 R0 4



Teff T0

4 

R R0

2

ri .t / : R

(13)

Here  D Πddy yD1 and y D r=ri . Assuming that radiation diffusion holds at r < ri and approximating the layers close to the recombination wavefront with a plane-parallel atmosphere in radiative equilibrium, the effective temperature Teff 4 4 can be related to the gas recombination temperature Trec at ri by: Teff D 2Trec . We note that sometimes a color correction factor fc D Tph =Teff is introduced when estimating the effective temperature from the measured photospheric continuum temperature Tph of the SN, because in SN atmospheres radiative transfer processes may induce distortions of the continuum from a Planckian. fc departs more significantly from unity close to the recombination phase, when metal absorption lines become pronounced and suppress the blue part of the SN spectrum. In the following, we will assume f D 1 and will encompass possible uncertainties induced by variations of f in the value of the recombination temperature Trec . Inserting Eq. (13) into the time-dependent part of the energy equation finally gives an ordinary differential equation for the motion of the recombination wavefront that can be solved numerically for ri .t / (Zampieri et al. 2003). Equation (13) then gives immediately .t /. The diffusion luminosity is then: 4 ri .t /2 c LD 3



@w0 @r

 D ri

4 caR T04 R0  ri .t /.t /: 30 R

(14)

To this luminosity, we have to add also the radiative energy released by the recombination process itself and the energy liberated by the sweeping of the recombination wavefront through the plasma (advection luminosity): 4 Lrec D 4 ri .t /2 vi .aR Trec C Qion /;

(15)

where vi D dri =dt is the wavefront velocity and Qion the energy per unit mass released by recombination.

30 Light Curves of Type II Supernovae

749

In the optically thin region (A), the deposition of gamma ray photon energy through Comptonization and photoelectric absorption of heavy elements is the dominant thermal and radiative process. The radioactive decay time is shorter than the expansion timescale, so that the internal energy and the P d V work can be neglected in the energy equation. The luminosity emitted in this region is then easily obtained integrating over volume the gas emissivity, which is equal to the heating of the ejecta provided by the energy deposition from radioactive isotopes. If "P represents the energy input per unit mass and time from radioactive material, the total power from radioactive decays in region (A) is then: Z

M

Q D m.ri /

"P d m D 4 0 R03 X f .t /

Z

1

y 2 .y/dy;

(16)

ri =R

where X and .r=R/ are the mass fraction and radial distribution of the relevant radioactive isotope and f .t / is the specific rate of energy deposition of the considered decay channel. 56 Ni and its decay product 56 Co are the two most relevant species powering the light curve of a type II SN for the first few years after explosion. For them: f .t / D Œ3:9  1010 e t= N i C 7:2  109 .e t= C o  e t= N i / erg g1 s1 , where N i D 8:8 days and C o D 111 days. The amount of radioactive energy deposited in the ejecta and then reemitted as optical photons depends on the fraction of gamma rays that are absorbed. If  is the optical depth to gamma rays in the ejecta, it is then: L D .1  e   /Q ;

(17)

where it is usually assumed that all the trapped energy from radioactive decays is absorbed locally at the point of emission. For Type II SNe, during the first few hundreds of days after explosion, the density is sufficiently high that  >> 1 and then L ' Q (complete trapping of the gamma rays). The total luminosity emitted during recombination is then: Ltot D L C Lrec C L :

(18)

Lrec is typically larger than or comparable to L during this phase (see also Arnett 1996).

3.3

Ongoing Internal Power from Unstable Isotopes

When the recombination wavefront has swept through all the ejecta, the envelope is completely transparent to optical photons. The only ongoing internal power is that from radioactive decays. The luminosity emitted in this phase is again obtained from Eqs. (16) and (17) with ri D 0:

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L. Zampieri

L D 4 0 R03 X f .t /.1  e   /

Z

1

y 2 .y/dy D .1  e   /M f .t /;

(19)

0

where M is the total mass of the radioactive isotope.

4

Radiation-Hydrodynamics Modeling of Supernova Ejecta

Modeling SN ejecta means computing the evolution of their physical variables after shock and reverse shock passage and determining their total radiative output. The approximate semi-analytic treatment presented in the previous section is an example of modeling. Such a treatment has the advantage of being simple and in many cases adequate to obtain a solid physical understanding of several basic processes occurring in the ejecta. However, it is approximate and neglects some important aspects, such as the actual velocity, density, and heavy element distributions of the post-shock material. In order to compute the evolution of SN ejecta starting from realistic initial conditions resulting from a stellar evolution code coupled with numerical computations of the explosion phase, a full radiation-hydrodynamics calculation is needed. This has been accomplished by several authors. Here we give a short summary of the basic equations. To keep the treatment simple, we will focus on radiation-hydrodynamics modeling in spherical symmetry, although asymmetries in the explosion and multidimensional effects during the evolution of the ejecta are relevant in certain cases and can be treated only in 2D or 3D radiationhydrodynamics simulations.

4.1

The Full Radiation-Hydrodynamics Approach in Spherical Symmetry

Several detailed numerical treatments of the radiation-hydrodynamics equations of an expanding SN envelope have been presented in the literature (e.g., Balberg et al. 2000; Bersten et al. 2011; Blinnikov and Bartunov 1993; Chieffi et al. 2003; Dessart and Hillier 2010; Kasen and Woosley 2009; Pumo and Zampieri 2011; Utrobin 2007; Young 2004; Woosley and Weaver 1995; Zampieri et al. 1998). One common limitation of most of the previous studies is that radiative transfer is treated in the diffusion approximation. In the reference frame comoving with the ejecta, the full (relativistic) radiationhydrodynamics equations in spherical symmetry, including the first two moments of the radiative transfer equation governing the evolution of the radiation field, can be cast in the form: 1 @" 1 @ Cp c @t c @t

  1 C kP .aR T 4  w0 / D "P 

energy eq.

(20)

30 Light Curves of Type II Supernovae

GM 1 @u C K C 2 2 D0 Euler eq. c @t c r   1 @ @r 4 r 2 C uK D 0 continuity eq. c @t @m

751

(21) (22)

1 @w0 4  @.w1 a2 r 2 / C z0 w0 C 2 D kP .aR T 4  w0 / zero-th moment eq. (23) c @t a @m  1 @w1 4 2 1 @.a4 w0 / C 2z1 w1 C r C c @t 3 a4 @m 1 @.ar 3 f w0 / D kR w1 first moment eq.; (24) r3 @m where m is the Lagrangian mass; u D @r=@t , , T , p, and " are the ejecta 4-velocity, density, temperature, pressure, and total specific energy density; and w0 and w1 are the radiation energy density and flux (both in units of erg cm3 ). p and " depend on  and T and are specified through the gas equation of state. kP and kR are the usual Planck and Rosseland mean opacities. The function K appearing in the Euler (and also the continuity) equation accounts for the gas pressure and radiation forces and is reported below (Eq. (27)). The third term in the same equation is the gravitational pull of the mass M contained inside R m the radius r.m/, including the mass of the central remnant Mc : M D Mc C 0 4 r 2 .@r=@m/d m. The terms z0 and z1 in the radiation moment equations (Eqs. (23) and (24)) are also reported below (Eqs. (28) and (29)). The function f relates the second-order moment of the radiation intensity (w2 ) to w0 . Finally, D .1 C u2  2GM=c 2 r/1=2 (generalized Lorentz factor) and a D a.t; m/ are relativistic functions. The latter links the coordinate time with the time of the observer comoving with the ejecta. They obey the equations (Zampieri et al. 1998): @r  D0 @m 1 @a K C D 0: a @m 4 r 2

4 r 2

(25) (26)

In the nonrelativistic limit (u 0 at the photosphere will have the possibility of Doppler shifting into Sobolev resonance with a spectral line of rest frequency 0 . Depending on the line optical depth, a fraction of such photons will be scattered. From the observer’s perspective (Fig. 5), this scattering will remove some photons and add others. Specifically, photons that were initially directed toward the observer can be scattered

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S.A. Sim

Fig. 5 Idealized picture of line formation in SN ejecta during the photospheric phase in a “corehalo” approximation. The photosphere (white region) surrounds an optically thick core and is assumed to be geometrically thin. Continuum photons travel through the surrounding expanding ejecta in which they can undergo line scattering. Three example photons that undergo line scattering are illustrated (scattering locations indicated with white crosses). Photon 1 is scattered out of the observer line of sight (los), contributing to blueshifted absorption in the profile. Photons 2 and 3 are scattered into the line of sight, yielding redshifted and blueshifted emission, respectively (see text). The envelope material is color coded to qualitatively indicate the line-of-sight velocity for the observer

out of the line of sight (e.g., photon 1 in Fig. 5). Since such photons necessarily scatter in the approaching side of the ejecta (i.e., they reach Sobolev resonance in the ejecta layers between the photosphere and the observer), their observer-frame frequencies must be greater than 0 and so their removal will give rise to blueshifted absorption. In contrast, photons can be scattered into the observer’s line of sight from both the approaching and receding regions of the ejecta (e.g., photons 2 and 3 in Fig. 5): thus the emission component of the profile is expected to contain both blueshifted and redshifted photons produced across the range of velocities present in the ejecta. This combination of blueshifted absorption and broad emission is generic for scattering-dominated line profiles in SN ejecta, and the shape and strength of the profile are controlled primarily by the variation of optical depth with velocity in the ejecta. Four example, (idealized) line profiles are shown in Fig. 6, each calculated from a spherical model with a different optical depth distribution.

31 Spectra of Supernovae During the Photospheric Phase

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Fig. 6 Example calculations of scattering line profiles in SNe (flux versus apparent redshift velocity). Each panel shows the profile shape for an isolated pure-scattering spectral line formed in homologously expanding ejecta in which the Sobolev optical depth depends on velocity as S D 0 .v=8000 km s1 /n . The values adopted for 0 and n are indicated in each panel. In each case, the blue line shows the complete line profile; the black line shows the attenuated continuum spectrum; and the gray-shaded region indicates the radiation contributed by scattering into the line of sight. All calculations were made using an idealized “core-halo” approximation (see Sect. 5.1) in which a geometrically thin blackbody photosphere is assumed to be located at 8000 km s1 . The blueshift velocity corresponding to this imposed photosphere is indicated by the vertical line in each panel. Note that for all the cases shown with modest optical depth at the photosphere ( 0 D 2), the deepest absorption occurs close to the photospheric velocity, but there is a notable offset for the higher optical depth ( 0 D 200) case. Calculations were made using the TARDIS code (Kerzendorf and Sim 2014).

4.2

Recombination Emission

Although the characteristic profile with blueshifted absorption and redshifted emission is common to many classes of SNe, emission components can be enhanced by additional processes (Sect. 3.2). Particularly notable is the role of recombination line emission in hydrogen-rich SNe: the emission component of, e.g., H˛ in SNe IIP often significantly outweighs the absorption (see, e.g., Kirshner and Kwan 1975). Modeling of this recombination is thus necessarily included in theoretical work focused on the quantitative study of SNe IIP, and this is one of the reasons why codes

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that adopt a scattering-dominated approach to line profile formation (e.g., Fisher 2000; Kerzendorf and Sim 2014; Mazzali 2000) cannot be quantitatively applied to the modeling of H profiles in Type II spectra. Although a complete discussion is beyond the scope of this article, we note that recombination emission is also key to understanding of Type IIn spectra: these objects form a very diverse class, but have in common early-phase spectra that contain emission line profiles with narrow cores (formed in circumstellar material) and broad bases (shaped by electron scattering; Chugai 2001; Dessart et al. 2009, see Sect. 3.2).

5

Widely Used Approximations in Spectral Modeling

As noted in Sect. 2, the most sophisticated modeling is done with radiative transfer codes that simulate thermalization and scattering in detail and that incorporate nonLTE physics in the calculation of atomic level populations for a wide range of ions. In such calculations, artificial photospheric boundary conditions are avoided, and a self-consistent ultraviolet-to-infrared spectrum can be produced. Clearly, such high-quality calculations are important for precision work. However, these complicated approaches have the drawback of being relatively computationally expensive. Consequently, it remains the case that many studies continue to employ significant approximations. We have already discussed the Sobolev approximation for line opacity in Sect. 4.1.2. In the subsections below, we comment on several more approximations that are used, their utility, and their drawbacks.

5.1

The “Core-Halo” Approximation

The most basic picture of the photospheric phase (Fig. 5) lends itself to a simple model in which the SN ejecta are divided into an optically thick “core” surrounded by a “halo” of expanding ejecta in which the spectral features are formed. A major approximation used by several of the most flexible spectral modeling codes is to assume that the “core” region effectively emits as a continuum source (usually assumed to be a black body) and that the spectrum formation problem can be addressed by modeling the transport of this radiation through the “halo.” Although crude, this has practical advantages over more sophisticated methods that avoid this division. Most importantly, it allows for the development of codes that are sufficiently computationally inexpensive to explore the large parameter space of compositions (and density/degree of ionization) that may be needed to match an observation. This approach also easily allows for modelling in which the luminosity can be directly inputted (and, e.g., fixed to match observations) without the need to simulate photon diffusion from high optical depths. Such utility, however, does come at the cost of having an oversimplified description for the continuum formation and a relatively poor model for the overall SED, particularly at long wavelengths. For example, as discussed for SNe Ia by

31 Spectra of Supernovae During the Photospheric Phase

785

Mazzali (2000, see also Sauer et al. 2006), although adopting a simple photospheric boundary condition can provide a good match at blue wavelengths, it can lead to increasingly poor agreement in the red part of the optical spectrum (and beyond) owing to the low thermalization opacities (see Sect. 3.1). This limitation must always be borne in mind when modeling SN spectra using a “core-halo” approximation, with particular caution applied to interpreting the full SED shape.

5.2

Spherical Symmetry

It is possible to incorporate full 2D/3D geometries in radiative transfer calculations for SNe (see, e.g., Dessart and Hillier 2011; Hauschildt and Baron 2010; Höflich et al. 2006; Kasen et al. 2006; Kromer and Sim 2009; Wollaeger et al. 2013). Such studies have shown that global departures from spherical symmetry can lead to spectra whose properties vary significantly with observer orientation (effects can include changes in individual line profile shapes and widths, but also overall SED color due to, e.g., altered line blocking). Departures from symmetry on relatively short length scales (“clumping”) can also affect the strength of spectral features, if sufficiently strong (e.g., Chugai and Utrobin 2014; Thomas et al. 2002). It would be very challenging to fully explore the role of departures from spherical symmetry when empirically modeling observed spectra: the substantial increase in the size (and degeneracy) of the parameter-space to be explored would be prohibitive for all but the simplest of modeling approaches. Consequently, it remains a common practice in many analyses to assume that the ejecta are smooth and spherically symmetric. This approach can be motivated by the generally low levels of linear polarization generally observed in the majority of SN explosion (specifically SNe IIP and SNe Ia) and, empirically, by the success of 1D models in quantitatively matching observed photospheric spectra. However, particularly for SNe Ib/c, there is observational evidence in favor of large-scale departures from spherical symmetric (Maund et al. 2007; Tanaka et al. 2008). Aside from modeling spectropolarimetry, the main application of multidimensional radiative transfer calculations for SNe at photospheric phases is in making predictions for hydrodynamical explosion models. Particularly for SNe Ia, there is now a range of explosion scenarios for which the explosion (and associated nucleosynthesis) has been simulated in 2D or 3D (see, e.g., Röpke et al. 2011). Most such models predict departures from spherical symmetry, although the nature and consequence of these asymmetries can vary substantially. Synthetic spectra obtained from multidimensional radiative transfer calculations therefore have a role in establishing the validity of proposed models and distinguishing between them.

5.3

Time Independence

Many of the spectral modeling methods applied to SNe have their origin in the study of steady-state stellar atmospheres. However, in expanding SN ejecta, a steady-state

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approximation is not exact, and the role of time dependence in the formation of SN spectra has been considered. As explained by Hillier and Dessart (2012), time dependence affects SN spectral synthesis in two ways: time dependence (i) in the radiation field and (ii) in the rate equations governing excitation and ionization. Time dependence in radiation transport has been incorporated in several of the current generation of radiative transfer codes, including (Hillier and Dessart 2012; Jack et al. 2009; Kasen et al. 2006; Kromer and Sim 2009). It is particularly easy to incorporate in codes that use Monte Carlo methods (Lucy 2005), where it introduces no substantial complications. Indeed, as argued by Lucy (2005), explicitly accounting for the finite speed of light actually simplifies matters since it can help alleviate efficiency issues associated with Monte Carlo techniques at high optical depths. Although this time dependence is clearly critical to the modeling of light curves, Kasen et al. (2006) show that the direct influence on the strength and shape of spectral features is SNe Ia models that are relatively modest: i.e., spectra obtained from“snapshot” calculations (in which photons do not diffuse in time) are remarkably similar to those obtained from full calculations. However, as discussed by Hillier and Dessart (2012), the effects are larger in SNe with more massive ejecta (e.g., SNe IIP). The role of time dependence in the rate equations is also significant, particularly for the modeling of SNe IIP (Dessart and Hillier 2008; Utrobin and Chugai 2005). Specifically, as discussed by Dessart and Hillier (2008), the effective recombination time for both H and He in the SN envelope may become comparable to the flow timescale, meaning that time-dependent terms will become significant in the rate equations. This influences the modeling of key spectral lines, including H˛ across a wide range of epochs, and can be critical to explain the strength of H˛ at relatively late epochs (see discussion by Dessart and Hillier 2008).

6

Some Applications of Spectral Modeling

Over the decades of observation of photospheric phase spectra for SNe, there have been many different studies that utilize a variety of models for spectrum formation to interpret data. To overview all studies that have been made is far beyond the scope of this article. Instead, we will only attempt to highlight some of the common approaches that are currently used and provide references for further reading.

6.1

Line Identification

The first, and arguably most important, information that can be inferred from the analysis of spectra is qualitative determination of which ions are present in the SN ejecta. Owing to the large velocities and associated blending of features (see Sect. 3.1), this line-identification problem can be challenging, particularly for metalrich SNe I, and often relies on a combination of experience and use of spectral modeling tools.

31 Spectra of Supernovae During the Photospheric Phase

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The SYNOW / SYN++ code (Fisher 2000; Thomas et al. 2011) is widely used for line identification in most classes of SNe. This code combines a core-halo approximation (Sect. 5.1) with the Sobolev approximation (Sect. 4.1.2) to calculate the strength and shape of line features across the spectrum for comparison to observations. The code does not impose any particular ionization approximation; it allows the user to vary the contribution of each ion to the spectrum in order to find a good match. This empirical approach gives maximum flexibility when searching for consistent line identifications and determining an approximate photospheric velocity (or identifying features associated with ions that are detached: i.e., appear to be present only at range of velocities that does not extend down to the photosphere). This approach has been widely used in the interpretation, and empirical subclassification, of SNe Ia (see, e.g., Branch et al. 2005, 2009, and references therein), in the characterization of SNe Ibc (e.g., Millard et al. 1999) and, more recently, in the emerging class of superluminous SNe (e.g., Nicholl et al. 2014). The major advantage of this class of spectral modeling is the ease with which calculations can be carried out (runtimes of seconds), which makes it practical to use algorithms to systematically explore parameter spaces (Thomas et al. 2011). However, the lack of a self-consistent treatment of ionization (or thermal properties) mean that important physical quantities (such as absolute elemental abundances or densities) cannot be easily extracted and considerable care must be taken if information beyond a qualitative estimate of composition (and/or velocity) is required.

6.2

Empirical Determination of Composition

To quantitatively infer elemental composition, it is necessary to use more sophisticated methods that estimate self-consistent ionization/excitation states in the ejecta. A variety of approaches can be used, but for semiempirical modeling, codes that retain a “core-halo” photospheric boundary condition (see, e.g., Mazzali 2000, and similar codes) have proved effective. Their modest computational expense makes it relatively easy to search for good spectral fits despite the need to explore large parameter spaces. In particular, while early semiempirical modeling typically considered modeling single spectra using single-composition ejecta models, modern studies attempt to develop semiempirical stratified models that match time-series of spectra (Sasdelli et al. 2014; Stehle et al. 2005, and references therein). The results of such analyses place constraints on the required elemental yields, velocities, and degrees of (effective) mixing in metal-rich SNe and thus inform the development of explosion/progenitor theories. As one example, Fig. 7 shows a comparison of the observed spectrum of the peculiar Type I supernova SN 2015H to a simple spectral model developed by Magee et al. (2016) using the TARDIS radiative transfer code (Kerzendorf and Sim 2014). This illustrates that good matches to data can be achieved with relatively simple methods. It also highlights the complexity of spectrum formation in metal-

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Fig. 7 Spectral modeling of the peculiar supernova SN 2015H. The lower panel shows a comparison of the model spectrum (blue) to the observed spectrum (black) at an epoch of 6 days after peak brightness. The model is based on a power-law density profile with elemental abundances varied to match the data (see Magee et al. 2016). The upper panel illustrates how the synthetic calculation can be used to understand the formation of the spectral features. The color coding in the positive region (above white dashed line) indicates which elements are responsible for the last interaction of escaping photons in the simulation (the area under the spectrum is shaded proportional to the contribution of each element; elements are identified in the color bar). The colors below the white line indicate which elements are responsible for absorbing (or scattering) photons out of each wavelength bin. Black-shaded regions indicate contributions to the spectrum that have emerged from the inner boundary of the calculation without interaction; gray indicates regions where only electron scattering has occurred (Figure from Magee et al., Astronomy & Astrophysics, 589, A89. DOI: 10.1051/0004-6361/20152836, 2016, reproduced with permission ©ESO)

rich supernovae: the iron-group elements blanket most of the spectrum and few regions are affected by only one species. However, it is recognized that there will always be some level of degeneracy in empirical spectral modeling and limitations imposed by approximations made, which can be difficult to quantify. For example, it is common to impose a specific density profile for the SN ejecta that is based on some known explosion model (or else to adopt a simple analytic form). Also, in the interests of efficiency, semiempirical work often makes use of approximate non-LTE ionization schemes (e.g., Mazzali and Lucy 1993) which can be effective but require that care is taken in the description of, e.g., the ionizing far-UV flux (Pauldrach et al. 1996). In addition,

31 Spectra of Supernovae During the Photospheric Phase

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whenever a sharp photospheric boundary condition is used, the usual caveats for quantitative interpretation (Sect. 5.1) apply.

6.3

Synthetic Spectra for Explosion Models

Although the approaches described above can be guided by theoretical explosion models (e.g., by adopting an ejecta density profile or constraining relative elemental yields), their focus is typically on identifying what is required of an explosion in order to match the data. A complementary approach is to start from specific explosion models (provided, e.g., by hydrodynamical simulations) and calculate synthetic observables. In this case, the radiative transfer calculation, in principle, introduces no additional free parameters (i.e., the input model specifies the full density/composition structure) or degeneracies that need to be explored. This is often the style of modeling to which the most sophisticated radiative transfer codes are applied (e.g., Baron et al. 2006; Dessart and Hillier 2005b, 2010; Höflich et al. 1998; Kasen et al. 2006; Kromer and Sim 2009; Sauer et al. 2006). Such calculations yield synthetic spectra, light curves, and/or spectropolarimetry that can be compared to data to assess the effectiveness of the model. Fig. 8 shows example comparisons of synthetic spectra and spectropolarimetry for a 3D white-dwarf thermonuclear explosion model to observations of a normal SN Ia. In this case it can be seen that the overall agreement in the shape of the spectra and the degree of polarization are relatively good, providing support for the model. However, there is also clear disagreement in the shapes and strengths of notable features, such as Si II 6355 and the Ca II infrared triplet (8567 Å). These

P (%)

Scaled Fλ

3.0

3.0 SN 2001el −7 d N100-DDT n5 −7 d

2.0

SN 2001el −2 d N100-DDT n5 −2 d

SN 2001el +7 d N100-DDT n5 +7 d

2.0

1.0

1.0

0.0

0.0

0.6

0.6

0.4

0.4

0.2

0.2

0.0

5000

6000

7000

˚ Wavelength (A)

8000

5000

6000

7000

˚ Wavelength (A)

8000

5000

6000

7000

8000

0.0

˚ Wavelength (A)

Fig. 8 Synthetic spectra (upper panels, red) and degree of polarization (lower panels, red) computed for a selected line of sight in the N100-DDT white-dwarf thermonuclear explosion model of Seitenzahl et al. (2013) for three epochs (7 , 2, and C7 days relative to maximum light, left to right). For comparison, observations of the normal SN Ia SN 2001el are shown in black (data from Wang et al. 2003). The error bars drawn in the lower panels indicate the scale of Monte Carlo noise in the simulated spectropolarimetry (see Bulla et al. 2016 for details) (Figure reproduced from Bulla et al. 2016, Monthly Notices of the Royal Astronomical Society, 462, 1039. DOI: 10.1093/mnras/stuw1733)

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S.A. Sim

discrepancies can be used to identify shortcomings of the underlying model and motivate refinement and/or development of alternative explosion simulations. Studies of this type have now been carried out for models of most major classes of SN and provide a powerful means to quantitatively evaluate the successes and failures of explosion models. Analysis of these full simulations also provides the best insight to understand the interplay among physical processes and help refine approximations that can be adopted in more simplified codes. Nevertheless, the substantial computational expense for full explosion model simulations means that such calculations are still relatively rare and it is expensive to systematically “tweak” models to quantitatively match observations. Furthermore, even the most sophisticated codes still make a number of assumptions: currently, the majority of studies made either neglect (or at least significantly simplify) the treatment of nonLTE effects or else are limited to studies of spherically symmetric models.

6.4

Distance Determination

Throughout the history of the modeling and interpretation of SN spectra, there has been continued interest in the use of Type IIP SNe as distance indicators (e.g., Baron et al. 2004; Dessart and Hillier 2006; Eastman et al. 1996; Kirshner and Kwan 1974). Several distinct approaches have been suggested, but the underlying principle of several is that if a physical model for the SN spectrum can be developed, that model will predict the true luminosity, which can then be compared to the observed flux to infer distance. The methods used have been gradually refined, and it has been shown that distances accurate to 10% can be achieved, provided that sufficiently highquality, detailed spectral models are developed for good quality data sets (Dessart and Hillier 2006). Thus, with modern spectral modeling, the prospects are now good for accurate distance measurements from samples of SNe II.

7

Conclusions

Despite their complexity, the observation and analysis of photospheric-phase spectra remains central to the study of supernovae: such data are relatively easy to obtain (compared to e.g., late-phase spectra, when the supernova is much fainter, or to polarimetry, for which very high signal to noise is needed) and are much more informative than photometry alone. Thus continued advancement in our quantitative ability to interpret and model photospheric phase spectra is essential. In this short article, we have only scratched the surface of this topic and must direct the reader to the references given for more complete, quantitative discussions. We hope, however, to have given the reader a flavor of both the physics at work in the formation of photospheric-phase spectra and how its study can be used to help unravel the mysteries of supernova explosions.

31 Spectra of Supernovae During the Photospheric Phase

8

791

Further Reading

Further background information on the physical processes mentioned in Sect. 3 are given, for example, in the textbooks by Rybiki and Lightman (1985) and Tennyson (2011). Hubeny and Mihalis (2015) provide a substantial introduction to the theory of spectral formation, including for expanding atmospheres (see also Lamers and Casinelli 1999). For details of particular applications, and the radiative transfer codes/techniques currently used, we refer the reader to the references given in Sects. 5 and 6.

9

Cross-References

 Introduction to Supernova Polarimetry  Observational and Physical Classification of Supernovae  Spectra of Supernovae in the Nebular Phase

References Auer LH, van Blerkom D (1972) Electron scattering in spherically expanding envelopes. ApJ 178:175 Baron E, Bongard S, Branch D, Hauschildt PH (2006) Spectral modeling of SNe Ia near maximum light: probing the characteristics of hydrodynamical models. ApJ 645:480 Baron E, Hauschildt PH, Nugent P, Branch D (1996) Non-local thermodynamic equilibrium effects in modelling of supernovae near maximum light. MNRAS 283:297 Baron E, Nugent PE, Branch D, Hauschildt PH (2004) Type IIP supernovae as cosmological probes: a spectral-fitting expanding atmosphere model distance to SN 1999em. ApJL 616:L91 Blinnikov SI, Eastman R, Bartunov OS, Popolitov VA, Woosley SE (1998) A comparative modeling of supernova 1993J ApJ 496:454 Branch D, Baron E, Hall N, Melakayil M, Parrent J (2005) Comparative direct analysis of type Ia supernova spectra. I. SN 1994D. PASP 117:545 Branch D, Chau Dang L, Baron E (2009) Comparative direct analysis of type Ia supernova spectra. V. Insights from a larger sample and quantitative subclassification. PASP 121:238 Bulla M, Sim SA, Kromer M, Seitenzahl IR, Fink M, Ciaraldi-Schoolmann F et al (2016) Predicting polarization signatures for double-detonation and delayed-detonation models of Type Ia supernovae. MNRAS 462:1039 Chugai NN (2001) Broad emission lines from the opaque electron-scattering environment of SN 1998S. MNRAS 326:1448 Chugai NN, Utrobin VP (2014) Disparity between H ˛ and H ˇ in SN 2008 in: inhomogeneous external layers of type IIP supernovae? Astron Lett 40:111 Dessart L, Hillier DJ (2005a) Distance determinations using type II supernovae and the expanding photosphere method. A&A 439:671 Dessart L, Hillier DJ (2005b) Quantitative spectroscopy of photospheric-phase type II supernovae. A&A 437:667 Dessart L, Hillier DJ (2006) Quantitative spectroscopic analysis of and distance to SN 1999em. A&A 447:691

792

S.A. Sim

Dessart L, Hillier DJ (2008) Time-dependent effects in photospheric-phase type II supernova spectra. MNRAS 383:57 Dessart L, Hillier DJ (2010) Supernova radiative-transfer modelling: a new approach using nonlocal thermodynamic equilibrium and full time dependence. MNRAS 405:2141 Dessart L, Hillier DJ (2011) Synthetic line and continuum linear-polarization signatures of axisymmetric type II supernova ejecta. MNRAS 415:3497 Dessart L, Hillier DJ, Gezari S, Basa S, Matheson T (2009) SN 1994W: an interacting supernova or two interacting shells? MNRAS 394:21 Eastman RG, Pinto PA (1993) Spectrum formation in supernovae – numerical techniques. ApJ 412:731 Eastman RG, Schmidt BP, Kirshner R (1996) The atmospheres of type II supernovae and the expanding photosphere method. ApJ 466:911 Fisher A (2000) Direct analysis of Type Ia supernovae spectra. PhD thesis. University of Oklahoma Hauschildt PH, Baron E (1999) Numerical solution of the expanding stellar atmosphere problem. J Comput Appl Math 109:41 Hauschildt PH, Baron E (2010) A 3D radiative transfer framework. VI. PHOENIX/3D example applications. A&A 509:A36 Hillier DJ (1991) The effects of electron scattering and wind clumping for early emission line stars. A&A 247:455 Hillier DJ, Dessart L (2012) Time-dependent radiative transfer calculations for supernovae. MNRAS 424:252 Höflich P, Gerardy CL, Marion H, Quimby R (2006) Signatures of isotopes in thermonuclear supernovae. New Astron Rev 50:470 Höflich P, Wheeler JC, Thielemann FK (1998) Type Ia supernovae: influence of the initial composition on the nucleosynthesis, light curves, and spectra and consequences for the determination of ˝ M and . ApJ 495:617 Hubeny I, Mihalis D (2015) Theory of stellar atmospheres. Princeton University Press, Princeton Jack D, Hauschildt PH, Baron E (2009) Time-dependent radiative transfer with PHOENIX. A&A 502:1043 Jeffery DJ (1995a) An expansion opacity formalism for the Sobolev method. A&A 299:770 Jeffery DJ (1995b) The Sobolev optical depth for time-dependent relativistic systems. ApJ 440:810 Karp AH, Lasher G, Chan KL, Salpeter EE (1977) The opacity of expanding media – the effect of spectral lines. ApJ 214:161 Kasen D (2006) Secondary maximum in the near-infrared light curves of type Ia supernovae. ApJ 649:939 Kasen D, Thomas RC, Nugent P (2006) Time-dependent Monte Carlo radiative transfer calculations for three-dimensional supernova spectra, light curves, and polarization. ApJ 651:366 Kerzendorf WE, Sim SA (2014) A spectral synthesis code for rapid modelling of supernovae. MNRAS 440:387 Kirshner RP, Kwan J (1974) Distances to extragalactic supernovae. ApJ 193:27 Kirshner RP, Kwan J (1975) The envelopes of type II supernovae. ApJ 197:415 Kromer M, Sim SA (2009) Time-dependent three-dimensional spectrum synthesis for type Ia supernovae. MNRAS 398:1809 Lamers HJGLM, Casinelli JP (1999) Introduction to stellar winds. Cambridge University Press, Cambridge Lucy LB (1999) Improved Monte Carlo techniques for the spectral synthesis of supernovae. A&A 345:211 Lucy LB (2005) Monte Carlo techniques for time-dependent radiative transfer in 3-D supernovae. A&A 429:19 Magee MR, Kotak R, Sim SA, Kromer M, Rabinowitz D, Smartt SJ et al (2016) The type Iax supernova, SN 2015H. A white dwarf deflagration candidate. A&A 589:A89 Maund JR, Wheeler JC, Patat F, Baade D, Wang L, Höflich P (2007) Spectropolarimetry of the type Ib/c SN 2005bf. MNRAS 381:201

31 Spectra of Supernovae During the Photospheric Phase

793

Mazzali PA (2000) Applications of an improved Monte Carlo code to the synthesis of early-time supernova spectra. A&A 363:705 Mazzali PA, Lucy LB (1993) The application of Monte Carlo methods to the synthesis of earlytime supernovae spectra. A&A 279:447 Millard J, Branch D, Baron E, Hatano K, Fisher A, Filippenko AV, Kirshner RP, Challis PM, Fransson C, Panagia N, Phillips MM, Sonneborn G, Suntzeff NB, Wagoner RV, Wheeler JC (1999) Direct analysis of spectra of the type IC supernova SN 1994I. ApJ 527:746 Nicholl M, Smartt SJ, Jerkstrand A, Inserra C, Anderson JP, Baltay C et al (2014) Superluminous supernovae from PESSTO. MNRAS 444:2096 Nomoto K, Thielemann F-K, Yokoi K (1984) Accreting white dwarf models of type I supernovae. III – carbon deflagration supernovae. ApJ 286:644 Patat F, Baade D, Höflich P, Maund JR, Wang L, Wheeler JC (2009) VLT spectropolarimetry of the fast expanding type Ia SN 2006X. A&A 508:229 Pauldrach AWA, Duschinger M, Mazzali PA, Puls J, Lennon M, Miller DL (1996) NLTE models for synthetic spectra of type IA supernovae. The influence of line blocking. A&A 312:525 Pinto PA, Eastman RG (2000) The physics of type IA supernova light curves. II. Opacity and diffusion. ApJ 530:757 Röpke FK, Seitenzahl IR, Benitez S, Fink M, Pakmor R, Kromer M, Sim SA, Ciaraldi-Schoolmann F, Hillebrandt W (2011) Modeling type Ia supernova explosions. Prog Part Nucl Phys 66:309 Rybiki GB, Lightman AP (1985) Radiative processes in astrophysics. Wiley, Weinheim Sasdelli M, Mazzali PA, Pian E, Nomoto K, Hachinger S, Cappellaro E, Benetti S (2014) Abundance stratification in type Ia supernovae – IV. The luminous, peculiar SN 1991T. MNRAS 445:711 Sauer DN, Hoffmann TL, Pauldrach AWA (2006) Non-LTE models for synthetic spectra of type Ia supernovae/hot stars with extremely extended atmospheres. II. Improved lower boundary conditions for the numerical solution of the radiative transfer. A&A 459:229 Seitenzahl IR, Ciaraldi-Schoolmann F, Röpke FK, Fink M, Hillebrandt W, Kromer M et al (2013) Three-dimensional delayed-detonation models with nucleosynthesis for type Ia supernovae. MNRAS 429:1156 Sobolev VV (1960) Moving envelopes of stars. Harvard University Press, Cambridge Stehle M, Mazzali PA, Benetti S, Hillebrandt W (2005) Abundance stratification in type Ia supernovae – I. The case of SN 2002bo. MNRAS 360:1231 Tanaka M, Kawabata KS, Maeda K, Hattori T, Nomoto K (2008) Optical spectropolarimetry and asphericity of the type Ic SN 2007gr. ApJ 689:1191 Tennyson J (2011) Atomic spectroscopy: an introduction to the atomic and molecular physics of astronomical spectra. World Scientific Publishing Co. Pte. Ltd, Hackensack Thomas RC, Kasen D, Branch D, Baron E (2002) Spectral consequences of deviation from spherical composition symmetry in type Ia supernovae. ApJ 567:1037 Thomas RC, Nugent PE, Meza JC (2011) SYNAPPS: data-driven analysis for supernova spectroscopy. PASP 123:237 Utrobin VP, Chugai NN (2005) Strong effects of time-dependent ionization in early SN 1987A. A&A 441:271 Wang L, Baade D, Höflich P, Kokhlov A, Wheeler JC, Kasen D et al (2003) Spectropolarimetry of SN 2001el in NGC 1448: asphericity of a normal type Ia supernova. ApJ 591:1110 Wollaeger RT, van Rossum DR, Graziani C, Couch SM, Jordan IV GC, Lamb DQ, Moses GA (2013) Radiation transport for explosive outflows: a multigroup hybrid Monte Carlo method. ApJS 209:36

Spectra of Supernovae in the Nebular Phase

32

Anders Jerkstrand

Abstract

When supernovae enter the nebular phase after a few months, they reveal spectral fingerprints of their deep interiors, glowing by radioactivity produced in the explosion. We are given a unique opportunity to see what an exploded star looks like inside. The line profiles and luminosities encode information about physical conditions, explosive and hydrostatic nucleosynthesis, and ejecta morphology, which link to the progenitor properties and the explosion mechanism. Here, the fundamental properties of spectral formation of supernovae in the nebular phase are reviewed. The formalism between ejecta morphology and line profile shapes is derived, including effects of scattering and absorption. Line luminosity expressions are derived in various physical limits, with examples of applications from the literature. The various physical processes at work in the supernova ejecta, including gamma deposition, non-thermal electron degradation, ionization and excitation, and radiative transfer, are described and linked to the computation and application of advanced spectral models. Some of the results derived so far from nebular-phase supernova analysis are discussed.

Contents 1 2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Line Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Spherical Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Asymmetric Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Radiative Transfer Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Line Luminosities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Line Transfer in the Sobolev Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

796 797 798 801 803 806 807

A. Jerkstrand () Astrophysics Research Centre (ARC), Queen’s University Belfast, Belfast, UK Max-Planck Institute for Astrophysics, Garching, Germany e-mail: [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_29

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3.2 Local Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Optical Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Non-local-Thermodynamic-Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Radioactive Powering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Deposition of Decay Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Degradation of Non-thermal Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Spectral Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Nebula Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Level Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Radiative Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Application of Spectral Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Hydrogen-Rich SNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Stripped-Envelope SNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Thermonuclear Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

808 809 813 814 815 816 819 821 823 824 826 826 828 829 832 836 838 838 839

Introduction

As the supernova expands, reduced column densities reduce the optical depths. Recombination removes free electrons, which further reduces the Thomson opacity. Decreasing temperatures lead to lower populations of excited states, reducing the number of optically thick lines and bound-free continua. After a few months, the nebula becomes mostly optically thin and its deep interior becomes visible. It then joins the class of emission line nebulae, which includes also HII regions, planetary nebulae, and active galactic nuclei. The spectrum changes from having a blackbody character with atmospheric absorption lines imposed to an emission line spectrum rich in spectral fingerprints from the newly synthesized elements. The supernova continues to shine due to radioactive decay of isotopes such as 56 Ni produced in the explosion. Eventually the supernova enters the “supernova remnant” phase. There is no generally agreed definition of when this occurs, but the term “remnant” usually refers to spatially resolved supernovae of age 102 –104 years where powering occurs by circumstellar interaction or a central pulsar (as in the case of the Crab). By “nebular phase” we usually refer to epochs from a few months to a few years. Most supernovae become too faint to be observed after this time, unless they enter into a phase of strong circumstellar interaction, which brings them toward a remnant phase. By studying nebular-phase supernovae, we can learn about many important properties of the exploded star. The late-time light curves provide constraints on the amount and distribution of radioactive isotopes created in the explosion. The spectral line strengths allows inference of ionic masses, emitting volumes, and physical conditions. The line profiles give information on the expansion velocity, the morphology and mixing of the ejecta, and dust formation. Putting all this information together gives us an opportunity to determine the properties of the progenitor stars, test stellar evolution and nucleosynthesis theory, put constraints

32 Spectra of Supernovae in the Nebular Phase

797

on the explosion mechanism, and improve our understanding of the formation of black holes and neutron stars. The modelling and interpretation of nebular-phase supernova spectra are, however, formidable challenges. Complexities include heterogeneous composition throughout the nebula, fast and differential velocity field, non-thermal processes, and a non-local-thermodynamic-equilibrium (NLTE) gas state. This means that there is a long way to go from having an observed spectrum to inferring physical properties of the ejecta. This text is written with the aims to explain the basic aspects of nebular-phase line formation, demonstrate the use of simple models and analytic methods, provide guidance to the ingredients and application of advanced models, and review of some of the results obtained so far. We begin in Sect. 2 by studying how line profiles are formed in the expanding nebula. In Sect. 3 we study the connection between physical conditions and line luminosities. Section 4 reviews how powering occurs in the typical scenario of a radioactive energy source, and Sect. 5 reviews how physical conditions are calculated once the powering situation is known. Section 6 serves to review the availability of advanced models and to illustrate some output and results of these.

2

Line Profiles

By the time the supernova enters the nebular phase, it has reached homologous expansion (purely radial velocities with V D r=t ). The line broadening due to the expansion (typically a few 1000 km s1 ) is about three orders of magnitude larger p than the line broadening due to thermal motions (V0 D kT =m, a few km s1 for the atoms), and the line profiles are therefore determined by the velocity structure of the nebula, but not by its temperature. Figure 1 illustrates the situation. Here the supernova is represented as a homologously expanding sphere with maximum velocity Vmax . Let the x-axis be along the line of sight, and the y and z axes be perpendicular (z into the paper). Define  D  0 , where 0 is the line rest frame center frequency and is the observed frequency. The observed flux at frequency has contribution from emission in the sheet perpendicular to the line of sight centered at projected velocity Vx D  = 0 c (distance x D Vx t from the center) having thickness Vx D x=t equal to the intrinsic line width V0 (which we assume is constant for now). Because the thermal line widths are small (V0  Vmax ), the observed line profile provides a “scan” through the nebula, each frequency giving a 2D integration of the emission from the sheet at the corresponding resonance depth. From a given surface segment of the sheet, with area dA, the observed flux is dF D I d ! where I is the specific intensity in the direction of the observer and d ! D 4 dA=.4 D 2 / D dA=D 2 is the solid angle subtended by the segment dA as seen by the observer at distance D. Integrating over segments, the total flux is F D D

2

Z

C1

Z

C1

I .x. /; y; z/dyd z zD1

yD1

(1)

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Fig. 1 Geometry of line formation

2.1

Spherical Symmetry

If we assume spherical symmetry, it is enough to use a single perpendicular (cylindrical) coordinate, which we denote as p. Each annulus has area dA D 2 pdp, so d ! D 2 pdp=D 2 , giving Z pmax .x/ 2 F D 2 D I .x. /; p/pdp (2) 0

1=2  2 where pmax D Rmax  x2 , where Rmax is the outer radius of the nebula. Because  2  2 1=2 p D r x , pdp D rdr and Z Rmax I .r; x/rdr (3) F D 2 D 2 rDx. /

The specific intensity I is obtained by solving the transfer equation dI D j ds  ˛ I ds through the sheet, where j and ˛ are emission and absorption coefficients. For an optically thin line (the optically thick case gives the same solution with a suitable choice of emissivity, see later), using that V0 =Vmax  1 (so r is kept fixed in the integrand) Z xCx=2 I .r; x C x=2/ D j .r; x 0 /dx 0 (4) xx=2

32 Spectra of Supernovae in the Nebular Phase

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In the comoving frame, the emissivity is j .r/ D j0 .r/.r;  0 /, where .r;  0 / R C =2 is the intrinsic line profile, normalized so that  00=2 .r;  0 /d D 1 (in our heuristic picture, the line profile is a box but the results hold generally). In the observer frame, ignoring v=c effects on the intensity, j .r; x/ D j0 .r/.r; 0  0 /, where the comoving frequency 0 D .1  Vx =c/. Because dx D d Vx t D .d = 0 / ct , the integral is ct I .r; x C x=2/ D 0

Z

C 0 =2

j0 .r/.r; 0  0 /d 0 D

 0 =2

ct j0 .r/ 0

(5)

Finally, the line profile is F D 2 D

2 ct

0

Z

Rmax

j0 .r/rdr

(6)

j0 .V /Vd V

(7)

rDx. /

Or, using r D V t , we can also write this as

F D 2 t 2 D 2

ct 0

Z

Vmax

V . /

One may in principle attempt to determine j0 .V / by discretizing this equation and fitting a least-squares solution to an observed line profile. Fransson and Chevalier (1989) suggest a variant of this, where j0 .V / at a given V is directly estimated from the derivative of the line profile dF .V / ct D 2 t 2 D 2 j0 .V /V dV 0

(8)

So far, this inverse mapping method has not been applied much in the literature. A desirable goal is to obtain the density distribution .V / of the emitting ion. But connecting j0 .V / to .V / requires knowing other functions such as temperature T .V / and electron density ne .V /. For an explicit calculation of the line profile from the gas state, one needs to insert the expression for j0 . It is given by j0 D

1 nu AˇS h 0 4

(9)

where nu is the number density of the upper level, A is the radiative decay rate, and ˇS is the local escape probability (see Sect. 3.1), which allows also optically thick lines to be treated in this formalism. Some limiting cases for line profiles are now derived, with illustrations in Fig. 2.

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Fig. 2 Line profiles (F ) for six types of ejecta distributions

2.1.1 Uniform Sphere With j0 .V / D constant, Eq. 7 becomes (using interchangeably  0 D 0 V =c) " 2 #  V 2 2 ct 2 F D t D V j0 1  (10) 0 max Vmax p The line profile is parabolic in shape. The FWHM of this profile is 2  Vmax . We can easily understand the parabolic shape as arising from the parabolic function describing the area of the resonance sheets.

2.1.2 With

Gaussian Profile  j0 .V / D jmax exp

V 2 2V02

 (11)

we get  V 2 Vd V 2V02 V . /   V 2 2 2 ct 2 jmax V0 exp D 2 t D 0 2V02

F D 2 t 2 D 2

ct jmax 0

Z



1

exp

(12)

The line profile is also Gaussian with a FWHM corresponding to the FWHM of the emissivity function (=2.35 V0 ).

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2.1.3 Thin Shell With a thin shell, j0 .V / D j0 , between Vmax  V and Vmax , we get i ct 1 h 2  .Vmax  V /2  F D 2 t 2 D 2 j0 Vmax 0 2 ct 2 t 2 D 2 j0 Vmax V D constant 0

(13) (14)

The line profile is a box, bounded by ˙Vmax .

2.1.4 Thick Shell Let the inner edge be Vin . For V < Vin , the lower integration limit is set by Vin and the flux is therefore independent of V and constant. For Vin < V < Vmax , the solution is the same as the uniform sphere case. "  #  Vin 2 2 2 ct 2 F D t D j0 Vmax 1  (15) ; V < Vin 0 Vmax " 2 #  V 2 2 ct 2 F D t D j0 Vmax 1  (16) ; V > Vin 0 Vmax The line profile is flat topped with parabolic wings.

2.2

Asymmetric Distributions

We now study a few nonspherically symmetric configurations, starting with disks. For the disks, the discussion is based on an edge-on viewing angle, but the line profiles will keep their shapes, squeezed in width, for other viewing angles.

2.2.1 Uniform Disk For a uniform disk (consider Fig. 1 as now showing a face-on disk with the observer edge-on to the right), the sheet area equals the p thickness of the disk z times the 2 distance between the inner and outer edges (2 Rmax  x 2 ). Specifically, from Eq. 1 we get ct ct F D 2D 2 j0 zymax . / D 2t 2 D 2 j0 Vz Vmax 0 0

s 1



V Vmax

2 (17)

This profile is less sharply peaked than the uniform sphere or Gaussian distributions.

2.2.2 Disk with Hole In this case F D D 2 z2

Z

ymax .x/

I .x. /; y/dy ymin .x/

(18)

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A. Jerkstrand

q p 2 2 where ymax .x/ D Rmax  x 2 and ymin .x/ D Rhole  x 2 for x < h, where h D Rhole =Rmax is the normalized hole radius, and ymin D 0 otherwise. Then F D 2t 2 D 2 2s 4 1



V Vmax

s

2 

h2

 

s

V Vmax 

1

2

V Vmax

3 5 ;

2

ct j0 Vz Vmax  0 

 ;

V Vmax V Vmax

(19)

 h

(21)



The high velocities have the same solutionras the uniform disk. Once the hole is 2 r 2   V V crossed (V < Vmax h), the projected area is 1  Vmax  h2  Vmax . The second term grows faster with decreasing V =Vmax , and the line profile develops two horns at plus and minus the velocity of the inner edge of the disk. Figure 2 summarizes the various line profiles discussed.

2.2.3 Many Clumps If the emission comes from a large number of clumps with a more or less random distribution within a spherically symmetric or axisymmetric region, the line profiles will have a global shape determined by the equations above (using the probability distribution as j0 .V /) but with small-scale structure determined by the random positions of the clumps. Assume that we have N identical clumps with (comoving) expansion velocities Vc (their “width” is Vc ), distributed randomly within a sphere of velocity Vmax . The resulting line profile will have squiggles with statistical properties depending on N and " D Vc =Vmax . Figure 3 shows the result of simulating a line profile with Fig. 3 Line profile resulting from random draws of N D 103 clumps and " D 0:05, distributed in a uniform spherical region

32 Spectra of Supernovae in the Nebular Phase

803

N D 103 and " D 0:05. A quantitative method to use the statistical properties of these fluctuations to infer the statistical properties of the clump distribution was developed by Chugai (1994). Its deployment needs high-resolution spectroscopy and is therefore suitable for the most nearby supernovae.

2.2.4 Comments A final few comments are in place. We have derived line profile shapes neglecting effects of time delays and relativistic effects, apart from Doppler shifts. Addressing the first point, photons arriving from the receding side of the SN were emitted a time tdelay 2Vmax t =c before photons from the approaching side. If there is an evolution of emissivity j0 on the evolutionary timescale t , there is therefore a damping of the red side of the line compared to the blue of order 2Vmax =c, which is a few percent for typical Vmax . But if evolution occurs on a faster radioactive timescale, the effect is increased by a factor tdelay = decay . tdelay 2Vmax t =c e decay D e decay

(22)

For example, if t D 500d and decay D 111d (as for 56 Co), then t = decay D 4:5, and if Vmax D 5000 km s1 , the factor becomes 15%. It may be increased further if gamma ray leakage further shortens the timescale over which emissivity changes. The source movement also increases the blue intensity as the observed time interval is shorter than in the emitting frame, and vice versa decreases the red side. The Lorentz transformations of specific intensity give a . = 0 /3 factor or a change of order 3Vmax =c in our nonrelativistic limit. With Vmax =c of a few percent, the total additional effect is of order 5–10%.

2.3

Radiative Transfer Effects

So far we have assumed that apart from self-absorption (which can be treated as a modification to the emissivity j0 in the Sobolev approximation, see Sect. 3.1), the photons escape freely the nebula. For any given epoch, this is a reasonable approximation beyond some wavelength. At short wavelengths, various opacities remain, however, for years or decades and can alter both line profiles and luminosities.

2.3.1 Continuous Scattering Opacity Continuous scattering may occur by free electrons or dust. This leads to one or several “bounces” for the photons in the homologous (Hubble) flow. Because the comoving frame wavelength is always lower than in the original emitting frame, there is on average a net energy loss, and the line profile becomes distorted with an enhanced red tail. In the nebular phase, the electron scattering optical depth is e . 1, and the majority of photons will experience zero or one scattering event. The line profile

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A. Jerkstrand

Fig. 4 Line profiles resulting from a scattering opacity (e.g., electron or dust scattering) in a uniform sphere. The wavelength shifts of the peaks are written out

distortions are thus relatively mild. Figure 4 shows the resulting line profiles for e D 1; 2; 3 in a uniform sphere setup, from a Monte Carlo simulation. The scattering opacity produces blueshifts of the peak, although quite weak. For example, at e D 1, a shift of =max D 0:13 is obtained (or 390 km s1 for a 3000 km s1 broad line). If one considers also the frequency redistribution in the comoving frame due to the thermal p motions of the scattering particles, a further symmetric broadening on the scale kT =m occurs as well. Only electrons provide any significant thermal effect due to their low mass. Still, at 5000 K the thermal electron velocity is just 300 km s1 , much lower than the supernova expansion velocity, so this effect can be ignored unless very detailed results are needed.

2.3.2 Continuous Absorptive Opacity Continuous absorption (photon destruction) may occur by photoionization or dust. At long wavelengths also free-free absorption may occur. Assume that an absorptive opacity is present with an absorption coefficient ˛ (cm1 ). Consider, for example, purely absorbing dust that reemits at mid-infrared (MIR) wavelengths beyond our consideration. The emergent flux is by extension of Eq. 2 F D 2 D 2

Z 0

pmax.x/

I .x. /; p/e  .x. /;p/ pdp

(23)

32 Spectra of Supernovae in the Nebular Phase

805

The optical depth is .x; p/ D ˛ 

p  R2  p 2  x

(24)

where we now denote R D Rmax , and so F D 2 D

2 ct

Z

0

pmax.x/

j0 .r.x; p//e

  p ˛ xC R2 p 2

pdp

(25)

0

For constant emissivity, F D 2 D 2

ct j0 0

Z

pmax.x/

e

  p ˛ xC R2 p 2

pdp

(26)

0

p p 0 0 R2  p 2 , so p D R2  x 02 , xmin D R and xmax D Substitute x 0 D p 0 2 2 R  pmax D x. This last equality holds for positive x only. Then x dx 0 D 2pdp and Z

x

1 0 e ˛ .xCx /   x 0 dx 0 2

(27)

i ct 1 h  0 .1x/ O . 0  1/ C 0 xO C 1 j0 2 e 0 ˛

(28)

F D 2 D D D 2

2 ct

0

j0

x 0 DR

where 0 D ˛ R and we have denotedp xO D  = max . p 0 For negative x, use instead x 0 D  R2 p 2 . Then p D R2 x 02 , xmin D R 0 0 0 and xmax D jxj D x, x dx D 2pdp, and

D D 2

ct j0 0

Z

x

1 0 e ˛ .xx /   x 0 dx 0 2

(29)

i ct 1 h  0 .1x/ O . 0  1/  e 2 0 xO . 0 xO  1/ j0 2 e 0 ˛

(30)

F D 2 D 2

x 0 DR

These expressions can be used to fit line profiles affected by a destructive opacity to estimate 0 . The line profiles for 0 D 0:5; 1, and 2 are plotted in Fig. 5. There are two main differences to scattering opacities. First, there is no production of a red tail with =max > 1. Second, for a given 0 , the peaks are more strongly blueshifted. The location of the peak is found from equating the derivative of Eq. 28 to zero, giving xO peak D 1 

ln .1 C 0 / 0

(31)

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A. Jerkstrand

Fig. 5 Line profiles resulting from a destructive opacity, uniform sphere case

2.3.3 Line Absorption If line opacity can be described as a large set of finely spaced lines, its effect can be treated as a continuous opacity as described in the sections above. For scattering/absorption by one or a few lines, no generic treatment is possible, and a diverse set of line profiles can be produced. A common scenario is that only the longer wavelength line in a doublet or triplet emerges, as the bluer components are absorbed. Figure 6 shows six examples of line profiles from a doublet, separated by xO D 0:5. Here, equal emissivity in both lines gives a symmetric line in the optically thin case, a distorted line peaking close to the redder line wavelength for optically thick scattering, and again a symmetric but damped and flattened line for optically thick destructive opacity. The dashed, dot-dashed, and dotted curves show the cases when only the first (blue) line emits.

3

Line Luminosities

In this section expressions for line luminosities in different physical limits are examined. Physical conditions, such as temperature and electron density, are here parameters. The processes determining these are discussed in the following sections. As a first step, we consider how to treat line transfer in the supernova.

32 Spectra of Supernovae in the Nebular Phase

807

0

Fig. 6 Line profiles resulting from a doublet separated by =0 D 0:5: The center wavelengths are marked by dashed vertical lines. Solid lines correspond to equal (before transfer) emissivities in both lines, and dashed (optically thin), dot-dashed (scattering), and dotted (destructive) correspond to emission in only the blue line

3.1

Line Transfer in the Sobolev Approximation

Supernovae are still dense enough in the nebular phase that line optical depths can be high. It is in general a difficult problem to solve the radiative transfer through optically thick lines. Sobolev (1957) showed that a great simplification can be achieved in the high-velocity gradient limit, meaning situations where the velocity gradient of the expanding nebula is large enough that line profiles are traversed on a length scale smaller than the length scale over which physical conditions change. In the case of homologous expansion, the optical depth to traverse a line in this limit is given by the Sobolev optical depth   g l nu 1 gu 3 t (32) S D A nl 1  8 gl gu nl where gu and gl are the statistical weights of the upper and lower levels, nu and nl are the number densities,  is the wavelength, and t is time. For photons emitted in the line, the average escape probability can be shown to be ˇS D

1  e  S S

(33)

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A. Jerkstrand

These simplifications mean that we do not have to compute the detailed transfer through each line, but can treat them as infinitely narrow with optical depth and escape probability given by the expressions above. The total luminosity in the transition is given by the volume integral Z LD

nu Ah ˇS .nl ; nu /ˇd V

(34)

where ˇ is the angle-averaged nonlocal escape probability (with respect to absorption by photoionization, other lines, dust, etc). We will for now proceed by putting ˇ D 1; this factor can easily be added on to the final formulae if relevant.

3.2

Local Thermodynamic Equilibrium

In Local Thermodynamic Equilibrium (LTE), nu and nl are related by the temperature only. LTE requires that both populations and depopulations of the level occur mainly by thermal collisions or by radiative interaction with a (possibly diluted) blackbody radiation field. As a starting point, one can consider the competition between thermal collisional deexcitation, with a rate ne Q.T /, where Q.T / is the collision rate (cm3 s1 ), and spontaneous radiative deexcitation, with a rate AˇS . The critical density is defined as the electron density above which collisional deexcitations dominate: ncrit e .T; nl ; nu / D

AˇS .nl ; nu / Q.T /

(35)

Note the difference from static media in that there may be a dependency on density as well as temperature. The temperature dependence of Q.T / is usually quite weak, so ncrit depends only weakly on T . Q.T / is given by (see, e.g., Osterbrock and e Ferland 2006) Q D 8:6  106 T 1=2 gu1 # .T /

cm3 s1

(36)

where # .T / is the effective collision strength, which depends on the cross section function for the particular transition, but is typically of order unity and with a normally weak temperature dependency. The electron density in a uniform sphere is  1 ne D 2  109 mp



M 1 Mˇ



V 3000 km s1

3

 3  t xe  f 1 3 cm 0:1 200 d 0:1 (37)

where  is the mean atomic weight, mp is the proton mass, xe D ne =nnuclei is the electron fraction, and f is the filling factor. To have critical densities below typical

32 Spectra of Supernovae in the Nebular Phase

809

nebular densities of ne 109 cm3 (i.e., LTE), Eq. 35 with a typical value Q107 cm3 s1 shows that transitions need to be forbidden/semi-forbidden (A . 102 s1 ) or effectively forbidden/semi-forbidden (AˇS . 102 s1 ). The second requirement for LTE, population by thermal collisions, requires the upper level (energy Eu ) to be reachable from the thermal pool, Eu . a few  kT . Because T . 5000 K = 0.4 eV in the nebular phase, that means Eu . a few eV. The lines fulfilling both of these criteria are low-lying forbidden transitions in atoms and ions of, e.g., C, N, O, Si, S, Ca, Fe, Co, and Ni. Table 1 lists some important transitions, all clearly detected in nebular SNe (there are more transitions fulfilling the criteria but which have not clearly been identified, because they are either too weak or blended with other lines). Some lines that are not in the table warrant comment. To populate a level mainly by thermal collisions requires not only low enough excitation energy but also a reasonably high abundance compared to the next ionization stage; recombinations may otherwise become the dominant population mechanism. A recombinationdominated situation often arises for neutral elements with low-ionization potential, such as Na I and Mg I. A second issue is for resonance lines. These may fulfil AˇS . 102 s1 , but their high optical depth means they can become dominated by scattering. A line like Na I 5890 Å for example, has both of these properties and would be poorly modelled as an LTE emission line.

3.3

Optical Depth

For lines connected to the ground multiplet, the optical depths can be estimated by taking Ml  .gl =gg /Mion , where gg is the total ground multiplet statistical weight. This assumes that most atoms are in the ground multiplet and that this is in LTE, both normally good approximations. Then, Eq. 32 gives, for a uniform sphere, ignoring stimulated emission:     3 1 Mion  V 29 gu S D 4:3  10 mp f 1 t 2 A3 gg 1 Mˇ 3000 km s1 (38)   1 Define " D 4:3  1029 mp gu =gg A3 (atomic constants only,  is the mean molecular weight and mp is the proton mass) and "n D "=1014 . Then, the time at which S D 1 is     3=2  Mion 1=2 V f 1=2 1=2 (39) tthin D 370d "n 1 Mˇ 0:1 3000 km s1 This equation has stronger dependencies on Mion and V than the inversion of the LTE equation (37) has; thus, estimates for the duration of the optically thick phase are more uncertain than estimates for the duration of the LTE phase. Column 10 in Table 1 lists the epochs (tthi n ) at which the lines become optically thin for typical masses, V D 3000 km s1 , and f D 0:1.

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A. Jerkstrand

Table 1 Commonly observed SN lines that are expected to be in LTE for some part of the nebular phase. For doublets and triplets, only one of the components is listed. The line wavelengths (col. 2) are followed by level IDs in parenthesis by energy ordering. The effective collision strengths # (column 6), and resulting critical densities (column 7), are for T D 5000 K and ˇS D 1 (if the line is optically thick tLTE can be longer). Column 8 lists the length of time the line is in LTE, using  1=3  1 .xe =0:1/1=3 .f =0:1/1=3 ). The tt hi n V =3000 km s1 Eq. 37 (tLTE scales with M =1 Mˇ   1=2 1 3=2 .f =0:1/ values (column 10) scale with V =3000 km s . The mass scalings are based on typical masses in core-collapse supernova models. Estimates for decays to excited states are not attempted, but labeled “To exc.” Atomic data sources are given in Jerkstrand et al. (2011) t Eu .eV / gu A.s 1 / # ncri (cm3 ) tLTE (d) "n tt hi n .d / e  4 1.26 5 2:2  10 0.34 2:6  104 3700 0.04 25 M =0:1 1=2 Mˇ 8727 (5-4) 2.68 1 0.60 0.20 2:5  107 380 To exc.  3 N II 6583 (4-3) 1.89 5 2:9  10 1.4 8:5  104 2400 0.14 45 M =0:1 1=2 Mˇ  O I 6300 (4-1) 1.97 5 5:6  103 0.06 3:8  106 640 0.21 170 M =1 1=2 Mˇ 5577 (5-4) 4.18 1 1.3 0.07 1:5  108 190 To exc.  Si I 1.64 m (4-3) 0.78 5 2:7  103 0.1 1:0  106 800 1.0 120 M =0:1 1=2 Mˇ 1.10 m (5-4) 1.91 1 0.80 0.02 3:3  108 120 To exc.  S I 1.08 m (4-1) 1.15 5 0.028 0.1 1:1  107 350 2.6 200 M =0:1 1=2 Mˇ 7725 (5-4) 2.75 1 1.8 0.02 7:4  108 90 To exc.  Ca II 7291 (3-1) 1.70 6 1.3 7.3 8:8  106 350 162 480 M =0:01 1=2 Mˇ Fe II 7155 (17-6) 1.96 10 0.15 1.0 1:2  107 290 To exc.  3 1.26 m (10-1) 0.99 8 5:0  10 13 2:6  104 2200 0.21 55 M =0:1 1=2 Mˇ 1.64 m (10-6) 0.99 8 5:1  103 2.2 1:5  105 1200 To exc.  Co II 1.02 m (9-1) 1.22 9 0.054 0.32 1:2  107 280 1.9 160 M =0:1 1=2 Mˇ  9338 (10-1) 1.32 7 0.023 0.25 5:3  106 380 0.5 80 M =0:1 1=2 Mˇ  Ni II 7378 (7-1) 1.68 8 0.23 1.2 1:2  107 280 5.5 90 M =0:01 1=2 Mˇ

Ion CI

Line (Å) 9850 (4-3)

For lines decaying to excited states ([C I ] 8727, [O I] 5577, [Si I] 1.10 m, [S I] 7725, [Fe II] 7155, [Fe II] 1.26 m), transition to optical thinness will usually occur early as populations of excited states are much lower than in the ground multiplet. However, if the A-value is large, this should be more carefully checked. The transition time has in this case a strong temperature dependence through the sensitivity of populations of excited states.

32 Spectra of Supernovae in the Nebular Phase

811

In some cases two lines from the same ion can be used to determine the optical depth and thereby the density. As an example, the [O I] 6300 and 6364 Å lines arise from the same upper level (2p41 D), going to the first and second levels in the ground multiplet, respectively, with A6300 D 5:6  103 s1 and A6364 D 1:8  103 s1 . The ratio of their emissivities R D j0 .6300/=j0 .6364/ is RD

A6300 h 6300 ˇS;6300 A6364 h 6364 ˇS;6364

(40)

  Ignoring stimulated emission, S;6300 = S;6364 D 63003 =63643 .A6300 =A6364 / .n1 =n2 / .g2 =g1 / D 0:97A6300 =A6364 D 3:0, where we have assumed LTE within the ground multiplet and T  Eground (230 K) for the ground multiplet populations, so n1 =n2 D g1 =g2 . Then RD

1  exp . 6300 /   1  exp  13 6300

(41)

In the optically thick limit R ! 1, and in the optically thin limit R ! 3. By studying how the ratio transitions from the thick to thin regime over time, the density of O I can be estimated. Initial application for SN 1987A resulted in OI .t / D 1:7  1012 .t =100d/3 g cm3 (Li and McCray 1992; Spyromilio and Pinto 1991). The mass can be estimated from MOI D O I 4

V 3 t 3 fO , but the filling 3 max factor fO needs to be determined by some other method.

3.3.1 LTE, Optically Thin Case If the whole ion is modelled in LTE, Nu D Ngu Z.T /1 e Eu =kT , where N is the total number of ions, and Z.T /is the partition function. Optical thinness means ˇS D 1. Then, with N D Mion = mp , Eq. 34 becomes  1 gu Eu =kT e L D Mion mp Ah Z.T /

(42)

One may also consider a variant, where it is not assumed that the whole ion is in LTE, but only that the upper and lower states are in LTE with each other (thermal collisions dominate transitions in both directions). Then, if the lower state is in the ground multiplet, and we approximate Mg  Mion , Eq. 42 is recovered with Z.T / replaced by gg . The mass of the emitting ion Mion can therefore be estimated if the temperature can be determined. The most robust mass inferences can be made from lines with Eu  kT (so e Eu =kT ! 1), which means  & 3 m .T =5000 K/1 . For temperatures of a few thousand K, these are MIR lines. However, mass ratios may be robustly determined also in the Eu & kT regime, if Eu;1 Eu;2  kT . For example, Jerkstrand et al. (2015b) used the LTE and optically thin formula for [Ni II] 7378 and [Fe II] 7155 to estimate the Ni/Fe mass ratio in core-collapse supernovae.

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A. Jerkstrand

3.3.2 LTE, Optically Thick Case In the optically thick limit, ˇS ! 1= S , and Eq. 32 and Eq. 34 give L D 8 3 h V t 1

For LTE,

gl nu gu nl

gl nu   gu nl 1  gglunnul

(43)

D e h =kT , and so

L D 8 3 h V t 1 D 4 V .ct /1 

1 e h =kT

1

1 2hc 2 5 e h =kT  1 4 V D B .T / ct

(44) (45) (46)

The luminosity thus depends on the volume and the temperature, but not the mass. Because the line width is proportional to , the peak spectral flux is proportional to B .T /. The peak flux values of separated lines (and ignoring further transfer effects) would therefore follow a blackbody function. We can use optically thick LTE lines to determine the volume of the emitting region if we know the temperature or the temperature if we know the volume. Volume determinations are most robust if h  kT , for which we get L D 8 3 t 1 V kT

.h  kT /

(47)

Because the volume span can be directly inferred from the line expansion velocities (Vspan D 4 =3 .Vmax t /3 ), in practice this means that V =Vspan gives us the filling factor f of the emitting region: what fraction of the volume is effectively responsible for emission of that line. Li et al. (1993) performed LTE modelling for Fe MIR lines with optical depth effects to estimate f and T .t / in SN 1987A. Jerkstrand et al. (2012) showed that [Fe II] 17.94 m and [Fe II] 25.99 m fall in the optically thick LTE regime for many hundred days in Type II models and determined f in SN 2004et. In Type Ia SNe, [Ni II] 6.634 m, [Ni III] 7.350 m, [Co III] 11.88 m, and [Fe II] 17.93 m can similarly be useful probes (Maeda et al. 2010). From Table 1, there are few optical/near-infrared (NIR) lines where one can be confident to be in the optically thick LTE regime. [Ca II] 7291, 7323 is a candidate in SNe where the emission is from the synthesized calcium. In the early nebular phase, [O I] 6300, 6364, [Si I] 1.64 m, [S I] 1.08 m, and [Co II] 1.02 m would also in many situations be in this regime.

32 Spectra of Supernovae in the Nebular Phase

3.4

813

Non-local-Thermodynamic-Equilibrium

Outside LTE, the limiting formula depends on which mechanisms are assumed to dominate the populations and depopulations of the upper state. In general, one obtains expressions involving the number abundance of the feeding state and physical quantities such as temperature and electron density. If the goal is to estimate ion masses, it is desirable that this feeding state should be a ground state, as one may often approximate the mass of ions in the ground state to equal the total element mass. Sometimes the coupling to a ground state can occur in several steps, as in recombination cascades. The most common populating mechanisms are thermal collisions, non-thermal collisions, photoexcitation, and recombination. We will here consider two cases in particular, thermal collisionally excited lines and recombination lines.

3.4.1 Thermal Collisionally Excited Lines The statistical equilibrium is letting f denote the feeding state (which may not be the same as the lower state l), and N D nV : Nf Quf .T /

gu .Eu Ef /=kT e ne D Nu .Aul ˇS;ul C Qul .T /ne / gf

(48)

Let us consider the regime ne  ncrit e . Then

Nu D Nf

Quf .T / ggfu e .Eu Ef /=kT ne Aul ˇS;ul

(49)

The line luminosity becomes, using Eq. 34,  1 gu L D mp h  Mf Quf .T / e .Eu Ef /=kT ne gf

(50)

To determine the mass Mf , we would need to know both temperature and electron density. If neither is known, these lines have to be used in conjunction with other lines to make combined constraints. For example, if we have two emission lines from the same ion, being pumped from the same feeder state, then L1 h 1 Q1f .T / gu1 .E2 E1 /=kT D e L2 h 2 Q2f .T / gu2

(51)

Thus, such a line ratio may be used to determine the temperature at late times (when NLTE and optically thin conditions are more likely).

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3.4.2 Recombination Lines If the upper level is populated by recombinations (directly and/or through cascades via recombinations to higher levels), the equilibrium is (assuming u is predominantly radiatively emptied in the ul transition) NC ne ˛ueff .T / D Nu Aul ˇS;ul eff

where ˛u

(52)

is the effective recombination rate. Then  1 L D h mp  MC ne ˛ueff .T /

(53)

Determination of the mass MC of the recombining ion requires knowledge of the electron density and the temperature. The temperature dependence of the effective recombination rates is, however, moderate, and so a determination of MC ne with relatively small uncertainty is possible. Recombination lines from two different elements residing in the same zone allow an estimate of the ratio of ion masses, because the electron density cancels out, and the ratio of effective recombination rates will often be almost temperature-independent. Emission lines from levels more than a few eV above the ground state are often powered by recombination. Examples include H Balmer lines, some He lines, O I 7774, and Mg I 1.50 m. Techniques to use O I 7774 as a diagnostic line are discussed in Maurer et al. (2010) and the use of O I 7774, O I 9263, O I 1.129+1.130 m, O I 1.316 m, and Mg I 1.50 m recombination lines in Jerkstrand et al. (2015a).

3.5

Discussion

As we have seen, the luminosity in different line limits depends on different combinations of mass, volume, temperature, and electron density. In general one needs multiple lines, preferably formed in different limits, to break the degeneracies and determine unique values for these parameters. Analytic line formation limits are easy to use, provide an understanding of line luminosity evolutions, and can be very useful diagnostics for some lines. The key to their application is to provide convincing arguments for the validity of the physical regime. This in turn can come from three different approaches: (1) Demonstration that with any reasonable assumptions of physical conditions, the regime is fulfilled with good margin and (2) inference from observations and (3) by inspection of forward models. An added difficulty in SNe, compared to, for example, HII regions, is the high expansion velocities which make many lines blended with each other. Consideration of possible blending contaminations should always be done.

32 Spectra of Supernovae in the Nebular Phase

4

815

Radioactive Powering

Baade (1945) discovered that supernovae decline on exponential tails with a timescale of about 70d. The evolution of an explosion without further energy input produces neither enough luminosity nor such an exponential behavior. This led Borst (1950) to suggest that there is a radioactive power source. Following this were 20 years of speculation on what radioisotope this could be, including an ill-fated suggestion of 254 Californium by Burbidge, Baade, and Hoyle. Finally Colgate and McKee (1969) provided the right answer; it is the second stage of the radioactive decay chain 56 Ni ! 56 Co ! 56 Fe. 56 Co decays on a timescale of 111d to 56 Fe, and at the same time, the source of iron in the Universe had been identified. The solution came after the demonstration of 56 Ni production in high-temperature silicon burning by Bodansky et al. (1968). In SNe, the relevant decay processes are electron captures (EC) and ˇ C decays. In the first step, the nucleus transmutes by the conversion of a proton to a neutron. In electron captures this energy is emitted as a neutrino, and in ˇ C decays, the energy is shared between a neutrino and the positron. The nucleus is usually left in some excited state, which then cascades to the ground state by emission of gamma rays or by ejecting an inner-shell electron in an internal conversion. Following both electron captures and internal conversions, further emission of X-rays and/or Auger electrons occurs as the inner hole is filled. The positrons annihilate with free electrons when they are slowed down to thermal energies, producing two 511 keV gamma rays for antiparallel spins and three gamma rays with a total energy 1022 keV for parallel spins. The decay power is

P .t / D N .t /

QO

(54)

where N .t / is the number of isotopes at time t , QO is the average decay energy excluding neutrinos, and is the decay timescale. Note that QO is different from the normal Q-value, because a significant part of the decay energy will be emitted as neutrinos that escape the remnant. For a primary isotope (like 56 Ni) N .t / D N0 e t=

(55)

whereas for a secondary isotope (like 56 Co)

N .t / D N0

    exp  t  exp  tp 1

p

(56)

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A. Jerkstrand

Table 2 Decay data for the most common radioactive isotopes. Fractions of decay energy going to -rays, positrons, electrons, and X-rays are listed. Annihilation radiation from positrons is included in the gamma fraction (contribution in parenthesis). Fractions smaller than 103 have been put to zero (Data from Nuclear Data Sheets 2011) Decay feC fe fX ray Source QO (keV decay1 ) f 56

Ni ! 56 Co Co ! 56 Fe 57 Ni ! 57 Co 57 Co ! 57 Fe 44 Ti ! 44 Sc 44 Sc ! 44 Ca 55 Co ! 55 Fe 55 Fe ! 55 Mn 22 Na ! 22 Ne 60 Co ! 60 Ni

56

8.77d 111d 35h 391d 88y 6h 17h 3.87y 2.60y 5.27y

1724 3732 2096 143 150 2732 2429 5.6 2392 2600

0.996 0.966 (0.053) 0.924 (0.21) 0.850 0 0.78(0.35) 0.822(0.32) 0 0.918(0.38) 0.963

0 0.032 0.074 0 0 0.22 0.18 0 0.082 0

0.0025 0.001 0.001 0.125 0.070 0 0.001 0.71 0 0.037

0.0013 0 0 0.025 0.929 0 0 0.29 0 0

Si burning Si burning ˛-rich freeze-out Si burning C burning C burning

where p is the parent decay timescale (e.g., 8.8d for 56 Ni). We can write N0 D

M0 mp

(57)

where M0 is the mass of the primary species (weight ) synthesized in the explosion. Also other radionuclides are made in the explosion and may provide important input once most of the 56 Co has decayed after a few hundred days. These include 57 Ni/57 Co, 44 Ti/44 Sc, 55 Co/55 Fe, 22 Na, and 60 Co. Decay data for the most common isotopes are listed in Table 2.

4.1

Deposition of Decay Products

4.1.1 Gamma Rays The gamma rays from radioactive decays are at MeV energies. The most important degradation process is Compton scattering. Because the gamma ray energy is much higher than the excitation and ionization potentials of bound electrons (. 1 keV), the opacity is almost independent of the physical state of the matter – the cross sections for incoherent scattering on various bound electrons are similar to those for free electrons, given by the Klein-Nishina formula. The local absorption thus depends only on the total density of electrons (free + bound). For E > 1:022 MeV, pair production can occur, and for E 0:1 MeV, photoelectric absorption becomes important as well. Photoelectric absorption will introduce some dependency on composition, but a relatively small fraction of the initial decay energy will be absorbed by this process. When the gamma ray Compton scatters, it loses some fraction of its energy and changes its direction. A detailed solution to the energy deposition requires computation of the multiple scattering processes. The first such calculation in the supernova context was carried out by Colgate et al. (1980). The transfer process can

32 Spectra of Supernovae in the Nebular Phase

817

be quite well described with a gray opacity  D 0:03.Ye =0:5/ cm2 g1 for the case of 56 Co gamma rays, where Ye is the ratio of the total number of electrons to the total number of nucleons. With this opacity, a uniform sphere becomes optically thin to the gamma rays at tt rap

 D 33d

M 1 Mˇ



E

1=2

1051 erg

(58)

For Type Ia and some Type Ib/c SNe, gamma ray escape needs to be considered already during the diffusion phase, whereas Type II SNe (M 10) enter the tail phase (100–200d) still well before any significant escape occurs; this offers an opportunity to determine the 56 Co mass by measuring the bolometric luminosity. Once gamma ray escape has begun, fitting the observed bolometric light curve in 2 can give an estimate for the tail phase to a function such as P .t /  1  e .t=t /  , and from that ME 1=2 . If both the radioactive source and ejecta are distributed as a uniform sphere, the mean intensity is with rO D r=Rmax 1 J .r/ O D 2

Z

1

I .r; O /d 

(59)

1

1 D S 2

Z

1

p   2 2 1  e   1Or .1 /  rO  d 

(60)

1

where S is the source function. This integral has no analytic solution, but for the   1 limit Z 1p 1 J .r/ O D S  O  (61) 1  rO 2 .1  2 / C rd 2 1    rO C 1 1  rO 2 1 ln (62) D j Rmax 1 C 2 2rO 1  rO where j is the gamma ray emissivity. This function has its maximum at rO D 0 and a value of half the maximum at rO D 1 (see also Kozma and Fransson 1992). For rO > 1, the mean intensity can be shown to fall off p as 1=2 1 C .1  rO 2 /=rO ln.1 C r/= O rO 2  1 for the optically thin case, and   p O function 1=2 1  1  rO 2 for the optically thick case. Figure 7 shows the J .r/ in the optically thin limit, as well as the numerical solution for D 10. The deposition per mass is 4 J  . Thus, Fig. 7 helps to envision how the absorption in a shell depends on its location with respect to the radioactive source (in the optically thin case). Core-collapse explosion models predict density profiles that roughly follow  / r 2 in the inner layers steepening to r 10 in the outer. Thus, the bulk of the mass is relatively well described by a set of equal-width shells of similar mass (4 r 2 rr 2 = constant).

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Fig. 7 The solid line shows the gamma ray radiation field for a uniform source distribution (between 0 < rO < 1), in the optically thin limit. The dashed line shows the numerical solution for  D 10. Note that both functions are normalized to unity at rO D 0

Because the gamma field intensity depends sensitively on location, it is important for modelling to use realistic ejecta models capturing the outcome of the mixing processes occurring in the explosion. For Type IIP SNe, the situation is relatively satisfactory, because simulations have shown that the metal regions approach the limit of complete macroscopic mixing, and it should be a good approximation to have the 56 Ni, Si, and O zones occupy the same volume (macroscopically but not microscopically mixed). For stripped-envelope SNe, the situation is less clear and modelling becomes more uncertain.

4.1.2 Leptons The leptons deposit their energy by colliding with the bound and free electrons in the SN ejecta. The effective opacity is around eC D10 cm2 g1 (Axelrod 1980; Colgate et al. 1980) for positrons and similar for electrons. Because the leptons are trapped for much longer than the gamma rays, there is a phase where they take over as the dominant power source. This occurs when   flep =f .D 0:033 for 56 Co/ (Table 2), which for a uniform sphere is at  tlep D 180d

M 1 Mˇ



E 1051 erg

1=2 

flep =f 0:032

1=2 (63)

32 Spectra of Supernovae in the Nebular Phase

819

A successful identification of this transition phase would allow an estimate of ME 1=2 . Because 57 Co takes over powering at 1000d, this transition never occurs in Type II SNe for 56 Co positrons (M 10 Mˇ ! tlep D 1800d ), but in Type Ia and Type Ib/c SNe, the predicted transition occurs somewhere between 250d (M D 1:4 Mˇ ; E D 1) and 900d (M D 5 Mˇ ; E D 1). Unless other effects come into play, the bolometric light curve will then flatten onto the 56 Co decay rate, having been steeper before due to  -ray escape. In practice, it has proven difficult to demonstrate this transition for several reasons. SNe are dim at late times, and estimating the photometry is difficult, with crowded fields and possible contamination by a remnant or companion. The temperatures are low, and the true bolometric luminosity is difficult to determine lacking NIR and MIR observations (with molecule and dust formation adding to the problem). Finally, time-dependent effects (freeze-out) come into play at similar epochs and also lead to flattening of the light curve. The leptons may also escape eventually. If there is no magnetic field, or if the magnetic field is radially combed (see Colgate et al. 1980), their trapping t rap time is about 20 times longer than the gamma ray trapping time (tlep D   1=2 ). But a non-ordered magnetic field even at weak 620d .M =1 Mˇ / E=1051 erg levels will lock the positrons in Larmor orbits and keep them trapped on very small scales: RL D 1:8  106 Rmax



B 106 G

1 

V 3000 km s1

1 

t 100d

1 (64)

where RL is the Larmor radius and Rmax is the radius of the SN.

4.2

Degradation of Non-thermal Electrons

After a few scatterings, the gamma rays have been downgraded to . 0:1 MeV and are quickly photoabsorbed. In their wake we have a set of mildly relativistic electrons with typical energies between 0.1 and 1 MeV. These electrons in turn lose their energy by collisions with free and bound electrons leading to ionization, excitation, and heating of the gas. This process is familiar to us from a closer-tohome environment of aurorae. The collisional ionizations lead to the creation of further high-energy electrons, generally referred to as secondaries. The secondaries have, however, much lower energies than the primaries, 10–100 eV. The degradation process can be modelled with Monte Carlo methods (Fransson and Chevalier 1989; Shull 1979) or formal solutions (Kozma and Fransson 1992; Lucy 1991; Xu and McCray 1991). A simplified formal solution is the continuousslowing-down approximation (Axelrod 1980), which is quite accurate for the primary electrons, but not for the secondaries. An important property of this process is that the solution has no strong dependence on the energy of incoming primary particles, as long as its over 1 keV.

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This allows for generic solvers that do not need information about which highenergy particle source is involved. There is also only a weak dependency on density, leaving the relative abundances of ions and electrons as the main parameters of the problem. Ionization. Non-thermal ionization determines the ionization balance for the major species and thereby which ions form the spectrum. To solve for the fractions of energy going into different channels, one needs to know the differential cross sections for the collisional ionization processes, i. e.,  .Ei n ; Eout /. For many elements these differential cross sections are not known, neither experimentally nor observationally, and an approximate treatment is needed. The method of Kozma and Fransson (1992), for example, applies a differential form measured for O I to all ions. For the integrated cross sections, for electron energies much higher than the excitation/ionization potential I , one may use the Bethe approximation for both ionization and excitation cross sections. The cross section for ion i , transition j , is

col l;ij .E/ D



a02  c1;ij ln E C c2;ij E  I ; E

(65)

where E is the energy of the electron, a0 is the Bohr radius, and c1;ij and c2;ij are constants depending only on level energies and transition strengths. For lower energies, specific calculations or experimental data for the collision cross sections are needed. For even moderately ionized plasmas with xe & 0:1, only a moderate fraction, 1–20% of the energy, goes to ionization. This increases toward a plateau value of 50% for more neutral gas. Excitation. The coefficient c1;ij is, for bound-bound transitions, proportional to the oscillator strength fij . Allowed transitions (fij 1) will therefore in general be more important than forbidden ones (fij  1). Non-thermal excitations tend to populate high-lying states connected to the ground state by allowed transitions, which leads to UV emissivity. Because of both photoelectric and line opacity, this UV emission does not escape directly but scatters and undergoes fluorescence. For this reason, models that include non-thermal excitation should preferably also include radiative transfer. Consideration of non-thermal excitation becomes more important for later epochs; the declining electron fraction gives less heating and more energy going into excitation (and ionization), and the declining temperature makes the resulting fluorescence into the optical and NIR more prominent as thermal emission shifts into the MIR (the so-called infrared catastrophe). However, these processes also affect the spectrum in indirect ways. The increased population of excited states can lead to photoionization from these levels and a higher electron fraction. For example, H˛ in Type II SNe arises mainly as a non-thermal excitation first populates n D 2, the H I

32 Spectra of Supernovae in the Nebular Phase 1.0 O I ionization

Heating

0.6 0.4 Excitation O II ionization

0.2 0.0 –4.0

–3.0

–2.0 log (xe)

–1.0

Energy fraction

Energy fraction

1.0 0.8

821

0.8

Heating Fe I ionization

0.6 0.4 0.2

Fe I excitation Fe II exc. and ion.

0.0 –4.0

–3.0

–2.0 log (xe)

–1.0

Fig. 8 The fraction of radioactive powering going into heating, ionization, and excitation in a pure oxygen plasma (left) and a pure iron plasma (right), as function of the electron fraction xe (From Kozma and Fransson 1992)

atom is then photoionized from this state, and in the ensuing recombination process, H˛ is emitted (see also Sec. 6.1.1). Heating. As long as the plasma is ionized to xe & 0:1, most of the non-thermal energy goes to heating of the gas. The fraction grows monotonically with increasing ionization state. The SN spectrum will therefore be dominated by cooling emission, which is dominated by lines. In Type Ia SNe, the ionization state is high compared to core-collapse SNe, and Axelrod (1980) obtained solutions of the heating fraction close to unity. The ionization balance depends of course critically on the exact value of the ionization fraction, even if it is small. Figure 8 shows example solutions for pure oxygen and iron plasmas in the lowionization limit (only neutral and first ionization stages present). The distribution of non-thermal electrons, ionization, temperature, and excitation are all connected equation systems. Thus, one needs to iterate – the non-thermal rates are calculated given an ionization and excitation structure. These are then updated (also following updates of temperature, radiative rates).

5

Spectral Modelling

A spectral model defines a scope and a set of physical approximations and assumptions to compute the emergent flux. Spectral models can be divided into two categories: (1) models for individual line luminosities (or sets of lines) and (2) models for the full spectrum of the SN (or some range of the spectrum). The modeller should ideally not only set up and compute the model but also use physical reasoning to assess which predictions are robust and which depend more sensitively on ill-constrained assumptions. There are a large number of physical processes at play in supernova ejecta that each can be treated in several different approximations. The basic ingredients in

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a nebular model, with different levels of approximation, are listed below together with examples of models implementing them (for a series of papers by the same first author using the same technique, only the first paper is listed): • Nebula structure – 1D, 1-zone (Axelrod 1980; Mazzali et al. 2001; Ruiz-Lapuente and Lucy 1992) – 1D, multi-zone, no mixing (Fransson and Chevalier 1989; Liu et al. 1997a; Mazzali et al. 2007; Ruiz-Lapuente et al. 1995; Sollerman et al. 2000) – 1D, multi-zone, artificial mixing (Dessart and Hillier 2011; Houck and Fransson 1996; Jerkstrand et al. 2011; Kozma and Fransson 1998a; Sollerman et al. 2000) – 2D (Maeda et al. 2006) – 3D (Kozma et al. 2005) • Gamma ray transfer – Local deposition (Dessart and Hillier 2011) – Gray transfer (Axelrod 1980; Houck and Fransson 1996; Jerkstrand et al. 2011; Kozma and Fransson 1998a; Liu et al. 1997a; Mazzali et al. 2001) – Compton scattering (Eastman and Pinto 1993; Fransson and Chevalier 1989) – Compton scattering + photoelectric (Dessart et al. 2013) – Compton scattering + photoelectric + pair production (Maurer et al. 2011) • Non-thermal processes – Pure heating (Dessart and Hillier 2011) – Fixed heating and ionization (0.97-0.03) (Mazzali et al. 2001; Ruiz-Lapuente and Lucy 1992) – Heating, ionization, and excitation – continuous slowing down (Axelrod 1980; Eastman and Pinto 1993) – Heating, ionization, and excitation – full solution(Dessart et al. 2013; Jerkstrand et al. 2011; Kozma and Fransson 1992; Liu et al. 1997a) • Level populations – LTE – NLTE with collisional excitation/deexcitation and radiative decay terms (Axelrod 1980; Mazzali et al. 2001; Ruiz-Lapuente and Lucy 1992) – NLTE with comprehensive set of processes (Fransson and Chevalier 1989; Houck and Fransson 1996; Jerkstrand et al. 2012; Maurer et al. 2011) – NLTE with comprehensive set of processes, time-dependent (Dessart et al. 2013; Kozma and Fransson 1998a) • Temperature – Non-thermal heating, line cooling (Axelrod 1980; Mazzali et al. 2001; RuizLapuente and Lucy 1992) – Non-thermal and photoelectric heating, line, recombination, and free-free cooling (Houck and Fransson 1996; Jerkstrand et al. 2011; Maurer et al. 2011) – Non-thermal and photoelectric heating, line, recombination, and free-free cooling, time-dependent (Kozma and Fransson 1998a)

32 Spectra of Supernovae in the Nebular Phase

823

• Radiative transfer – Sobolev approximation locally, no global transport (Kozma and Fransson 1998a; Liu et al. 1997a; Maeda et al. 2006; Mazzali et al. 2001) – Sobolev approximation locally, global transport (Jerkstrand et al. 2011; Maurer et al. 2011) – Full transport locally and globally, time-dependent (Dessart and Hillier 2011) The number of atoms and levels modelled and the quality of the atomic data library have large impact on the accuracy of the model. Before comparing a model to data, it is important to understand the setup and limitations and assess the ability to predict any given observable. Gamma ray deposition and non-thermal processes have been covered already, and we discuss the other components in more detail here.

5.1

Nebula Structure

One of the biggest challenges to SN spectral modelling is to capture the complex structures evidenced by observations of SN remnants and also obtained in multi-D explosion simulations. Most models are set up in 1D, and some consideration of these mixing effects is needed. It is important to distinguish between microscopic and macroscopic mixing. Microscopic mixing. Each nuclear burning stage gives unique nucleosynthesis products, and these do not readily become mixed with each other on atomic scales in the SN ejecta because the supersonic flow freezes out composition on velocity scales vtherm .t /, which is . 10 km s1 already after a few days. Diffusion is also inefficient in the very early phases when temperatures are still high. The cross section for atomic collisions is of order  D a02 1016 cm2 , where a0 is the Bohr radius. For ion collisions Coulomb interactions give somewhat larger values for typical temperatures. The “optical depth” is D  nL =  nV t . Of order 2 scatterings are needed to travel a distance . The time between scatterings is t D =vtherm D 1= nvtherm . The total time to diffuse through the nebula is tatomicd iff D

. nL/2  nL2 3 M D D  nvtherm vtherm 4 Vmax t vtherm .T /m N

(66)

For any reasonable values of M; Vmax ; T , the diffusion time is longer than the age of the Universe, and negligible mixing occurs. This idea is supported by several lines of evidence. For instance, models for molecule formation show that microscopically mixed ejecta fail to produce the observed amounts of molecules (e.g., Gearhart et al. 1999; Liu and Dalgarno 1996). Spectral models with full microscopic mixing also generally fare worse than models without such mixing (Fransson and Chevalier 1989).

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Macroscopic mixing. Macroscopic mixing, on the other hand, is known to occur vigorously during the explosion of many progenitor structures. The dominant mechanism is typically Rayleigh-Taylor mixing, which arises behind the reverse shocks created at composition interfaces where r 3 shows a positive derivative. The mixing effects are strong in explosion simulations of H-rich SNe, with red supergiants becoming more mixed than blue supergiants (e.g., Herant and Woosley 1994). Simulations of He core explosions show strong mixing for low-mass progenitors but weaker for high-mass ones (e.g., Shigeyama et al. 1990). The lack of O/He and He/H interfaces in Type Ic SNe makes mixing harder to obtain. The implication is that hydrogen-rich SNe are poorly represented by 1D explosion models, and either 2D/3D models or 1D models with artificial macroscopic mixing are preferred. For stripped-envelope SNe, there is more freedom within current uncertainties in the mixing processes. In Type Ia SNe, Rayleigh-Taylor instabilities also occur, with buoyant hot 56 Ni rising up between downflows of C and O, in particular in deflagration models (e.g., Röpke et al. 2007). Most multi-zone models computed so far either retain the structures obtained in 1D or apply some kind of artificial mixing where multi-D simulations may be used as guidance.

5.2

Level Populations

At nebular times LTE can in general not be assumed. The level populations have to be determined by solving a set of NLTE equations describing the various populating and depopulating mechanisms. Letting nij k denote the number of ions of element i ionization state j and excitation state k, each equation has the form XXX XXX d nij k nij k d   D ni 0 j 0 k 0 Ri 0 j 0 k 0 ;ij k  nij k Rij k;i 0 j 0 k 0 dt  dt 0 0 0 0 0 0 i

j

k

i

j

k

(67) The rates R depend in general on ne , T , radiation field J , and non-thermal electron distribution nnt .E/. In the Sobolev approximation, they also depend on the level populations nij k themselves. Charge transfer (ct) also implies dependencies on number densities of colliding partners. All normal processes have i 0 D i , but radioactive decay and molecule and dust formation allows i 0 ¤ i . If we ignore this for now, so dropping the i index, we can break up all processes populating/depopulating a level into the groups of ionization, recombination, excitation, and deexcitation. Letting R denote a radiative process, and C a collisional, these group can be further broken up into Rion D Rphotoion: C Cthermal

ion:

C Cnonthermal

ion:

C Cct;ion:

Rrec D Rstim: rec: C Rrad: rec: C Rd iel: rec: C C3body rec: C Cct;rec Rexc D Rphotoexc: C Cthermal

exc:

C Cnonthermal

Rdeexc: D Rstim: em: C Rspont: decay C Cthermal

exc:

deexc:

C Cnonthermal

deexc:

(68)

32 Spectra of Supernovae in the Nebular Phase

825

which gives an overview of the physical processes involved. Let N be the typical number of excited states modelled in each ion. Any given level can transition to any other level in that ion, in the ion below, or above, i.e., to 3N other levels. The number of transition pairs is Nionstages 3N 2 =2104 Nionstages per chemical species for N D 100. The modelling of just a few species would require specification of 105 transition rates R, each in turn containing 15 individual rates (Eq. 68), some of which are temperature dependent. The only rates that are available in batch reading on this scale are spontaneous radiative decay rates. Photoionization and non-thermal ionization rates require cross sections as functions of energy, and simplifying treatments, or inclusion of only some transitions, is necessary. The following considerations help: • For excited nonmetastable states, Rexc D Rion D Rrec D 0, and Rdeexc D Rspont: decay are accurate approximations. These states, with A  1, are emptied on fractions of a second ( 1=A) by spontaneous decay, much shorter than any other process can operate. • For ground states, Cthermal: ion D 0 and C3body rec: D 0 are accurate approximations because nebular temperatures are too low for these processes to be competitive. Steady-state corresponds to ignoring the time-derivative terms in Eq. 67, so a (nonlinear) algebraic equation system follows, which is straightforwardly solved by Newton-Raphson iteration. This is justified as long as the reaction timescales are short compared to dynamic and radioactive timescales. The is   slowest reaction typically radiative recombination, where trec 1= .˛ne / 1d 107 cm3 =ne . The simplest possible scheme for NLTE excitation solutions is to include spontaneous radiative rates, treated in the Sobolev approximation, and thermal collisional rates. This gives a reasonable approximation for plasmas with xe & 0:1 because heating then accounts for most of the energy deposition (Sect. 4.2), and the reprocessing of this energy is mainly done by collisional cooling. The next natural step is to add recombination, which enables accounting of a non-thermal ionization energy and production of recombination lines. Coupling the radiation field to the NLTE solutions requires addition of line absorption and photoionization rates. The most advanced models include also non-thermal excitations, photoionization from excited states, and charge transfer reactions. Charge transfer (CT) is an important process at high densities and low ionization: a relatively unique astrophysical environment found in supernovae at late times. By this process electrons jump from one ion to another, for example, O I + H II $ O II + H I

(69)

Both species in the outgoing channel may be left in excited states. The important role of this process in governing the ionization balance in SNe was pointed out by Meyerott (1978). The fast rates are of order C T 109 cm3 s1 , to be compared with radiative recombination rates of order RR 1012 cm3 s1 . Thus, even an

826

A. Jerkstrand

atomic abundance of 103 per electron can lead to recombination by charge transfer dominating the ionization balance. The process is typically fast between neutral atoms and singly ionized ions and if the energy defect is small. Ion-ion reactions require high temperatures due to the Coulomb barrier and are of less importance. Modelling is hampered by many unknown or poorly known rates. Most rates that have been calculated involve H and He, for application in HII regions and planetary nebulae, but SN modelling mainly needs rates between metals. When the reaction is fast in both directions, the effect of CT is to link the ionization balance of the less abundant element to the more abundant. As an example, for a solar composition gas, the primordial O attains the same ionization balance as H by this mechanism.

5.3

Temperature

The temperature evolution is obtained by solving the first law of thermodynamics, which for homologous expansion and pressure from a perfect monoatomic gas is d T .t / H .T /  C .T / 2T .t / T .t / dxe .t / D   3 dt t 1 C xe .t / dt k n.t / 2

(70)

where H .t / and C .t / are the heating and cooling rates (which depend on the NLTE solutions nij k ). The heating is usually dominated by non-thermal heating, and the cooling by collisional excitation of fine-structure lines (which then decay radiatively). The thermal equilibrium approximation corresponds to setting H .T / D C .T / and solving the resulting algebraic system for T ; this is a good approximation if the cooling/heating timescales are short compared to the dynamic and radioactive decay timescales. This is usually fine for several hundred days into the nebular phase. For example, de Kool et al. (1998) and Kozma and Fransson (1998a) find this approximation to hold for 600–800d for the H zone and several years or decades for the metal zones in models for SN 1987A. Once collisional cooling becomes slow, adiabatic cooling takes over, and the solution to Eq. 70 is T .t / / t 2 (ignoring the last term involving xe which typically has a small effect). Once molecules begin to form, the cooling becomes more efficient and the temperature can become significantly lower than models without molecules would suggest. While a few studies have addressed formation and cooling of molecules in single-zone setups, they are typically not included in multi-zone models.

5.4

Radiative Transfer

Supernova ejecta remain optically thick to line blocking below 4000–5000 Å for years or even decades. Figure 9 illustrates this, showing the photon escape probability in a Type IIP SN at 300d. Thus, to model the appearance of the SN at short

32 Spectra of Supernovae in the Nebular Phase

827

1

Escape probability

0.8

0.6

0.4

0.2

0 0

5000

λ [A]

10000

15000

Fig. 9 The probability for a photon emitted from the center of the SN to escape the ejecta without being absorbed in a line, for a Type II model at 300 days (From Jerkstrand 2011)

wavelengths, as well as lines at longer wavelengths influenced by fluorescence, this transfer must be considered. There are two conceptual approaches – solution of the radiative transfer equation and Monte Carlo simulations of the photon propagation. Formal solution of the transfer equation can be done by short characteristics (integration of source function along rays). This is often used to get Eddington factors, and alternated with solutions to the moment equations (which remove the angular variable) in a Variable Eddington factor scheme (e.g., Hillier & Dessart 2012). The moment equations allow implicit coupling of electron scattering, and in some cases line scattering. The basic concept in the Monte Carlo approach is to follow energy packets as they propagate through the ejecta, using random numbers to determine their interactions and trajectory changes (e.g., Jerkstrand et al. 2011; Li & McCray 1996). Two properties of the SN make the machinery relatively straightforward to set up – homology (Hubble flow) makes the expansion isotropic from any point in the ejecta, and the large velocity gradient allows the Sobolev approximation which means that the photon can be transported from line to line, without having to consider line overlap. Different algorithms may be chosen depending on the desired degree of coupling to the gas state. Iteration between NLTE solutions and radiative transfer have good convergence properties in late-time SN environments, because the dominant excitation and ionization processes are typically collisional (non-thermal and thermal). In practice, only lines and photoionization continua from ground states and (effectively) metastable states need to be considered. What happens to a photon absorbed in a resonance line? For allowed lines, the Regemorter formula (van Regemorter 1962) gives an estimate of the effective

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A. Jerkstrand

collision strength, # 2  106 3 Agu Py , where for purposes here we can take  3 Py D 0:1. Then Qres 5  1016 A =3000 Å cm3 s1 . The ratio of probabilities for collisional deexcitation (i.e., thermalization) and scattering is then      3  Qres ne ne ptherm S D  pscat ter A= S 108 cm3 107 3000 Å

(71)

Because ne . 108 cm3 in the nebular phase only the most optically thick lines ( S & 107 ) may suffer thermalization. Note that even if collisional deexcitation is unimportant, multiple scatterings may still lead to enhanced thermalization by other processes such as photoionization as the photons increase their dwell time in the ejecta. Fluorescence gives a capping of this trapping by moving photons out to optically thinner wavelengths after a handful of scatterings. Modern codes treat the complex global transport through hundreds of thousands of lines. However, simplified approaches are also conceivable. Axelrod (1980) devised an approximate method to treat the global line transfer in a single-zone model. In this method, a position and angle-averaged probability to be absorbed in any other transition (using the Sobolev approximation) is calculated (compare with the average continuum escape probability of Osterbrock (1989)). To avoid coupling between the radiation field and the optical depths (the method is in the “no coupling” regime), it is then assumed that absorption occurs only from low-lying states whose populations are calculated without any coupling to the radiation field. The fluorescence is finally obtained by coupling the high-lying state populations through the averaged probabilities, which gives a linear system of equations. The method showed relatively good results for reproducing the blue regions of Type Ia SNe. While the method is outdated for modelling of quite well-understood SN classes, it can still find use in rapid exploration of model scenarios for new SN types.

6

Application of Spectral Models

Spectral models may be used to compare with observations to find the best matches in terms of progenitors, nucleosynthesis, and mixing. Overall, the application of models may be divided into: • • • • •

Test the viability of a particular explosion model for an observed SN or SN class Estimate a physical parameter by optimizing a model over this parameter Identify lines Determine physical conditions and regimes Estimate bolometric correction factors

Apart from these concrete purposes, a model gives opportunity to improve our general understanding of what is going on in the SN. As in all science, the end use of such fundamental information cannot always be predicted.

32 Spectra of Supernovae in the Nebular Phase

6.1

829

Hydrogen-Rich SNe

Nebular multi-zone spectral models of H-rich SNe have been presented by Fransson and Chevalier (1987), Kozma and Fransson (1998a, b), de Kool et al. (1998), Dessart and Hillier (2011), Dessart et al. (2013), and Jerkstrand et al. (2011, 2012, 2014, 2015b). This “first principles” model set is complemented by a set of more parameterized models studying specific line formation in H (Xu et al. 1992), He (Li and McCray 1995), O (Li and McCray 1992), Ca (Li et al. 1993), and Fe (Li et al. 1993) in SN 1987A. The output of the Fransson and Chevalier (1987), Kozma and Fransson (1998a, b), and de Kool et al. (1998) models (all for SN 1987A) are line luminosity tracks, whereas the other papers present spectra. Figure 10 shows two model examples, from Dessart et al. (2013) and Jerkstrand et al. (2014). Current-day models are quite successful at reproducing the main spectral features, such as Mg I] 4571, Na I, [O I] 6300, 6364, H˛, [Fe II] 7155, [Ca II] 7291, 7323, and Ca II NIR, as well as the underlying quasi-continuum. This provides some important verification for standard stellar evolution and SN theory, and for the spectral formation calculations. Three of the most prominent lines in nebular Type IIP spectra are H˛, [O I] 6300, 6364, and [Ca II] 7291, 7323. The formation of these lines is reviewed in some more detail below.

6.1.1 Hydrogen Lines The models show that the H lines are formed mainly by recombination. The ionization is achieved in a two-step process; first n D 2 is populated by non-thermal excitations and then follows a Balmer photoionization. The ionizing photons come partly from H itself in the form of two-photon emission (from n D 2) and partly from line emission from other elements. Apart from H˛, there are no other Balmer lines produced for several hundred days. Kirshner and Kwan (1975), and later Xu et al. (1992) and Kozma and Fransson (1992), demonstrated that this is because the Balmer series is optically thick (“Case C”), and conversion occurs through other series (e.g., Hˇ (n D 4 to n D 2)) which converts to Pa˛ (n D 4 to n D 3) + H˛ (n D 3 to n D 2). The Balmer lines are thick because n D 2 acts like a metastable state due to the enormous optical depth in Ly˛ ( S 1010 ). Modelling of the H lines is also complicated by breakdown of the Sobolev approximation for the Lyman lines – at very high S values, one must consider line overlap as well as the possibility that the photons scatter into regions of the ejecta with different composition. Considering Ly˛ escape, the n D 2 population may decrease, which in turn decreases the number of photoionizations and the recombination line luminosities throughout. Considering Lyˇ escape, the H˛ luminosity specifically may decrease while not impacting the other H lines. An important result from H line modelling in SN 1987A is that H gas must occupy most of the volume of the central few 1000 km s1 and absorb about half of the gamma rays (Xu et al. 1992). Combined with the lack of flat-topped line profiles, the picture is clear that strong mixing occurs in the explosion and drags hydrogen

830

A. Jerkstrand

–1 F (10 – 15 erg s– 1 cm– 2 ˚ A )

10

SN 2012aw 15 M model

250 d

5 0 4

332 d

0 2

[C a I I ]

[O I ]

2

[O I ] Na I

Mg I ]

Ca I I

[Fe I I ]

O I

7000

8000

369 d

1 0 451 d

0.5 5000

4000

Fλ [10–15 erg s–1 cm–2 Å–1]

0 3000

3

6000

λ (A˚)

9000

10000

SN 1999em – 26/09/2000 E(B–V)=0.10 Source: Lick Model: s15N@340d

2

1

0

4000

5000

6000 λ [Å]

7000

8000

Fig. 10 Examples of Type IIP spectral models. Top: A MZAM S D 15 Mˇ spectral model from Jerkstrand et al. (2014), compared to SN 2012aw. Bottom: A spectral model from Dessart et al. (2013), compared to SN 1999em

envelope material down toward low velocities, in line with multi-D hydrodynamic simulations. Kozma and Fransson (1998b) estimate a total H zone mass of 8 Mˇ in SN 1987A (about half of which is H, the rest He). Standard stellar evolution models with a 8 Mˇ H zone give satisfactory fits to H lines also in many other Type II SNe (Jerkstrand et al. 2012, 2014).

6.1.2 Oxygen Lines The [O I] 6300, 6364 lines are efficient cooling lines and typically reemit a large fraction of the heating of the oxygen-zone layers. Their strengths are thus indicators of the oxygen mass, which from stellar evolution models is strongly dependent on

32 Spectra of Supernovae in the Nebular Phase

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L([O I] 6300, 6364) (% of 56Co power)

10

8

1987A 1988A 1990E 1999em

2002hh 2004et 2006bp 2006my

2007it 2012A 2012aw 2012ec 25 19

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Fig. 11 Model tracks for luminosities in [O I] 6300, 6364 for 4 different progenitors (MZAM S D 12; 15; 19; 25 Mˇ ), compared to a sample of 12 Type II SNe (From Jerkstrand et al. 2015b)

the progenitor mass. Model luminosity tracks for different MZAMS are presented in Jerkstrand et al. (2012, 2014) (see also Fig. 11). The method is particularly useful for observations around a year after explosion; when the [O I] lines become optically thin, temperatures and densities are in a regime favorable to [O I] 6300, 6364, and we are confident that MO  MOI . The current picture points to relatively limited amounts of oxygen produced in Type IIP SNe and an origin in MZAMS . 20 Mˇ stars (Fig. 11). Another method to determine progenitor masses using the widths of the [O I] lines has been proposed by Dessart et al. (2010). The luminosity of the O I doublet depends in general on MOI ; e E=T .t/ (E is the transition energy) and ne .t / in the optically thin NLTE phase (Sect. 3.4). LTE is valid until quite late times removing the ne dependency, but the exponential dependency on T .t / makes it difficult to make any meaningful estimates of MOI by inverse analytic modelling. Between T D 3000 K and T D 6000 K, the inferred O I mass changes by a factor of 45! Thus, one needs strong constraints on the temperature. One approach is to use the [O I] 5577 / [O I] 6300, 6364 ratio as a thermometer. The measurement of [O I] 5577 is intricate as it is weak in Type II SNe, but the method has been demonstrated to be feasible and in good agreement with forward modelling (Jerkstrand et al. 2014). Few other oxygen lines are distinct in Type II SNe. One exception is O I 1.13 m which is often observed to be strong, well above any plausible recombination luminosity. Its high strength likely arises as a fluorescence effect when Lyˇ photons are absorbed in O I 1025, a process that gives indication of mixing of O and H clumps on small scales (Oliva 1993).

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6.1.3 Calcium Lines Kirshner and Kwan (1975), and later Li et al. (1993), demonstrated that the [Ca II] 7291, 7323 lines in H-rich SNe arise mainly from primordial (solar abundance) Ca in the H envelope of the progenitor and not from the synthesized calcium. The reason is the much larger mass of the H zone (10 Mˇ ) compared to the Si/S/Ca zone (0:1 Mˇ ), which leads to more energy being reprocessed there. In addition, [Ca II] 7291, 7323 is a very efficient cooling channel that emits a large fraction of deposited energy even when the calcium abundance is low (solar). Thus, the [Ca II] emission lines probe mainly the amount of energy processed by the hydrogen gas, and one expects them to be stronger for higher H zone masses and for closer mixing with 56 Ni. Kozma and Fransson (1998b) could confirm the dominance of H zone emission of [Ca II], but pointed out that a contribution by the O zone can occur in models using efficient convection and overshooting, where some Ca has been mixed out into the O layers. Both [Ca II] 7291, 7323 and the Ca II NIR triplet are initially formed by thermal collisional excitation. The Ca II NIR / [Ca II] 7291, 7323 ratio decreases with time as the temperature decreases. At later times fluorescence following UV pumping in the Ca II HK lines becomes important. Li et al. (1993) estimate an epoch of 350d for this, while Kozma and Fransson (1998b) find 500–800d in their models. Fluorescence takes over in the triplet first, roughly when T . 5000 K. In the limit that both [Ca II] 7291, 7323 and Ca II NIR are driven by HK pumping, their intensity ratios will approach unity. The high optical depth of the triplet lines means that the Ca II 8498 line can scatter in the Ca II 8542 line (1500 km s1 separation), and the Ca II 8542 line can scatter in the Ca II 8662 line (4200 km s1 separation). To what extent this happens depends on the distribution of the H zone gas and its temperature. In Fig. 10 (top), it can be seen that full scattering to the 8662 line has occurred in the model, whereas the observed spectrum shows a distinct 8542 line that has not scattered. One should also note that O I 8446 will scatter in the Ca II NIR triplet, and [C I] 8727 can blend with its red wing.

6.2

Stripped-Envelope SNe

The first stripped-envelope nebular spectral models were calculated by Fransson and Chevalier (1989), of 4 and 8 Mˇ He core explosions (Type Ib SN). The models produced emission lines of Mg I] 4571, [O I] 5577, Na I D, [O I] 6300, 6364, O I 7774, [Ca II] 7300, and Ca II NIR + [C I] 8727, as typically observed. The models were important in self-consistently predicting the range of temperatures and ionization expected, T D 2000–8000 K and xe 0:1. It was shown that an assumption of strong microscopic mixing of the SN ejecta gives model spectra discrepant with observations, consistent with the expected inefficiency of atomic diffusive mixing (Sect. 5.1). The implication is that caution is needed in interpreting single-zone models for core-collapse SNe, and for highest accuracy, multi-zone explosion modelling is needed.

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833

Multi-zone spectral models of Type IIb SNe (only small amounts of hydrogen left) have been computed by Houck and Fransson (1996), Maurer et al. (2010), and Jerkstrand et al. (2015a). These models were used to study the behavior of H˛ from the hydrogen shell, the emission from the helium envelope, and the oxygen-line brightness. The SNe modelled so far show nucleosynthesis pointing to an origin in low or intermediate-mass stars, where the hydrogen envelope stripping must have occurred by Roche-lobe overflow to a companion. Problems to explain apparent late-time H alpha emission appear to have been resolved by including [N II] 6548, 6583 emission from the helium envelope (Jerkstrand et al. 2015a), which mimics broad H˛ emission. The first nebular Type Ic models were calculated by C. Kozma and presented in Sollerman et al. (2000). These were 1D models of energetic explosions of 6 and 14 Mˇ CO cores, with the aim to model SN 1998bw – the first SN associated with a gamma ray burst. As for other SN classes, 1D explosion models gave poor reproduction of observed line profiles, demonstrating that some kind of mixing or asymmetric explosion occurs also in Type Ic SNe. The model set was important in showing that models that give good fits to early-time light curves and spectra can still be rejected from late-time comparisons. A single-zone approach has been taken in a series of papers by P. Mazzali (e.g., Mazzali et al. 2001, 2004, 2010) (see Fig. 12 for an example). The majority of SNe analyzed with single-zone models have oxygen mass estimates of 0.5–1.5 Mˇ , which suggests a low/intermediate progenitor mass range. Some show only a few tenths of solar mass of oxygen (e.g., Sauer et al. 2006), indicating that nature can produce bare CO cores of as low mass as 2 Mˇ . The Axelrod method has also been implemented in 2D (Maeda et al. 2006). 2D explosion models offer a way to reproduce narrow lines from intermediate-mass element and broad lines from irongroup elements, as observed in SN 1998bw, if the viewing angle is close to pole-on (Figure 12, right). Discussions of observed oxygen-line profiles can be found in, e.g., Modjaz et al. (2008), Maeda et al. (2008), Taubenberger et al. (2009), and Milisavljevic et al. (2010). In the following sections, some further comments are given on the formation of lines of magnesium, oxygen, and calcium, which are typically strong in strippedenvelope SN spectra.

6.2.1 Magnesium Lines The most prominent Mg line is Mg I] 4571, which is the first transition in Mg I. Models show that the neutral fraction is typically small (xMgI 103 ) due to efficient photoionization both from ground state and excited states (Jerkstrand et al. 2015a). This puts the line formation in a regime where both cooling and recombination can be important. The luminosity can show a dramatic increase at density thresholds above which cooling takes over. The line may be affected by line blocking to a significant extent, the efficiency of which increases rapidly blueward of 5000 Å. This produces an asymmetric line profile with a blueshifted peak. Another distinct line produced that has been observed in many SNe is Mg I 1.504 m. This is a pure recombination line, free of line blocking. As models often give

[Co II] 9340, 9345

[C I] 9825, 9850

Fλ (10–16 erg s–1 cm–2 Å–1+ const

4

Ca II IR [C I] 8727

Ca II] 7291, 7324 o I 7773, [s I] 7722

Na I D

[Fe II] 5112, 5159, 5220, 5261, 5273, 5334, 5376 etc.

2

[O I] 6300, 6363

[0 1] 5577

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Mg I] 4570, [s I] 4589

A. Jerkstrand

Ca II H&K [S II] 4069, 4076

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BP8 (+const)

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BP2 (+const)

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4000 5000 6000 7000 8000 9000 0

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Fig. 12 Examples of stripped-envelope models. Left: A single-zone Type Ic model compared to SN 2007gr (Mazzali et al. 2010). Right: A 2D Type Ic model compared to SN 1998bw (Maeda et al. 2006). The effects of increasing the explosion asymmetry (BP value) are illustrated

MMg  MMgII , this line becomes proportional to the magnesium mass and can be used as a diagnostic of this (Jerkstrand et al. 2015a, 2017).

6.2.2 Oxygen Lines The [O I] 6300, 6364 doublet is, as in Type II SNe, an important coolant of the oxygen layers and therefore a good diagnostic of their mass. Due to the higher expansion velocities in stripped-envelope SNe compared to H-rich SNe, the lines enter the optically thin regime at an earlier epoch, with t 6300 D 1 at 360d for M D 1, f D 0:1 and V D 3500 km s1 (using Eq. 39). Because the core expansion is faster than the line separation between the 6300 and 6364 lines (3047 km s1 ), the lines are blended and the line ratio has to be estimated by fitting the single blended feature. [O I] 5577 is often distinct early on, and the [O I] 5577 / [O I] 6300, 6364 ratio may be used as a thermometer. This method breaks down quite early as [O I] 5577 falls out of LTE. This occurred after 150d in a model grid of Type IIb SNe (Jerkstrand et al. 2015a). The [O I] 5577/[O I] 6300, 6364 ratio has been shown to depend on clumping (e.g., Maurer et al. 2010) and holds some promise to be used as diagnostic for this. When O I 7774, O I 9264, O I 1.129+1.130 m, and O I 1.316 m are formed in the recombination regime, their strengths may be used to estimate the quantity ne f 1=2 , under the assumption that nOII ne . Effective recombination rates to be used for this have been calculated by Maurer et al. (2010) and Jerkstrand et al. (2015a). However, models also demonstrate complications and deviation from this regime. The metastable behavior of many excited states in O I leads to significant

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optical depths for hundreds of days, and this produces a scattering contribution to the lines. At high densities cooling can occur in the O I 7774 transition (Maurer et al. 2010), significantly boosting it over its recombination luminosity. While O I 7774 is relatively free from contaminations, O I 9263, O I 1.13 m, and O I 1.31 m can be significantly blended with other lines (Jerkstrand et al. 2015a).

6.2.3 Calcium Lines [Ca II] 7291, 7323 is typically the main coolant of the explosive oxygen burning ashes (the layer containing Si/S/Ca), and the calcium line strengths therefore relate to how much energy is reprocessed by these layers. Standard explosion models ejecting 0.1 Mˇ of Si/S/Ca material have been shown to give good agreement with Type IIb SNe (Jerkstrand et al. 2015a). The Ca II NIR lines, other the other hand, are after 200d formed mainly by fluorescence following HK absorption, mainly in the 56 Ni zone (ashes of silicon burning). The [O I] 6300, 6364 / [Ca II] 7291, 7323 ratio is often used in the literature as a diagnostic of core mass, but there are many issues with this method. The calcium emission in stripped-envelope SNe comes from an explosively made region, whose size and distribution depend on the explosion energy. As long as the link between progenitor mass and explosion energy is unknown, a diagnostic involving calcium is not robustly linked to core mass. Using models with E 1 B, figure 13 shows model tracks of the [O I] 6300, 6364/[Ca II] 7392, 7323 ratio from the models of Fransson and Chevalier (1989), Houck and Fransson (1996), and J15a. The grids indicate an increase of this ratio

Fig. 13 Model predictions of the [O I] 6300, 6364 / [Ca II] 7291, 7323 ratio in stripped-envelope SNe. The He8.4 and He4.5 models are from Fransson and Chevalier (1989). The He4.0 model is from Houck and Fransson (1996). The He3.1, He3.5, and He5.9 Mˇ models (colored lines) are from J15a. The grid demonstrates complex dependency on He core mass, velocity (last 4 digits in km/s), time, as well as nucleosynthesis model

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with helium core mass, for other parameters fixed (and keep the caveat mentioned above in mind). The Fransson and Chevalier (1989) grid shows a decrease of the ratio with higher core velocity, and all grids shows strong time dependency. As discussed in Fransson and Chevalier (1989), the very low ratios for the 4.5 Mˇ He cores are due to a large fraction of calcium in the O/Mg zone, something seen more rarely in modern explosion models. They are therefore marked in parenthesis.

6.3

Thermonuclear Supernovae

The first Type Ia nebular models were computed by Axelrod (1980). These models are single-zone, pure iron-group composition, with relatively simple physics. The model spectra nevertheless showed good resemblance with observed Type Ia spectra, strengthening the exploding white dwarf idea to explain Type Ia SNe. In particular were the strongest observed lines reproduced by Fe II emission at 5200 and 7155 Å, Fe III emission at 4700 Å, and Co III emission at 5900 Å. The cobalt line evolution showed consistency with a declining abundance of cobalt, providing strong support for the 56 Co decay model. Axelrod could also show that the “quasicontinuum” between the strong lines was formed by the overlap of a large number of weaker spectral lines, not needing any true continuum emission. Axelrod’s technique, albeit without the global radiative transport component, has been adapted and applied to analyze Type Ia spectra in many subsequent papers. Single-zone models likely work reasonably well due to the homogenous composition of Type Ia SNe. Ruiz-Lapuente and Lucy (1992) developed a method to use Type Ia nebular spectra to determine the extinction toward the SN. Multi-zone nebular models of the fast deflagration simulation W7 of Nomoto et al. (1984) have been presented in several papers (Fransson and Jerkstrand 2015; Leloudas et al. 2009; Liu et al. 1997a; Maeda et al. 2010; Maurer et al. 2011; Mazzali et al. 2011; Ruiz-Lapuente et al. 1995; Sollerman et al. 2004) using a variety of codes. Liu et al. (1997a) showed that the very high 58 Ni abundance in W7 (Ni/Fe = 4 times solar) gave a much too strong [Ni II] 7378 line, and SNe with MIR data show the same discrepancy for [Ni II] 6 m (Leloudas et al. 2009). However, Ruiz-Lapuente and Lucy (1992) estimate a ratio of 3 in SN 1995G, suggesting some variety. Liu et al. (1997a) show how the ionization state and temperature increases with velocity coordinate (to about 8000 km s1 ), varying from FeI+FeII-dominated mix and T 3000 K at the center to Fe III + Fe IVdominated mix and T 7000K at 8000 km s1 , at 300d. Liu et al. (1998) discuss the physical ionization mechanisms at late times, finding non-thermal ionization and charge transfer to be more important processes than photoionization. Models generally show continuously decreasing ionization with time, with Fe I becoming the dominant ion after about 2 years (Fransson and Jerkstrand 2015; Sollerman et al. 2004). Even before this time, Fe I plays an important role in the optical radiative transfer (Axelrod 1980). Ruiz-Lapuente (1996), Liu et al. (1997a), and Mazzali et al. (2015) computed sub-Chandrasekhar models, pointing out that they are hotter and more ionized than

32 Spectra of Supernovae in the Nebular Phase

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W7 in the central regions, producing somewhat higher Fe III/Fe II line ratios. They also have weaker [Ni II] lines due to the smaller amount of 58 Ni. Liu et al. (1997a) found a better fit for the sub-Chandra model to a series of observed SNe, whereas Ruiz-Lapuente (1996) favored the W7 model for SN 1994D. Eastman and Pinto (1993) and Liu et al. (1997b) computed spectra of the delayed detonation model DD4 of Woosley and Weaver (1994). Pure deflagration models were studied by Kozma et al. (2005), who found strong O I and C I lines in these to be inconsistent with observations. Two examples of spectral models are shown in Fig. 14.

1

a Chandrasekhar (W7) 0.8 d=16 Mpc H0 =68 km s–1 Mpc–1

0.6

fλ (erg s–1 cm–2 Å–1)

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Fig. 14 Examples of Type Ia model spectra, from Ruiz-Lapuente (1996). Chandra (top) and subChandra (bottom) models compared to SN 1994D. See also Mazzali et al. (2015) for a model with line IDs

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For the first few hundred days, the ejecta are hot and ionized. Most radioactive energy is converted to heat and is reemitted in the optical and NIR. The spectrum is dominated by efficient cooling lines of iron, cobalt, and nickel. At later times, the ejecta pass through a rapid phase of cooling as the cooling switches from excited multiplets to ground multiplet transitions. The bulk of SN emission then moves to the mid-infrared, an effect dubbed the infrared catastrophe. The optical and nearinfared regions then become dominated by fluorescence of UV emission (Fransson and Jerkstrand 2015), and an accurate radiative transfer treatment is necessary. The fluorescence maintains optical output at about 20% of the bolometric luminosity.

7

Conclusions

Supernovae in the nebular phase provide a wealth of information about the interiors of the exploded stars. From the first simple models devised some 35 years ago, we today have sophisticated codes capable of testing stellar evolution, explosion, and nucleosynthesis models to a high level of detail. The nucleosynthesis of isotopes such as oxygen, magnesium, and nickel can be estimated, providing constraints on both progenitors and explosion physics. Some signatures need advanced models for interpretation, whereas some can be analyzed in simpler analytic approaches. The vast majority of core-collapse SNe show nucleosynthesis consistent with an origin as MZAMS . 20 Mˇ stars, and there may be a shortage of events from more massive progenitors compared to standard IMF expectations. Line profiles may be used to probe the morphology of the ejecta for the various elements, which puts multiD hydrodynamic models to the test. Line luminosities provide information about masses, emitting volumes, and physical conditions. The evolution of light curves provides results on masses of radioactive isotopes such as 56 Co, 57 Co, and 44 Ti. By continuing efforts at determining the nucleosynthesis and inner ejecta morphology for SNe of different types, much remains still to be learned both about supernovae and about the origin of the elements.

8

Cross-References

 Dust and Molecular Formation in Supernovae  Nucleosynthesis in Hypernovae Associated with Gamma Ray Bursts  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Nucleosynthesis in Thermonuclear Supernovae  Spectra of Supernovae During the Photospheric Phase  The Multidimensional Character of Nucleosynthesis in Core-Collapse Super-

novae Acknowledgements I would like to thank J. Spyromilio, C. Fransson, K. Maeda, R. McCray, S. Taubenberger, J. Sollerman, P. Mazzali, S. Smartt, P. Murdin, M. Ergon, and P. Ruiz-Lapuente for useful comments on the manuscript.

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References Axelrod TS (1980) Late time optical spectra from the Ni-56 model for Type 1 supernovae. PhD thesis, University of California, Santa Cruz Baade W (1945) B Cassiopeiae as a supernova of Type I. ApJ 102:309. doi:10.1086/144761 Bodansky D, Clayton DD, Fowler WA (1968) Nuclear quasi-equilibrium during silicon burning. ApJS 16:299. doi:10.1086/190176 Borst LB (1950) Supernovae. Phys Rev 78:807–808. doi:10.1103/PhysRev.78.807.2 Chugai NN (1994) The oxygen mass in SN 1987A: making use of fluctuations in the (O I) lambda lambda 6300, 6364 profile. ApJ 428:L17–L19. doi:10.1086/187382 Colgate SA, McKee C (1969) Early supernova luminosity. ApJ 157:623. doi:10.1086/150102 Colgate SA, Petschek AG, Kriese JT (1980) The luminosity of Type I supernovae. ApJ 237:L81–L85. doi:10.1086/183239 de Kool M, Li H, McCray R (1998) Thermal evolution of the envelope of SN 1987A. ApJ 503: 857–876. doi:10.1086/306016 Dessart L, Hillier DJ (2011) Non-LTE time-dependent spectroscopic modelling of Type II-plateau supernovae from the photospheric to the nebular phase: case study for 15 and 25 M‹ progenitor stars. MNRAS 410:1739–1760. doi:10.1111/j.1365-2966.2010.17557.x Dessart L, Livne E, Waldman R (2010) Determining the main-sequence mass of Type II supernova progenitors. MNRAS 408:827–840. doi:10.1111/j.1365-2966.2010.17190.x Dessart L, Hillier DJ, Waldman R, Livne E (2013) Type II-Plateau supernova radiation: dependences on progenitor and explosion properties. MNRAS 433:1745–1763. doi:10.1093/mnras/stt861 Eastman RG, Pinto PA (1993) Spectrum formation in supernovae – numerical techniques. ApJ 412:731–751. doi:10.1086/172957 Fransson C, Chevalier RA (1987) Late emission from SN 1987A. ApJ 322:L15–L20. doi:10.1086/185028 Fransson C, Chevalier RA (1989) Late emission from supernovae – a window on stellar nucleosynthesis. ApJ 343: 323–342. doi:10.1086/167707 Fransson C, Jerkstrand A (2015) Reconciling the infrared catastrophe and observations of SN 2011fe. ApJL 814:L2. doi:10.1088/2041-8205/814/1/L2 Gearhart RA, Wheeler JC, Swartz DA (1999) Carbon monoxide formation in SN 1987A. ApJ 510:944–966. doi:10.1086/306588 Herant M, Woosley SE (1994) Postexplosion hydrodynamics of supernovae in red supergiants. ApJ 425:814–828. doi:10.1086/174026 Hillier DJ, Dessart L (2012) Time-dependent radiative transfer calculations for supernovae. MNRAS 424:252–271. doi:10.1111/j.1365-2966.2012.21192.x Houck JC, Fransson C (1996) Analysis of the late optical spectra of SN 1993J. ApJ 456:811. doi:10.1086/176699 Jerkstrand A (2011) Spectral modeling of nebular-phase supernovae. PhD thesis, Faculty of Science, Department of Astronomy, University of Stockholm. Advisor: Claes Fransson Jerkstrand A, Fransson C, Kozma C (2011) The 44 Ti-powered spectrum of SN 1987A. A&A 530:A45. doi:10.1051/0004-6361/201015937 Jerkstrand A, Fransson C, Maguire K, Smartt S, Ergon M, Spyromilio J (2012) The progenitor mass of the Type IIP supernova SN 2004et from late-time spectral modeling. A&A 546:A28. doi:10.1051/0004-6361/201219528 Jerkstrand A, Smartt SJ, Fraser M, Fransson C, Sollerman J, Taddia F, Kotak R (2014) The nebular spectra of SN 2012aw and constraints on stellar nucleosynthesis from oxygen emission lines. MNRAS 439:3694–3703. doi:10.1093/mnras/stu221 Jerkstrand A, Ergon M, Smartt SJ, Fransson C, Sollerman J, Taubenberger S, Bersten M, Spyromilio J (2015a) Late-time spectral line formation in Type IIb supernovae, with application to SN 1993J, SN 2008ax, and SN 2011dh. AA 573:A12. doi:10.1051/0004-6361/201423983

840

A. Jerkstrand

Jerkstrand A, Smartt SJ, Sollerman J, Inserra C, Fraser M, Spyromilio J, Fransson C, Chen TW, Barbarino C, Dall’Ora M, Botticella MT, Della Valle M, Gal-Yam A, Valenti S, Maguire K, Mazzali P, Tomasella L (2015b) Supersolar Ni/Fe production in the Type IIP SN 2012ec. MNRAS 448:2482–2494. doi:10.1093/mnras/stv087 Jerkstrand A, Smartt SJ, Inserra C, Nicholl M, Chen T-W, Krühler T, Sollerman J, Taubenberger S, Gal-Yam A, Kankare E, Maguire K, Fraser M, Valenti S, Sullivan M, Cartier R, Young DR (2017) Long-duration superluminous supernovae at late times. ApJ 835:13. doi:10.3847/1538-4357/835/1/13 Kirshner RP, Kwan J (1975) The envelopes of Type II supernovae. ApJ 197:415–424. doi:10.1086/153527 Kozma C, Fransson C (1992) Gamma ray deposition and nonthermal excitation in supernovae. ApJ 390:602–621. doi:10.1086/171311 Kozma C, Fransson C (1998a) Late spectral evolution of SN 1987A. I. Temperature and ionization. ApJ 496:946–966. doi:10.1086/305409 Kozma C, Fransson C (1998b) Late spectral evolution of SN 1987A. II. Line emission. ApJ 497:431–457. doi:10.1086/305452 Kozma C, Fransson C, Hillebrandt W, Travaglio C, Sollerman J, Reinecke M, Röpke FK, Spyromilio J (2005) Three-dimensional modeling of Type Ia supernovae – the power of late time spectra. AAP 437:983–995. doi:10.1051/0004-6361:20053044 Leloudas G, Stritzinger MD, Sollerman J, Burns CR, Kozma C, Krisciunas K, Maund JR, Milne P, Filippenko AV, Fransson C, Ganeshalingam M, Hamuy M, Li W, Phillips MM, Schmidt BP, Skottfelt J, Taubenberger S, Boldt L, Fynbo JPU, Gonzalez L, Salvo M, ThomasOsip J (2009) The normal Type Ia SN 2003hv out to very late phases. AAP 505:265–279. doi:10.1051/0004-6361/200912364 Li H, McCray R (1992) The forbidden O I 6300, 6364 A doublet of SN 1987A. ApJ 387:309–313. doi:10.1086/171082 Li H, McCray R (1995) The He I emission lines of SN 1987A. ApJ 441:821–829. doi:10.1086/175405 Li H, McCray R (1996) Ultraviolet opacity and fluorescence in supernova envelopes. ApJ 456:370. doi:10.1086/176659 Li H, McCray R, Sunyaev RA (1993) Iron, Cobalt, and Nickel in SN 1987A. ApJ 419:824. doi:10.1086/173534 Liu W, Dalgarno A (1996) Formation and destruction of silicon monoxide in SN 1987A. ApJ 471:480. doi:10.1086/177982 Liu W, Jeffery DJ, Schultz DR (1997a) Nebular spectra of Type IA supernovae. ApJL 483:L107– L110. doi:10.1086/310752 Liu W, Jeffery DJ, Schultz DR (1997b) Nebular spectra of the unusual Type IA supernova 1991T. ApJ 486: L35–L38. doi:10.1086/310832 Liu W, Jeffery DJ, Schultz DR (1998) Ionization of Type IA supernovae: electron impact, photon impact, or charge transfer? ApJ 494:812–815. doi:10.1086/305249 Lucy LB (1991) Nonthermal excitation of helium in Type Ib supernovae. ApJ 383:308–313. doi:10.1086/170787 Maeda K, Nomoto K, Mazzali PA, Deng J (2006) Nebular spectra of SN 1998bw revisited: detailed study by one- and two-dimensional models. ApJ 640:854–877. doi:10.1086/500187 Maeda K, Kawabata K, Mazzali PA, Tanaka M, Valenti S, Nomoto K, Hattori T, Deng J, Pian E, Taubenberger S, Iye M, Matheson T, Filippenko AV, Aoki K, Kosugi G, Ohyama Y, Sasaki T, Takata T (2008) Asphericity in supernova explosions from late-time spectroscopy. Science 319:1220. doi:10.1126/science.1149437 Maeda K, Taubenberger S, Sollerman J, Mazzali PA, Leloudas G, Nomoto K, Motohara K (2010) Nebular spectra and explosion asymmetry of Type Ia supernovae. ApJ 708:1703–1715. doi:10.1088/0004-637X/708/2/1703 Maurer I, Mazzali PA, Taubenberger S, Hachinger S (2010) Hydrogen and helium in the late phase of supernovae of Type IIb. MNRAS 409:1441–1454. doi:10.1111/j.1365-2966.2010.17186.x

32 Spectra of Supernovae in the Nebular Phase

841

Maurer I, Jerkstrand A, Mazzali PA, Taubenberger S, Hachinger S, Kromer M, Sim S, Hillebrandt W (2011) NERO- a post-maximum supernova radiation transport code. MNRAS 418:1517– 1525. doi:10.1111/j.1365-2966.2011.19376.x Mazzali PA, Nomoto K, Patat F, Maeda K (2001) The nebular spectra of the hypernova SN 1998bw and evidence for asymmetry. ApJ 559:1047–1053. doi:10.1086/322420 Mazzali PA, Deng J, Maeda K, Nomoto K, Filippenko AV, Matheson T (2004) Properties of two hypernovae entering the nebular phase: SN 1997ef and SN 1997dq. ApJ 614:858–863. doi:10.1086/423888 Mazzali PA, Kawabata KS, Maeda K, Foley RJ, Nomoto K, Deng J, Suzuki T, Iye M, Kashikawa N, Ohyama Y, Filippenko AV, Qiu Y, Wei J (2007) The aspherical properties of the energetic Type Ic SN 2002ap as inferred from its nebular spectra. ApJ 670:592–599. doi:10.1086/521873 Mazzali PA, Maurer I, Valenti S, Kotak R, Hunter D (2010) The Type Ic SN 2007gr: a census of the ejecta from late-time optical-infrared spectra. MNRAS 408:87–96. doi:10.1111/j.1365-2966.2010.17133.x Mazzali PA, Maurer I, Stritzinger M, Taubenberger S, Benetti S, Hachinger S (2011) The nebular spectrum of the Type Ia supernova 2003hv: evidence for a non-standard event. MNRAS 416:881–892. doi:10.1111/j.1365-2966.2011.19000.x Mazzali PA, Sullivan M, Filippenko AV, Garnavich PM, Clubb KI, Maguire K, Pan Y-C, Shappee B, Silverman JM, Benetti S, Hachinger S, Nomoto K, Pian E (2015) Nebular spectra and abundance tomography of the Type Ia supernova SN 2011fe: a normal SN Ia with a stable Fe core. MNRAS 450:2631–2643. doi:10.1093/mnras/stv761 Meyerott RE (1978) On the interpretation of the spectra of Type I supernovae. ApJ 221:975–989. doi:10.1086/156103 Milisavljevic D, Fesen RA, Gerardy CL, Kirshner RP, Challis P (2010) Doublets and double peaks: late-time [O I] 6300, 6364 line profiles of stripped-envelope, core-collapse supernovae. ApJ 709:1343–1355. doi:10.1088/0004-637X/709/2/1343 Modjaz M, Kirshner RP, Blondin S, Challis P, Matheson T (2008) Double-peaked oxygen lines are not rare in nebular spectra of core-collapse supernovae. ApJ 687:L9. doi:10.1086/593135 Nomoto K, Thielemann F-K, Yokoi K (1984) Accreting white dwarf models of Type I supernovae. III – Carbon deflagration supernovae. ApJ 286:644–658. doi:10.1086/162639 Oliva E (1993) The Oi-Lyman fluorescence revisited and its implications on the clumping of hydrogen O/h mixing and the pre-supernova oxygen abundance in supernova 1987A. A&A 276:415 Osterbrock DE (1989) Astrophysics of gaseous nebulae and active galactic nuclei Osterbrock DE, Ferland GJ (2006) Astrophysics of gaseous nebulae and active galactic nuclei Röpke FK, Hillebrandt W, Schmidt W, Niemeyer JC, Blinnikov SI, Mazzali PA (2007) A threedimensional deflagration model for Type Ia supernovae compared with observations. ApJ 668:1132–1139. doi:10.1086/521347 Ruiz-Lapuente P (1996) The hubble constant from 56Co-powered nebular candles. ApJ 465:L83. doi:10.1086/310155 Ruiz-Lapuente P, Lucy LB (1992) Nebular spectra of Type IA supernovae as probes for extragalactic distances, reddening, and nucleosynthesis. ApJ 400:127–137. doi:10.1086/171978 Ruiz-Lapuente P, Kirshner RP, Phillips MM, Challis PM, Schmidt BP, Filippenko AV, Wheeler JC (1995) Late-time spectra and Type IA supernova models: new clues from the hubble space telescope. ApJ 439:60–73. doi:10.1086/175151 Sauer DN, Mazzali PA, Deng J, Valenti S, Nomoto K, Filippenko AV (2006) The properties of the ‘standard’ Type Ic supernova 1994I from spectral models. MNRAS 369:1939–1948. doi:10.1111/j.1365-2966.2006.10438.x Shigeyama T, Nomoto K, Tsujimoto T, Hashimoto M-A (1990) Low-mass helium star models for Type Ib supernovae – light curves, mixing, and nucleosynthesis. ApJ 361:L23–L27. doi:10.1086/185818 Shull JM (1979) Heating and ionization by X-ray photoelectrons. ApJ 234:761–764. doi:10.1086/157553

842

A. Jerkstrand

Sobolev VV (1957) The diffusion of L˛ radiation in nebulae and stellar envelopes. Sovast 1:678 Sollerman J, Kozma C, Fransson C, Leibundgut B, Lundqvist P, Ryde F, Woudt P (2000) SN 1998bw at late phases. ApJ 537:L127–L130. doi:10.1086/312763 Sollerman J, Lindahl J, Kozma C, Challis P, Filippenko AV, Fransson C, Garnavich PM, Leibundgut B, Li W, Lundqvist P, Milne P, Spyromilio J, Kirshner RP (2004) The late-time light curve of the Type Ia supernova 2000cx. AAP 428:555–568. doi:10.1051/0004-6361:20041320 Spyromilio J, Pinto PA (1991) Oxygen in supernovae. In: Danziger IJ, Kjaer K (eds) European Southern Observatory Conference and Workshop Proceedings. European Southern Observatory Conference and Workshop Proceedings, vol 37, p 423 Taubenberger S, Valenti S, Benetti S, Cappellaro E, Della Valle M, Elias-Rosa N, Hachinger S, Hillebrandt W, Maeda K, Mazzali PA, Pastorello A, Patat F, Sim SA, Turatto M (2009) Nebular emission-line profiles of Type Ib/c supernovae – probing the ejecta asphericity. MNRAS 397:677–694. doi:10.1111/j.1365-2966.2009.15003.x van Regemorter H (1962) Rate of collisional excitation in stellar atmospheres. ApJ 136:906. doi:10.1086/147445 Woosley SE, Weaver TA (1994) Sub-Chandrasekhar mass models for Type IA supernovae. ApJ 423:371–379. doi:10.1086/173813 Xu Y, McCray R (1991) Energy degradation of fast electrons in hydrogen gas. ApJ 375:190–201. doi:10.1086/170180 Xu Y, McCray R, Oliva E, Randich S (1992) Hydrogen recombination at high optical depth and the spectrum of SN 1987A. ApJ 386:181–189. doi:10.1086/171003

Interacting Supernovae: Spectra and Light Curves

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Sergei Blinnikov

Abstract

The ejecta of a supernova explosion expand with a very high velocity and they immediately impact the circumstellar material. The manifestation of this impact depends mainly on the density of the circumstellar material and on the velocity contrast between the ejecta and that material. We describe the effects of the interaction of supernova ejecta with circumstellar material on the observed spectral features and light curves of supernovae. The most interesting effect of the interaction is the powerful production of light by radiating shock waves. Many superluminous supernovae may be explained by this mechanism. We describe the relevant physical picture for the efficient production of light in those objects, which is most effective when the mass of circumstellar material is large and slowly moving.

Contents 1 2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interaction Regimes and Spectral Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Rarefied CSM: Absorption Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Dense CSM: Emission Lines and Continuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Cool Dense Shell Fragmentation and CSM Lumpiness . . . . . . . . . . . . . . . . . . . . . Supernovae Powered by Collision of Massive Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Multiple Shell Ejection by Massive Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Interaction with Radiation Trapping Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Hydrodynamical Evolution in Synthetic Models . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 General Properties of the Interacting SLSN Light Curves: From Visible Light to X-Ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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S. Blinnikov () Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), Kashiwa, Chiba, Japan e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_31

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4 Strong Shock Waves with Internal Energy (e.g., Ionisation) and Radiation . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

All supernovae (SN) interact with interstellar matter at some stage. If the density of the nearby matter is not high then this interaction becomes observable only some decades after the explosion as X-rays from a young supernova remnant. In this chapter we concentrate on cases when the density in the vicinity of the exploding star is much higher than average in the interstellar medium. The interaction of supernova ejecta with circumstellar material (CSM), such as a strong pre-supernova wind or the debris of previous episodes of mass ejection, may lead to periods of enhanced radiation power lasting from hours to months in visible light, the ultraviolet or the infrared, and/or in radio and X-rays, and to peculiarities in the Supernova (SN) spectra (such as narrow lines). This case is called an interacting supernova. In this chapter, we concentrate on the theory of such supernovae. We describe the effects of the interaction of SN ejecta with circumstellar material on spectral features of observed supernovae in Sect. 2. The most interesting effect of ejecta-CSM interaction is the powerful production of light by radiating shock waves, which we discuss in Sect. 3.

2

Interaction Regimes and Spectral Signatures

Historically, the first identification of a supernova-CSM interaction was the discovery of strong radio emission from SN 1979C, which followed an ejecta-wind interaction model (Chevalier 1982b). Here, we concentrate on the manifestations of ejecta-wind interaction in visible light, which are of crucial importance for understanding this phenomenon. Specific features in the spectra of supernovae may provide earlier evidence of an interaction with a dense circumstellar wind long before the radio emission (if any) becomes detectable; furthermore, spectral line profiles can provide information about the wind morphology (some information may also be extracted also from light curves). All stars lose mass in the form of stellar winds. If the mass loss is weak, MP  1014 Mˇ /yr (this value is typical for our Sun), its influence on the supernova outburst can be neglected. For many types of pre-supernova stars the winds may be much more powerful. In addition to quasi-steady winds, other hydrodynamic events such as pulsations, eruptions, and violent mass transfer in a binary star, occurring prior to a SN explosion (Smith 2014), may strongly enhance the density of the circumstellar matter. This may lead to many interesting peculiarities in the observations.

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The evaluation of the mass-loss rate, MP , for a pre-supernova star is based on the idealisation of a spherically symmetric wind with velocity u through a sphere of an arbitrary radius r : MP  Area  mass flux density D 4 r 2 .r/u.r/:

(1)

In reality the density and velocity fluctuate at any given r, sometimes greatly, and the measurement of MP is not an easy task. The structure of the CSM formed by violent mass ejections before the supernova explosion may be quite complicated. Yet very often it is described in terms of an ideal “wind”. A standard idealisation of the steady wind flow for r much larger than the radius R of the star is the assumption that the velocity is constant in space and time. For u D const.r/ and constant MP we should have from the definition (1): .r/ D

MP / r 2 : 4 r 2 u

(2)

One should remember that the simple law (2) for the flow has a very limited applicability. We can speak safely of a “wind” when the mass-loss rate MP is weak, like the wind of solar-type stars, MP  1014 Mˇ /yr, but those weak winds do not produce observable features in supernova fluxes and spectra. Interesting events occur when the mass-loss rate is much larger: MP & 104 Mˇ /yr. For some interacting supernovae, the “wind” interpretation suggests MP  1 Mˇ /yr. This enormous mass-loss rate cannot be sustained by a pre-supernova star for many years, and the CSM that it generates must terminate near the star. This implies automatically that the “wind” picture is self-contradictory, because it assumes a steady outflow with velocity independent of the distance from the star. In reality, a wind flow with velocity constant in space is impossible if the mass-loss rate is so monstrous. The wind density parameter w

MP u

(3)

is very useful for direct estimates of density .r/ D

w : 4 r 2

(4)

The value of w is less than 1014 g cm1 for red supergiants. This is more than two orders of magnitude below typical estimates of w  1016 g cm1 for SNe IIn and four orders of magnitude below superluminous SNe IIn having w  1018 g cm1 (Smith et al. 2009). Interacting Type II supernovae (SN Type II) show a wide range of properties. The density and temporal characteristics of the CSM for different types of interacting SN Type II have previously been summarised by Chugai (1997b) and Benetti (2000).

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In terms of the “wind,” the two main parameters that define the characteristics of those events are the mass-loss rate MP and the type of the wind (uniform or clumpy). Interacting supernovae have been classified by Turatto (2003). The taxonomy for SN Type II is based on the strength of the CSM-ejecta interaction signatures. Classical SN Type II are the most frequent. Here the emission is determined by the thermal bath in the ejecta whose entropy was raised by the shock wave from the SN explosion. The entropy, and hence light production, may also be raised by a radioactive material, such as 56 Ni or 56 Co. For these events CSM-ejecta interaction is negligible (at least in the early phases). Very often they are divided into plateau (II-P) and linear (II-L) subtypes depending on the shape of the light curve in the V band. (One should remember that a “linear” light curve is one with a straight line fit for the dependence of magnitude on time, whereas for the flux or luminosity the same physical emission law is the exponential function of time.) The division between II-P and II-L is not sharp and the boundary between II-P and II-L is not clearly defined. It may correspond to a range in the hydrogen envelope masses from 10 Mˇ in SN Type II-P to  1 Mˇ in II-L. The difference in hydrogen mass could be due to different mass-loss histories and progenitor masses. Moreover, some supernovae with hydrogen-free spectra, which may be classified like Type I near the maximum light, behave as like Type II on later epochs, when hydrogen is clearly visible, such as SN 2014C (Margutti et al. 2017). See also Nomoto et al. (2005) on SN 2002ic, which was discovered as Type Ia, but showed hydrogen lines later. Similar behaviour has also been seen also for some superluminous supernovae (SLSN) discovered as Type I which may show hydrogen lines a month or so after peak luminosity (Benetti et al. 2014). This demonstrates that the hydrogen envelope can be lost not long before the SN explosion and excited by the shock a bit later. Along the sequence of interacting SNe discussed in Chugai (1997b), Benetti (2000) and Turatto (2003) in different notations the explosions take place in a progressively more dense CSM, which in turn provides evidence of progressively more intense mass loss by the progenitor stars or other violent events in presupernovae. The Type IIn (“n” here denotes narrow emission lines in their spectra) is the most interesting for the theory of interacting supernovae. Type IIn supernovae are thought to happen inside a dense wind MP > 104 u10 Mˇ /yr (where u10 is the wind velocity in units of 10 km/s), which can be either clumpy or uniform, and what we see is not the explosion itself, but the product of the interaction. Let us consider the observable signatures of interaction of supernova ejecta with CSM as a function of increasing density of the CSM.

2.1

Rarefied CSM: Absorption Signatures

Ejecta of a supernova explosion expand with a very high velocity. The ejecta immediately impact the circumstellar material. The manifestation of this impact depends mainly on the density of the CSM and on the velocity difference between

33 Interacting Supernovae: Spectra and Light Curves Fig. 1 Schematic view of the interaction of a supernova with the pre-supernova wind. The outer and inner shock waves (dashed lines) produce a double-shock structure, with a contact discontinuity (solid line) between. Wind clouds (bottom part of the sketch) are crushed by slow shocks driven by the shocked intercloud wind or ejecta (From Chugai 1997a)

847

shocked Wind

shocked ejecta

SN ejecta

wind

shocked wind cloud

wind cloud

the ejecta and the CSM. If the density of the CSM is relatively small, the emission from the CSM-ejecta interaction becomes visible only after the SN has become faint, sometimes several years after the explosion. Many of those events are SNe II-L. This is consistent with the assumption that SNe II-L experience stronger mass loss during their evolution in their pre-supernova lives. An ejecta-wind interaction is shown schematically in Fig. 1. It shows the major structures both for a spherically-symmetric smooth wind (top quadrant) and a clumpy wind (lower quadrant). The ejecta of a supernova may be thought of as a freely-expanding (u D r=t ), roughly homogeneous spherical ball with a density cutoff at its outer edge. A supernova in a spherically-symmetric, smooth circumstellar wind creates a standard double-shock wave structure, with a contact discontinuity between (Chevalier 1982b). If the density in the wind is not high, then the forward shock propagating in the wind is fast, hot (T up to 109 K),and adiabatic. The reverse shock propagating into the supernova envelope is slow and radiative: it creates a thin, cool, dense shell at the contact discontinuity. Numerous hydrodynamic models for the shock breakout phase predict the formation of a thin dense shell at the outer boundary of the SN ejecta. This is explained by the transition from the adiabatic to the radiative regime of shock wave propagation in the outermost layers of the exploding star. Simple considerations of radiative diffusion (Chevalier 1981) give an estimate for the shell mass:

Ms  2  104



R 500 Rˇ

2 

ub 104 km s1

1 

 0:4 cm2 g1

1 Mˇ ;

(5)

where R is the radius of either the progenitor star or of the dense CSM envelope which may surround the supernova, ub is the velocity at shock breakout, before free expansion has been established, and  is opacity of the matter in the shell formation

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layers. We see that the shell mass may grow from a tiny fraction of the star mass for ordinary supernovae to several Mˇ in strongly-CSM-interacting SNe embedded into huge massive clouds. The interaction with a clumpy wind differs from the case of smooth, sphericallysymmetric wind in at least one important respect: apart from the main shock wave in the intercloud wind, we also have slow shocks propagating in dense clouds. Shocked clouds may be responsible for the bulk of X-ray and optical emission in some SNe of Type II. For a very dense “wind” typical for SLSN the picture is different from that presented in Fig. 1. In particular, the forward shock may be radiative as well, and high T is never reached; see Sect. 2.3. Chugai et al. (2007) proposed diagnostics for circumstellar interaction in Type II-P supernovae by the detection of high-velocity absorption features in H˛ and He I 10830 Å lines during the photospheric stage; see Fig. 2. To demonstrate the method, they computed the ionisation and excitation of H and He in supernova ejecta taking into account time-dependent effects and X-ray irradiation. They found that the interaction with a typical red supergiant wind should result in enhanced excitation of the outer layers of unshocked ejecta and the emergence of corresponding high-velocity absorption, that is, a depression in the blue absorption wing of H˛ and a pronounced absorption of He I 10830 Å at a radial velocity of about 104 km s1 . They identified a high-velocity absorption

Fig. 2 Schematic picture of the formation of H˛ without and with CS interaction. In the absence of CS interaction (upper diagram), the absorption component forms in the inner layers of ejecta (1) against the photosphere (Ph); the outer recombined ejecta (RE) do not contribute to the absorption line profile (upper right). With CS interaction (lower diagram), the double-shocked structure arises at the SN/wind interface with the forward shock (f ), reverse shock (r), and contact surface where the cool dense shell occurs (c). The X-rays, primarily from the reverse shock, ionize and excite the layers (2) which produce a depression in the blue wing of the undisturbed absorption (bottom right). (From Chugai et al. 2007)

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in H˛ and He I 10830 Å lines of SN 1999em and in H˛ of SN 2004dj as being due to that effect. The derived mass-loss rate was close to 106 Mˇ yr1 for both supernovae, assuming a wind velocity 10 km s1 . The evolution of the high-velocity absorption for the classical Type II SN 1999em showed that there is an optimal phase at about the middle of the plateau (50 d) when the CS interaction effect is most pronounced. At an early stage (e.g., on day 20) the CS interaction effect was not clearly seen because of the merging of high velocity absorption with the strong undisturbed absorption, whereas at a later stage (e.g., 80 d) high-velocity absorption became very faint. Some weakly interacting supernovae may have a narrow optical maximum and low luminosity at the stage when the light curve is powered by radioactive decay. The case of a moderate-density wind may correspond to SN 1987B-type supernovae, which show signatures of interaction with a wind and have relatively low luminosity (Schlegel et al. 1996). The theory developed in Chugai et al. (2007) has been supported by observations of a number of SNe II. The bright Type II-P SN 2009bw had spectra revealing high-velocity lines of H˛ and Hˇ until about 3 months after the shock breakout. This suggests a possible early interaction between the SN ejecta and pre-existing circumstellar material (Inserra et al. 2012). Close inspection of the spectra of the Type II-L supernova SN 2013by indicated asymmetric line profiles and signatures of high-velocity hydrogen (Valenti et al. 2015). A very similar Type II-L, SN 2013ej, had weak signs of interaction (Bose et al. 2015). All three objects showed a very fast transition to the tail (nebular) phase and a rather low mass of radioactive 56 Ni. The presence of high-velocity features in those Type II SNe can indeed be interpreted as interaction between rapidly expanding SN ejecta and CSM. For hydrogen-free, weakly interacting supernovae, other predictions for spectral features have been made. Raskin and Kasen (2013) discuss those predictions for SN Type Ia. SN Type Ia supernovae may be caused by the merger of two white dwarfs. The merger may be preceded by the ejection of some mass from the two stars in “tidal tails,” creating a circumstellar medium around the system. The observational signatures from this material depend on the lag time between the start of the merger and the ultimate explosion. If the time lag is fairly short, then the interaction of the supernova ejecta with the tails could lead to detectable shock emission at radio, optical, and/or X-ray wavelengths. At somewhat later times, the tails produce relatively broad NaID absorption lines with velocity widths of the order of the white dwarf escape speed (1000 km s1 ). That none of these signatures have been detected in normal SNe Ia constrains the lag time to be either very short (.100 s) or fairly long (&100 yr). If the tails have expanded and cooled over timescales 104 yr, then they could be observable through narrow NaID and Ca II H&K absorption lines in the spectra, which are seen in some fraction of SNe Ia. Synthesised NaID line profiles show that, in some circumstances, tidal tails could be responsible for narrow absorptions similar to those observed.

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The alternative scenario for SN Type Ia is the explosion of one white dwarf pushed over the Chandrasekhar mass by accretion, the single degenerate scenario. In this case, one may expect a nonnegligible amount of hydrogen to remain unaccreted in the CSM. This question was addressed in a paper (Nomoto et al. 2005) devoted to SN Type Ia showing hydrogen features in their spectra. Among the important issues in identifying the progenitor system of SNe Ia, they focussed mostly on circumstellar interaction in SN 2002ic, and gave a brief discussion on the controversial issues of the effects of rotation in merging double degenerates and steady hydrogen shell burning in accreting white dwarfs. SN 2002ic was a unique supernova which showed the typical spectral features of SNe Ia near maximum light, but also apparent hydrogen features that have usually been absent in SNe Ia. Based on hydrodynamical models of circumstellar interaction in SN Ia (Nomoto et al. 2005), one may conclude that its circumstellar medium was aspherical (or highly clumpy) and contained 1.3 Mˇ . More intensive stellar winds may blow away not only a hydrogen, but also a helium envelope. As a result, a Type Ibn SN can be produced. Supernovae exploding in a dense CSM are considered in the next section.

2.2

Dense CSM: Emission Lines and Continuum

In addition to some features observed in absorption (see Sect. 2.1) the ejecta-wind interaction gives rise to four major signs (not always observed simultaneously) in the supernova display in visible light (Chugai 1997a): (i) (ii) (iii) (iv)

narrow emission lines from the photoionised undisturbed wind broad emission lines from shocked and/or undisturbed photoionised ejecta an intermediate emission line component from the shocked wind clouds continuum from shocked ejecta or/and wind clumps.

As discussed in Sect. 2.1, if the density of the CSM is relatively small, the emission from CSM-ejecta interaction becomes visible only after the SN has become faint several years after the explosion. At the other extreme, the CSM near the SN may be so dense that the ejecta interact with the wind at early phases and dominate the SN emission. With improved statistics and quality of observations we have now observed counterparts for the different scenarios. Hydrogen-rich supernovae with a strong interaction are called SNe IIn. The ejecta interact with the dense CSM surrounding them soon after the explosion and emission from the SN itself is overwhelmed by the emission arising from the interaction (Grasberg and Nadezhin 1986). Historically, one of the good examples of this class was SN 1988Z. Recently, much more powerful SLSNe have been discovered which are explained by the interaction between the ejecta and a wind. The most remarkable observational features of Type IIn supernovae known up to now are: (i) their optical spectrum, dominated by intense emission lines. (ii) their slow spectral evolution.

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(iii) their slow luminosity evolution. sometimes, for several months the flux changes at a rate of only 0.004 mag/day (by contrast with classical SNe II-P, U and B fluxes decline as slowly as the V -band). (iv) Furthermore, some of these supernovae (but not all) are among the most powerful radio supernovae and/or X-ray emitters. (v) Finally, there are some indications that Type IIn SNe have an IR excess, due to dust formation. The interaction of the ejecta of a supernova explosion with the dense circumstellar medium plays a significant role in the output energy of these Type IIn supernovae. This interaction produces a radiative shock which becomes more and more important as the density of the CSM increases. For number densities of the order of 107 cm3 , it is the dominant physical process. Direct measurements of the CSM in SNe IIn are possible thanks to highresolution spectra (better than 10 km/s), provided by echelle spectrographs: for example, for early work see Salamanca (2003), and more recently Kankare et al. (2012). Echelle spectra of Type IIn SN show a very narrow P Cygni line atop the broad emission lines H˛ and Hˇ . These narrow P Cygni profiles originate in the dense and slowly expanding (u  100 km/s) medium into which the SN shock progresses. This points to a massive and slow wind of the progenitor just before its explosion as a supernova. If such material is created by a wind not long before the explosion, then the mass-loss rate must be of the order of 102 Mˇ yr1 or higher. This value is much larger than the typical mass-loss rate of the winds of OB stars, or indeed yellow and red supergiants. Leloudas et al. (2015) simulated spectra making the transition from SN Type Ia to SN Type IIn (with growing density of CSM). They constructed spectra of supernovae interacting strongly with a circumstellar medium in a simplified model by adding SN templates, a black-body continuum, and an emission-line spectrum. A more advanced simulation taking account of radiative transfer supports the simple model as a good first-order approximation. In a Monte Carlo simulation a large number of parameters are varied, such as the SN type, luminosity and phase, the strength of the CSM interaction, the extinction, and the signal-to-noise ratio .S =N / of the observed spectrum. Leloudas et al. (2015) used Monte Carlo methods to generate more than 800 spectra, and distributed them to 10 different people for classification. They studied how the different simulation parameters affected the appearance of the spectra and therefore their classification. SNe Type IIn showing some structure over the continuum were characterised as “SNe IInS” to allow for a better quantification. It was demonstrated that the flux ratio of the underlying SN to the continuum fV is the single most important parameter determining whether a spectrum can be classified correctly. Other parameters, such as extinction, S =N , and the width and strength of the emission lines, do not play a significant role. In the simulation, thermonuclear SNe were progressively classified as Ia-CSM, IInS, and IIn as fV decreased. The transition between Ia-CSM and IInS occurs at fV  0.2–0.3. It was therefore possible to determine that SNe Ia-CSM are found at the absolute magnitude range 19:5 > M > 21:6 (extinction corrected), in very

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good agreement with observations, and that the faintest SN IIn that can hide a SN Ia has M D 20:1. “91T-like” superluminous supernovae of Type Ia (named after the bright supernova SN 1991T) show at early times weak silicon and calcium lines, leading to a nearly featureless continuum. The literature sample of SNe Ia-CSM shows an association with 91T-like SNe Ia. Leloudas et al. (2015) studied whether this association could be attributed to a luminosity bias (91T-like being brighter than normal events), but the data suggest the association is real, with underlying physical origins. It is proposed that 91T-like explosions result from single degenerate progenitors that have earlier generated their CSM. Despite the spectroscopic similarities between SNe Ibc and SNe Ia, the number of misclassifications between these types was very small in the simulation by Leloudas et al. (2015) and mostly when the spectra had low signal-to-noise ratios. Combined with the SN luminosity function needed to reproduce the observed SN Ia-CSM luminosities, it is unlikely that SNe Ibc constitute an important contaminant within this sample. Leloudas et al. (2015) show how Type II spectra transition to IIn and how the H˛ profiles vary with fV . SNe IIn fainter than M D 17:2 are unable to mask SNe II-P brighter than M D 15. The spectra obtained are in good agreement with real data. Another way to find the history of mass loss of pre-supernovae is to study the bolometric light curves of the SNe. The shape of light curves must depend on the interaction of ejecta and CSM. Moriya et al. (2014) presented results of a systematic study of the mass-loss properties of Type IIn supernova progenitors over the decades before their explosion. An analytic light-curve model was applied to 11 Type IIn supernova bolometric light curves to derive properties of their circumstellar medium. A detailed comparison between the analytic predictions and detailed numerical radiation hydrodynamic simulations supported the results. The mass-loss histories were reconstructed based on the estimated CSM properties. The estimated mass-loss rates were mostly higher than 103 Mˇ yr1 , consistent with those obtained by other methods. The mass-loss rates were often found to be constantly high for decades prior to the explosion. This indicates that there exists some mechanism to sustain the high mass-loss rates of Type IIn supernova progenitors for this time. Thus, the shorter, eruptive mass-loss events observed in some progenitors of Type IIn supernova are not always responsible for creating their dense circumstellar media. In addition, it is found that Type IIn supernova progenitors may tend to increase their mass-loss rates as they approach the time of their explosion. Massive stars exploding in a He-rich circumstellar medium produce Type Ibn supernovae, that is, hydrogen-free, helium-rich supernovae showing narrow lines. A good example was SN 2014av, the spectra of which were studied by Pastorello et al. (2016). The spectra were initially characterised by a hot continuum. Later on, the temperature declined and a number of lines became prominent mostly in emission. In particular, later spectra were dominated by strong and narrow emission features of HeI typical of Type Ibn SNe, although there was a clear signature

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of lines from heavier elements (in particular OI, MgII, and CaII). A forest of relatively narrow FeII lines was also detected showing P-Cygni profiles, with the absorption component blue-shifted by about 1200 km s1 . Another spectral feature often observed in interacting SNe, a strong blue pseudo-continuum, was seen in the latest spectra of SN 2014av. Another example was the peculiar Type Ib SN 2006jc (Foley et al. 2007; Pastorello et al. 2007), with good optical photometry and spectra. Strong and relatively narrow He I emission lines indicated that the progenitor star exploded inside a dense circumstellar medium (CSM) rich in He. An exceptionally blue apparent continuum persisted from the first spectrum, obtained 15 days after discovery, through to the last spectrum 1 month later. One or two of the reddest He I line profiles in the spectra were double-peaked, suggesting that the CSM has an aspherical geometry. The He-rich CSM, aspherical geometry, and line velocities indicate that the progenitor star was an early-type (hot massive) Wolf–Rayet star (W–R star) of spectral class WNE. Two years before the SN, a luminous outburst similar to those seen in luminous blue variables (LBVs) was observed. This event is suspected to have produced the dense CSM. Such an eruption associated with a W–R star had not been seen before, indicating that the progenitor star may have recently transitioned from the LBV phase.

2.3

Cool Dense Shell Fragmentation and CSM Lumpiness

For, a very dense “wind” typical of SLSN, the pattern of the flow is different from that presented in Fig. 1. The velocity profiles show a multireflection structure which forms from the very beginning of the ejecta–wind interaction. The structure evolves very quickly to the standard two-shock (forward and reverse) picture. This does not depend on the initial velocity profile in the envelope. Very crudely the evolution looks like a self-similar behaviour analogous to the Nadyozhin–Chevalier solution (Chevalier 1982a; Nadezhin 1985). However, due to high density, both forward and reverse shocks are radiative and they merge, forming the dense shell; see Fig. 3. The thin dense shell with a very large radius would most probably be unstable and fragment into smaller lumps. This in turn leads to the flow becoming essentially multidimensional. Theoretical studies of the stability of those cool dense shells (CDS) are still at an early stage of development. Nevertheless, the analysis of observations leads to certain conclusions on CDS fragmentation. Chugai (2009) has shown that fragmentation of CDS helps to explain peculiar properties of the light curves and continua of enigmatic Type Ibn supernovae, and argued in favour of early strong circumstellar interaction. This interaction explains the high luminosity and short rise time of SN 1999cq, and the cool dense shell formed in shocked ejecta can explain the smooth early continuum of SN 2000er and unusual blue continuum of SN 2006jc (Type Ibn). The dust was shown to condense in the CDS at about day 50. Monte Carlo modelling of the HeI 7065 Å line profile

Fig. 3 Long-living dense shells (Sorokina et al. 2016)

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33 Interacting Supernovae: Spectra and Light Curves

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affected by the dust occultation supported a picture in which the dust resides in the fragmented CDS, whereas HeI lines originate from circumstellar clouds shocked and fragmented in the forward shock wave; see Fig. 1. The fragmentation of the CDS formed in SNe II-P (see Eq. (5) for the estimate of the shell mass) may help to understand some properties observed in these classical objects. Utrobin and Chugai (2015) studied the well-observed Type II-P SN 2012A with hydrodynamic modelling. They used the early hydrogen H˛ and Hˇ lines as clumpiness diagnostics: the presence of clumps explained the ratio of those spectral lines. Hydrodynamic simulations showed that the clumpiness modified the early light curve and increased the maximum velocity of the outer layers.

3

Supernovae Powered by Collision of Massive Shells

There are strong arguments to believe that SN Type IIn are powered by collisions of SN ejecta with massive shells (leftover from previous explosions) surrounding the star. The idea of producing a large radiative flux during the interaction of the gas ejected in subsequent explosions was suggested by Grasberg and Nadezhin (1986) as an explanation of SNe IIn. A physical mechanism for those multiple explosions (pulsational pair instability) was proposed by Heger and Woosley (2002). Woosley et al. (2007) employed this model to explain the Type II superluminous SN 2006gy as a moderately energetic explosion (3  1051 ergs) without any radioactive material.

3.1

Multiple Shell Ejection by Massive Stars

Pulsational pair instability (Heger and Woosley 2002) is a physically justified mechanism for producing multiple ejections of shells in the pre-supernova evolution of massive stars. The main uncertainty in those models is the mass-loss rate, especially at stages close to the final SN explosion. Models explored in Woosley et al. (2007) with initial masses M < 240 Mˇ retained a sufficient mass of hydrogen to produce SNe IIn. More massive stars with initial masses of 140, 200, and 250 Mˇ and having a metallicity Z = 0.004 were considered in Yoshida et al. (2016). Those stars lose all their hydrogen and a large fraction of their helium layer. Still they have CO cores of 40–60 Mˇ and they experience pulsational pair-instability (PPI) after carbon burning. This instability induces strong pulsations of the whole star and a part of the outer envelope is ejected. During the PPI period of 1–2000 years, they experience several pulsations. The larger CO-core model has the longer PPI period and ejects the larger amount of mass. In as much as almost all surface He is lost by the pulsations, these stars become Type Ic supernovae when they explode. The interaction between the

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circumstellar shell ejected by PPI and the supernova ejecta can be an origin of Type I superluminous supernovae. The PPI is good mechanism for massive stars but it cannot work for stars with initial mass appreciably less than 100 Mˇ simply because their evolutionary tracks on the c  Tc diagram never reach the region of pair-creation. However, there are many examples of interacting supernovae which had progenitors of modest masses. That is why one should look for other paths for massive shell ejections. Because many stars are members of binary systems, the effects of binary evolution may play an important role in forming dense CMS in pre-supernovae. Interacting supernovae, including SNe IIn and SLSNe, appear to have lost perhaps several solar masses of their envelopes in tens to hundreds of years before the explosion. In order to explain the close timing of the mass-loss and supernova events, Chevalier (2012) explores the possibility that the mass loss is driven by common envelope evolution of a compact object (neutron star or black hole) in the envelope of a massive star. The supernova is then triggered by the inspiral of the compact object into the central core of the companion star. The expected rate of such events is smaller than the observed rate of Type IIn supernovae, but the rates are uncertain and might be reconciled. The velocity of mass loss is related to the escape velocity from the common envelope system and is comparable to the observed velocity of hundreds of kilometres per second in Type IIn events. Some supernovae of this type show evidence of energies in excess of the canonical 1051 erg, which might be the result of explosions from rapid accretion onto a compact object through a disk. A somewhat similar scenario of a neutron star merging with a red supergiant is put forward by Barkov (2012). One of the ensuing SN explosions may be of the interacting type. A magnetar with a millisecond period may also be formed and produce a superluminous event of another type. Justham et al. (2014) found paths to relate luminous blue variables and Superluminous Supernovae (SLSNe) with binary mergers. Observational evidence suggests that the progenitor stars of some core-collapse supernovae (CCSNe) are luminous blue variables (LBVs), perhaps including some Type II SLSNe. They examined models in which massive stars gain mass from a companion soon after the end of core hydrogen burning. The post-accretion stars spend their core helium-burning phase as blue supergiants, and many examples are consistent with being LBVs at the time of core collapse. Other examples are yellow supergiants at explosion. The rate of appropriate binary mergers may match the rate of SNe with immediate LBV progenitors; for moderately optimistic assumptions (Justham et al. 2014) estimate that the progenitor birth rate is 1 % of the CCSN rate. A strong stellar mass loss during the final years before core collapse may be caused by effects which are as yet unexplored in detail. One proposal (Shiode and Quataert 2014) is that internal gravity waves are excited by core convection, enhance the core fusion power, and transport a super-Eddington energy flux out to the stellar envelope, driving mass loss. Another (Moriya 2014) is that the core mass decreases due to neutrino losses and ensuing mass ejection.

33 Interacting Supernovae: Spectra and Light Curves

3.2

857

Interaction with Radiation Trapping Effects

The most important effect in the physics of interacting supernovae is the production of a powerful flux of light from the collision of fast-moving ejecta with the dense CMS. Let us make an estimate. Using standard notations: 4 2 L D 4  Teff Rph :

(6)

For a supernova at age t D 10 d, with typical velocity at the level of the photosphere u D 109 cm/s (i.e., 104 km/s), we get Rph D ut  1015 cm. For a typical Teff  104 K, then L  1043 erg/s. The luminosity L goes down over a timescale of some weeks. Thus, in “standard” SN explosions, ordinary, noninteracting supernovae produce 1049 ergs in photons during the first year after the explosion. An energy of 1051 ergs remains as kinetic energy of the ejecta. This energy is radiated by the supernova remnant (mostly as X-rays) much later, during the millennia after the explosion. The energy is produced in the shocks produced by ejecta interacting with the ordinary interstellar medium, which has a number density 1 cm3 . If the density of the CSM is 109 times higher, then a large fraction of the kinetic energy will be radiated away much faster, on a timescale of a year. We may have the same typical Teff  104 K, so the photons will be much softer than X-ray, emitted mostly in the visible or ultraviolet range. However, Rph  1016 cm is much larger and the luminosity goes up approaching L  1045 erg/s for some period of time. Thus a superluminous supernova (SLSN) can be produced with the explosion energy on the standard scale of 1 foe  1051 ergs, but a major fraction of this energy is lost during the first year. Let us give some further simple estimates, instead of writing down full systems of hydrodynamic equations (the reader may find some useful detailed formulas in Sect. 4). If we have a blob of matter with mass m1 and momentum p1 its energy is E1 D

p1 2 : 2m1

(7)

If it is colliding with another blob with mass m0 and zero momentum we get for the final energy of two merged blobs in a fully inelastic collision E2 D

p1 2 : 2.m1 C m0 /

(8)

The momentum is conserved, but because E2 < E1 , an energy E1  E2 is lost and radiated away. If m0  m1 only a tiny fraction of E1 is radiated, but if m0  m1 , then E2  E1 and almost all initial E1 is radiated away. This means that collisions of low mass, fast-moving ejecta with heavy (dense), slowly-moving blobs of CSM are efficient in producing many photons. Of course one should remember that the momentum of the two merged blobs may be different

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from the initial p1 if we have a directed flux of newborn photons which carry some net momentum away. There is not much sense in evaluating this effect using the order-of-magnitude estimates because details of the production of photons may be complicated. The degree of “inelasticity” of the collision depends on the pattern of hydrodynamic flow and on the properties of emission/absorption of the plasma, for example, on its composition. However, these details and an accurate account of the conservation of momenta and energy must be covered in full radiation hydrodynamic simulations. Now let us estimate simply the temperature behind the shock front. The pressure behind the shock front is Ps where we have P s   0 D 2 D n0 m i D 2

(9)

if the density upstream of the front is 0 , and D is the velocity of the front. The density  D nmi with n the number density and mi the average mass of the ions. The estimate (9) follows from momentum conservation: the momentum flux is P C u2 for the flow having velocity u. P is negligible ahead of the front where the matter is cold. A more accurate expression for Ps is given in Sect. 4, Eq. (11). The estimate (9) gives for a nonrelativistic plasma with pressure P D nkB T : kB T s  m i D 2

(10)

which suggests very high temperatures, in the keV range, and higher for shock velocities larger than a thousand km/s. For exact coefficients see Eq. (13) in Sect. 4. We do not give numerical estimates for these quantities here because in many cases in supernova envelopes they are misleading. In reality, the plasma in supernova conditions is at least partly relativistic: we have a huge number of photons with P D aT 4 =3, and so Ts is appreciably lower due to the high heat capacity of photon gas. Equations (17) and (18) in Sect. 4 show that, taking account of radiation and with D of order of a thousand km/s and   1012 g  cm3 , we have Ts D 4:3  104 K, well below the X-ray range of temperatures, but high enough to support a high L for a long time at large R.

3.3

Hydrodynamical Evolution in Synthetic Models

Now we describe some results of numerical simulations which take into account radiation trapping effects in interacting supernovae. For illustration we use the results from Sorokina et al. (2016). The simulations use pre-supernovae structures obtained either from evolutionary codes or artificially constructed. In any case, the initial models have a fast moving part which may be called “ejecta.” This part has mass Mej and radius Rej . Mej can be much less than the total mass of the collapsing core; it is just a convenient form of parametrisation of models.

859

log r

33 Interacting Supernovae: Spectra and Light Curves

log r, cm

Fig. 4 Two typical examples of the initial density structures for interacting supernovae. The solid line shows a windlike model. The dashed line shows a model with a detached shell

To make an interacting model the ejecta are surrounded by a rather dense envelope, a “wind,” with mass Mw extended to the radius Rw . The outer radius of this envelope must be large 1016 cm, or even larger for extreme cases. The envelope may have a power-law density distribution  / r p , which simulates the wind that surrounds the exploding star. For a steady wind, p D 2. However, in the very last stages of the evolution of a pre-supernova star the wind may not be steady and the parameter p may vary in the range between 1.5 and 3.5. Another kind of envelope, detached from the ejecta by a region of lower density, is also considered. The density distributions for a couple of typical models are shown in Fig. 4. Light curves are calculated for SNe exploding within these envelopes. A shock wave forms at the border between the ejecta and the envelope. The shock very efficiently converts the energy of the ordered motion of expanding gas to that of the chaotic thermal motion of particles, whose energy can easily be radiated. As a result, one may expect to obtain light curves powerful enough to explain at least a part of superluminous SNe without an assumption of unusually high explosion energy. The detailed computations support those expectations. For Type IIn SLSNe, hydrogen-rich envelopes are used. For SLSN I, typically carbon-oxygen models with different C to O ratios or helium models are employed. The models may contain some amount of radioactive elements such as 56 Ni, but it is not necessary in this class of simulations in as much as the effect of pure ejectaCSM interaction is sufficient to explain the majority of SLSNe, with zero amount of 56 Ni. The synthetic light curves in Sorokina et al. (2016) are calculated using a multigroup radiation hydrodynamic code STELLA in its standard setup. The code simulates spherically symmetric hydrodynamic flows coupled with multigroup radiative transfer. The opacity routine takes into account electron scattering, free-

860

Fig. 5 (Continued)

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33 Interacting Supernovae: Spectra and Light Curves

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free and bound-free processes. The contribution of spectral lines (i.e., bound–bound processes) is treated in an approximation of “expansion” opacity. The explosions have been simulated as a “thermal bomb” with variable energy Eexpl of the order 2–4 foe, which is a bit larger than in a standard 1 foe supernova, but much lower than invoked in hypernovae or in pair-instability supernovae. Figure 5 shows how the profiles of density, velocity, temperature, and Rosseland mean optical depth evolve along time for one of the models. The upper panels correspond to the evolution before maximum of the light curve (which happens on day 22 after the explosion for that model). The lower panels show the evolution after maximum. At the very beginning, the shock wave structure starts to form due to collision between the ejecta and the CSM. Then the emission from the shock front heats the gas in the envelope, thus making it opaque, and the photosphere moves to the outermost layers rather quickly. When the photospheric radius reaches its maximum, one can observe maximal emission from the supernova. The speed of the growth of the photospheric radius depends on the mass of the envelope, because more photons must be emitted from the shock to heat larger mass envelopes. Another parameter which impacts the initial growth of the photospheric radius is the chemical composition of the envelope. For example, the light curve rises faster for a CO envelope than for a He one, because a lower temperature is needed to reach high opacity in a CO mixture. This light curve behaviour can help set the composition for some observed SLSNe. The plots on the lower part of Fig. 5 show the stages when the photosphere slowly moves back to the centre, and the envelope and the ejecta finally become fully transparent. At the beginning of this post-maximum stage all gas in the envelope is already heated by the photons which came from the shock region and diffused through the envelope to the outer edge. The whole system (ejecta and envelope) becomes almost isothermal. The shock becomes weaker with time and emits fewer photons which can heat up the envelope, therefore the temperature of the still unshocked envelope falls. The shocked material is gathered into a thin dense layer (see Fig. 3), which finally contains almost all mass in the system. Formation of this layer leads to numerical difficulties, which significantly limit the timestep of the calculation. Another problem can also take place due to the thin layer formation: a thin dense shell with a very large radius would most probably be unstable and can fragment into smaller lumps. Then the problem would become multidimensional.

J Fig. 5 Evolution of radial profiles of the density (solid lines), velocity (in 108 cm s1 , dots), matter temperature (dashes), and Rosseland optical depth (dash-dots) for one of the models in Sorokina et al. (2016). The scale for the density is on the left y-axis, for other quantities, on the right y-axis. Upper panels: evolution of the hydrodynamical structure before maximum; very soon after the explosion and at days 4 and 25. Lower panels: the same parameters, but after maximum; at days 60, 80, and 151. Note that different scales for the axes are used on the left and right panels

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On the velocity profiles, the multireflection structure forms from the very beginning. It evolves very quickly to the standard two-shock (forward and reverse) picture. This does not depend on the initial velocity profile in the envelope. The interaction of the ejecta with the envelope leads to similar final velocity structures. The behaviour looks self-similar, analogous to the solution found by Nadezhin (1985) and Chevalier (1982a) but with radiation.

3.4

General Properties of the Interacting SLSN Light Curves: From Visible Light to X-Ray

Many properties of SLSN light curves may be explained by a pure effect of interaction with the CSM, without 56 Ni or any other additional energy source inside the models. All the emission comes from the transformation of ordered particle motion into a chaotic state when gas passes through a shock wave. When the shock reaches the outer edge of the extended envelope and there is no material in front of the shock any more, then no source of energy remains. The gas loses its thermal energy through radiation and cools down very quickly. This corresponds to a sharp drop in flux in all spectral bands. This drop is a typical feature of the light curves for the interacting models, though it is not always observed because it happens a few months after maximum (if the envelope is extended enough) and the supernova may be unobservable, or another energy source (such as radioactivity) may dominate at this phase. One clearly needs a very large radius envelope to produce an extremely bright and long-lasting event for a model without a huge explosion energy. One also needs high densities for strong production of light by the shock (see the estimates in Sect. 4). But when the density is too high, the mass of the envelope and the optical depth of the shell become too large. This would make the supernova appear red and would not match with observations of SLSNe-I, which tend to be blue; see, for example, Quimby et al. (2011). Thus an enhanced envelope mass must be accompanied by an enhanced explosion energy which will lead to the formation of stronger and hotter shocks. Figure 6 demonstrates how the model with hydrodynamic evolution shown in Fig. 5 reproduces multiband observations of the well-studied SLSNe SN 2010gx. The general trend is described very well by the interacting model. One should point out the parallel behaviour of fluxes in different filters for a long time near the maximum light. This is a general property of shocks producing light and their velocity is more or less constant in slowly-varying density. Analysis of X-ray emission associated with SNe IIn allows us to draw some conclusions on the structure of CSM around those supernovae. In many cases X-rays appear after the flux in visible bands goes down. This is natural, because while the shock is buried within the dense layers its temperature cannot be high (see Eq. 18). The X-ray emission resulting from the ejecta-CSM interaction depends, among other parameters, on the density of this medium, and therefore the variation in the X-ray luminosity can be used to study the variation in the density structure of the

33 Interacting Supernovae: Spectra and Light Curves

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N0

Fig. 6 Synthetic light curves for the model from Fig. 5, one of the best for SN 2010gx, in r, g, B, and u filters compared with Pan-STARRS and PTF observations. Pan-STARRS points are designated with open squares (u, g, and R bands), and PTF points, with filled circles (B and r bands). Four pink points in the beginning of the r band show PTF observations in the Mould R-band which is similar to the SDSS r band

medium. Dwarkadas (2011) and Dwarkadas and Gruszko (2012) explore the X-ray emission and light curves of all known supernovae, in order to study the nature of the medium into which they are expanding. It was found that in the context of the theoretical arguments that have generally been used in the literature, many young SNe, and especially those of Type IIn SNe, which are the brightest X-ray luminosity class, do not appear to be expanding into steady winds. Some Type IIn SNe appear to have very steep X-ray luminosity declines, indicating that the density declines much more steeply than r 2 . However, other Type IIn SNe show a constant or even increasing X-ray luminosity over periods of months to years. Many other SNe do not appear to have declines consistent with expansion in a steady wind. SNe with lower X-ray luminosities appear to be more consistent with steady wind expansion, although the numbers are not large enough to make firm statistical comments. The numbers do indicate that the expansion and density structure of the circumstellar medium must be investigated before assumptions can be made of steady wind expansion. Unless a steady wind can be shown, mass-loss rates deduced using this assumption may need to be revised. Many other types of interacting supernovae are X-ray emitters. A classic example is SN 1979C of Type II-L. Immler et al. (2005) presents the long-term X-ray lightcurve, constructed from all the X-ray data available, which reveals that SN 1979C was still radiating at a flux level similar to that detected by ROSAT in 1995, showing no sign of a decline in a period of 16–23 years after its outburst. The high inferred X-ray luminosity (L0:32 D 8  1038 ergs s1 ) is caused by the interaction of the SN shock with dense circumstellar matter, likely deposited by a

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strong stellar wind from the progenitor .vw  10 km s1 / with a high mass-loss rate of MP  1:5  104 Mˇ yr1 . The peculiar Type Ib SN 2006jc has been observed with the UV/Optical Telescope (UVOT) and X-Ray Telescope (XRT) on board the Section observatory over a period of 19–183 days after the explosion (Immler et al. 2008). Signatures of interaction of the outgoing SN shock with dense circumstellar material were detected, such as strong X-ray emission (L0:210 > 1039 erg s1 ) and the presence of Mg II 2800 Å line emission visible in the UV spectra. In combination with a Chandra observation obtained on day 40 after the explosion, the X-ray light curve is constructed, which shows a unique rise of the X-ray emission by a factor of 5 over a period of 4 months, followed by a rapid decline. They interpret the unique X-ray and UV properties as a result of the SN shock interacting with a shell of material that was deposited by an outburst of the SN progenitor 2 years prior to the explosion. These results are consistent with the explosion of a Wolf–Rayet star that underwent an episodic mass ejection qualitatively similar to those of luminous blue variable stars prior to its explosion. This led to the formation of a dense (107 cm3 ) shell at a distance of 1016 cm from the site of the explosion, which expands with the WR wind at a velocity of .1300 ˙ 300/ km s1 . Interacting supernovae which are not very luminous, such as SN 2006jc (Immler et al. 2008) or SN 2009ip, were observed in X-rays near maximum light (Margutti et al. 2014). More luminous ones have been discovered in the X-ray range much later for an obvious reason: they have the high column density needed to produce many visible photons in radiating shocks and the high-density shells would screen X-rays even if they were produced. Another reason for the lack of powerful X-ray emission in SLSNe was already given: it is the low temperature of the shocked matter in radiation-dominated shocks. An interesting example illustrating this is SN 2010jl. Optical to hard X-ray observations reveal an explosion embedded in a 10 solar mass cocoon (Chandra et al. 2015; Ofek et al. 2014). The growth of X-ray flux began with the decline of the visible flux which should be related with the shock leaving the dense layers of the envelope surrounding the supernova.

4

Strong Shock Waves with Internal Energy (e.g., Ionisation) and Radiation

In this section we derive some of the properties of strong shock waves, pointing out some of the idealisations which are usually made. We use standard notations for density , velocity u, pressure P , and thermodynamic energy E, and define a vector U with components:

U1 D ;

33 Interacting Supernovae: Spectra and Light Curves

865

the density of the momentum U2 D u  j; and the total energy density U3 D E C

u2 : 2

We also define a vector F having as components the flux of mass, F1 D u; the flux of momentum, F2 D u2 C P; and the flux of energy F3 D .E C

u2 C P /u; 2

and we have a general law of conservation: @U @F D : @t @x In a stationary case, that is, @U=@t D 0, we get F D const. We have already introduced above a standard notation for the flux of mass, j , and we see now that it is constant in a stationary flow: j  u D const: It is convenient to use a specific volume (per unit mass): V 

1 : 

From F2 D u2 C P D j 2 V C P D const we obtain: j 2 V0 C P 0 D j 2 Vs C P s ; And this implies: Ps D P0 C j 2 .V0  Vs / :

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The subscript “0” for ; V; u; P; E denotes the initial values upstream (ahead of the shock front), and the subscript “s” corresponds to the values downstream, in the shocked matter. It is most convenient to work in the reference frame where the front is at rest. Then the speed of the shock D is just u0 , because by definition it is measured relative to the unshocked matter. Now F3 D const gives:     1 1 E0 C j 2 V0 C P0 u0 D Es C j 2 Vs C Ps us 2 2 If we make the replacement here of ui D jVi , we get:     1 1 E0 C j 2 V0 C P0 jV0 D Es C j 2 Vs C Ps jVs : 2 2 From here 1 1 E0 V0 C j 2 V02 C P0 V0 D Es Vs C j 2 Vs2 C Ps Vs ; 2 2 and 1 .E0 C P0 /V0 C j 2 .V02  Vs2 / D .Es C Ps /Vs : 2 But .V02  Vs2 / D .V0  Vs /.V0 C Vs / and Ps D P0 C j 2 .V0  Vs / obtained above implies V0  Vs D .Ps  P0 /=j 2 , therefore j 2 cancels in the numerator and denominator:  P0 / 1 / .Ps / .E0 C P0 /V0 C j 2 .V0 C Vs / D .Es C Ps /Vs : 2 j2 Thus     P0 C Ps P0 C Ps E0 C V0 D E s C Vs ; 2 2 and we obtain a general formula for the compression in the flow (e.g., on a shock front): Vs 2E0 C P0 C Ps D : V0 2Es C P0 C Ps An equation of state E D E.P; V /, or P D P .E; V /, gives the shock adiabat. For a general equation of state in a strong shock (Ps  P0 ; Es  E0 ), which is most important in supernova envelopes,

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1 Vs 2E0 =.P0 C Ps / C 1  ; D V0 2Es =.P0 C Ps / C 1 2Es =Ps C 1 or s V0 2Es D 1C ; 0 Vs Ps in the general case, and s V0 2  C1 D 1C D ; 0 Vs  1  1 for the case of an equation of state with  D const. Let P D .  1/Etr , where Etr is the translational internal energy, that is, the kinetic energy of the particles in plasma, and let E D Etr C Q, where Q is, for example, the ionisation potential energy. Then in a strong shock 2Q s V0 2E2tr C 2Q 2 C D 1C D1C ; 0 Vs Ps  1 .  1/E2tr that is s 2Q V0  C1 C D  : 0 Vs  1 .  1/E2tr For  D 5=3 this gives s V0 3Q D 4C : 0 Vs E2tr This is formula (3.71) in Zeldovich and Raizer. We found from the conservation of momentum (F2 D const) that Ps D P0 C j 2 .V0  Vs /; that is, j2 D

Ps . C 1/ Ps  P0 Ps Ps D  D ; V0  V s V0  V s V0 Œ1  .  1/=. C 1/ 2V0

This is valid for a strong shock, constant  , and small Q. Hence, 0 u20 D

Ps . C 1/ ; 2

that is, Ps D

2 0 u20 :  C1

(11)

868

S. Blinnikov

Note that  here must be taken for the gas behind the strong shock in as much as the pressure P0 is negligible and its equation of state is irrelevant. For a nonrelativistic plasma with pressure P D RT = we get from (11) 0 u20 D

. C 1/Rs Ts ; 2

so u20 D

. C 1/2 RTs . C 1/Rs Ts D : 20  2.  1/

The post-shock temperature Ts for the strong shock, constant  , and small Q is (from the last equation) Ts D

2.  1/u20  : . C 1/2 R

For  D 5=3 we get Ts D

3u20  : 16R

(12)

If we put here D8 D u0 =108 cm/s, then D8 is the shock speed in units of 1000 km/s and we get Ts .K/ D 2:25  107 D82

(13)

Ts .keV/ D 1:94D82

(14)

in Kelvins or

in keV. Here  D A=.1 C Z/ for plasma (because n D nbaryon = D nion A= D nion C ne D nion C Znion ). Note that a typical value for D in SNe is about 10,000 km/s, thus T will be of order 109 K or hundreds of keV. R  kB =mp where mp is the proton mass, therefore we have kB Ts  mp Ds2 :

(15)

This estimate is the same as that used in Sect. 3.2, Eq. (10) if we put mi D mp . Using  D const is a favourite approximation in many papers and simulations in astrophysics, but in supernovae it is a very bad one, and almost irrelevant. The value of  varies because of the ionisation/excitation of the atoms. It changes a great deal on the shock front when it goes through the cold layers and heats the plasma so strongly that radiation pressure dominates downstream behind the front. In that case

33 Interacting Supernovae: Spectra and Light Curves

869

(which is quite general for supernova shock breakout) the formulas (13) and (14) are not applicable and even misleading. The equations for mass, momentum, and energy conservation are more complicated for radiative shock waves when one has to account for the transfer of the momentum and energy of the photons. Nevertheless there are two important limiting cases for strong shocks with radiation, when simple expressions can be derived. In the first limiting case, we may have relatively cold gas upstream with P0  Ps in the strong shock, and the gas downstream is opaque with the pressure dominated by radiation. Due to the high heat capacity of photon gas, the temperature behind the front is orders of magnitude lower than in Eqs. (13) and (14), and may be estimated as in Sect. 3.2. Let us put radiation pressure for Ps into Eq. (11), we get 2 aTs4 D 0 u20 : 3  C1

(16)

We have  D 4=3 for the radiation-dominated gas, and, substituting u0 D D, we obtain  Ts D

18 0 D 2 7a

1=4 :

(17)

That is, 1=4

1=2

Ts .K/ D 4:3  104 12 D8 ;

(18)

  1012 g  cm3 , if we normalise density for  D 1012 g  cm3 and take D in units of 1000 km/s. One can see that the shock temperature in reality is much less than in (14). The second important limiting case takes place when the radiation is not trapped, and its pressure and momentum may be neglected, but when it is very efficient in heat transport. Now the energy is not conserved, and the energy flux F3 is no longer constant. Instead of this, we may have the constancy of temperature ahead and behind the front. Mass and momentum conservation give as before: Ps D P0 C j 2 .V0  Vs /:

(19)

Now, both upstream and downstream the pressure is P D RT = with the same T , thus the strong shock condition, Ps  P0 means not a high T behind the front, but s  0 . Ps  0 u20 , which we get from (19), gives D 2 s : D 0 RT

(20)

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The isothermal temperature T here is much less than the temperature found in Eqs. (13) and (14) for adiabatic shocks, hence the compression in isothermal shocks may be orders of magnitude larger than the canonical . C 1/=.  1/ of adiabatic shocks. This is a typical situation for the formation of cool dense shells in interacting supernovae. The exact values of T and of the compression depend on the details of the properties of plasma with respect to heat conduction, but one should remember that those dense shells may become unstable, and the exact numbers found in idealised, accurately plane parallel or spherically symmetric calculations may not be very useful.

5

Conclusions

Interacting supernovae manifest themselves through many peculiar features in their spectra, and through powerful X-ray and/or radio emission. The most important effect of the interaction between SN ejecta and the circumstellar medium is the production of light by radiating shock waves. Many (but not all) superluminous supernovae may be explained by this mechanism.

6

Cross-References

 Interacting Supernovae: Types IIn and Ibn Acknowledgements The work was supported by a grant from the Russian Science Foundation, 14-12-00203. The author is grateful to colleagues at ITEP, INASAN, Kavli IPMU, SAI MSU, NSU, VNIIA, FTI, and MPA for numerous discussions and collaborations.

References Barkov MV (2012) Close binary progenitors of hypernovae. Int J Mod Phys Conf Ser 8:209–219. doi:10.1142/S2010194512004618 Benetti S (2000) Interacting Type II supernovae & Type IId. Mem. Soc. Astron. It. 71:323–329 Benetti S, Nicholl M, Cappellaro E, Pastorello A, Smartt SJ, Elias-Rosa N, Drake AJ, Tomasella L, Turatto M, Harutyunyan A, Taubenberger S, Hachinger S, Morales-Garoffolo A, Chen TW, Djorgovski SG, Fraser M, Gal-Yam A, Inserra C, Mazzali P, Pumo ML, Sollerman J, Valenti S, Young DR, Dennefeld M, Le Guillou L, Fleury M, Léget PF (2014) The supernova CSS121015:004244+132827: a clue for understanding superluminous supernovae. MNRAS 441:289–303. doi:10.1093/mnras/stu538, 1310.1311 Bose S, Sutaria F, Kumar B, Duggal C, Misra K, Brown PJ, Singh M, Dwarkadas V, York DG, Chakraborti S, Chandola HC, Dahlstrom J, Ray A, Safonova M (2015) SN 2013ej: a Type IIL supernova with weak signs of interaction. ApJ 806:160. doi:10.1088/0004-637X/806/2/160, 1504.06207 Chandra P, Chevalier RA, Chugai N, Fransson C, Soderberg AM (2015) X-ray and radio emission from Type IIn supernova SN 2010jl. ApJ 810:32. doi:10.1088/0004-637X/810/1/32, 1507.06059

33 Interacting Supernovae: Spectra and Light Curves

871

Chevalier RA (1981) Hydrodynamic models of supernova explosions. Fundam Cosmic Phys 7: 1–58 Chevalier RA (1982a) Self-similar solutions for the interaction of stellar ejecta with an external medium. ApJ 258:790–797. doi:10.1086/160126 Chevalier RA (1982b) The radio and X-ray emission from Type II supernovae. ApJ 259:302–310. doi:10.1086/160167 Chevalier RA (2012) Common envelope evolution leading to supernovae with dense interaction. ApJ 752:L2. doi:10.1088/2041-8205/752/1/L2, 1204.3300 Chugai NN (1997a) Supernovae in dense winds. Astrophys Space Sci 252:225–236 Chugai NN (1997b) The origin of supernovae with dense winds. Astron Rep 41:672–681 Chugai NN (2009) Circumstellar interaction in Type Ibn supernovae and SN 2006jc. MNRAS 400:866–874. doi:10.1111/j.1365-2966.2009.15506.x, 0908.0568 Chugai NN, Chevalier RA, Utrobin VP (2007) Optical signatures of circumstellar interaction in Type IIP supernovae. ApJ 662:1136–1147. doi:10.1086/518160, astro-ph/0703468 Dwarkadas VV (2011) On luminous blue variables as the progenitors of corecollapse supernovae, especially Type IIn supernovae. MNRAS 412:1639–1649. doi:10.1111/j.1365-2966.2010.18001.x, 1011.3484 Dwarkadas VV, Gruszko J (2012) What are published X-ray light curves telling us about young supernova expansion? MNRAS 419:1515–1524. doi:10.1111/j.1365-2966.2011.19808.x, 1109.2616 Foley RJ, Smith N, Ganeshalingam M, Li W, Chornock R, Filippenko AV (2007) SN 2006jc: a Wolf-Rayet star exploding in a dense He-rich circumstellar medium. ApJ 657:L105–L108. doi:10.1086/513145, astro-ph/0612711 Grasberg EK, Nadezhin DK (1986) Type-II supernovae – two successive explosions. Sov Astron Lett 12:68–70 Heger A, Woosley SE (2002) The nucleosynthetic signature of population III. ApJ 567:532–543. doi:10.1086/338487, astro-ph/0107037 Immler S, Fesen RA, Van Dyk SD, Weiler KW, Petre R, Lewin WHG, Pooley D, Pietsch W, Aschenbach B, Hammell MC, Rudie GC (2005) Late-time X-ray, UV, and optical monitoring of supernova 1979C. ApJ 632:283–293. doi:10.1086/432869, astro-ph/0503678 Immler S, Modjaz M, Landsman W, Bufano F, Brown PJ, Milne P, Dessart L, Holland ST, Koss M, Pooley D, Kirshner RP, Filippenko AV, Panagia N, Chevalier RA, Mazzali PA, Gehrels N, Petre R, Burrows DN, Nousek JA, Roming PWA, Pian E, Soderberg AM, Greiner J (2008) Swift and Chandra detections of supernova 2006jc: evidence for interaction of the supernova shock with a circumstellar shell. ApJ 674:L85–L88. doi:10.1086/529373, 0712.3290 Inserra C, Turatto M, Pastorello A, Pumo ML, Baron E, Benetti S, Cappellaro E, Taubenberger S, Bufano F, Elias-Rosa N, Zampieri L, Harutyunyan A, Moskvitin AS, Nissinen M, Stanishev V, Tsvetkov DY, Hentunen VP, Komarova VN, Pavlyuk NN, Sokolov VV, Sokolova TN (2012) The bright Type IIP SN 2009bw, showing signs of interaction. MNRAS 422:1122–1139. doi:10.1111/j.1365-2966.2012.20685.x, 1202.0659 Justham S, Podsiadlowski P, Vink JS (2014) Luminous blue variables and superluminous supernovae from binary mergers. ApJ 796:121. doi:10.1088/0004-637X/796/2/121, 1410.2426 Kankare E, Ergon M, Bufano F, Spyromilio J, Mattila S, Chugai NN, Lundqvist P, Pastorello A, Kotak R, Benetti S, Botticella MT, Cumming RJ, Fransson C, Fraser M, Leloudas G, Miluzio M, Sollerman J, Stritzinger M, Turatto M, Valenti S (2012) SN 2009kn – the twin of the Type IIn supernova 1994W. MNRAS 424:855–873. doi:10.1111/j.1365-2966.2012.21224.x, 1205.0353 Leloudas G, Hsiao EY, Johansson J, Maeda K, Moriya TJ, Nordin J, Petrushevska T, Silverman JM, Sollerman J, Stritzinger MD, Taddia F, Xu D (2015) Supernova spectra below strong circumstellar interaction. A&A 574:A61. doi:10.1051/0004-6361/201322035, 1306.1549 Margutti R, Milisavljevic D, Soderberg AM, Chornock R, Zauderer BA, Murase K, Guidorzi C, Sanders NE, Kuin P, Fransson C, Levesque EM, Chandra P, Berger E, Bianco FB, Brown PJ, Challis P, Chatzopoulos E, Cheung CC, Choi C, Chomiuk L, Chugai N, Contreras C, Drout MR, Fesen R, Foley RJ, Fong W, Friedman AS, Gall C, Gehrels N, Hjorth J, Hsiao E, Kirshner R, Im M, Leloudas G, Lunnan R, Marion GH, Martin J, Morrell N, Neugent KF, Omodei N,

872

S. Blinnikov

Phillips MM, Rest A, Silverman JM, Strader J, Stritzinger MD, Szalai T, Utterback NB, Vinko J, Wheeler JC, Arnett D, Campana S, Chevalier R, Ginsburg A, Kamble A, Roming PWA, Pritchard T, Stringfellow G (2014) A panchromatic view of the restless SN 2009ip reveals the explosive ejection of a massive star envelope. ApJ 780:21. doi:10.1088/0004-637X/780/1/21, 1306.0038 Margutti R, Kamble A, Milisavljevic D, Zapartas E, de Mink SE, Drout M, Chornock R, Risaliti G, Zauderer BA, Bietenholz M, Cantiello M, Chakraborti S, Chomiuk L, Fong W, Grefenstette B, Guidorzi C, Kirshner R, Parrent JT, Patnaude D, Soderberg AM, Gehrels NC, Harrison F (2017) Ejection of the massive hydrogen-rich envelope timed with the collapse of the stripped SN 2014C. ApJ 835:140. doi:10.3847/1538-4357/835/2/140, 1601.06806 Moriya TJ (2014) Mass loss of massive stars near the Eddington luminosity by core neutrino emission shortly before their explosion. A&A 564:A83. doi:10.1051/0004-6361/201322992, 1403.2731 Moriya TJ, Maeda K, Taddia F, Sollerman J, Blinnikov SI, Sorokina EI (2014) Mass-loss histories of Type IIn supernova progenitors within decades before their explosion. MNRAS 439: 2917–2926. doi:10.1093/mnras/stu163, 1401.4893 Nadezhin DK (1985) On the initial phase of interaction between expanding stellar envelopes and surrounding medium. Astrophys Space Sci 112:225–249. Preprint ITEP-1, 1981, doi:10.1007/BF00653506 Nomoto K, Suzuki T, Deng J, Uenishi T, Hachisu I (2005) Progenitors of Type Ia supernovae: circumstellar interaction, rotation, and steady hydrogen burning. In: Turatto M, Benetti S, Zampieri L, Shea W (eds) 1604-2004: supernovae as cosmological lighthouses. Astronomical Society of the Pacific conference series, vol 342, p 105. astro-ph/0603432 Ofek EO, Zoglauer A, Boggs SE, Barriére NM, Reynolds SP, Fryer CL, Harrison FA, Cenko SB, Kulkarni SR, Gal-Yam A, Arcavi I, Bellm E, Bloom JS, Christensen F, Craig WW, Even W, Filippenko AV, Grefenstette B, Hailey CJ, Laher R, Madsen K, Nakar E, Nugent PE, Stern D, Sullivan M, Surace J, Zhang WW (2014) SN 2010jl: optical to hard X-ray observations reveal an explosion embedded in a ten solar mass Cocoon. ApJ 781:42. doi:10.1088/0004-637X/781/1/42, 1307.2247 Pastorello A, Smartt SJ, Mattila S, Eldridge JJ, Young D, Itagaki K, Yamaoka H, Navasardyan H, Valenti S, Patat F, Agnoletto I, Augusteijn T, Benetti S, Cappellaro E, Boles T, Bonnet-Bidaud JM, Botticella MT, Bufano F, Cao C, Deng J, Dennefeld M, Elias-Rosa N, Harutyunyan A, Keenan FP, Iijima T, Lorenzi V, Mazzali PA, Meng X, Nakano S, Nielsen TB, Smoker JV, Stanishev V, Turatto M, Xu D, Zampieri L (2007) A giant outburst two years before the corecollapse of a massive star. Nature 447:829–832. doi:10.1038/nature05825, astro-ph/0703663 Pastorello A, Wang XF, Ciabattari F, Bersier D, Mazzali PA, Gao X, Xu Z, Zhang JJ, Tokuoka S, Benetti S, Cappellaro E, Elias-Rosa N, Harutyunyan A, Huang F, Miluzio M, Mo J, Ochner P, Tartaglia L, Terreran G, Tomasella L, Turatto M (2016) Massive stars exploding in a Herich circumstellar medium - IX. SN 2014av, and characterization of Type Ibn SNe. MNRAS 456:853–869. doi:10.1093/mnras/stv2634, 1509.09069 Quimby RM, Kulkarni SR, Kasliwal MM, Gal-Yam A, Arcavi I, Sullivan M, Nugent P, Thomas R, Howell DA, Nakar E, Bildsten L, Theissen C, Law NM, Dekany R, Rahmer G, Hale D, Smith R, Ofek EO, Zolkower J, Velur V, Walters R, Henning J, Bui K, McKenna D, Poznanski D, Cenko SB, Levitan D (2011) Hydrogen-poor superluminous stellar explosions. Nature 474:487–489. doi:10.1038/nature10095, 0910.0059 Raskin C, Kasen D (2013) Tidal tail ejection as a signature of Type Ia supernovae from white dwarf mergers. ApJ 772:1. doi:10.1088/0004-637X/772/1/1, 1304.4957 Salamanca I (2003) The dense circumstellar material around Type IIn supernovae. In: Perez E, Gonzalez Delgado RM, Tenorio-Tagle G (eds) Star formation through time. Astronomical Society of the Pacific conference series, vol 297. Astronomical Society of the Pacific, San Francisco, p 429 Schlegel EM, Kirshner RP, Huchra JP, Schild RE (1996) The peculiar Type II SN 1987B in NGC 5850. AJ 111:2038. doi:10.1086/117939

33 Interacting Supernovae: Spectra and Light Curves

873

Shiode JH, Quataert E (2014) Setting the stage for circumstellar interaction in corecollapse supernovae. II. Wave-driven mass loss in supernova progenitors. ApJ 780(1):96. http://stacks.iop.org/0004-637X/780/i=1/a=96 Smith N (2014) Mass loss: its effect on the evolution and fate of high-mass stars. ARA&A 52: 487–528. doi:10.1146/annurev-astro-081913-040025, 1402.1237 Smith N, Hinkle KH, Ryde N (2009) Red supergiants as potential Type IIn supernova progenitors: spatially resolved 4.6 m CO emission around VY CMa and betelgeuse. AJ 137:3558–3573. doi:10.1088/0004-6256/137/3/3558, 0811.3037 Sorokina E, Blinnikov S, Nomoto K, Quimby R, Tolstov A (2016) Type I superluminous supernovae as explosions inside non-hydrogen circumstellar envelopes. ApJ 829:17. doi:10.3847/0004-637X/829/1/17, 1510.00834 Turatto M (2003) Classification of supernovae. In: Weiler K (ed) Supernovae and gamma-ray bursters. Lecture notes in physics, vol 598. Springer, Berlin, pp 21–36. astro-ph/0301107 Utrobin VP, Chugai NN (2015) Parameters of Type IIP SN 2012A and clumpiness effects. A&A 575:A100. doi:10.1051/0004-6361/201424822, 1411.6480 Valenti S, Sand D, Stritzinger M, Howell DA, Arcavi I, McCully C, Childress MJ, Hsiao EY, Contreras C, Morrell N, Phillips MM, Gromadzki M, Kirshner RP, Marion GH (2015) Supernova 2013by: a Type IIL supernova with a IIP-like light-curve drop. MNRAS 448: 2608–2616. doi:10.1093/mnras/stv208, 1501.06491 Woosley SE, Blinnikov S, Heger A (2007) Pulsational pair instability as an explanation for the most luminous supernovae. Nature 450:390–392. doi:10.1038/nature06333, 0710.3314 Yoshida T, Umeda H, Maeda K, Ishii T (2016) Mass ejection by pulsational pair instability in very massive stars and implications for luminous supernovae. MNRAS 457:351–361. doi:10.1093/mnras/stv3002, 1511.01695

Thermal and Non-thermal Emission from Circumstellar Interaction

34

Roger A. Chevalier and Claes Fransson

Abstract

It has become clear during the last decades that the interaction between the supernova ejecta and the circumstellar medium is playing a major role both for the observational properties of the supernova and for understanding the evolution of the progenitor star leading up to the explosion. In addition, it provides an opportunity to understand the shock physics connected to both thermal and nonthermal processes, including relativistic particle acceleration, radiation processes, and the hydrodynamics of shock waves. This chapter has an emphasis on the information we can get from radio and X-ray observations, but also their connection to observations in the optical and ultraviolet. We first review the different physical processes involved in circumstellar interaction, including hydrodynamics, thermal X-ray emission, acceleration of relativistic particles, and non-emission processes in the radio and X-ray ranges. Finally, we discuss applications of these to different types of supernovae.

Contents 1 2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Ejecta Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Ambient Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shock Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Shock Structure and Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Postshock Conditions and Radiative Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Asymmetries, Shells, and Clumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

876 876 877 878 879 879 880 886

R.A. Chevalier () Department of Astronomy, University of Virginia, Charlottesville, VA, USA e-mail: [email protected] C. Fransson Department of Astronomy and Oskar Klein Centre, Stockholm University, Stockholm, Sweden e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_34

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4

Thermal Emission from Hot Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Optically Thin Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Optically Thick Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Reprocessing of X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Nonthermal Emission from Relativistic Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Particle Acceleration and Magnetic Field Amplification in Shocks . . . . . . . . . . . 5.2 Optically Thin Synchrotron Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Inverse Compton X-Ray Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 The Radio Spectrum Including Absorption Processes . . . . . . . . . . . . . . . . . . . . . . 5.5 Radio and High-Energy Signatures of Cosmic Ray Acceleration . . . . . . . . . . . . . 6 Examples of Circumstellar Emission from Different SN Types . . . . . . . . . . . . . . . . . . . 6.1 Type IIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Type IIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Type IIb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Type IIn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Type Ib/c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Type Ibn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8 Relativistic Expanding Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.9 Type Ia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

887 887 888 890 893 893 895 898 900 905 906 906 908 909 912 917 922 926 926 927 928 929 929

Introduction

This review is partly an update of our previous review from 2003 on circumstellar interaction (Chevalier and Fransson 2003), mainly adding new developments during the last decade. In this review we are concentrating on the physical processes and only discuss individual objects of different supernova types as examples of these. While the focus is on radio and X-rays, there is an especially close connection between the X-rays and optical observations, and where relevant we also discuss observations in this wavelength band. Massive stars are known to have strong winds during their lives. At the time of the supernova (SN hereafter) explosion, the rapidly expanding gas plows into the surrounding medium, creating shock waves. The shock waves heat the gas, giving rise to X-ray emission. A fraction of this may be reprocessed into optical and ultraviolet (UV) radiation, which in extreme cases may dominate the emission from the SN ejecta. The shock waves also accelerate particles to relativistic speeds. Relativistic electrons radiate synchrotron emission in the magnetic fields that are present; the magnetic field may be amplified by turbulence near the shock and/or the downstream region.

2

Initial Conditions

For the most part, the structure of the supernova ejecta can be separated from that of the ambient medium and then their interaction can be discussed. This is not the case around the time of shock breakout, when the diffusion time for photons in the

34 Thermal and Non-thermal Emission from Circumstellar Interaction

877

shocked region first becomes comparable to the age of the supernova. Radiative acceleration of the pre-shock gas leads to the dissolution of the radiation dominated shock wave, which is followed by the formation of a viscous shock wave in the surrounding medium. Radiative pre-acceleration of surrounding gas gives a velocity v / r 2 due to the flux divergence and is typically only important at early times.

2.1

Ejecta Structure

After the shock wave has passed through the progenitor star, the gas evolves to free expansion, v D r=t , where t is the age of the explosion. In free expansion, the density of an element of gas drops as t 3 so that the density profile is described by a function / t 3 f .r=t /. The profile f .r=t / can typically be described by a function that is a steep power law at high velocities and flat in the central region. The outer steep power law region is especially important for circumstellar interaction because it is the region that typically gives rise to the observed emission. The outer edge of a star has a density profile that can be approximated by  D a.r  r/ı , where a is a constant and r is the outer edge of the star. For a radiative envelope, ı D 3, and for a convective envelope, ı  1:5. The supernova shock wave accelerates through the outer layers of the star due to the cumulation effect of energy going into a vanishingly small amount of matter. The acceleration of the shock wave through the outer layers of the star and the subsequent evolution to free expansion can be described by a self-similar solution (Ro and Matzner 2013; Sakurai 1960). The power law exponent in this case is not determined by dimensional analysis, but by the passing of the solution through a critical point; it is a self-similar solution of the second kind. The solution applies to a planar shock breakout, i.e., the breakout occurs over a distance that is small compared to stellar radius. In that case the power law profile is steepened by two powers of r in going to spherical expansion. The result of the self-similar solution is that n D 10:2 for ı D 3 and n D 12 for ı D 1:5. There is also a self-similar solution for an accelerating shock in an atmosphere with an exponential density profile. The resulting value of n is 8.67, which is also the value obtained in the limit ı ! 1. The overall result of these considerations is that the outer part of a core collapse supernova can be approximated by a steep power law density profile or ej / r n where n is a constant. After the first few days, the outer parts of the ejecta expand with constant velocity, V .m/ / r for each mass element, m, so that r.m/ D V .m/t and .m/ D o .m/.to =t /3 . Therefore, ej D o

  3  t V0 t n : t0 r

(1)

This expression takes into account the free expansion of the gas. The inner density distribution cannot be analytically calculated in a straightforward way, but physical arguments imply a roughly r 1 density profile (Chevalier

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and Soker 1989; Matzner and McKee 1999). self-similar solution, the coefficient of the density must be determined by numerical simulation of the whole explosion. The outer power law is only approached asymptotically so the power law index of the density profile applicable to a given situation is smaller than the asymptotic value. The self-similar solution assumes that the flow is adiabatic, which is not the case once radiation can diffuse from the shocked layer. For a radiation dominated shock, the shock thickness corresponds to an optical depth of approximately s D c=v, where v is the shock velocity and c is the speed of light. Once the shock wave reaches an optical depth of s from the surface, radiation can escape and the shock wave acceleration through the layers of decreasing density ends.

2.2

Ambient Medium

Because of their large luminosity, massive stars lose mass in all evolutionary stages. What is most important for at least the early interaction between the supernova and ambient medium is the mass loss immediately before the explosion. Red supergiants have slow winds with velocities 10–50 km s1 . The mass loss rates of most red supergiants are in the range 106 –105 Mˇ yr1 , but there are also a number of stars undergoing a super-wind phase with very high mass loss rate, 104 –103 Mˇ yr1 . This includes stars like VY CMa, NML Cyg, and IRC10420. It is obvious both from the mass loss rates and their small fraction of the total number of red supergiants that this is a short-lived phase. Compact progenitors, like WR stars and blue supergiants, have similar mass loss rates 106 –104 Mˇ yr1 but wind velocities 1000–3000 km s1 . See Smith (2014) for an extended discussion. There are supernovae that show evidence for larger mass loss rates occurring somewhat before the supernova explosion, in particular Type IIn SNe (see Sect. 6.4 and Smith and Arnett 2014). The driving mechanism for the mass loss is not understood nor is the reason why it should occur close to the time of the explosion. Such strong mass loss rates are observed during the outbursts of luminous blue variables (LBVs) and they are frequently mentioned in this context. Other possibilities are turbulence in the late phases of stellar evolution and/or binary interaction (Chevalier 2012; Shiode and Quataert 2014; Smith and Arnett 2014). If the mass loss parameters stay approximately constant leading up to the explosion, the circumstellar density is given by

cs D

MP ; 4 uw r 2

(2)

where MP is the mass loss rate, uw the wind velocity, and r the radius. In most cases it is the CSM density which is most observationally relevant and can be measured. It is therefore convenient to scale this by the mass loss rate and wind velocity to that typical of a red supergiant. We therefore introduce a mass loss rate parameter C defined by

34 Thermal and Non-thermal Emission from Circumstellar Interaction

MP D 6:303  1014 uw

MP 5 10 Mˇ yr1

!



879

1 uw  6:303  1014 C g cm1 1 10 km s (3)

The CS density is then cs D 5:016  1017 C



r 1015 cm

2

g cm3 :

(4)

Note that C varies by a large factor for different types of progenitors. For a red supergiant with MP D 105 Mˇ yr1 and uw  10 km s1 C  1, while for a fast wind, like that from a WR star or blue supergiant with uw  1000 km s1 , C  0:01 for the same mass loss rate. An LBV with MP D 0:1 Mˇ yr1 and uw  100 km s1 has C  103 . Most of our discussion in the following will be based on the assumption of a spherical geometry. There is, however, strong evidence that both the ejecta and the CSM may be very complex. An example of a both anisotropic and clumpy CSM medium is that of the red supergiant VY CMa (Smith et al. 2009), while the famous Eta Car nebula has a more regular, bipolar structure, with a dense shell containing 10 Mˇ of mainly molecular gas (Smith 2006). Both anisotropies and clumpiness can have strong observational consequences for the CSM interaction with the SN ejecta.

3

Shock Interaction

3.1

Shock Structure and Evolution

When the radiation dominated shock front in a supernova nears the stellar surface, a radiative precursor to the shock forms when the radiative diffusion time is comparable to the propagation time. There is radiative acceleration of the gas and the shock disappears when optical depth c=v is reached (Ensman and Burrows 1992). The fact that the velocity decreases with radius implies that the shock will reform as a viscous shock in the circumstellar wind. This occurs when the supernova has approximately doubled in radius. The interaction of the ejecta, expanding with velocity &104 km s1 , and the nearly stationary circumstellar medium results in a reverse shock wave propagating inwards (in mass) and an outgoing circumstellar shock. The density in the circumstellar gas is given by Eq. (2). As discussed above, hydrodynamical calculations show that to a good approximation the ejecta density can be described by Eq. (1). A useful self-similar solution for the interaction can then be found (Chevalier 1982a, b; Nadezhin 1985). Here we sketch a simple derivation. More details can be found in these papers, as well as in the review (Chevalier 1990). Assume that the shocked gas can be treated as a thin shell with mass Ms , velocity Vs , and radius Rs . Balancing the ram pressure from the circumstellar gas and the

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impacting ejecta, the momentum equation for the shocked shell of circumstellar gas and ejecta is Ms

d Vs D 4 Rs2 Œej .Vej  Vs /2  cs Vs2 : dt

(5)

Here, Ms is the sum of the mass of the shocked ejecta and circumstellar gas. The P s =uw , and that behind swept up mass behind the circumstellar shock is Mcs D MR R1 2 3 n the reverse shock Mrev D 4 Rs .r/r dr D 4 to Vo .t =Rs /n3 =.n3/, assuming that Rs >> Rp , the radius of the progenitor. With Vej D Rs =t we obtain " # MP 4 o to3 Von t n3 d 2 Rs Rs C uw .n  3/ Rsn3 dt 2 "   #  3 n n3  Rs dRs 2 dRs 2 MP 2 o to Vo t D 4 Rs  : (6)  Rsn t dt 4 uw Rs2 dt This equation has the power law solution  Rs .t / D

8 o to3 Von uw .n  4/.n  3/ MP

1=.n2/

t .n3/=.n2/ :

(7)

The form of this similarity solution can be written down directly by dimensional analysis from the only two independent quantities available, o to3 Von and MP =uw . The solution applies after a few expansion times, when the initial radius has been “forgotten.” The requirement of a finite energy in the flow implies n > 5. More accurate similarity solutions, taking the structure within the shell into account, are given in (Chevalier 1982a; Nadezhin 1985). In general, these solutions differ by less than 30% from the thin shell approximation.

3.2

Postshock Conditions and Radiative Cooling

The maximum ejecta velocity close to the reverse shock depends on time as Vej D Rs =t / t 1=.n2/ . The velocity of the circumstellar shock is Vs .t / D

.n  3/ Rs .t / .n  3/ dRs .t / D D Vej / t 1=.n2/ dt .n  2/ t .n  2/

(8)

with Rs .t / given by Eq. (7), while the reverse shock velocity is Vrev D Vej  Vs D

Vej : .n  2/

(9)

Assuming cosmic abundances and equipartition between ions and electrons, the temperature of the shocked circumstellar gas is

34 Thermal and Non-thermal Emission from Circumstellar Interaction

Tcs D 1:36  109



n3 n2

2 

Vej 4 10 km s1

881

2 K

(10)

and at the reverse shock Trev D

Tcs : .n  3/2

(11)

The time scale for equipartition between electrons and ions is 1:5   1 ne Te teq  2:5  107 s: 109 K 107 cm3

(12)

Here Te is the electron temperature in either region. One finds that the reverse shock is marginally in equipartition, unless the temperature is &5  108 K. The ion temperature behind the circumstellar shock is &6  109 K for V4 & 1:5 and the density a factor &4 lower than behind the reverse shock. Ion-electron collisions are therefore ineffective, and Te 1 eV. At lower temperatures, the  D 0:34 cm2 =g approximation leads to an underestimate of Tph , by 20% at 0.7 eV. This is due to the reduction in opacity accompanying H recombination. The reduced opacity implies that the photosphere penetrates deeper into the expanding envelope, to a region of higher temperature. The photospheric radius is not significantly affected and is well described by Eq. (61). 4.3.2 He Envelopes For He-dominated envelopes, the constant opacity approximation does not provide an accurate description of Tph . We therefore replace Eqs. (61) and (62) with an approximation, given in Eqs. (67) and (68), which takes into account the reduction of the opacity due to recombination, based on the numeric calculation. The approximation of Eq. (67) differs by less than 8% from the result of a numerical calculation using the OP opacity tables down to Tph ' 1 eV. The temperature does not decrease significantly below ' 1 eV due to the rapid decrease in opacity below this temperature, which is caused by the nearly complete recombination. On the timescale of interest, 1 h t 1 day, the photospheric temperature is in the energy range of 3 eV T 1 eV. In this temperature range (and for the characteristic densities of the photosphere), the opacity may be crudely approximated by a broken power law, .T =1:07 eV/0:88 ; T > 1:07 eVI  D 0:085 .cm2 =g/ (66) .T =1:07 eV/10 ; T 1:07 eV: Using this opacity approximation, we find that Eq. (62) for the photospheric temperature is modified to ( 0:20 0:38 t5 ; Tph 1:07 eVI 1:33eVf0:02 R;12 (67) Tph .t / D 0:12 ; Tph < 1:07 eV: 1:07 eV.t =tb / Here, R D 1012 R;12 cm and tb is the time at which Tph D 1:07 eV, and we have neglected the dependence on E and M , which is very weak. The photospheric radius, which is less sensitive to the opacity modification, is approximately given by 0:39 rph .t / D 2:8  1014 f0:038 E51 .M =Mˇ /0:28 t50:75 cm:

(68)

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Here we have neglected the dependence on R , which is weak. For Tph > 1:07 eV, the bolometric luminosity is given by L D 3:3  1042

0:84 0:85 E51 R;12

f0:15 .M =Mˇ /0:67

t50:03 erg s1 :

(69)

The following comment is in place here. The strong reduction in opacity due to He recombination implies that the photosphere reaches deeper into the envelope, to larger values of ım , where the initial density profile is no longer described by Eq. (4) and the evolution of the ejecta is no longer given by the eqs. of Sect. 4.1. This further complicates the model for the emission on these timescales.

4.3.3 C/O and He-C/O Envelopes Finally, we consider in this section envelopes composed of a mixture of He and C/O. At the relevant temperature and density ranges, the C/O opacity is dominated by Thomson scattering of free electrons provided by these atoms, and is not very sensitive to the C:O ratio. Denoting by 1-Z the He mass fraction, the C/O contribution to the opacity may be crudely approximated, within the relevant temperature and density ranges, by  D 0:043 Z.T =1 eV/1:27 cm2 =g:

(70)

This approximation holds for a 1:1 C:O ratio. However, since the opacity is not strongly dependent on this ratio, Tph obtained using Eq. (70) holds for a wide range of C:O ratios (see discussion at the end of this subsection). At the regime where the opacity is dominated by C/O, Eq. (62) is modified to 0:19 0:35 Tph .t / D 1:5eVf0:017 Z0:2 R;12 t5 :

(71)

In the absence of He, i.e., for Z D 1, Tph is simply given by Eq. (71). For a mixture of He-C/O, Z < 1, Tph may be obtained as follows. At high temperature, where He is still ionized, the He and C/O opacities are not very different and Tph obtained for a He envelope, Eq. (67), is similar to that obtained for a C/O envelope, Eq. (71). At such temperatures, we may use Eq. (67) for an envelope containing mostly He, and Eq. (71) with Z D 1 for an envelope containing mostly C/O (a more accurate description of the Z-dependence may be straightforwardly obtained by an interpolation between the two equations). At lower temperature, the He recombines and the opacity is dominated by C/O. At these temperatures, Tph is given by Eq. (71) with the appropriate value of Z. The transition temperature is given by THeC=O D 1 Z0:1 eV:

(72)

The photospheric radius, which is less sensitive to the opacity variations, is well approximated by Eq. (68). At the stage where the opacity is dominated by C/O, the bolometric luminosity is given by

36 Shock Breakout Theory

L D 4:7  1042

989 0:83 0:8 E51 R;12

f0:14 Z0:63 .M =Mˇ /0:67

t50:07 erg s1 :

(73)

For C/O envelopes, the analytic approximation for Tph derived above, Eq. (71), differs by less than 6% from the result of a numerical calculation using the OP opacity tables down to Tph ' 0:5 eV. For Z in the range 0:7 > Z > 0:3, the approximations obtained by using Eqs. (67) and (71) with a transition temperature given by Eq. (72) hold to better than 10% down to Tph ' 0:8 eV.

4.4

Color Temperature

We have shown in Sect. 4.2 that photon diffusion is not expected to significantly affect the luminosity. Such diffusion may, however, modify the spectrum of the emitted radiation. We discuss below in some detail the expected modification of the spectrum. For the purpose of this discussion, it is useful to define the “thermalization depth,” rther , and the “diffusion depth,” rdiff . rther .t / < rph .t / is defined as the radius at which photons that reach rph .t / at t “thermalize,” i.e., the radius from which photons may reach the photosphere without being absorbed on the way. This radius may be estimated as the radius for which sct abs  1 (Mihalas and Mihalas 1984), where sct and abs are the optical depths for scattering and absorption provided by plasma lying at r > rther .t /. rther is thus approximately given by 3.rther  rph /2 sct .rther /abs .rther /2 .rther / D 1;

(74)

where sct and abs are the scattering and absorption opacities, respectively (typically, the opacity is dominated by electron scattering). rdiff is defined as the radius (below the photosphere) from which photons may escape (i.e., reach the photosphere) over a dynamical time (i.e., over t , the timescale for significant expansion). We approximate rdiff by rph D rdiff C

p ct =3sct .rdiff /.rdiff /;

(75)

where c is the speed of light. For rdiff < rther , photons of characteristic energy 3T .rther ; t / > 3Tph will reach the photosphere, while for rther < rdiff photons of characteristic energy 3T .rdiff ; t / > 3Tph will reach the photosphere. Thus, the spectrum will be modified from a black body at Tph and its color temperature, Tcol (with specific intensity peaking at 3Tcol ) will be Tcol > Tph . Approximating Tcol D T .rther / for rdiff < rther and Tcol D T .rdiff / for rdiff > rther , the ratio Tcol =Tph was calculated in Rabinak and Waxman (2011) assuming that the scattering opacity is dominated by Thomson scattering of free electrons (with density provided by the OP tables), and estimating abs D   sct (recall that 

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is the Rosseland mean of the opacity). It would have been more accurate to use an average of the absorptive opacities over the relevant wavebands, which are not provided by the OP table. However, since the dependence of the color temperature .1=8/ on the absorptive opacity is weak, Tcol / abs , the corrections are not expected to be large. Under the above assumptions, Tcol =Tph is approximately given, for t 1 day, by fT  Tcol =Tph  1:2:

(76)

Using Eq. (76) with Eqs. (62), (67), and (71) for the photospheric (effective) temperature, the progenitor radius may be approximately inferred from the color temperature by 

R  0:70  1012

Tcol .fT =1:2/eV

4

t51:9 f0:1 cm

(77)

t51:9 f0:1 cm

(78)

t51:9 f0:1 Z cm

(79)

for H envelopes, 11



R  1:2  10

Tcol .fT =1:2/eV

4:9

for He envelopes with T > 1:07 eV, and 11



R  0:58  10

Tcol .fT =1:2/eV

5:3

for He-C/O envelopes when the C/O opacity dominates (the transition temperature is given in Eq. (72)).

4.5

Removing the Effect of Reddening

We show in this section that the effects of reddening on the observed UV/O signal may be removed using the UV/O light curves. This is particularly important for ˛ inferring R , since R / Tcol with 4 ˛ 5 (see Eqs. (77), (78), and (79)). The model-specific intensity, f , is given by f .; t / D

 r 2 ph

D

4  Tph

Tcol gBB .hc=Tcol /e   ; hc

(80)

15 x 5 ;

4 ex  1

(81)

where gBB .x/ D

36 Shock Breakout Theory

991

D is the distance to the source, and  is the extinction optical depth at . Let us define t .t; / by Tcol Œt D t .t; / D 0 Tcol .t /;

(82)

for some chosen 0 . With this definition, the scaled light curves, fQ Œ; t .t; / 



D rph .t /

2 

Tcol .t / Tph .t /

4 

T0 Tcol .t /

5  f .; t /

(83)

(where T0 is an arbitrary constant) are predicted to be the same for any  up to a factor e   , T0 fQ Œ; t .t; / D  T04 gBB Œhc=0 Tcol .t /  e   : hc

(84)

Let us consider now how the scalings defined above allow one to determine the relative extinction in cases where the model parameters fE; M; R g are unknown, and hence fTcol ; Tph ; rph g.t /, which define the scalings, are also unknown. For simplicity, let us first consider the case where the time dependence of the photospheric radius and temperature are well approximated by power laws, Tph / t ˛T ;

rph / t ˛r ;

(85)

and the ratio Tcol =Tph is independent of time. This is a good approximation for the time dependence of rph in general and for the time dependence of Tcol and Tph for Tph > 1 eV (see Eqs. (61), (62), (67), (68), (71), and (76)). In this case Eq. (82) gives  t .t; / D

 0

1=˛T t;

(86)

and Eq. (83) may be written as   .2˛r C5˛T /=˛T 2˛r C5˛T t 0 # "    1=˛T  f ; t : 0

fQ Œ; t .t; / D Const: 



(87)

The value of the constant that appears in Eq. (87), for which the normalization of fQ is that given by Eq. (84), is not known, since it depends on the model parameters fE; M; R g. However, for any choice of the value of the constant, fQ defined by Eq. (87) is predicted by the model to be given by Eq. (84) up to a wavelengthindependent multiplicative factor. Thus, the ratio of the scaled fluxes defined in Eq. (87) determines the relative extinction,

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fQ Œ1 ; t .t; 1 / D e 2  1 : fQ Œ2 ; t .t; 2 /

(88)

Let us consider next the case where the time dependence of Tcol and Tph is not a simple power-law. Tcol and Tph are determined by the composition and progenitor radius R , and are nearly independent of E and M . Adopting some value of R , Eq. (82) may be solved for t .t; I R / and Eq. (83) may be written as fQ Œ; t .t; I R / D Const:  t 2˛r Tph .t /4 Tcol .t /1  f .; t /:

(89)

The model predicts therefore that scaling the observed flux densities using the correct value of R , the observed light curves at all wavelengths should be given by Eq. (84), up to a multiplicative wavelength-independent constant. For this value of R , the ratio of the scaled fluxes at different wavelengths is independent of t and given by Eq. (88). The value of R may be therefore determined by requiring the ratios of scaled fluxes to be time independent, and the relative extinction may then be inferred from Eq. (88).

5

Using Stellar-Surface Breakout and Cooling Emission Observations to Constrain Progenitor and Explosion Parameters

5.1

Breakout Burst

The properties of the breakout burst depend on the radius of the star R , the velocity of the breakout vbo , and to a lesser extent on the density at breakout bo and thus can be used to constrain these parameters. Thesepin turn can be used to constrain global properties of the ejecta (in particular v D E=M ) through the approximate hydrodynamic relations (27) and (28). The properties are insensitive to the density profile. The first detected bursts will likely have a limited amount of photons. Even with a few tens of photons, the total energy in the burst Ebo and the frequency peak at which the fluence peaks (in terms of energy per logarithmic frequency) are likely to be reliably measurable and are expressed in Eqs. (31) and (50). These quantities are insensitive to slight deviations from spherical symmetry. The total energy in the burst is approximately equal to 2 times the peak fluence per logarithmic frequency (Eq. (51)), and thus measuring the peak is sufficient for both quantities. The low dependence on the breakout density implies that the measurement of these quantities is sufficient to obtain an approximate measurement of the progenitor radius (velocity from (50) and then radius from (31)). The timescale of the burst is also likely measurable and provides an upper limit for the radius since the burst duration must be greater than the light crossing time R=c.

36 Shock Breakout Theory

993

If the light curve can be reliably determined and exact spherical symmetry is assumed, the light curve can provide an independent measurement of R. In this case, the luminosity and temperature evolution can be calculated accurately (Katz et al. 2012b; Sapir and Halbertal 2014; Sapir et al. 2011, 2013). In particular, the peak bolometric luminosity is approximately given by equation 39 (using equations 5 and 32) in Katz et al. (2012b). The amplitude of the bolometric luminosities at intermediate times R=c . t . R=4vbo is insensitive to deviations from spherical symmetry and is given by Eq. (32). If measured (overcoming the likely challenge of ISM absorption given the decreasing temperatures), the luminosity at such times may provide an independent robust measurement of the radius. For large RSG progenitors, where the emitted energy is largest, the expected temperatures, of tens of eV, are such that most of the radiation is expected to be absorbed in the ISM. Very small progenitors such as Wolf-Rayet (WR) stars are expected to produce multi-keV photons but with a very small output E . 2  2 1044 R11 erg (see Eq. 31, assuming nonrelativistic breakout vbo < 1010 cm=s). The most promising progenitors for observable breakout bursts are intermediate-sized BSG progenitors, where keV photons may be produced with observable outputs (see Sect. 7.1).

5.2

Post-breakout Cooling

The post-breakout cooling emission is nearly independent of the density structure of the outer envelope as long as the emission is dominated by ı  1 shells, see Eq. (52). In this limit, the luminosity L and the effective temperature T of the emitted radiation are determined by R , E=M , and . Tph .t / and L.t / are given by Eqs. (62) and (63) for H-dominated envelopes, by Eqs. (67) and (69) for He envelopes, and by Eqs. (71, 72, and 73) for He:C/O envelopes. The ratio of color to photospheric temperature is approximately Tcol =Tph D 1:2 (see Sect. 4.4), and the spectral luminosity per unit wavelength  may be approximated by L .t / D L.t /

Tcol gBB .hc=Tcol /; hc

(90)

where gBB is the normalized Planck function, gBB .x/ D

15 x 5 :

4 ex  1

(91)

The very weak dependence of T on E=M implies that R = may be inferred from a measurement of the color temperature (see Eqs. (77), (78), and (79)) and that E=M may be inferred from the bolometric luminosity L. Several points should be carefully taken into consideration when inferring R and E=M from observations. Let us first consider the effects of reddening. The strong dependence of R on T (see Eqs. (77), (78), and (79)) implies that an estimate of R based on a

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determination of T from the spectrum observed at a given time t would be sensitive to reddening. On the other hand, the value of T at a given t may be inferred from the light curve at a given wavelength, L .t /, since the time t at which L .t / reaches its maximum is approximately the time at which T crosses hc=4 (the exact value is determined from the model’s L.t / and T .t /). Moreover, inferring T from the shape of the light curve allows one to infer the reddening by comparing the fluxes observed at different wavelengths, as explained in some detail in Sect. 4.5. Finally, in order to infer E=M from the luminosity L, the absolute value of the extinction should be determined. This cannot be done without some assumption on the relation between the (measured) reddening and the absolute extinction. Next, temporal and spatial opacity variations due to recombination should be taken into account for envelopes that are not H dominated (see Eqs. (66) and (70)). The opacity variations lead to a modification of the model light curves, as described in Sects. 4.3.2 and 4.3.3. A detailed measurement of the light curve may thus constrain the composition of the outer envelope. Finally, it should be noted that the model described here is valid only at early times, of order a few days, during which the emission is dominated by ı  1 shells (see Eq. (52)) and T & 1 eV (see Eqs. (62), (67), and (71)). At later time, as the photosphere penetrates to larger ı values, the evolution is no longer described by the simple self-similar solution given here and depends on the detailed structure of the ejecta. Moreover, as T drops below 0.7 eV for H-dominated envelopes, or 1 eV for He-dominated envelopes, recombination leads to a strong decrease of the opacity with decreasing temperature. At this stage the photosphere penetrates deep into the ejecta, to a depth where the temperature is sufficiently high to maintain significant ionization and large opacity. This enhances the dependence on the details of the envelope structure and implies that detailed radiation transfer models are required to describe the emission (our simple approximations for the opacity no longer hold). An accurate and robust determination of R , and hence of E=M , requires an accurate determination of T , at times when T depends mainly on R (see Eqs. (77), (78), and (79)) and independent of the details of the ejecta structure, i.e., at T & 1 eV. An accurate determination of T requires one to observe at  < hc=4T D 0:3.T =1eV/1 , in order to identify the peak in the light curve (or the spectral peak if extinction effects can be reliably removed). UV observations are thus required for a robust and accurate determination of R and E=M . An elaborate example of the application of the method described above for inferring progenitor parameters may be found in Rabinak and Waxman (2011). Analysis of the early UV/O observations of the type Ib SN 2008D led to a determination of the progenitor’s radius, R  1011 cm, which cannot be directly inferred from later time observations, of E=M , E51 =.M =Mˇ /  0:8, of the reddening, E.B  V / D 0:6, and to an indication that the He envelope of SN 2008D contained a significant C/O fraction. The inferred values of E=M and of the reddening, as well as the inferred presence of C/O, are consistent with later observations of the main SN light curve (Mazzali et al. 2008; Modjaz et al. 2009; Tanaka et al. 2009). The inferred radius constrains progenitor models and is consistent with the calculations of Tanaka et al. (2009).

36 Shock Breakout Theory

995

The example of SN 2008D demonstrates the importance of including the time dependence of the opacity, using Eqs. (67), (68), and (69) instead of Eqs. (62) and (63), which are valid for constant opacity (H-dominated) envelopes. It also demonstrates the importance of deviations from the solution presented here at late times (see Eq. (52)), when ıph  1 no longer holds. In the analysis of SN 2008D given in Rabinak and Waxman (2011), the model presented above was extended to large values of ı in order to extend the model predictions to t  2 d. Analyses that do not include the opacity variation with time and extend the analytic model beyond the limit of Eq. (52) (e.g., Bersten et al. 2013; Chevalier and Fransson 2008) would find model predictions that are inconsistent with observations and with the results of Rabinak and Waxman (2011) (e.g., compare fig. 7 of Bersten et al. 2013 with fig. 10 of Rabinak and Waxman 2011).

6

Open Theoretical Issues

We discuss in this section two topics, which are currently under vigorous theoretical investigation, and for which complete (near) exact solutions, as described in the preceding sections for stellar surface breakouts, are not yet available: breakouts from extended circumstellar media (Sect. 6.1) and relativistic breakouts (Sect. 6.2). We outline the main open questions and the gaps in the theoretical analyses that need to be closed.

6.1

Breakouts from an Extended Circumstellar Medium

In cases where the SN progenitor is surrounded by extended circumstellar medium (CSM), with optical depth exceeding c=vbo; where vbo; is the breakout velocity from the stellar surface, the RMS continues to propagate into the CSM, and breakout occurs at a radius Rbo > R , at which the optical depth of the overlying material drops below c=vs . The presence of such extended CSM may be the result of a massive wind or of the ejection of outer envelope shells prior to the SN explosion. The dynamics of the RMS depositing energy into the CSM depends on the CSM density structure. One may consider, for example, a blast-wave driven by an ejecta expanding through a continuous wind or a blast wave generated by the collision of an expanding ejecta with a detached CSM shell. The characteristic duration of the pulse is tbo  Rbo =c  Rbo =vbo , where vbo is the breakout velocity in the CSM, and the characteristic luminosity may be estimated as M v2bo =tbo with M , the shocked CSM mass, estimated from 2  M =4 Rbo  c=vbo (e.g., Chevalier and Irwin 2011; Ofek et al. 2010), tbo  105

Rbo;14 s; vbo;9

Lbo 

4 c Rbo v2bo  1044 Rbo;14 v2bo;9 erg=s; 

(92)

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where Rbo D 1014 Rbo;14 cm, vbo D 109 vbo;9 cm=s. In the case of an extended wind, the timescale may be increased by a factor  log.c=vs /, and the luminosity scale may be correspondingly reduced, due to photon diffusion at < c=vs . The spectrum of the emitted radiation is difficult to calculate, due to reasons detailed below. In general, as the shock wave is converted from an RMS to a collisionless shock at breakout (Katz et al. 2012, a), a transition from UV-dominated spectra to X-ray-dominated spectra is expected. For fast breakouts, v=c > 0:1, significant Xray emission is expected at breakout, while for slower breakouts X-ray emission is expected to become dominant at later times (e.g., Balberg and Loeb 2011; Chevalier and Irwin 2011, 2012; Katz et al. 2012; Svirski and Nakar 2014a; Svirski et al. 2012). High-energy photon (h  me c 2 ) and neutrino (multi-TeV) emission is also expected and may be detectable by existing telescopes, due to the acceleration of electrons and protons to high energy at the collisionless shock (Ackermann et al. 2015; Katz et al. 2012, a; Kowalski 2015; Murase et al. 2011, 2014; Zirakashvili and Ptuskin 2016). CSM breakouts may thus produce large luminosities, due to conversion of kinetic energy to thermal energy at large radius, in which case adiabatic expansion losses are greatly reduced. This requires a significant optical depth at large radii. For a steady wind with constant mass loss, MP , and velocity, vw , the requirement is MP  .4 c=/.vw =vbo /Rbo  103 .vw =103 vbo /Rbo;14 Mˇ =yr. There is significant and increasing evidence that large mass-loss episodes closely preceding the stellar explosion are not uncommon (see Sect. 7.2 for more details). The early light curves of SNe of type IIn are consistent with being generated by wind breakouts (Drout et al. 2014; Gezari et al. 2015; Ofek et al. 2014b) with inferred mass-loss rates >103 Mˇ =yr (e.g., Fransson et al. 2014; Kiewe et al. 2012; Moriya and Maeda 2014; Moriya et al. 2014b; Ofek et al. 2014c; Taddia et al. 2013), far exceeding the rates expected for line-driven winds (see Langer 2012 for review). The detection of pre-SN “precursors” in several (mostly IIn) SNe (Corsi et al. 2014; Foley et al. 2007; Fraser et al. 2013; Mauerhan et al. 2013, 2014; Ofek et al. 2013a; Pastorello et al. 2007, 2013), and the indication that such precursors are common for IIn SNe on a month timescale preceding the explosion (Ofek et al. 2014a), provides independent evidence for intense mass-loss episodes in many SN progenitors shortly before the explosion. Finally, the strong emission of super-luminous SNe (of type II/I(c)) may be interpreted as due to breakouts from extended CSM with (shocked) mass comparable to the SN ejecta mass (Balberg and Loeb 2011; Chatzopoulos et al. 2012; Chevalier and Irwin 2011; Ginzburg and Balberg 2012; Miller et al. 2009; Moriya et al. 2011, 2013a; Ofek et al. 2010; Quimby et al. 2007; Smith and McCray 2007; Smith et al. 2007, 2010; Woosley et al. 2007). We do not elaborate here on the theory of CSM breakouts. This is due to the fact that a complete theoretical analysis, as the one presented in the preceding sections for the stellar surface breakout/post-breakout cooling problem, is not yet available for CSM breakouts. The hydrodynamics of CSM breakouts and the resulting bolometric light curves have been thoroughly studied using analytic, semianalytic, and numeric methods for various CSM structures (e.g., Balberg and Loeb

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2011; Chatzopoulos et al. 2012, 2013; Chevalier and Irwin 2011; Ginzburg and Balberg 2012, 2014; Moriya et al. 2011, 2013b; Nakar and Piro 2014; Ofek et al. 2010; Piro 2015; Svirski and Nakar 2014a; Svirski et al. 2012). The study of the resulting spectra is ongoing and not yet complete. Analytic analyses provide heuristic qualitative descriptions of the expected spectra or characteristic radiation temperature (e.g., Balberg and Loeb 2011; Chevalier and Irwin 2012; Katz et al. 2012; Ofek et al. 2010; Svirski and Nakar 2014a; Svirski et al. 2012), while numeric analyses (e.g., Ginzburg and Balberg 2012; Kasen et al. 2011; Moriya et al. 2011, 2013b; Roth and Kasen 2015) do not yet include all the relevant physical process, as discussed in some detail below. The theoretical uncertainties affect the analysis of observations, as discussed in Sect. 7.2. The main challenge, that theoretical analyses of the CSM breakout spectra face, is related to the fact that the plasma in the shock transition region, where most of the radiation is generated, is not in general in thermal equilibrium, combined with the fact that the shock wave changes its structure in a complicated manner on a timescale comparable to the dynamical timescale, R=vs . In the stellar surface breakout situation, the mass lying ahead of the shock at breakout is small, and the escaping radiation is capable of accelerating the overlying shells to high velocity, followed by a phase of free expansion (see Sect. 3). In the CSM breakout case, the mass lying ahead of the shock at breakout may be large, and the radiation escaping from the RMS may not carry sufficient momentum to accelerate the overlying shells to high velocity. As a result, the faster inner shells drive a collisionless shock through the overlying CSM (Katz et al. 2012a). The electron spectrum at the shock transition, which determines the emitted radiation spectrum, is determined by interaction of the accelerated electrons with the ambient radiation, which is initially dominated by the RMS generated radiation diffusing outward and later by Bremsstrahlung emission at the shock transition (Chevalier and Irwin 2011, 2012; Svirski et al. 2012). An accurate, self-consistent description of the evolution of the shock structure and of the emitted radiation is not yet available though progress has been made (Balberg and Loeb 2011; Chevalier and Irwin 2011, 2012; Svirski and Nakar 2014a; Svirski et al. 2012). We briefly discuss below the implied challenges to analytic and numeric calculations. Analytic analyses are challenged by several major factors. • The nonsteady nature of the shock structure at breakout implies that solutions of steady shock structure are not applicable (e.g., for stellar surface breakout, the breakout radiation temperature is 2–5 times lower than given by a steady RMS with v D vbo (Sapir et al. 2013)). The situation is more complicated than in the stellar surface case, due to the RMS-collisionless transition. • The diversity and complexity of the spatial density profiles limit the usefulness of analytic (e.g., self-similar) solutions for the hydrodynamics. • The formation of a collisionless shock leads to the generation of nonthermal highenergy particles and photons. The complicated interaction of radiation with highenergy electrons and the resulting complicated spectra are difficult to describe analytically.

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Numeric analyses are challenged by several major factors as well. • The formation of a collisionless shock and the generation of nonthermal highenergy particles and photons is difficult to include, and is not included in current numerical calculations. • Inelastic Compton scattering plays a crucial role in determining the electron temperature and photon spectrum. This is quite challenging to include in radiation-hydro codes, and is not included in current numerical calculations (e.g., Ginzburg and Balberg 2012; Kasen et al. 2011; Moriya et al. 2011; see discussion in Kasen et al. 2011). A Monte-Carlo algorithm, that in principle could accommodate a description of inelastic Compton scattering, was recently described in Roth and Kasen (2015), but a calculation including inelastic Compton scattering was not implemented. • The cooling time of shock-heated electrons is much smaller than the dynamical time, which implies that in order to correctly determine their temperature (and the emitted radiation spectrum) a challengingly high resolution is required. • The rapid electron cooling also leads, at high velocity, to a separation between the electron and the proton temperatures, which is not included in current numerical calculations.

6.2

Relativistic Breakouts

Several complications arise if the shock reaches mildly or ultra-relativistic velocities as it approaches the surface (Budnik et al. 2010; Katz et al. 2010; Levinson and Bromberg 2008; Nakar and Sari 2012; Weaver 1976) . The modifications required to the analysis presented in Sect. 3 can be separated to those that are related to the high expected temperatures, which exceed tens of keV for vs & 0:2c (see Eq. (47)) and to modifications due to the high velocities of the plasma. The high temperatures give rise to the following corrections and new effects: • A significant amount of electron-positron pairs may be produced, increasing the optical depth of a given fluid element by orders of magnitude; • Compton equilibrium is not necessarily maintained at each point, and the spectrum needs to be calculated in a self-consistent way; • Klein-Nishina corrections to the Compton cross section must be included; • Relativistic corrections to the photon generation rate and spectrum (e.g., electronelectron Bremsstrahlung) need to be included. The presence of high velocities requires additional modifications: • The radiation field is far from being isotropic and the diffusion approximation is not valid; • The hydrodynamic solution of the shock propagation as it approaches the surface requires a relativistic treatment.

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The velocity effects are particularly severe if the shock reaches ultra-relativistic speeds. The steady-state structure of the relevant relativistic shocks has been solved numerically for ultra-relativistic shocks by Budnik et al. (2010), and its structure is approximately understood analytically (Budnik et al. 2010; Katz et al. 2010; Nakar and Sari 2012). The time-dependent problem of a relativistic breakout has been addressed using rough analytical arguments by Nakar and Sari (2012), who provided order of magnitude estimates for the emitted spectrum and light curve and its scaling properties with the breakout properties. As far as we know, an accurate calculation of a relativistic breakout, similar to the nonrelativistic breakout calculations described in Sect. 3, is yet to be preformed. Given the complexity of the problem, we believe that such a calculation is necessary for confirming the order of magnitude estimates of Nakar and Sari (2012) as well as for providing accurate predictions.

7

Breakout and Post-breakout Observations

7.1

Stellar-Surface Breakouts and Post-breakout Cooling Emission

7.1.1 Stellar-Surface Breakouts Shock breakout from a stellar surface is expected to produce a flash of X-rays with photon energies in the range 50–10;000 eV, and total energy, E  2  2 1047 R13 vbo;9 erg s1 (See Eq. 31) emitted over a timescale of tens of seconds to a few hours. While the vast majority of supernovae are expected to have a nonrelativistic shock breakout burst, a certain detection is yet to be found (see discussion below of the best candidate: the X-ray burst XRF080109 associated with the supernova SN 2008D). For large RSG progenitors, where the emitted energy is largest, the expected temperatures, of tens of eV, are such that most of the radiation is expected to be absorbed in the ISM. Smaller progenitors may produce & keV emission with smaller outputs. Probably the most easily detectable breakouts are in supernovae with “intermediate size,” blue-super-giant (BSG) progenitors such as SN 1987A (Calzavara and Matzner 2004a; Sapir et al. 2013). The current and past X-ray telescopes with highest potential detection rate of breakout bursts are ROSAT and 4 1:5 XMM-Newton which have similar values of A1:5 deg2 , where eff  FOV  10 cm 2 2 Aeff is the effective area (200 cm for ROSAT and 1000 cm for XMM-Newton) and FOV is the field of view (3:6 deg2 for ROSAT and 0:2  0:3 deg2 for XMMNewton, see comparison of different detectors in table 3 of Sapir et al. 2013). XMM-Newton has much higher resolution and thus lower background making it the best detector so far for finding breakout bursts. Indeed, the expected number of background events within a single pixel, assuming a background X-ray flux of nbackground 0:01counts cm2 deg2 s1 and an integration time of 1000 s is 0:1 for XMM-Newton (PSF of 105 deg2 ) and 4 for ROSAT (PSF of and 0:002 deg2 ).

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We are not aware of an attempt to systematically search for breakout bursts in the archival data of XMM-Newton even though detectable burst are expected to exist in the data (Calzavara and Matzner 2004a; Sapir et al. 2013). The total emitted energy in the breakout burst from a BSG is given by (see Eq. 31) Ebo D 4  1046



R 3  1012 cm

2 

 vbo 9 1 2  10 cm s

(93)

where the radius and breakout velocity are normalized to values expected to SN 1987A, R  3  1012 cm, vbo  2  109 cm s1 (see discussion in Sapir and Halbertal (2014) and references therein). The total number of emitted photons is thus expected to be Ebo N D D 2  1055 hh i



Ebo 1046:5 erg



hh i 1keV

1 :

(94)

The expected number of photons is likely lower due to some absorption in the ISM. Assuming ndet photons are required for a detection, the co-moving radial distance to which such an event can be seen using a detector with an effective area Aeff is 

N d D 2900 1055

1=2 

Aeff 1000 cm2

1=2 

ndet 1=2 Mpc 10

(95)

which corresponds to a redshift of order z  1 (assuming H0 D 70 km s1 Mpc1 , ˝M D 0:3 and ˝ D 0:7, z D 1 corresponds to d D 3300 Mpc). Note that the number of photons arriving at the detector depends on the co-moving radial distance, unlike the instantaneous energy flux which depends on the luminosity distance. Note also that some suppression is expected given that the photons will be redshifted, and some will not fall within the detector’s band. The rate of BSG SNe is about a fraction of fBSG  0:010:03 of “Core Collapse” (CC) SNe (Kleiser et al. 2011; Pastorello et al. 2012; Smartt et al. 2009; Taddia et al. 2016). The rate of CC SNe at redshift of z < 1 is estimated to be (see figure 10 of Madau and Dickinson (2014), and references therein) nP CC  .1 C z/3  104 Mpc3 yr1 ;

(96)

The expected observable rate of BSG with 0:5 < z < 1 and more than 10 photons is therefore NP BSG  1:5



nP BSG;eff 3  106 Mpc3 yr 1



Aeff 1000 cm2

3=2 

FOV 0:2 deg2



N;eff 1055

3=2

yr1 : (97)

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Given the >10 year lifetime of XMM-Newton, with an effective area of 1000 cm2 at h D keV and a field of view of 0:2 deg2 (exact values depending on the mode and frequency XMM-Newton Users Handbook 2016), several events may exist in the data. Evidently, this estimate has large uncertainties (BSG SNe rate and properties, absorption), and the number of events may range from none to tens. The result in (97) assumes a redshift of 0:5 < z < 1 and ignores modest corrections within this range. We note that few attempts to identify 100 s timescale X-ray bursts in the archival data of ROSAT have been made with the aim of detecting Gamma-ray burst afterglows (Greiner et al. 2000; Vikhlinin 1998). While most bursts are associated with M stars, the possibility that a few of them are breakouts has not been ruled out to the best of our knowledge. Future X-ray missions such as eROSITA (Merloni et al. 2012), HXMT (Xie et al. 2015) and Einstein Probe (Yuan et al. 2015) may significantly increase the prospects for detecting breakouts. In particular, wide-field detectors such as Einstein Probe with its 60 deg  60 deg field of view may allow the detection of breakout bursts which can be later associated supernovae detected by deep wide-field optical surveys such as the planned ZTF and LSST. Perhaps the best shock breakout candidate is the high-energy X-ray flash (XRF080109) preceding the type Ib supernova (SN 2008D) that was serendipitously discovered by the SWIFT X-ray telescope during an observation of the NGC 2770 galaxy (Soderberg et al. 2008). The XRF had a total emitted energy of E  2:5  1045 erg and duration of 300 s. The association with a supernovae and the fact such energies and timescales are within the range of shock breakouts lead several authors to suggest a shock breakout origin (e.g., Chevalier and Fransson 2008; Katz et al. 2010; Soderberg et al. 2008). The fluence spectrum of the burst is hard and is consistent with a power law F / 0 (Modjaz et al. 2009; Soderberg et al. 2008). The spectrum can also be fitted by the expected fluence spectrum of spherically symmetric breakouts (Sapir et al. 2013), with h peak  4 keV, with some tension at the highest energy bins. The velocity inferred from this peak photon energy implies vbo  0:15c and fastest parts of the ejecta moving at 0:3 c which is consistent with radio observations (Soderberg et al. 2008). Assuming a He envelope and  D 0:2, the progenitor’s radius can then be found using the total emitted energy (see (31)) R  5  1011 cm:

(98)

The inferred radius is larger than the stellar radius R  1011 cm inferred from the post-breakout emission (Rabinak and Waxman 2011) (see Sect. 7.1.2) and from the radii of WR progenitors typically associated with this type Ib SN. This suggests that the breakout may have taken place within an extended distribution of matter around the star (Katz et al. 2010; Soderberg et al. 2008; Svirski and Nakar 2014b) (a wind or a nonstandard outer envelope; recall that the mass lying ahead of the breakout radius is only 4 R2 c=v  107 Mˇ , while the emission of post-breakout cooling radiation on a fraction of a day timescale is from shells of mass 103 Mˇ ). The breakout explanation is challenged by the fact that the implied light-crossing time,

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R=c, is about 20 times smaller than the observed burst duration implying (within the breakout interpretation) either a nonspherical shock wave reaching different points on the surface at different times or that the stellar envelope is enshrouded by a moderately optically thick circumstellar material (CSM) (Katz et al. 2010; Soderberg et al. 2008; Svirski and Nakar 2014b). In particular, Svirski and Nakar (2014b) claim that a single model involving a dense wind can explain the timescale, energy scale, and the observed spectrum using an approximate analytic calculation (Svirski and Nakar 2014a). The optical, low-energy tail of shock breakout may be detected with sufficient cadence and sensitivity. Two type II-P supernovae were recently reported to be discovered in the data of the planet transit search mission KEPLER, with 30min cadence and excellent photometric accuracy (Garnavich et al. 2016, the SN identification is based on light curves alone). In particular, the early rise of the light curve of one of these supernovae (KSN 2011d) seems to be consistent with having a breakout burst lasting a few hours. While the data does not allow a clear conclusion (in our view), this work demonstrates that the required sensitivity has been roughly reached, motivating future similar searches.

7.1.2 Post-breakout Cooling Emission Following breakout, the expanding cooling envelope produces a bright, L  1043 erg=s, UV emission on a timescale of hours to days (Sect. 4). As discussed in some detail in Sect. 5, a measurement of the color temperature enables one to determine R , and a measurement of L enables one to determine R E=M . The simple model described in Sect. 4 applies up to 1.M =Mˇ /1=2 d (assuming E51 =.M =Mˇ / ' 1, see Eq. (52)). Since the temperature at this time is 1 eV (see Eqs. (62), (67), and (71)), corresponding to a f peak at 0:3, this implies that UV observations at early time are required in order to determine R . Early, 1 d, observations of SN light curves became available recently with the beginning of the operation of wide-field-sensitive optical surveys, like the Palomar Transient Factory (PTF, (Law et al. 2009; Rau et al. 2009), and iPTF, (Gal-Yam et al. 2011)), the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS, (Kaiser et al. 2002)), and the All-Sky Automated Survey for Supernovae (ASAS-SN, (Shappee et al. 2014)). The sensitivity of these surveys allows one to detect post-breakout cooling emission on a day timescale from large, RSG, progenitors, and to set upper limits on the emission from smaller, BSG/WR progenitors (recall that L / ER =M ). In most cases, early UV observations (from space) are not available, hence limiting the ability to constrain R . The rate of detection of SNe at t 1 d will increase as new surveys become operative, like Keller et al. (2007), the Zwicky Transient Facility (ZTF, (Law et al. 2009)), and the Large Synoptic Survey Telescope (LSST, (LSST Science Collaboration 2009)). ZTF will provide, for example, 10/2/1 RSG/BSG/WR shock cooling detections per year at t < 1 d at g-band, and LSST will roughly double this rate (Ganot et al. 2016). This will significantly improve the ability to constrain models. However, a real breakthrough would require wide-field space UV observatory like the proposed ULTRASAT satellite (Sagiv et al. 2014), which will provide a tenfold increase in

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detection rate compared to the ZTF (Ganot et al. 2016) and, most crucially, will provide early UV measurements. The main constraints inferred from observations of post-breakout shock cooling emission are briefly summarized below. • Type II SNe. – A simultaneous PTF (optical) and GALEX (space, NUV) search for early UV SNe emission resulted in the detection of 7 SNe of type II, typically at 3 d past the explosion (Ganot et al. 2016). The observations are consistent with explosions of RSGs, with R  3  1013 cm and E=M  0:1  1051 =Mˇ . However, the quality of the data is not sufficient for accurately inferring R and E=M . Three earlier examples of UV emission on 2 d timescale from type II SNe, two serendipitous detections by GALEX (Gezari et al. 2008; Schawinski et al. 2008) and one resulting from a coordinated GALEX-PanSTARRS search (Gezari et al. 2010), yielded similar conclusions. Note that in earlier papers, a clear distinction between “shock breakout” emission and “post-breakout cooling” emission was not made. Hence, although the UV emission is referred to in Gezari et al. (2008) and Schawinski et al. (2008) as “shock breakout” emission, it is probably related to the post-breakout cooling phase (Gezari et al. 2010; Rabinak and Waxman 2011). – A PTF search for early SN emission yielded detections of 57 SNe of type II, with good R-band sampling at t < 10 d (Rubin et al. 2016). These observations lead to determinations of E=M to within a factor of 5, with an average of 0:1  1051 erg=Mˇ and a positive correlation of E=M with 56 Ni mass, and yielded only weak constraints on R (note that in the RJ regime, L / T 3 L / .E=M /R1=4 ). Comparing a large sample of SNII light curves to the post-breakout cooling model predictions, radii much smaller than expected for RSG progenitors were inferred in Gall et al. (2015) and González-Gaitán et al. (2015). However, this conclusion is obtained by comparing the data to the model well beyond the model’s validity time (Rubin et al. 2016). Comparing multiband light curves of two individual SNII to the model prediction of Rabinak and Waxman (2011), but limiting the analysis to t < 1 week, radii consistent with 1013:5 cm are inferred in Valenti et al. (2014) and Bose et al. (2015). • Type Ib/c SNe. – The non-detection of post-breakout cooling emission in observations of two SNe of type Ic (PTF 10vgv, 1994I) (Corsi et al. 2012) and one SN of type Ib (iPTF13bvn) (Cao et al. 2013) was used to set upper limits on the progenitor radii of R =Rˇ < .1; 0:25; few/, respectively, implying WR progenitors (or CO cores of stars stripped in binary systems). – There are two examples in which a serendipitous detection by the SWIFT satellite of an X-ray/ -ray flush preceding the UV/optical emission of a type Ib=c SN lead to early space UV/O observations of the SN emission: the low-luminosity GRB (LLGRB) GRB 060218 (E  1049 erg) associated with SN 2006aj (Campana et al. 2006; Mazzali et al. 2006; Pian et al. 2006;

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Soderberg et al. 2006) and the X-ray flash (XRF) XRO080109 (EX  1046 erg) associated with SN 2008D (Mazzali et al. 2008; Soderberg et al. 2008). The preceding LLGRB/XRF have been suggested to be generated by a breakout through a wind and will thus be discussed in the following subsection. The UV/O emission observed on a 1 d timescale is consistent with post-breakout cooling emission (Campana et al. 2006; Chevalier and Fransson 2008; Rabinak and Waxman 2011; Soderberg et al. 2008; Waxman et al. 2007). As explained at the end of Sect. 5, the early emission of SN 2008D was used to determine the progenitor’s radius, R  1011 cm, E=M , E51 =.M =Mˇ /  0:8, and the reddening, E.B  V / D 0:6 (Rabinak and Waxman 2011). A detailed analysis of this type was not carried out for SN 2006aj. • Type Ia SNe. A recent review of the observational constraints on the progenitors of Ia SNe may be found in Maoz et al. (2014). Here we briefly describe the main aspects related to very early observations: – The non-detection of post-breakout cooling emission has been used to put stringent constraints on the radii of the progenitors, of order 0:1Rˇ (Bloom et al. 2012; Im et al. 2015; Nugent et al. 2011; Zheng et al. 2013), strongly constraining the possible progenitors. The main factor contributing to the uncertainty in this limit is the uncertainty in the determination of the explosion time. The most stringent limit, R =Rˇ < 0:05, was obtained for SN 2011fe (Bloom et al. 2012; Mazzali et al. 2014; Nugent et al. 2011; Piro et al. 2013; Piro and Nakar 2014). – The collision of the expanding SN ejecta with a stellar companion may lead to significant emission of radiation and hence to deviations from a “standard” early light curve. Additional deviations may be due to mixing of Ni in the outer envelope. These topics are beyond the scope of this review, and we refer the reader to Maoz et al. (2014) for a detailed discussion. • “Double-peak SNe”. The bolometric light curves of several SNe, mainly of the IIb class (Arcavi et al. 2011; Van Dyk et al. 2014; Wheeler et al. 1993) (super-luminous double-peaked SNe are discussed in the senc subsection), show a “double-peak” behavior: a first peak at a few days after the explosion, preceding the main SN peak (on timescale of tens of days). It is commonly accepted that the first peak is produced by the post-breakout shock cooling radiation from an extended, R  1013 cm, low mass, M 0:1Mˇ envelope (Bersten et al. 2012; Nakar and Piro 2014; Piro 2015; Woosley et al. 1994). Such a low mass shell would become transparent after a few days of expansion, producing a first peak in the light curve well before the time at which the bulk of the ejecta becomes transparent. The model described in Sect. 4 does not apply, of course, up to times at which the envelope becomes transparent (see, e.g., Eq. (52)) and cannot therefore describe the behavior near the bolometric peak. However, it should apply to the early rising part of the light curve, since this part is not sensitive to the details of the density structure.

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Extended CSM Breakouts

Breakouts from an extended CSM at large radii are very bright on days’ timescale (see Eq. (92)). The main observational challenge to inferring stringent constraints on the progenitors and on their environment is the lack of UV/X-ray measurements, which are required in order to determine the characteristic plasma parameters. As explained in some detail in Sect. 6.1, a major additional challenge is the lack of a complete quantitative model describing the spectra of the emitted radiation. In particular, it is difficult to determine the density distribution and the origin of the extended CSM (winds, pre-ejected shells) and also whether or not late injection of energy into the expanding ejecta plays a significant role (see below). These gaps are reflected in the following discussion of observations of CSM breakouts: • Type IIn/Ibn SNe. There is significant and increasing evidence that the early light curves of SNe of these types are generated by wind breakouts (Drout et al. 2014; Gezari et al. 2015; Ofek et al. 2014b). However, the inferred mass loss, 103 Mˇ =yr, is typically higher than expected in stellar evolution models (Ofek et al. 2014b, c), and there are discrepancies between the observed and the predicted X-ray emission (Ofek et al. 2013b). The lack of complete selfconsistent theoretical models does not allow ruling out other models and hinders the inference of stringent quantitative constraints (quoting Ofek et al. (2013b): “We still do not have a good theoretical understanding of the expected X-ray spectral evolution. . . our observations cannot yet be used to rule out other alternatives”). These conclusions are based on the following main observations. – The light curves of 15 IIn SNe observed by PTF on times scales of 10 d are consistent with CSM breakouts with vbo  109 cm=s and mass-loss rates of MP  103 Mˇ =yr (Ofek et al. 2014b) (analyzing the same data, it is concluded in Moriya and Maeda (2014) that the MP distribution is wide, spanning an order of magnitude). – Observations of 12 PAN-STARRS transients (Drout et al. 2014), with characteristic L  1043 erg=s and rise times 1 eV (or with breakouts from nonstandard extended low mass envelopes with similar breakout parameters). – X-ray (XRT and Chandra) observations of 19 SNe of type IIn and one of type Ibn (Ofek et al. 2013b) yielded mixed conclusions regarding the wind breakout origin of these events, as some were consistent and some too bright for CSM breakouts. • Super luminous (SL) SNe. – A few dozens of examples are known (see Gal-Yam 2012 for a review) of extremely bright, L > 1044 erg=s, SNe of type II (H rich) and I(c) (H poor) (we do not discuss here SLSN of type R, which are likely powered by radioactive decay). The observed radiation may be interpreted as a breakout from extended CSM, with Rbo  1015 cm and vbo  109 cm=s, which is H-rich/poor

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for SLSN-II/I(c) (e.g., Balberg and Loeb 2011; Ginzburg and Balberg 2012; Moriya et al. 2013a; Ofek et al. 2010). The origin and structure of the CSM (extended envelope, wind, pre-ejected shell) are not well constrained. An alternative type of models was suggested, in which the expanding SN ejecta is continuously heated as it expands by a long lasting “central engine” such as a “magnetar” or an accreting black hole (Dessart et al. 2012; Dexter and Kasen 2013; Howell et al. 2013; Inserra et al. 2013; Kasen and Bildsten 2010; Maeda et al. 2007; Metzger et al. 2015; Nicholl et al. 2013; Woosley 2010). In these models, the deposition of thermal energy in the ejecta at large radii circumvents the adiabatic losses due to the large expansion factors. Finally, we note that “quark-nova” modes have also been suggested as an explanation of SLSNe (Leahy and Ouyed 2008; Ouyed et al. 2012). – Several SLSN of type I with double-peak bolometric light curves have been recently reported (Leloudas et al. 2012; Nicholl and Smartt 2016; Nicholl et al. 2015; Smith et al. 2016). Similarly to the type IIb double-peaked events (see preceding subsection), the first peak is commonly interpreted as the postbreakout cooling emission from an extended CSM, although it is not clear whether or not this material is part of an extended stellar envelope (e.g., Piro 2015). The origin of the second peak is debated, with tendency to prefer models with a “central engine” heating as the second peak driver. Proponents of the central engine magnetar models have furthermore suggested that the first peak may due to shock breakout from ejecta that was inflated to large radius by the energy output of the magnetar (Kasen et al. 2015). • Low luminosity GRBs (LLGRBs) and X-ray flashes (XRFs). – It has been suggested, based mainly on qualitative order of magnitude analyses, that LLGRBs and XRFs associated with SNe are produced by shock breakouts (Campana et al. 2006; Katz et al. 2010; Kulkarni et al. 1998; Li 2007; Nakar 2015; Nakar and Sari 2012; Tan et al. 2001; Waxman et al. 2007), possibly through extended CSM environments. The high temperatures of the bursts (tens – hundreds of keV, see (47)) and properties of the later radio and X-ray emission suggest that if true, these breakouts require relativistic corrections making quantitative estimates difficult. A rough analytic estimate of the properties of relativistic breakouts was carried out in Nakar and Sari (2012) based on the properties of relativistic radiation mediated shocks (Budnik et al. 2010; Katz et al. 2010), leading to relativistic corrections to the breakout temperatures, energies, and durations. With these corrections, the long duration t  1000 s LLGRBs associated with SNe, GRBs 060218SN 2006aj (Campana et al. 2006), and GRB 100316D-SN 2010bh (Starling et al. 2011) as well as the short duration t  30 s LLGRBs associated with SNe, GRB 980425-SN 1998bw (Galama et al. 1998), GRB 031203- SN 2003lw (Malesani et al. 2004) were shown to be broadly consistent with spherical breakouts from a spherical surface. The radius required by the longer LLGRBs is quite extended &1013 suggesting a CSM origin (e.g., Campana et al. 2006) or an extended progenitor (Nakar 2015, allowing a possible unification model with cosmological GRBs). Alternatively, the long duration

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may be a result of a significant departure from spherical symmetry (e.g., Waxman et al. 2007). – Due to the uncertainties in the model, and to the fact that existing analyses do not usually account for all of the observed radiation components, there is no consensus regarding this interpretation and various alternative models are being discussed, mostly involving the presence of relativistic jets (see, e.g., a recent discussion in Irwin and Chevalier (2016)).

References Ackermann M, Arcavi I, Baldini L, Ballet J, Barbiellini G, Bastieri D, Bellazzini R, Bissaldi E, Blandford RD, Bonino R, Bottacini E, Brandt TJ, Bregeon J, Bruel P, Buehler R, Buson S, Caliandro GA, Cameron RA, Caragiulo M, Caraveo PA, Cavazzuti E, Cecchi C, Charles E, Chekhtman A, Chiang J, Chiaro G, Ciprini S, Claus R, Cohen-Tanugi J, Cutini S, D’Ammando F, de Angelis A, de Palma F, Desiante R, Di Venere L, Drell PS, Favuzzi C, Fegan SJ, Franckowiak A, Funk S, Fusco P, Gal-Yam A, Gargano F, Gasparrini D, Giglietto N, Giordano F, Giroletti M, Glanzman T, Godfrey G, Grenier IA, Grove JE, Guiriec S, Harding AK, Hayashi K, Hewitt JW, Hill AB, Horan D, Jogler T, Jóhannesson G, Kocevski D, Kuss M, Larsson S, Lashner J, Latronico L, Li J, Li L, Longo F, Loparco F, Lovellette MN, Lubrano P, Malyshev D, Mayer M, Mazziotta MN, McEnery JE, Michelson PF, Mizuno T, Monzani ME, Morselli A, Murase K, Nugent P, Nuss E, Ofek E, Ohsugi T, Orienti M, Orlando E, Ormes JF, Paneque D, Pesce-Rollins M, Piron F, Pivato G, Rainò S, Rando R, Razzano M, Reimer A, Reimer O, Schulz A, Sgrò C, Siskind EJ, Spada F, Spandre G, Spinelli P, Suson DJ, Takahashi H, Thayer JB, Tibaldo L, Torres DF, Troja E, Vianello G, Werner M, Wood KS, Wood M (2015) ApJ 807:169. doi:10.1088/0004-637X/807/2/169 Arcavi I, Gal-Yam A, Yaron O, Sternberg A, Rabinak I, Waxman E, Kasliwal MM, Quimby RM, Ofek EO, Horesh A, Kulkarni SR, Filippenko AV, Silverman JM, Cenko SB, Li W, Bloom JS, Sullivan M, Nugent PE, Poznanski D, Gorbikov E, Fulton BJ, Howell DA, Bersier D, Riou A, Lamotte-Bailey S, Griga T, Cohen JG, Hachinger S, Polishook D, Xu D, Ben-Ami S, Manulis I, Walker ES, Maguire K, Pan YC, Matheson T, Mazzali PA, Pian E, Fox DB, Gehrels N, Law N, James P, Marchant JM, Smith RJ, Mottram CJ, Barnsley RM, Kandrashoff MT, Clubb KI (2011) ApJ 742:L18. doi:10.1088/2041-8205/742/2/L18 Balberg S, Loeb A (2011) MNRAS 414:1715. doi:10.1111/j.1365-2966.2011.18505.x Bersten MC, Benvenuto OG, Nomoto K, Ergon M, Folatelli G, Sollerman J, Benetti S, Botticella MT, Fraser M, Kotak R, Maeda K, Ochner P, Tomasella L (2012) ApJ 757:31. doi:10.1088/0004-637X/757/1/31 Bersten MC, Tanaka M, Tominaga N, Benvenuto OG, Nomoto K (2013) ApJ 767:143. doi:10.1088/0004-637X/767/2/143 Blandford RD, Payne DG (1981) MNRAS 194:1041. doi:10.1093/mnras/194.4.1041 Blinnikov SI, Eastman R, Bartunov OS, Popolitov VA, Woosley SE (1998) ApJ 496:454. doi:10.1086/305375 Blinnikov S, Lundqvist P, Bartunov O, Nomoto K, Iwamoto K (2000) ApJ 532:1132. doi:10.1086/308588 Bloom JS, Kasen D, Shen KJ, Nugent PE, Butler NR, Graham ML, Howell DA, Kolb U, Holmes S, Haswell CA, Burwitz V, Rodriguez J, Sullivan M (2012) ApJ 744:L17. doi:10.1088/2041-8205/744/2/L17 Bose S, Valenti S, Misra K, Pumo ML, Zampieri L, Sand D, Kumar B, Pastorello A, Sutaria F, Maccarone TJ, Kumar B, Graham ML, Howell DA, Ochner P, Chandola HC, Pandey SB (2015) MNRAS 450:2373. doi:10.1093/mnras/stv759 Budnik R, Katz B, Sagiv A, Waxman E (2010) ApJ 725:63. doi:10.1088/0004-637X/725/1/63 Burrows A (2013) Rev Mod Phys 85:245. doi:10.1103/RevModPhys.85.245

1008

E. Waxman and B. Katz

Calzavara AJ, Matzner CD (2004a) MNRAS 351:694. doi:10.1111/j.1365-2966.2004.07818.x Calzavara AJ, Matzner CD (2004b) MNRAS 351:694. doi:10.1111/j.1365-2966.2004.07818.x Campana S, Mangano V, Blustin AJ, Brown P, Burrows DN, Chincarini G, Cummings JR, Cusumano G, Della Valle M, Malesani D, Mészáros P, Nousek JA, Page M, Sakamoto T, Waxman E, Zhang B, Dai ZG, Gehrels N, Immler S, Marshall FE, Mason KO, Moretti A, O’Brien PT, Osborne JP, Page KL, Romano P, Roming PWA, Tagliaferri G, Cominsky LR, Giommi P, Godet O, Kennea JA, Krimm H, Angelini L, Barthelmy SD, Boyd PT, Palmer DM, Wells AA, White NE (2006) Nature 442:1008. doi:10.1038/nature04892 Cao Y, Kasliwal MM, Arcavi I, Horesh A, Hancock P, Valenti S, Cenko SB, Kulkarni SR, Gal-Yam A, Gorbikov E, Ofek EO, Sand D, Yaron O, Graham M, Silverman JM, Wheeler JC, Marion GH, Walker ES, Mazzali P, Howell DA, Li KL, Kong AKH, Bloom JS, Nugent PE, Surace J, Masci F, Carpenter J, Degenaar N, Gelino CR (2013) ApJ 775:L7. doi:10.1088/2041-8205/775/1/L7 Chandrasekhar S (1939) An introduction to the study of stellar structure. The University of Chicago Press, Chicago Chatzopoulos E, Wheeler JC, Vinko J (2012) ApJ 746:121. doi:10.1088/0004-637X/746/2/121 Chatzopoulos E, Wheeler JC, Vinko J, Horvath ZL, Nagy A (2013) ApJ 773:76. doi:10.1088/0004-637X/773/1/76 Chevalier RA (1982) ApJ 258:790. doi:10.1086/160126 Chevalier RA (1992) ApJ 394:599. doi:10.1086/171612 Chevalier RA, Fransson C (1994) ApJ 420:268. doi:10.1086/173557 Chevalier RA, Fransson C (2008) ApJ 683:L135. doi:10.1086/591522 Chevalier RA, Irwin CM (2011) ApJ 729:L6. doi:10.1088/2041-8205/729/1/L6 Chevalier RA, Irwin CM (2012) ApJ 747:L17. doi:10.1088/2041-8205/747/1/L17 Colgate SA (1968) Can J Phys Suppl 46:476 Colgate SA (1975) In: Bergman PG, Fenyves EJ, Motz L (eds) Seventh Texas symposium on relativistic astrophysics. Annals of the New York academy of sciences, vol 262, pp 34–46. doi:10.1111/j.1749-6632.1975.tb31418.x Corsi A, Ofek EO, Gal-Yam A, Frail DA, Poznanski D, Mazzali PA, Kulkarni SR, Kasliwal MM, Arcavi I, Ben-Ami S, Cenko SB, Filippenko AV, Fox DB, Horesh A, Howell JL, Kleiser IKW, Nakar E, Rabinak I, Sari R, Silverman JM, Xu D, Bloom JS, Law NM, Nugent PE, Quimby RM (2012) ApJ 747:L5. doi:10.1088/2041-8205/747/1/L5 Corsi A, Ofek EO, Gal-Yam A, Frail DA, Kulkarni SR, Fox DB, Kasliwal MM, Sullivan M, Horesh A, Carpenter J, Maguire K, Arcavi I, Cenko SB, Cao Y, Mooley K, Pan YC, Sesar B, Sternberg A, Xu D, Bersier D, James P, Bloom JS, Nugent PE (2014) ApJ 782:42. doi:10.1088/0004-637X/782/1/42 Dessart L, Hillier DJ (2010) MNRAS 405:2141. doi:10.1111/j.1365-2966.2010.16611.x Dessart L, Hillier DJ, Waldman R, Livne E, Blondin S (2010) MNRAS 426:L76. doi:10.1111/j.1745-3933.2012.01329.x Dexter J, Kasen D (2013) ApJ 772:30. doi:10.1088/0004-637X/772/1/30 Drout MR, Chornock R, Soderberg AM, Sanders NE, McKinnon R, Rest A, Foley RJ, Milisavljevic D, Margutti R, Berger E, Calkins M, Fong W, Gezari S, Huber ME, Kankare E, Kirshner RP, Leibler C, Lunnan R, Mattila S, Marion GH, Narayan G, Riess AG, Roth KC, Scolnic D, Smartt SJ, Tonry JL, Burgett WS, Chambers KC, Hodapp KW, Jedicke R, Kaiser N, Magnier EA, Metcalfe N, Morgan JS, Price PA, Waters C (2014) ApJ 794:23. doi:10.1088/0004-637X/794/1/23 Ensman L, Burrows A (1992) ApJ 393:742. doi:10.1086/171542 Epstein RI (1981) ApJ 244:L89. doi:10.1086/183486 Falk SW (1978) ApJ 225:L133. doi:10.1086/182810 Falk SW, Arnett WD (1973) ApJ 180:L65. doi:10.1086/181154 Falk SW, Arnett WD (1977) ApJS 33:515. doi:10.1086/190440 Foley RJ, Smith N, Ganeshalingam M, Li W, Chornock R, Filippenko AV (2007) ApJ 657:L105. doi:10.1086/513145 Fransson C, Ergon M, Challis PJ, Chevalier RA, France K, Kirshner RP, Marion GH, Milisavljevic D, Smith N, Bufano F, Friedman AS, Kangas T, Larsson J, Mattila S, Benetti S, Chornock R, Czekala I, Soderberg A, Sollerman J (2014) ApJ 797:118. doi:10.1088/0004-637X/797/2/118

36 Shock Breakout Theory

1009

Fraser M, Magee M, Kotak R, Smartt SJ, Smith KW, Polshaw J, Drake AJ, Boles T, Lee CH, Burgett WS, Chambers KC, Draper PW, Flewelling H, Hodapp KW, Kaiser N, Kudritzki RP, Magnier EA, Price PA, Tonry JL, Wainscoat RJ, Waters C (2013) ApJ 779:L8. doi:10.1088/2041-8205/779/1/L8 Galama TJ, Vreeswijk PM, van Paradijs J, Kouveliotou C, Augusteijn T, Böhnhardt H, Brewer JP, Doublier V, Gonzalez JF, Leibundgut B, Lidman C, Hainaut OR, Patat F, Heise J, in’t Zand J, Hurley K, Groot PJ, Strom RG, Mazzali PA, Iwamoto K, Nomoto K, Umeda H, Nakamura T, Young TR, Suzuki T, Shigeyama T, Koshut T, Kippen M, Robinson C, de Wildt P, Wijers RAMJ, Tanvir N, Greiner J, Pian E, Palazzi E, Frontera F, Masetti N, Nicastro L, Feroci M, Costa E, Piro L, Peterson BA, Tinney C, Boyle B, Cannon R, Stathakis R, Sadler E, Begam MC, Ianna P (1998) Nature 395:670. doi:10.1038/27150 Gall EEE, Polshaw J, Kotak R, Jerkstrand A, Leibundgut B, Rabinowitz D, Sollerman J, Sullivan M, Smartt SJ, Anderson JP, Benetti S, Baltay C, Feindt U, Fraser M, GonzálezGaitán S, Inserra C, Maguire K, McKinnon R, Valenti S, Young D (2015) A&A 582:A3. doi:10.1051/0004-6361/201525868 Gal-Yam A (2012) Science 337:927. doi:10.1126/science.1203601 Gal-Yam A, Kasliwal MM, Arcavi I, Green Y, Yaron O, Ben-Ami S, Xu D, Sternberg A, Quimby RM, Kulkarni SR, Ofek EO, Walters R, Nugent PE, Poznanski D, Bloom JS, Cenko SB, Filippenko AV, Li W, Silverman JM, Walker ES, Sullivan M, Maguire K, Howell DA, Mazzali PA, Frail DA, Bersier D, James PA, Akerlof CW, Yuan F, Law N, Fox DB, Gehrels N (2011) ApJ 736:159. doi:10.1088/0004-637X/736/2/159 Gandel’Man GM, Frank-Kamenetskii DA (1956) Sov Phys Dokl 1:223 Ganot N, Gal-Yam A, Ofek EO, Sagiv I, Waxman E, Lapid O, Kulkarni SR, Ben-Ami S, Kasliwal MM, Chelouche D, Rafter S, Behar E, Laor A, Poznanski D, Nakar U, Maoz D, Trakhtenbrot B, Neill JD, Barlow TA, Martin CD, Gezari S, Arcavi I, Bloom Js, Nugent PE, Sullivan M (2016) ApJ 820:57 Garnavich PM, Tucker BE, Rest A, Shaya EJ, Olling RP, Kasen D, Villar A (2016) ApJ 820:23. doi:10.3847/0004-637X/820/1/23 Gezari S, Dessart L, Basa S, Martin DC, Neill JD, Woosley SE, Hillier DJ, Bazin G, Forster K, Friedman PG, Le Du J, Mazure A, Morrissey P, Neff SG, Schiminovich D, Wyder TK (2008) ApJ 683:L131. doi:10.1086/591647 Gezari S, Rest A, Huber ME, Narayan G, Forster K, Neill JD, Martin DC, Valenti S, Smartt SJ, Chornock R, Berger E, Soderberg AM, Mattila S, Kankare E, Burgett WS, Chambers KC, Dombeck T, Grav T, Heasley JN, Hodapp KW, Jedicke R, Kaiser N, Kudritzki R, Luppino G, Lupton RH, Magnier EA, Monet DG, Morgan JS, Onaka PM, Price PA, Rhoads PH, Siegmund WA, Stubbs CW, Tonry JL, Wainscoat RJ, Waterson MF, Wynn-Williams CG (2010) ApJ 720:L77. doi:10.1088/2041-8205/720/1/L77 Gezari S, Jones DO, Sanders NE, Soderberg AM, Hung T, Heinis S, Smartt SJ, Rest A, Scolnic D, Chornock R, Berger E, Foley RJ, Huber ME, Price P, Stubbs CW, Riess AG, Kirshner RP, Smith K, Wood-Vasey WM, Schiminovich D, Martin DC, Burgett WS, Chambers KC, Flewelling H, Kaiser N, Tonry JL, Wainscoat R (2015) ApJ 804:28. doi:10.1088/0004-637X/804/1/28 Ginzburg S, Balberg S (2012) ApJ 757:178. doi:10.1088/0004-637X/757/2/178 Ginzburg S, Balberg S (2014) ApJ 780:18. doi:10.1088/0004-637X/780/1/18 González-Gaitán S, Tominaga N, Molina J, Galbany L, Bufano F, Anderson JP, Gutierrez C, Förster F, Pignata G, Bersten M, Howell DA, Sullivan M, Carlberg R, de Jaeger T, Hamuy M, Baklanov PV, Blinnikov SI (2015) MNRAS 451:2212. doi:10.1093/mnras/stv1097 Grassberg EK, Imshennik VS, Nadyozhin DK (1971) Ap&SS 10:28. doi:10.1007/BF00654604 Greiner J, Hartmann DH, Voges W, Boller T, Schwarz R, Zharikov SV (2000) A&A 353:998 Hillebrandt W, Kromer M, Röpke FK, Ruiter AJ (2013) Front Phys 8:116. doi:10.1007/s11467-013-0303-2 Howell DA, Kasen D, Lidman C, Sullivan M, Conley A, Astier P, Balland C, Carlberg RG, Fouchez D, Guy J, Hardin D, Pain R, Palanque-Delabrouille N, Perrett K, Pritchet CJ, Regnault N, Rich J, Ruhlmann-Kleider V (2013) ApJ 779:98. doi:10.1088/0004-637X/779/2/98

1010

E. Waxman and B. Katz

Im M, Choi C, Yoon SC, Kim JW, Ehgamberdiev SA, Monard LAG, Sung HI (2015) ApJS 221:22. doi:10.1088/0067-0049/221/1/22 Imshennik VS, Utrobin VP (1977) Sov Astron Lett 3:34 Inserra C, Smartt SJ, Jerkstrand A, Valenti S, Fraser M, Wright D, Smith K, Chen TW, Kotak R, Pastorello A, Nicholl M, Bresolin F, Kudritzki RP, Benetti S, Botticella MT, Burgett WS, Chambers KC, Ergon M, Flewelling H, Fynbo JPU, Geier S, Hodapp KW, Howell DA, Huber M, Kaiser N, Leloudas G, Magill L, Magnier EA, McCrum MG, Metcalfe N, Price PA, Rest A, Sollerman J, Sweeney W, Taddia F, Taubenberger S, Tonry JL, Wainscoat RJ, Waters C, Young D (2013) ApJ 770:128. doi:10.1088/0004-637X/770/2/128 Irwin CM, Chevalier RA (2016) MNRAS 460:1680 Janka HT (2012) Annu Rev Nucl Part Sci 62:407. doi:10.1146/annurev-nucl-102711-094901 Kaiser N, Aussel H, Burke BE, Boesgaard H, Chambers K, Chun MR, Heasley JN, Hodapp KW, Hunt B, Jedicke R, Jewitt D, Kudritzki R, Luppino GA, Maberry M, Magnier E, Monet DG, Onaka PM, Pickles AJ, Rhoads PHH, Simon T, Szalay A, Szapudi I, Tholen DJ, Tonry JL, Waterson M, Wick J (2002) In: Tyson JA, Wolff S (eds) Survey and other telescope technologies and discoveries. Proceedings of the SPIE, vol 4836, pp 154–164. doi:10.1117/12.457365 Kasen D, Bildsten L (2010) ApJ 717:245. doi:10.1088/0004-637X/717/1/245 Kasen D, Woosley SE, Heger A (2011) ApJ 734:102. doi:10.1088/0004-637X/734/2/102 Kasen D, Metzger BD, Bildsten L (2015) ArXiv e-prints Katz B, Budnik R, Waxman E (2010) ApJ 716:781. doi:10.1088/0004-637X/716/1/781 Katz B, Sapir N, Waxman E (2012) Death of massive stars. In: Proceedings of the IAU Symposium, vol 279, pp 274–281 Katz B, Sapir N, Waxman E (2012a) In: Death of massive stars: supernovae and gamma-ray bursts. IAU symposium, vol 279, pp 274–281. doi:10.1017/S174392131201304X Katz B, Sapir N, Waxman E (2012b) ApJ 747:147. doi:10.1088/0004-637X/747/2/147 Keller SC, Schmidt BP, Bessell MS, Conroy PG, Francis P, Granlund A, Kowald E, Oates AP, Martin-Jones T, Preston T, Tisserand P, Vaccarella A, Waterson MF (2007) PASA 24:1. doi:10.1071/AS07001 Kiewe M, Gal-Yam A, Arcavi I, Leonard DC, Emilio Enriquez J, Cenko SB, Fox DB, Moon DS, Sand DJ, Soderberg AM, CCCP T (2012) ApJ 744:10. doi:10.1088/0004-637X/744/1/10 Klein RI, Chevalier RA (1978) ApJ 223:L109. doi:10.1086/182740 Kleiser IKW, Poznanski D, Kasen D, Young TR, Chornock R, Filippenko AV, Challis P, Ganeshalingam M, Kirshner RP, Li W, Matheson T, Nugent PE, Silverman JM (2011) MNRAS 415:372. doi:10.1111/j.1365-2966.2011.18708.x Kowalski M (2015) J Phys Conf Ser 632(1):012039. doi:10.1088/1742-6596/632/1/012039 Kulkarni SR, Frail DA, Wieringa MH, Ekers RD, Sadler EM, Wark RM, Higdon JL, Phinney ES, Bloom JS (1998) Nature 395:663. doi:10.1038/27139 Langer N (2012) ARA&A 50:107. doi:10.1146/annurev-astro-081811-125534 Lasher G, Chan KL (1975) Bulletin of the American astronomical society, vol 7, p 505 Lasher GJ, Chan KL (1979) ApJ 230:742. doi:10.1086/157133 Law NM, Kulkarni SR, Dekany RG, Ofek EO, Quimby RM, Nugent PE, Surace J, Grillmair CC, Bloom JS, Kasliwal MM, Bildsten L, Brown T, Cenko SB, Ciardi D, Croner E, Djorgovski SG, van Eyken J, Filippenko AV, Fox DB, Gal-Yam A, Hale D, Hamam N, Helou G, Henning J, Howell DA, Jacobsen J, Laher R, Mattingly S, McKenna D, Pickles A, Poznanski D, Rahmer G, Rau A, Rosing W, Shara M, Smith R, Starr D, Sullivan M, Velur V, Walters R, Zolkower J (2009) PASP 121:1395. doi:10.1086/648598 Leahy D, Ouyed R (2008) MNRAS 387:1193. doi:10.1111/j.1365-2966.2008.13312.x Leloudas G, Chatzopoulos E, Dilday B, Gorosabel J, Vinko J, Gallazzi A, Wheeler JC, Bassett B, Fischer JA, Frieman JA, Fynbo JPU, Goobar A, Jelínek M, Malesani D, Nichol RC, Nordin J, Östman L, Sako M, Schneider DP, Smith M, Sollerman J, Stritzinger MD, Thöne CC, de Ugarte Postigo A (2012) A&A 541:A129. doi:10.1051/0004-6361/201118498 Levinson A, Bromberg O (2008) Phys Rev Lett 100(13):131101. doi:10.1103/PhysRevLett.100. 131101 Li LX (2007) MNRAS 375:240. doi:10.1111/j.1365-2966.2006.11286.x

36 Shock Breakout Theory

1011

LSST Science Collaboration, Abell PA, Allison J, Anderson SF, Andrew JR, Angel JRP, Armus L, Arnett D, Asztalos SJ, Axelrod TS et al (2009) ArXiv e-prints Madau P, Dickinson M (2014) ARA&A 52:415. doi:10.1146/annurev-astro-081811-125615 Maeda K, Tanaka M, Nomoto K, Tominaga N, Kawabata K, Mazzali PA, Umeda H, Suzuki T, Hattori T (2007) ApJ 666:1069. doi:10.1086/520054 Malesani D, Tagliaferri G, Chincarini G, Covino S, Della Valle M, Fugazza D, Mazzali PA, Zerbi FM, D’Avanzo P, Kalogerakos S, Simoncelli A, Antonelli LA, Burderi L, Campana S, Cucchiara A, Fiore F, Ghirlanda G, Goldoni P, Götz D, Mereghetti S, Mirabel IF, Romano P, Stella L, Minezaki T, Yoshii Y, Nomoto K (2004) ApJ 609:L5. doi:10.1086/422684 Maoz D, Mannucci F, Nelemans G (2014) ARA&A 52:107. doi:10.1146/annurev-astro-082812141031 Matzner CD, McKee CF (1999) ApJ 510:379. doi:10.1086/306571 Mauerhan JC, Smith N, Filippenko AV, Blanchard KB, Blanchard PK, Casper CFE, Cenko SB, Clubb KI, Cohen DP, Fuller KL, Li GZ, Silverman JM (2013) MNRAS 430:1801. doi:10.1093/mnras/stt009 Mauerhan J, Williams GG, Smith N, Smith PS, Filippenko AV, Hoffman JL, Milne P, Leonard DC, Clubb KI, Fox OD, Kelly PL (2014) MNRAS 442:1166. doi:10.1093/mnras/stu730 Mazzali PA, Deng J, Nomoto K, Sauer DN, Pian E, Tominaga N, Tanaka M, Maeda K, Filippenko AV (2006) Nature 442:1018. doi:10.1038/nature05081 Mazzali PA, Valenti S, Della Valle M, Chincarini G, Sauer DN, Benetti S, Pian E, Piran T, D’Elia V, Elias-Rosa N, Margutti R, Pasotti F, Antonelli LA, Bufano F, Campana S, Cappellaro E, Covino S, D’Avanzo P, Fiore F, Fugazza D, Gilmozzi R, Hunter D, Maguire K, Maiorano E, Marziani P, Masetti N, Mirabel F, Navasardyan H, Nomoto K, Palazzi E, Pastorello A, Panagia N, Pellizza LJ, Sari R, Smartt S, Tagliaferri G, Tanaka M, Taubenberger S, Tominaga N, Trundle C, Turatto M (2008) Science 321:1185. doi:10.1126/science.1158088 Mazzali PA, Sullivan M, Hachinger S, Ellis RS, Nugent PE, Howell DA, Gal-Yam A, Maguire K, Cooke J, Thomas R, Nomoto K, Walker ES (2014) MNRAS 439:1959. doi:10.1093/mnras/stu077 Merloni A, Predehl P, Becker W, Böhringer H, Boller T, Brunner H, Brusa M, Dennerl K, Freyberg M, Friedrich P, Georgakakis A, Haberl F, Hasinger G, Meidinger N, Mohr J, Nandra K, Rau A, Reiprich TH, Robrade J, Salvato M, Santangelo A, Sasaki M, Schwope A, Wilms J, t German eROSITA Consortium (2012) ArXiv e-prints Metzger BD, Margalit B, Kasen D, Quataert E (2015) MNRAS 454:3311. doi:10.1093/mnras/ stv2224 Mihalas D, Mihalas BW (1984) Foundations of radiation hydrodynamics. Oxford University Press, New York Miller AA, Chornock R, Perley DA, Ganeshalingam M, Li W, Butler NR, Bloom JS, Smith N, Modjaz M, Poznanski D, Filippenko AV, Griffith CV, Shiode JH, Silverman JM (2009) ApJ 690:1303. doi:10.1088/0004-637X/690/2/1303 Modjaz M, Li W, Butler N, Chornock R, Perley D, Blondin S, Bloom JS, Filippenko AV, Kirshner RP, Kocevski D, Poznanski D, Hicken M, Foley RJ, Stringfellow GS, Berlind P, Barrado y Navascues D, Blake CH, Bouy H, Brown WR, Challis P, Chen H, de Vries WH, Dufour P, Falco E, Friedman A, Ganeshalingam M, Garnavich P, Holden B, Illingworth G, Lee N, Liebert J, Marion GH, Olivier SS, Prochaska JX, Silverman JM, Smith N, Starr D, Steele TN, Stockton A, Williams GG, Wood-Vasey WM (2009) ApJ 702:226. doi:10.1088/0004-637X/702/1/226 Moriya TJ, Maeda K (2014) ApJ 790:L16. doi:10.1088/2041-8205/790/2/L16 Moriya T, Tominaga N, Blinnikov SI, Baklanov PV, Sorokina EI (2011) MNRAS 415:199. doi:10.1111/j.1365-2966.2011.18689.x Moriya TJ, Blinnikov SI, Tominaga N, Yoshida N, Tanaka M, Maeda K, Nomoto K (2013a) MNRAS 428:1020. doi:10.1093/mnras/sts075 Moriya TJ, Blinnikov SI, Baklanov PV, Sorokina EI, Dolgov AD (2013) MNRAS 430:1402. doi:10.1093/mnras/stt011 Moriya TJ, Maeda K, Taddia F, Sollerman J, Blinnikov SI, Sorokina EI (2014) MNRAS 439:2917. doi:10.1093/mnras/stu163

1012

E. Waxman and B. Katz

Murase K, Thompson TA, Lacki BC, Beacom JF (2011) PRD 84(4):043003. doi:10.1103/ PhysRevD.84.043003 Murase K, Thompson TA, Ofek EO (2014) MNRAS 440:2528. doi:10.1093/mnras/stu384 Nakar E (2015) ApJ 807:172. doi:10.1088/0004-637X/807/2/172 Nakar E, Piro AL (2014) ApJ 788:193. doi:10.1088/0004-637X/788/2/193 Nakar E, Sari R (2010) ApJ 725:904. doi:10.1088/0004-637X/725/1/904 Nakar E, Sari R (2012) ApJ 747:88. doi:10.1088/0004-637X/747/2/88 Nicholl M, Smartt SJ (2016) MNRAS 457:L79 Nicholl M, Smartt SJ, Jerkstrand A, Inserra C, McCrum M, Kotak R, Fraser M, Wright D, Chen TW, Smith K, Young DR, Sim SA, Valenti S, Howell DA, Bresolin F, Kudritzki RP, Tonry JL, Huber ME, Rest A, Pastorello A, Tomasella L, Cappellaro E, Benetti S, Mattila S, Kankare E, Kangas T, Leloudas G, Sollerman J, Taddia F, Berger E, Chornock R, Narayan G, Stubbs CW, Foley RJ, Lunnan R, Soderberg A, Sanders N, Milisavljevic D, Margutti R, Kirshner RP, Elias-Rosa N, Morales-Garoffolo A, Taubenberger S, Botticella MT, Gezari S, Urata Y, Rodney S, Riess AG, Scolnic D, Wood-Vasey WM, Burgett WS, Chambers K, Flewelling HA, Magnier EA, Kaiser N, Metcalfe N, Morgan J, Price PA, Sweeney W, Waters C (2013) Nature 502:346. doi:10.1038/nature12569 Nicholl M, Smartt SJ, Jerkstrand A, Sim SA, Inserra C, Anderson JP, Baltay C, Benetti S, Chambers K, Chen TW, Elias-Rosa N, Feindt U, Flewelling HA, Fraser M, Gal-Yam A, Galbany L, Huber ME, Kangas T, Kankare E, Kotak R, Krühler T, Maguire K, McKinnon R, Rabinowitz D, Rostami S, Schulze S, Smith KW, Sullivan M, Tonry JL, Valenti S, Young DR (2015) ApJ 807:L18. doi:10.1088/2041-8205/807/1/L18 Nugent PE, Sullivan M, Cenko SB, Thomas RC, Kasen D, Howell DA, Bersier D, Bloom JS, Kulkarni SR, Kandrashoff MT, Filippenko AV, Silverman JM, Marcy GW, Howard AW, Isaacson HT, Maguire K, Suzuki N, Tarlton JE, Pan YC, Bildsten L, Fulton BJ, Parrent JT, Sand D, Podsiadlowski P, Bianco FB, Dilday B, Graham ML, Lyman J, James P, Kasliwal MM, Law NM, Quimby RM, Hook IM, Walker ES, Mazzali P, Pian E, Ofek EO, Gal-Yam A, Poznanski D (2011) Nature 480:344. doi:10.1038/nature10644 Ofek EO, Rabinak I, Neill JD, Arcavi I, Cenko SB, Waxman E, Kulkarni SR, Gal-Yam A, Nugent PE, Bildsten L, Bloom JS, Filippenko AV, Forster K, Howell DA, Jacobsen J, Kasliwal MM, Law N, Martin C, Poznanski D, Quimby RM, Shen KJ, Sullivan M, Dekany R, Rahmer G, Hale D, Smith R, Zolkower J, Velur V, Walters R, Henning J, Bui K, McKenna D (2010) ApJ 724:1396. doi:10.1088/0004-637X/724/2/1396 Ofek EO, Sullivan M, Cenko SB, Kasliwal MM, Gal-Yam A, Kulkarni SR, Arcavi I, Bildsten L, Bloom JS, Horesh A, Howell DA, Filippenko AV, Laher R, Murray D, Nakar E, Nugent PE, Silverman JM, Shaviv NJ, Surace J, Yaron O (2013a) Nature 494:65. doi:10.1038/nature11877 Ofek EO, Fox D, Cenko SB, Sullivan M, Gnat O, Frail DA, Horesh A, Corsi A, Quimby RM, Gehrels N, Kulkarni SR, Gal-Yam A, Nugent PE, Yaron O, Filippenko AV, Kasliwal MM, Bildsten L, Bloom JS, Poznanski D, Arcavi I, Laher RR, Levitan D, Sesar B, Surace J (2013b) ApJ 763:42. doi:10.1088/0004-637X/763/1/42 Ofek EO, Sullivan M, Shaviv NJ, Steinbok A, Arcavi I, Gal-Yam A, Tal D, Kulkarni SR, Nugent PE, Ben-Ami S, Kasliwal MM, Cenko SB, Laher R, Surace J, Bloom JS, Filippenko AV, Silverman JM, Yaron O (2014a) ApJ 789:104. doi:10.1088/0004-637X/789/2/104 Ofek EO, Arcavi I, Tal D, Sullivan M, Gal-Yam A, Kulkarni SR, Nugent PE, Ben-Ami S, Bersier D, Cao Y, Cenko SB, De Cia A, Filippenko AV, Fransson C, Kasliwal MM, Laher R, Surace J, Quimby R, Yaron O (2014b) ApJ 788:154. doi:10.1088/0004-637X/788/2/154 Ofek EO, Zoglauer A, Boggs SE, Barriére NM, Reynolds SP, Fryer CL, Harrison FA, Cenko SB, Kulkarni SR, Gal-Yam A, Arcavi I, Bellm E, Bloom JS, Christensen F, Craig WW, Even W, Filippenko AV, Grefenstette B, Hailey CJ, Laher R, Madsen K, Nakar E, Nugent PE, Stern D, Sullivan M, Surace J, Zhang WW (2014c) ApJ 781:42. doi:10.1088/0004-637X/781/1/42 Ouyed R, Kostka M, Koning N, Leahy DA, Steffen W (2012) MNRAS 423:1652. doi:10.1111/j.1365-2966.2012.20986.x Pastorello A, Smartt SJ, Mattila S, Eldridge JJ, Young D, Itagaki K, Yamaoka H, Navasardyan H, Valenti S, Patat F, Agnoletto I, Augusteijn T, Benetti S, Cappellaro E, Boles T, Bonnet-Bidaud

36 Shock Breakout Theory

1013

JM, Botticella MT, Bufano F, Cao C, Deng J, Dennefeld M, Elias-Rosa N, Harutyunyan A, Keenan FP, Iijima T, Lorenzi V, Mazzali PA, Meng X, Nakano S, Nielsen TB, Smoker JV, Stanishev V, Turatto M, Xu D, Zampieri L (2007) Nature 447:829. doi:10.1038/nature05825 Pastorello A, Pumo ML, Navasardyan H, Zampieri L, Turatto M, Sollerman J, Taddia F, Kankare E, Mattila S, Nicolas J, Prosperi E, San Segundo Delgado A, Taubenberger S, Boles T, Bachini M, Benetti S, Bufano F, Cappellaro E, Cason AD, Cetrulo G, Ergon M, Germany L, Harutyunyan A, Howerton S, Hurst GM, Patat F, Stritzinger M, Strolger LG, Wells W (2012) A&A 537:A141. doi:10.1051/0004-6361/201118112 Pastorello A, Cappellaro E, Inserra C, Smartt SJ, Pignata G, Benetti S, Valenti S, Fraser M, Takáts K, Benitez S, Botticella MT, Brimacombe J, Bufano F, Cellier-Holzem F, Costado MT, Cupani G, Curtis I, Elias-Rosa N, Ergon M, Fynbo JPU, Hambsch FJ, Hamuy M, Harutyunyan A, Ivarson KM, Kankare E, Martin JC, Kotak R, LaCluyze AP, Maguire K, Mattila S, Maza J, McCrum M, Miluzio M, Norgaard-Nielsen HU, Nysewander MC, Ochner P, Pan YC, Pumo ML, Reichart DE, Tan TG, Taubenberger S, Tomasella L, Turatto M, Wright D (2013) ApJ 767:1. doi:10.1088/0004-637X/767/1/1 Pian E, Mazzali PA, Masetti N, Ferrero P, Klose S, Palazzi E, Ramirez-Ruiz E, Woosley SE, Kouveliotou C, Deng J, Filippenko AV, Foley RJ, Fynbo JPU, Kann DA, Li W, Hjorth J, Nomoto K, Patat F, Sauer DN, Sollerman J, Vreeswijk PM, Guenther EW, Levan A, O’Brien P, Tanvir NR, Wijers RAMJ, Dumas C, Hainaut O, Wong DS, Baade D, Wang L, Amati L, Cappellaro E, Castro-Tirado AJ, Ellison S, Frontera F, Fruchter AS, Greiner J, Kawabata K, Ledoux C, Maeda K, Møller P, Nicastro L, Rol E, Starling R (2006) Nature 442:1011. doi:10.1038/nature05082 Piro AL (2015) ApJ 808:L51. doi:10.1088/2041-8205/808/2/L51 Piro AL, Nakar E (2013) ApJ 769:67. doi:10.1088/0004-637X/769/1/67 Piro AL, Nakar E (2014) ApJ 784:85. doi:10.1088/0004-637X/784/1/85 Piro AL, Chang P, Weinberg NN (2010) ApJ 708:598. doi:10.1088/0004-637X/708/1/598 Quimby RM, Aldering G, Wheeler JC, Höflich P, Akerlof CW, Rykoff ES (2007) ApJ 668:L99. doi:10.1086/522862 Rabinak I, Waxman E (2011) ApJ 728:63. doi:10.1088/0004-637X/728/1/63 Rabinak I, Livne E, Waxman E (2012) ApJ 757:35. doi:10.1088/0004-637X/757/1/35 Rau A, Kulkarni SR, Law NM, Bloom JS, Ciardi D, Djorgovski GS, Fox DB, Gal-Yam A, Grillmair CC, Kasliwal MM, Nugent PE, Ofek EO, Quimby RM, Reach WT, Shara M, Bildsten L, Cenko SB, Drake AJ, Filippenko AV, Helfand DJ, Helou G, Howell DA, Poznanski D, Sullivan M (2009) PASP 121:1334. doi:10.1086/605911 Roth N, Kasen D (2015) ApJS 217:9. doi:10.1088/0067-0049/217/1/9 Rubin A, Gal-Yam A, De Cia A, Horesh A, Khazov D, Ofek EO, Kulkarni SR, Arcavi I, Manulis I, Yaron O, Vreeswijk P, Kasliwal MM, Ben-Ami S, Perley DA, Cao Y, Cenko SB, Rebbapragada UD, Wo´zniak PR, Filippenko AV, Clubb KI, Nugent PE, Pan YC, Badenes C, Howell DA, Valenti S, Sand D, Sollerman J, Johansson J, Leonard DC, Horst JC, Armen SF, Fedrow JM, Quimby RM, Mazzali P, Pian E, Sternberg A, Matheson T, Sullivan M, Maguire K, Lazarevic S (2016) ApJ 820:33 Sagiv I, Gal-Yam A, Ofek EO, Waxman E, Aharonson O, Kulkarni SR, Nakar E, Maoz D, Trakhtenbrot B, Phinney ES, Topaz J, Beichman C, Murthy J, Worden SP (2014) AJ 147:79. doi:10.1088/0004-6256/147/4/79 Sakurai A (1960) Commun Pure Appl Math 13:353. doi:10.1002/cpa.3160130303 Sapir N, Halbertal D (2014) ApJ 796:145. doi:10.1088/0004-637X/796/2/145 Sapir N, Katz B, Waxman E (2011) ApJ 742:36. doi:10.1088/0004-637X/742/1/36 Sapir N, Katz B, Waxman E (2013) ApJ 774:79. doi:10.1088/0004-637X/774/1/79 Schawinski K, Justham S, Wolf C, Podsiadlowski P, Sullivan M, Steenbrugge KC, Bell T, Röser HJ, Walker ES, Astier P, Balam D, Balland C, Carlberg R, Conley A, Fouchez D, Guy J, Hardin D, Hook I, Howell DA, Pain R, Perrett K, Pritchet C, Regnault N, Yi SK (2008) Science 321:223. doi:10.1126/science.1160456 Seaton MJ (2005) MNRAS 362:L1. doi:10.1111/j.1365-2966.2005.00019.x Sedov LI (1959) Similarity and dimensional methods in mechanics. Academic Press, New York

1014

E. Waxman and B. Katz

Shappee B, Prieto J, Stanek KZ, Kochanek CS, Holoien T, Jencson J, Basu U, Beacom JF, Szczygiel D, Pojmanski G, Brimacombe J, Dubberley M, Elphick M, Foale S, Hawkins E, Mullins D, Rosing W, Ross R, Walker Z (2014) American astronomical society meeting abstracts, vol 223, p 236.03 Smartt SJ (2009) ARA&A 47:63. doi:10.1146/annurev-astro-082708-101737 Smartt SJ, Eldridge JJ, Crockett RM, Maund JR (2009) MNRAS 395:1409. doi:10.1111/j.1365-2966.2009.14506.x Smith N, McCray R (2007) ApJ 671:L17. doi:10.1086/524681 Smith N, Li W, Foley RJ, Wheeler JC, Pooley D, Chornock R, Filippenko AV, Silverman JM, Quimby R, Bloom JS, Hansen C (2007) ApJ 666:1116. doi:10.1086/519949 Smith N, Chornock R, Silverman JM, Filippenko AV, Foley RJ (2010) ApJ 709:856. doi:10.1088/0004-637X/709/2/856 Smith M, Sullivan M, D’Andrea CB, Castander FJ, Casas R, Prajs S, Papadopoulos A, Nichol RC, Karpenka NV, Bernard SR, Brown P, Cartier R, Cooke J, Curtin C, Davis TM, Finley DA, Foley RJ, Gal-Yam A, Goldstein DA, González-Gaitán S, Gupta RR, Howell DA, Inserra C, Kessler R, Lidman C, Marriner J, Nugent P, Pritchard TA, Sako M, Smartt S, Smith RC, Spinka H, Wolf RC, Zentano A, Abbott TMC, Benoit-Lévy A, Brooks D, Buckley-Geer E, Carnero Rosell A, Carrasco Kind M, Carretero J, Crocce M, Cunha CE, da Costa LN, Desai S, Diehl HT, Doel P, Estrada J, Evrard AE, Flaugher B, Fosalba P, Frieman J, Gerdes DW, Gruen D, Gruendl RA, James DJ, Kuehn K, Kuropatkin N, Lahav O, Li TS, Marshall JL, Martini P, Miller CJ, Miquel R, Ogando R, Plazas AA, Romer AK, Roodman A, Rykoff ES, Sanchez E, Scarpine V, Schubnell M, Sevilla-Noarbe I, Soares-Santos M, Sobreira F, Suchyta E, Swanson MEC, Tarle G, Thomas RC, Walker AR, Wester W (2016) ApJ 818:L8 Soderberg AM, Kulkarni SR, Nakar E, Berger E, Cameron PB, Fox DB, Frail D, Gal-Yam A, Sari R, Cenko SB, Kasliwal M, Chevalier RA, Piran T, Price PA, Schmidt BP, Pooley G, Moon DS, Penprase BE, Ofek E, Rau A, Gehrels N, Nousek JA, Burrows DN, Persson SE, McCarthy PJ (2006) Nature 442:1014. doi:10.1038/nature05087 Soderberg AM, Berger E, Page KL, Schady P, Parrent J, Pooley D, Wang XY, Ofek EO, Cucchiara A, Rau A, Waxman E, Simon JD, Bock DCJ, Milne PA, Page MJ, Barentine JC, Barthelmy SD, Beardmore AP, Bietenholz MF, Brown P, Burrows A, Burrows DN, Byrngelson G, Cenko SB, Chandra P, Cummings JR, Fox DB, Gal-Yam A, Gehrels N, Immler S, Kasliwal M, Kong AKH, Krimm HA, Kulkarni SR, Maccarone TJ, Mészáros P, Nakar E, O’Brien PT, Overzier RA, de Pasquale M, Racusin J, Rea N, York DG (2008) Nature 453:469. doi:10.1038/nature06997 Starling RLC, Wiersema K, Levan AJ, Sakamoto T, Bersier D, Goldoni P, Oates SR, Rowlinson A, Campana S, Sollerman J, Tanvir NR, Malesani D, Fynbo JPU, Covino S, D’Avanzo P, O’Brien PT, Page KL, Osborne JP, Vergani SD, Barthelmy S, Burrows DN, Cano Z, Curran PA, de Pasquale M, D’Elia V, Evans PA, Flores H, Fruchter AS, Garnavich P, Gehrels N, Gorosabel J, Hjorth J, Holland ST, van der Horst AJ, Hurkett CP, Jakobsson P, Kamble AP, Kouveliotou C, Kuin NPM, Kaper L, Mazzali PA, Nugent PE, Pian E, Stamatikos M, Thöne CC, Woosley SE (2011) MNRAS 411:2792. doi:10.1111/j.1365-2966.2010.17879.x Svirski G, Nakar E (2014a) ApJ 788:113. doi:10.1088/0004-637X/788/2/113 Svirski G, Nakar E (2014b) ApJ 788:L14. doi:10.1088/2041-8205/788/1/L14 Svirski G, Nakar E, Sari R (2012) ApJ 759:108. doi:10.1088/0004-637X/759/2/108 Taddia F, Stritzinger MD, Sollerman J, Phillips MM, Anderson JP, Boldt L, Campillay A, Castellón S, Contreras C, Folatelli G, Hamuy M, Heinrich-Josties E, Krzeminski W, Morrell N, Burns CR, Freedman WL, Madore BF, Persson SE, Suntzeff NB (2013) A&A 555:A10. doi:10.1051/0004-6361/201321180 Taddia F, Sollerman J, Fremling C, Migotto K, Gal-Yam A, Armen S, Duggan G, Ergon M, Filippenko AV, Fransson C, Hosseinzadeh G, Kasliwal MM, Laher RR, Leloudas G, Leonard DC, Lunnan R, Masci FJ, Moon DS, Silverman JM, Wozniak PR (2016) A&A 588:A5. doi:10.1051/0004-6361/201527811 Tan JC, Matzner CD, McKee CF (2001) ApJ 551:946. doi:10.1086/320245

36 Shock Breakout Theory

1015

Tanaka M, Tominaga N, Nomoto K, Valenti S, Sahu DK, Minezaki T, Yoshii Y, Yoshida M, Anupama GC, Benetti S, Chincarini G, Della Valle M, Mazzali PA, Pian E (2009) ApJ 692:1131. doi:10.1088/0004-637X/692/2/1131 Taylor G (1950) Proc R Soc London Ser A 201:175. doi:10.1098/rspa.1950.0050 Tolstov AG, Blinnikov SI, Nadyozhin DK (2013) MNRAS 429:3181. doi:10.1093/mnras/sts577 Tominaga N, Morokuma T, Blinnikov SI, Baklanov P, Sorokina EI, Nomoto K (2011) ApJS 193:20. doi:10.1088/0067-0049/193/1/20 Utrobin VP (2007) A&A 461:233. doi:10.1051/0004-6361:20066078 Valenti S, Sand D, Pastorello A, Graham ML, Howell DA, Parrent JT, Tomasella L, Ochner P, Fraser M, Benetti S, Yuan F, Smartt SJ, Maund JR, Arcavi I, Gal-Yam A, Inserra C, Young D (2014) MNRAS 438:L101. doi:10.1093/mnrasl/slt171 Van Dyk SD, Zheng W, Fox OD, Cenko SB, Clubb KI, Filippenko AV, Foley RJ, Miller AA, Smith N, Kelly PL, Lee WH, Ben-Ami S, Gal-Yam A (2014) AJ 147:37. doi:10.1088/0004-6256/147/2/37 Vikhlinin A (1998) ApJ 505:L123. doi:10.1086/311606 Von Neumann J (1947) Blast waves. Los Alamos science laboratory technology series, vol 7. Los Alamos Waxman E, Mészáros P, Campana S (2007) ApJ 667:351. doi:10.1086/520715 Weaver TA (1976) ApJS 32:233. doi:10.1086/190398 Wheeler JC, Barker E, Benjamin R, Boisseau J, Clocchiatti A, de Vaucouleurs G, Gaffney N, Harkness RP, Khokhlov AM, Lester DF, Smith BJ, Smith VV, Tomkin J (1993) ApJ 417:L71. doi:10.1086/187097 Woosley SE (2010) ApJ 719:L204. doi:10.1088/2041-8205/719/2/L204 Woosley SE, Eastman RG, Weaver TA, Pinto PA (1994) ApJ 429:300. doi:10.1086/174319 Woosley SE, Blinnikov S, Heger A (2007) Nature 450:390. doi:10.1038/nature06333 Xie F, Zhang J, Song LM, Xiong SL, Guan J (2015) Ap&SS 360:13. doi:10.1007/s10509-015-2559-1 XMM-Newton Users Handbook (2016) Issue 2.13.1, 2016 (ESA: XMM-Newton SOC) Yuan W, Zhang C, Feng H, Zhang SN, Ling ZX, Zhao D, Deng J, Qiu Y, Osborne JP, O’Brien P, Willingale R, Lapington J, Fraser GW, The Einstein Probe Team (2015) ArXiv e-prints Zheng W, Silverman JM, Filippenko AV, Kasen D, Nugent PE, Graham M, Wang X, Valenti S, Ciabattari F, Kelly PL, Fox OD, Shivvers I, Clubb KI, Cenko SB, Balam D, Howell DA, Hsiao E, Li W, Marion GH, Sand D, Vinko J, Wheeler JC, Zhang J (2013) ApJ 778:L15. doi:10.1088/2041-8205/778/1/L15 Zirakashvili VN, Ptuskin VS (2016) APh 78:28

Introduction to Supernova Polarimetry

37

Ferdinando Patat

If light is man’s most useful tool, polarized light is the quintessence of utility. William Shurcliff Polarized Light: Production and Use (Harvard University Press, 1962)

Abstract

The main purpose of this chapter is to help the reader understand an observational paper on supernova polarimetry, write an observing proposal, and plan photometric observations and reduce the resulting data. Although it focuses on the specific case of supernovae, the concepts presented here are applicable to other astrophysical cases. After introducing the mathematical formalism in the context of classical wave theory, the chapter follows with a description of the Stokes parameters and their physical meaning. It then presents the basics of dichroism, phase retardation, and birefringence to provide the required framework for understanding the workings of astronomical polarimeters. The discussion mainly deals with linear polarimetry, but circular polarimetry is also briefly treated. After illustrating the main instrumental problems, the chapter goes through the basic steps of data reductions and error estimates. The rest of the chapter is dedicated to a summary of the findings in the supernova field, by going through the polarimetric properties of the main sub-types.

Contents 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Sources of Polarization in the Astrophysical Context . . . . . . . . . . . . . . . . . . . . . . 1.2 Mathematical Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1018 1018 1019

F. Patat () European Southern Observatory (ESO), Garching, Germany e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_110

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1.3 Stokes Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Introducing Mueller Matrix Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Dichroism and Linear Polarizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Phase Retardation and Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Measuring Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Linear Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Circular Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Dual-Beam Polarimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Wollaston Prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Normalized Flux Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Instrumental Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 HWP Chromatism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Observations, Calibrations, and Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Polarimetric Standard Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Flat Fielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Wavelength Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Uncertainties and Signal-to-Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Polarimetry of Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 A Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 A SN Polarization Primer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 The Ubiquitous Interstellar Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 The Q-U Plane and the Dominant Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 The Polarimetric SN Zoo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 SN 1993J and Type IIb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Type II-P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Type IIn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Type Ib/c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Thermonuclear SNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1020 1023 1025 1025 1027 1027 1028 1029 1029 1030 1032 1032 1033 1033 1034 1034 1035 1036 1036 1037 1039 1040 1043 1043 1043 1044 1044 1044 1045 1047 1048 1048

Introduction

Linear polarimetry of unresolved sources is the most powerful and direct tool to probe asymmetries in the emitting material. The photodisk of a Type Ia supernova (SN) at maximum light has a diameter of about 100 AU (i.e., 1015 cm). At the distance of SN 2014J, one of the closest Type Ia ever observed, this subtends an angle of about 9 as. This is well beyond the capability of any existing and foreseeable interferometric instrument. Therefore, although interferometry may one day allow us to observe details on the photosphere of a SN, this will probably take quite a long time (or require a very nearby event).

1.1

Sources of Polarization in the Astrophysical Context

A monochromatic light wave is always totally linearly polarized, meaning that there is a unique plane of oscillation. However, when one is to consider the superposition of all wavefunctions describing a packet of photons randomly emitted by a source,

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the polarizations of the single waves cancel out, leading to a null net polarization. The vast majority of astrophysical sources emit unpolarized light, and polarization is acquired through the following main mechanisms. 1. 2. 3. 4. 5. 6.

scattering on electrons (Thomson, e.g., in the Solar Corona) scattering on molecules (Rayleigh, e.g., Earth’s atmosphere) scattering on small grains (Mie, e.g., light echoes or reflection nebulae) resonant scattering (affects spectral lines only, e.g., Quasars) dichroic absorption of magnetically aligned grains (e.g., interstellar dust) strong magnetic fields (circular polarization, e.g., peculiar stars)

In general, Thomson scattering on free electrons is the dominant polarizing mechanism in SN, and it produces linear polarization perpendicular to the scattering plane.

1.2

Mathematical Formalism

Although polarization can be described using quantum mechanics, its description in terms of classical wave theory is better suited for the purposes of this chapter. In this context, the monochromatic plane wave solution that one obtains solving Maxwell equations can be written as   z Ex D Ex0 cos !t  2 C ˚x    z 0 Ey D Ey cos !t  2 C ˚y  where ! is the frequency, t is time,  is the wavelength, and Ex and Ey are the components of the electric field measured on the plane perpendicular to the propagation direction, which takes place along the z-axis. These two equations can be combined to give the expression: !2  2 Ey Ex Ex Ey C  2 0 0 cos.˚y  ˚x / D sin2 .˚y  ˚x / Ex0 Ey0 Ex Ex which describes an ellipse. If one applies the following coordinates rotation, Ex D Ex0 cos   Ey0 sin  Ey D Ex0 sin  C Ey0 cos  the polarization ellipse can be written in its canonical form: 

Ex0 a

2 C

Ey0 b

!2 D1

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where 2

2

a2 D Ex0 sin2   Ex0 Ey0 sin.˚y  ˚x / sin 2 C Ey0 cos2  2

2

b 2 D Ex0 cos2  C Ex0 Ey0 sin.˚y  ˚x / sin 2 C Ey0 sin2  in which: tan 2 D 2 and

Ex0 Ey0 Ex02  Ey02

cos.˚y  ˚x /

(1)

 2  2 a2 C b 2 D Ex0 C Ey0

One can show that ˙ab D Ex0 Ey0 sin.˚y ˚x /, where the C and  signs indicate right- and left-handedness, respectively. The above relations also imply that: ˙

Ex0 Ey0 2ab D 2 sin.˚y  ˚x / a2 C b 2 Ex02 C Ey02

(2)

Equations 1 and 2 define all ellipsometric parameters, and lead to the definition of the Stokes Parameters.

1.3

Stokes Parameters

The Stokes parameters were named after G. G. Stokes, who first introduced them in 1852. They are defined as follows. 2

2

2

2

I D Ex0 C Ey0 Q D Ex0  Ey0

U D 2Ex0 Ey0 cos.˚y  ˚x / V D 2Ex0 Ey0 sin.˚y  ˚x / All Stokes parameters have the dimensions of intensity. The meaning of the first parameter (I D a2 C b 2 ) is obvious: it is the modulus of the vector describing the electric field, and this is why it is called Intensity. The meanings of Q, U , and V are less obvious. A first hint is obtained comparing their definitions to Equations 1 and 2, which give: U D tan 2 Q V 2ab D˙ 2 I a C b2

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These expressions establish the relation between the Stokes parameters and the ellipsometric parameters. Whereast the ratio U =Q gives the azimuthal orientation of the polarization ellipsoid, V =I is related to its shape (and its handedness). From the above, it is clear that Q expresses the horizontal preference (U = 0 implies  = 0), and U expresses the +45ı preference (Q D 0 implies  = +45ı ). Finally, V indicates the right-handed circular preference (V = 1 implies a = b). From their definition one also has that: V D tan.˚y  ˚x / U implying that the circular polarization is related to a phase shift between the x and y components of the electric field. When V = 0 the electric field oscillates on a plane whose orientation  is constant in time: under these circumstances the beam is defined as fully linearly polarized. This is why Q and U completely define the linear polarization, whereas V defines the circular polarization. For a generic combination of incoherent waves (i.e., all having different phases), it is always Q2 CU 2 CV 2 I 2 , where the equality sign only holds for a monochromatic coherent wave. The Stokes parameters fully describe the polarization state of a light beam, regardless of its partial/total polarization and irrespective of its spectrum (monochromatic vs. polychromatic). The quadridimensional vector that has the Stokes parameters as components is called the Stokes vector, and is often indicated as SfI; Q; U; V g. Stokes vectors are additive so that, for instance, the polarization status of a beam resulting from the sum of two beams is described by the sum of their Stokes vectors. This is true only if there is no phase correlation between the two beams, which otherwise need to be treated using the Jones vectors (but this is not discussed here). The link between Stokes parameters and observables becomes clearer with some further algebra. After putting tan  D ˙b=a, one can show that: cos 2 D

a2  b 2 a2 C b 2

Because it is also: 2

sin 2 D cos 2 D

2

Ex0  Ey0 a2  b 2 2Ex0 Ey0 a2  b 2

cos.˚x  ˚y /

the Stokes parameters Q, U , and V can be rewritten as Q D cos 2 cos 2 I U D cos 2 sin 2 I V D sin 2 I

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Fig. 1 The Poincaré sphere for fully polarized light

which allow a graphic representation of fully polarized light on the so-called Poincaré sphere. The intensity normalized parameters are also called normalized Stokes parameters, and the resulting vector is dubbed a normalized Stokes vector. N UN , VN (by definition it is IN D 1). It is important to note that We indicate them as Q, normalized Stokes vectors are NOT additive. For fully polarized light, all polarization states can be represented by points on the Poincaré sphere surface. Figure 1 shows a few examples with a graphical representation of the pattern described by the tip of the electric field vector. Partially polarized states are represented by points inside the sphere. Some examples for fully polarized ideal cases are presented in Table 1. In general, and especially in the astrophysical context, light is only partially polarized. In this generic case, the Stokes parameters still give a correct description of the polarization state, but it is QN 2 C UN 2 C VN 2 1. The overall polarization degree P is defined as the distance of the .Q; U; V / point from the center of the Poincaré sphere: p q Q2 C U 2 C V 2  QN 2 C UN 2 C VN 2 P D I which can be separated into linear and circular: PL D PC D VN

q QN 2 C UN 2

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Table 1 Polarization parameters for some totally polarized ideal cases Pattern Linear hor. Linear vert. Linear +45 Linear –45 Linear Circular R.H. Ell. hor. R.H. Ell. vert. R.H.

 0 90 45 –45 any (0–180) – 0 90

˚y  ˚y – – 0 ˙180 0 or ˙180 90 90 90

b/a 0 0 0 0 any (>0) 1 0.5 0.5

Stokes vector (1,1,0,0) (1,–1,0,0) (1,0,1,0) (1,0,–1,0) (1, cos 2, sin 2, 0) (1,0,0,1) (1,0.6,0,0.8) (1,–0.6,0,0.8)

For a fully polarized and coherent beam, the Stokes parameters are constant in time, because the wave phase is also. However, in the real cases of incoherent light beams, the Stokes parameters are necessarily time averages over time ranges that are much larger than the electric field oscillation period: 2

2

2

2

I D < Ex0 C Ey0 > Q D < Ex0  Ey0 > U D 2 < Ex0 Ey0 cos ˚ > V D 2 < Ex0 Ey0 sin ˚ > where we set ˚ D ˚y  ˚x . For an incoherent, completely unpolarized beam, Q D U D V =0, whereas only I ¤ 0. In other words, a totally unpolarized beam can be imagined as the superposition of two perpendicular plane waves with intensities and phases randomly changing on time scales larger than the oscillation period.

1.4

Introducing Mueller Matrix Calculus

Mueller matrices allow an easy and elegant treatment of a number of problems in polarimetry. The effects of instrumental optics or physical processes (i.e., scattering, etc.) on an incoming beam characterized by a given Stokes vector can be described as follows. 0

m11 B m21 M ıSDB @ m31 m41

m12 m22 m32 m42

m13 m23 m33 m43

10 m14 I B Q m24 C CB m34 A @ U m44 V

1 C C A

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F. Patat

where M is the Mueller matrix describing the process (or the optical component). A Mueller matrix that we use extensively is that describing a perfect linear polarizer with a generic polarization angle : 0

ML;

1 c2 s2 2 B 1 c2 c2 c2 s2 D B 2 2 @ s2 c2 s2 s2 0 0 0

1 0 0C C 0A 0

(3)

where, for convenience, the sin and cos operators were replaced by s and c, respectively. This can be used to model two very simple cases. The first is that of a generic input beam going through a perfect  = 0 linear polarizer, which is described by the product: 0

1 1B 1 ML;0 ı S D B 2 @0 0

1 1 0 0

0 0 0 0

10 1 0 I C B 0CBQC C D 1 .I C Q; I C Q; 0; 0/ A @ 0 UA 2 0 V

The second is very similar, but now the polarization angle is  = 90ı : 0

1 1B 1 ML;90 ı S D B 2@ 0 0

1 1 0 0

10 1 00 I BQC 0 0C C B C D 1 .I  Q; I C Q; 0; 0/ 0 0A@U A 2 00 V

Although these transformations are very basic, they provide a fundamental route to the derivation of the Stokes parameters. One fundamental aspect to bear in mind is that polarization cannot be measured directly. Although technological progress may enable this in the future, for the time being the available detectors can only count photons and therefore only allow intensity measurements. In other words, it is only possible to measure the I component of Stokes vectors directly. From the two examples above it is clear that if we indicate with fk and f? the two intensity measurements along the x- and y-axis, these are: fk D

1 .I C Q/I 2

f? D

1 .I  Q/ 2

therefore one can compute QN as fk  f? QN D fk C f? and I D fk C f? . This very basic result shows two fundamental aspects: using a perfect linear polarizer one can measure intensity changes that are directly related

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to the input linear polarization, and to determine fully the Stokes parameters, one needs to obtain measures along a number of directions on the x; y plane. There are two ways of achieving this goal: either by rotating the polarizer or by rotating the plane of oscillation of the electric field. Both methods are used in practice (and, as we show, sometimes simultaneously). The choice is normally dictated by practical/technological aspects.

1.5

Dichroism and Linear Polarizers

Some crystalline materials absorb more light in one incident plane than another, thus light proceeding through the material acquires an increasing level of linear polarization. This anisotropy is called dichroism or diattenuation. For example, tourmaline shows a strong dichroism. Polaroid filters are built using stretched long polymeric molecules mixed with iodine atoms, which attach themselves to the aligned chains. The iodine atoms provide electrons that can move easily along the chains, but not perpendicular to them. The direction perpendicular to the polyvinyl chains is the pass direction because the electrons cannot move freely to absorb energy. Although both technologies are used in astronomical polarimeters, the first is more common, and it is deployed in the very popular Wollaston prism (see below).

1.6

Phase Retardation and Birefringence

A consequence of Eq. 1 is that the introduction of a phase shift ˚ D 2 = produces a rotation in the angle . In particular, if  D =2, the rotation is  = 2. In nature, certain crystals have different indices of refraction (and hence different light propagation speeds) associated with different crystallographic directions. Often mineral crystals show two distinct indices. This property is referred to as birefringence and is quantified as the difference n between the two refractive indices. For instance, calcite shows a large birefringence, and it is therefore widely used to produce retarder plates (and polarizing prisms). The direction along which light speed is higher (or, conversely, the refractive index is smaller) is the fast axis. In the following we indicate with the angle  the orientation of the fast axis of the retarder with respect to the  = 0 direction. The Mueller matrix describing a generic waveplate with retardance ˚ is: 0

MR;˚;

1 B 0 DB @ 0 0

0 2 2 C s2 c˚ c2 c2 s2 .1  c˚ / s2 s˚

0 c2 s2 .1  c˚ / 2 2 s2 C c2 c˚ c2 s˚

1 0 s2 s˚ C C c2 s˚ A c˚

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F. Patat

The phase retardance imparted by a waveplate (normally expressed as a fraction of the wavelength) depends on its thickness, on n, and on the given wavelength. Because of this, a retarder plate for a given retardance (e.g., =2) is built for working in a specific wavelength range. Within that range, the retardance shows a wavelength dependency, which is minimized in what are called super-achromatic retarder plates. We get back to this when describing real cases. A first notable case is that of a half-wave (˚ D ) retarder plate (HWP for short), which is described by the Mueller matrix: 0

MH;

1 B 0 DB @ 0 0

0 c4 s4 0

0 s4 c4 0

1 0 0 C C 0 A 1

A generic incoming beam characterized by S.I; Q; U; V / passing through an HWP is therefore transformed as MH; ı S D .I; Q cos 4 C U sin 4 ; Q sin 4  U cos 4 ; V / which means that although the intensity of the beam is unchanged and the linear polarization degree is conserved, the polarization angle is rotated by 4 on the Q; U plane (and the V -handedness is inverted). An ideal HWP does not produce any effect on an unpolarized light beam. Another interesting case can be obtained when the phase retardation corresponds to =4 (˚ D =2). Using the Stokes parameters definition one deduces that if S.I; Q; U; V / is the input vector, the =4-retarded vector is S.I; Q; V; U /. This means that a quarter-wave plate (QWP for short) fully converts circular polarization into linear polarization with  = 45ı , whereas the total polarization degree is conserved. The opposite is also true: linear polarization is fully converted to circular polarization if  = 45ı . Exactly because of this, circular polarization filters are built coupling a linear polarizer with a QWP with its fast axis mounted at 45ı . The general Mueller matrix of a QWP is: 0

MQ;

1 B 0 DB @ 0 0

0 2 c2 c2 s2 s2

0 c2 s2 2 s2 c2

1 0 s2 C C c2 A 0

Therefore, an incoming circularly polarized beam is transformed as follows MQ; ı S.I; 0; 0; V / D .I; V sin 2 ; V cos 2 ; 0/ This has an important implication: circular polarization can be converted into linear polarization, which can then be analyzed with a linear polarizer.

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With this we have completed the description of the essential elements of an astronomical polarimeter, which are the retarder (half- or quarter-wave) and the analyzer (a linear polarizer).

2

Measuring Polarization

As we have already clarified, polarization cannot be measured directly and it has to be derived from a set of intensity measurements taken along different directions. This is achieved in two different ways for linear and circular polarimetry.

2.1

Linear Polarization

In principle, one could derive linear polarization simply by rotating a linear polarizer and measuring the light intensity as a function of the rotation angle. If the incoming light is polarized to some degree, this would produce an intensity modulation, with a period of 180ı . We have seen that: p q Q2 C U 2 P D  QN 2 C UN 2 I U 1  D arctan 2 Q

(4)

which can be inverted to yield: QN D P cos 2 I UN D P sin 2

(5)

If we now compute the intensity component f of the S transformed by a perfect linear polarizer we have that: f D ŒML . / ı SI D

1 .I C Q cos 2 C U sin 2 / 2

Therefore, what one measures on the detector is: f D

1 .I C IP cos 2 cos 2 C IP sin 2 sin 2 / 2

or, in other words: 2f D 1 C P cos.2  2 / I

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where  is the polarization angle and  is the polarization direction of the linear polarizer. Therefore, by fitting the observed 2f =I values one can get, in principle, I , P , and  (which is the same as obtaining I , Q, and U ). However, sky transparency and seeing variations hinder the application of this method, as they introduce artificial flux variations that turn into a spurious polarization signal. In the case of SNe, the expected levels of polarization are of the order of 1%. If one wants to achieve, say, a polarization signal-to-noise ratio P =P >3, then the required photometric stability is of the order of a few milli-mag. Even under very good photometric conditions in excellent sites, this places a very stringent (and often prohibitive) requirement. The problem can be reduced by modulating the incoming beam on timescales shorter than those of the atmospheric fluctuations, which implies that the detector must be read out very fast. These constraints limit the application of this kind of polarimeter to the cases where the photon shot noise is much larger than the read-out noise. That is to say that only bright stars can be observed in this way, at least from the ground. In space things are different, as there are no transparency and seeing variations. (see, for instance, HST imaging polarimetry on NICMOS or ACS.) As we show in the next section, in ground-based instruments the problem is solved by obtaining measurements along at least two directions simultaneously.

2.2

Circular Polarization

Although the application of polarimetry to the SN field is practically limited to the linear flavor, it is worth mentioning circular polarimetry here as well. As we have anticipated, circular polarization can be estimated by converting it to linear polarization and measuring the intensity modulation along a number of directions. When a general light beam described by S.I; Q; U; V / goes through a QWP, it is transformed as follows (where for convenience we have dropped the 2 subscript). S0 .I; c 2 Q C cs U C s V; cs Q C s 2 U  c V; s Q C c U / which implies that all the circular polarization information is transferred to the linear polarization Stokes parameters Q and U that, in turn, can be analyzed by a linear polarizer. For the sake of simplicity, let us examine the case in which the QWP with fast axis direction identified by  is followed by an ideal horizontal polarizer. The intensity component of the transformed Stokes vector is then: f D

 1 2 I C c2 Q C c2 s2 U C s2 V 2

This finding has an important implication: under general circumstances (i.e., Q; U ¤ 0), there is crosstalk between linear and circular polarization. This means that for measuring V one needs to get rid of the linear polarization component in the intensity signal. In an ideal case, this can be achieved by nulling cos2 2 and

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cos 2 sin 2, that is, for  D ˙k 4 , where k = 1, 2, . . . . Because the number of unknowns is two (I and V ) at least two measurements are needed. For instance, if we indicate with fC45 and f45 the two intensities measured on  D ˙45ı , we then have I D fC45 C f45 and fC45  f45 VN D fC45 C f45 More in general, V can be obtained from a series of measurements. Of course, the absolute orientation of the QWP on the plane of the sky is irrelevant, provided that the angle between the QWP fast axis and the linear polarizer is kept at a fixed separation of 45ı . As in the case of linear polarimetry, transparency and seeing variations between the various measurements can introduce spurious circular polarization signals and therefore, for ground-based observations, one needs to devise a way of removing this problem as well.

3

Dual-Beam Polarimeters

As we have seen in the previous section, polarization (both linear and circular) can be derived combining intensity measurements obtained along different directions. More precisely, each of the Stokes parameters Q, U , and V can be computed combining at least two directions. This means that if one is able to obtain simultaneous measurements of pairs of polarization states, one can circumvent the transparency and seeing variations, as these would affect the two states in an identical way.

3.1

The Wollaston Prism

In practice this is obtained using the so-called Wollaston prism (WP), named after W. H. Wollaston who invented it. This optical element is composed of two orthogonal calcite prisms glued together, thus incoming unpolarized light is split into two beams with orthogonal polarization states. The two output beams diverge by an angle that is typically indicated as the throw. In astronomical polarimeters the throw is in the range of 10-20 arcs. The beam with polarization perpendicular to the optical axis of the prism is dubbed the ordinary ray (o-ray), and the other is called the extraordinary ray (e-ray). When a WP is inserted along the light path, the image formed on the focal plane of the telescope is split into two images that are angularly separated by the throw and differ by their polarization state. Obviously, if one is to observe a crowded field or an extended object, this would cause image overlap, which would seriously hinder the analysis. In the case of a SN superimposed on a galaxy background, the WP

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F. Patat

Fig. 2 Examples of polarimetric observations with VLT-FORS1. Left: panoramic polarimetry of M83. Right: spectropolarimetry of SN 2006X

would cause part of the background of the o-ray to fall onto the SN image in the e-ray, hence mixing the polarization states of the background. This problem is circumvented by introducing a special mask on the focal plane of the telescope, with alternate opaque and transparent strips spaced by an angular amount equal to the WP throw. This solves the overposition problem, but it effectively allows one to cover only half of the field of view. Therefore, if one is after panoramic imaging polarimetry of the whole field of view, then one needs to use two telescope pointings separated by an angular distance equal to the throw and perpendicular to the mask direction. For single isolated objects (such as polarimetric standard stars or even bright SNe projected on negligible backgrounds) this is not a problem and observations can be conducted without using a focal plane mask. For spectropolarimetry, the mask is typically replaced by a special slit with alternate opaque and transparent slots so that, for instance, an object acquired under one of the transparent slots would produce two spectra. Real examples of imagingand spectropolarimetry obtained with the dual-beam VLT-FORS1 polarimeter are shown in Fig. 2.

3.2

Normalized Flux Differences

Recalling the general matrix of a linear polarizer (Eq. 3), the system obtained coupling a WP to a HWP is described by the following matrix. 2 3 1 ˙ cos 4 ˙ sin 4 14 M ./ D ˙1 cos 4 sin 4 5 2 0 0 0

37 Introduction to Supernova Polarimetry

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where, for convenience, we have omitted the circular polarization terms. If we indicate with i a series of fast axis HWP angles, the intensities of the ordinary and extraordinary beams fO;i and fE;i are given by: fO;i D

1 2

.I C Q cos 4i C U sin 4i /

fE;i D

1 2

.I  Q cos 4i  U sin 4i /

If observations with N HWP angles are obtained, this is a system of 2N equations. Because there are three unknowns (I; Q; U /, at least N = 2 positions are required. The availability of two simultaneous measurements allows the introduction of the normalized flux differences: Fi 

fO;i  fE;i fO;i C fE;i

that have the favorable property of being independent of variations in sky transparency and seeing. From the above equations one has that fO;i C fE;i D I , so that the problem reduces to solving the N equations: Fi D QN cos 4i C UN sin 4i which can also be rewritten as Fi D P cos.4i  2/. In principle, one can take any set of HWP angles, but the best choice is to rotate the HWP in steps of 22ı .5, as this has certain advantages: (1) it minimizes the error on the Stokes parameters (for instance, Patat and Romaniello 2006), and (2) it makes the solution of the above equations trivial. With this choice, the Fi depends on QN and UN only, thus one can easily invert the equations and obtain: QN D

2 N

UN D

2 N

PN 1 iD0

PN 1 iD0

Fi cos. 2 i / Fi sin. 2 i /

These are nothing other than the Discrete Fourier Transforms of QN and UN , which are even and odd functions of , respectively. It is easy to verify that these equations are just the averages of the N =2 redundant estimates of QN and UN . For instance, for the very frequent case in which N = 4, one has: F0  F2 QN D 2

F 1  F3 I UN D 2

In principle, one can fully solve the linear polarimetry problem by taking N = 2 angles, in which case it is trivially QN D F1 and UN D F2 . However, as we show, multiple estimates are required to remove instrumental problems.

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Similar considerations apply to circular polarimetry, which can be measured replacing the HWP with the QWP oriented at 45ı with respect to the WP. In this case, V is simply equal to the normalized flux difference derived from the single QWP angle. Nevertheless, in order to remove instrumental effects, it is necessary to use at least two QWP angles, typically –45ı and +45ı , so that: FC45  F45 VN D 2

3.3

Instrumental Problems

What we have described thus far refers to ideal optical components. For instance, we have assumed that the WP splits an incoming unpolarized light into two identical beams, or that the retardance angle of the retarder plate corresponds exactly to its nominal value. In reality this is never the case. These problems and their cures are described in Patat and Romaniello (2006) and Bagnulo et al. (2009). Here it suffices to say that, to first order, the most relevant ones are solved introducing redundancy in the measurements, that is, obtaining observations at a number of HWP (or QWP) angles larger than what is strictly required for deriving the Stokes parameters. Typically this means four HWP angles for linear polarimetry and two QWP angles for circular polarimetry. In the latter case it is interesting to note that, in order to remove possible crosstalk between linear polarization and circular polarization, it is a good habit to take two sets of QWP angle pairs, with a 90ı rotation of the instrument (while keeping the WP-QWP offset to ˙45ı ). With this rotation the sign of V does not change, but the signs of Q and U (as “seen” by the instrument) do change. Therefore, taking the average of the values derived from the two pairs leads to a first-order cancellation of the crosstalk. Normally polarimeters are mounted at the Cassegrain focus of the telescope, because this is a circularly symmetric optical scheme. This implies that on-axis polarization is expected to be null, because of the symmetric cancellation of polarization introduced by reflection and transmission. This is not the case if the polarimeter is mounted at the Nasmyth focus, where the presence of an inclined flat mirror introduces spurious polarization. This, coupled with field rotation in Alt-Az telescopes (which produces time-variable instrumental polarization), makes the use of Nasmyth polarimeters very difficult for the SN case.

3.4

HWP Chromatism

Although good polarimeters make use of super-achromatic HWPs, a residual, wavelength-dependent retardance offset ./ is always present. In principle, this can be derived by a high signal-to-noise observation of a polarimetric standard star. However, the retardance offset is normally tabulated in the instrument’s manual. The correction to be applied is a simple rotation:

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Q0 D Q cos 2./  U sin 2./ U0 D Q sin 2./ C U cos 2./ For broadband polarimetry the correction can be computed by weighing the tabulated values with the filter response function. For super-achromatic HWPs the typical peak-to-peak chromatism is on the order of 10ı .

4

Observations, Calibrations, and Data Reduction

As we have explained, polarimetric observations should always be taken using more position angles than strictly required by the mathematical solution of the problem. This has to be taken into account while planning observations. In addition, a set of calibrations that are specific to polarimetry must be included.

4.1

Polarimetric Standard Stars

In addition to the usual calibrations (bias, flat field, arc lamps), it is very important to obtain observations of polarized and unpolarized standard stars. Unpolarized standards allow one to check the level of the instrumental polarization, its wavelength dependency, and its stability with time. Therefore, it is a good habit to observe one or more such stars during each epoch. In the case when the instrumental polarization is found to be nonnull (which practically means larger than a few 0.1%), it can be subtracted vectorially from the measured Stokes vector. Note that normally the instrumental polarization is very small (i.e., 200). To make a real example, a SN with V D 12:7, observed with FORS2 and the 300 V grism (12Å full width half maximum) and a 1 arcs slit and N D 4 HWP angles, requires 4  600 D 1800 s of integration. This is still not sufficient to reach SNR D 700 per pixel, and the spectra need to be rebinned to about 10 pixels (increasing the SNR by about a factor of 3). This is for an 8.2-m telescope. For a 4-m class telescope the exposures have to be multiplied by a factor 4. For a 2-m class telescope the required exposure times become prohibitive and limit SN spectropolarimetry to very nearby objects. (SN 2014J was such an example.) As the SN fades away, things of course get more cumbersome so that, as a matter of fact, there are very few SN observed later than one month past maximum

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light. Remarkable exceptions are type IIPs on their plateau (but note that they are generally fainter than other SN types) or type IIn, which remain bright for a longer time. (SN 2009ip is a notable example.) One important aspect to be considered in this context is the polarization bias (also known as d.c. bias). This descends from the fact that P is defined positive and thus, when Q and U are small, the negative side of the error distributions is mirrored to the positive side, hence producing systematically higher values of P . The difference between the real and the measured polarization is called polarization bias. This becomes relevant when the polarization signal-to-noise P =P is small. For instance, in the extreme case of null intrinsic polarization, with N = 4 HWP positions and SNR = 100 one would measure a most probable value of 0:7%. In the SN field this is a comparatively large value. Therefore, a polarisation bias correction needs to be applied, or at least taken into account. For instance, P could show an increase across a deep absorption trough of a P-Cygni profile just because there the lower signal-to-noise systematically pushes the noise on P in the positive direction. Although statistical estimators for correcting the polarization bias exist, they are statistical and give you the most probable correction. (see, e.g., Patat and Romaniello 2006 for a general discussion on this topic.) Therefore, it is always a good habit to show plots of Q and U independently, because the Stokes parameters deviate from a Gaussian distribution much later than P . For small signal-to-noise ratios, more reliable statistical error estimates can be obtained via MC simulations. In any case, every instrument has its limits and, at some point, these will be reached and any increase of the signal-to-noise will only make them more evident, and it will not be possible to improve on the accuracy of the estimated Stokes parameters. Some of the problems can be mitigated with a full Fourier analysis based on N = 16 HWP position angles. This is only possible for bright stars, whereas it is practically infeasible for most SNe. In the case of FORS1/2, it is estimated that the minimum achievable uncertainty is 0.05%, which implies that below 0.2% one can only put upper limits on the polarization signal.

6

Polarimetry of Supernovae

6.1

A Brief History

The first ground-breaking step in the field was done by Shapiro and Sutherland (1982), who first showed the theoretical importance of polarimetry for understanding SN geometry. A few years later McCall (1984) predicted the inverted P-Cyg polarization profile. More quantitative theoretical predictions for different axial ratios were made by Höflich (1991), later followed by the work of Kasen et al. (2003). On the experimental side, the first robust detection of polarization in a SN is that of SN 1987A (Cropper et al. 1988), followed by that of 1993J (Doroshenko et al. 1995; Trammel et al. 1993; Tran et al. 1997). The first systematic and pioneering campaign was started in 1994 at the McDonald observatory by Lifan Wang and Craig Wheeler. With the start of ESO-VLT operations and the deployment of FORS1, the collaboration was widened and the project augmented in scope. Doug

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Leonard and Alex Filippenko also started a project using the 10-m Keck telescope and, more recently, Masomi Tanaka and Koji Kawabata initiated a similar campaign at the Subaru telescope. Mainly because of the need of a large collecting area and a stable polarimeter, but also because of the general perception about polarimetry, this technique is only now beginning to gain popularity in the community. Other groups with access to polarimeters have started successful campaigns. (see, for instance, the SN spectropolarimetry Project led by Nathan Smith.)

6.2

A SN Polarization Primer

The essence and the importance of SN polarimetry is well captured by this statement from Wang et al. (2006): Spectropolarimetry is a straightforward, powerful diagnostic tool for supernova explosions. Contrary to conventional perceptions that the interpretation of polarimetry data is complicated and heavily model dependent, many important insights on the geometric structure of supernovae ejecta can be derived from diagnostic analyses that do not rely on detailed modelling.

Let us see what the grounds are for this statement. As first stipulated by the seminal theoretical works cited above, in SNe the source of continuum polarization is Thomson scattering on free electrons that are abundant in the atmospheres of these objects, especially at early epochs. As in the more familiar case of a reflection on a lake’s surface, the photons scattered by an electron acquire linear polarization with a position angle that is perpendicular to the scattering plane. Polarization induced by electron scattering is wavelength independent and depends on the scattering angle (subtended by the incoming and outgoing photon directions). The polarization is maximum for a scattering angle of 90ı . If one imagines being able to resolve the photodisk of a perfectly spherical SN, this implies that the polarization is null on the center of the photodisk and it grows towards its limb. The polarization angle shows a pattern tangential to concentric circles centered on the photodisk’s center. Because of the symmetry of the system, for each point on a given circle there will always be another point for which the polarization degree is identical, but the polarization angle is perpendicular, therefore the corresponding Stokes vectors cancel out. If one integrates over the whole photodisk (which is equivalent to bringing the object at a sufficiently large distance to make it unresolved), the net polarization signal is nulled. Deviations from sphericity would lead to a partial cancellation, leaving a residual polarization that can be measured and is directly related to the degree of asphericity. In addition, the detection of a defined polarization position angle would signal the presence of a symmetry axis and also reveal its orientation on the plane of the sky. This would be the case, for instance, of an ellipsoidal geometry. Detailed calculations show that although the polarization signals are not very strong even for strongly prolate or oblate ellipsoids (e.g., Höflich 1991), the expected signals are detectable by modern instrumentation. The bottom line is that a continuum, wavelength-independent linear polarization is expected in a SN as the result of incomplete cancellation by overall deviations from spherical symmetry. This is, of course, a simplified picture, because it assumes

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there is a well-defined photosphere which, especially in some SN types (e.g., Type Ia), is only a very crude approximation. However, it gives a first-order idea as to why one can conclude, without invoking detailed modeling, that detecting a non-null continuum polarization gives a direct insight to the overall explosion geometry. And from this descends one of the most important results achieved by SN spectropolarimetry in the last 15 years: although normal Type Ia do not show evident signs of continuum polarization above a few 0.1% (and are therefore globally spherical), core-collapse events do show signals that exceed 1%, hence pointing to marked departures from spherical explosions. Above its photosphere a SN also has what might be called an extended and rapidly expanding atmosphere with layers of various elements, possibly mixed. If the atmosphere were chemically and geometrically spherically symmetric, it would not introduce additional polarization to that originally acquired via Thomson scattering. At most, one would observe continuum depolarization corresponding to emission line peaks. (emission arises from light scattered into the line of sight and this effectively acts as a depolarizing mechanism, because it randomly destroys the geometrical information.) In the most general case in which material is clumped and only partially covers the photodisk, this leads to incomplete cancellation of the underlying electron scattering polarization. Inasmuch as the “obscuration” is maximum at the minimum of the absorption troughs, one expects to have the polarization peaks corresponding to the absorptions seen in the intensity spectrum, whereas polarization should be minimum at the peak of the emission part of the profile. This is often indicated as an inverted P-Cyg profile and it was first observed in SN 1987A (Cropper et al. 1988). The take-home message is that, whereas continuum polarization signals an overall asphericity, line polarization is a symptom of chemical asymmetries. Lines may form over a wide range of velocities and in an homologous expansion velocity means radius. Therefore, it is important to study the behavior of polarization degree and angle as a function of wavelength, so that it is in principle possible to get information on the 3D structure of the absorbing material and see whether this is different from different elements, With the final aim of understanding and better constraining the explosion model and the underlying progenitor nature. Of course, a picture in which the continuum forms at a well-defined photosphere is extremely simplified. For instance, in Type Ia the photosphere does not really exist, as it spans a wide range in velocities. The usual criticism to the above picture is that not even a single photon received by the observer freely escaped from the atmosphere without being processed by an atomic transition. That is to say, none of the photons escaping the SN carries the original geometric imprint. As absorption and re-emission take place multiple times and at random positions, the geometric information is destroyed, therefore polarization is much less sensitive to asphericity than one would like it to be. Although this is certainly true, both classical (e.g., Höflich 1991) and more recent models (Bulla et al. 2015a, b) show that, for instance, markedly aspherical Type Ia explosions would generate polarization signals that were never detected thus far. The bottom line is that polarimetry provides a unique tool for probing geometry.

37 Introduction to Supernova Polarimetry

6.3

1039

The Ubiquitous Interstellar Polarization

Whenever there is dust along the line of sight, there is reddening and there is polarization, which is a plague similar to what extinction is for spectrophotometry. Interstellar polarization (ISP) is produced by aligned dust grains that preferentially absorb light along one direction, leaving a net polarization (along the orthogonal direction) with a position angle that is wavelength independent. ISP is present along the lines of sight to reddened Galactic stars: the larger the reddening, the larger is the ISP. The effects of ISP are nasty, especially when it is comparable in strength to the intrinsic SN signal. In addition, as it combines vectorially with the incoming signal, its consequences are not immediately obvious. The only safe assumption one can make is that if the ISP arises in dust that is sufficiently far away from the explosion, it should not change with time, implying that any observed changes can be ascribed to variations inherent to the SN. There are some problems with the ISP correction. The first is that it is difficult to estimate, and the second is that one typically needs to make some assumption on its wavelength dependency. Studies in our own Galaxy (for instance, Serkowski, Matheson, and Ford 1975) have shown that there is a relation between reddening and polarization: E.B  V / P

9 Although this empiric relation tells us that, say, for E.B  V / = 1 one can expect polarization levels up to 10%, this is only an upper limit. The physical reason resides in the variable polarization efficiency of different dust size distributions and composition. (for instance, although all kinds of dust do generate reddening, not all dust compositions lead to grain alignment by magnetic torques.) Therefore, although reddening is certainly a proxy to polarization, it cannot be used to derive accurate estimates. The second issue is related to the ISP wavelength dependence. For Milky Way (MW) dust, Serkowski, Matheson, and Ford (1975) found this empirical relation from studying a larger number of lines of sight in the Galaxy, which is known as the Serkowski law:   max P ./ D Pmax exp Kln2  where Pmax and max indicate the maximum polarization degree and its wavelength, which shows a dependence on the total to selective absorption ratio: RV D .5:6 ˙ 0:3/max where max is expressed in m. For the canonical Milky Way (MW) RV D 3:1, this gives max D 0:55 m. This dependence establishes a physical link between reddening and polarization through the dust grain size (or better said, size distribution). If the Serkowski law also holds outside the MW (and in principle there is no reason as to why this should not be the case), it would be sufficient to determine the ISP (and its angle) at some wavelength to be able to derive QISP and UISP and

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subtract them from the measured polarization signal. For instance, one could try to get a proxy to the ISP at emission line peaks, where the depolarization is supposed to be maximum and reconstruct the rest of the ISP function using a Serkowski law, with some reasonable choice of its parameters. Note that when Pmax is small, the expected variation across the optical domain is very small, thus assuming a constant ISP is a good approximation. This does not hold when Pmax exceeds several percents. Nevertheless, in recent years, it became clear that in a number of moderately and highly reddened SNe (both thermonuclear and core-collapse), in which the ISP was definitely dominating over the intrinsic polarization, the observed wavelength dependence was not described by a Serkowski-like law. In addition to increasing the complexity of the problem, this finding has stimulated the discussion about dust composition in the SN environments, especially for Type Ia, for which in the past values of RV systematically lower than the canonical MW value were found (Patat et al. 2015). The problem of ISP correction remains open. Although several approaches were proposed (see, for instance, next section), the most promising one was the direct derivation of ISP via late time observations, at epochs when the intrinsic polarization was supposed to be gone, diluted by the ejecta expansion. Although this is a direct method, it is expensive in terms of telescope time and has been applied to very few objects. Paradoxically, highly reddened objects are easier to deal with, because in those cases the continuum polarization dominates so heavily over the SN signal that it is possible to remove it confidently. (see, e.g., the cases of SNe 2006X and 2014J.) Nevertheless, by doing this, one possibly also removes part of the intrinsic continuum polarization, depending on the mutual orientation of ISP and the SN dominant axis (if there is one).

6.4

The Q-U Plane and the Dominant Axis

As we have seen in the previous sections, it is possible to derive the Stokes parameters within certain spectral bins. If these bins are wide (say, many hundreds of Å or more) one talks about broad band polarimetry. This is normally used only for targets that require prohibitive exposure times even with 8—10m class telescopes (say, V > 16–17).The advantage is that, if signal-to-noise allows, polarimetry of a number of targets in the field can be obtained in one single telescope pointing. The disadvantage is that it is impossible to disentangle between continuum and lines, which makes the ISP correction even more cumbersome. On the contrary, if the bins are sufficiently small to allow the resolution of spectral features, one enters the realm of spectropolarimetry. We focus on this second flavor, because this is what really provides physical insights and allows one to distinguish between continuum and line polarization. Essentially, spectropolarimetry provides the wavelength dependence of polarization degree (P ) and angle (). Nevertheless, a more informative representation of polarimetric data is achieved plotting the binned data on the Q  U plane, which

37 Introduction to Supernova Polarimetry

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Fig. 3 Two examples of Q  U plots. Left panels: Q  U plane; right panels, P and  plots

can be seen as the equatorial plane of the Poincaré sphere (see Sect. 1.3). There are two main advantages in using this visualization: Q and U do not suffer from the polarization bias, and possible alignments and deviations from these alignments are much easier to be identified. Figure 3 shows two illustrative examples. The first (upper panels) presents a case in which the Q; U points obey a Serkowski law (see Sect. 6.3) with Pmax D 1:0%, K D 1:15, max D 0:55 m and  D 22ı . The points are clustered in a cloud with a very mild wavelength-dependent polarization degree. Because of the distance of the points from the origin of the Q  U plane, the polarization angle is also constant. From this one would erroneously deduce that there is a prevailing direction, which is usually indicated as the dominant axis (Wang et al. 2003; Wang and Wheeler 2007). However, the Q  U plane plot reveals that there is no dominant axis. The second example (lower panels) portrays an example in which dP =d  ¤ 0 and a dominant axis is definitely present. Nevertheless, the  plot shows a very marked polarization angle change that, at face value, would lead to the opposite conclusion. This is because although the points are aligned along a dominant axis, this does not go through the origin of the Q  U plane. A typical reason for the displacement is the presence of ISP. When this is small (say, of the order of a few percent or less), to first order it can be considered as a wavelength-independent translation on the Q  U plane. Under this assumption, one can estimate two possible limit solutions for QISP and UISP , both lying on the dominant axis, placed at either side of the observed points.

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What is important to remember is that the presence of a dominant axis in the ISP-corrected Q  U plane indicates the presence of an axial symmetry in the explosion geometry. On the contrary, points that deviate from the dominant axis signal departures from the axial symmetry. Very remarkably, this is seen across the absorption troughs, in which Q and U typically describe loops. Examples for the Si II 6355 line are shown in Fig. 4 for the well-studied Type Ia SN 2006X. In the cases where a dominant axis is present, one can describe the polarization data along the axis (Pd ) and orthogonal to the axis (Po ). These are obtained from Q and U by a simple coordinate rotation. Like the Stokes parameters, Pd and Po do not suffer from polarization bias. In addition, being a measure relative to the dominant axis, Po does not suffer from ISP.

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Fig. 4 Si II 6355 loops on the Q  U plane for SN 2006X on eight different epochs. The dotted line traces the average dominant axis, and the solid line is the linear weighted fit to the displayed Si II data (Patat et al. 2009)

37 Introduction to Supernova Polarimetry

7

1043

The Polarimetric SN Zoo

This final section presents a brief summary of the main findings ordered by SN type. Most notable events (such as SN 1987A) are described separately.

7.1

SN 1987A

This SN, the first with a robust polarization detection, displayed a significant largescale asymmetry with a well-defined dominant axis consistent with a jet-like flow, but with a marked departure from axial symmetry. The overall structure of SN 1987A was remarkably axially symmetric from deep inside the oxygen-rich zone out to the hydrogen envelope. A persistent polarization position angle of the dominant axis across a broad wavelength range was observed. This was accompanied by a lack of significant evolution of the polarization position angle, indicating that the photosphere at early and late epochs shared the same geometric properties. The likely cause for departure from spherical symmetry is the nonspherical distribution of the source of ionization in the form of a clump of radioactive nickel and cobalt. The dominant axis was aligned with the mystery spot, whereas it was 15ı off with respect to the circumstellar rings.

7.2

SN 1993J and Type IIb

SN 1993J presented a marked, wavelength-independent continuum polarization at the level of 1:6˙0:1%, implying a globally asymmetric explosion with an axial ratio larger than 1.5. The H˛ emission line did show a 0.5% depolarization, suggesting that the continuum polarization was acquired well below the line-forming region, that is, very close to the photosphere. SN 2001ig displayed a low continuum polarization level (0:2%) at early epochs, indicating a roughly spherical, H-dominated envelope, with an asphericity smaller than 10%. At about one month, when the H envelope became optically thin the continuum polarization increased to 1%, hence revealing a highly asymmetric H-core. Asymmetries in the He layer were also shown by levels of polarization that reached about 0.8%. A rotation of about 40ı was observed between the two epochs, thus indicating that the H-envelope (not affected by the explosion) was sufficiently extended to be decoupled from the He layer, whose shape was related to the explosion. Clear loops through the H, He, O, and Ca line profiles were seen, pointing at departures from spherical symmetry in the SN ejecta. In general, the polarization properties of Type IIb are in excess of those of Type IIP (see below), but indicate a similar scenario: a spherically symmetric H envelope shielding a highly asymmetric He core. The differences seen in SNe 1993J, 1996cb, and 2001ig demonstrated that IIb are not geometrically homogeneous.

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F. Patat

Type II-P

This class of core-collapse SNe present a low, wavelength-independent continuum polarization (definitely symptomatic of Thomson scattering) during the plateau phase, during which no change in the dominant axis is observed. On the contrary, a rapid rise of polarization is observed at the end of the plateau, during which the dominant axis is seen to change, but not in all objects. In general, polarimetry provides evidence for a strongly nonspherical explosion. A likely cause of the early polarization is an asymmetric distribution of radioactive elements that distorts the ionization and excitation structure, although the density structure remains essentially spherically symmetric.

7.4

Type IIn

For this class of objects the scenario is complicated by the dominating ejecta– CSM interaction. Although only a few objects of this class were observed thus far, they generally display a significant continuum polarization (2.0–2.6%) with a constant polarization angle. This indicates a strong asymmetry in the region where the continuum forms. As this takes place in the ejecta–CSM interaction region, it is not clear whether this asymmetry is intrinsic to the explosion material or to the geometry of the material lost by the system prior to the explosion. Marked continuum depolarization is observed at the wavelengths of strong emission lines, again indicating that narrow and intermediate emission components must arise well above the electron-scattering photosphere. The geometries of the broad-line region and the photosphere are definitely different.

7.5

Type Ib/c

For these objects, polarimetry revealed global asymmetries of 10–20%. Although there are variations, all observed cases suggest the existence of a strongly nonspherical explosion, possibly “stalled” within the core, or a tilted-jet, where the tilt refers to the misalignment between the overall ellipsoidal shape of the ejecta and the jetlike structure. This is indicated by the different polarization angles shown by the continuum (which shows a degree of polarization larger than 1%) and by the lines (He, Ca, . . . ). The main polarimetric properties of core-collapse events can be summarized as follows. • They are all polarized and hence substantially asymmetric. This is a general property of core-collapse, not the peculiarity of single events. Although each individual supernova has its own properties, basic themes do emerge. • The fundamental cause of the asymmetry is deep in the ejecta and is a generic property of core-collapse events. The asymmetry is characterized by a dominant

37 Introduction to Supernova Polarimetry

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axis. The most straightforward explanation is a strongly nonspherical explosion that may have a jet or jet-like structure. • Atop this basic structure there are significant, composition-dependent structures that signal generic, large-scale departures from axial symmetry.

7.6

Thermonuclear SNe

P (%)

At variance with core-collapse events, core-normal Type Ia show a very low continuum polarization ( 0.3%) on which absorption line polarization emerges, especially during the pre-maximum phases. Line peak polarization is typically of the order of 1% and is most prominent in the Si II 6355 and in the near-IR Ca II triplet absorptions. The Si polarization reaches a maximum around five days before maximum light and then decreases, to completely disappear a few weeks after (see Fig. 5). The general picture provided by polarimetry is that Type Ia are globally spherical explosions but do show chemical asymmetries. A remarkable aspect is the lack of polarization in the OI 7774 line. This is interpreted as evidence for the existence of unburned Oxygen that conserves the pristine spherical symmetry of the progenitor. In addition, because elements such

2.0 1.5 1.0 0.5 0.0 2.0 1.5 1.0 0.5 0.0 2.0 1.5 1.0 0.5 0.0 2.0 1.5 1.0 0.5 0.0

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Fig. 5 Spectropolarimetric evolution of SN 2006X (Patat et al. 2009)

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as Si and Ca show nonnull polarization signals over similar velocity ranges, this implies that protrusions of intermediate mass elements are present within the unburned O layer. At early epochs, the Ca II NIR triplet high-velocity component is strongly polarized, whereas the photospheric component is much less so. As time goes by the low-velocity feature grows in polarization, probably when the photosphere crosses the inner boundary of the Ca region. This so-called Ca repolarization seems to be a common feature (although only a few objects have polarimetry available at about one month past maximum), and it is possibly related to the presence of high-velocity components. In the well-studied Type Ia SN 2012fr low- and highvelocity features are orthogonal and both display axial symmetry. Indeed, late time spectropolarimetry of Type Ia may allow the study of protrusions at the chemical boundaries. Another interesting aspect that has emerged in recent years is the correlation between the peak polarization shown by Si II 6355 at 5 days before maximum light (PSiII )and the decline rate m15 (Fig. 6). If we accept the decline rate as a measure of the SN brightness and that brighter Type Ia have a larger 56 Ni mass, we can then conclude that SNe with lower polarization have gone through more complete nuclear burning. This may be a reasonable conclusion, as more complete burning tends to be more efficient in destroying chemical inhomogeneities, and thus produces more “spherical” explosions. A similar correlation also exists between PSiII and the velocity gradient vP SiII (Maund et al. 2010), in the sense that the higher vP SiII , the larger is PSiII . This implies that the velocity gradient is predominantly related to the asymmetries of

Fig. 6 The m15 versus PSiII relation. The dotted lines trace the 1- level of the intrinsic polarization distribution generated by the MonteCarlo simulation discussed by Wang et al. (2007). The shaded area indicates the rms deviation of the data points from the best-fit relation. The red symbol on the lower right indicates the subluminous SN 2005ke

37 Introduction to Supernova Polarimetry

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the SN. In turn, this links vP SiII to the viewing angle. Rather than as an effect of random distributions of absorbing blobs in the line-forming region, this seems to be related to a very common property, which may indicate an ignition offset from the center. In this scenario, high-velocity gradient SNe are those with an offset Si distribution mixed into the outer, unburned O layer in the direction of the observer. At significant angles from the offset direction, Si is found in a thinner layer, more evenly excited by the underlying radioactive 56 Ni substrate, hence leading to a lowvelocity gradient event, with a lower PSiII . Subluminous Type Ia (a.k.a. SN 1991bg-like) deserve a separate discussion. Although spectropolarimetry is available for only two of them (SNe 1999by and 2005ke), the findings are very similar, and lead to the following conclusions. • They do not obey the polarization versus decline rate relation of core-normal Type Ia. • The line polarization is systematically smaller than in core-normal events, whereas the continuum polarization is nonnull and grows to the red. • The comparatively large continuum polarization is explained in terms of a global asymmetry (15%), not present in normal Ia. Whether this is the result of a very fast white dwarf rotation or a merger remains to be clarified. • In the two subluminous events, the lines of intermediate mass elements form far from chemical boundaries, and over a large velocity range. This causes a blocking of the entire photosphere, and hence a weak line polarization. The above facts indicate that subluminous events are not a variation of the standard explosions that apparently explain the bulk of the type Ia population. Rather they are indicative of distinct explosion mechanisms. The challenge of the next years is the extension of spectropolarimetry to later epochs (to probe deeper chemical boundaries) and to the near-IR. Another poorly studied field is that of circular polarimetry, which may be able to provide otherwise elusive information on magnetic fields. There were very few measurements thus far, only providing upper limits, the tightest being that of the Type Ia SN 2012fr (Maund et al. 2013).

8

Further Reading

General introductions on astronomical polarimetry can be found in the classical books by Shurcliff (1966), Tinbergen (1996), and Leroy (2000). The book by Goldstein (2010) provides more details on polarimetry in general, and the lecture by Keller (2000) is a must for those who are interested in the technical/instrumental aspects of the problem. The review by Wang and Wheeler (2007) remains the general beginner’s reference in the field. For details on single objects and more recent findings, the reader needs to refer to the specialized publications.

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Cross-References

 Hydrogen-Poor Core-Collapse Supernovae  Hydrogen-Rich Core-Collapse Supernovae  Interacting Supernovae: Types IIn and Ibn  Observational and Physical Classification of Supernovae  Superluminous Supernovae  The Extremes of Thermonuclear Supernovae  Type Ia Supernovae Acknowledgements I would like to thank D. Baade, P. Höflich, J. Maund, L. Wang, and J. C. Wheeler for all these years of fruitful collaboration. I owe them much of what I know about SN polarimetry. Long and illuminating discussions with my students A. Cikota and T. Faran are also gratefully acknowledged.

References Bagnulo S, Landolfi M, Landstreet JD, Landi Degl’Innocenti E, Fossati L, Sterzik M (2009) Stellar spectropolarimetry with retarder waveplate and beam splitter devices. PASP 121:993–1015 Bulla M, Sim SA & Kromer M (2015a) Polarization spectral synthesis for Type Ia supernova explosion models. MNRAS 450:967–981 Bulla M, Sim S. A, Pakmor R, Kromer M, Taubenberger S, Röpke FK, Hillebrandt W, Seitenzahl IR (2015b) Type Ia supernovae from violent mergers of carbon-oxygen white dwarfs: polarisation signatures. MNRAS 455:1060–1070 Cropper M, Bailey J, McCowage J, Cannon RD, Couch, WJ (1988) Spectropolarimetry of SN 1987A – observations up to 1987 July 8. MNRAS 231:695–722 Doroshenko VT, Efimov Yu S, Shakhovskoi NM (1995) UBVRI photometry and polarimetry of SN 1993J in the galaxy M 81. Astron Lett 21:513–527 Goldstein DH (2010) Polarized light, 3rd edn. CRC Press, Boca Raton Höflich P (1991) Asphericity effects in scattering dominated photospheres. A&A 246:481 Kasen D, Nugent P, Wang L, Howell DA, Wheeler JC, Höflich P et al (2003) Analysis of the flux and polarization spectra of the Type Ia supernova SN 2001el: exploring the geometry of the high-velocity ejecta. ApJ 593:788–808 Keller C (2000) Instrumentation for astrophysical spectropolarimetry, XII canary Island school on astrophysics. http://www.noao.edu/staff/keller/lectures/ Leroy JL (2000) Polarization of light and astronomical observation. Gordon & Breach Science Publishers, Amsterdam Maund JR, Höflich P, Patat F, Wheeler JC, Zelaya P, Baade D et al (2010) The unification of asymmetry signatures of Type Ia supernovae. ApJ Lett 725:167–171 Maund JR, Spyromilio J, Höflich PA, Wheeler JC, Baade D, Clocchiatti A et al (2013) Spectropolarimetry of the Type Ia supernova 2012fr. MNRAS 433:L20–L24 McCall ML (1984) Are supernovae round? I – the case for spectropolarimetry. MNRAS 210: 829–837 Patat F, Romaniello M (2006) Error analysis for dual-beam optical linear polarimetry. PASP 118:146–161 Patat F, Baade D, Höflich P, Maund JR, Wang L, Wheeler JC (2009) VLT spectropolarimetry of the fast expanding Type Ia SN 2006X. A&A 508:229–246 Patat F, Taubenberger S, Cox NLJ, Baade D, Clocchiatti A, Höflich P et al (2015) Properties of extragalactic dust inferred from linear polarimetry of Type Ia supernovae. A&A 577:53

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Serkowski K, Matheson DS, Ford VL (1975) Wavelength dependence of interstellar polarization and ratio of total to selective extinction. ApJ 196:261–290 Shapiro PR, Sutherland PG (1982) The polarization of supernova light – a measure of deviation from spherical symmetry. ApJ 263:902–924 Shurcliff WA (1966) Polarized light, production and use. Harvard University Press, Cambridge Tinbergen J (1996) Astronomical polarimetry. Cambridge University Press, Cambridge Trammel SR, Hines DC, Wheeler JC (1993) Spectropolarimetry of SN 1993J in NGC 3031. ApJ 414:L21-L24 Tran HD, Filippenko AV, Schmidt GD, Bjorkman KS, Jannuzi BT, Smith PS (1997) Probing the geometry and circumstellar environment of SN 1993J in M81. PASP 109:489–503 Wang L, Baade D, Höflich P, Wheeler JC (2003) Spectropolarimetry of SN 2001el in NGC 1448: asphericity of a normal Type Ia supernova. ApJ 591:1110–1128 Wang L, Baade D, Höflich P, Wheeler JC, Kawabata K, Khokhlov A et al (2006) Premaximum spectropolarimetry of the Type Ia SN 2004dt. ApJ 653:490–502 Wang L, Baade D, Patat F (2007) Spectropolarimetric diagnostics of thermonuclear supernova explosions. Science 315:212 Wang L, Wheeler JC (2007) Spectropolarimetry of supernovae. ARA&A 46:433–474

Part VI Explosion Mechanisms of Supernovae

Explosion Physics of Core-Collapse Supernovae

38

Thierry Foglizzo

Abstract

The physical ingredients and processes ruling the violent death of a massive star are reviewed, from the collapse of its core to the birth of a neutron star and the ejection of the stellar envelope. The crucial phase of this transition results from the complex interplay of many fields of physics: quantum physics, gravitation, nuclear physics, neutrino physics, and magnetohydrodynamics. Recent numerical simulations have revealed the diversity of explosion paths induced by the diversity of progenitor structures. 3D simulations are now capable of exploring the consequences of pre-collapse asymmetries in the stellar core, such as the distribution of angular momentum, magnetic fields, and combustion inhomogeneities. They also revealed the limitations of the 2D results which assumed an axisymmetric evolution. Even with the fastest computers, physical approximations are still unavoidable to calculate neutrino transport. We describe the explosion physics based on the most robust results, privileging simplified descriptions conducive to the deepest physical understanding. We emphasize the role of hydrodynamical instabilities and their consequences on the nonspherical character of the explosion.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiphysics: Quantum Mechanics, Relativity, and Nuclear EOS . . . . . . . . . . . . . . . . . 2.1 Gravity, Special Relativity, Quantum Mechanics, and the Chandrasekhar Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Gravitational Energy and Dissociation Through the Accretion Shock . . . . . . . . . 2.3 Neutrino Physics: Neutronization, Neutrino Absorption, and Neutrino Pairs . . .

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T. Foglizzo () Laboratoire AIM (CEA/Irfu, CNRS/INSU, University Paris Diderot), CEA Saclay, Gif sur Yvette, Paris, France e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_52

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2.4 General Relativity, Nuclear Compressibility, and the Maximum Mass of Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Rotational and Magnetic Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Multidimensional Hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Observational Evidence for Multidimensional Physics . . . . . . . . . . . . . . . . . . . . . 3.2 Buoyancy-Driven Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The Standing Accretion Shock Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Consequences on the Diversity of Explosion Paths . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Multidimensional Impact of Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1060 1062 1063 1063 1063 1065 1068 1069 1069 1070 1070

Introduction

The explosion of massive stars has challenged our theoretical understanding for several decades, despite the observation of hundreds of new supernovae in distant galaxies every year. Within a few million years after their birth, the core of massive stars is able to accumulate a critical mass of iron from nuclear fusion. At this point of stellar evolution, their outer radius can exceed several hundred millions kilometers, unless a significant fraction of their envelope has been lost through a wind or in a binary interaction. The fate of this supergiant depends on the dynamics of the gas in the inner few hundred kilometers: the collapsing core is expected to bounce into an explosion in less than a second, while giving birth to a neutron star or a black hole. In this tiny region of space illustrated in Fig. 1, the mechanism of the explosion depends crucially on complex physical processes involving general relativity, multidimensional magnetohydrodynamics, nuclear physics, and neutrino interactions. The subsequent gravitational unbinding of the stellar envelope is a formality compared to the difficulty of escaping the steep potential well close to the proto-neutron star, against a heavy rain of free-falling iron reaching one tenth of the speed of light at 300 km from the center. Once the explosion shock is launched from the inner region, it takes several hours of propagation across the envelope before its visible breakout at the stellar surface. The only direct evidence of the dynamics of the first second can be expected from neutrinos and gravitational waves. The few neutrinos observed from SN 1987A in the neighborhood of the Milky Way have strengthened the scenario imagined by Colgate and White (1966) based on the collapse of the iron core of a massive star. Unfortunately no galactic supernova has been observed in better detail since then. The physics of core-collapse supernovae presented in this chapter is largely based on the scenario of delayed neutrino-driven explosions proposed by Bethe and Wilson (1985), described in Sect. 2.3 and in a dedicated chapter in this book ( Chap. 40, “Neutrino-Driven Explosions” by H.T. Janka). This framework has produced robust explosions only for the lightest progenitors (Kitaura et al. 2006). Numerical simulations suggest that the explosion of stars more massive than 10Msol depends strongly on transverse motions induced by hydrodynamical instabilities presented in Sect. 3. These calculations require very high-performance computers to treat multidimensional neutrino transport. A direct

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Fig. 1 Characteristic timescales and length scales from the birth of a 15Msol star to its death as a supernova with the formation of a neutron star. The arrows follow the evolution of the diameter of the star (pink arrow) and the stages of nucleosynthesis in its core from hydrogen to iron (blue arrow). The explosion physics described in this chapter corresponds to the transition between the collapse of the iron core (purple arrow) and the launch of the shock accompanied by the formation of the neutron star (yellow arrows) (Credit for the simulation: R. Kazeroni/CEA. Credits for the images of SN 1987A: HST/NASA, Cassiopeia A: NASA/JPL-Caltech, Vela: Rosat/NASA, the Crab pulsar: Chandra X-ray Observatory/NASA)

Boltzmann approach in 3D is currently limited to very short timescales (Sumiyoshi et al. 2015). Progress over the last 20 years has benefited from the acceleration of processors speeds, the improved efficiency of numerical schemes, better adapted grid geometries, and the development of new techniques for approximate neutrino transport. Progress has also been achieved on the physical side with the discovery of new hydrodynamical instabilities, the accurate calculation of general relativistic effects, and the inclusion of magnetic fields. A better understanding of neutrino interactions revealed unexpected effects such as the possible role of strangeness in neutrino-nucleon scattering. Observations have also contributed to this progress by constraining the equation of state at nuclear density from the detection of 2Msol neutron stars.

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Despite the difficulties of the theoretical modeling within the delayed neutrinodriven framework, which can be disappointing, we consider that the numerical uncertainties associated with multidimensional calculations are still too large to support a pessimistic position. Nevertheless, we must not forget that alternate scenarios should also be explored even if none of these is convincing yet. Additional effects may involve strong large-scale magnetic fields yet to be explained (Moiseenko et al. 2006) or an ad hoc phase transition to quark matter (Fischer et al. 2011).

2

Multiphysics: Quantum Mechanics, Relativity, and Nuclear EOS

The explosion physics involves a wide range of densities from a few 109 g=cm3 in the iron core to a few 1015 g=cm3 inside the proto-neutron star. These two extremes correspond to the existence of two critical masses. The first one defines the maximum mass of a gravitating gas supported by the degeneracy pressure of relativistic electrons (noted MCh ). The second critical mass is the maximum mass of a gravitating gas supported by the strong interaction between neutrons (noted MTOV ), above which it collapses to a black hole. The collapse of the stellar core starts when its mass reaches the threshold MCh , which happens as a natural consequence of nucleosynthesis if the star is massive enough (10–100Msol ). The main difficulty of supernova theory is to identify the robust mechanism responsible for the launch of an explosion before the mass accumulated at the center reaches the critical threshold MTOV .

2.1

Gravity, Special Relativity, Quantum Mechanics, and the Chandrasekhar Mass

The nuclear reactions at the center of a star feed on the nuclear binding energy which increases from hydrogen to iron (Fig. 2). If the star is massive enough, each stage of nuclear burning is followed by a contraction of the stellar core which increases the density and temperature of the ashes until the next threshold of nuclear burning is reached. Since the iron group elements have the highest binding energy per nucleon, iron is bound to accumulate as an inert core of stably stratified ashes. The death of a star is triggered by the sudden loss of electronic pressure as its core approaches the Chandrasekhar mass. This threshold is a consequence of quantum mechanics, Newtonian gravity, and special relativity, together with electric neutrality between charged particles (i.e., electrons and protons). As densities approach 7  109 g=cm3 in the iron core, the 26 electrons of 56 Fe are packed so closely that the Heisenberg relation pe xe „ relating their interspacing xe and momentum pe implies relativistic velocities. Using the electron fraction Ye to relate the electron interspacing to the gas density   mp =.Ye xe3 /,  1  13  „ Ye  3  pe   4:8 : (1) me c me c mp 7  109 g=cm3

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Fig. 2 Binding energy per nucleon. Fusion reactions in the stellar core extract the binding energy of nuclei from hydrogen to iron. Heavier nucleons up to silver may be formed by explosive nucleosynthesis during the supernova explosion. The heaviest elements are probably formed in other sites such as coalescing neutron stars

The stellar core dominated by the pressure of degenerate relativistic electrons Pdeg  pe c=3xe3 is described by an adiabatic constant  D 4=3 with an entropy set by the electron fraction: Pdeg 4

3

 

Ye mp

 43 „c:

(2)

The central density diverges as the mass of this gas approaches a critical value which scaling / .„c=G/3=2 Ye2 =m2p is directly deduced from a dimensional analysis of the hydrostatic equilibrium rPdeg D GM .r/=r 2 using Eq. (2). An exact calculation yields the Chandrasekhar mass MCh : 

MCh

„c  3:0 G

 32

Ye2  1:4Msol m2p



Ye 0:5

2 :

(3)

As the mass of the iron core approaches this critical threshold, the density at the center is able to increase up to the point where the reactions of electron capture and photo-dissociation decrease the electron fraction Ye , decrease the pressure support, and further decrease the Chandrasekhar mass in a runaway process.

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In the intermediate range 9–10Msol , the collapse begins before the burning of oxygen into silicon and iron; the Chandrasekhar mass is reached by the degenerate core of oxygen, neon, and magnesium, leading to an electron capture supernova (Kitaura et al. 2006). At the higher end of stellar mass distribution M > 100Msol , an explosion can take place well before these late stages as the radiation pressure from gamma rays is decreased by a runaway production of electrons and positrons in their oxygen core. This mechanism is referred to as pair-instability supernova.

2.2

Gravitational Energy and Dissociation Through the Accretion Shock

As the pressure support disappears in the stellar core, the collapsing iron gas reaches free-fall velocities which are supersonic. The contraction of the iron core into a proto-neutron star of 30 km produces a gigantic gravitational energy Ecollapse of the order of: Ecollapse 

 2  Mns GMns2 30 km  1:7  1053 erg : Rns Rns 1:4Msol

(4)

This energy increases as the mass accumulates up to the typical observed mass of neutron stars 1.4Msol and as its radius contracts to 30 km during the first few hundred milliseconds after bounce. Ecollapse and its time dependence are sensitive to the inner composition and dynamics, the stiffness of the equation of state, and the detailed microphysics, as well as the external pressure exerted by the infalling gas. Regardless of this complexity, the energy Ecollapse is two orders of magnitude larger than both the kinetic energy 1–21051 erg observed in the ejecta of a typical supernova and the energy 0.4–1.21051 erg needed to gravitationally unbind the stellar matter outside the iron core (Ugliano et al. 2012). A fraction of the gravitational energy of contraction is used to transform iron nuclei into the neutrons composing the neutron star. At a rate of 8:8 MeV=nucleon (Fig. 2), Edisso

  Mns Mns 52 :   8:8 MeV  2:2  10 erg mn 1:4Msol

(5)

This dissociation is initiated where the kinetic energy of free fall is converted into heat, across an accretion shock produced by the deceleration onto the surface of the proto-neutron star. The kinetic energy of free-falling iron nuclei exceeds their dissociation energy below 220 km: 1 m v2 2 n ff

8:8 MeV



220 km r



Mns 1:4Msol

 :

(6)

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The energy cost of dissociation has a dramatic effect on the dynamics of the shock wave: instead of an elastic spherical bounce, the shock stalls at about 150 km from the center of the star while most of the gravitational energy of contraction is converted into neutrinos which escape from the star with little interactions (Sect. 2.3), and while hydrodynamical instabilities break the spherical symmetry (Sect. 3). If the shock is successfully revived, the reactions of recombination restitute the dissociation energy of the ejected gas as the shock moves outward beyond 220 km. According to Fig. 2, the nuclear burning of oxygen into silicon and iron could contribute to the explosion energy only if several tenth of solar masses were involved (Nakamura et al. 2014):   MO MO :  0:8 MeV  1:4  1050 erg mn 0:1Msol

2.3

(7)

Neutrino Physics: Neutronization, Neutrino Absorption, and Neutrino Pairs

The neutrinosphere is defined as the surface of the dense region ( > 1011 g=cm3 ) within which neutrino transport is diffusive. Inside the neutrinosphere, a thermal equilibrium of gamma photons, particles, and antiparticles creates pairs of neutrinos and antineutrinos which diffuse out. The outgoing flux of neutrinos and antineutrinos is dominantly emitted by the neutrinosphere like a black body, but an additional component comes from the cooling region above it where electrons are captured by protons to form neutrons and electronic neutrinos: p C e  ! n C e :

(8)

Note that this efficient cooling reaction is possible only for relativistic electrons, since the proton is lighter than the neutron. Denoting by e the Lorentz factor of the electron: e >

mn  mp  2:5: me

(9)

A small fraction of the outgoing neutrinos and antineutrinos is captured by neutrons and protons in the post-shock region: e C n ! p C e  ; C

N e C p ! n C e :

(10) (11)

These reactions are the main sources of heating close to the shock, in a region referred to as the gain layer (r  60–150 km) where the negative entropy gradient favors neutrino-driven convection.

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Fig. 3 A stationary shock stalls at 150 km from the center, while neutrinos and antineutrinos diffuse out of the central proto-neutron star. Iron nuclei heated up across the shock are dissociated into nucleons. Electron capture produces neutrons and neutrinos (dark blue region). The explosion relies on the capture of neutrinos and antineutrinos in the gain region (light blue region)

The radial structure of the accretion flow can thus be schematized into four successive regions delimited by the shock, the gain radius, and the neutrinosphere (Fig. 3). The actual set of interactions is more complex, involving nuclei of intermediate mass between the nucleons and the iron atoms (mainly alpha particles), all types of neutrinos and antineutrino species and their scattering on particles and antiparticles. In particular, the scattering cross section of neutrinos on neutrons may be sensitive to their strangeness in a way which could influence the explosion threshold (Melson et al. 2015).

2.4

General Relativity, Nuclear Compressibility, and the Maximum Mass of Neutron Stars

The corrections due to general relativity can be interpreted in classical terms as a deepening of the gravitational potential, which increases the energy available for the explosion (Bruenn et al. 2001). The magnitude of general relativistic effects can be estimated by comparing the radius of the proto-neutron star to its Schwarzschild radius: 2GMns ; c2    30 km Mns :  0:14 1:4Msol Rns

RSch 

(12)

RSch Rns

(13)

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General relativistic corrections affecting the size of the contracting neutron star are thus expected to impact the energy budget of the explosion, even to second order in (RSch =Rns ). The most recent multidimensional simulations of core collapse adopt a full GR framework in 3D (Kuroda et al. 2014, Abdikamalov et al. 2015, Müller 2015). An important by-product of general relativity is the perspective of identifying the signature of the explosion mechanism through the detection of gravitational waves ( Chap. 63, “Gravitational Waves from Core-Collapse Supernovae” by K. Kotake). The most dramatic consequence of general relativity is the existence of a threshold for the maximum mass of neutrons closely packed against each other, noted MTOV since it was first estimated in 1939 by Tollman, Oppenheimer, and Volkov. Progress in the study of nuclear matter later emphasized the role of the strong interaction between neutrons, which can be approximated as a gas with an adiabatic index  D 2 (e.g. Fig. 2 in Lattimer 2012) to be compared with  D 4=3 for the relativistic electrons of the iron core. The nonrelativistic character of degenerate neutrons packed together can be estimated using the Heisenberg relation when the distance between neutrons is comparable to the size of a free neutron:   13 ns pn  0:18  1: mn c 1015 g=cm3

(14)

Without solving the equations of general relativity, the existence of a limiting mass for neutron stars can be deduced from the small compressibility of nuclear matter, by calculating the Schwarzschild radius associated to a sphere of incompressible neutrons. Its Schwarzschild radius scales linearly with its mass M, whereas its physical radius R scales like M 1=3 :

R

M 4

 3 ns

! 13 :

(15)

The mass Mcrit above which the radius of a sphere with uniform density ns is smaller than its Schwarzschild radius is:  Mcrit 

3c 6 5 2 G 3 ns

 12  4Msol :

(16)

Despite the extreme simplicity of this calculation, it is interesting to note that a mass commensurate with the mass of a neutron star can be derived from the typical density of a neutron ns , the speed of light c, and the gravity constant G. For comparison, applying the same argument to typical atomic densities such as “incompressible” liquid water (1proton=Angstrom3 D 1:7 g=cm3 ) would imply a critical mass of 108 Msol .

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The density of a real neutron star is not uniform of course, and its composition includes a fraction of electrons and protons. Besides, the nuclear compressibility extrapolated from laboratory experiments is still debated (230 ˙ 40 MeV in Khan et al. 2012). The exact value of the maximum mass of neutron stars is not fully determined yet, but several observations suggest that it exceeds 2Msol (Antoniadis et al. 2013). It takes only a few seconds for the free-falling envelope of the star to accumulate a mass MTOV at the center, depending on the assumed equation of state of nuclear matter and the compactness  of the stellar core (O’Connor and Ott 2011; Peres et al. 2013). This latter parameter compares the radius of the inner 2:5Msol to its Schwarzschild radius, the more compact core structures corresponding to the shortest time of collapse to a black hole.

2.5

Rotational and Magnetic Energies

Theoreticians have tried to understand the explosion mechanism without relying on the rotational energy because the majority of massive stars are believed to end their life with an explosion despite the moderate angular momentum in their cores. Angular momentum can be efficiently evacuated outward during stellar evolution through magnetic fields (Heger et al. 2005) or internal gravity waves (Fuller et al. 2015). The observed spin period of the residual neutron star (few 10–100 ms) would correspond to a modest rotation of the iron core if one assumes that they carry the same angular momentum. Besides, the general arguments predicting angular momentum transport are currently revised in the direction of a slower core rotation in order to account for the asteroseismic measurements in evolved low-mass stars (Cantiello et al. 2014). The scaling of rotational energy using angular momentum conservations is: Erot  2:8  1050 erg



Mns 1:4Msol



Rns 10 km

2 

10 ms Pns

2 :

(17)

The differential rotation on which the magnetic energy can feed is only a fraction of the rotational energy. In contrast, a fast rotation in a minority of occurrences is believed to lead to energetic bipolar explosions referred to as hypernovae, with explosion energies which can exceed 1052 ergs. Observed signatures of these bipolar explosions include spectroscopic features such as double-peaked profiles in the oxygen emission line (Maeda et al. 2008). Such explosions are probably mediated by the efficient conversion of rotational energy into magnetic energy. Between the extreme cases of rotation-dominated hypernovae and the explosion of nonrotating stars, a modest amount of rotational and/or magnetic energy can affect the development of multidimensional instabilities and influence the birth conditions of pulsars, if not the explosion scenario itself.

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3

Multidimensional Hydrodynamics

3.1

Observational Evidence for Multidimensional Physics

Although the supernova remnants are globally spherical, a closer look at their inner parts reveals several hints of asymmetrical conditions of explosion. In particular, spectropolarimetry at the beginning of the nebular phase indicates that the asymmetry of the inner regions of type IIP supernovae increases inward (Leonard et al. 2006). Large-scale inhomogeneities in the distribution of 44 Ti have been observed in Cassiopeia A (Grefenstette et al. 2014), suggesting an asymmetric nucleosynthesis. The velocity distribution of pulsars (Hobbs et al. 2005) also requires a significant degree of explosion asymmetry which cannot be explained by the orbital velocity of a binary system disrupted by the explosion. Moreover, the ejecta of SN 1987A appear elongated in a direction which does not coincide with the symmetry axis of the circumstellar medium (Larsson et al. 2013).

3.2

Buoyancy-Driven Instabilities

Buoyancy plays a major role in breaking the spherical symmetry during core collapse, because the entropy produced by the shock increases downward in several regions. The Brunt-Väisälä frequency !BV characterizes the stability of the vertical exchange of gas layers, including the gradients of electronic fraction Ye : 2 !BV

1 D 

"

@ @S

 Ye ;P

dS C dr



@ @Ye

 S;P

dYe dr

#

d˚ : dr

(18)

The destabilizing contribution of the gradients of Ye is dominant inside the protoneutron star, where the convective instability referred to as Ledoux convection has a modest effect on the neutrino luminosity (Dessart et al. 2006) but may contribute to the generation of the magnetic field of the pulsar (Thompson and Duncan 1993). The amount of entropy produced by a shock depends on the relative velocity of the incoming supersonic gas. The velocity vff of this upstream gas increases inward following an approximate free-fall profile:  vff 

2GMns r

 12 :

(19)

As the shock moves outward and decelerates to reach its stalled position, the downstream distribution of entropy decreases outward. The resulting instability, referred to as prompt convection, triggers some vortical motions which homogenize the entropy profile on a short timescale (50 ms pb).

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Fig. 4 The size of the convective cells produced by neutrino-driven convection is comparable to the size of the gain region (Adapted from Foglizzo et al. 2006)

Fig. 5 Effect of advection on the convective growth rate measured by the  parameter. The growth rate is normalized by the maximum value of the Brunt-Väisälä local growth rate. The horizontal axis measures the horizontal wave number normalized by the vertical size H of the gain region (Adapted from Foglizzo et al. 2006)

The dominant effect of buoyancy takes place inside the gain region (100– 150 km) where the negative entropy gradient is governed by the reactions of neutrino absorption. This instability is known as neutrino-driven convection (Herant et al. 1992). The horizontal length scale of the transverse motions is comparable to the radial size of the gain region (Fig. 4), corresponding typically to a spherical harmonics l  6 in the linear regime. Larger azimuthal scales appear if the radial size of the gain region increases. However, the gain region is unstable only if buoyancy is strong enough to overcome the downward motion associated to advection (Foglizzo et al. 2006). The criterion for linear instability can be expressed as  > 3 (Fig. 5), where the parameter  compares the local Brunt-Väisälä timescale 1=!BV and the advection timescale across the gain region: Z

shock



!BV gain

dr : vr

(20)

The possibility that convection may be triggered by finite amplitude density perturbations has been pointed out by Scheck et al. (2008). The nonlinear outcome of this convective instability seems to correspond to a flow where the parameter  averaged over spherical shells is close to marginal stability   3 (Fernandez et al.

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2014). The convective instability is favorable to an explosion because the post-shock pressure is increased by the turbulent motions: the shock is pushed outward and the size of the gain region is increased. Besides this pressure effect, the gas entrained in convective motions stays longer in the gain region than if its trajectory was radial. It is thus exposed to the neutrino flux for a longer time (Couch and Ott 2015; Murphy and Burrows 2008). Once the shock is launched, its propagation across the onion-like structure of the star triggers interchange motions at the composition interfaces. Such motions are the consequence of the Richtmyer-Meshkov instability, which can be viewed as a Rayleigh-Taylor instability of the interface experiencing an impulsive acceleration rather than a permanent one. The resulting mixing and inhomogeneities have important consequences on the light curve and spectrum of the supernova and the emergence time of X-rays and gamma rays. The amplitude of these interface instabilities is sensitive to the initial degree of asphericity of the shock. The asymmetric shock produced by hydrodynamic instabilities seems compatible with the strong mixing and high Ni clump velocities observed in SN 1987A (Utrobin et al. 2015).

3.3

The Standing Accretion Shock Instability

The standing accretion shock instability (SASI) is a global instability of the shock which is dominated by large-scale oscillations (Blondin et al. 2003). Motions can be oscillatory (m D 0) as observed in 2D axisymmetric simulations or spiral patterns (m D ˙1; ˙2) as observed in 3D simulations (Blondin and Mezzacappa 2007; Hanke et al. 2013). The mechanism of this instability is due to an unstable advective-acoustic cycle between the shock and the proto-neutron star, as illustrated in Fig. 6 (Foglizzo et al. 2007; Guilet and Foglizzo 2012). As the spherical shock reaches its stalled position,

Fig. 6 Mechanism of the SASI. Acoustic waves (wavy arrows) reaching the shock trigger the formation of entropy and vorticity perturbations (circular arrows). Their advection toward the proto-neutron star generates an acoustic feedback with a larger amplitude than the initial acoustic wave

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small perturbations generate both entropy and vorticity perturbations which are advected toward the neutron star. Such perturbations would be independent of acoustic perturbations if the post-shock flow was uniform. However, both velocity and temperature gradients in the underlying accretion flow are responsible for a linear coupling between advected and acoustic perturbations. The subsonic flow is strongly decelerated close to the neutrinosphere, where cooling by neutrino emission is strongest. In addition, adiabatic compression by gravity is responsible for a temperature gradient. As a consequence, vorticity and entropy perturbations reaching the neutron star produce some acoustic feedback. This acoustic feedback is able to reach the shock and trigger the formation of new entropy and vorticity perturbations which amplitudes are a factor Q larger than the initial ones (Foglizzo 2009). The typical oscillation time is the advection timescale adv from the shock to the neutrinosphere. If Q > 1, the growth rate !i associated to this advective-acoustic cycle is:

!i 

1 adv

log jQj:

(21)

The nonlinear saturation of SASI takes place when the amplitude of the entropy and vorticity waves produced by the shock oscillations is large enough to produce their disruption by the parasitic growth of Kelvin-Helmholtz and Rayleigh-Taylor instabilities (Guilet et al. 2010). The turbulent motions induced by SASI (Endeve et al. 2012) are also able to add a turbulent component to the thermal pressure and push the shock further out, thus enlarging the gain region until the shock is revived by neutrino absorption. An analogue of SASI has been observed in a shallow water experiment, where acoustic waves and shocks in a compressible gas are replaced by surface gravity waves and hydraulic jumps in water. The gravitational field of the neutron star is mimicked by the hyperbolic shape of the potential surface on which water flows radially, and a stationary hydraulic jump is produced by a central cylinder mimicking the neutron star surface (Foglizzo et al. 2012). Water is evacuated by overflowing over the upper edge of the central cylinder. Despite the absence of entropy effects and the viscous drag slowing down the free fall of water, this experiment demonstrates a dynamics very similar to the dynamics observed in gas accretion in cylindrical geometry (Fig. 7). The oscillation timescale (3 s) is hundred times slower than the 30 ms SASI oscillations, and the typical radius of the hydraulic jump (15 cm) is one million times shorter than the shock distance (150 km). If the stellar core does not contain angular momentum, the oscillations of the shock grow exponentially in a random direction and may turn into a rotating motion along a random axis once nonlinear amplitudes are reached (Blondin and Mezzacappa 2007; Kazeroni et al. 2016). The development of this large-scale instability can be disrupted by abrupt changes in the size of the post-shock cavity as observed with the arrival of the Si/SiO interface (Hanke et al. 2013).

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Fig. 7 Nonlinear development of the spiral SASI mode viewed in entropy (top). The same dynamics is observed in the numerical simulation of shallow water equations (left) and in the supernova fountain (right) (Credit R. Kazeroni/AIM-CEA, M. González/AIM-Univ Paris Diderot)

The spiral mode of SASI is able to separate the flow into a prograde region following the external regions of the post-shock flow and a retrograde region which is advected toward the neutron star (Blondin and Mezzacappa 2007; Guilet and Fernandez 2014). This behavior is also observed in the supernova fountain (Foglizzo et al. 2012). If the shock is revived by neutrino energy and ejects the prograde angular momentum, the central pulsar is born with the opposite angular momentum. This spin-up of pulsars born from nonrotating stellar cores may reach rotation periods of the order of 100 ms. Conversely, the preferred development of the spiral mode of SASI in the same direction as the rotating stellar core would lead to a spin down of the pulsar compared to an axisymmetric evolution where the angular momentum would be simply advected (Blondin and Mezzacappa 2007; Yamasaki and Foglizzo 2008). The larger shock amplitude is favorable to the shock revival (Iwakami et al. 2014). Another large-scale instability m D 1; 2 takes place when the rotation rate is increased, known as the low T/W instability in neutron stars rotating differentially. It is based on the amplification of acoustic waves reflected on a surface of corotation. This instability also takes place during the formation of a proto-neutron star and could be a source of gravitational waves. Recent simulations by Kuroda et al. (2014) suggest that the interplay with SASI deserves further clarification. Either dominated by spiral or sloshing motions, the dominant l D 1 character of SASI is responsible for a displacement of the center of mass of the proto-neutron star in the direction opposite to the asymmetric ejecta. This mechanism seems to be able to explain the velocity distribution of pulsars up to 1000 km/s (Scheck et al. 2006). The opposite linear momentum is distributed in the asymmetric ejecta. The proto-neutron star continues to be accelerated due to the asymmetric gravitational

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pull, over a 3 s timescale which can continue significantly later than the accretion timescale (Wongwathanarat et al. 2013). Asymmetric explosions produce more heavy elements in the direction where the shock is stronger, as anticipated by Wongwathanarat et al. (2013). These results are compatible with the observations of 44 Ti in Cassiopeia A by Grefenstette et al. (2014), where the clumps are predominantly in the half plane opposite to the direction of the compact remnant. The large-scale oscillations of the shock are also responsible for a modulation of the neutrino flux produced in the accretion flow above the neutrinosphere, with a characteristic period comparable to the advection timescale from the shock to the neutrinosphere. Such oscillations could be detected by the IceCube detector in Antarctica if a supernova explodes in our galaxy (Tamborra et al. 2013, and  Chap. 40, “Neutrino-Driven Explosions” by H.T. Janka in this book).

3.4

Consequences on the Diversity of Explosion Paths

Both neutrino-driven convection and SASI are able to develop and sustain non-radial motions during several hundred milliseconds after bounce. Both generate vorticity and turbulence which contribute to push the shock further out, thus enlarging the size of the gain region where neutrinos energy can be intercepted. Both allow for simultaneous accretion and ejection. Gravitational energy from accretion can be fed into the explosion over a much longer timescale than in spherical symmetry. Such topology has been observed in the axisymmetric simulations of Müller (2015) over several seconds. The physical understanding of the mechanisms of these two instabilities indicates that the conditions favoring their development are distinct: - Neutrino-driven convection is efficient if the neutrino luminosity is high and if the buoyancy timescale is shorter than a third of the advection time ( > 3) - SASI is favored by a short advection time because its growth rate scales like 1= adv . The nonlinear saturation amplitude is also highest if the advection time is short, because parasitic instabilities need a larger SASI amplitude to grow against a fast downward flow. Conversely, neutrino heating would limit the amplitude of SASI by favoring the parasitic growth of the Rayleigh-Taylor instability on the entropy waves produced by SASI. These properties help interpret the recent numerical simulations showing different paths to explosion (Müller et al. 2012), either mediated by neutrino-driven convection or SASI. The neutrino luminosity, the mass accretion rate, and the efficiency of neutrino cooling affect the shock radius and the  parameter (Fernandez et al. 2014; Scheck et al. 2008). As noted by Cardall and Budiardja (2016), the SASI instability is able to produce the same effect as neutrino-driven convection, while neutrino absorption is weak: the gain region is able to capture neutrinos more efficiently once enlarged by turbulent pressure and buoyant entropy bubbles.

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The multidimensional evolution is also influenced by the pre-collapse inhomogeneities associated with the combustion of oxygen and silicon (Couch and Ott 2015 and  Chap. 69, “Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Supernova Mechanism” By S.M. Couch in this Handbook) which may favor SASI or convection if the size of the inhomogeneities is adapted to the structure of the post-shock eigenmodes (Müller and Janka 2015). Additional diversity relative to the stellar structure may come from binary interactions during the lifetime of the star, which could affect the distribution of angular momentum in the stellar core and confuse the identification of the initial stellar mass on the main sequence (de Mink et al. 2014).

3.5

Multidimensional Impact of Magnetic Fields

The turbulent motions associated to SASI are able to amplify small-scale magnetic fields up to magnetar strength, with uncertain results on the dynamics of the explosion (Endeve et al. 2012; Obergaulinger et al. 2014). The magnetorotational instability (MRI) can lead to an efficient growth of the magnetic field in the vicinity of the proto-neutron star (Mösta et al. 2015). The higher the differential rotation, the faster the growth of the magnetic field and the stronger its effects. Past simulations have generally assumed that a large-scale magnetic field results from the hypothetical growth of a dynamo based on the MRI and observe the formation of magnetic jets and a bipolar explosion (Burrows et al. 2007). Future ab initio calculations of the magnetic field in a proto-neutron star will have to take into account the effect of neutrinos on the dynamics of this instability, which can act as a viscosity or a drag force depending on their mean free path (Guilet et al. 2015).

4

Conclusions

Recent progress in supernova theory has emphasized the impact of the stellar core structure on the multidimensional dynamics, which results in a diversity of paths toward an explosion ultimately driven by neutrinos. The parameter space describing the diversity of progenitor structures has not been explored with 3D simulations yet. This parameter space has to be defined by improved theories of stellar evolution, which would ideally include the 3D distribution of angular momentum, magnetic fields, and combustion inhomogeneities. Much work and numerical resources are still needed to evaluate the robustness in 3D of the many results obtained from 2D numerical simulations of core collapse, especially when a turbulent cascade is involved (Abdikamalov et al. 2015; Hanke et al. 2012; Müller 2015). The approximations for neutrino transport are still debated, and checking the numerical convergence is made more difficult by the stochastic nature of some instabilities. While theoretical efforts still have a long way to go to describe the dynamics of the first second from first principles, some direct comparison with a real supernova

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would be very helpful. The most direct signature is expected from the detection of neutrinos ( Chap. 59, “Neutrino Emission from Supernovae” by H.T. Janka) and gravitational waves ( Chap. 63, “Gravitational Waves from Core-Collapse Supernovae” by K. Kotake). Hopefully modern detectors will be ready and sensitive enough when the next supernova explodes in our galaxy and close enough to be detected.

5

Cross-References

 Gravitational Waves from Core-Collapse Supernovae  Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Super-

nova Mechanism  Neutrino-Driven Explosions  Neutrino Emission from Supernovae Acknowledgements This work is part of the ANR-funded project SN2NS ANR-10-BLAN-0503. TF acknowledges the help of Rémi Kazeroni, Jérôme Guilet, Matthias González, Frédéric Masset, and Gilles Durand.

References Abdikamalov E, Ott CD, Radice D, Roberts LF, Haas R, Reisswig C, Mösta P, Klion H, Schnetter E (2015) Neutrino–driven turbulent convection and standing accretion shock instability in three– dimensional core-collapse supernovae. ApJ 808:70 (22p) Antoniadis J, Freire PCC, Wex N, Tauris TM, Lynch RS, van Kerkwijk MH, Kramer M, Bassa C, Dhillon VS, Driebe T, Hessels JWT, Kaspi VM, Kondratiev VI, Langer N, Marsh TR, McLaughlin MA, Pennucci TT, Ransom SM, Stairs IH, van Leeuwen J, Verbiest JPW, Whelan DG (2013) A massive pulsar in a compact relativistic binary. Science 340:1233232 (9p) Bethe HA, Wilson JR (1985) Revival of a stalled supernova shock by neutrino heating. ApJ 295:14–23 Blondin JM, Mezzacappa A (2007) Pulsar spins from an instability in the accretion shock of supernovae. Nature 445:58–60 Blondin JM, Mezzacappa A, DeMarino C (2003) Stability of standing accretion shocks, with an eye toward core-collapse supernovae. ApJ 584:971–980 Bruenn SW, De Nisco KR, Mezzacappa A (2001) General relativistic effects in the core collapse supernova mechanism. ApJ 560:326–338 Burrows A, Dessart L, Livne E, Ott CD, Murphy J (2007) Simulations of magnetically driven supernova and hypernova explosions in the context of rapid rotation. ApJ 664:416–434 Cantiello M, Mankovich C, Bildsten L, Christensen–Dalsgaard J, Paxton B (2014) Angular momentum transport within evolved low-mass stars. ApJ 788:93 (7p) Cardall CY, Budiardja RD (2016) Stochasticity and efficiency in simplified models of core-collapse supernova explosions. ApJL 813:L6 (6p) Colgate SA, White RH (1966) The hydrodynamic behavior of supernovae explosions. ApJ 143:626–681 Couch SM, Ott CD (2015) The role of turbulence in neutrino-driven core-collapse supernova explosions. ApJ 799:5 (12p) de Mink SE, Sana H, Langer N, Izzard RG, Schneider FRN (2014) The incidence of stellar mergers and mass gainers among massive stars. ApJ 782:7 (8p)

38 Explosion Physics of Core-Collapse Supernovae

1071

Dessart L, Burrows A, Livne E, Ott CD (2006) Multidimensional radiation/hydrodynamic simulations of proto–neutron star convection. ApJ 645:534–550 Endeve E, Cardall CY, Budiardja RD, Beck SW, Bejnood A, Toedte RJ, Mezzacappa A, Blondin J (2012) Turbulent magnetic field amplification from spiral SASI modes: implications for corecollapse supernovae and proto-neutron star magnetization. ApJ 751:26 (28p) Fernandez R, Müller B, Foglizzo T, Janka HT (2014) Characterizing SASI- and convectiondominated core-collapse supernova explosions in two dimensions. MNRAS 440: 2763–2780 Fischer T, Sagert I, Pagliara G, Hempel M, Schaffner–Bielich J, Rauscher T, Thielemann FK, Käppeli R, Martínez–Pinedo G, Liebendörfer M (2011) Core–collapse supernova explosions triggered by a quark-hadron phase transition during the early post-bounce phase. ApJSS 194: 39 (28p) Foglizzo T (2009) A simple toy model of the advective-acoustic instability. I. perturbative approach. ApJ 694:820–832 Foglizzo T, Scheck L, Janka HT (2006) Neutrino–driven convection versus advection in corecollapse supernovae. ApJ 652:1436–1450 Foglizzo T, Galletti P, Scheck L, Janka HT (2007) Instability of a stalled accretion shock: evidence for the advective-acoustic cycle. ApJ 654:1006–1021 Foglizzo T, Masset F, Guilet J, Durand G (2012) Shallow water analogue of the standing accretion shock instability: experimental demonstration and a two-dimensional model. PRL 108: 051103 (4p) Fuller J, Cantiello M, Lecoanet D, Quataert E (2015) The spin rate of pre-collapse stellar cores: wave-driven angular momentum transport in massive stars. ApJ 810:101 (13p) Grefenstette BW, Harrison FA, Boggs SE, Reynolds SP, Fryer CL, Madsen KK, Wik DR, Zoglauer A, Ellinger CI, Alexander DM, An H, Barret D, Christensen FE, Craig WW, Forster K, Giommi P, Hailey CJ, Hornstrup A, Kaspi VM, Kitaguchi T, Koglin JE, Mao PH, Miyasaka H, Mori K, Perri M, Pivovaroff MJ, Puccetti S, Rana V, Stern D, Westergaard NJ, Zhang WW (2014) Asymmetries in core-collapse supernovae from maps of radioactive 44 Ti in Cassiopeia A. Nature 506:339–342 Guilet J, Fernandez R (2014) Angular momentum redistribution by SASI spiral modes and consequences for neutron star spins. MNRAS 441:2782–2798 Guilet J, Foglizzo T (2012) On the linear growth mechanism driving the standing accretion shock instability. MNRAS 421:546–560 Guilet J, Sato J, Foglizzo T (2010) The saturation of SASI by parasitic instabilities. ApJ 713:1350– 1362 Guilet J, Müller E, Janka HT (2015) Neutrino viscosity and drag: impact on the magnetorotational instability in protoneutron stars. MNRAS 447:3992–4003 Hanke F, Marek A, Müller B, Janka HT (2012) Is strong SASI activity the key to successful neutrino-driven supernova explosions? ApJ 755:138 (23p) Hanke F, Müller B, Wongwathanarat A, Marek A, Janka HT (2013) SASI activity in threedimensional neutrino-hydrodynamics simulations of supernova cores. ApJ 770:66 (16p) Heger A, Woosley SE, Spruit HC (2005) Presupernova evolution of differentially rotating massive stars including magnetic fields. ApJ 626:350–363 Herant M, Benz W, Colgate S (1992) Postcollapse hydrodynamics of SN 1987A – two-dimensional simulations of the early evolution. ApJ 395:642–653 Hobbs G, Lorimer DR, Lyne AG, Kramer M (2005) A statistical study of 233 pulsar proper motions. MNRAS 360:974–992 Iwakami W, Nagakura H, Yamada S (2014) Critical surface for explosions of rotational corecollapse supernovae. ApJ 793:5 (16p) Kazeroni R, Guilet J, Foglizzo T (2016) New insights on the spin-up of a neutron star during core collapse. MNRAS 456:126–135 Khan E, Margueron J, Vidaña I (2012) Constraining the nuclear equation of state at subsaturation densities. PRL 109:092501 (4p)

1072

T. Foglizzo

Kitaura FS, Janka HT, Hillebrandt W (2006) Explosions of O-Ne-Mg cores, the Crab supernova, and subluminous type II-P supernovae. A&A 450:345–350 Kuroda T, Takiwaki T, Kotake K (2014) Gravitational wave signatures from low-mode spiral instabilities in rapidly rotating supernova cores. Phys Rev D 89:044011 (22p) Larsson J, Fransson C, Kjaer K, Jerkstrand A, Kirshner RP, Leibundgut B, Lundqvist L, Mattila S, McCray R, Sollerman J, Spyromilio J, Wheeler JC (2013) The morphology of the ejecta in supernova 1987a: a study over time and wavelength. ApJ 768:89 (17p) Lattimer JM (2012) The nuclear equation of state and neutron star masses. Annu Rev Nucl Part Sci 62:485–515 Leonard DC, Filippenko AV, Ganeshalingam M, Serduke FJD, Li W, Swift BJ, Gal–Yam A, Foley RJ, Fox DB, Park S, Hoffman JI, Wong DS (2006) A non-spherical core in the explosion of supernova SN 2004dj. Nature 440:505–507 Maeda K, Kawabata K, Mazzali PA, Tanaka M, Valenti S, Nomoto K, Hattori T, Deng J, Pian E, Taubenberger S, Iye M, Matheson T, Filippenko AV, Aoki K, Kosugi G, Ohyama Y, Sasaki T, Takata T (2008) Asphericity in supernova explosions from late–time spectroscopy. Science 319:1220–1223 Melson T, Janka HT, Bollig R, Hanke F, Marek A, Müller B (2015) Neutrino–driven explosion of a 20 solar-mass star in three dimensions enabled by strange-quark contributions to neutrino– nucleon scattering. ApJL 808:L42 (8p) Mösta P, Ott CD, Radice D, Roberts LF, Schnetter E, Haas R (2015) A large-scale dynamo and magnetoturbulence in rapidly rotating core-collapse supernovae. Nature 528:376–379 Moiseenko SG, Bisnovatyi-Kogan GS, Ardeljan NV (2006) A magnetorotational core-collapse model with jets. MNRAS 370:501–512 Müller B (2015) The dynamics of neutrino-driven supernova explosions after shock revival in 2D and 3D. MNRAS 453:287–310 Müller B, Janka HT (2015) Non-radial instabilities and progenitor asphericities in core-collapse supernovae. MNRAS 448:2141–2174 Müller B, Janka HT, Heger A (2012) New two-dimensional models of supernova explosions by the neutrino-heating mechanism: evidence for different instability regimes in collapsing stellar cores. ApJ 761:72 (12p) Murphy JW, Burrows A (2008) Criteria for core-collapse supernova explosions by the neutrino mechanism. ApJ 688:1159–1175 Nakamura K, Takiwaki T, Kuroda T, Kotake K (2014) Revisiting impacts of nuclear burning for reviving weak shocks in neutrino-driven supernovae. ApJ 782:91 (14p) Obergaulinger M, Janka HT, Aloy MA (2014) Magnetic field amplification and magnetically supported explosions of collapsing, non-rotating stellar cores. MNRAS 445:3169–3199 O’Connor E, Ott CD (2011) Black hole formation in failing core-collapse supernovae. ApJ 730: 70 (20p) Peres B, Oertel M, Novak J (2013) Influence of pions and hyperons on stellar black hole formation. PhRvD 87:043006 (21p) Scheck L, Kifonidis K, Janka HT, Müller E (2006) Multidimensional supernova simulations with approximative neutrino transport I. Neutron star kicks and the anisotropy of neutrino-driven explosions in two spatial dimensions. A&A 457:963–986 Scheck L, Janka HT, Foglizzo T, Kifonidis K (2008) Multidimensional supernova simulations with approximative neutrino transport II. Convection and the advective-acoustic cycle in the supernova core. A&A 477:931–952 Sumiyoshi K, Takiwaki T, Matsufuru H, Yamada S (2015) Multi-dimensional features of neutrino transfer in core-collapse supernovae. ApJS 216:5 (37p) Tamborra I, Hanke F, Müller B, Janka HT, Raffelt G (2013) Neutrino signature of supernova hydrodynamical instabilities in three dimensions. PRL 111:121104 (5p) Thompson C, Duncan RC (1993) Neutron star dynamos and the origins of pulsar magnetism. ApJ 408:194–217 Ugliano M, Janka HT, Marek A, Arcones A (2012) Progenitor-explosion connection and remnant birth masses for neutrino-driven supernovae of iron-core progenitors. ApJ 757:69 (10p)

38 Explosion Physics of Core-Collapse Supernovae

1073

Utrobin VP, Wongwathanarat A, Janka HT, Müller E (2015) Supernova 1987A: neutrino-driven explosions in three dimensions and light curves. A&A 581:40 (18p) Wongwathanarat A, Janka HT, Müller E (2013) Three-dimensional neutrino-driven supernovae: neutron star kicks, spins, and asymmetric ejection of nucleosynthesis products. A&A 552: A126 (25p) Yamasaki T, Foglizzo T (2008) Effect of rotation on the stability of a stalled cylindrical shock and its consequences for core-collapse supernovae. ApJ 679:607–615

Neutron Star Matter Equation of State

39

Jorge Piekarewicz

Abstract

Neutron stars are highly compact objects with masses comparable to that of our Sun but radii of only about 10 km. The structure of neutron stars is encapsulated in the Tolman-Oppenheimer-Volkoff (TOV) equations, which represent the generalization of Newtonian gravity to the domain of general relativity. Remarkably, the only input required to solve the TOV equations is the equation of state of cold, neutron-rich matter in chemical equilibrium. In this contribution we derive analytic expressions for the equation of state of an electrically neutral, relativistic free Fermi gas of neutrons, protons, and electrons in chemical equilibrium. Then, we introduce simple “scaling” concepts to rewrite the TOV equations in a form amenable to standard numerical algorithms. Finally, we highlight the ongoing synergy between astrophysics and nuclear physics that will need to be maintained, and indeed enhanced, to elucidate some of the most fascinating and challenging problems associated with the structure, dynamics, and composition of neutron stars.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Neutron Star Matter Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Tolman-Oppenheimer-Volkoff Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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J. Piekarewicz () Department of Physics, Florida State University, Tallahassee, FL, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_54

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Introduction

One century ago, on November 25, 1915, Albert Einstein published his landmark paper on Die Feldgleichungen der Gravitation (Einstein 1915); see Fig. 1. Almost two decades later in an experiment with no connection with the new laws of gravitation, Chadwick discovered the neutron (Chadwick 1932). Very soon after Chadwick’s announcement, the term neutron star appears in writing for the first time in the 1933 proceedings of the American Physical Society by Baade and Zwicky who wrote: With all reserve we advance the view that supernovae represent the transition from ordinary stars into “neutron stars”, which in their final stages consist of extremely closed packed neutrons (Baade and Zwicky 1934). It appears, however, that a couple of years earlier, Landau speculated on the existence of dense stars that look like giant atomic nuclei (Yakovlev et al. 2013). Ultimately in 1939, it would fall on the able hands of Oppenheimer and Volkoff to perform the first calculation of the structure of neutron stars by employing the full power of Einstein’s theory of general relativity (Oppenheimer and Volkoff 1939). Using what it is now commonly referred to as the Tolman-Volkoff-Oppenheimer (TOV) equations (Oppenheimer and Volkoff 1939; Tolman 1939), Oppenheimer and Volkoff demonstrated that a neutron star supported exclusively by the quantum mechanical pressure from its degenerate neutrons will collapse into a black hole once its mass exceeds seven tenths of a solar mass. It would take almost 30 years after the seminal work by Oppenheimer and Volkoff for a young graduate student by the name of Jocelyn Bell to discover “pulsars” which—after a period of confusion in which they were mistaken as potential beacons from an extraterrestrial civilization—were finally identified as

Fig. 1 A copy of Einstein’s historical article on “The Field Equations of Gravitation” that revolutionized our understanding of the laws of gravitation next to a picture of a young Einstein during his 1905–1915 “decade mirabilis”

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rapidly rotating neutron stars (Hewish et al. 1968). Since then, the field has evolved enormously and to date a few thousands neutron stars have been observed (Lattimer and Prakash 2004). Recently, the existence of neutron stars with masses as large as two solar masses has been firmly established (Antoniadis et al. 2013; Demorest et al. 2010). This represents a maximum mass limit nearly three times larger than the original prediction by Oppenheimer and Volkoff. Given that the only physics accounted for by Oppenheimer and Volkoff is rooted in the Pauli exclusion principle, the mere existence of massive neutron stars highlights the vital role that nuclear interactions play in explaining the structure and composition of neutron stars. But how do nuclear interactions leave their imprint on the structure of neutron stars? It is a remarkable fact—and one responsible for creating a unique synergy between astrophysics and nuclear physics—that the only input required to solve the TOV equations is the equation of state (EOS) of neutron-rich matter. The EOS encodes a fundamental relation between the pressure P and two other (intensive) thermodynamic quantities, such as the density n and the temperature T . The best known equation of state is that of a classical ideal gas: P D n kB T , where kB is Boltzmann’s constant. However, unlike a classical ideal gas, neutron stars are highly degenerate objects where quantum effects play a predominant role. That is, the thermodynamic regime of relevance to neutron stars involves high densities and low temperatures, such that the interparticle separation is small relative to the thermal de Broglie wavelength of the particle. These conditions are well satisfied in a neutron star despite that its core temperature of T . 109 K is enormous for normal standards. Yet, this temperature is small relative to the “Fermi temperature” TF , a quantity that provides a convenient proxy for the density. In the case of neutron stars, the dimensionless ratio of the physical temperature of the stellar core to its Fermi temperature is very small indeed, i.e., T =TF . 103 . This suggests an important approximation: Neutron stars may be effectively treated at zero-temperature systems. Although in this chapter we will focus on the equation of state of a uniform system of neutrons, protons, and electrons at zero temperature and in chemical equilibrium, the structure and composition of a neutron star are much more interesting and significantly more complex. Thus, aided by Fig. 2, we now embark on a very brief journey through a neutron star (Piekarewicz 2014). The outermost surface of the neutron star contains a very thin atmosphere of only a few centimeters thick that is believed to be composed of hydrogen, but may also contain heavier elements such as helium and carbon. The electromagnetic radiation that reaches both terrestrial and space-based telescopes is often used to constrain critical parameters of the neutron star. For example, assume blackbody emission from a stellar surface at a temperature T provides a determination of the neutron star radius R through the Stefan-Boltzmann law: L D 4  R2 T 4 , where L is the stellar luminosity and  the Stefan-Boltzmann constant. Just below the atmosphere lies the 100 m thick envelope that acts as “blanket” between the hot interior and the “cold” surface. Further, below lies the nonuniform crust which is speculated to consist of exotic structures, such as Coulomb crystals of very neutron-rich nuclei as well as nuclear pasta phases. The nonuniform crust sits above a uniform liquid core that consists

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Fig. 2 An accurate rendition of the fascinating structure and exotic phases in the interior of a neutron star—courtesy of Dany Page

of neutrons, protons, and electrons. Finally, there is also the fascinating possibility, marked with a question mark in Fig. 2, of an inner core made of strange quark matter or some other exotic state of matter. However, as alluded earlier in this paragraph, we will limit our discussion to the uniform stellar core that accounts for practically all the mass and for nearly 90 % of the size of a neutron star. We have organized this chapter as follows. In Sect. 2, we discuss the two main ingredients required to understand the structure of neutron stars: (a) the equation of state of an electrically neutral, relativistic free Fermi gas of neutrons, protons, and electrons in chemical equilibrium and (b) the solution of the TOV equations.

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We then proceed in Sect. 3 to present results for the structure of neutron stars using both the simple EOS derived in Sect. 2 and more sophisticated ones whose derivation is beyond the scope of this contribution. Finally, we conclude in Sect. 4 with a summary of our main results and with a brief discussion of some of the most interesting and challenging open questions that remain to date.

2

Formalism

The two topics developed in this section lie at the heart of the physics of neutron stars. The first topic centers around the equation of state of neutron star matter. Here, we start by deriving analytic expressions for the equation of state of a relativistic free Fermi gas of neutrons. This derivation serves as the cornerstone for addressing the equation of state of a multicomponent system consisting of neutrons, protons, and electrons in chemical equilibrium. The second topic introduces the TOV equations and develops a scaling transformation that is vital in treating systems with enormous disparity in scales, such as neutron stars. For example, with masses comparable to that of our Sun but largely supported by the pressure of its neutrons, neutron stars involve a mass disparity of 57 orders of magnitude! It is important to underscore that the topics addressed in this section should be treated as two independent modules. Given the pedagogical nature of this volume as well as the inherit complexity of the equation of state, we treat neutrons, protons, and electrons as noninteracting Fermi gases with correlations limited to those induced by the Pauli exclusion principle. Yet, fundamental concepts that are critical to our understanding of neutron stars, such as the nuclear symmetry energy and chemical equilibrium, are discussed in sufficient detail. On the other hand, the TOV module is general, at least for the widely used case of spherically symmetric neutrons stars in hydrostatic equilibrium. As developed, all that is required as input for the TOV equations is the equation of state: specifically, a relation between the pressure and the energy density.

2.1

Neutron Star Matter Equation of State

The main objective of this section is to obtain the equation of state of neutron star matter, simulated as an electrically neutral system of neutrons, protons, and electrons in chemical equilibrium. However, for pedagogical reasons we find it convenient to start by developing the EOS of a one-component relativistic Fermi gas (e.g., of neutrons) followed by a discussion of a two-component Fermi gas (of neutrons and protons) where the critical concept of the nuclear symmetry energy is introduced.

2.1.1 A One-Component Relativistic Fermi Gas Although the pioneering calculation by Oppenheimer and Volkoff represents the first application of general relativity to the structure of neutron stars, the assumption for

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the underlying EOS was simple, namely, that of a degenerate gas of noninteracting neutrons (Oppenheimer and Volkoff 1939). The zero-temperature EOS of a free Fermi gas of neutrons (or in generalpany fermion) of mass m satisfying the relativistic dispersion relation .p/ D .pc/2 C .mc 2 /2 is given by the following expression for the energy density (E  E=V ) in terms of the number density .n  N =V ): E.n/ D

.mc 2 /4 1 .„c/3 2

Z

xF

p x 2 1 C x 2 dx

0

8 3 ˆ 106 g cm3 , T > 2:5  109 K as found in Seitenzahl et al. 2009) in the hotspot on the surface of the primary WD. After the initial discovery of the violent merger scenario (Pakmor et al. 2010), the emergence of conditions that lead to the formation of a detonation has been confirmed by many different studies (Moll et al. 2014; Pakmor et al. 2010, 2011, 2012b; Sato et al. 2016; Tanikawa et al. 2015). The critical difference to older simulations that did not reach sufficient temperatures during the mergers seems to be the numerical resolution. In particular, for smoothed particle hydrodynamics (SPH) simulations of the inspiral and merger, a resolution of at least a million particles per WD seems to be required as the peak temperature in the hotspots increases with resolution (Pakmor et al. 2012a). However, even at the highest feasible resolution the peak temperatures still do not seem to be converged (Tanikawa et al. 2015). However, it is still unclear which double CO WD binaries are able to detonate carbon in the merger. Generally, a more massive primary WD will make the interaction more violent because it is more compact and provides a deeper gravitational potential for the accretion stream. Similarly, a larger mass ratio will make the secondary WD more compact and increase the density of the accretion stream on the final orbits as the secondary WD stays intact longer. In an early study Pakmor et al. (2011) found that a binary system with a 0:9 Mˇ primary CO WD requires a mass ratio q 0:85 to ignite. Recently, Sato et al. (2016) ran a parameter study at high resolution (i.e., particle numbers larger than 106 per WD) and constrained the critical mass ratio for ignition qcr depending on the mass of the primary WD M1 to

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0:9 0:94   lie between qcr D 0:82 MMˇ1 and qcr D 0:80 MMˇ1 . However, they also found that their results are still not converged with numerical resolution and that the true critical mass ratio may be smaller.

2.2

Helium Ignition

An alternative ignition scenario is the ignition of helium in a shell around the primary WD. Helium is easier to ignite than carbon owing to its smaller Coulomb barrier. Moreover, if some carbon is microscopically mixed with helium, alpha capture on 12 C replaces the triple-alpha reaction as initial nuclear reaction and the temperature and density required for a nuclear runaway in the helium shell drop significantly (Seitenzahl et al. 2009). Helium burning can aid the path to a violent merger in different ways. In the simplest extension of the violent merger scenario, burning the helium shell helps to ignite carbon on the interface between the helium shell and the carbon core of the primary WD. Moreover, the lower ignition point can lead to a nuclear runaway in the helium shell already during the accretion phase before the binary system reaches its final binary orbit. In addition to aiding the formation of a carbon detonation on the surface of the carbon core, the helium detonation can propagate in the helium shell around the primary WD and send a spherical shock wave into the carbon core. If this shock wave converges at a point with high enough density, it can ignite a carbon detonation there. This scenario to ignite a carbon detonation has been previously studied as the double-detonation scenario (see, e.g., Fink et al. 2007, 2010; Moll and Woosley 2013). Including helium in the composition of the outermost layer of particles of each WD in a sample of binary systems, Raskin et al. (2012) found that the helium is burned before the merger for massive primary WDs but does not ignite carbon directly. More recently, however, Pakmor et al. (2013) showed that when the helium shell is properly resolved, the helium detonation can propagate around the primary WD. It then converges in the CO core and can ignite a carbon detonation for a helium shell as small as 102 Mˇ on a primary CO WD of 1:1 Mˇ . For both cases, initial ignition of helium and initial ignition of carbon, the conditions that lead to ignitions are still not completely understood. If the helium shell around the primary WD is sufficiently massive to allow for a thermonuclear runaway in the helium shell and the formation of a detonation, it will almost always propagate around the primary WD (Shen and Moore 2014) and ignite the carbon core of the primary WD via a converging shock wave (Fink et al. 2007; Shen and Bildsten 2014). In case the primary WD somehow completely lost its helium shell during its evolution, it can still accrete enough helium from the helium shell of the secondary WD if present and proceed to the same scenario. Likely only in the case when there is not enough helium in the whole binary system, direct carbon ignition in the merger becomes important.

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The Explosion, Synthetic Observables, and Comparison to Observations

After the point where a nuclear flame ignites has been found, the explosion has to be simulated to determine the outcome of a scenario. Moreover, SNe Ia cannot be directly compared to observations, because the set of quantities known about the final ejecta are not directly observable. To bridge this gap, additional 3D radiation transfer simulations have to be performed on the ejecta of the explosion. Synthetic observables obtained this way can then directly be compared to observed SNe Ia (see, e.g., Kasen et al. 2006; Kromer and Sim 2009). So far only there are only a few explosion simulations available of the carbon ignited violent merger scenario that include radiative transport postprocessing and generate synthetic observables (Moll et al. 2014; Pakmor et al. 2010, 2011, 2012b). However, they are sufficient to establish the general properties of explosions in the violent merger scenario and compare them to observations to determine general strengths and weaknesses of this scenario.

3.1

The Structure of the Ejecta

The general structure of the explosion ejecta in the violent merger scenario is very similar even for initial binaries with very different masses. When the secondary is destroyed, a carbon detonation forms on the surface of the primary WD. The detonation then completely burns the primary WD. The explosion of the primary WD closely resembles the toy model of a centrally ignited isolated sub-MC h WD (see, e.g., Sim et al. 2010), as the secondary will not disturb it except for binary systems with two almost exactly equally massive WDs. After the primary WD has been burned, its hot ashes expand in a strong spherical shock wave . At this time, the secondary WD is mostly destroyed, and its material forms a very asymmetric torus around the primary WD. When the ashes of the primary WD hit the material of the secondary WD, they are hindered, and the initially spherical ejecta geometry becomes asymmetric. The degree of asymmetry depends on the exact state of the secondary WD. The more compact the secondary WD still is, the smaller is its impact on the ejecta of the primary WD. Moreover, when the ashes of the primary WD hit the material of the secondary WD, it may also be burned. However, in contrast to the primary WD, the destruction of the secondary WD has already significantly lowered its central density. Therefore, even quite massive secondary WDs will only burn to intermediate mass elements and oxygen but not produce any iron group elements. If the material of the secondary WD is burned, it also starts to expand a few seconds after the primary WD, filling the center of the ejecta. As the hot and dense ejecta expand into essentially empty space (although there may be low-density circumstellar material around under certain conditions Raskin and Kasen 2013; Shen et al. 2013), they will quickly enter the phase of

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homologous expansion (about 100 s after the first detonation forms, the deviation from homologous expansion is typically at most a few percent). The typical structure of the ejecta when they have reached homologous expansion is shown in Fig. 2 for the example of the merger of a 1:1 Mˇ CO WD and a 0:9 Mˇ CO WD (Pakmor et al. 2012b). The general structure of the ejecta is qualitatively similar to the layered composition obtained from toy models of centrally ignited sub-MC h -WDs (Sim et al. 2010). The outer layers are dominated by oxygen and surround a layer of intermediate mass elements. The center is mostly dominated by iron group elements. However, in the very center the composition is again almost purely oxygen, which originates from the burning of the secondary WD. The outer layers are almost spherical, but the inner parts of the ejecta can be rather asymmetric in their density structure as well as the composition. In particular the very asymmetric distribution of intermediate mass elements in the plane of rotation is a direct consequence of the interaction of the ejecta of the primary WD with the surrounding material of the secondary WD. In the vertical direction, in contrast, the ejecta of the primary WD can expand freely, and the ejecta are more symmetric.

3.2

Synthetic Observables

Comparing explosion models to observations turns out to be rather difficult, because most quantities that can be easily measured in simulations (e.g., density distribution, nuclear abundances) cannot be directly observed and vice versa (spectra, light curves). Therefore, an additional step is needed to compare explosion models directly to observational data that is the generation of synthetic observables. This is usually done in postprocessing using a radiative transfer code. To date, synthetic observables are available only for a handful of violent merger models. Thus, a final assessment of this scenario will have to wait until more models are available that cover a wide range of parameters, in particular in the mass combinations of the two WDs. Nevertheless, we can already infer a few general properties from the synthetic observables of violent merger models that are available.

3.2.1 Light Curves An example for the broadband light curves for the violent merger of a 1:1 Mˇ CO WD and a 0:9 Mˇ CO WD is shown in Fig. 3. There is generally good agreement between the model and observed color light curves from typical normal SNe Ia. In particular U-, B-, V-, and R-band agree very well with observations. The deviation in the I-band is most likely caused by shortcomings of the radiative transfer modeling of the Ca-triplet (Pakmor et al. 2012b). In the bluer bands (U, B), there is significant line of sight scatter. This is a direct consequence of the asymmetries of the ejecta. The redder bands are significantly less sensitive to the asymmetries and show only very little scatter.

y [1011 cm]

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Fig. 2 Density and composition of the explosion following the violent merger of a 1:1 Mˇ CO WD and a 0:9 Mˇ CO WD (Pakmor et al. 2012b) 100 s after the carbon detonation was ignited. The columns show, from left to right, density, oxygen mass fraction, the mass fraction of intermediate mass elements (IMEs), and the mass fraction of iron group elements (IGEs). The top and bottom rows show the x-y plane and the x-z plane, respectively

z [1011 cm]

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Fig. 3 Color light curves for the explosion following the violent merger of a 1:1 Mˇ CO WD and a 0:9 Mˇ CO WD and comparison with observational data taken from Pakmor et al. (2012b). The black line shows the angle-averaged light curve of the model, and the gray lines indicate the scatter for different lines of sight (Figure from Pakmor et al. 2012b, Figure 3)

A significant discrepancy between model and observations arises in the bolometric light curve several 10 days after maximum. As shown in the top-left panel of Fig. 3 at late times, the bolometric light curve declines significantly slower than observed normal SNe Ia, even though at maximum the brightness in most bands agrees well. Moreover, there is essentially no line of sight scatter in the decline rate of the bolometric light curve. Since the bolometric light curve is a rather robust feature of an explosion model, this may point to an overall too large mass of the explosion compared to observed normal SNe Ia that leads to additional trapping of  -photons at late times and increases the bolometric luminosity. This is consistent with attempts to reconstruct the ejecta mass of SNe Ia from observations that find ejecta masses typically below MC h (Scalzo et al. 2014; Stritzinger et al. 2006).

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3.2.2 Spectra A typical spectrum for a violent merger explosion at maximum light is shown in Fig. 4 again for the violent merger of a 1:1 Mˇ CO WD and a 0:9 Mˇ CO WD. Overall it agrees well with the observed spectrum. In particular, the positions of the lines in the synthetic spectrum which are a measure of the ejecta velocities where the line forms agree well with the line positions in the observed spectrum. Note that the agreement is significantly better than for a toy model of the explosion of an isolated WD with the same mass as the primary WD here (Sim et al. 2010). This is a result of the presence of the secondary WD, which reduces the ejecta velocities of the ashes of the primary WD as they have to escape the potential of the secondary WD. A spectral feature of particular interest for the violent merger model is the recently discovered oxygen emission line in nebular spectra of some peculiar subluminous SNe Ia (Kromer et al. 2016; Taubenberger et al. 2013). Line velocities indicate that this line forms at the center of the ejecta, therefore requiring significant amounts of oxygen there. As shown in Fig. 2, explosions in the violent merger scenario can naturally explain this feature, while other scenarios cannot. However, normal SNe Ia clearly do not show any oxygen emission lines in their nebular spectra. There are two different paths to avoid an oxygen line in nebular spectra in the violent merger scenario. If the secondary WD is not burned, the central ejecta material will be the ash of the primary WD only that does not contain any oxygen in its center. Moreover, even if there is oxygen at the center of the ejecta, it is possible that the line does not form, either if the oxygen is not excited by nearby radioactive material or if the oxygen is completely ionized. In particular the last possibility

Fig. 4 Angle averaged maximum light optical spectrum for the explosion following the violent merger of a 1:1 Mˇ CO WD and a 0:9 Mˇ CO WD and comparison with observational data taken from Pakmor et al. (2012b) (Figure from Pakmor et al. 2012b, Figure 4)

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seems to be a natural explanation for normal SNe Ia that are significantly brighter than the subluminous SNe Ia the oxygen line has been observed in. Future synthetic nebular spectra of violent merger explosions should be able to solve this question.

3.2.3 Polarization We recently found that the asymmetry of the ejecta is the cause for another discrepancy of explosions from the violent merger model from typical normal SNe Ia. While the scatter between different lines of sight is hard to observe, spectropolarimetry allows for a direct assessment of the symmetry of the ejecta. The level of polarization inferred from synthetic polarization spectra for the violent merger of a 1:1 Mˇ CO WD and a 0:9 Mˇ CO WD discussed above is consistent with the low level of polarization of 1% (Wang et al. 2007) only for lines of sight in the plane of rotation. For directions out of this plane, the level of polarization is significantly higher and inconsistent with most normal SNe Ia but may explain rare highly polarized events (Bulla et al. 2016).

3.3

Ignition via the Helium Shell

As discussed in Sect. 2.2, it has recently been shown that binary systems in the violent merger scenario previously thought to ignite carbon may already explode early via the helium shell of the primary WD and the double-detonation mechanism. Although detailed explosion simulations of this modified scenario are not available today, we can make a few general statements how the properties of the explosion will change compared to the original violent merger scenario. The likely most important difference will be the state of the secondary WD at the time the primary WD explodes. If the explosion happens at least a few orbits before the secondary WD is destroyed, its geometric effect on the ejecta of the primary WD will be significantly smaller, and the explosion will be more symmetric. Moreover, if primary and secondary WDs are still well separated when the primary WD explodes, it seems possible that the secondary survives without being burned. This would have important consequences for the total ejecta mass and provide a possibility for an observational confirmation of this scenario when the surviving secondary WD can be detected. Finally, the helium ashes in the outermost layers of the explosion will imprint themselves on the observed spectra, although the mass of the helium shell may be small enough for this effect to be small (Kromer et al. 2010; Pakmor et al. 2013).

4

Can Violent Mergers Be the Main Channel for Normal SNe Ia?

It is a very different question to ask if a scenario can constitute the dominant fraction of normal SNe Ia compared to asking if a scenario can produce a realistic SN Ia. The latter mostly requires synthetic observables produced by a scenario to be reasonably

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consistent with observational data of individual SNe Ia. This can be the case for completely different scenarios for the same observed SN Ia (see, e.g., Röpke et al. 2012), because different scenarios can agree well overall but show very different deviations from observations. Since detailed theoretical models are always the result of a multistage process (e.g., for the violent merger models described above) with many uncertainties, it is then very hard to argue for preference of one model over the other to better explain an individual event taking into account synthetic observables only. Explaining the bulk of SNe Ia in a scenario, in contrast, is much more demanding. To achieve this the scenario not only has to explain the range of observational properties and their scatter within the population but also general properties of the population of SNe Ia like their rates, delay times, and statistical correlations between observational properties of SNe Ia and their local environment. Here, we will briefly discuss the different properties of the population of normal SNe Ia and analyze to which degree violent mergers can reproduce them.

4.1

Brightness Distribution

The observed range of brightnesses of normal SNe Ia and their distribution is the first parameter any scenario attempting to explain the bulk of normal SNe Ia needs to reproduce. In the violent merger scenario, the brightness of the explosion is directly linked to the mass of the primary WD prior to the explosion (see above, the same is true for all sub-Chandrasekhar-mass explosion scenarios). For normal SNe Ia the range of 56 Ni masses inferred from observations roughly ranges from 0.3 to 0:9 Mˇ . For detonations of sub-Chandrasekhar-mass CO WDs, this corresponds to a white dwarf mass between 0.9 and 1.1 Mˇ (Sim et al. 2010). Therefore, variations in the mass of the primary WD can in principle explain the observed range of brightnesses of normal SNe Ia in the violent merger scenario. A second question is then whether the observed distribution of brightnesses is reproduced by the violent merger scenario. Again, this translates to a comparison of the distribution of primary WD masses at the time of the merger that is expected, for example, from binary population synthesis modeling, with the observed brightness distribution. As shown in Ruiter et al. (2013), the violent merger scenario can in principle explain the main features of the observed brightness distribution of SNe Ia, i.e., the peak at a brightness corresponding to a 56 Ni mass of about 0:6 Mˇ , a steep decline for brighter events, and an extended tail to fainter events. Note, however, that detailed shape of the brightness distribution of SNe Ia from the violent merger scenario depends significantly on the assumptions about the conditions that will lead to an explosion (see also Sect. 2).

4.2

Rates and Delay Times

In addition to general properties of the observed population of SNe Ia, the scenario that contributes the dominant fraction of SNe Ia also needs to be able to explain

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their observed rate and delay times. In particular explaining the total SN Ia rate of about 2 ˙ 1 SNe Ia per 1000 Mˇ of stellar mass formed has been a long-standing problem (Maoz and Mannucci 2012). Recent observational results indicate that the total merger rate of double CO WD systems is roughly in agreement with the observed SNe Ia rate (Maoz and Mannucci 2012; Ruiter et al. 2009). However, this also includes mergers with primary WDs that are significantly less massive than 0:9 Mˇ and binaries with small mass ratios. These systems therefore would not lead to a normal SN Ia in the violent merger scenario, reducing the predicted event rate from the violent merger scenario significantly below the observed SNe Ia rate. Nevertheless, the estimated merger rate still carries significant uncertainties, and better observational constraints and theoretical modeling are required. An additional constraint for the scenario that contributes the majority of SNe Ia is given by the observed delay time distribution of SNe Ia. Current observations seem to agree that the delay time distribution, i.e., the distribution of delays between the formation of stars and their explosion as a SN Ia, is well described by a t 1 power-law (Maoz and Mannucci 2012). This t 1 power-law dependence is a generic consequence of any merger scenario for SNe Ia in which the explosion happens close to the time when the binary system merges and for which the time from formation to merger is dominated by the slow inspiral owing to loss of energy and angular momentum to gravitational waves (Maoz and Mannucci 2012). Therefore, the observed delay time distribution can naturally be explained in the violent merger scenario.

4.3

Secondary Effects

When a scenario can reproduce the primary parameters of the population of SNe Ia, it is interesting to look at secondary parameters and a large number of observed secondary correlations. Those include, for example, the correlation between absolute brightness and decline rate in the B-band (Phillips et al. 1999), the correlation of the brightness of SNe Ia with properties of their host galaxies (Sullivan et al. 2010), and the correlation between asymmetries of the explosion and properties of late-time nebular spectra (Maeda et al. 2010). So far, none of these correlations have been studied explicitly for the violent merger scenario. Future, large parameter studies will be needed to determine if these correlations can be reproduce in the violent merger scenario.

4.4

The Class of Faint 2010lp-Like SNe Ia

Independently of its potential to explain normal SNe Ia, it is interesting to investigate if other subclasses of SNe Ia can be explained by the violent merger scenario. The most interesting case for violent double CO WD mergers is arguably the class of faint SNe Ia that resemble SN 2010lp (Kromer et al. 2013). These objects have similar spectra as the larger class of subluminous, fast-declining, 91bg-like

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objects, but their light curves decline much slower, indicating that the ejecta contain significantly more mass. As shown for SN 2010lp and SN iPTF14atg, violent mergers are able to very well reproduce the observed light curves of these objects and their maximum light spectra (Kromer et al. 2013, 2016). Moreover, the two objects, SN 2010lp and SN iPTF14atg, are so far the only SNe Ia that feature oxygen emission lines in their nebula spectra, which can also naturally be explained in the violent merger scenario (Kromer et al. 2016; Taubenberger et al. 2013).

5

Conclusions

Violent mergers, i.e., mergers of two WDs that lead to an explosion in the immediate precursor of the merger or during the actual merger, are one of the newest additions to the list of scenarios for SNe Ia. They are also the first success to find a plausible explosion scenario for mergers of two WDs. However, the complex dynamics leading up to the merger and during the merger make the violent merger scenario hard to simulate, and thus only a small number of explosion simulations exist today for this scenario. Currently published explosion simulations for the violent merger scenario indicate that it can reproduce the observables of normal SNe Ia at least as well as other explosion scenarios in full 3D explosion simulations. Moreover, there is promise that the violent merger scenario can explain general properties of the population of normal SNe Ia including the brightness distribution and delay times. In addition, they very successfully explain the class of subluminous 02es-like SNe Ia. Nevertheless, we clearly need more simulations that cover the full parameter space of the violent merger scenario and in particular explore helium ignition before we can fully assess the contribution of violent mergers to SNe Ia.

6

Cross-References

 Dynamical Mergers  Explosion Physics of Thermonuclear Supernovae and Their Signatures  Introduction to Supernova Polarimetry  Light Curves of Type I Supernovae  Nucleosynthesis in Thermonuclear Supernovae  Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs  The Extremes of Thermonuclear Supernovae  Type Ia Supernovae Acknowledgements This work has been supported by the European Research Council under ERC-StG grant EXAGAL-308037 and by the Klaus Tschira Foundation.

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References Bulla M, Sim SA, Pakmor R, Kromer M, Taubenberger S, Röpke FK, Hillebrandt W, Seitenzahl IR (2016) Type Ia supernovae from violent mergers of carbon-oxygen white dwarfs: polarization signatures. Mon Not R Astron Soc 455:1060–1070. doi:10.1093/mnras/stv2402 Fink M, Hillebrandt W, Röpke FK (2007) Double-detonation supernovae of sub-Chandrasekhar mass white dwarfs. Astron Astrophys 476:1133–1143. doi:10.1051/0004-6361:20078438, arXiv:0710.5486 Fink M, Röpke FK, Hillebrandt W, Seitenzahl IR, Sim SA, Kromer M (2010) Double-detonation sub-Chandrasekhar supernovae: can minimum helium shell masses detonate the core? Astron Astrophys 514:A53. doi:10.1051/0004-6361/200913892 Iben I Jr, Tutukov AV (1984) Supernovae of type I as end products of the evolution of binaries with components of moderate initial mass (M not greater than about 9 solar masses). Astrophys J Suppl Ser 54:335–372. doi:10.1086/190932 Kasen D, Thomas RC, Nugent P (2006) Time-dependent Monte Carlo radiative transfer calculations for three-dimensional supernova spectra, light curves, and polarization. Astrophys J 651:366–380. doi:10.1086/506190, arXiv:astro-ph/0606111 Kromer M, Sim SA (2009) Time-dependent three-dimensional spectrum synthesis for Type Ia supernovae. Mon Not R Astron Soc 398:1809–1826. doi:10.1111/j.1365-2966.2009.15256.x, arXiv:0906.3152 Kromer M, Sim SA, Fink M, Röpke FK, Seitenzahl IR, Hillebrandt W (2010) Double-detonation sub-Chandrasekhar supernovae: synthetic observables for minimum helium shell mass models. Astrophys J 719:1067–1082. doi:10.1088/0004-637X/719/2/1067, arXiv:1006.4489 Kromer M, Pakmor R, Taubenberger S, Pignata G, Fink M, Röpke FK, Seitenzahl IR, Sim SA, Hillebrandt W (2013) SN 2010lp—a type Ia supernova from a violent merger of two carbon-oxygen white dwarfs. Astrophys J 778:L18. doi:10.1088/2041-8205/778/1/L18, arXiv:1311.0310 Kromer M, Fremling C, Pakmor R, Taubenberger S, Amanullah R, Cenko SB, Fransson C, Goobar A, Leloudas G, Taddia F, Röpke FK, Seitenzahl IR, Sim SA, Sollerman J (2016) The peculiar type Ia supernova iPTF14atg: Chandrasekhar-mass explosion or violent merger? Mon Not R Astron Soc 459:4428–4439. doi:10.1093/mnras/stw962, arXiv:1604.05730 Maeda K, Taubenberger S, Sollerman J, Mazzali PA, Leloudas G, Nomoto K, Motohara K (2010) Nebular spectra and explosion asymmetry of type Ia supernovae. Astrophys J 708:1703–1715. doi:10.1088/0004-637X/708/2/1703, arXiv:0911.5484 Maoz D, Mannucci F (2012) Type-Ia supernova rates and the progenitor problem: a review. PASA 29:447–465. doi:10.1071/AS11052, arXiv:1111.4492 Moll R, Woosley SE (2013) Multi-dimensional models for double detonation in subChandrasekhar mass white dwarfs. Astrophys J 774:137. doi:10.1088/0004-637X/774/2/137, arXiv:1303.0324 Moll R, Raskin C, Kasen D, Woosley SE (2014) Type Ia supernovae from merging white dwarfs. I. Prompt detonations. Astrophys J 785:105. doi:10.1088/0004-637X/785/2/105, arXiv:1311.5008 Nomoto K, Kondo Y (1991) Conditions for accretion-induced collapse of white dwarfs. Astrophys J 367:L19–L22. doi:10.1086/185922 Pakmor R, Kromer M, Röpke FK, Sim SA, Ruiter AJ, Hillebrandt W (2010) Sub-luminous type ia supernovae from the mergers of equal-mass white dwarfs with mass 0.9 mˇ . Nature 463:61– 64. doi:10.1038/nature08642, arXiv:0911.0926 Pakmor R, Hachinger S, Röpke FK, Hillebrandt WA (2011) Violent mergers of nearly equal-mass white dwarf as progenitors of subluminous type Ia supernovae. Astron Astrophys 528:A117+. doi:10.1051/0004-6361/201015653, arXiv:1102.1354 Pakmor R, Edelmann P, Röpke FK, Hillebrandt W (2012a) Stellar GADGET: a smoothed particle hydrodynamics code for stellar astrophysics and its application to type Ia supernovae from white dwarf mergers. Mon Not R Astron Soc 424:2222–2231. doi:10.1111/j.1365-2966.2012.21383.x, arXiv:1205.5806

1272

R. Pakmor

Pakmor R, Kromer M, Taubenberger S, Sim SA, Röpke FK, Hillebrandt W (2012b) Normal type Ia supernovae from violent mergers of white dwarf binaries. Astrophys J 747:L10. doi:10.1088/2041-8205/747/1/L10, arXiv:1201.5123 Pakmor R, Kromer M, Taubenberger S, Springel V (2013) Helium-ignited violent Mergers as a unified model for normal and rapidly declining type Ia supernovae. Astrophys J 770:L8. doi:10.1088/2041-8205/770/1/L8, arXiv:1302.2913 Perlmutter S, Aldering G, Goldhaber G, Knop RA, Nugent P, Castro PG, Deustua S, Fabbro S, Goobar A, Groom DE, Hook IM, Kim AG, Kim MY, Lee JC, Nunes NJ, Pain R, Pennypacker CR, Quimby R, Lidman C, Ellis RS, Irwin M, McMahon RG, Ruiz-Lapuente P, Walton N, Schaefer B, Boyle BJ, Filippenko AV, Matheson T, Fruchter AS, Panagia N, Newberg HJM, Couch WJ, The Supernova Cosmology Project (1999) Measurements of Omega and Lambda from 42 high-redshift supernovae. Astrophys J 517:565–586. doi:10.1086/307221, arXiv:astroph/9812133 Phillips MM, Lira P, Suntzeff NB, Schommer RA, Hamuy M, Maza J (1999) The reddening-free decline rate versus luminosity relationship for type Ia supernovae. Astron J 118:1766–1776. doi:10.1086/301032, arXiv:astro-ph/9907052 Raskin C, Kasen D (2013) Tidal tail ejection as a signature of Type Ia supernovae from white dwarf mergers. Astrophys J 772:1. doi:10.1088/0004-637X/772/1/1, arXiv:1304.4957 Raskin C, Scannapieco E, Fryer C, Rockefeller G, Timmes FX (2012) Remnants of binary white dwarf mergers. Astrophys J 746:62. doi:10.1088/0004-637X/746/1/62, arXiv:1112.1420 Riess AG, Filippenko AV, Challis P, Clocchiatti A, Diercks A, Garnavich PM, Gilliland RL, Hogan CJ, Jha S, Kirshner RP, Leibundgut B, Phillips MM, Reiss D, Schmidt BP, Schommer RA, Smith RC, Spyromilio J, Stubbs C, Suntzeff NB, Tonry J (1998) Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron J 116:1009–1038. doi:10.1086/300499, arXiv:astro-ph/9805201 Röpke FK, Kromer M, Seitenzahl IR, Pakmor R, Sim SA, Taubenberger S, Ciaraldi-Schoolmann F, Hillebrandt W, Aldering G, Antilogus P, Baltay C, Benitez-Herrera S, Bongard S, Buton C, Canto A, Cellier-Holzem F, Childress M, Chotard N, Copin Y, Fakhouri HK, Fink M, Fouchez D, Gangler E, Guy J, Hachinger S, Hsiao EY, Chen J, Kerschhaggl M, Kowalski M, Nugent P, Paech K, Pain R, Pecontal E, Pereira R, Perlmutter S, Rabinowitz D, Rigault M, Runge K, Saunders C, Smadja G, Suzuki N, Tao C, Thomas RC, Tilquin A, Wu C (2012) Constraining type Ia supernova models: SN 2011fe as a test case. Astrophys J 750:L19. doi:10.1088/2041-8205/750/1/L19, arXiv:1203.4839 Ruiter AJ, Belczynski K, Fryer C (2009) Rates and delay times of type Ia supernovae. Astrophys J 699:2026–2036. doi:10.1088/0004-637X/699/2/2026, arXiv:0904.3108 Ruiter AJ, Sim SA, Pakmor R, Kromer M, Seitenzahl IR, Belczynski K, Fink M, Herzog M, Hillebrandt W, Röpke FK, Taubenberger S (2013) On the brightness distribution of type Ia supernovae from violent white dwarf mergers. Mon Not R Astron Soc 429:1425–1436. doi:10.1093/mnras/sts423, arXiv:1209.0645 Saio H, Nomoto K (1985) Evolution of a merging pair of C+O white dwarfs to form a single neutron star. Astron. Astrophys. 150:L21–L23 Saio H, Nomoto K (1998) Inward propagation of nuclear-burning shells in merging C-O and He white dwarfs. Astrophys J 500:388–397. doi:10.1086/305696, arXiv:astro-ph/9801084 Sato Y, Nakasato N, Tanikawa A, Nomoto K, Maeda K, Hachisu I (2016) The critical mass ratio of double white dwarf binaries for violent merger-induced Type Ia supernova explosions. Astrophys J 821:67. doi:10.3847/0004-637X/821/1/67, arXiv:1603.01088 Scalzo R, Aldering G, Antilogus P, Aragon C, Bailey S, Baltay C, Bongard S, Buton C, CellierHolzem F, Childress M, Chotard N, Copin Y, Fakhouri HK, Gangler E, Guy J, Kim AG, Kowalski M, Kromer M, Nordin J, Nugent P, Paech K, Pain R, Pecontal E, Pereira R, Perlmutter S, Rabinowitz D, Rigault M, Runge K, Saunders C, Sim SA, Smadja G, Tao C, Taubenberger S, Thomas RC, Weaver BA, Nearby Supernova Factory (2014) Type Ia supernova bolometric light curves and ejected mass estimates from the nearby supernova factory. Mon Not R Astron Soc 440:1498–1518. doi:10.1093/mnras/stu350, arXiv:1402.6842

45 Violent Mergers

1273

Schmidt BP, Suntzeff NB, Phillips MM, Schommer RA, Clocchiatti A, Kirshner RP, Garnavich P, Challis P, Leibundgut B, Spyromilio J, Riess AG, Filippenko AV, Hamuy M, Smith RC, Hogan C, Stubbs C, Diercks A, Reiss D, Gilliland R, Tonry J, Maza J, Dressler A, Walsh J, Ciardullo R (1998) The high-Z supernova search: measuring cosmic deceleration and global curvature of the universe using Type IA supernovae. Astrophys J 507:46–63. doi:10.1086/306308, arXiv:astroph/9805200 Schwab J, Shen KJ, Quataert E, Dan M, Rosswog S (2012) The viscous evolution of white dwarf merger remnants. arXiv:1207.0512 Seitenzahl IR, Meakin CA, Townsley DM, Lamb DQ, Truran JW (2009) Spontaneous initiation of detonations in white dwarf environments: determination of critical sizes. Astrophys J 696:515– 527. doi:10.1088/0004-637X/696/1/515, arXiv:0901.3677 Shen KJ, Bildsten L (2014) The ignition of carbon detonations via converging shock waves in white dwarfs. Astrophys J 785:61. doi:10.1088/0004-637X/785/1/61, arXiv:1305.6925 Shen KJ, Moore K (2014) The initiation and propagation of helium detonations in white dwarf envelopes. Astrophys J 797:46. doi:10.1088/0004-637X/797/1/46, arXiv:1409.3568 Shen KJ, Bildsten L, Kasen D, Quataert E (2012) The long-term evolution of double white dwarf mergers. Astrophys J 748:35. doi:10.1088/0004-637X/748/1/35, arXiv:1108.4036 Shen KJ, Guillochon J, Foley RJ (2013) Circumstellar absorption in double detonation type Ia supernovae. Astrophys J 770:L35. doi:10.1088/2041-8205/770/2/L35, arXiv:1302.2916 Sim SA, Röpke FK, Hillebrandt W, Kromer M, Pakmor R, Fink M, Ruiter AJ, Seitenzahl IR (2010) Detonations in sub-Chandrasekhar-mass c+o white dwarfs. Astrophys J 714:L52–L57. doi:10.1088/2041-8205/714/1/L52, arXiv:1003.2917 Stritzinger M, Leibundgut B, Walch S, Contardo G (2006) Constraints on the progenitor systems of type Ia supernovae. Astron Astrophys 450:241–251. doi:10.1051/0004-6361:20053652, arXiv:astro-ph/0506415 Sullivan M, Conley A, Howell DA, Neill JD, Astier P, Balland C, Basa S, Carlberg RG, Fouchez D, Guy J, Hardin D, Hook IM, Pain R, Palanque-Delabrouille N, Perrett KM, Pritchet CJ, Regnault N, Rich J, Ruhlmann-Kleider V, Baumont S, Hsiao E, Kronborg T, Lidman C, Perlmutter S, Walker ES (2010) The dependence of type Ia supernovae luminosities on their host galaxies. Mon Not R Astron Soc 406:782–802. doi:10.1111/j.1365-2966.2010.16731.x, arXiv:1003.5119 Tanikawa A, Nakasato N, Sato Y, Nomoto K, Maeda K, Hachisu I (2015) Hydrodynamical evolution of merging carbon-oxygen white dwarfs: their pre-supernova structure and observational counterparts. Astrophys J 807:40. doi:10.1088/0004-637X/807/1/40, arXiv:1504.06035 Taubenberger S, Kromer M, Pakmor R, Pignata G, Maeda K, Hachinger S, Leibundgut B, Hillebrandt W (2013) [O I] 6300, 6364 in the nebular spectrum of a subluminous type Ia supernova. Astrophys J 775:L43. doi:10.1088/2041-8205/775/2/L43, arXiv:1308.3145 Timmes FX (1994) On the acceleration of nuclear flame fronts in white dwarfs. Astrophys J 423:L131–L134. doi:10.1086/187254 Timmes FX, Woosley SE, Weaver TA (1995) Galactic chemical evolution: hydrogen through zinc. Astrophys J Suppl Ser 98:617–658. doi:10.1086/192172, arXiv:astro-ph/9411003 Wang L, Baade D, Patat F (2007) Spectropolarimetric diagnostics of thermonuclear supernova explosions. Science 315:212–214. doi:10.1126/science.1121656, arXiv:astro-ph/0611902 Webbink RF (1984) Double white dwarfs as progenitors of R Coronae Borealis stars and type I supernovae. Astrophys J 277:355–360. doi:10.1086/161701 Whelan J, Iben IJ (1973) Binaries and supernovae of type I. Astrophys J 186:1007–1014 Yoon SC, Podsiadlowski P, Rosswog S (2007) Remnant evolution after a carbon-oxygen white dwarf merger. Mon Not R Astron Soc 380:933–948. doi:10.1111/j.1365-2966.2007.12161.x, arXiv:0704.0297

Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs

46

Ken’ichi Nomoto and Shing-Chi Leung

Abstract

The thermonuclear explosion of a Chandrasekhar mass white dwarf is an important class of supernovae which can attribute to various subclasses of Type Ia supernovae and accretion induced collapse. Type Ia supernovae are not only essential as their roles of standard candle in the discovery of dark energy, but also robust sources of iron-peak elements for the galactic chemical evolution. In this chapter we discuss the physics of the explosion mechanisms of the Chandrasekhar mass white dwarf. First we review the possible evolutionary paths for the accreting white dwarf to increase its mass to the Chandrasekhar mass in the binary systems. When the white dwarf’s mass reaches near the Chandrasekhar limit, carbon burning is ignited and grows into deflagration in the central region. We review the principle component of deflagration physics and how it is implemented in supernova simulations. We then review the physics of detonation by examining its structure. We also discuss how the detonation is triggered physically and computationally. At last, we describe how these components are applied to various explosion mechanisms, including the deflagration-detonation transition, pure deflagration, and gravitationally confined detonation. Their typical behaviour, nucleosynthesis, and applications to the galactic chemical evolution and observed supernovae are examined.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Degenerate Scenario for Progenitors of Type Ia Supernovae . . . . . . . . . . . . . . . 2.1 Accretion-Induced Hydrogen Shell Burning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 He Shell Burning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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K. Nomoto • S.-C. Leung Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan e-mail: [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_62

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2.3 Four Types of Type Ia Supernovae (SNe Ia) in the Single-Degenerate (SD) Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Companion Stars in the SD Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Rotating White Dwarf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 One-Dimensional Explosion Models of Chandrasekhar Mass White Dwarfs . . . . . . . . 3.1 Nucleosynthesis in Deflagration and Detonation . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Observable Characteristics of Chandrasekhar Mass Models . . . . . . . . . . . . . . . . . 4 Multi-Dimensional Models and Diversity of Explosion Mechanisms . . . . . . . . . . . . . . 4.1 Deflagration-Detonation Transition (DDT) Model . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Pure Turbulent Deflagration (PTD) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Gravitationally Confined Detonation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Spectral Diagnostics of Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Chemical Evolution of Galaxies and Supernova Remnants . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: A Short Review of Detonation Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deflagration to Detonation Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physics of Detonation and Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Open Questions in Detonation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

The thermonuclear explosion of a white dwarf with a mass near the Chandrasekhar limit is an important class of supernovae which can attribute to various subclasses of Type Ia supernovae. Type Ia supernovae are not only essential as their roles of standard candle in the discovery of dark energy, but also robust sources of iron-peak elements for the galactic chemical evolution. In this chapter we discuss the physics of the explosion mechanisms of the Chandrasekhar mass white dwarf. First we review the possible evolutionary paths for the accreting white dwarf to increase its mass to the Chandrasekhar mass in the binary systems. When the white dwarf’s mass reaches near the Chandrasekhar limit, carbon burning is ignited and grows into deflagration in the central region. We review the principle component of deflagration physics and how it is implemented in supernova simulations. We then review the physics of detonation by examining its structure. We also discuss how the detonation is triggered physically and computationally. At last, we describe how these components are applied to various explosion mechanisms, including the deflagration-detonation transition, pure deflagration, and gravitationally confined detonation. Their typical behaviour, nucleosynthesis, and applications to the galactic chemical evolution and observed supernovae are examined.

2

Single-Degenerate Scenario for Progenitors of Type Ia Supernovae

The thermonuclear explosion of a C+O white dwarf has successfully explained the basic observed features of Type Ia supernovae (SNe Ia). Both the Chandrasekhar and the sub-Chandrasekhar mass models have been examined (Livio 2000). However,

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no clear observational indication rejects how the white dwarf mass grows until C ignition, i.e., whether the white dwarf accretes H/He-rich matter from its binary companion [single-degenerate (SD) scenario] or whether two C+O white dwarfs merge [double-degenerate (DD) scenario] (e.g., Arnett 1996; Hillebrandt and Niemeyer 2000; Iben and Tutukov 1984; Ilkov and Soker 2012; Maoz et al. 2014; Nomoto 1982; Nomoto et al. 1994, 1997, 2000a, 2009; Webbink 1984).

2.1

Accretion-Induced Hydrogen Shell Burning

Here we focus on the SD scenario for the Chandrasekhar mass (Chandra) models of SN Ia, where an accreting C+O white dwarf (WD) increases its mass to the Chandrasekhar mass limit. If the mass donor is a normal star, a hydrogen shell burning is ignited when the mass of the accumulated hydrogen-rich matter reaches the ignition mass Mig .D MH /, which is presented as contours on the MWD  MP .D dMH =dt / plane in Fig. 1. For a given MP , Mig is smaller for a larger MWD because of the smaller radius R and thus higher pressure for the same mass of accreted matter (see Eq. (3) below). For a given MWD , Mig is smaller for a higher MP because of the faster compressional heating and thus higher temperature of accreted matter. The stability of the hydrogen burning shell in the accreting white dwarf is crucial for its evolution. Figure 1 summarizes the properties of hydrogen shell burning (Kato et al. 2014; Nomoto 1982; Nomoto et al. 2007). 1. The hydrogen shell burning is unstable to flash in the area below the solid line to show MP stable . This stability line (dashed line) is approximately represented by Kato et al. (2014)

MP stable D 4:17  107



 MWD  0:53 Mˇ yr1 : Mˇ

(1)

2. Above the dash-dotted line for MP cr (= .dM =dt /RH ), the accreted matter is accumulated faster than consumed into He by H-shell burning. This critical accretion rate is represented as Kato et al. (2014)

MP cr D 8:18  107



 MWD  0:48 Mˇ yr1 : Mˇ

(2)

3. For the region with MP > MP cr , the accreted matter is piled up to form a redgiant-size envelope (Nomoto et al. 1979). This could lead to the formation of a common envelope and prevent further mass accretion onto the white dwarf. This problem for has been resolved by the strong optically thick winds (Hachisu et al. 1996, 1999a, b). If the wind is sufficiently strong, the white dwarf radius stays small enough to avoid the formation of a common envelope. Then steady

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Fig. 1 The properties of accreted hydrogen-rich materials as functions of MWD and dMH =dt (Nomoto 1982). Hydrogen burning is stable in the region indicated by “Steady H-Burn” between the two lines of MP stable in Eq. (1) and MP cr .D .dM =dt /RH ) in Eq. (2) (Kato et al. 2014). In the region below MP stable , hydrogen shell burning is thermally unstable, and the WD experiences shell flashes. Black solid lines indicate the hydrogen-ignition masses MH , the values of which are shown beside each line. In the region above .dM =dt /RH (and below the Eddington limit .dM =dt /EH ), optically thick winds are accelerated, which prevents the formation of a red-giantsize envelope with the piled-up accreted material

hydrogen burning increases its mass at a rate MP cr by blowing the extra mass away in a wind. 4. In the area MP stable < MP < MP cr , accreting white dwarfs are thermally stable so that hydrogen burns steadily in the burning shell. Then the white dwarf mass increases at a rate of MP . 5. For MP < MP stable , the flash of hydrogen shell burning is stronger (weaker) for lower (higher) MP and thus for larger (smaller) Mig and larger (smaller) MWD . This is because the pressure P at the bottom of the thin accreted envelope is higher (lower) as given by

P D

GMWD Mig ; 4 R4

(3)

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(where the WD radius R is smaller for larger MWD ), so that the flash reaches higher (lower) temperature. If the shell flash is strong enough to trigger a nova outburst, most part of the envelope is lost from the system. Moreover, a part of the original white dwarf matter is dredged up and lost in the outburst wind. Then MWD decreases after the nova outburst. This would be the case for MP < 109 Mˇ yr1 . If the shell flash is weak enough, on the other hand, the ejected mass is smaller than the mass which hydrogen burning converts into helium. Then MWD increases. This would be the case for smaller Mig and thus MP > 108 Mˇ yr1 . In either case, the hydrogen flash recurs, and the recurrence period is proportional to Mig /MP , which is shorter for higher MP . If the recurrence period is short, the flashes are observed as recurrent novae, which occurs in the upper-right region of this region.

2.2

He Shell Burning

For MP > 108 Mˇ yr1 . H burning produces a thin He layer, and He flashes are ignited when the He mass reaches a certain critical value. In the early stages of the He shell flash, the envelope is electron degenerate and geometrically almost flat. Thus the temperature at the bottom of the He burning shell increases because of the almost constant pressure there as given by Eq. (3). Heated by nuclear burning, the helium envelope gradually expands, which decreases the pressure. Then, the temperature attains its maximum and starts decreasing. The maximum temperature is higher for more massive WD and more massive envelope because of higher pressure. The strength depends on the He envelope mass Menv , thus depending on the accretion rate. The He envelope mass Menv is larger for the slower mass-accumulation rate of the He layer MP He . For MP He  1  108 Mˇ yr1 , Menv exceeds a critical value where the density at its bottom becomes high enough to induce a He detonation. This would result in the sub-Chandrasekhar mass explosion. For higher MP He , the He shell flashes are not strong enough to induce a He detonation. Then, such flashes recur many times with the increasing WD mass MWD toward the Chandrasekhar mass. Eventually, this leads to the initiation of SNe Ia. Nucleosynthesis in such He shell flashes has been calculated for various set of (MWD , Menv ) (Nomoto et al. 2013; Shen and Bildsten 2007). For higher maximum temperatures, heavier elements, such as 28 Si and 32 S, are synthesized. However, the maximum temperature is not high enough to produce 40 Ca. After the peak, some amount of He remains unburned in the flash and burns into C+O during the stable He shell burning. In this way, it is possible that interesting amount of intermediate mass elements (IME), including Si and S, already exist in the unburned C+O layer at Mr 1:2Mˇ .

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WD

MS

a mass stripping

winds

b

torus

torus c

hot WD winds 1000 km/s

line of sight

expanding torus

10-100 km/s

d Fig. 2 A schematic configuration of a binary evolution including mass-stripping effect (Hachisu et al. 2008a). (a) Here we start a pair of a C+O WD and a more massive main-sequence (MS) star with a separation of several to a few tens of solar radii. (b) When the secondary evolves to fill its Roche lobe, mass transfer onto the WD begins. The mass transfer rate exceeds a critical rate Mcr for optically thick winds. Strong winds blow from the WD. (c) The hot wind from the WD hits the secondary and strips off its surface. (d) Such stripped-off material forms a massive circumstellar disk or torus and it gradually expands with an outward velocity of 10–100 km s1 . The interaction between the WD wind and the circumstellar torus forms an hourglass structure. The WD mass increases up to MIa D 1:38 Mˇ and explodes as an SN Ia

2.3

Four Types of Type Ia Supernovae (SNe Ia) in the Single-Degenerate (SD) Scenario

Based on the above properties of accretion-induced hydrogen shell burning, the binary system in the SD scenario evolves through stages (a)–(d) below (also shown in Fig. 2a–d: Hachisu et al. 2008a).

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The more massive (primary) component of a binary evolves to a red-giant star (with a helium core) or an AGB star (with a C+O core) and fills its Roche lobe. Mass transfer from the primary to the secondary begins and a common envelope is formed. After the first common envelope evolution, the separation shrinks and the primary component becomes a helium star or a C+O WD. The helium star evolves to a C+O WD after a large part of helium is exhausted by core helium burning. We eventually have a close pair of a C+O WD and a main-sequence (MS) star (Fig. 2a). Further evolution of the system depends on the binary parameters. Depending on at which stage SNe Ia are triggered, the SD scenario predicts the following four variations of SNe Ia.

2.3.1 SNe Ia-Circumstellar Matter (CSM) After the secondary evolves to fill its Roche lobe, the mass transfer to the WD begins. This mass transfer occurs on a thermal timescale because the secondary mass is more massive than the WD. The mass transfer rate exceeds MP cr for the optically thick wind to blow from the WD (Hachisu et al. 1996, 1999a, b) (Fig. 2b). Optically thick winds from the WD collide with the secondary surface and strip off its surface layer. This mass-stripping attenuates the rate of mass transfer from the secondary to the WD, thus preventing the formation of a common envelope for a more massive secondary in the case with than in the case without this effect. Thus the mass-stripping effect widens the donor mass range of SN Ia progenitors (Fig. 2c). Such stripped-off matter forms a massive circumstellar torus on the orbital plane, which may be gradually expanding with an outward velocity of 10–100 km s1 (Fig. 2d), because the escape velocity from the secondary surface to L3 point is vesc  100 km s1 . Subsequent interaction between the fast wind from the WD and the very slowly expanding circumbinary torus forms an hourglass structure (Fig. 2c–d). When we observe the SN Ia from a high inclination angle such as denoted by “line of sight,” circumstellar matter can be detected as absorption lines like in SN 2006X. This scenario predicts the presence of several types of circumstellar matter around the binary system, which are characterized various wind velocities vw : (1) white dwarf winds with such high velocities as vw  1000 km s1 , (2) slow dense matter stripped off the companion star by the white dwarf wind, (3) slow wind matter ejected from a red-giant, and (4) moderate wind velocities blown from the mainsequence star. The above features are supported by observations of the presence of circumstellar matter in some SNe Ia (Foley et al. 2012; Patat et al. 2007; Sternberg et al. 2011) and the detection of H in circumstellar-interaction-type supernovae (Ia/IIn) such as SN 2002ic (Hamuy et al. 2003). SN 2002ic shows the typical spectral features of SNe Ia near maximum light but also apparent hydrogen features that have been absent in ordinary SNe Ia. Its light curve has been reproduced by the model of interaction between the SN Ia ejecta and the H-rich circumstellar medium (Fig. 3) (Nomoto et al. 2005).

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Fig. 3 The observed light curve of SN Ia 2002ic (filled circles) and the calculated light curve with circumstellar interaction (Nomoto et al. 2005)

2.3.2 SNe Ia-Supersoft X-Ray Sources (SSXS) When the mass transfer rate decreases to the following range: MP stable < MP < MP cr , optically thick winds stop, and the WDs undergo steady H burning. The WDs are observed as supersoft X-ray sources (SSXSs) until the SN Ia explosion. The stripped-off material forms circumstellar matter (CSM) but it has been dispersed too far to be detected immediately after the SN Ia explosion. 2.3.3 SNe Ia-Recurrent Novae (RN) When the mass transfer rate from the secondary further decreases below the lowest rate of steady hydrogen burning, i.e., MP transfer < MP stable , hydrogen shell burning is unstable to trigger a mild flashes, which recur many times in a short period as a recurrent nova (RN) (e.g., Hachisu and Kato 2001). Its recurrent period is as short as  1 yr, which can be realized for high M and high MP as discussed in Sect. 2.1. These flashes burn a large enough fraction of accreted hydrogen to increase M to SNe Ia. Observationally, PTF11kx (Dilday et al. 2012) provides strong evidences that the accreting white dwarf was a recurrent nova and the companion star was a red supergiant. 2.3.4 SNe Ia-He White Dwarf In the rotating white dwarf scenario, which will be discussed in the later section (e.g., Benvenuto et al. 2015), ignition of central carbon burning is delayed in some cases due to the larger Chandrasekhar mass of the rotating white dwarfs than nonrotating white dwarfs. This delay time after the end of accretion up to the SN Ia

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explosion depends on the timescale of angular momentum loss from the C+O white dwarfs and could be long enough for the companion star to evolve into a He white dwarf and for circumstellar materials to disperse. For such a delayed SN Ia, it would be difficult to detect a companion star or circumstellar matter.

2.4

Companion Stars in the SD Scenario

In SD scenario, SNe Ia can occur for a wide range of MP . The progenitor white dwarfs can grow their masses to the Chandrasekhar mass by accreting hydrogenrich matter at a rate as high as MP & 107  106 Mˇ yr1 (e.g., Hachisu et al. 1996, 1999a, b; Han and Podsiadlowski 2004; Langer et al. 2000; Li and van den Heuvel 1997; Nomoto et al. 2000b). Two types of binary systems can provide such high accretion rates, i.e., (1) a white dwarf and a lobe-filling, more massive (up to  7Mˇ ), slightly evolved mainsequence or subgiant star (WD + MS) and (2) a white dwarf and a lobe-filling, lessmassive (typically  1Mˇ ), red-giant (WD + RG) (Hachisu et al. 1999a, b). Figure 4 shows these two regions of (WD + MS) and (WD+RG) in the log P  M2 (orbital period – secondary mass) plane (Hachisu et al. 2008b). Here the metallicity of Z D 0:02 and the initial white dwarf mass of MWD;0 D 1:0 Mˇ are assumed. The initial system inside the region encircled by a thin solid line (labeled “initial”) increases its WD mass up to the critical mass (MIa D

Fig. 4 The regions that produce SNe Ia are plotted in the log P  M2 (orbital period – secondary mass) plane for the (WD + MS) system (left) and the (WD + RG) system (right) (Hachisu et al. 2008b). Currently known positions of the recurrent novae and supersoft X-ray sources are indicated by a star mark (?) for U Sco, a triangle for T CrB, a square for V Sge, but by arrows for the other three recurrent novae, V394 CrA, CI Aql, and RS Oph. Two subclasses of the recurrent novae, the U Sco type and the RS Oph type, correspond to the WD + MS channel and the WD + RG channel of SNe Ia, respectively

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1:38 Mˇ ) for the SN Ia explosion, the regions of which are encircled by a thick solid line (labeled “final”). Note that the “initial” region of WD + MS systems extends up to such a massive (M2;0  5  6 Mˇ ) secondary, which consists of a very young population of SNe Ia with such a short delay time as t . 0:1 Gyr. On the other hand, the WD + RG systems with a less massive RG (M2;0  0:9  1:0 Mˇ ) consist of a very old population of SNe Ia of t & 10 Gyr. Delay time distribution (DTD) of SNe Ia on the basis of the above SD model (Fig. 4) has a featureless power law being in good agreement with the observation (Hachisu et al. 2008b). This is because the mass of the secondary star of the SN Ia system ranges from M2:0  0:9 to 6 Mˇ due to the effects of the WD winds and the mass stripping. In our model, moreover, the number ratio of SNe Ia between the WD + MS component and the WD + RG component is rMS=RG D 1:4. Such almost equal contributions of the two components help to yield a featureless power law.

2.5

Rotating White Dwarf

2.5.1 Uniform Rotation and Delayed Carbon Ignition In the above sections, some observations that support the SD scenario are given. However, there has been no direct indication of the presence of companions, e.g., the lack of companion stars in images of SN 2011fe (Li et al. 2011) and some Type Ia supernova remnants (Schaefer and Pagnotta 2012). The rotating white dwarf scenario solves this missing-companion problem (Benvenuto et al. 2015; Di Stefano et al. 2011; Hachisu et al. 2012a; Justham 2011). The rotating WD evolves as follows Hachisu et al. (2012a) and Benvenuto et al. (2015). 1. For certain ranges of binary parameters, the accretion rate (MP ) always exceeds 107 Mˇ y1 so that the WD increases its mass until it undergoes “prompt” carbon ignition. The mass of the uniformly rotating WD at the carbon ignition, MigR , is larger for smaller MP . For MP D 107 Mˇ y1 , MigR D 1.43 Mˇ , which is the largest mass because nova-like hydrogen flashes prevent the the WD mass from growing for the lower MP . Because of the centrifugal force in the rotating WD, MigR D 1.43 Mˇ is larger than MigNR D 1.38 Mˇ (Nomoto et al. 1984). 2. For adjacent ranges of binary parameters, the mass of the rotating WD exceeds MigNR D 1.38 Mˇ but does not reach MigR D 1.43 Mˇ because of the decreasing accretion rate. After the accretion rate falls off, the WD undergoes the angular momentum-loss (J-loss) evolution. The exact mechanism and the time scale of the J-loss are highly uncertain, although the magneto-dipole braking WD is responsible. J-loss induces the contraction of the WD, which leads to the “delayed” carbon ignition after the “delay” time due to neutrino and radiative cooling.

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Fig. 5 The evolutionary tracks of the center of the WD up to the onset of the hydrodynamical explosion (Benvenuto et al. 2015). "nuc D " indicates the conditions at which neutrino losses equal nuclear energy release, while SP D 0 show the stages at which central entropy per baryon begins to increase. Thick black and thin red lines correspond to the treatments of screening given by Kitamura (2000) and Potekhin and Chabrier (2012), respectively. Arrows indicate the sense of the evolution

Figure 5 shows the evolution of the center of the WD since before the end of accretion up to the onset of the hydrodynamical stage (Benvenuto et al. 2015). The uppermost line corresponds to the case (1) evolution that leads to the “prompt” carbon ignition. Below that, the lines from upper to lower correspond to the evolutions with increasing J-loss timescale ( J D 1, 3, 10, 30, 100, 300, and 1000 Myr, respectively) that lead to the “delayed” carbon ignition. In what binary systems (P and M2 ) the uniformly rotating WD undergoes the delayed carbon ignition? The result for the initial WD masses of 0:9 Mˇ is shown in Fig. 6. Here the binary systems starting from the “painted” region of the (P M2 ) plane reach 1:38 Mˇ < M < 1:43 Mˇ , while the systems starting from the blank region encircled by the solid line reach M D 1:43 Mˇ . The occurrence frequency of the delayed carbon ignition would roughly be one-third of the total frequency of the carbon ignition. For the values of J considered here, the WD spends a time to undergo SN Ia explosion enough for the donor star to evolve to a structure completely different from the one it had when acted as a donor. For the red-giant donor, its H-rich envelope would be lost as a result of H-shell burning and mass loss so that it would become a He WD in 10 Myr. For the main-sequence donor, it would also evolve to become a low mass He WD in 1 Myr, a hot He WD in 10 Myr, and a cold He WD in 1000 Myr (Di Stefano et al. 2011). So, the J-losses should delay the explosion a time enough for the former donor to be undetectable. Therefore, this scenario provides a way to account for the failure in detecting companions to SNe Ia. Such He white dwarf companions would be faint enough not to be seen before or after the Type Ia supernova explosion. This new single-degenerate scenario can

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Fig. 6 The outcome of the binary evolution of the WD + companion star systems is shown in the parameter space of the initial orbital period P and the companion mass M2 for the initial WD mass of 0:9 Mˇ (Benvenuto et al. 2015). The mass M of the WD starting from the “painted” region reaches 1:38 Mˇ < M < 1:43 Mˇ (delayed carbon ignition), while the systems starting from the blank region encircled by the solid line reach M D 1:43 Mˇ (prompt carbon ignition)

explain in a unified manner why no signatures of the companion star are seen in some Type Ia supernovae, whereas some Type Ia supernovae indicate the presence of the companion star.

2.5.2 Differential Rotation and Super-Chandra SNe Ia If the accretion leads to nonuniform, differentially rotating WDs, carbon ignition occurs at super-Chandrasekhar masses (Hachisu et al. 2012b). The WD mass can increase by accretion up to 2.3 (2.7) Mˇ from the initial value of 1.1 (1.2) Mˇ , being consistent with high luminosity SNe Ia such as SN 2003fg, SN 2006gz, SN 2007if, and SN 2009dc (Kamiya et al. 2012). Such very bright super-Chandrasekhar mass SNe Ia are suggested to born in a low metallicity environment.

3

One-Dimensional Explosion Models of Chandrasekhar Mass White Dwarfs

In the Chandrasekhar mass models, carbon burning ignited in the central region is unstable to flash because of strong electron degeneracy and release a large amount of nuclear energy explosively. However, the central density is too high, and thus the shock wave is too weak to initiate spontaneously a carbon detonation (because of temperature-insensitive pressure of strongly degenerate electrons). Then the explosive thermonuclear burning front propagates outward as a convective deflagration wave (subsonic flame) (e.g., Arnett 1996; Nomoto et al. 1984).

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Rayleigh-Taylor instabilities at the flame front cause the development of turbulent eddies, which increase the flame surface area, enhancing the net burning rate and accelerating the flame. In the 1D convective deflagration model W7 (Nomoto et al. 1984), the flame speed is prescribed by time-dependent mixing-length theory with the mixing length being 0.7 of the pressure scale height. In some cases the deflagration may undergo “deflagration to detonation transition (DDT)” (Khokhlov 1991). In the 1D DDT model WDD2 (Iwamoto et al. 1999), DDT is assumed to occur when the density at the flame front decreases to 2  107 g cm3 . Such a turbulent nature of the flame propagation has been studied in multidimensional simulations as will be described in the subsequent sections (Hillebrandt and Niemeyer 2000).

3.1

Nucleosynthesis in Deflagration and Detonation

In this section, we use 1D hydrodynamical models W7 and WDD2 to summarize the products of explosive nucleosynthesis which takes place behind the deflagrationdetonation wave. Figures 7 and 8 show the isotopic distributions as a function of the enclosed mass for W7 (Nomoto et al. 1984; Mori et al. 2016) and WDD2 (Iwamoto et al. 1999; Mori et al. 2016). In the inner core of W7, the temperature behind the deflagration wave exceeds  5  109 K, so that the reactions are rapid enough (compared with the expansion timescale) to realize nuclear statistical equilibrium (NSE), thus synthesizing Fepeak elements, mainly 56 Ni of 0:65 Mˇ (Nomoto et al. 1984; Mori et al. 2016). The surrounding layers gradually expand during the subsonic flame propagation, so that the densities and temperatures get lower. As a result, explosive burning produces the intermediate mass elements Si, S, Ar, and Ca due to lower peak temperatures than in the central region. In WDD2, the flame speed is assumed to be slower than W7 so that the mass of the materials undergoing deflagration is smaller. Instead, the detonation produces 56 Ni and Si, S, Ar, and Ca in the outer layers. The total amount of 56 Ni is 0:67 Mˇ (Iwamoto et al. 1999; Mori et al. 2016). In these Chandrasekhar mass models, the central densities of the WDs are so high (3  109 g cm3 for W7 and WDD2) that the Fermi energy of electrons tends to exceed the energy thresholds of the electron captures involved. Electron captures reduce the electron mole fraction, Ye , that is the number of electrons per baryon. As a result of electron capture, the Chandrasekhar mass model synthesizes a significant amount of neutron-rich species, such as 58 Ni, 56 Fe, 54 Fe, and 55 Mn. Figures 9 and 10 show the abundance ratios of the integrated amount of species relative to 56 Fe with respect to the solar abundance ratio. It is seen that some neutron-rich species are enhanced relative to 56 Fe. The detailed abundance ratios with respect to 56 Fe depends on the convective flame speed and the central densities and also the weak reaction rates. In Figs. 7 and 8, the most updated weak reaction rates are applied for electron capture (Mori et al. 2016).

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It is also important to note that the synthesized amounts of neutron-rich species (58 Ni, 56 Fe, 54 Fe, and 55 Mn) differ between the Chandra and sub-Chandra models because of the difference in the central densities of the WDs (Yamaguchi et al. 2015).

3.2

Observable Characteristics of Chandrasekhar Mass Models

Flux (erg cm–2 s–1 Hz–1)

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The main observable characteristics of SNe Ia are their optical light curves and spectra. The light curves are powered primarily via the decays of 56 Ni and its daughter 56 Co. The early spectra are characterized by the presence of strong absorption lines of Si as well as lines from intermediate mass elements such as Ca, S, Mg, and O as well as the Fe-peak elements Fe, Ni, and Co as seen in Fig. 11 (Krause et al. 1997). The late-time spectra show emission lines of Fe-peak elements, which include those of stable Ni, i.e., neutron-rich 58 Ni. It is thus evident that the light curves and spectra are closely related to the nucleosynthesis, which is crucial to study the unresolved issues regarding the explosion models and the progenitors of SNe Ia.

Nugent normal type la

SN 1994D High-velocity Ca II SN 1572 (Tycho)

SN 2001el

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Fig. 11 Observed spectra at near maximum light of several Type Ia supernovae, including Tycho’s supernova 1572, with the line identifications of several elements (Krause et al. 1997)

46 Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs 46.0 SN 1994D

45.0 Log [Fλ] (in arbitrary units)

Fig. 12 Comparison between the observed spectra of Type Ia supernova (SN 1994D at maximum light and SN 1992A at 5 days after maximum light) with the synthetic spectra of the carbon deflagration model W7 at 20 days and 23 days after the explosion, respectively (Nugent et al. 2000)

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Both W7 and WDD2 models are successful in reproducing the basic features of SN Ia light curves and spectra near maximum light as seen from the synthetic spectra of W7 in Fig. 12 (Nugent et al. 2000). Important point is that the subsonic deflagration decreases the densities of the Chandrasekhar mass WD before the deflagration or detonative wave arrives, which is necessary to synthesize enough amount of intermediate mass elements (Ca, S, Si, Mg, and O) rather than to incinetrate most of C+O into NSE (Fe-peak elements) (Arnett 1969). This demonstrates the important roles of 1D hydrodynamical models even these are approximate: thermonuclear explosion models of WDs work to explain the basic features of “typical” SNe Ia as far as those models form the abundance distributions like W7 and WDD2. Clarifying how those abundance distributions are actually realized is the task of multi-dimensional simulations as will be described in the next sections.

4

Multi-Dimensional Models and Diversity of Explosion Mechanisms

As discussed with 1D hydrodynamical simulations, carbon burning in the center grows into deflagration and detonation. To understand these processes, we

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summarize two-dimensional hydrodynamical simulations of the explosion phase of a carbon-oxygen white dwarf carried out by Leung and Nomoto (2017b). The hydrodynamics code is extended from the prototype for modeling supernova explosion (Leung et al. 2015a), which has been used to model subluminous SNe Ia (Leung et al. 2015b) and Chandrasekhar Mass SNe Ia (Leung and Nomoto 2017a). It uses the weighted essentially non-oscillatory (WENO) fifth-order scheme for spatial discretization and the five-step, third-order, non-strong stability-preserving Runge-Kutta scheme for time discretization. The Helmholtz equation of state is used to describe the microphysics, which contains an ideal degenerate electron gas at any relativistic level, a classical ideal gas of ions, a photon gas assuming Planck distribution and electron-positron pair. The screening of electron gas is included. To describe the explosion, the level set is applied to track both the fronts of deflagration and detonation. The energy release assumes a three-step scheme, the carbon burning, burning toward the nuclear quasi-statistical equilibrium (NSE) and burning toward NSE. The seven-isotope network containing 4 He, 12 C, 16 O, 20 Ne, 24 Mg, 28 Si, and 56 Ni is used to describe the chemical composition of matter. To determine the propagation of deflagration, the turbulent flame speed formula (Pocheau 1994; Schmidt et al. 2006) is used with the one-equation model for the evolution of turbulence. For the detonation speed and its energy production, the pathological detonation is assumed as described in details in the Appendix. For models with DDT transition, detonation is triggered when locally Ka D 1 is satisfied.

4.1

Deflagration-Detonation Transition (DDT) Model

The deflagration-detonation transition (DDT) model (Khokhlov 1991) combines the slow burning phase at the beginning and the rapid explosion phase afterward, which provides sufficient time for electron capture, and ensures most of the fuel, in the form of carbon-oxygen mixture, is burnt before the WD expansion ceases the nuclear reaction (Iwamoto et al. 1999). Figure 13 shows the temperature color-plot for the turbulent deflagration with DDT in a typical SNe Ia model. For the WD, the central density of 3  109 g cm3 with an isothermal profile of 108 K is assumed. The composition is assumed to be at solar metallicity with X .12 C/=X .16 O/ D 1 by mass. The turbulent flame allows the flame to propagate quickly before the Rayleigh-Taylor instabilities become important. This ensures that sufficient amount of matter is burnt before the density of flame front is low enough to trigger detonation. The typical temperature in the deflagration zone is around 5  109 K at the time when detonation is commenced. Owing to the low-density fuel, the temperature in the ash made by detonation is comparably lower, at 3  109 K. Due to the correlated shock, hot spots can be found when the high-velocity flow collides with the boundary, which can be as high as 7109 K. However, this feature might not appear so frequently in three-dimensional simulations because of the lower degree of symmetry.

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Fig. 13 The temperature color-plot of the turbulent deflagration model with DDT at about 0.4 s after DDT is triggered (Leung and Nomoto 2017b). The solid lines stand for the shape of the deflagration and detonation front. The central density is set at 3  109 g cm3 with isothermal profile of 108 K. The composition is assumed to be at solar metallicity with X.12 C/=X.16 O/ D 1 by mass. The c3 flame is chosen as the initial flame 10 Fe Ni scaled mass fraction

Fig. 14 The chemical abundance of the typical SNe Ia using the DDT model presented in Fig. 22 (Leung and Nomoto 2017b). The ratio is ŒX=X.56 Fe/=ŒX=X.56 Fe/ˇ . The two lines stand for the typical uncertain range of a factor of 2

Cr

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Figure 14 shows the chemical abundance of the DDT model by calculating nucleosynthesis using the tracer particles data. In the SN Ia simulation, due to the heavy computation of multidimensional hydrodynamics, the large nuclear reaction network is used for a post-process, where the thermodynamics trajectories of the massless particles are used only to follow the fluid advection without affecting

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the hydrodynamics. In the hydrodynamics, only the simplest network can capture the essence of deflagration and detonation to reduce the workload in isotope advection. With those two networks, reasonably accurate energy production in the hydrodynamics and a detailed nucleosynthesis structure can be obtained. Almost all C + O fuel is consumed; thus, only a trace of 16 O is left behind. On the contrary, other ˛-chain isotopes, such as 28 Si, 32 S, 36 Ar, and 40 Ca, are very close to the solar abundance. The isotopes with an odd atomic number is always under-produced as expected. Most iron-peak elements, such as chromium, iron, manganese, and nickel, are mostly consistent with solar abundance, with a slight overproduction of 54 Fe and 58 Ni.

4.2

Pure Turbulent Deflagration (PTD) Model

The 2D pure deflagration model has its theoretical weakness in terms of significant unburnt material at the core. However, with the rapidly growing observation data of supernovae, some peculiar SNe Ia whose explosion observables are incompatible with the standard picture can be explained by this model.

4.2.1 Weak Explosion Theoretically, flame has been suggested to fail to develop into detonation in the following two cases. First possibility is the hybrid white dwarf with a C + O core and an O+Ne envelope. This type of white dwarf has been suggested to be originated from a main-sequence star around 10 Mˇ . In the main-sequence star evolution, a C+O core of mass 0:6  1:0 Mˇ is formed. When the inner core cools down and contracts, the the surface of the carbon-oxygen core can be hot enough to carry out carbon burning. In the standard picture, the burning appears in the form of flame, which gradually propagates inward due to thermal diffusion. At the end, the flame reaches the center such that the core becomes carbon-free. However, whether the carbon flame can spread from the core surface to the center depends strongly on the convective boundary mixing (Denissenkov et al. 2013). This is a poorly known quantity due to its multidimensional nature. Within the theoretical uncertainties, the carbon flame can be stopped, leaving a small carbonoxygen core and a neon-oxygen envelope. Second, the model is the same as the typical explosion by a carbon-oxygen white dwarf, but without detonation transition. Notice that whether or not the detonation can start is still a matter under debate. In general it requires certain mechanism, for example, turbulent diffusion, in order to create a temperature gradient which allows supersonic burning as suggested by Zel’dovich gradient mechanism. In fact, whether turbulence can or cannot provide the required diffusion to smear out the flame is uncertain due to the lack of required resolution for resolving the heat diffusion around the flame surface. As a result, in another limit, it is possible that the explosion develops as pure turbulent flame without any transition (Fink et al. 2014). In all cases, the flame ceases to develop into detonation even when the flame has reached the distributed burning regime. As a result, with the energy from the

46 Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs

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0

Fig. 15 The temperature color-plot of a SN Ia model using the pure turbulent deflagration model at time 1.3 s (Leung and Nomoto 2017b). The solid lines stand for the shape of the deflagration. The central density is set at 3  109 g=cm3 with isothermal profile of 108 K. The composition is assumed to be at solar metallicity with X.12 C/=X.16 O/ D 1 by mass. An initial c3 flame is patched as to bypass the slow simmering phase

carbon deflagration only, the star is barely unbound. This means the ejecta mass is much lower than usual SNe Ia. And the ejecta velocity is also much lower. Without detonation, the iron-production is much lower than typical SNe Ia. The corresponding isotope ratio of those iron-peaked elements will be much higher. In observations, this type of objects show a very transient and dim signal. The light curve is much different from those of usual SNe Ia. With a low 56 Ni production, the peak luminosity can be lower by 2–5 by absolute magnitude and shows no secondary maximum due to turbulent mixing. The optical signal is also viewingangle dependent that preserves moderately the anisotropy of the flame. The model has been applied to explain the prototypical SN Iax 2002cx (Kromer et al. 2013) and the dimmest SN Iax 2008ha (Kromer et al. 2015). Figure 15 shows the flame structure of one of the realization using the pure turbulent deflagration model (Leung and Nomoto 2017b). The model is chosen to be typical for SNe Ia, with a central density of 3  109 g cm3 and an isothermal profile of 108 K. The composition is assumed to be at solar metallicity with X .12 C/=X .16 O/ D 1 by mass. At about 1 s after the flame has started, the energy release is mostly finished. The flame preserve the initial three-finger structure. The large-scale Rayleigh-Taylor instability is enhanced, showing injection of cold fuel into ash between the “fingers.” Furthermore, curly shape appears along the finger structure, which demonstrates the Kelvin-Helmholtz instabilities perturbing

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Fe

Ni

Cr scaled mass fraction

Fig. 16 The chemical abundance ŒX=X.56 Fe/=ŒX=X.56 Fe/ˇ of the typical SN Ia using the PTD model. The two lines stand for the typical uncertain range of a factor of 2

K. Nomoto and S.-C. Leung

1

Mn C

Ne O

Si

S Ar Ca

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Co

Ti

0.01 10

20

30

40 A

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the flame surface. The outer atmosphere is mildly heated up due to the expansion of the inner matter. Figure 16 shows the chemical composition of the pure turbulent deflagration (PTD) model (Leung and Nomoto 2017b) similar to Fig. 14. Without the detonation, most of the low-density material remains unburnt. As a result there is a significant amount of 12 C and 16 O. 20 Ne, which is a product of deflagration at low-density is largely preserved. However, due to the slow propagation of flame at density 107 g cm3 , most intermediate mass elements (IME) is under-produced. The ironpeak elements, in general, are well produced. Since the ratio is taken against 56 Fe, where in the PTD model a smaller amount is produced, the overproduction of 54 Fe and 58 Ni become more severe, even when their net value is closed to the DDT case. Comparing with Fig. 16, it can be seen that most iron-peak elements are produced during the deflagration phase, while the IME are produced by detonation. Notice that there is no clear cut for which elements are solely produced by deflagration and detonation, especially near the deflagration-detonation transition. Compression and expansion due to shock interaction can for example create iron-peak elements in the detonation region. Furthermore, due to the asymmetric structure of the flame, some high-density fuel can be burnt by detonation instead of deflagration, which creates a significant amount of 56 Ni. The upper panel of Fig. 17 shows the luminosity against time for the hybrid WD model (Leung and Nomoto 2017b). The initial stellar model is the same as the PTD and DDT model, which is a WD at 3  109 g cm3 , isothermal profile at 108 K. But the chemical composition is different. It has an inner core of X .12 C/ D 0:49, X .12 O/ D 0:49, and X .22 Ne/ D 0:02; the inner envelope of X .12 C/ D 0:03. X .16 O/ D 0:49, X .20 Ne/ D 0:46, and X .22 Ne/ D 0:02; and an outer envelope with the same composition as the core. To compare the difference in the burning energetic, we also include the results from the PTD and the DDT model. For the hybrid WD, the carbon deflagration stops once the flame reach the interface. The luminosity drops at t D 0:8 s. Owing to the slower burning toward

mburn (solar mass)

luminosity (1050 erg/s)

46 Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs

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DDT model PTD model Hybrid CO WD

50 0 1.5 1 0.5 0

0

0.5

1

1.5

time (s) Fig. 17 Panel: The luminosity against time for the hybrid WD model with an ONe envelop in one of the realization (Leung and Nomoto 2017b). The central density is chosen to be 3  109 g cm3 with an isothermal profile at 108 K. A c3 flame is patched to trigger the deflagration phase. For comparison, those of the PTD model and the DDT model are shown

NQSE and NSE, together with the ˛-recombination during the expansion, the luminosity is observable until t D 0:9 s. In both PTD and DDT models, there is no such limit and thus the burning can last for about 1 s. Certainly, a sharp peak in the DDT model demonstrates the powerful energy release in the detonation phase. In the lower panel, we plot similar to the upper panel but for the burnt mass. Coinciding with the luminosity evolution, the hybrid WD model stops its burning at t D 1:0 s, showing that only the CO core is consumed. On the contrary, the PTD model can burn about 0:6 Mˇ at the end of simulation, while the DDT model can burn all the material before the rapid expansion. Figure 18 shows the energy evolution for the hybrid WD model (Leung and Nomoto 2017b). The total energy reaches its equilibrium value at t  0:8 s. Also, it is only slightly above zero, which suggests that the star is barely unbound by the deflagration. The kinetic energy grows slowly in the beginning, since nuclear energy is released in the form of the internal energy. Around t  0:8 s, it increases faster and reaches its equilibrium at t  1 s. Notice that the continuing growth of the kinetic energy means that the hot matter continues to do work on the expanding matter toward the atmosphere. Figure 19 shows the ratios of ŒX =X .56 Fe/=ŒX =X .56 Fe/ˇ in this type of SN Ia (Leung and Nomoto 2017b). As expected, the suppression of detonation and the suspension of deflagration in the outer envelope reduce the production of many isotopes. The iron-peak elements such as 54 Fe and 58 Ni, which are mostly produced by detonation, are significantly enhanced relative to 56 Fe. The intermediate mass elements along the ˛-chain such as 28 Si, 32 S, and 36 Ar are under-produced because they are primarily made by detonation in the region of lower density ( 107 g cm3 ).

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Etot Ekin Eint |Epot|

energy (1050 erg)

30

20

10

0

−10

0

0.5

1

1.5

time (s) Fig. 18 The time evolution of the total, kinetic, internal and potential energy of the same model as in Fig. 17 (Leung and Nomoto 2017b)

scaled mass fraction

10

Fe

Ni

Cr 1

C

O

Ne

Si S

0.1

0.01 10

20

30

Ar Ca

40 A

Ti V

Fe

50

60

70

Fig. 19 The chemical abundance ratios ŒX=X.56 Fe/=ŒX=X.56 Fe/ˇ of the hybrid WD model for an SN Ia presented in Fig. 18 (Leung and Nomoto 2017b)

4.2.2 Failed Explosion For a binary system with massive WD (> 1:2 Mˇ ), the ignition density is much higher than standard SNe Ia that the released energy cannot unbind the star owing to the efficient energy loss by neutrino and also electron capture. This is also known as the accretion-induced collapse. For an ONeMg WD, the typical ignition density (109:95 g cm3 ) is higher than that of CO WD (2  109 g cm3 ) (Nomoto and Kondo 1991; Schwab et al. 2015). The energy released during deflagration is much smaller than its CO counterpart due to its higher initial binding energy. The high

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density also makes the electron capture rate more efficient than that in CO WD. Notice that the majority of WD pressure comes from the electron gas. Due to weak interaction, the reaction e C p ! n C e occurs. In particular, for burnt matter with temperature high enough to reach NSE, it contains a significant amount of ironpeaked elements, in which high-Ye isotopes tend to interact with the surrounding electron to form low-Ye but stabler isotopes. The reduction of the electron fraction can significantly lower the pressure, even when its temperature has been raised to 1010 K. Furthermore, at this density range, matter is almost transparent to neutrino. The neutrino product can most likely escape from the star without interacting with matter or disposing energy. Therefore, it serves as another source of energy loss. Both factors can considerably lower the pressure of the burnt matter, which stops the flame propagation. The central density increases as a result. Notice that when the density increases, the equilibrium value of Ye (the value where the beta decay balances the electron capture) decreases. It thus further decreases the pressure in the burnt region and triggers an inward matter flow. The induced gravitational collapse results in a neutron star. After the bounce shock has formed when the matter in the core reaches nuclear density, the bounce shock once stalls outside the neutron star, heat is lost by its own neutrino emission. The stalled shock revived again by the energy deposition from neutrino emitted from the neutron star. As a result, the shock ejects the low-density matter in the envelope and the accretion disk (Kitaura et al. 2006).

4.3

Gravitationally Confined Detonation Model

Another direction for the SNe Ia is the gravitationally confined detonation model (Plewa 2007). It is unclear from the first principle whether turbulence at such high density and high Reynolds number behaves as observed in terrestrial experiments. In another extreme, a flame can be completely unperturbed by the local eddy motion and only subject to large-scale hydrodynamic instabilities, such as the RayleighTaylor instability. In that case, the deflagration propagates in a laminar flame speed, which leads to a small amount of mass being burnt (0.1 Mˇ ) before the flame quenches. Therefore, the burnt matter cannot drive efficiently the matter flow to create detonation spontaneously. Instead, the hot matter flows to the surface and expands. After some time, the hot matter converges again at the point opposite to where it rises at the beginning and sinks. Due to gravitational attraction, the downward flow accumulates and compresses the matter below, which heats up the matter. Once the matter is hot enough to burn carbon, the increased thermal pressure further provides the pressure force to create an ingoing jet, which becomes the seed for the first detonation. This type of explosion is in general stronger than DDT model because most matter is not burnt in the deflagration phase. Due to the rapid expansion after detonation, most matter preserve a high-Ye value. Also, because of the supersonic propagation of the detonation wave, matter does not have sufficient time to mix before they are ejected. So, the ejecta show a clear stratified structure in the core,

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despite that on the surface there could be a trace of the deflagration ash. Because a considerable amount of 56 Ni is produced, the model has been applied to explain luminous SNe Ia such as SN 1991T. However, the synthetic spectra cannot match well owing to the strong viewing angle dependence and the strong calcium, silicon, and sulfur lines, which are unobserved in SN 1991T (Seitenzahl et al. 2016).

5

Discussion

5.1

Spectral Diagnostics of Nucleosynthesis

We have discussed many current models and the implementation techniques in previous sections. The hydrodynamics simulation and corresponding nucleosynthesis can be applied to observations through chemical abundances. Through the use of tracer particles, the thermodynamics trajectories of individual fluid parcels can be traced. This provides the necessary data for tracing the nuclear reactions. As one example, we apply such an approach to the Chandra vs. sub-Chandra issue. For nucleosynthesis yields, whether the explosion is Chandra or sub-Chandra is crucial, because the central density of the white dwarf affects the abundance ratio of Fe-peak elements. Both Chandra and sub-Chandra explosion models can synthesize relevant amounts of 56 Ni for Type Ia supernovae (Hillebrandt and Niemeyer 2000). However, the amount of other Fe-peak elements differs, because the ignition density is different: The density can be as high as >109 g cm3 in the Chandra model whereas as low as 107 g cm3 in the sub-Chandra model. In the Chandra model, the thermonuclear runaway starts with the ignition of deflagration (Nomoto et al. 1976, 1984). In the high-temperature and high-density bubble, materials are incinerated into nuclear statistical equilibrium and undergo electron capture. Electron capture by free protons and Fe-peak elements leads to the synthesis of 58 Ni, 54 Fe, and 56 Fe (not via 56 Ni decay). These neutron-rich Fe-peak elements form a hole that is almost empty of 56 Ni (e.g. Nomoto et al. 1984). In the sub-Chandra model, the ignition density is too low for electron capture to take place. The neutron excess is produced only by the initial CNO elements, which are converted to 14 N and to 22 Ne. Thus, this excess also depends on the initial metallicity. As a result, 58 Ni is almost uniformly distributed with a mass fraction as small as 0.01 (e.g., Shigeyama et al. 1992). Such differences in the mass and the distribution of 58 Ni can be observationally investigated by late- phase (1 year since the explosion) spectroscopy at near-infrared wavelengths Hillebrandt and Niemeyer 2000). Because ejecta become optically thin at late times, spectroscopy provides an unbiased, direct view of the innermost regions. Optical observations have shown [FeII]  7155 and [NiII]  7378 for several SNe Ia (Maeda et al. 2010). The [NiII]  7378 line is emitted from the electron capture region of the ejecta; the relatively narrow width (3,000 km s1 ) of this line provides further support of this finding. Thus, the existence of the [NiII] line implies ignition at high density, which would supports the Chandra model (Nomoto et al. 2013).

46 Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs

5.2

1301

Chemical Evolution of Galaxies and Supernova Remnants

SNe Ia are important to cosmic chemical evolution due to their delayed production of iron-peak elements. Then, the evolution of certain elements can reflect the role of SNe Ia in chemical enrichment. Manganese is one of the important elements to constrain the SNe Ia model. Figure 20 shows the evolution of Manganese as a function of metallicity (Leung and Nomoto 2017b) where the galactic chemical evolution is calculated as described in Leung and Nomoto (2017a). The stellar abundances are taken from galactic disk F and G dwarfs (Reddy et al. 2003), cluster and field stars (Sobeck et al. 2006) and from thin discs (Feltzing et al. 2007). At low metallicity, [Mn/Fe] does not vary much because of the delay effects. Notice that a white dwarf cannot give rise to SNe Ia instantaneously after the formation of the progenitor WD. The CO WD have masses have masses from 0.6 to 1.0 Mˇ . The mass accretion from its companion star in the single-degenerate scenario starts after the companion star . 8Mˇ / has evolved slightly off the mainsequence star and become a red giant. per year). Hence, after the formation of WD in the primary star, another 10610 years are required for the WD to gain mass till the Chandrasekhar mass. Therefore, there is a delay in the first SNe Ia event since the progenitor star is formed. When Z > 0:1Zˇ the [Mn/Fe] ratio increases quickly, demonstrating that the SNe Ia is an vital source for manganese to explain the evolution of manganese abundance.

0

[Mn/Fe]

-0.1

Typical Type Ia supernova Sobeck et al., 2006 Reddy et al., 2003 Feltzing et al., 2007

-0.2

-0.3

-0.4

-0.5 -1.5

-1

-0.5

0

[Z/Zsun] Fig. 20 [Mn/Fe] against [Fe/H] in Galactic chemical evolution (Leung and Nomoto 2017a, b). The numerical models are chosen based on three criteria. 1. The SNe Ia model should be able to represent the normal SNe Ia in general, namely 56 Ni about 0.6 Mˇ . 2. The manganese should be able to explain the solar abundance in the galactic chemical evolution model. 3. The nickel should satisfy the constraints from the solar abundance

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8

ρc = 5x10 g cm

0.035

ρc = 7.5x10 g cm 9

-3

9

-3

9

-3

Ni mass (solar mass)

ρc = 1x10 g cm

57

-3

8

ρc = 3x10 g cm

0.03

ρc = 5x10 g cm

SN 2012cg

-3

Z = 5 Zsun

Z = 5 Zsun

0.025

0.02 Z = 5 Zsun 0.015 solar value 0.01

0.2

Z = 0 Zsun

0.4 56

Z = 0 Zsun

0.6

Z = 0 Zsun

0.8

Ni mass (solar mass)

Fig. 21 57 Ni against 56 Ni for models with different central densities and metallicity of 0, 1, 3 and 5 Zˇ (Leung and Nomoto 2017b). The configuration is chosen based on the benchmark model as shown in Fig. 20. The observational data from SN 2012cg (Graur et al. 2016) is shown.

Besides galactic chemical evolution, the model parameter of an individual SN Ia explosion can be studied by looking at the supernova remnant or from its decay lines. Given the observational data, for example isotopes of Ni by the nickel decay, or manganese as from the decayed remnants, constraints on the supernova properties can be derived. In Fig. 21 the mass fractions 57 Ni against 56 Ni for different central densities is plotted. The observational data from a recent SNe Ia, the SN 2012cg (Graur et al. 2016), is included in the figure. This SNe Ia is regarded as one of the typical SNe Ia with normal luminosity based on its optical signals, i.e. light curves and spectra. By spanning different parameters to look for the model with similar production of 57 Ni against 56 Ni, this SN Ia has a rather low central density at the moment of explosion. In contrast, it has a high metallicity (five times of the solar metallicity). This demonstrates how one can extract the stellar properties through the use of chemical abundance. Another example is the observational data from SNe Ia remnant 3C 397. In Figure 22 the [Mn/Fe] ratio against [Ni/Fe] ratio of different SNe Ia models and of the SNe Ia remnant 3C 397 (Yamaguchi et al. 2015) is plotted. Using the nucleosynthesis data from many SNe Ia models, one can predict the SNe Ia progenitor. In particular, the supernova remnant shows strong hints on its high central density and high metallicity, at the moment of its explosion. Certainly, the above two models demonstrate only the preliminary in searching for stellar parameters. Degeneracy may still persist by other configurations such as different initial flame. The degeneracy can be resolved when more than one isotopes or elements are involved in the comparison.

46 Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs

8

ρc = 5x10 g cm

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ρc = 7.5x10 g cm 9

-3

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-3

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ρc = 3x10 g cm

[Mn/Fe]

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ρc = 1x10 g cm ρc = 5x10 g cm

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3C 397

Z = 5 Zsun 0.5 0.6

0.01 0.7

Z = 0 Zsun

0.8 0.9

0

0

0.2

0.1 [Ni/Fe]

Fig. 22 [Ni/Fe] against [Mn/Fe] for models with different central densities and metallicity of 0, 1, 3 and 5 Zˇ (Leung and Nomoto 2017b). Similar to Fig. 21, the models are chosen based on the benchmark model in Fig. 20. The observational data from 3C 397 (Yamaguchi et al. 2015) is shown. The purple lines stand for the contours of constant MNi models.

6

Cross-References

 Electron Capture Supernovae from Super Asymptotic Giant Branch Stars  Evolution of Accreting White Dwarfs to the Thermonuclear Runaway  Nucleosynthesis in Thermonuclear Supernovae  Type Ia Supernovae  Type Iax Supernovae

Appendix: A Short Review of Detonation Physics Deflagration to Detonation Transition In the previous section why the deflagration phase is necessary and how to implement the flame physics in SNe Ia simulation are discussed. In this section the motivation of including detonation in the framework, its background physics, and the implementation technique are further discussed. The multidimentional turbulent flame model attempts to introduce a flameacceleration scheme which allows the flame to burn more material before the expansion of the WD quenches the flame. It is found that the multidimentional PTD model predicts a significant amount of unburnt carbon and oxygen in the central region. As a result, the explosion energy inclines to the weaker side of the observed explosion.

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If the transition of deflagration to detonation occurs, the above problem might be solved. Detonation wave is the propagation of burning through shock compression. Unlike the deflagration counterpart, the supersonic motion of detonation can ensure that all necessary material in WD is burnt before the density becomes too low to sustain nuclear burning. This also bypasses the inconsistency of pure detonation model which tends to overproduce 58 Ni and 54 Fe due to electron capture (see Figs. 9 vs. 10, and Figs. 16 vs. 14) because in DDT model, deflagration part is confined in small mass region and the detonation mostly burns the outer material, which has too low density for electron capture to take place.

Physics of Detonation and Transition The detonation in general consists of three parts, the pre-shock region, the reaction zone, and the post-reaction zone region. To study the detonation structure, one usually solve the eigenstate(s) for the steady-state detonation wave structure equations (Sharpe 1999). By assuming the matter remains in thermodynamics equilibrium, that " D

X @" @" @" jT;Xi C j;Yi C j;T ; @ @T @Yi i

(4)

the steady-state Euler equation can be written as af2   R d D ; dx v $ )  1 ( "    # N  dT @p d Yi @p d  X @p 2 D  u  ; dx @T ;Y @ T;Y dx iD1 @Xi ;T;Yj ¤i dx R dY D ; dx v

(5) (6)

(7)

where  D af2  v 2

(8)

is the sonic parameter, af2

 D

@p @

 T;Y

"

p C  2



@" @

 T;Y

#

@p @T

 ;T



@" @T

1 (9) ;Y

is the sound speed of constant composition (also known as frozen sound speed in the literature of detonation), and

46 Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs

1 i D 2 af

(

1305

    1 @" @p @p  @Yi ;T;Yj ¤i @T ;Y @T ;Y " #)    @q @"  @Yi ;T;Yj ¤;i @Yi Yj ¤i

(10)

density (g/cm3)

is the thermicity constant, such that   R is the thermicity. It should be noted that at Eq. (7), the denominator  can bring subtlety to the calculation. In Chapman-Jouget detonation,  is always positive that the solution is continuous everywhere. However, for realistic equation of states and network,  can change sign. It corresponds to the point that the fluid velocity equals to the frozen speed of sound. At this point, there are two solutions for the detonation. First, by direct integration, the zone beyond that points has supersonic velocity. This corresponds to self-sustained detonation wave. Second, the reaction zone remains to be subsonic everywhere. This produces cusps in both density and temperature at that point, so that the solution remains continuous while satisfying the above equations. In general, only the second solution represents the stable detonation wave which occurs in SNe Ia. In Fig. 23 the density and temperature of a typical detonation wave is plotted. After the shock, there is a buffer zone which allows the temperature to increase. Once the matter reaches 4  109 K, the burning of carbon and oxygen becomes explosive that the temperature can be doubled within a few 102 cm. At about 0.1 cm, the drop of density has significantly led to a jump in the fluid

2.0×109 1.5×109

temperature (K)

1.0×1099 9×10

6×109

3×109 -4 1×10

1×10-2

1×100 x (cm)

1×102

1×104

Fig. 23 Upper panel: The density profile of the detonation wave at density 109 g cm3 . The detonation is assumed to start with a post-shock temperature 3:5  109 K with a composition 50 %12 C and 50 %16 O by mass. Lower panel: Same as above, but for the temperature profile

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1 4

He C O 20 Ne 24 Mg 12 16

mass fraction

0.1

28

Si S 36 Ar 40 Ca 44 Ti 48 Cr 52 Fe 56 Fe 32

0.01

0.001

1×10-4

1×10-2

1×100

1×102

1×104

x (cm)

Fig. 24 The chemical profile of the detonation wave for a detonation wave at density 109 g cm3

velocity, due to mass conservation. This makes the wave reach the frozen sound speed. At that point, the solution to the pathological detonation is connected, which ensures the ash propagates subsonic everywhere. The density reaches its equilibrium 1 cm, while the temperature reaches equilibrium at about 102 cm. In Fig. 24 the abundance profile for the same detonation wave is plotted. Similar to deflagration, at x < 102 cm, 12 C burns to form 20 Ne and 4 He. At 102 < x < 101 cm, both carbon and oxygen burning produce intermediate mass isotopes such as 32 S, 36 Ar, 40 Ca, and 44 Ti. At 102 < x < 102 cm, the matter slowly converts to NSE that ironpeak isotopes, including 48 Cr, 52 Fe, and 56 Ni form. The matter reaches equilibrium and no net change is observed beyond x > 102 cm. In SNe Ia simulations, the detonation energy and composition table need to be computed prior to the hydrodynamics simulations. This is because the table includes solving the equations for the detonation wave structure in order to find the energy release, propagation velocity for the pathological detonation, and ash composition as a function of density. In general, it depends on temperature as well. Owing to the electron degeneracy and that the nuclear binding energy change is much larger than the matter internal energy, the exact yield is less sensitive to the choice of temperature than that of density. After that, similar to the deflagration, the front is tracked by some discontinuity tracking scheme. By extracting the geometric properties of the front, corresponding energy and composition of the fluid swept by detonation wave are changed. One technical difference between deflagration and detonation is that detonation does not start at the beginning of the simulation and requires certain trigger. In practice, detonation is assumed to start when the local Karlovitz number Ka 1, namely, the ratio between turbulence length scale and the flame width. When it is

46 Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs

50

energy (10 erg)

40

1307

Etotal Ekin Eint |Epot|

20

0

DDT

Pure turbulent deflagration phase

0

0.5 time (s)

1

Fig. 25 The time evolution of the total, kinetic, internal, and potential energy of the same model as in Fig. 13

satisfied, the eddies around the thick flame becomes important to diffuse the heat from the hot ash to the cold fuel and cease the explosive burning. The hot region can carry out carbon burning simultaneously, creating a supersonic pulse and the shock. The shock then develops into detonation and burns the remaining fuel. To demonstrate the technique in carrying out detonation physics in Type Ia supernova simulations, a two-dimensional hydrodynamics simulation for the explosion phase of a carbon-oxygen core is presented. The configuration is similar to the model in Sect. 4.1. In Fig. 25 the energy evolution is plotted. The phase before DDT that has started is exactly the same as the PTD model since the same initial model and flame physics are used. But once DDT is triggered, the two models deviate. The total energy increases much faster to a much higher equilibrium value. It also leads to the global heating of matter, as shown by the increase of internal energy. Kinetic energy also continues to grow, in contrast to the asymptotic behavior as shown in the PTD counterpart.

Open Questions in Detonation It should be noted that there are two outstanding questions in the detonation transition remain unresolved. In one way, detonation transition is shown to be possible in the form of shock compression in a closed system and by turbulent compression in an open system. Certainly, the environment of a WD belongs to the latter one, where turbulent diffusion is relied to generate a smeared hot spot which can undergo supersonic heating. However, in the large-eddy simulations, it

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is shown that the typical turbulence strength is only marginally strong to diffuse the thermal energy. In terms of power spectrum, the probability of finding a fluid element with the required velocity fluctuation is small. Certainly, in most SNe Ia simulation, subgrid turbulence are used to estimate the turbulent kinetic energy. This points to the uncertainty in the subgrid turbulence model. Future work in how to achieve a robust turbulence model will offer important insight to the feasibility of the DDT model. Second, the exact Karlovitz number for DDT is not exactly known. In SNe Ia simulation in the literature, typical value of Ka  1. However, in direct numerical simulation of DDT for the H2 -air flame, at least Ka D 100 is required. Certainly, a one-one correspondence between the H2 -air flame and the carbon-oxygen flame cannot be drawn straightforwardly due to the huge differences in the equation of states and reaction channel. Despite that, the terrestrial flame experiment has demonstrated that the detonation transition can be much harder than one has assumed. It is therefore necessary to understand the critical Ka for DDT transition for a carbon-oxygen WD and if it can be achieved in hydrodynamics simulation. Acknowledgements This work has been supported in part by Grants-in-Aid for Scientific Research (JP26400222, JP16H02168, JP17K05382) from the Japan Society for the Promotion of Science and by the WPI Initiative, MEXT, Japan.

References Arnett D (1969) A possible model of supernovae: detonation of 12C. Ap & SS 5:180–212 Arnett D (1996) Supernovae and nucleosynthesis. Princeton University Press, Princeton Benvenuto OG, Panei JA, Nomoto K, Kitamura H, Hachisu I (2015) Final evolution and delayed explosions of spinning white dwarfs in single degenerate models for Type Ia supernovae. ApJL 809:L6 Denissenkov PA, Herwig F, Truwan JW et al (2013) The C-flame quenching by convective boundary mixing in super-AGB stars and the formation of hybrid C/O/Ne white dwarfs and SN progenitors. ApJ 772:37–45 Dilday B, Howell DA, Cenko SB et al (2012) PTF 11kx: A Type Ia supernova with a symbiotic nova progenitor. Science 337:942 Di Stefano R, Voss R, Claeys JSW (2011) Spin-up/spin-down models for Type Ia supernovae. ApJL 738:L1 Fink M, Kromer M, Seitenzahl IR et al (2014) Three-dimensional pure deflagration models with nucleosynthesis and synthetic observables for Type Ia supernovae. MNRAS 438:1762–1782 Foley RJ, Simon JD, Burns CR et al (2012) Linking Type Ia supernova progenitors and their resulting explosions. ApJ 752:101 Hachisu I, Kato M (2001) Recurrent novae as a progenitor system of Type Ia supernovae. I. RS Ophiuchi subclass: systems with a red giant companion. ApJ 558:323 Hachisu I, Kato M, Nomoto K (1996) A new model for progenitor systems of Type Ia supernovae. ApJL 470:97 Hachisu I, Kato M, Nomoto K, Umeda H (1999a) A new evolutionary path to Type IA supernovae: a helium-rich supersoft X-ray source channel. ApJ 519:314 Hachisu I, Kato M, Nomoto K (1999b) A wide symbiotic channel to Type IA supernovae. ApJ 522:487

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Hachisu I, Kato M, Nomoto K (2008a) Young and massive binary progenitors of Type Ia supernovae and their circumstellar matter. ApJ 679:1390–1404 Hachisu I, Kato M, Nomoto K (2008b) The delay-time distribution of Type Ia supernovae and the single-degenerate model. ApJ 683:L27 Hachisu I, Kato M, Nomoto K (2012a) Final fates of rotating white dwarfs and their companions in the single degenerate model of Type Ia supernovae. ApJL 756:L4 Hachisu I, Kato M, Saio H, Nomoto K (2012b) A single degenerate progenitor model for Type Ia supernovae highly exceeding the Chandrasekhar mass limit. ApJ 744:69 Hamuy M, Phillips MM, Suntzeff NB et al (2003) An asymptotic-giant-branch star in the progenitor system of a Type Ia supernova. Nature 424:651 Han Z, Podsiadlowski Ph (2004) The single-degenerate channel for the progenitors of Type Ia supernovae. MNRAS 350:1301 Hillebrandt W, Niemeyer JC (2000) Type Ia supernova explosion models. ARAA 38:191 Iben I Jr, Tutukov AV (1984) Supernovae of Type I as end products of the evolution of binaries with components of moderate initial mass (M not greater than about 9 solar masses). ApJS 54:335 Ilkov M, Soker N (2012) Type Ia supernovae from very long delayed explosion of core-white dwarf merger. MNRAS 419:1695 Iwamoto K, Brachwitz F, Nomoto K et al (1999) Nucleosynthesis in Chandrasekhar mass models for Type IA supernovae and constraints on progenitor systems and burning-front propagation. ApJS 125:439–463 Justham S (2011) Single-degenerate Type Ia supernovae without hydrogen contamination. ApJL 730:L34 Kamiya Y, Tanaka M, Nomoto K et al (2012) Super-Chandrasekhar-mass light curve models for the highly luminous Type Ia supernova 2009dc. ApJ 756:191 Kato M, Saio H, Hachisu I, Nomoto K (2014) Shortest recurrence periods of novae. ApJ 793:136 Khokhlov AM (1991) Delayed detonation model for Type IA supernovae. A & A 245: 114–128 Kitamura H (2000) Pycnonuclear reactions in dense matter near solidification. ApJ 539:888 Kitaura FS, Janka H-Th, Hillebrandt W (2006) Explosions of O-Ne-Mg cores, the Crab supernova, and subluminous type II-P supernovae. A & A 450:345 Krause O, Tanaka M, Usuda T, Hattori T, Goto M, Birkmann S, Nomoto K (1997) Tycho Brahe’s 1572 supernova as a standard Type Ia as revealed by its light-echo spetraum. Nature 456:617 Kromer M, Fink M, Stanishev V (2013) 3D deflagration simulations leaving bound remnants: a model for 2002cx-like Type Ia supernovae. MNRAS 429:2287–2297 Kromer M, Ohlmann ST, Pakmor R et al (2015) Deflagrations in hybrid CONe white dwarfs: a route to explain the faint Type Iax supernova 2008ha. MNRAS 450:3045–3053 Langer N, Deutschmann A, Wellstein S, Höflich P (2000) The evolution of main sequence star + white dwarf binary systems towards Type Ia supernovae. A & A 362:1046 Leung S-C, Nomoto K (2017a) Nucleosynthesis of iron-peak elements in Type-Ia supernovae. JPS Conf Proc 14:020506 Leung S-C, Nomoto K (2017b) Dependence of nucleosynthesis on model parameters of Type Ia supernovae. ApJ (submitted) Leung S-C, Chu M-C, Lin L-M (2015a) A new hydrodynamics code for Type Ia supernovae. MNRAS 454:1238 Leung S-C, Chu M-C, Lin L-M (2015b) Dark matter admixed Type Ia supernovae. MNRAS 812:110 Li X-D, van den Heuvel EPJ (1997) Evolution of white dwarf binaries: supersoft X-ray sources and progenitors of Type IA supernovae. A & A 322:L9 Li W, Bloom JS, Podsiadlowski P et al (2011) Exclusion of a luminous red giant as a companion star to the progenitor of supernova SN 2011fe. Nature 480:348 Livio M (2000) The progenitors of Type Ia supernovae. In: Niemeyer JC, Truran JW (eds) Type Ia supernovae, theory and cosmology. Cambridge University Press, Cambridge, p 33 Maeda K et al (2010) An asymmetric explosion as the origin of spectral evolution diversity in Type Ia supernovae. Nature 466:82

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Maoz D, Mannucci F, Nelemans G (2014) Observational clues to the progenitors of Type Ia supernovae. ARAA 52:107 Mori K et al (2016) Impact of new Gamow-Teller strengths on explosive Type Ia supernova nucleosynthesis. ApJ 833:179 Nomoto K (1982) Accreting white dwarf models for Type I supernovae. I – presupernova evolution and triggering mechanisms. ApJ 253:798 Nomoto K, Sugimoto D, Neo S (1976) Carbon deflagration supernova, an alternative to carbon detonation. Ap & SS 39:L37–L42 Nomoto K, Nariai K, Sugimoto D (1979) Rapid mass accretion onto white dwarfs and formation of an extended envelope. PASJ 31:287 Nomoto K, Thielemann F-K, Yokoi K (1984) Accreting white dwarf models of Type I supernovae. III – carbon deflagration supernovae. ApJ 286:644–658 Nomoto K, Yamaoka H, Shigeyama T, Kumagai S, Tsujimoto T (1994) Type I supernovae and evolution of interacting binaries. In: Bludmann S et al. (eds) Proceedings of session LIV held in Les Houche 1990. Supernovae, NATO ASI series C, vol 199. North-Holland Nomoto K, Iwamoto K, Kishimoto N (1997) Type Ia supernovae: their origin and possible applications in cosmology. Science 276:1378 Nomoto K, Umeda H, Kobayashi C et al (2000a) Type Ia supernova progenitors, environmental effects, and cosmic supernova rates. In: Niemeyer JC and Truran JW (eds) Type Ia Supernovae, Theory and Cosmology, Cambridge University Press, p.63 Nomoto K, Umeda H, Kobayashi C et al (2000b) Type Ia supernovae: progenitors and evolution with redshift. In: Cosmic Explosions: AIP Conf Proc 522:35 Nomoto K, Suzuki T, Deng J, Uenishi T, Hachisu I (2005) Progenitors of Type Ia Supernovae: circumstellar interaction, rotation, and steady hydrogen burning. In: Turatto et al (eds) 16042004: Supernovae as Cosmological Lighthouses, ASP conference series, 342:105 Nomoto K, Saio H, Kato M, Hachisu I (2007) Thermal stability of white dwarfs accreting hydrogen-rich matter and progenitors of Type Ia supernovae. ApJ 663:1269 Nomoto K, Kamiya Y, Nakasato N et al (2009) Progenitors of Type Ia supernovae: single degenerate and double degenerates. AIPC 1111:267 Nomoto K, Kamiya M, Nakasato N (2013) Type Ia supernova models and progenitor scenarios. In: Di. Stefano R et al (eds) IAU Symposium 281, Binary Paths to Type Ia Supernovae Explosions, Cambridge University Press, Cambridge, p. 253–260 Nugent P et al (2000) Synthetic spectra of hydrodynamical models of Type Ia supernovae. ApJ 485:812 Patat F, Chandra P, Chevalier R et al (2007) Detection of circumstellar material in a normal Type Ia supernova. Science 317:924 Plewa T (2007) Detonating failed deflagration model of thermonuclear supernovae. I. Explosion dynamics. ApJ 657:942–960 Pocheau A (1994) Scale invariance in turbulent front propagation. PRE 49:1109–1122 Potekhin AY, Chabrier G (2012) Thermonuclear fusion in dense stars. Electron screening, conductive cooling, and magnetic field effects. Astron Astropart 538:AA115 Schaefer BE, Pagnotta A (2012) An absence of ex-companion stars in the Type Ia supernova remnant SNR 0509-67.5. Nature 481:164 Schmidt W, Niemeyer JC, Hillebrandt W, Roepke FK (2006) A localised subgrid scale model for fluid dynamical simulations in astrophysics. II. Application to Type Ia supernovae. A & A 450:283–294 Schwab J, Quataert E, Bildsten L (2015) Thermal runaway during the evolution of ONeMg cores towards accretion-induced collapse. MNRAS 453:1910–1927 Seitenzahl IR, Kromer M, Ohlmann ST et al (2016) Three-dimensional simulations of gravitationally confined detonations compared to observations of SN 1991T. A & A 592:A57 Sharpe GJ (1999) The structure of steady detonation waves in Type Ia supernovae: pathological detonations in C+O cores. MNRAS 310:1039–1052 Shen K, Bildsten L (2007) Thermally stable nuclear burning on accreting white dwarfs. ApJ 660:1444

46 Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs

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Shigeyama T, Nomoto K, Yamoka H, Thielemann F-K (1992) Possible models for the Type IA supernova 1990N. ApJL 386:13 Sternberg A, Gal-Yam A, Simon JD et al (2011) Circumstellar material in Type Ia supernovae via sodium absorption features. Science 333:856 Webbink RF (1984) Double white dwarfs as progenitors of R Coronae Borealis stars and Type I supernovae. ApJ 277:355 Yamaguchi H et al (2015) A Chandrasekhar mass progenitor for the Type Ia supernova remnant 3C 397 from the enhanced abundances of Nickel and Manganese. ApJ 801:L31

Further Reading Barth TJ, Deconinck H (1999) High-order methods for computational physics. Lecture notes in computational science and engineering, vol 9. Springer, New York Calder AC, Townsley DM, Seitenzahl IR et al (2007) Capturing the fire: flame energetics and neutronization for Type Ia supernova simulations. ApJ 656:313–332 Clement MJ (1993) Hydrodynamical simulations of rotating stars. I – A model for subgrid-scale flow. ApJ 406:651–660 Feltzing S, Fohlman M, Bensby T (2007) Manganese trends in a sample of thin and thick disk stars. The origin of Mn. A & A 467:665 Förster F, Lesaffre P, Podsiadlowski P (2010) Simplified hydrostatic carbon burning in white dwarf interiors. ApJS 190:334 Garcia-Senz D, Woosley SE (1995) Type IA supernovae: the flame is born. ApJ 454:895–900 Golombek I, Niemeyer JC (2005) A model for multidimensional delayed detonations in SN Ia explosions. A & A 438:611–616 Graur O et al (2016) Late-time photometry of Type Ia supernova SN 2012cg reveals the radioactive decay of 57 Co. ApJ 819:31 Hachisu I (1986) A versatile method for obtaining structures of rapidly rotating stars. ApJS 61:479 Hicks EP (2015) Rayleigh-Taylor unstable flames – fast or faster? ApJ 803:72 Jackson AP, Townsley DM, Calder AC (2014) Power-law wrinkling turbulence-flame interaction model for astrophysical flames. ApJ 784:174 Kerzendorf WE, Schmidt BP, Asplund M et al (2009) Subaru high-resolution spectroscopy of star G in the Tycho supernova remnant. ApJ 701:1665 Kerzendorf WE, Schmidt BP, Laird JB et al (2012) Hunting for the progenitor of SN 1006: highresolution spectroscopic search with the FLAMES instrument. ApJ 759:7 Khokhlov AM, Oran E, Wheeler JC (1997) Deflagration-to-detonation transition in thermonuclear supernovae. ApJ 478:678–688 Kobayashi C, Nakasato N (2011) Chemodynamical simulations of the milky way galaxy. ApJ 729:16 Lesaffre P, Podsiadlowski P, Tout CA (2005) A two-stream formalism for the convective Urca process. MNRAS 356:131 Likewski AM, Hillebrandt W, Woosley SE et al (2000) Distributed burning in Type Ia supernovae: a statistical approach. ApJ 503:405–413 Livne E, Asida SM, Hoeflich P (2005) On the sensitivity of deflagrations in a Chandrasekhar mass white dwarf to initial conditions. ApJ 632:443–449 Maeda K et al (2010) Nebular spectra and explosion asymmetry of Type Ia supernovae. ApJ 708:1703 Maeder A (2009) Physics, formation and evolution of rotating stars. Springer, Berlin Mazzali PA, Sullivan M, Filippenko AV et al (2015) Nebular spectra and abundance tomography of the Type Ia supernova SN 2011fe: a normal SN Ia with a stable Fe core. MNRAS 450:2631 Niemeyer JC, Hillebrandt W (1995) Turbulent nuclear flames in Type IA supernovae. ApJ 452:769–778

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Nomoto K (1982) Accreting white dwarf models for Type 1 supernovae. II – off-center detonation supernovae. ApJ 257:780 Nomoto K, Kondo Y (1991) Conditions for accretion-induced collapse of white dwarfs. ApJL 367:19–22 Nomoto K, Suzuki T, Deng J, Uenishi T, Hachisu I, Mazzali P (2004) Circumstellar interaction of Type Ia supernova SN 2002ic. Front Astropart Phys Cosmol: RESCEU Int Symp Ser 6:323 Ostriker JP, Bodenheimer P (1968) Rapidly rotating stars. II. Massive white dwarfs. ApJ 151:1989 Pakmor R, Kromer M, Roepke FK et al (2010) Sub-luminous Type Ia supernovae from the mergers of equal-mass white dwarfs with mass 0.9 Msolar. Nature 463:61 Piersanti L, Gagliardi S, Iben I, Tornambe A (2003) Carbon-oxygen white dwarf accreting cO-rich matter. II. Self-regulating accretion process up to the explosive stage. ApJ 598:1229 Piro AL (2008) The internal shear of Type Ia supernova progenitors during accretion and simmering. ApJ 679:616 Poludenko AY, Gardiner TA, Oran ES (2011) Spontaneous transition of turbulent flames to detonations in unconfined media. PRL 107:054501 Reddy BE, Tomkin J, Lambert DL, Allende Prieto C (2003) The chemical compositions of galactic disc F and G dwarfs. MNRAS 340:304 Reinecke M, Hillebrandt W, Niemeyer JC et al (1999a) A new model for deflagration fronts in reactive fluids. A & A 347:724–733 Reinecke M, Hillebrandt W, Niemeyer JC (1999b) Thermonuclear explosions of Chandrasekharmass C+O white dwarfs. A & A 347:739–747 Reinecke M, Hillebrandt W, Niemeyer JC (2002) Three-dimensional simulations of Type Ia supernovae. A & A 391:1167–1172 Roepke FK (2007) Flame-driven deflagration-to-detonation transitions in Type Ia supernovae? ApJ 668:1103–1108 Rueda JA, Boshkayev K, Izzo L et al (2013) A white dwarf merger as progenitor of the anomalous X-ray pulsar 4U 0142+61?. ApJL 772:L24 Saio H, Nomoto K (2004) Off-center carbon ignition in rapidly rotating, accreting carbon-oxygen white dwarfs. ApJ 615:444 Seitenzahl IR et al (2013) Solar abundance of manganese: a case for near Chandrasekhar-mass Type Ia supernova progenitors. A & A 559:L5 Sethian JA (1996) Level set method. Cambridge University Press, Cambridge Shih T-H, Liou WW, Shabbir A et al (1994) A new k  " eddy viscosity model for high reynolds number turbulent flows. Comput Fluids 24:227–238 Shih T-H, Zhu J, Lumley JL (1995) A new Reynolds stress algebraic equation model. Comput Methods Appl Mech Eng 125:287–302 Sobeck JS, Ivans II, Simmerer JA et al (2006) Manganese abundances in cluster and field stars. AJ 131:2949 Timmes FX (2000) Physical properties of Laminar Helium deflagrations. ApJ 528:913–945 Timmes FX, Woosley SE (1992) The conductive propagation of nuclear flames. I – degenerate C + O and O + NE + MG white dwarfs. ApJ 396:649–667 Townsley DM, Calder AC, Asida SM et al (2007) Flame evolution during Type Ia supernovae and the deflagration phase in the gravitationally confined detonation scenario. ApJ 668:1118–1131 Uenishi T, Nomoto K, Hachisu I (2003) Evolution of rotating accreting white dwarfs and the diversity of Type Ia supernovae. ApJ 595:1094 Wang R, Spiteri RJ (2007) Linear instability of the fifth-order WENO method. SIAM J Numer Anal 45:1871 Wang B, Justham S, Liu Z-W et al (2014) On the evolution of rotating accreting white dwarfs and Type Ia supernovae. MNRAS 445:2340 Woosley SE, Weaver TA (1994) Sub-Chandrasekhar mass models for Type IA supernovae. ApJ 423:371 Wunsch W, Woosley SE (2004) Convection and off-center ignition in Type Ia supernovae. ApJ 616:1102–1108

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Yoon S-C, Langer N (2004) Presupernova evolution of accreting white dwarfs with rotation. A & A 419:623 Yoon S-C, Langer N (2005) On the evolution of rapidly rotating massive white dwarfs towards supernovae or collapses. A & A 435:967 Zhang Y (2009) A two-dimensional flame tracking algorithm with application to Type Ia supernova. Nonlinear Phys 22:1909–1925 Zingale M, Dursi LJ (2007) Propagation of the first flames in Type Ia supernovae. ApJ 656:333– 346 Zingale M, Nonaka A, Almgren AS et al (2011) The convective phase preceding Type Ia supernovae. ApJ 740:8–25

Part VII Stellar Remnants: Neutron Stars and Black Holes

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The Masses of Neutron Stars Jorge E. Horvath and Rodolfo Valentim

Abstract

We present in this article an overview of the problem of neutron star masses. After a brief appraisal of the methods employed to determine the masses of neutron stars in binary systems, the existing sample of measured masses is presented, with a highlight on some very well-determined cases. We discuss the analysis made to uncover the underlying distribution and a few robust results that stand out from them. The issues related to some particular groups of neutron stars originated from different channels of stellar evolution are shown. Our conclusions are that the last century’s paradigm that there a single, 1:4 Mˇ scale is too simple. A bimodal or even more complex distribution is actually present. It is confirmed that some neutron stars have masses of 2 Mˇ , and, while there is still no firm conclusion on the maximum and minimum values produced in nature, the field has entered a mature stage in which all these and related questions can soon be given an answer.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods and Tools for the Measurements of Neutron Star Masses . . . . . . . . . . . . . . . . 2.1 Kepler’s Third Law and the Mass Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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J.E. Horvath () Departmento de Astronomia, Universidade de São Paulo (USP), São Paulo, SP, Brazil Instituto de Astronomia, Geofísica e Ciências Atmosféricas USP, Cidade Universitária São Paulo, SP, Brazil e-mail: [email protected] R. Valentim Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo (UNIFESP), Diadema, SP, Brazil e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_67

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2.2 Photometry, Spectroscopy and Related Complementary Tools . . . . . . . . . . . . . . . 2.3 The Sample and the Analysis of the Neutron Star Mass Distribution . . . . . . . . . . 2.4 Analysis of the Neutron Star Mass Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Existence of a Group of Neutron Stars Around 1.25 Mˇ . . . . . . . . . . . . . . . . . . . 2.6 Heavy Neutron Stars in Close Binary Systems (“Spiders”) . . . . . . . . . . . . . . . . . . 2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Shortly after the discovery of pulsars (Hewish et al. 1968) and the identification of the pulsar in the Crab Nebula (Staelin 1968; see Sects. 1.1 and 2.4), a great deal of theoretical and observational effort was directed to assess the physical features of these objects and their relation to their birth events. Even though early studies considered a wide range of possible values for the masses (i.e., theoretical cooling (Tsuruta et al. 1972) and related works (Sects. 7.2 and 7.7)), the work on the presupernova evolution provided a clue about a possible “canonical” 1:4 Mˇ imprinted on neutron stars at birth. This value was justified by the state of an iron core in a massive star just prior to the beginning of its collapse (Sect. 2.3). The mass of this core is (almost) invariant, since it has to be supported by electron degeneracy pressure. This core turns into a neutron star (after radiating 10% of its energy) of a slightly lower mass. Later observational work was actually very successful in reducing the errors (see below), thus providing support to the idea of a single-mass scale. Moreover, for almost 30 years, the measurements of available neutron star systems (Thorsett 1999) proved to be consistent with the postulated unique value as suggested by that theoretical idea. The actual accretion history of those systems did not seem to make a large difference on the final neutron star mass, at least at a first glance, and the twenty-first century started with this as a firm paradigm. However, intensive work performed by independent groups, both in the field of theory and especially on the observational side, changed the situation and added considerable interest to the study of neutron star masses. We shall present below the basic arguments and evidence leading to believe that the old paradigm of a single-mass scale has to be abandoned. First, the main tools and methods for the measurements of neutron star masses will be presented. An evaluation of the distribution of masses and its theoretical context will follow. The chapter ends with the statement of the conclusions on this subject.

2

Methods and Tools for the Measurements of Neutron Star Masses

2.1

Kepler’s Third Law and the Mass Function

Presently, all the determinations of neutron star masses have been performed for objects in binary systems. The fundamental quantity to be measured as a first step is the mass function of the binary

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f D

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.m2 sin i /3 4 2 x 3 D .m1 C m2 /2 Tˇ Pb2

(1)

which can be determined directly from the observables of the right-hand side, the projected semiaxis of the orbit (x/ and the period of the binary (Pb / after the introduction of the constant Tˇ D GMˇ =c 3 D 4:925490947s. In addition to Pb and x, three Keplerian parameters can also be measured (Manchester and Taylor 1977), namely, the eccentricity e and the time and longitude of the periastron T0 and !0 . The complete determination of the system still requires the measurements of at least two post-Keplerian parameters which are (different) functions of the five Keplerian parameters. These post-Keplerian parameters are the advance of the periastron !, P the orbital decay of the period PPb (dominated by the emission of gravitational waves from the varying quadrupole moment along the orbit evolution), the  parameter combining the variations of the transverse Doppler shift and gravitational redshift, and the so-called “range” r and “shape” s. Since all them depend on the theory of gravitation, their measurement open the possibility of testing GR itself through pulsar timing. Even if only one post-Keplerian parameter is measured, some statements about the masses are possible. However, these measurements are possible with accuracy only for close binaries with eccentric orbits. Therefore, in the general case, additional information on the companion mass m2 and the inclination of the orbit respect to the line of sight sin i should be provided by independent techniques to determine the neutron star mass m1 (Kramer et al. 2006).

2.2

Photometry, Spectroscopy and Related Complementary Tools

The theory of stellar evolution and the tools developed by astronomers along the twentieth century are the key ingredients to obtain complementary information to determine the masses of neutron stars. The systems in which the companion is directly observed feature main sequence, post-main sequence, and white dwarf stars. Optical observations can be performed, but they are of little utility whenever m1  m2 , which is the case, for example, of the PSR J0045-7319 system (Nice 2004), in which large errors remain because of the limited usefulness of the mass function in Eq. (1). Low-mass companions and evolved objects for which m1  m2 are more amenable to optical observations, in the sense of the complementary information needed to determine the neutron star mass m1 . The case of white dwarfs is particularly relevant, since a few of the most interesting systems belong to this class. Even though the white dwarfs can be very faint (V 24 is not uncommon), their radii can be nevertheless estimated by measuring the optical flux FO , the effective temperature Teff and having a good idea of the distance d , through the simple relation !   FO 1=2 d RWD D (2) 2  Teff

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where  is the Stefan-Boltzmann constant. Once the radius is determined, a reasonable estimate of the white dwarf mass can be made using the theoretical relations for a given composition, with temperature corrections to the cold equation of state if necessary. An alternative approach is to fit a synthetic atmosphere to the observed spectral features, in order to obtain the surface gravity log g. The latter quantity combined with Teff , for example, gives a determination of the mass, which of course subject to some uncertainty coming from the effects of finite temperature and the chemical abundances. The masses of m2 may be overestimated, and this effect is translated to the pulsar mass m1 in the final calculations. Spectral information of the system, in particular variability along the orbit, can be of great importance especially in the cases of interacting systems. The latter generally display variability due to accretion/winds which should be understood properly before any statement about the mass of the neutron star can be made. Thus, additional models for the geometry of the system should be used, and in extreme cases, the heating of the companion by the winds are important and may dominate the uncertainties (see below). It is unfortunate that one particular feature, namely, the presence of redshifted lines from the neutron star itself, does not seem to be present in the X-ray spectra with sufficient significance. If measured, redshifted lines carrying information about the quotient M =R could be very useful. For example, the claim by Cottam et al. (2002) on the presence of absorption lines in the X-ray spectra bursts of the source EXO0748-676 could not be confirmed but constitute an excellent example of how to extract important information about a compact star which may be attempted in other cases. An important complementary method to determine pulsar masses is the Shapiro delay, i.e., the retardation of the pulses due to the gravitational field of the companion. The effect is particularly strong when nearly edge-on binaries are observed. The two parameters that control the behavior of the pulses are then m2 (generating the field) and sin i . The measurement of the arrival times may be combined with the Keplerian parameters to yield the masses and the inclination which reproduce the data best. Finally, a handful of alternative methods including polarization measurements (Thorsett 1990), scintillation (Cordes 1986), and even microlensing of background stars by isolated pulsars (Dai et al. 2015; Horvath et al. 1996) have been proposed but did not produce sensible results as yet. More work will be needed to convert these ideas into useful tools for pulsar mass determinations.

2.3

The Sample and the Analysis of the Neutron Star Mass Distribution

The largest sample of measured neutron star masses available for analysis is maintained by J. Lattimer. The compilation is publicly accessible online at http:// www.stellarcollapse.org/. It is periodically updated with new determinations to keep

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it useful for the community. The latest (Dec 2015) version was made available for this paper by its author. Systems are separated into four classes according to the nature of the companion and include neutron star-neutron star (double neutron star, in which at least one component is a pulsar), neutron star-white dwarf, neutron star-main sequence, and neutron star-X-ray/optical binaries. The references in Fig. 1 describe in detail each of the works reporting the techniques and models employed for the determinations. A few remarkable cases among these mass determinations merit a highlight. The first is the very high accuracy achieved after several decades of work in the double neutron star systems. In these cases, the determination of all post-Keplerian parameters has been possible, and therefore the masses are now known beyond four decimal places in at least one system. This is a remarkable achievement and puts double neutron stars among the most accurately measured star masses overall, including their “normal” main sequence relatives. In fact, the latest determination of a double neutron star system by Martínez et al. (2015) yielded a very asymmetric system, in contrast with the nearly equal-mass binaries of this type known up today. In addition, the mass of one of the stars is only m2 D 1:174 ˙ 0:004 Mˇ , which is the lowest mass measured with confidence. If it is indeed a neutron star, this determination contributes to the quest of the minimum mass that can be produced in nature, which is set by evolutionary considerations and not by the existence of any physical limit, at least in the measured range. Another benchmark determination was the work of Demorest (2010) measuring the Shapiro delay in the system of PSR J1614-2230. This effect stems from the effects of the gravitational well of the companion as is seen at different phases along the orbit. In general, and even after several years of timing, the Shapiro delay may remain “hidden” if it is too small. The case of the PSR J1614-2230 benefited from a combination of an almost edge-on system with a relatively high mass of the companion white dwarf (0:500 ˙ 0:006 Mˇ /. The determination with high accuracy needed a sophisticated statistical analysis to subtract a full GR timing (i.e., non-Shapiro delay contributions) and provided a firm number for the mass as m1 D 1:97 ˙ 0:04 Mˇ , now widely accepted by the community. This stands among the top masses ever measured with a value well beyond the “old” 1:4 Mˇ paradigm. A similar number for the mass of the system PSR J0348C0432 has been obtained by Antoniadis (2013) using the methods described above. The companion is a low-mass helium white dwarf which was characterized by a combination of phaseresolved spectra, fitting of synthetic spectra, and a theoretical finite-temperature mass-radius relation. The fitting procedures yielded very accurate results (Fig. 2), and therefore the masses of the components were determined. The high value m1 D 2:01 ˙ 0:04 Mˇ reinforces the presence of a mass scale substantially higher than the 1:4 Mˇ formerly supported. Both 2 Mˇ objects are therefore examples that the accretion history can substantially affect the mass of a compact object although the exact amount of matter onto it depends on several factors that vary in each case. With these considerations in mind, we shall now discuss the main features of the analysis performed and the meaning of the results.

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Fig. 1 The sample of neutron star masses maintained at stellarcollapse.org as displayed, Oct. 28, 2015. The four groups are explicitly indicated, and the letters correspond to the references to the original works. The best determined values are accurate to the point in which the error bars fall inside the symbols. Systematic errors can shift the centroid in some cases and constitute a major warning against a literal interpretation of the given numbers. References are indicated with a letter on each point: [a] Clark et al. (2002); [b] Rawls (2011); [c] Mason (2011); [d] Casares et al. (2010); [e] Thorsett (1999); [f] Mason (2010); [g] Nice (2005); [h] Nice (2001); [j] Bhat et al. (2008); [k] Guillemot (2012); [l] Gelino et al. (2003); [m] Lange et al. (2001); [n] Muñoz (2005); [o] Kiziltan (2013); [p] Verbiest et al. (2008); [q] Weisberg et al. (2010); [r] Splaver (2005); [s] Lynch (2012); [t] González et al. (2011); [u] Hotan (2006); [v] Antoniadis (2012); [w] Mason (2012); [x] Jacoby (2006); [y] Nice (2008); [z] Champion et al. (2005); [A] Corongiu et al. (2007); [B] Kasian (2008); [C] Janssen (2008); [D] Stairs (2002); [E] Antoniadis (2013); [F] Steeghs (2007); [H] Freire (2008b); [I] Freire (2008a); [J] Ferdman et al. (2010); [K] Deller (2012); [L] Bhalerao et al. (2012); [M] Nice (2001); [N] Freire (2011); [O] Bassa et al. (Bassa et al.); [P] Demorest (2010); [Q] vanKerkwijk et al. (2011); [R] Romani (2012); [S] Ransom et al. (2014); [T] Coe et al. (2013)

47 The Masses of Neutron Stars

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400 12

Radial Velocity (km s−1)

300

11 10 9 8

200 100

e d

0

g −100 b

−200 −300 −1.0

−0.5

0.0 Orbital Phase

0.5

1.0

−40

−20

0

20

40

Δλ (Å)

Fig. 2 The fittings to the radial velocity (left) and Balmer lines (right) obtained by Antoniadis et al. (2013) to the system harboring PSR J0348C0432 and its white dwarf companion. Solid lines are the best fit to the orbit (left) and three atmospheric models, showing that slight changes in Teff and/or log g worsen the accurate result obtained for the values (10120 ˙ 47st at ˙ 90sys ; 6:035 ˙ 0:032st at ˙ 0:06sys ). These measurements, when combined with the Keplerian parameters, determine the value of the pulsar with high accuracy

2.4

Analysis of the Neutron Star Mass Distribution

At least four different groups (Kiziltan et al. 2013; Özel et al. 2012; Valentim et al. 2011; Zhang et al. 2011) have presented independent analysis of the mass distribution (Fig. 3). All but Zhang et al. (2011) employed Bayesian analysis techniques. While they differ somewhat in the criteria to select the size of the sample (e.g., trying to avoid a contamination with biased/uncertain determinations), all the reported results are indicative of the presence of at least two mass scales. The group of Özel (2012) found a mean mass of 1:28 Mˇ for nonrecycled highmass binaries and slow pulsars, 1:33 Mˇ for double neutron stars, and 1:48 Mˇ for recycled neutron stars, all them showing different dispersions. Zhang et al. (2011) reported a bimodality at 1:37 and 1:57 Mˇ when the sample is divided by a 20-ms period possibly separating the nonrecycled to the recycled population, although their true focus was somewhat different than the other works, being more related to the spin evolution of the systems itself. Kiziltan (2013), on the other hand, presented an analysis in which just double neutron stars and neutron stars with white dwarf companions were selected. Their results yielded peaks at 1:33 and 1:55 Mˇ and allowed skewed distributions. The work of Valentim et al. (2011) included all the objects available in the stellarcollapse.org database at the time and found (within a Gaussian parameterization as in Özel 2012) the values 1:37 and 1:73 Mˇ , also with quite different widths (narrow and wide, respectively) for the assumed Gaussian profiles. These differences may be entirely due to the selection of the sample itself.

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Fig. 3 The histogram of the masses of neutron stars in binary systems presented by Valentim et al. (2011). Note that new objects have been added to the database in Fig. 1, and therefore the exact numbers of the mass scales may differ when the updated database is used

With the availability of more measured masses, these analyses can be refined and further compared. For example, the issue of the masses “at birth” complicates a clear separation between nonrecycled and recycled systems from the point of view of the total accreted mass. This is because of the well-known jump in the iron core for progenitor masses >19 Mˇ in the main sequence. The generated iron cores may indeed grow to 1:8 Mˇ at the moment of collapse because of convection in the carbon burning stage (Timmes et al. 1996). Therefore, and after allowing for the binding energy of the neutron star respect to the previous state, there may be a 0:3 Mˇ difference at birth between these heavy objects and the more common 1:4 Mˇ cousins coming from lighter progenitors. The degeneracy between the initial mass and accreted mass could be important in many cases and is not easy to break. In other words, even if the accretion has been substantial, the initial mass of the neutron star cannot be determined with precision, and the assumption of a 1:4 Mˇ often made could be quite misleading.

2.5

Existence of a Group of Neutron Stars Around 1.25 Mˇ

Stellar evolution calculations agree on the formation of very degenerate O-MgNe cores for the lowest end of stars 8  11 Mˇ (the latter figure depending on the detailed physics of the evolution, which could change somewhat the actual number). These cores are expected to eventually collapse because of electron

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capture. Some actual systems have been discussed in Poelarends (2008) among other works. Podsiadlowski (2005) proposed that this “characteristic mass” of the neutron stars formed from this mass range, with a typical amount of ejected mass, would finally produce low-mass neutron stars of 1:25 Mˇ . The formation of this “canonical” mass and its identification as a separate peak in the mass distribution suggests one robust evolutionary path toward collapse/formation and should occur, preferentially, in binaries with low eccentricity and aligned orbits (Schwab et al. 2008) to form the systems in which the masses are presently observed. In those binary systems, low masses are formed when a white dwarf has O-Ne-Mg core accretes mass from the companion. The core density reaches a well-defined critical value (4:5  109 g cm3 / triggering electron captures onto Mg and subsequently Ne and causing a loss of hydrostatic support in the core and the onset of the collapse. These are the key aspects of these e-capture supernova, and since the 8  11 Mˇ (and possibly even up to 12 Mˇ ) progenitor stars are the most abundant among massive stars, their neutron star descendants should be well represented in the sample. An inspection of Fig. 1 reveals a handful of objects with masses consistent with this value. In fact, even if former analysis (Valentim et al. 2011) casted some doubts on the significance of the peak, newer evidence has reinforced the idea that e-capture supernova neutron stars are indeed present in the sample, as argued by (Schwab et al. 2008). It is interesting to point out that the “old” picture of a single-mass scale had not identified any problem between the theoretical prediction (Timmes et al. 1996) and the actual measured values, which in spite of being close should have stood as a separate channel.

2.6

Heavy Neutron Stars in Close Binary Systems (“Spiders”)

There is one class of interacting millisecond pulsars in close binaries which is particularly interesting to assess the effects of the accretion history and maximum achievable mass. The first object of this type was discovered by Fruchter (1988) and showed signals that an outflow was evaporating the companion, now reduced to a Jupiter-scale object. Because of a previous accretion phase in which the pulsar become accelerated to millisecond periods, while its wind was destroying the donor star at present, this system was dubbed a black widow in parallel to the behavior of that class of spiders. Later, a similar group was identified in a different region of the orbital period-donor mass and received the name of redbacks which are Australian spiders related to black widows (Roberts 2013). The connection between the two groups was explored by means of evolutionary calculations (Benvenuto et al. 2012), and it was shown that a long accretion stage ( 2  3 Gyr/ shaped by X-ray back illumination led to systems (within a very restricted region of parameter space) which transit toward the redback region and later, when the donor became degenerate, widen their orbits while the evaporation of the donor proceeded. The importance of these systems for the problem of neutron star masses stems from the very long evolution times, and in spite that the exact amount of mass ending

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on the neutron star itself could not be calculated, several tenths of Mˇ are expected as a general feature (see Tauris (2015) for an alternative view and connections with other neutron star systems). This is why the determinations of vanKerkwijk et al. (2011) for the “original” black widow PSR 1957C20 (2:4 ˙ 0:12 Mˇ / and Romani (2012) in the case of PSR J13113430 (concluding that m1 > 2:1 Mˇ / came to support these theoretical trajectories. However, the issue of the masses is far from being settled. For example, Romani (2015) found that a simple direct heating model formerly employed for the atmosphere of PSR J1311–3430 is inadequate, and therefore a systematic deviation of the mass from its true value leads to an unreliable estimation. The mass of the pulsar in the black widow system PSR J1311–3430 may be as low as 1:8 Mˇ . A confirmation of the mass of PSR 1957 C 20 with confidence on the absence of possible systematic effects would be very important as well. In any case, the black widow and redback pulsars are expected to contain the most massive neutron stars in nature, and this is why their study is so important for this field. The measurements of magnetic fields in the ball park of 108 G for systems with ages 10 Gyr is also revealing features of magnetic field evolution which are still under work when this article goes to the press.

2.7

Conclusions

We have presented the general outline of neutron star mass determinations and discussed the picture emerging from the analysis of the available sample, comprising more than 70 objects at present. For most of the determinations, the systematic errors still affect the determinations, and the observations carry error bars that are significant in most cases. Exceptions to this picture include the binary neutron stars and a few other objects. The most important conclusion of the large amount of work performed in the field is that the “old” view of a single 1:4 Mˇ mass scale is untenable, since evidence for substantially heavier neutron stars is now available. It is still unclear exactly what kind of distribution is present in the data, and while bimodality is rooted in the theoretical framework, the role of the accretion history of the systems has to be clarified to address this point (see (Özel and Freire 2016) for a comprehensive discussion of the masses and related issues). It is also fair to state that the peak at 1:25 Mˇ expected to form from the lightest progenitor collapses in the range 8  11 Mˇ is actually present in the sample with increasing levels of significance. Finally, we should point out that there is no hint as yet about the actual maximum mass of neutron stars, but only a consensus on the 2 Mˇ determinations which seem robust. The upper limit may be set by evolution (Kiziltan et al. 2013) or fundamental physical factors, and it is of course extremely important to address the nature of the equation of state above nuclear saturation density and the nature of matter under extreme conditions (Lattimer 2012). Acknowledgements The authors wish to acknowledge the financial support of the Fapesp Agency (São Paulo) through the grant 2013/26258-4. J.E.H. has been partially supported by the CNPq Agency (Brazil) by means of a research

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References Antoniadis J, van Kerkwijk MH, Koester D, Freire PCC, Wex N, Tauris TM, Kramer M, Bassa CG (2012) The relativistic pulsar-white dwarf binary PSR J1738+0333 – I. Mass determination and evolutionary history. MNRAS 423:3316–3327 Antoniadis J, Freire PCC, Wex N, Tauris TM, Lynch RS, van Kerkwijk MH, Kramer M, Bassa C, Dhillon VS, Driebe T, Hessels JWT, Kaspi VM, Kondratiev VI, Langer N, Marsh TR, McLaughlin MA, Pennucci TT, Ransom SM, Stairs IH, van Leeuwen J, Verbiest JPW, Whelan DG (2013) A massive pulsar in a compact relativistic binary. Science 340:448-450 Bassa CG, Jonker PG, in‘t Zand JJM, Verbunt F (2006) Two new candidate ultra-compact X-ray binaries. A&A 446:L17–L20 Benvenuto OG, De Vito MA, Horvath JE (2012) Evolutionary Trajectories of Ultracompact "Black Widow" Pulsars with Very Low Mass Companions, ApJ 753: L33–L36 Bhalerao VM, van Kerkwijk MH, Harrison FA (2012) Constraints on the compact object mass in the eclipsing high-mass x-ray binary XMMU J013236.7+303228 in M 33. ApJ 757:10 Bhat NDR, Bailes M, Verbiest JPW (2008) Gravitational-radiation losses from the pulsar whitedwarf binary PSR J1141 6545. Phys Rev D 77:124017 Casares J, Gonzalez Hernandez JI, Israelian G, Rebolo R (2010) On the mass of the neutron star in Cyg X-2. MNRAS 401:2517–2520 Champion DJ, Lorimer DR, McLaughlin MA, Xilouris KM, Arzoumanian Z, Freire PCC, Lommen AN, Cordes JM, Camilo F (2005) Arecibo timing and single-pulse observations of 17 pulsars. MNRAS 363:929–936 Clark J, Goodwin SP, Crowther PA, Kaper L, Fairbairn M, Langer N, Brocksopp C (2002) Physical parameters of the high-mass X-ray binary 4U1700-37. A&A 392:909–920 Coe MJ, Angus R, Orosz JA, Udalski, A (2013) A detailed study of the modulation of the optical light from Sk160/SMC X-1. MNRAS 433:746–750 Cordes J (1986) Space velocities of radio pulsars from interstellar scintillations. ApJ 311:183–196 Corongiu A, Kramer M, Stampers BW, Lyne AG, Jessner A, Possenti A, D’Amico N, Löhmer O (2007) The binary pulsar PSR J1811-1736: evidence of a low amplitude supernova kick. A&A 462:703–709 Cottam J, Paerels F, Méndez M (2002) Gravitationally redshifted absorption lines in the X-ray burst spectra of a neutron star. Nature 420:51–54 Dai S, Smith MC, Lin MX, Yue YL, Hobbs G, Xu RX (2015) Gravitational microlensing by neutron stars and radio pulsars: event rates, timescale distributions, and mass measurements. ApJ 802:A120 Deller AT, Archibald AM, Brisken WF, Chatterjee S, Janssen GH, Kaspi VM, Lorimer D, Lyne AG, McLaughlin MA, Ransom S, Stairs IH, Stappers B (2012) A parallax distance and mass estimate for the transitional millisecond pulsar system J1023+0038. ApJL 756:L25–L30 Demorest PB, Pennucci T, Ransom SM, Roberts MSE, Hessels JWT (2010) A two-solar-mass neutron star measured using Shapiro delay. Nature 467:1081–1083 Ferdman RD (2008) Ph.D. thesis, University of British Columbia Ferdman RD, Stairs IH, Kramer M, McLaughlin MA, Lorimer DR, Nice DJ, Manchester RN, Hobbs G, Lyne AG, Camilo F, Possenti A, Demorest PB, Cognard I, Desvignes G, Theureau G, Faulkner A, Backer DC (2010) A precise mass measurement of the intermediate-mass binary pulsar PSR J1802–2124. ApJ 711:764–771 Freire PCC, Wolszcan A, van den Berg M, Hessels JWT (2008a) A massive neutron star in the globular cluster M5. ApJ 679:1433–1442 Freire PCC, Ransom SM, Bégin S, Stairs IH, Hessels JWT, Frey LH, Camilo F (2008b) Eight new millisecond pulsars in NGC 6440 and NGC 6441. ApJ 675:670–682 Freire PCC, Bassa CG, Wex N, Stairs IH, Champion DJ, Ransom SM, Lazarus P, Kaspi VM, Hessels JWT, Kramer M, Cordes JM, Verbiest JPW, Podsiadlowski P, Nice DJ, Deneva JS, Lorimer DR, Stappers BW, McLaughlin MA, Camilo F (2011) On the nature and evolution of the unique binary pulsar J1903+0327. MNRAS 412:2763–2780

1328

J.E. Horvath and R. Valentim

Fruchter AS, Stinebring DR, Taylor, J. H. (1988) A millisecond pulsar in an eclipsing binary, Nature. 333 (6170): 237–239 Gelino DM, Tomsick JA, Heindl WA (2003) Measuring the orbital inclination angle for the lowmass x-ray binary XTE J2123-058. Bull Am Astron Soc 34:1199 González ME, Stairs IH, Ferdman RD, Freire PCC, Nice DJ, Demorest PB, Ransom SM, Camilo F, Hobbs G, Manchester RN, Lyne AG (2011) High-precision timing of five millisecond pulsars: space velocities, binary evolution, and equivalence principles. ApJ 743:A102. http://adsabs.harvard.edu/cgi-bin/author_form?author=Kramer,+M& fullauthor=Kramer,%20M.&charset=UTF-8&db_key=AST[t] Guillemot L, Freire PCC, Cognard I, Johnson,TJ, Takahashi Y, Kataoka J, Desvignes G, Camilo F, Ferrara EC, Harding AK, Janssen GH, Keith M, Kerr M, Kramer M, Parent D, Ransom SM, Ray PS, Saz Parkinson PM, Smith DA, Stappers BW, Theureau G (2012) Discovery of the millisecond pulsar PSR J2043+1711 in a Fermi source with the Nançay Radio Telescope. MNRAS 422:1294–1305 Hewish A, Bell SJ, Pilkington JDH, Scott PF, Collins RA (1968) Observation of a rapidly pulsating radio source. Nature 217:709–713 Horvath JE (1996) Possible determination of isolated pulsar masses with gravitational microlensing. MNRAS 278:L46–L48 Hotan AW, Bailes M, Ord SM (2006) High-precision baseband timing of 15 millisecond pulsars. MNRAS 369:1502–1520 Jacoby BA, Cameron PB, Jenet FA, Anderson SB, Murty RN, Kulkarni SR (2006) Measurement of orbital decay in the double neutron star binary PSR B2127+11C. ApJL 644:L113–L116 Janssen GH, Stappers BW, Kramer M, Nice DJ, Jessner A, Cognard I, Purver MB (2008) Multitelescope timing of PSR J1518+4904. A&A 490:753–763 Kasian L (2008) Timing and precession of the young, relativistic binary pulsar PSR J1906+0746. In: Bassa C, Wang Z, Cumming A, Kaspi VM (eds) AIP conference series 983, 40 years of pulsars: millisecond pulsars, magnetars and more. AIP, New York, pp 485–487 Kiziltan B, Kottas A, De Yoreo M, Thorsett SE (2013) The neutron star mass distribution. ApJ 778:A66 Kramer M, Stairs IH, Manchester RN, McLaughlin MA, Lyne AG, Ferdman RD, Burgay M, Lorimer DR, Possenti A, D’Amico N, Sarkisian JM, Hobbs GB, Reynolds JE, Freire PCC, Camilo F (2006) Tests of general relativity from timing the double pulsar. Science 314: 97–102 Lange Ch, Camilo F, Wex N, Kramer M, Backer DC, Lyne AG, Doroshenko O (2001) Precision timing measurements of PSR J1012+5307. MNRAS 326:274–282 Lattimer J (2012) The nuclear equation of state and neutron star masses. Annu Rev Nuc Part Phys 62:485–515 Lynch RS, Freire PCC, Ransom SM, Jacoby BA (2012) The timing of nine globular cluster pulsars. ApJ 745:A109 Manchester RN, Taylor JH (1977) Pulsars. Freeman, San Francisco Martínez JG, Stovall K, Freire PCC, Deneva JS, Jenet FA, McLaughlin MA, Bagchi M, Bates SD, Ridolfi A (2015) Pulsar J0453+1559: a double neutron star system with a large mass asymmetry. ApJ 812:A143 Mason AB, Norton AJ, Clark, JS, Negueruela I, Roche P (2010) Preliminary determinations of the masses of the neutron star and mass donor in the high mass X-ray binary system EXO 1722–363. A&A 509:A79 Mason AB, Norton AJ, Clark JS, Negueruela I, Roche P (2011) The masses of the neutron and donor star in the high-mass X-ray binary IGR J18027-2016. A&A 532:A124 Mason AB, Clark JS, Norton AJ, Crowther PA, Tauris TM, Langer N, Negueruela I, Roche P (2012) The evolution and masses of the neutron star and donor star in the high mass X-ray binary OAO 1657–415. MNRAS 422:199-206 Muñoz-Darias T, Casares J, Martínez-Pais IG (2005) The “K-Correction” for irradiated emission lines in LMXBs: evidence for a massive neutron star in X1822-371 (V691 CrA). ApJ 635: 502–507

47 The Masses of Neutron Stars

1329

Nice DJ, Splaver EM, Stairs IH (2001) On the mass and inclination of the PSR J2019+2425 binary system. ApJ 549:516–521 Nice DJ, Splaver EM, Stairs IH (2004) Heavy neutron stars? A status report on Arecibo timing of four pulsar – white dwarf systems. In: Camilo F, Gaensler BM (eds) Young neutron stars and their environments, IAU symposium, vol 218. Astronomical Society of the Pacific, San Francisco, pp 282 Nice DJ, Splaver EM, Stairs IH (2005) Masses, parallax, and relativistic timing of the PSR J1713+0747 binary system. In: Rasio F, Stairs IH (eds) Binary radio pulsars, vol 328. Astronomical Society of the Pacific, San Francisco, pp 371 Nice DJ, Stairs IH, Kasian LE (2008) Masses of neutron stars in binary pulsar systems. In: Bassa C, Wang Z, Cumming A, Kaspi VM (eds) AIP conference series, vol 983. 40 years of pulsars: millisecond pulsars, magnetars and more. AIP, New York, pp 453–458 Özel F, Psaltis D, Narayan R, Santos Villareal A (2012) On the mass distribution and birth masses of neutron stars. ApJ 757:A55 Özel F, Freire P (2016) Masses, Radii, and the Equation of State of Neutron Stars. Annual Review of Astronomy and Astrophysics 54: 401–440 Podsiadlowski Ph, Dewi JDM, Lesaffre P, Miller JC, Newton WG, Stone JR (2005) The double pulsar J0737-3039: testing the neutron star equation of state. MNRAS 361:1243–1249 Poelarends AJT, Herwig F, Langer N, Heger A (2008) The supernova channel of super-AGB stars. ApJ 675:614–625 Ransom S, Stairs IH, Archibald AM, Hessels JWT, Kaplan DL, van Kerkwijk MH, Boyles J, Deller AT, Chatterjee S, Schechtman-Rook A, Berndsen A, Lynch RS, Lorimer DR, KarakoArgaman C, Kaspi VM, Kondratiev VI, McLaughlin MA, van Leeuwen J, Rosen R, Roberts MSE, Stovall K (2014) A millisecond pulsar in a stellar triple system. Nature 505: 520–524 Rawls ML, Orosz JA, McClintock JE, Torres MAP, Bailyn CD, Buxton MM (2011) Refined neutron star mass determinations for six eclipsing x-ray pulsar binaries. ApJ 730:25–36 Roberts MSE (2013) Surrounded by spiders! New black widows and redbacks in the Galactic field. In: van Leewen J (ed) Neutron stars and pulsars: challenges and opportunities after 80 years. Proceeding of the IAU, vol 291. Cambridge University Press, Cambridge, pp 127–132 Romani RW, Filippenko AV, Silverman JM, Cenko S, Greiner J, Rau A, Elliott J, Pletsch HJ (2012) PSR J1311-3430: a heavyweight neutron star with a flyweight helium companion. ApJL 760:L36–L41 Romani RW, Filippenko AV, Cenko SB (2015) A spectroscopic study of the extreme black widow PSR J1311–3430. ApJ 804:A115 Schwab J, Podsiadwolski Ph, Rappaport S (2008) Further evidence for the bimodal distribution of neutron-star masses. ApJ 719:722–727 Splaver EM, Nice DJ, Stairs IH, Lommen AN, Backer DC (2005) Masses, parallax, and relativistic timing of the PSR J1713+0747 binary system. ApJ 620:405–415 Staelin DH, Reifenstein EC III (1968) Pulsating radio sources near the Crab Nebula. Science 162:1481–1483 Stairs IH, Thorsett SE, Taylor JH, Wolszczan A (2002) Studies of the relativistic binary pulsar PSR B1534+12. I. Timing analysis. ApJ 581:501–508 Steeghs D, Jonker PG (2007) On the mass of the neutron star in V395 Carinae/2S 0921-630. ApJL 669:L85–L88 Tauris T (2015) Habilitation thesis, arXiv:1501.03882 Thorsett SE, Chakrabarty D (1999) Neutron star mass measurements. I. Radio pulsars. ApJ 512:288–299 Thorsett SE, Stinebring DR (1990) Polarimetry of millisecond pulsars. ApJ 361:644–649 Timmes, F. X.; Woosley, S. E.; Weaver, Thomas A (1996) The Neutron Star and Black Hole Initial Mass Function, ApJ 457: 834-845 Tsuruta S, Canuto V, Lodenquai J, Ruderman M (1972) Cooling of pulsars. ApJ 176:739–750 Valentim R, Rangel E, Horvath JE (2011) On the mass distribution of neutron stars. MNRAS 414:1427–1431

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van Kerkwijk MH, Breton R, Kulkarni SR (2011) Evidence for a massive neutron star from a radial-velocity study of the companion to the black-widow pulsar PSR B1957+20. ApJ 728:A95 Verbiest JPW, Bailes M, van Straten W, Hobbs GB, Edwards RT, Manchester RN, Bhat NDR, Sarkissian JM, Jacoby BA, Kulkarni SR (2008) Precision timing of PSR J0437-4715 (2008) An accurate pulsar distance, a high pulsar mass, and a limit on the variation of Newton’s gravitational constant. ApJ 679:675–680 Weisberg JM, Nice DJ, Taylor JH (2010) Timing measurements of the relativistic binary pulsar PSR B1913+16. ApJ 722:1030–1034 Zhang CM, Wang J, Zhao YH, Yin HX, Song LM, Menezes DP, Wickramasinghe DT, Ferrario L, Chardonnet P (2011) Study of measured pulsar masses and their possible conclusions. A&A 527:A83

Nuclear Matter in Neutron Stars

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Pawel Haensel and Julian L. Zdunik

Abstract

Neutron stars are the densest stars in the universe. Their central density is expected to be many times higher than the density of atomic nuclei. Neutron star interior is expected to contain nuclear matter in different states, that change with increasing depth below the star surface. We review the structures made of nuclear matter inside a neutron star, from the ocean lying on the outer crust, through the inner crust and mantle, to the liquid core which constitutes some 97–99 % of the mass of observed neutron stars (higher the star mass, lower the mass fraction in the crust), and to the center. We stress the dominant role of nuclear forces in making possible existence of neutron stars with mass 2:0 Mˇ , detected recently. We describe basic features of the equation of state of neutron stars and relate them to the theoretical models of superdense nuclear matter. We review uncertainties in neutron star masses and radii, and the composition of the inner core, resulting from the lack of knowledge of nuclear forces in superdense nuclear and hyperonic matter in neutron star cores and from the deficiencies and approximations of the many-body theories.

Contents 1 2 3

4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nuclear Matter: Theory and Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nuclear Matter in the Crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Outer Crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Inner Crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Bottom Layer of the Crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Equation of State for the Crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nuclear Matter in the Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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P. Haensel () • J.L. Zdunik N. Copernicus Astronomical Center, Polish Academy of Sciences, Warszawa, Poland e-mail: [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_68

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5 6

Hyperon Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EOS of Neutron Star Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Microscopic Many-Body Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Effective Energy-Density Functional Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 EOS of NS Core and Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Neutron Star Models vs. Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Neutron stars (NS) observed, e.g., as radio pulsars, X-ray bursters, X-ray pulsars, and magnetars, are the densest stars in the universe. Recent discovery of two radio pulsars with mass close to 2:0 Mˇ gave a new impulse to NS studies. The expected radius of these most massive pulsars is R  10 km. This gives a rough estimate of their mean density M =. 4

R3 /  1015 g cm3 . Density in NS interior 3 has to grow with depth, and central density is a few times larger than the mean one. Generally, central density is expected to range from 5  1014 g cm3 to 2  1015 g cm3 , for the lightest (1:2 Mˇ ) and heaviest (2:0 Mˇ ) observed NS, respectively. It is therefore convenient to express the NS density in terms of nuclear density, 0 D 2:7  1014 g cm3 . This corresponds to the unit of the number density of nucleons 1:6  1038 cm3 , or using more suitable (nuclear) length unit 1 fm D 1013 cm, n0 D 0:16 fm3 . NS are relativistic objects, and therefore we have to use precise definitions of mass and density. In particular,  is mass-energy density,  D E=c 2 , where E is the total energy density including rest energy of the matter constituents. M denotes the gravitational mass of NS, which is the total energy of the star divided by c 2 . We consider also a baryon mass Mb , which is the number of baryons in NS times the baryon mass unit, Mb D ANS m0 . Typically, ANS  1057 . We will use m0 D mn . Very often NS are called “huge atomic nuclei consisting of 1057 nucleons”. Roughly, some 510 % are protons, their charge being neutralized by the electrons and muons. However, in contrast to the atomic nuclei, NS are bound by longrange gravitational force, and not by nuclear (strong) force. It is the gravity that compresses nuclear matter at the NS center, to 100 for the most massive ones. Actually, nuclear forces tend to expand NS core, counterbalancing gravitational attraction. The binding energy Mb  M is 0:2 M for a M D 1:4 Mˇ NS. This is about 190 MeV/nucleon, to be compared with maximum binding energy per nucleon in atomic nuclei 8 MeV. Internal structure of a NS, a picture resulting from decades of theoretical studies, is visualized in Fig. 1. The liquid core contains some 99 % of NS mass. The crust and the outer core ( < 20 ) are composed of nucleons and electrons, like the terrestrial matter. For  & 0 the outer core contains a very small admixture of muons. A “minimal model” of the inner core (20 <  < 100 ) assumes that the matter there is still composed predominantly of neutrons, with an admixture of

48 Nuclear Matter in Neutron Stars

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Fig. 1 Left: General picture of internal structure of a NS. Right: cross sections of NS models of different masses, calculated using the equation of state from Douchin and Haensel (2001). Numerical values of density, radial depth from the surface, and composition of the NS matter shells are given in Table 1

protons and leptons, and possibly some hyperons. In view of lack of observational evidence for the presence of “exotic phases” of dense matter in NS core, the minimal model is a reasonable working assumption. It is the model considered in the present chapter. The negatively charged electrons and muons neutralize the net positive charge of the baryon component of the matter and are also required to put the system in equilibrium with respect to weak interactions. It is fair to say that NS are predominantly composed of neutrons and more precisely of nuclear matter with a very large neutron excess, compressed by long-range gravitational force to 30 (for M  1:2 Mˇ ) or even 70  100 for M  2 Mˇ . The notion of nuclear matter appears as a (theoretical) extrapolation from terrestrial nuclear physics. Atomic nucleus can be approximated by a liquid drop made of N neutrons and Z protons, bound by strong interaction between A D N C Z nucleons. In such a liquid-drop model of nuclei, the limit of nuclear matter is obtained by switching off Coulomb repulsion and then making a transition A D N C Z ! 1. As in this limit the system is infinite and uniform, and we assume that it is spin unpolarized; the energy per nucleon, E (it does not include rest energies of nucleons), depends only on the neutron and proton number densities, nn and np , respectively. It is convenient to replace nn and np by another pair of variables, nucleon (more generally: baryon) number density nb D nn C np and neutron-excess parameter ı D .nn  np /=nb , so that nn D 12 nb .1 C ı/, np D 12 nb .1  ı/. Let us neglect mass difference between neutrons and protons. Then, charge symmetry of strong interaction implies that E does not change if protons are replaced by neutrons or vice versa, E.nb ; ı/ D E.nb ; ı/. At a fixed nb , E is therefore an even function of ı. For ı D 0 we are dealing with symmetric nuclear matter (SNM), while for ı D 1 we have the case of pure neutron matter (PNM).

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Stable heavy atomic nuclei (A > 100) have an excess of neutrons in order to counterbalance, by the short-range (strong) attraction, the destabilizing long-range Coulomb repulsion of protons which grows rapidly with Z. The heaviest stable terrestrial nuclei have A  210 and .N Z/=A  0:20. The upper bounds on A and Z result from Coulomb repulsion between protons. While Z electrons in an atom screen nuclear charge at the distance of the order of the atomic size .& 108 cm/, they are irrelevant within heavy nuclei size .1012 cm/. Superheavy nuclei with A  248 and .N  Z/=A  0:22 have a lifetime >104 yr. Nuclear matter in heavy and superheavy terrestrial nuclei has therefore a rather low neutron excess. Nuclear matter permeated by electrons and muons constitutes the bulk of the liquid NS core. Electrons and muons screen efficiently the proton charge, mean kinetic energies of fermions are 1 MeV, and therefore Coulomb interaction in the NS core can be neglected. Leptons can be treated as ideal Fermi gas, while nuclear matter is a strongly interacting Fermi system. All constituent particles are in equilibrium with respect to weak interaction which enforces a very low proton fraction (5 % at 0 ). Pressure is produced by the motion of degenerate fermions and by the strong interaction between nucleons. Strong interaction between nucleons is crucial for NS structure. Hydrostatic equilibrium of NS results from the balance between long-range gravitational force and the pressure gradient. General relativity predicts existence of the maximum mass, Mmax , above which hydrostatic equilibrium does not exist. Neglecting strong interaction, we estimate the maximum allowed NS mass using the EOS for the free Fermi gas (FFG) of neutrons and get Mmax D 0:7 Mˇ . Detection of 2:0 Mˇ proves a paramount importance of strong interaction for NS. It shows that strong interaction between nucleons triples the value of Mmax , compared to the FFG model.

2

Nuclear Matter: Theory and Experiment

Pure neutron matter and symmetric nuclear matter calculations represent the testing ground of nuclear many-body theories. Spin-unpolarized neutron matter is a one component strongly interacting Fermi system. Symmetric nuclear matter, due to charge symmetry of nuclear forces, can be formally treated (neglecting small effects like neutron-proton mass difference) as a one-component nuclear system. In general, however, calculations performed at a fixed value of neutron excess parameter ı yield the energy per nucleon vs. the nucleon number density nb . Examples of E.nb ; ı/ are shown in Fig. 2. They are calculated for a specific model of nuclear matter, but their qualitative features are generic. The minimum of the E.nb / curve for SNM (ı D 0) corresponds to a bound, stable, equilibrium state at zero pressure. The values of E and nb at this minimum will be denoted by Es and ns . Pressure P D n2b dE=dnb is positive for nb > ns and negative for nb > ns . The dotted segment corresponds to negative pressure and is therefore not relevant for the NS matter. The solid segment gives E.nb / for SNM compressed to a density nb > ns . Asymmetric nuclear matter with ı D 0:4

48 Nuclear Matter in Neutron Stars

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Fig. 2 Energy per nucleon vs. baryon number density of nuclear matter for three values of the neutron excess parameter ı. Calculations performed for SLy4 model of effective nucleon interaction. Figure 5.1 from Haensel et al. (2007)

corresponds to the neutron-drip point in a neutron star crust and to a central core of a newly born protoneutron star. Finally, ı D 1 curve corresponds to PNM. Minima of the E.nb / curves are indicated by filled dots. The many-body model used yields ns D 0:16 fm3 and Es D 16:0 MeV. With increasing ı, the self-bound state becomes shallower, the binding energy Bs .ı/ decreases, and ns .ı/ decreases, too. Eventually, the bound state of asymmetric nuclear matter disappears. As it is clear from Fig. 2, Bs D Es is the maximum binding energy per nucleon in nuclear matter. The binding energy per nucleon B.A; ı/ in a self-bound (i.e., bound under zero pressure) system of A nucleons with a nonzero neutron excess parameter ı will be smaller than Bs . The value of B.A; ı/ will tend to Bs from below, if A ! 1, ı ! 0, and the Coulomb forces are switched off. Simultaneously, the mean number density of the system will tend to ns . This property, resulting from the interplay of the short-distance repulsion and the longdistance attraction in the nucleon-nucleon interaction, is called saturation; Bs is called the binding energy at saturation, and ns is the saturation density. Consider the case of small ı and small   .nb  ns /=ns , characteristic of terrestrial nuclei. Using nb D ns .1 C /, and keeping up to the cubic terms in small parameters, we get 1 1 E.nb ; ı/ ' Es C Esym ı 2 C K2 C Lı 2  ; 9 3

(1)

where Esym and K are, respectively, the nuclear symmetry energy and incompressibility, and L is the slope parameter of the symmetry energy. The values extracted from the experimental nuclear physics data are ns ' 0:16 fm3 , Es ' 16:0 MeV, K ' 230 ˙ 40 MeV, Esym ' 32 ˙ 2 MeV, and L ' 55 ˙ 15 MeV.

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Microscopic calculations, starting from realistic interaction between nucleons, show that quadratic approximation for E.nb ; ı/ with respect to ı is very precise even when ı is close to one, and for density much higher than ns , E.nb ; ı/ ' E .SNM/ .nb / C S .nb /ı 2 :

(2)

Notice that S .ns / D Esym . Therefore, as a consequence of Eq. (2), energy per nucleon in pure neutron matter of baryon density nb can be very well (within a percent) calculated from E PNM .nb /  E SNM .nb / C S .nb / :

3

(3)

Nuclear Matter in the Crust

NS is born as very hot object, with internal T  1011 K. Its outer layers are then liquid, a hot plasma of nuclei, nucleons, and leptons, in full thermodynamic equilibrium corresponding to a minimum of free energy per nucleon F D E  T S , where S is the entropy per nucleon, at a fixed mean baryon density nb . After a few decades, NS cools to internal temperature 108 K, and NS matter with  > 106 g cm3 becomes strongly degenerate. This means that the mean kinetic energy of electrons, due to their fermionic nature (Pauli exclusion principle), is then significantly higher than the thermal energy contribution  kB T (kB is the Boltzmann constant). Consequently, the EOS of the matter for  > 106 g cm3 can be very precisely calculated using the T D 0 approximation (see Fig. 4). In the meantime the inner fragment of the outer layer will solidify due to Coulomb repulsion between fully ionized atomic nuclei, forming the crust, while the outer layer will remain liquid forming an ocean. The bottom of the ocean moves outward during the NS cooling. This is visualized in Fig. 4. It is commonly assumed that during the cooling and crystallization process, the element of NS matter followed the path of full thermodynamic equilibrium, leading toward the ground state of the matter, minimizing energy per nucleon at given mean baryon density nb . It is a good approximation for an isolated (single) NS born in a supernova (SN) explosion. A different scenario corresponds to a NS that passed a long (108 yr or longer) accretion stage in a low-mass X-ray binary. It will be briefly described at the end of this section.

3.1

Outer Crust

Consider first the density range 106 g cm3 <  < 1011 g cm3 . Matter is a plasma of nuclei and electrons. Electrons form a quasi-uniform nearly free Fermi gas permeating nuclei. The ground state of the matter corresponds to well-defined mass number and atomic number of nuclei A and Z; nuclei will be also called ions (i) – with charge Ze. The total energy per nucleon is E D EN C ECoul C Ee , where

48 Nuclear Matter in Neutron Stars

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nucleon contribution EN D Mexp .A; Z/c 2 =A (here Mexp .A; Z/ is experimental mass of .A; Z/ nucleus), and ECoul is the Coulomb contribution from e-e, e-i, and i-i interaction. ECoul can be quite precisely calculated via a standard procedure consisting in dividing the plasma into spherical electrically neutral “ion cells” (Wigner-Seitz cells) of volume Vcell D 1=ni , with ion at the cell center. The values A; Z in the ground state (GS) of the matter are determined from the condition E Dminimum under constraint of charge neutrality Zni D ne . With increasing matter density, the values .A; Z/GS change. Pressure has to be continuous in the stellar interior and strictly increases with increasing depth. To a good approximation, it is given by the pressure of the electron gas, P  Pe . Therefore, a transition surface between the two layers, .A; Z/ and .A0 ; Z 0 /, is associated with a density jump at this surface. The proton fraction Yp D Z=A decreases monotonously. This is enforced by the presence of electrons, their contribution to the energy per nucleon E for   106 g cm3 growing as Ee / 1=3 .Yp /4=3 . Near 1011 g cm3 the mass of the GS nucleus is no longer experimentally available, and we have to use many-body theory to calculate it (and masses of its neighbors in the A  Z plane). As the number of neutrons in the nucleus N D A  Z increases, the energy of the highest neutron energy level (Fermi energy) increases too. Moreover, as Z=A decreases with increasing density, the n-n interaction, which is much less attractive than the n-p one, becomes more and more important. These effects push the Fermi energy of neutron in nuclei upward. Finally, the threshold called neutrondrip point is reached, ND , such that for  > ND  4  1011 g cm3 , the GS is reached with some neutrons forming a neutron gas outside nuclei. This occurs at Z=A  0:3 and A  130. The neutron-drip surface constitutes the bottom of the outer crust. Within our approximation, positively charged nuclei (ions) and electrons constitute one-component plasma. Below melting temperature Tm .I Z; A/, it is a crystal of ions arranged in the body-centered cubic (bcc) lattice, and it is a strongly coupled Coulomb liquid for T > Tm .I Z; A/. The NS ocean is characterized by T > Tm .I Z; A/. Formulae for Tm can be found, e.g., in Haensel et al. (2007).

3.2

Inner Crust

For  > ND protons stay bound in nuclei, while neutrons can be present in one of the two states: bound in an attractive potential associated with a proton cluster, and resulting mainly from the n-p interaction, or moving quasi-freely (unbound) outside nuclei. Therefore, there are two phases of nucleons in the inner crust: (i) “nuclei”, droplets of nuclear matter with large neutron excess, with protons forming well-defined proton clusters, and (ii) a less dense neutron gas of unbound neutrons. The number of neutrons in “nuclei” is not well defined while Z of proton clusters is. Neutrons in neutron gas coexist with those bound by the proton clusters: the phase equilibrium between these two states is mediated by strong interactions. A rough classical picture of the inner crust consists of (quasi-spherical) droplets of

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nuclear matter of charge Ze and neutron excess increasing with , immersed in a quasi-uniform neutron gas. Both “nuclei” and neutron gas are permeated by quasiuniform electron gas. Coulomb repulsion between proton clusters leads to the crystal (bcc lattice) structure. As the attribution of neutrons to “nuclei” is ambiguous, and only the total number of neutrons in a given volume is well defined, it is convenient, as in the case of the outer crust, to divide the system into a collection of spherical (Wigner-Seitz) cells of volume Vcell D 1=ni and consider Ncell neutrons and Z protons in such a cell. The average baryon density nb D .Ncell C Z/=Vcell and charge neutrality condition is as in the outer crust ne D Z=Vcell . Energy of a cell at a given nb is .nuc/

.Coul/

Ecell .Ncell ; ZI nb / D Ecell .Ncell ; Z/ C Ecell

.e/

C Ecell :

(4)

It has to be minimized with respect to the distribution of nucleons within the cell, a difficult but feasible task if an effective interaction between nucleons is assumed. The shape of nuclear matter droplets in the GS of the matter is actually a result of the interplay between the Coulomb and surface energy of droplets. In the surface layer of a droplet, a smooth transition between the dense n-p phase (neutron-rich nuclear matter – a nucleon-liquid phase of baryon density nin ) and a less dense neutron matter (nucleon-gas phase of baryon density nout ) occurs. With increasing mean matter density , high neutron excess in the n-p droplets results in a “neutron skin” enveloping them. Simultaneously, nin decreases, nout increases, and surface tension between gas and liquid phases decreases.

3.3

Bottom Layer of the Crust

If the surface tension at the gas-liquid interface is sufficiently low (which might occur at 1014 g cm3 ), the spherical droplets of asymmetric nuclear matter become unstable with respect to deformation and fuse into cylindrical columns (rods) immersed in neutron gas. This is the first (least dense) layer of NS mantle containing liquid-crystal-like nuclear-matter structures immersed in a neutron gas. The upper edge density of the mantle is M  1014 g cm3 . At still higher , it is energetically preferable for the rods to fuse into plates interspaced with layers of neutron gas . At higher , nuclear matter plates stick together leaving columnar bubbles (tubes) filled with neutron gas, which at a still higher density become unstable with respect to breaking into spherical bubbles filled with neutron gas. The last transition at highest density CC (crust-core) consists in vanishing of bubbles of neutron matter and filling of all space with an uniform strongly asymmetric nuclear matter with a few percent of protons and Ye D Yp . This uniform plasma of neutrons, with a small admixture of protons and electrons, constitutes the (liquid) outer core of NS. The rod, plate, and tube phases of the mantle are very often called nuclear pastas, while the bubble phase is sometimes called Swiss cheese phase (Fig. 3). The mantle properties (shear moduli, thermal and electrical conductivities, and neutrino emissivity) are strongly anisotropic.

48 Nuclear Matter in Neutron Stars

a

1339

b

c

Fig. 3 Nuclear pastas’ structures in the neutron star mantle. Hatched regions: neutron-rich nuclear matter. Outside space is filled with neutron gas. (a) Nuclear matter droplets. (b) Nuclear matter rods. (c) Nuclear matter plates. Figure 3.9 from Haensel et al. (2007). If hatched regions are filled with neutron gas and the outside space filled with asymmetric nuclear matter, then we get (a0 ) neutron gas bubbles, (b0 ) neutron gas tubes, and (c0 ) neutron gas plates

3.4

Equation of State for the Crust

Outer crust For T D 0, the GS of the matter is bcc crystal of 56 Fe, with solid surface at P D 0 (NS surface). Observed NS have effective surface temperature Ts & 106 K and have therefore a gaseous (non-degenerate) atmosphere, with a T -dependent equation of state (EOS, P D P .; T /) visualized as red lines in Fig. 4. Here, we assume 56 Fe atmosphere. For Ts D 106 , 107 , 108 K, matter is strongly degenerate for  > 102 , 104 , and 105 g cm3 , respectively. Above  > 104 g cm3 , atoms are fully ionized, forming a plasma of nuclei and electrons (Haensel et al. 2007). The pressure in the outer crust is supplied mainly by the electron gas, Pe , with small corrections due to the Coulomb interactions, PL (L – comes from crystal lattice formed by nuclei, but the formulae for PL work also quite nicely for a liquid phase of the crust). Nucleons are bound in nuclei and therefore do not contribute

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Fig. 4 (Color online) Equation of state of neutron star matter, from the surface to the center. Atmosphere EOS are given by red lines for T D 106 ; 107 ; 108 K. The bottom of the NS ocean at these interior T is denoted by diamonds, going upward with increasing T . A zoomed insert shows the difference between the ground-state and accreted-crust EOS in the vicinity of the neutron-drip point

directly to the pressure. However, positively charged nuclei influence pressure via the interaction with electrons and the repulsion between themselves leading to the ion-crystal structure. The dependence of the proton fraction in the matter Yp D Z=A on  for the GS crust is given in Fig. 5. Inner crust Beyond ND ' 4  1011 g cm3 a gas of neutrons outside nuclei is present (neutron-drip effect). This gas coexists with nucleons bound in nuclei, and exerts pressure on nuclei, and modifies their surface properties. The total pressure is P D PN C Pe C PL , with nucleon contribution PN dominated by the pressure of neutron gas, modified by the presence of proton clusters with a fraction of neutrons being bound to them. Appearance of neutron gas for  > ND implies a transition to a two-phase nucleon system and therefore softens the EOS after neutron-drip point. This is clearly seen in the GS curve in Fig. 4. Then pressure contributed by the neutron gas increases, and the EOS hardens with increasing density. For   1014 g cm3 transition to the pasta phases can occur. This is not the case in Fig. 4, where the direct inner crust (spherical nuclei)-liquid core weak first-order transition (less than one percent density jump) takes place. The EOS hardens significantly in transition to a homogeneous phase, because the two-phase nature (dense nuclear

48 Nuclear Matter in Neutron Stars

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Fig. 5 Proton fraction in NS matter vs. density. Ground-state composition of the crust is assumed. Calculations for the outer crust are performed using experimental nuclear masses whenever they are available. At higher densities, the SLy4 effective energy-density functional is used (Douchin and Haensel 2001). The drops in Yp in the outer crust correspond to the change in the ground-state nuclide (they have a finite slope due to the density jump at the shells interface). The upper curve in the inner crust corresponds to nuclear matter inside the “nuclei,” while the lower curve is the value averaged over the ion (Wigner-Seitz) cell. Bottom panel: Yp comparison for different models of nuclear EOS describing NS core

liquid – less dense neutron gas) of the inner crust disappears and droplets of nuclear liquid merge into a uniform np matter. The EOS near CC deserves an additional comment. For the theoretical model of the crust-core transition to be physically meaningful, both the crust (or crust and mantle) and the liquid core EOS have to be based on the same nucleon interaction model. If it is so, we call the resulting crust-core EOS unified. The effect of the presence of the nuclear pastas layer on the EOS near CC is shown in Fig. 6. Accreted crust Hundreds of NS are observed as X-ray sources in low-mass X-ray binaries (LMXB). The mass of the companion is lower than Mˇ . Therefore, the accretion stage, when NS accretes matter from the companion, can last for 108 –109 yr. During the accretion stage, NS can be observed as X-ray burster. It is commonly accepted that the millisecond pulsars (rotation period CC matter is a uniform plasma composed of nucleons, electrons, and possibly muons. Nucleons form a strongly interacting Fermi liquid, while electrons and muons constitute nearly ideal Fermi gases. The energy per unit volume is E.nn ; np ; ne ; n / D EN .nn ; np / C Ee .ne / C E .n / ;

(5)

where EN is the nucleon contribution. We assume full thermodynamic equilibrium. Then the pressure and energy density depend on a single parameter (one-parameter EOS). Our choice is the baryon density nb . The equilibrium at given nb D nn C np corresponds to the minimum of E under the condition of electrical neutrality. Let us introduce the chemical potentials of the matter constituents, with j D @E=@nj .j D n; p; e; /. Minimization leads to  n D p C e ;

  D e ;

(6)

which expresses the equilibrium with respect to the weak-interaction processes n ! p C e C e ; p C e ! n C e ;

(7a)

n ! p C  C  ; p C  ! n C  :

(7b)

Notice that we consider NS core transparent for neutrinos. In such a case, neutrinos do not affect the matter thermodynamics, and one can put  e D  e D   D   D 0. Equations (6) supplemented by the constraints nn C np D nb , np D ne C n form a closed system of equations which determine the equilibrium composition of the npe matter.

48 Nuclear Matter in Neutron Stars

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Electrons are ultra-relativistic: e  122:1 .ne =0:05n0 /1=3 MeV :

(8)

Muons are present only if e > m c 2 D 105:65 MeV; in the opposite case, we are dealing with the npe matter. After the equilibrium has been determined, the pressure is calculated from the first law of thermodynamics (at T D 0): P D n2b

d.E=nb / : dnb

(9)

The proton fraction at a given nb is determined by a generalized symmetry energy S .nb /, Eq. (3). For Yp D np =nb D 12 .1  ı/  1, which is usually the case, we get Yp .nb / 

n0 64 ŒS .nb /3  5:76  102  3 2 .„c/3 nb nb



S .nb / 32 MeV

3 :

(10)

In particular, proton fraction at nb D ns ' n0 is directly determined by the nuclear symmetry energy. As the experimental value of Esym ' 32 MeV, the proton fraction in the neutron star matter at the normal nuclear density should be Yp .n0 / ' 6 %. Density dependence of the proton fraction Yp .nb / is crucial for the cooling of neutron stars. NS is formed as a hot compact object with an internal temperature T  1011 K in a gravitational collapse of a degenerate stellar core. During the initial 105 106 years of its life, a NS cools via neutrino emission from its core. The most efficient cooling channel is due to the so-called direct Urca (Durca) processes, Eq. (7). Consider first the electron Durca processes in the upper line of Eq. (7). These reactions are allowed only when Yp .nb / exceeds a threshold value YD  0:110:14. The threshold condition can be obtained as follows. Because neutrons, protons, and electrons form degenerate Fermi liquids, only the states close to the Fermi surfaces (within a shell of the thickness  kB T around the Fermi energy) are involved in the processes. Therefore, the momenta of neutrons, protons, and electrons can be approximated by their Fermi momenta pFj (j D n; p; e; ), while the neutrino momentum p  kB T =c  pFj . Neglecting small corrections kB T =c  pFj one sees that momentum conservation imposes the triangle rule: pFn < pFp C pFe ;

(11)

which is satisfied for Yp > YD . In the absence of muons, YD D 1=9; their presence slightly increases YD above 1=9, and YD may then become as large as 0.14. Replacing electrons by muons in Eq. (11), one can get the threshold proton fraction which opens the muon Durca process. This process becomes allowed at a slightly higher density than the electron one.

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Generally, the threshold density for Durca, D , where YD is reached, depends on a nuclear matter model. For some models, Yp never reaches YD in NS, and consequently Durca processes remain forbidden in NS cores. For Yp < YD , the neutrino emission proceeds then via the so-called modified Urca (Murca) processes with an additional nucleon in initial and final states. These additional (spectator) nucleons do not participate in beta processes but only open it via a momentum transfer mediated by strong interactions. This strongly suppresses the neutrino emission rate. If direct Urca processes operate, then a non-superfluid NS core cools to 109 K in a minute, and to 108 K in a year. If they are not allowed, the time scales will be 1 year and 105 years, respectively.

5

Hyperon Core

Since more than 50 years, it is believed that above some supranuclear density purely nucleon NS cores become unstable with respect to weak-interaction processes and that hyperons might replace the most energetic nucleons due to the strangenesschanging reactions. Consequently, NS with sufficiently high central density could have strangeness-carrying (strange) cores consisting of nucleon-hyperon (hypernuclear) matter; their EOS is denoted by EOS.H, in contrast to the purely nucleonic EOS.N. Consider the lightest hyperon . Its electric charge, spin, strangeness, and rest energy in vacuum are 0, 1/2, 1, and 1115 MeV, respectively. Weak interaction can transform a neutron into a  in npe matter provided n m c 2 C U ;

(12)

where n is neutron chemical potential (maximum energy of a disappearing neutron) and U is potential energy of a zero-momentum  in npe matter due to (strong) interaction with nucleons. U is expected to be negative (attractive potential). Notice that m c 2 C U is a minimum energy of a single  created in npe matter. The equality in Eq. (12) corresponds to the threshold density for s, ./ ./ t  20 30 . For  > t , , which is unstable in the vacuum, will not decay because the neutron states in npe matter are occupied and block the  decay due to the Pauli exclusion principle. Since some time, it is commonly believed that the ˙  hyperon will not appear in the NS cores because U˙ is essentially repulsive. In view of this, next hyperon to appear is &  of rest energy m&  c 2 D 1321 MeV, strangeness 2, and electric charge 1. Its presence in NS core requires n C e m&  c 2 C U&  ; .&  /

which might be possible above t

 30  40 .

(13)

48 Nuclear Matter in Neutron Stars

6

1345

EOS of Neutron Star Core

The “minimal” EOS of NS matter consisting of nucleons and leptons is denoted as EOS.N, while that allowing for the presence of hyperons EOS.H. There are two basic approaches to the calculation of the EOS. The first approach is based on the microscopic many-body theory starting from “bare” nucleon/hyperon forces (i.e., in the vacuum) derived from experimental data on baryon scattering and few-body nucleon/hyperon systems. The second approach applies phenomenological effective strong interactions, tested in nuclear and hypernuclear physics, and is much easier to use than the more fundamental microscopic approach.

6.1

Microscopic Many-Body Theories

It is based on the two-body nucleon forces (2BF) fitting a few thousand of data on nucleon-nucleon scattering and the properties of 2 H. Moreover, we are forced to consider three-body nucleon forces (3BF), needed to reproduce also the properties of “low-density” few-nucleon systems, 3 H, 3 He, and 4 He. Finally, for 2BF+3BF to be applied to dense nuclear systems, the 3BF is made density-dependent to fit semi-empirical parameters of nuclear matter at saturation. Numerous many-body calculations of EOS.N starting from 2BF+3BF and performed within the quantum many-body theories of dense matter yield Mmax > 2 Mˇ , which is a necessary condition for dense-matter theory to be consistent with observations (see, e.g., Chamel et al. 2013). The calculation of EOS.H necessitates models of nucleon-hyperon and hyperonhyperon forces. The nucleon-hyperon interaction is obtained from the analyses of hypernuclei and ˙  -atoms, while hyperon-hyperon forces are estimated studying double  hypernuclei. Studies of  and & hypernuclei yield the depth of a .N/ potential well binding of these hyperons in symmetric nuclear matter, U  .N/ 28 MeV and U&  18 MeV. Analysing ˙  -atoms (where an electron is .N/ .N/ replaced by ˙  ) results in an estimate U˙  C30 MeV. Repulsive U& turns out to eliminate ˙s from NS cores. The data on the hyperon interactions are scarce, or even nonexistent in many hyperon-nucleon and hyperon-hyperon channels, and therefore approximate symmetries of strong interactions, e.g., SU(6) symmetry, have to be widely used to get a complete hypernuclear interaction. Another painful problem is our ignorance concerning the three-body forces involving hyperons. Hyperons soften the EOS.H compared to the purely nucleonic EOS.N, and for a long time, microscopic calculations were not able to produce NS with hyperonic cores and M D 2 Mˇ . Only very recently the microscopic calculations of EOS.H that yield Mmax > 2:0 Mˇ have been successfuly performed (Katayama and Saito 2015; Yamamoto et al. 2014).

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Effective Energy-Density Functional Models

In contrast to the microscopic theories, the effective energy-density functional (EDF) models contain many adjustable parameters, and they have no direct relation to the scattering and few-body experimental data. The non-relativistic (NR) models are based on an effective nuclear Hamiltonian with parameters fitted to reproduce the properties of atomic nuclei and sometimes also adjusted to reproduce EOS of PNM obtained in macroscopic calculations. The NR-EDF depends on the nucleon densities and their spatial gradients. These EDF can be used for the calculations of the structure and EOS of the outer and inner crusts, mantle (nuclear pastas), and it is particularly simple to use them for the calculation of the EOS of the NS core. Causality of the EOS is not guaranteed for these EDF, and therefore they should be carefully selected to be used for NS. The relativistic mean field theory (RMF) of dense hadronic matter starts from a Lorentz-invariant Lagrangian density involving baryon and meson fields. The baryon-meson coupling constants, and the couplings in the meson self-interaction terms, are determined by fitting nuclear and hypernuclear data. The equations of motion for the hadron fields are solved in the mean-field approximation. The RMF approach results in an EDF that can be applied to the calculation of the structure and EOS of NS crust and core in a unified way. The RMF theory has two nice features. First, because it is Lorentz invariant, the EOS remains causal by construction. Secondly, the model can be readily extended from nuclear to hyperonic matter. This is why RMF was used extensively to calculate EOS.H (for a review see, e.g., Fortin et al. 2015).

6.3

EOS of NS Core and Causality

An EOS should respect a fundamental constraint stemming from the special theory of relativity; the speed of sound must not exceed c: vs D .dP =d/1=2 c :

(14)

The above condition is usually interpreted as equivalent to a more fundamental condition of causality (for a detailed discussion, see Fayngold 2008). One can easily construct so-called causal limit (CL) equation of state, matched smoothly to another EOS at the point .m ; Pm / and which is maximally stiff, vs D c for larger density, P

.CL/

D Pm C .  m /c 2 for  > m :

(15)

A true EOS of NS core is a line in the P   plane. Our ignorance implies that there are many proposed theoretical EOS satisfying necessary conditions fMmax ŒEOS > 2 Mˇ g^fvs cg and used as “the EOS.” They span over a characteristic horn-shaped region in the P   plane, similar to that shown in Fig. 7.

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Fig. 7 A set of the high-density EOS, in the P   plane, for  > 3  1014 g cm3 . Dotted line CL: causal limit EOS of the form P D .  1 /c 2 , where 1 D 5  1014 g cm3 . It crosses each of the considered EOS at some point .m ; Pm / such that m D 1 C Pm =c 2 . Dotted line FFG: EOS of a free Fermi gas of neutrons

7

Neutron Star Models vs. Observations

Using the EOS of NS matter, preferably in the form  D .P /, nb D nb .P / (pressure P is preferred as independent variable because it is strictly continuous and monotonic in NS, in contrast to  and nb , that can suffer discontinuities), one can calculate the NS models and confront them with observations. In this way we can use NS as unique cosmic laboratory to study nuclear and hypernuclear matter for the density up to 60 100 . The calculations of the NS models are done in general relativity using Einstein’s equations reduced to the case of hydrostatic equilibrium (Haensel et al. 2007). In what follows we consider the simplest models which are spherically symmetric. NS matter is treated as a perfect fluid, and effect of rotation, magnetic field, and elastic stresses within the crust are neglected. This is a very good approximation for observed NS. Then, P and  within the NS depend only on the radial coordinate r (for more details, see, e.g., Haensel et al. 2007). The equations of hydrostatic equilibrium are integrated from the star center [r D 0, P D Pc , c D .Pc )] outward, until NS surface with P D 0 is reached at r D R (this is circumferencial radius of NS, see, e.g., Haensel et al. 2007). The total mass-energy within radius R, divided by c 2 , is the gravitational mass of NS. The thickness of an accreted crust is larger than for the ground-state one, given in Table 1. For an accreted crust, the EOS is stiffer, and the crust thickness is larger by 0:2 and 0:1 km for M D 1:0 Mˇ and M D 1:4 Mˇ , respectively (Zdunik and Haensel 2011). For M & 2 Mˇ increase of the crust thickness is much smaller. Equilibrium NS models form a one-parameter family. We will label them by central density c . In this way we obtain M .c / and M .R/ curves, shown in Figs. 8

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Table 1 Neutron star structure based on the EOS calculated in Douchin and Haensel (2001), assuming for simplicity T D 0 (no atmosphere, no ocean on the outer crust). Ground-state crust is assumed. Four NS masses are considered: 1:0 Mˇ , 1:4 Mˇ , 2:0 Mˇ , and maximum allowable mass Mmax D 2:06 Mˇ . Maximum central density c D 3  1015 g cm3 is reached for M D Mmax . Depth is calculated in the inward radial direction  [g cm3 ] Depth [km] 1:0 Mˇ 1:4 Mˇ 2:0 Mˇ Mmax Constituent

Outer crust 8  4  1011

Inner crust 4  1011  1014

Outer core 1014  5  1014

Inner core 5  1014  3  1015

0.0–0.63 0.0–0.38 0.0–0.16 0.0–0.12 Nuclei, e

1.34–4.74 0.84–3.00 0.35–1.27 0.27–0.99 npe

4.74–11.85 3.00–11.70 1.27–10.63 0.99–10.02 n p e   ‹; : : :

Structure

Crystal

0.63–1.34 0.38–0.84 0.16–0.35 0.12–0.27 pn-clusters with bound-n unbound-n, e pn-clusters crystal e n gas

Uniform plasma Uniform plasma

7

8

9

6 5 4

3

2

Fig. 8 Gravitational mass M vs. central density c for non-rotating NS models based on a set of EOS.N and EOS.H. The hatched area is the fragment of the M  c plane covered by a large set of EOS.N and EOS.H satisfying conditions Mmax > 2Mˇ and vs c. Only a few examples of M .c / curves are explicitly shown, including the two extreme ones determining the border of a “theoretically predicted M  c area.” Adding additional observational/experimental constraints will make the thickness of the horn area shrink. Vertical lines crossing the M .c / lines indicate configurations with c =0 D 2; 3; : : :

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Fig. 9 Gravitational mass M vs. circumferential radius R for nonrotating NS models. Upper-left corner: (a) blue, excluded by the general theory of relativity (GTR) because R < 2 GM =c 2 ; (b) yellow, excluded due to (GTR)^.Pc < 1/; (c) green, excluded due to (GTR)^.vs < c/

and 9. Both M and R are measurable quantities. Models with M < 1 Mˇ are not astrophysically interesting. Configurations with dM =dc < 0 are unstable, and therefore they are not astrophysically interesting neither. The true EOS is unknown, and our set of “acceptable” theoretical EOS covers horn-shaped areas of the M  c and M  R planes. The theoretical uncertainties are quite large even at 1:4 Mˇ : its central density ranges between 2:20 and 3:70 . At a fixed c D 20 , the value of M ranges from 0:6 Mˇ to 1:2 Mˇ ! The maximum mass ranges from 2:1 Mˇ to 2:3 Mˇ . Mmax is a functional of the EOS. It is sensitive to the high-density segment of the EOS, 50 100 . The radius at a given mass M is also a functional of the EOS. Generally, it depends weakly on M in the mass range 0:5 Mˇ 1:6 Mˇ , but its value depends on the EOS for 1:50 30 . The radius R.1:4 Mˇ / ranges from 11 km to 14 km. Precise measurements of masses are possible, under favorable conditions, using timing data for some pulsars in binaries containing NS and white dwarf and in those containing two NS. Masses measured in eight NS-NS binaries range from 1:17 Mˇ to 1:56 Mˇ , and the mean mass value of NS mass in these binaries is 1:33 ˙ 0:09 Mˇ (Özel and Freire 2016). Precise measurements of mass were done for 18 millisecond pulsars (MSP) in binaries with white dwarfs (WD). While the lowest NS mass in NS-WD binaries is similar to that in NS-NS systems, there are seven masses >1:6 Mˇ and three masses >1:8 Mˇ , with the largest one

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2:01 ˙ 0:04 Mˇ (Antoniadis et al. 2016). The high masses are most likely not a result of accretion during recycling, but reflect high NS birth mass in core-collapse supernova (Antoniadis et al. 2016). The mean mass value for MSP is 1:55˙0:23 Mˇ (Özel and Freire 2016). The measurements of radius are mostly based on the analysis of thermal radiation from the surface of NS. A difficult starting condition is knowledge of the distance to NS. For the time being, the most promising are measurements for NS in X-ray transient sources in low-mass X-ray binaries. Two cases were found to be the most favorable: quiescent surface radiation (periods with no bursts) and thermonuclear X-ray bursts with photospheric radius expansion during bursting (accretion) periods. Additional effects (NS rotation, space-time curvature, atmospheric composition) have to be included. Optimal data selection is a subject of controversies between different teams (see, e.g., review Özel and Freire 2016). For M D 1:21:6 Mˇ , where theoretical EOS predict an approximate constancy of R, typical measured radii of NS in X-ray transients range from 9:5 ˙ 1:5 km to 12:0 ˙ 1 km, where we give 1   uncertainties (see Haensel et al. 2016 for references), but some teams claim much more precise values, e.g., 10:4 ˙ 0:6 km (Özel and Freire 2016). Some of the measured values of R rule out the theoretical EOS with R.M / dependence visualized in Fig. 9. However, we find it precocious to use these measurements to rule out models of dense matter before a reliable evaluation of the systematic errors in the measured R values is carried out. A lot is still to be done in this respect.

8

Conclusions

NS are unique cosmic laboratories to study nuclear matter under extreme physical conditions not available in terrestrial experiments. Proton fraction in nuclear matter in NS cores can be as low as 5 %. Measuring various parameters associated with NS structure (masses, radii), evolution (cooling, accretion), and dynamics (rotation, glitches, flares), we have a unique opportunity to study different states of nuclear matter. These different states of nuclear matter were reviewed in the present chapter. Inside NS, nuclear matter exists in various phases, from neutron-rich nuclei, proton clusters in neutron matter, neutron matter of subnuclear density in the inner crust, and possible pasta-like structures to uniform plasma of nucleons, and maybe some hyperons, permeated by a gas of electrons and muons. The density of nuclear matter at the center of the most massive pulsars (2:0 Mˇ ) can be many times higher than that in heavy nuclei. The very existence of 2:0 Mˇ NS puts strong constraints on the theories of nuclear matter, and particularly severe constraints on the strong interactions in dense baryon systems. Precise measurement of radii of NS of known mass will put an additional very strong constraints. Hopefully, the future constraints will make shrink the uncertainties and therefore eventually unveil the true equation of state of nuclear matter in NS.

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Cross-References

 Neutron Star Matter Equation of State  Strange Quark Matter Inside Neutron Stars  The Masses of Neutron Stars Acknowledgements This work was financially supported by the Polish National Science Centre through the OPUS grant 2013/11/ST9/04528.

References Antoniadis J, Tauris TM, Özel F, Barr E, Champion DJ, Freire PCC (2016, in press) The millisecond pulsar mass distribution: evidence for bimodality and constraints on the maximum neutron star mass. Astrophys J. arXiv:1605.01665v1 [astro-ph.HE] 5 May 2016 Chamel N, Haensel P (2008) Physics of neutron star crusts. Living Rev Relativ 11:10. http://www. livingreviews.org/lrr-2008-10 Chamel N, Haensel P, Zdunik JL, Fantina AF (2013) On the maximum mass of neutron stars. Int J Mod Phys E 22:1330018 Douchin F, Haensel P (2001) A unified equation of state of dense matter and neutron star structure. Astron Astrophys 380:151 Fayngold M (2008) Special relativity and how it works. Wiley-VCH, Weinheim Fortin M, Zdunik JL, Haensel P, Bejger M (2015) Neutron stars with hyperon cores: stellar radii and equation of state near nuclear density. Astron Astrophys 576:A68 Haensel P, Potekhin AY, Yakovlev DG (2007) Neutron Stars 1 Equation of state and structure. Springer, New York Haensel P, Bejger M, Fortin M, Zdunik JL (2016) Rotating neutron stars with exotic cores: masses, radii, stability. Eur Phys J A 52:59 Katayama T, Saito K (2015) Hyperons in neutron stars. Phys Lett B 747:43 Özel F, Freire P (2016) Masses, radii, and the equation of state of neutron stars. Ann Rev Astron Astrophys 54:401 Yamamoto Y, Furumoto T, Yasutake N, Rijken TA (2014) Hyperon mixing and universal manybody repulsion in neutron stars. Phys Rev C 90:045805 Zdunik JL, Haensel P (2011) Formation scenarios and mass-radius relation for neutron stars. Astron Astrophys 530:A137

Thermal Evolution of Neutron Stars

49

Ulrich R. M. E. Geppert

Abstract

The thermal evolution of neutron stars is a subject of intense research, both theoretical and observational. The evolution depends very sensitively on the state of dense matter at supranuclear densities, which essentially controls the neutrino emission. The evolution depends, too, on the structure of the stellar outer layers which control the photon emission. Various internal heating processes and the magnetic field strength and structure will influence the thermal evolution. Of great importance for the cooling processes is also whether, when, and where superfluidity and superconductivity appear within the neutron star. This article describes and discusses these issues and presents neutron star cooling calculations based on a broad collection of equations of state for neutron star matter and internal magnetic field geometries. X-ray observations provide reliable data, which allow conclusions about the surface temperatures of neutron stars. To verify the thermal evolution models, the results of model calculations are compared with the body of observed surface temperatures and their distribution. Through these comparisons, a better understanding can be obtained of the physical processes that take place under extreme conditions in the interior of neutron

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Equations and Physics Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Equation of State (EOS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Neutrino Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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U.R.M.E. Geppert () Janusz Gil Institute of Astronomy, University of Zielona Góra, Zielona Góra, Poland Institute for Space Systems, German Aerospace Center (DLR), Bremen, Germany e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_69

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2.3 Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 The Surface Photon Luminosity and the Envelope . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Effects of a Magnetic Field and of the Composition of the Envelope . . . . . . . . . . 3 Magnetic Field Effects in the Crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Heating Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Magnetic Field Decay and Joule Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Dissipative Motion of Vortex Lattices and Rotochemical Heating . . . . . . . . . . . . 5 Comparison with Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1359 1361 1362 1365 1367 1367 1368 1370 1372 1372 1372

Introduction

Neutron stars, the vast majority of them born in supernovae, are stellar objects with the most extreme properties in our universe. They possess the strongest magnetic fields and consist of matter whose density exceeds that of nuclear matter by about a factor of 10. This makes them highly relativistic stars. They are the by far greatest appearances of suprafluid matter, and in their deep interior, the matter is perhaps in a state resembling the state of matter as prevalent immediately after the hypothetical big bang. The idea that neutron stars may exist was first stated by L.D. Landau (1932) in connection with the discovery of the neutron. That supernovae are birthplaces of neutron stars was first suggested by Baade and Zwicky (1934), who wrote “With all reserve we advance the view that a super-nova represents the transition of an ordinary star into a neutron star, consisting mainly of neutrons.” Clearly, a neutron star born in such as violent process as a supernova is expected to have immediately after birth an extremely high heat content which causes temperatures of T . 1011 K. Such enormous temperatures challenged physicists to perform cooling calculations. The first attempts (Tsuruta 1965; Tsuruta and Cameron 1966) predated the discovery of the first neutron star as a radio pulsar in 1967 (Hewish et al. 1968). The result of this first cooling calculations – taking into account half a century of ever more precise observations and the enormous progress in theoretical physics – has proved still to be correct, for sure qualitatively. Cooling simulations, confronted with soft X-ray, extreme UV, UV, and optical observations of the thermal photon flux emitted from the surfaces of neutron stars, provide most valuable information about the physical processes operating in the interiors of these objects. The predominant cooling mechanism of hot (temperatures T . 1011 K), newly formed neutron stars is neutrino emission, with an initial cooling timescale of seconds. Neutrino cooling remains dominant for at least the first thousand years and typically for much longer in slow (standard) cooling scenarios. Photon emission eventually overtakes neutrino emission when the internal temperature has sufficiently dropped, to 108 K, with a corresponding surface temperature roughly two orders of magnitude smaller. The thermal evolution of neutron stars is sensitive to the adopted nuclear equation of state (EOS), the stellar mass, the assumed magnetic field strength, appearance

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of superfluidity, and the possible presence of color-superconducting quark matter. Therefore, theoretical cooling calculations serve as a principal window on the properties of superdense hadronic matter and neutron star structure. The thermal evolution of neutron stars also yields information about such temperature-sensitive properties as transport coefficients, crust solidification, and internal pulsar heating mechanisms. In this article an overview is given that presents basics of thermal evolution processes and reflects the current status of neutron star cooling calculations tested against the steadily growing body of observed cooling data. A more detailed presentation of the physical processes that determine the thermal evolution of neutron stars can be found in Yakovlev and Pethick (2004) and Page et al. (2006). Space limitation forbids a detailed discussion of observational data, and the reader who is interested in a broader and more detailed recent compilation is referred to Page et al. (2004) and Viganò et al. (2013) as well as to two observational reviews of Pavlov and Zavlin (2003) and Potekhin et al. (2014), to get a flavor of the difficulties involved in the analysis and interpretation of the data. Also for reasons of space, this article will consider only the simplest composition of neutron star matter, ions, electrons, free neutrons in the crust, neutrons, and an admixture of protons and electrons, that ensures charge neutrality in the core. A discussion of the effects of the presence of exotic particles as hyperons, of meson or kaon condensates as well as of de-confined quarks can be found in Page et al. (2006). This article is organized as follows. In Sect. 2 the basic equations and the physics input that govern neutron star thermal evolution are introduced. Magnetic field effects which influence the heat flux through the crust and the envelope of a neutron star are discussed in Sect. 3, while Sect. 4 is devoted to heating mechanisms that may decelerate the cooling process. Finally, in Sect. 5 a comparison of theory and observation is given.

2

Basic Equations and Physics Input

The basic features of the thermal evolution of a neutron star are easily grasped by simply considering the thermal energy conservation equation for the star. Since neutron stars are subject to general relativistic effects, this equation reads h i   d .e  Eth / @T E  e  O  r.e E  T / D e 2 L  L C H ; D Cv e  r dt @t

(1)

where Eth is the thermal energy content of the star, T its internal temperature, and Cv its total specific heat. e  ,  being the gravitational potential, is the so-called redshift factor which reflects the curvature of the space–time inside and outside of the neutron star. At its surface the relativistic corrections to Newtonian physics are about 30%. The energy sinks are the total neutrino luminosity L , described in Sect. 2.2, and the surface photon luminosity L , discussed in Sect. 2.4. The thermal conductivity O is in general, especially in the presence of strong magnetic fields, a

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tensor. Its effect on anisotropic heat transport is explained in Sect. 2.5. The source term H includes all possible “heating mechanisms,” which, for instance, convert magnetic, chemical, or rotational energy into heat. H is discussed in Sect. 4.

2.1

Equation of State (EOS)

The EOS closes the system of differential equations (“Einstein’s equations”, for details see Eqs. 1. . . 6 in Page et al. 2000), which determines the structure of the neutron star. In principle the EOS should give not only the relationship between pressure, density, temperature, and other state variables, i.e., P D P .; T; : : :/, but also the chemical composition of matter. The barotropic EOS P D P ./, where the pressure depends only on the density, is often used as a first approach to build neutron star models. However it turns out that the stability of magnetized neutron stars demands a non-barotropic EOS, i.e., the pressure is not only dependent on the density but additionally on the radially varying chemical composition of ions in the crust or protons and neutrons in the core (see, e.g., Reisenegger 2009). The cross section of a neutron star can be split roughly into three, possibly four, distinct regimes. Below a gaseous atmosphere, which is only a few centimeter thick, the first regime is the star’s outer crust, which consists of a lattice of atomic nuclei and a Fermi gas of relativistic, degenerate electrons. The second regime, known as the inner crust, where free neutrons appear, extends from the neutron drip density, at 4  1011 g cm3 , to a transition density of about 2  1014 g cm3 . Beyond that density the star’s third regime, the core, begins. Here, all atomic nuclei have dissolved into their constituents, i.e., protons and neutrons. A small fraction of electrons is also present, which ensures charge neutrality of the matter in the core. Furthermore, because of the high Fermi pressure, the inner core may be expected to contain baryon resonances, boson condensates, hyperons, and/or a mixture of deconfined up, down, and strange quarks. While neutron stars, whose core consists mainly of neutrons, protons, and electrons, are bound by gravitational forces, quark stars are held together by nuclear forces. These still hypothetical phases in the inner core region are beyond the scope of this handbook. The interested reader is referred to the textbook of Glendenning (2000) and to a very recent study of Sharma et al. (2015). The EOS of the outer and inner crust is rather well known. This is very different for the EOS of the star’s core which is only very poorly understood. There are different field theoretical approaches to derive EOS. A detailed presentation of the various EOS is given in Page et al. (2006). Each EOS model results in a certain mass–radius relation M D M .R/, where R is the radius of the neutron star, i.e., the EOS defines the compactness of the star. The more mass that is confined to a given volume, the more compact is the star. Increasing compactness will enhance the space–time curvature within the neutron star and its surroundings. As seen by a distant observer, the stronger the curvature of space–time, the slower the processes in the neutron star, e.g., magnetic field decay and heat transport.

49 Thermal Evolution of Neutron Stars

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3

2.5

RBHF UVII Vela X−1

|

Cyg X−2

2

M (Msun)

|

|

PSR 1913+16

1.5

| RH (p,n) RH (p,n,H)

|| RH (p,n,H,Q)

Bare strange star

1

|

Neutron gas

Strange star with nuclear crust

0.5

0 0

5

10

15

20

R (km)

Fig. 1 Neutron star mass versus radius relationship for different EOSs. The horizontal lines refer to the masses of Vela X-1 (1:88 ˙ 0:13 Mˇ ), Cyg X-2 (1:78 ˙ 0:23 Mˇ ), and PSR 1913+16 (1:4408 ˙ 0:0003 Mˇ ). For the relativistic Hartree (RH) EOS, three different chemical compositions of the core matter are assumed: only protons (p) and neutrons (n), additionally hyperons (H), and quarks (Q)

Mass-radius relationships for different EOS are shown in Fig. 1. These relationships are known to be very sensitive to the underlying model for the EOS. As is evident from Fig. 1, the EOS supposed to be valid for strange stars predicts the smallest radii, i.e., the highest compactness. Strange stars are a subclass of the up-to-now only hypothetically existing quark stars. These are not held together by gravitational forces as “normal” neutron stars but by nuclear forces. Their physics is beyond the scope of this article; further basic information can be found in Shapiro and Teukolsky (1983). The EOS based on the relativistic Hartree (RH) or Brueckner-Hartree-Fock (RBHF) approximations (see Weber 1999 and Glendenning 2000) return neutron star radii between 11 and 15 km. The nonrelativistic two-nucleon interaction EOS UVII (Wiringa et al. 1988) predicts a somewhat smaller radius .11 km. Therefore, except for the quark stars, which exist only hypothetically, neutron stars will certainly have radii not much smaller than 10 km and not significantly exceeding 15 km.

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Neutrino Processes

As already mentioned in the introduction, neutron stars are born with temperatures in excess of 1010 K. The dominating cooling mechanism of such objects for the first several thousand years after birth is neutrino emission from the core. After that, cooling via photon emission from the star’s surface takes over. Table 1 summarizes the dominant neutrino-emitting processes together with their efficiency for neutron star cooling. The interested reader is referred to Weber (1999), Pethick (1992), Yakovlev et al. (2001), and Voskresensky (2001) for more details. Direct Urca Processes. Beta decay and electron capture processes among nucleons, n ! p C e  C N e and p C e  ! n C e , also known as nucleon direct Urca processes, are only possible in neutron stars if the proton fraction exceeds a critical threshold (Lattimer et al. 1991). Otherwise energy and momentum cannot be conserved simultaneously for these reactions. For a neutron star made up of only neutrons, protons, and electrons, the critical proton fraction is around 11%. This follows readily from kFn D kFp C kFe (kFn;p;e being the Fermi momentum of neutrons, protons, electrons, respectively) combined with the condition of electric charge neutrality of neutron star matter. The triangle inequality then implies for the magnitudes of the particle momenta kFn kFp C kFe , and charge neutrality constrains the particle Fermi momenta according to kFp D kFe . Substituting kFp D kFe into the triangle inequality leads to kFn 2kFp so that (since n / kF3 ) nn 8np for the number densities of neutrons and protons. Expressed as a fraction of the system’s total baryon number density, n  np C nn , one thus arrives at np =n > 1=9 D 0:11 as quoted above. Modified Urca Processes. When the proton fraction is below the threshold of 11%, the direct Urca processes is impossible. In this case, the dominant neutrino emission process is a second-order process, a variant of the direct Urca process, called modified Urca process (Chiu and Salpeter 1964; Friman and Maxwell 1979),

Table 1 Dominant neutrino-emitting processes in neutron star cores. The many R factors are temperature-dependent control functions which take into account the effects of pairing as discussed in Sect. 2.3 Name Modified Urca cycle (neutron branch) Modified Urca cycle (proton branch) Bremsstrahlung Cooper pair formation Direct Urca cycle

Process n C n ! n C p C e  C N e n C p C e  ! n C n C e p C n ! p C p C e  C N e p C p C e  ! p C n C e n C n ! n C n C C N n C p ! n C p C C N p C p ! p C p C C N n C n ! Œnn C C N p C p ! Œpp C C N n ! p C e  C N e p C e  ! n C e

Emissivity (erg cm3 s1 ) 21021 R T98

Slow

1021 R T98

Slow

1019 R T98

Slow

51021 R T97 Slow 51019 R T97 1027 R T96

Fast

49 Thermal Evolution of Neutron Stars

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in which a bystander neutron or proton participates to allow momentum conservation (see Table 1). Since this modified Urca process involves five degenerate fermions, instead of three for the direct Urca processes, its efficiency is reduced, simply by phase-space limitation, by a factor of order .T =TF /2 (TF is the Fermi temperature of the nucleons and electrons). This reduction, for TF  100 MeV and T D 0:1 MeV ' 109 K, amounts to about six orders of magnitude (!) and an overall temperature dependence T 8 instead of T 6 . It is certainly the dominant process for not too high densities in the absence of pairing and is the essence of the “standard cooling scenario.” However, in the presence of pairing, neutrino emission by the constant formation and breaking of Cooper pairs (see Sect. 2.3) most probably dominates over the modified Urca process, at least as long as the core temperature is less than one order of magnitude lower than Tc . The most striking distinction between the direct and modified Urca processes is the huge difference, six orders of magnitude, in the efficiency of neutrino emissivities (see Table 1). As a consequence, neutron star whose core composition allows direct Urca processes will cool much faster than those where only modified Urca processes are possible.

2.3

Pairing

Pairing, i.e., the transition of a system of fermions into a bosonic superfluid/superconducting state via the formation of Cooper pairs, will unavoidably occur in a degenerate Fermi system in the case where there is any attractive interaction between the particles. A Cooper pair is a boson (integer spin) consisting of two fermions (half-integer spin) which are paired together by an attractive interaction. In the case of the baryons in the neutron star’s interior, there are many candidates for channels of attractive interactions, and the real question is rather what is the critical temperature Tc at which pairing occurs? Calculation of Tc is notoriously difficult, and results are often highly uncertain. Since pairing may have a great influence on the thermal evolution of neutron stars, this process and its consequences will be considered here. The reader interested in more details is referred to Dean and Hjorth-Jensen (2003) for a comprehensive review. For electrons which are present in the core matter too, there is no obvious attractive interaction which could lead to pairing with a Tc of significant value. In the case of nucleons, at low Fermi momenta, pairing is predicted to occur in the 1 S0 angular momentum state, while at larger momenta neutrons are possibly paired in the 3 P2 3F2 state. Neutron 1 S0 pairing occurs at densities corresponding to the crust and, possibly, the outermost part of the core. In the case of the proton 1 S0 pairing, the situation is more delicate since it occurs at densities in the outer core where protons are mixed, to a small amount, with neutrons. Predictions for Tc span a much wider range than in the case of the neutron 1 S0 gap. Whether or not neutrons pair in the 3 P2 3F2 channel is highly uncertain. Typical Tc as a function of the density is shown in Fig. 2. As soon as the temperature has fallen below 1010 K, the neutrons in the inner crust (1013 .

1360

U.R.M.E. Geppert

10 Soft

Critical Temperature [10 9 K]

Medium

n 1S0

8

Stiff

Core 6

4

1

p S0

2 3

n P2 0

12

10

13

14

10 10 Density [g cm -3 ]

15

10

Fig. 2 Pairing critical temperatures for neutrons in the 1 S0 state (Ainsworth et al. 1989) and 3 P2 state (Takatsuka 1972) and protons in the 1 S0 state (Baldo et al. 1992). The short dashed lines show the central densities of the three 1:4 Mˇ models with soft, medium, and stiff EOS, as studied in Page et al. 2000

 . 1014 g cm3 ) become superfluid; protons in the outer core pass over into a superconducting state later, if T . 6  109 K. Hence, neutron superfluidity will appear in the inner crust very early (hours to a few days) after the creation of a neutron star in a supernova. Superfluid 3 P2 neutrons will appear only if the outer core is cooled down below 109 K. The enormous impact of pairing on the cooling comes directly from the appearance of the energy gap  at the Fermi surface which leads to a suppression of all processes involving single-particle excitations of the paired species. When T  Tc , the suppression is of the order of e =kB T and hence dramatic. The suppression depends on the temperature dependence of  and the details of the phase space involved in each specific process. In numerical calculations it is introduced as a control function (the many R in Table 1). For the specific heat one has Cv .T / ! Cvpaired .T / D Rc .T =Tc /  Cvnormal .T / ;

(2)

and the control functions have been calculated for both 1 S0 and 3 P2 pairing by Levenfish and Yakovlev (1994). For neutrino processes there is a long family of control functions for all processes which must also consider which of the participating baryons are paired. As for Cv , the neutrino emissivity is controlled

Control Functions

49 Thermal Evolution of Neutron Stars

1

S0

cv

3 3

P2

1

S0

P2

εν

1361

PBF

p 1S0

1

n 3 P2

S0

3

P2

Fig. 3 Control functions for Cv (left panel), Eq. (2),  of the modified Urca process (central panel), Eq. (3), and the pair braking and formation (PBF) (right panel). The PBF turns on at T D Tc , with increasing efficiency when T decreases, since the energy of the emitted neutrinos is determined by the gap’s size which grows with decreasing temperature just below Tc , and is eventually exponentially suppressed when T Tc , as pair breaking is frozen because kB T 

 .T / !  paired .T / D R .T =Tc /   normal .T / ;

(3)

and the R ’s for many processes can be found in Yakovlev et al. (2001). A typical selection of them is shown in Fig. 3. Thus, in the superfluid/superconductive phase, pairing suppresses both the specific heat and the neutrino emissivities. Obviously, the neutrino-cooling timescale / Cv = is affected by pairing. Since the electrons do not pair, their contribution to Cv is not suppressed. Therefore, in general will increase in comparison to the normal (not superfluid) state of matter, i.e., the cooling will be decelerated by the appearance of pairing. This effect will be counteracted in the vicinity of the critical temperature (T  Tc ) by pair breaking and formation processes. Cooper Pair Breaking and Formation (PBF) Processes. Besides the above described, and well-known, suppressing effects on the specific heat and neutrino emissivities, the onset of pairing also opens new channels for neutrino emission. The superfluid or superconducting condensate is in thermal equilibrium with the single-particle excitations and the continuous formation and breaking of Cooper pairs, which are very intense at temperatures slightly below Tc . The formation of a Cooper pair liberates an energy which can be taken away by a - pair: (Flowers et al. 1976) X C X ! ŒXX  C C

(4)

where ŒXX  denotes a Cooper pair of particles X (X stands for neutrons, protons, but in general also for hyperons, quarks, etc.).

2.4

The Surface Photon Luminosity and the Envelope

The photon luminosity L is traditionally expressed as L D 4 R2  SB Te4 ;

(5)

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U.R.M.E. Geppert

which defines the effective temperature Te (SB being the Stefan-Boltzmann constant). The quantities L, R, and Te are local quantities as measured by an observer at the stellar surface. An external observer “at infinity” will measure these quantities red-shifted, i.e., L1 D e 2 L , T1 D e  Te , and R1 D e  R, so that 2 4 L1 D 4 R1  SB T1 :

(6)

The luminosity L, or L1 , is the main output of a cooling calculation, and it can equally well be expressed in terms of Te or T1 . Numerical simulations calculate the time evolution of the internal temperature T D T .; t / and luminosity L D L.; t / profiles up to an outer boundary b . At this point L.b /  L , and an envelope model is glued as an outer boundary condition. Typically b is taken as 1010 g cm3 , and the envelope is thus a thin layer, of the order of a hundred meters thick, which is treated in the plane-parallel approximation. Since the thermal relaxation timescale of the envelope is much shorter than the stellar evolution timescale, and neutrino emission in the envelope is negligible, hydrostatic equilibrium and heat transport reduce to ordinary differential equations which, with the appropriate physical input, are easily solved. The result is a surface temperature Ts  Te for each given Tb  T .b /. It is usually called a Tb  Ts or Tb  Te relationship. Through Eq. (5), this gives us a relationship between L.b /  L and T .b / which is the outer boundary condition for the cooling code. Tb  Te relations have been derived for the unmagnetized envelope first by Gudmundsson et al. (1983). Gluing an envelope to an interior solution is a standard technique in stellar evolution codes. For neutron stars it has two extra advantages: it relieves from solving for hydrostatic equilibrium in the interior, since matter there is degenerate, and, most importantly, it allows magnetic field effects to be easily included.

2.5

Effects of a Magnetic Field and of the Composition of the Envelope

Given its enormous gravitational forces, a neutron star should be a perfect example for a perfectly spherically symmetric object in which the heat transfer should proceed purely radially: the temperature should be a function of the radial coordinate only. However, a generic feature of neutron stars is the presence of a strong, in many cases even huge, magnetic field that affects the internal heat flow. The magnetic field has at least, and seen from large distances, a dipolar geometry. In the case where the magnetic axis is inclined with respect to the axis of rotation, the temperature distribution becomes a function of the radial (r), the meridional ( ), and the azimuthal (') coordinate. There are, however, strong indications that the internal and the very surface magnetic field have to have higher multipolar components (quadrupole, octopole,. . . ). Additionally, the presence of small-scale, strong, and extremely localized magnetic spots seems to be an inevitable feature of

49 Thermal Evolution of Neutron Stars

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radio pulsars, for a period of at least 106:::7 year (Geppert and Viganò 2014). That is why magnetic field effects on the thermal evolution have to be discussed here. The magnetic field slightly enhances heat transport along it but strongly suppresses it in the perpendicular direction, resulting in a highly nonuniform surface temperature (Greenstein and Hartke 1983). Assuming that magnetic field effects on heat transport are negligible at  > b , one can keep spherical symmetry in the interior and thus has a unique Tb at b . For this given uniform Tb , one can also piece together a set of envelope calculations for the various field strengths and orientations along the stellar surface, corresponding to the assumed magnetic field structure, and thus obtain a nonuniform surface temperature distribution Ts . ; / (Page 1995; Page and Sarmiento 1996). The effective temperature is simply obtained by averaging the locally emerging photon flux F . ; /  SB Ts4 . ; / over the whole stellar surface: ZZ 1 4 Te  (7) Ts4 . ; / sin  d d  4

Two examples of such temperature distributions are illustrated in Fig. 4. The overall effect on Te is nevertheless relatively small, as long as the crust and the envelope can be treated as isothermal. Then the envelope is nonmagnetic actually to a rather good approximation. However, the assumption of spherical symmetry at  > b is questionable and will be discussed in Sect. 3. Given that the overall effect of the magnetic field in the envelope ( < b ) is moderate and well understood, a major uncertainty about the envelope is its chemical composition. The standard neutron star crust is made of cold catalyzed matter, which means 56 Fe at low density (  106 ). However, real neutron stars

Fig. 4 Two examples of surface temperature distributions induced by the magnetic field, in an area preserving projection of the neutron star surface (gray shading, shown on the right scale, follows the surface flux instead of the temperature). The left panel assumes a dipolar field, with strength 1:2  1012 G at the pole located at . ; / D .90ı ; 90ı /: for a core temperature of 4:05  107 K, it gives Te D 5:43  105 K (see Eq. 7), while the maximum and minimal surface temperatures, at the magnetic poles and along the magnetic equator, respectively, are Tmax D 6:70  105 K and Tmin D 1:4  105 K. The right panel shows the effect the same dipolar field to which a quadrupolar component has been added: this results in Te D 5:31  105 K. This particular latter case allows us to reproduce the observed ROSAT X-ray pulse profile of Geminga (see Fig. 6 in Page and Sarmiento 1996) which shows a single, very broad pulse while a purely dipolar field would result in a double-pulse profile (assuming the observer is in the direction  ' 90ı and emission is isotropic blackbody). Finally, in absence of magnetic field, the same internal temperature would result in Te D 5:54  105 K

1364

U.R.M.E. Geppert

may be dirty and have lighter elements at their surface. As was shown by Chabrier et al. (1997), the presence of light elements in the envelope strongly enhances heat transport (the electron thermal conductivity within liquid ions is roughly proportional to 1=Z, where Z is ion’s charge, Yakovlev and Urpin 1980). This results in a significantly higher Te , for the same Tb , than in the case of a heavy element envelope. Due to pycnonuclear fusion (fusion reactions caused by the density of the reactants), light elements are unlikely to be present at densities above 109 g cm3 . At very high Te , light elements have little effect, but for Te within the observed range (105  106 K), the low-density layer of the envelope can be easily contaminated with light elements, and the Tb  Te relationship can be significantly altered. If only a small amount of light elements is present at the surface, their effect will only be felt a low Te . Figure 5 shows the Tb  Te relationships for various amounts of light elements and also, for comparison, the case of a magnetized envelope with a relatively weak 1011 G dipolar magnetic field. For larger magnetic field strength, for example, radio pulsars (B  1013 G) or magnetars (B  1015 G), the field effect on the Tb Te relationship is much stronger. Then, significant differences between the surface temperatures at poles and equator arise, and it is worthwhile to show Tb  Ts relationships separately for the heat flux through the envelope parallel or perpendicular to the magnetic field lines instead of an averaged Tb  Te relation (see Sect. 3, Fig. 6).

Log η = −7 −9 −11 −13 −15 −17

Pure heavy elements envelope: B= 0 G B = 1011 G

Fig. 5 Relationship between the red-shifted effective temperature Te1 and the interior temperature Tb at the bottom of the envelope of a neutron star, assuming various amounts of light elements parameterized by   gs214 ML =M (ML is the mass in light elements in the envelope, gs 14 the surface gravity in units of 1014 cm s1 , and M is the star’s mass), in the absence of a magnetic field Potekhin et al. (1997). Also shown are the Tb Te1 relationships for an envelope of heavy elements with and without the presence of a dipolar field of strength of a relatively weak 1011 G following Potekhin and Yakovlev (2001). Notice that the smaller is ML , the lower is the temperature at which its effect is felt

49 Thermal Evolution of Neutron Stars

1365

Fig. 6 Ts as a function of Tb .b D 4  1011 g cm3 , neutron drip density) for two neutron star models with different field strengths. The thin dashed lines are analytical fits from Potekhin and Yakovlev (2001) for the magnetic field parallel and perpendicular to the normal direction to the surface. The thick dashes are result of a fit for the perpendicular case, the solid are result of a full numerical 2D model calculation for a dipolar field which include the effect of neutrino emission in the outer crust and envelope (Figures from Pons et al. (2009))

3

Magnetic Field Effects in the Crust

All the heat stored in the core of the neutron star and eventually irradiated away from its surface by photons has to be transported through the crust. In the absence of rotation and magnetic field, this transport in the stably stratified layers of the crust is spherically symmetric. While the effects of rotation are quite small even for millisecond pulsars, the presence of magnetic fields may cause significant deviations from the spherical symmetry of the transport processes, even for quite “standard” field strength of &1012 G. Due to the classical Larmor rotation of electrons, a magnetic field causes anisotropy of the heat flux since the heat conductivity becomes a tensor whose components perpendicular, ? , and parallel, k , to the field lines become ? D

0 1 C .B /2

and

k D 0

(8)

where 0 is the conductivity in absence of magnetic field, B the electron cyclotron frequency, and the collisional relaxation time of the electrons with ions (in the liquid crustal layers) or photons and impurities in the crystallized crust. In the neutron star crust, B  1 is easily realized, and, as a result, heat flows preferentially along the field lines. This effect is, moreover, amplified at the surface by the well-known non-isotropy in the envelope as described in Sect. 2.4. The anisotropic temperature distribution in the subjacent crust depends strongly on the

1366

U.R.M.E. Geppert 1.00000

1.00

0.99998

0.80

0.99997

0.60

0.99995

0.40

0.99993

0.20

Fig. 7 Representation of both field lines and temperature distribution in the crust (whose radial scale has been stretched by a factor 5 for clarity of the figure), assuming B0 D 3  1012 G and Tcore D 106 K. The neutron star considered here has a 1.4 Mˇ mass and a radius of 11 km. The left panel corresponds to a crustal field, the right panel to a star-centered core field. Bars show the temperature scales in units of Tcore (Figure from Geppert et al. (2004))

internal geometry of the field (Geppert et al. 2004, 2006; Page et al. 2007; PérezAzorín et al. 2006). While outside the star, the magnetic field may be described by a dipolar one; its internal structure can be qualitatively very different. A star’s centered dipolar field, which is in wide regions of the crust almost radial (“core field”), causes only small deviations from isothermal temperature even for extreme field strengths. On the contrary, a field maintained by currents circulating exclusively in the crust (“crustal field”) has strong meridional components which suppress the radial heat transport and channels the flux toward the magnetic poles. In Fig. 7, both the temperature distribution and the field lines in the crust for the two qualitatively different field configurations are shown. The drastic difference in the crustal temperature distribution for the different field structures, which are characterized by the same dipolar field structure and strength outside the neutron star, causes significant differences in the surface temperature distribution which will have several observational consequences: 1. A nonuniform surface temperature induces a modulation of the observed soft X-ray thermal emission. The stronger channeling of the heat flow toward the polar regions in the case of a crustal field will result in larger amplitude in the pulse profile. 2. This may open a new way to distinguish between crustal and core magnetic fields: A strong crustal magnetic field implies a smaller effective area for thermally emitting cooling neutron stars. The small effective emitting area inferred from the blackbody spectra of PSR 0656+14, PSR 1055–52, and Geminga (Becker and Truemper 1997), as well as the large pulsed fraction of the X-ray flux of the neutron star in Kes79 (Shabaltas and Lai 2012), could be explained by the existence of a relatively small warm polar region, created by a strong crustal field and emitting almost all the thermal radiation. 3. The differences in the photon luminosities for a core or a crustal field will also affect the long-term cooling of neutron stars. A neutron star having a magnetic

49 Thermal Evolution of Neutron Stars

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field confined to its crust will stay warmer for a longer time, due to its lower photon luminosity, compared to a neutron star with a field penetrating its core.

4

Heating Mechanisms

The expression “heating mechanism” refers to the term “H ” in Eq. (1) and generically encompasses all possible dissipative processes which will inject heat into the star by tapping into various forms of energy: magnetic (Sect. 4.1), rotational or chemical (Sect. 4.2).

4.1

Magnetic Field Decay and Joule Heating

Given that most neutron stars have strong magnetic fields, magnetic energy is a natural reservoir from which to extract heat by the Joule effect from the decaying electric currents. Assuming a uniform internal field of strength B D 1013 B13 G, one can roughly estimate an amount Emag 

B2 4 2  R3  2  1043 B13 erg 8 3

(9)

of stored magnetic energy. With a field decay timescale D 106 6 years, this gives us an equivalent “magnetic heating luminosity”: Hmag '

Emag B2  6  1029 13 erg s1 6

(10)

In case of magnetars, which are young neutron stars ( 6 . 0:1) with a magnetic field B13 & 100, Eq. 10 returns a magnetic heating luminosity 1035 erg s1 . This means that for this class of neutron stars, the thermal luminosity is dominated by Joule heating. Observational evidence for this heating process has been found by Pons et al. (2007) and Viganò et al. (2013). The natural interpretation of the diagram in Fig. 8, which shows the relation between observed temperature and magnetic field of 30 isolated neutron stars, is that stars with fields of 1012 G cool much more rapidly than stars with fields of 1013 G and higher. Obviously, the latter is kept hot by decay of their strong magnetic field. For “standard” neutron stars with magnetic fields 1012:::13 G, Joule heating may be important at late times, after 107 year. An unmagnetized neutron star would have at such old ages Te < 104 K. The decay of a 1013 G field, however, holds the star at Te  5  104 K for about 109 year (see Page et al. 2000). Heating by accretion onto a neutron star which accepts matter from a companion star in a binary system plays a crucial role in the formation of millisecond pulsars, whose rotational period is in the order of 0:001 s. They were first detected as radio pulsars (Backer et al. 1982) but are now observed too in X-rays (Becker and Trümper

1368

U.R.M.E. Geppert

Fig. 8 Te vs. dipolar polar surface field strength Bd of isolated neutron stars. Represented are magnetars (soft gamma repeaters (SGRs) as stars, anomalous X-ray pulsars (AXPs) as diamonds), slowly rotating (P > 3 s, squares), and rapidly rotating (P < 0:5 s, triangles) neutron stars. Red symbols indicate young ( 0:1 Mˇ , and the B-field reaches a minimum value, and keeps constant as B  108 G, where the magnetosphere approaches the NS radius. 4. The minimum magnetic field B  108 has nothing to do with the initial field value, because it is determined by the NS radius, not by the initial conditions. 5. The accretion rate MP plays a role in the B-field evolution, because the magnetospheric radius is inversely related to MP and proportionally related to the B-field. The decay process of the magnetosphere means that the ratio of the Bfield to MP evolves with the accretion mass. For the same magnetosphere, the larger accretion rate corresponds to a higher B-field. 6. The accretion flow enters the polar cap, and then moves out in two directions: the horizontal equatorial side and radially, deeper into the core. If the magnetic frozen efficiency is low, the horizontal flow does not bring sufficient flux to the equatorial region, where the field lines are squeezed radially into the deep core. Accretion must be funnelled into the polar cap, otherwise it will be uniform, and random accretion of matter has too low an efficiency to push the field lines, which would create the phenomenon that the NS B-field decays too little, even though it accretes a mass of 0.1–0.2 Mˇ . 7. The magnetic field structure in an MSP is likely to be complicated. Its polar field is low, and there is a strong field constructed beneath the equatorial region, interior to the crust, therefore a multiple field strength exists in MSPs. 8. The evolution of a NS in the B-P diagram has been simulated with various initial conditions in ZK06, with results that are consistent with the observations (Pan et al. 2015). The B-P distribution of an MSP is uniform, which is unlike its initial distribution. The implication is that the initial distribution is due to the effects of the initial fields, whereas the final distribution of the B-field of MSPs hints that the magnetosphere approaches the NS radius. However, the distribution of NS radii should be uniform, ranging from 10 to 15 km.

5

Conclusions

The accretion-induced B-field decay model (ZK06) presented the conclusions that the B-field of NS decays in the binary accretion phase, but then remains the same after the accretion stops. The influence of accretion on the MSP displays three aspects: B-field decay, spin-up, and a mass increase. These phenomena have been derived from the observations. In addition to the accretion mass, the accretion rate also plays a role when the accretion mass is over about 0.1 Mˇ . The MSP enters the lowest state, while the magnetosphere shrinks onto the NS surface. For the same NS magnetosphere, comparable in size to the NS radius, the higher accretion rate corresponds to a higher magnetic field. Moreover, the minimum field has nothing to do with the initial field, because it is determined by the final “boundary condition”,

50 Evolution of the Magnetic Field of Neutron Stars

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the NS radius, which may be the reason why most MSPs share similar B-field values, unlike the distribution of the initial field.

6

Cross-References

 Detecting Gravitational Waves from Supernovae with Advanced LIGO  Neutron Stars as Probes for General Relativity and Gravitational Waves  Nuclear Matter in Neutron Stars  The Masses of Neutron Stars  Thermal Evolution of Neutron Stars Acknowledgements This work was supported by the National Natural Science Foundation of China (NSFC 11173034) and the National Basic Research Program of China (2012CB821800).

References Alpar MA, Cheng AF, Ruderman MA, Shaham J (1982) A new class of radio pulsars. Nature 300:728 Bhattacharya D, van den Heuvel EPJ (1991) Formation and evolution of binary and millisecond radio pulsars. Phys Rep 203:1 Blandford RD et al (1983) Thermal origin of neutron star magnetic fields. MNRAS 204:1025 Blondin JM, Freese K (1986) Is the 1.5-ms pulsar a young neutron star? Nature 323:786 Braithwaite J, Spruit HC (2004) A fossil origin for the magnetic field in A stars and white dwarfs. Nature 431:819 Burderi L, Di Salvo T (2013) On low mass X-ray binaries and millisecond pulsar. MmSAI 84:117 Caballero I, Wilms J (2012) X-ray pulsars: a review. MmSAI 83:230 Camilo F, Thorsett SE, Kulkarni SR (1994) The magnetic fields, ages, and original spin periods of millisecond pulsars. ApJ 421:L15 Coburn W, Heindl WA, Gruber DE et al (2001) Discovery of a cyclotron resonant scattering feature in the Rossi X-ray timing explorer spectrum of 4U 0352+309 (X Persei). ApJ 552:738 Cumming A (2004, to appear) Magnetic field evolution during neutron star recycling. In: Rasio FA, Stairs IH (eds) Binary radio pulsars, Aspen. ASP conference series. astro-ph/0404518 Cumming A et al (2001) Magnetic screening in accreting neutron stars. ApJ 557:958 Frank J, King A, Raine DJ (2002) Accretion power in astrophysics. Cambridge University Press, Cambridge Geppert U, Urpin V (1994) Accretion-driven magnetic field decay in neutron stars. MNRAS 271:490 Ghosh P, Lamb FK (1979) Accretion by rotating magnetic neutron stars. III-accretion torques and period changes in pulsating X-ray sources. ApJ 234:296 Konar S, Choudhury A (2004) Diamagnetic screening of the magnetic field in accreting neutron stars – II. The effect of polar cap widening. MNRAS 348:661 Kulkarni SR (1986) Optical identification of binary pulsars – implications for magnetic field decay in neutron stars. ApJ 306:L85 Lamb FK, Yu W (2005) Spin rates and magnetic fields of millisecond pulsars. In: Rasio FA, Stairs IH (eds) Binary radio pulsars, Aspen. ASP conference series, vol 328, n 299 Lorimer DR (2008) Living reviews of relativity, vol 11, no 8. http://relativity.livingreviews.org/ Articles/lrr-2008-8/

1384

C.M. Zhang

Lovelace RV, Romanova MM, Bisnovatyi-Kogan GS (2005) Screening of the magnetic field of disk accreting stars. ApJ 625:957. astro-ph/0508168 Lyne AG et al (2004) A double-pulsar system: a rare laboratory for relativistic gravity and plasma physics. Science 303:1153 Makishima K et al (1999) Cyclotron resonance effects in two binary X-ray pulsars and the evolution of neutron star magnetic fields. ApJ 525:978 Manchester RN, Hobbs GB, Teoh A, Hobbs M (2005) The Australia telescope national facility pulsar catalogue. AJ 129:4 Melatos A, Phinney ES (2001) Hydromagnetic structure of a neutron star accreting at its polar caps. Publ Astron Soc Aust 18:421 Pan YY, Wang N, Zhang CM (2013) Binary pulsars in magnetic field versus spin period diagram. Ap&SS 346:119 Pan YY, Song LM, Zhang CM, Guo YQ (2015) The simulation of the magnetic field and spin period evolution of accreting neutron stars. Astron Nachr 336:370 Papitto A, Torres DF, Rea N, Tauris T (2014) Spin frequency distributions of binary millisecond pulsars. A&A 566:64 Payne D, Melatos A (2004) Burial of the polar magnetic field of an accreting neutron star-I. Selfconsistent analytic and numerical equilibria. MNRAS 351:569 Phinney ES, Kulkarni SR (1994) Binary and millisecond pulsars. ARA&A 32:591 Ruderman M (2010) Causes and consequences of magnetic field changes in neutron stars. NewAR 54:110 Shapiro SL, Teukolsky SA (1983) Black holes, white dwarfs and neutron stars. Wiley, New York Shibazaki N, Murakami T, Shaham J, Nomoto K (1989) A unified model of neutron-star magnetic fields. Nature 342:656–658 Taam RE, van den Heuvel EPJ (1986) ApJ 305:235 Tauris TM (2015) Millisecond pulsars in close binaries. arXiv:1501.03882 Tauris TM, Langer N, Kramer M (2012) MNRAS 425:1601 Thompson C, Duncan R (1993) ApJ 408:194 Truemper J et al (1978) ApJ 219L:105 van den Heuvel EPJ (2004) Science 303:1143 Wijnands R, van der Klis M (1998) Nature 394:344 Zhang CM (2004) A&A 423:401 Zhang CM, Kojima Y (2006) MNRAS 366:137 Zhang CM et al (2011) A&A 527:83

X-Ray Pulsars

51

Roland Walter and Carlo Ferrigno

Abstract

X-ray pulsars shine thanks to the conversion of the gravitational energy of accreted material to X-ray radiation. The accretion rate is modulated by geometrical and hydrodynamical effects in the stellar wind of the pulsar companions and/or by instabilities in accretion disks. Wind-driven flows are highly unstable close to neutron stars and responsible for X-ray variability by factors &103 on time scale of hours. Disk-driven flows feature slower state transitions and quasiperiodic oscillations related to orbital motion and precession or resonance. On shorter time scales, and closer to the surface of the neutron star, X-ray variability is dominated by the interactions of the accreting flow with the spinning magnetosphere. When the pulsar magnetic field is large, the flow is confined in a relatively narrow accretion column, whose geometrical properties drive the observed X-ray emission. In low magnetized systems, an increasing accretion rate allows the ignition of powerful explosive thermonuclear burning at the neutron star surface. Transitions from rotation- to accretion-powered activity has been observed in rare cases and proved the link between these classes of pulsars.

Contents 1 2

3 4 5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wind-Driven Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Classical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Systems Close to Roche-Lobe Overflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Be X-Ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Disk-Driven Accretion Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accretion Column in Highly Magnetized Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Low Magnetized Systems and Accreting Millisecond Pulsars . . . . . . . . . . . . . . . . . . . .

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R. Walter () and C. Ferrigno ISDC, Geneva Observatory, University of Geneva, Versoix, Switzerland e-mail: [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_74

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6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Accreting binaries ( Chap. 56, “X-Ray Binaries”) are among the brightest X-ray point sources of our Galaxy and the first ones to be detected in the early days of X-ray astronomy (Giacconi et al. 1964). Their X-ray emission originates from the dissipation of gravitational energy in material accreted from a companion star to a compact object. A large fraction of the brightest X-ray binaries harbor neutron stars, known as “accreting pulsars” or “X-ray pulsars.” Neutron stars are the remnants of supernova explosion and are unique laboratories for the study of extreme densities, momentum, gravity, and magnetic fields. Understanding them requires all fields of modern physics: plasma physics, electrodynamics, magnetohydrodynamics, general relativity, and quantum physics (Chaps.  49, “Thermal Evolution of Neutron Stars”,  53, “Strange Quark Matter Inside Neutron Stars”,  54, “Neutron Stars as Probes for General Relativity and Gravitational Waves”). X-ray binaries are the result of complex evolutionary scenarios ( Chap. 57, “Supernovae and the Evolution of Close Binary Systems”) established using the full arsenal of stellar evolution, supernova explosions, exchange, and accretion processes. The neutron star magnetic field ( Chap. 50, “Evolution of the Magnetic Field of Neutron Stars”) and surface play key roles to determine how matter is accreted and where energy is dissipated. The pulsar magnetosphere dominates the flow of the accreted material within the Alfvén surface, where the bulk kinetic energy density of the gas is comparable to that of the magnetic field. This surface depends on the geometry of the magnetic field, of the accreting flow and of their interaction. Its characteristic size is a hundred times larger than the neutron star for a magnetic field of 1012 G and a luminosity reaching a fraction of the Eddington limit and can reach the surface of the neutron star when the magnetic field is below 108 G. An offset between rotation and magnetic axes is required to obtain the flux modulation characterizing bright X-ray pulsars. High (101114 G) surface magnetic fields are detected in young (106 y) highmass X-ray binaries (HMXB) with massive, O- and B-type, stellar companions (but see the peculiar Her X-1 with a magnetic field of 1012 G and a 2 Mˇ companion; Truemper et al. 1978). Low surface magnetic fields (. 1010 G) are present in old binary systems with low-mass (. 1 Mˇ ) companions (LMXB). HMXBs are concentrated in the galactic arms, close to their birthplace. LMXBs populate the bulge of the Galaxy and globular clusters, where they can also form through stellar capture. The Milky Way contains about 130 and 180 bright (>1035 erg/s) high- and low-mass X-ray binaries, respectively (Liu et al. 2007; Walter et al. 2015). The brightest sources dominate the X-ray emission of the Galaxy at a level of 1038 and

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1039 erg s1 for the high- and low-mass systems. HMXBs and the hot interstellar gas dominate the X-ray luminosity of star-forming galaxies, a tracer of their stellar formation rate (Grimm et al. 2003; Mineo et al. 2012). In this chapter, we will concentrate on the accretion flows driving X-ray variability (Sects. 2 and 3) and on the mechanisms driving X-ray emission in the direct vicinity of the pulsars (Sects. 4 and 5).

2

Wind-Driven Flows

In HMXBs, the pulsar attracts a small fraction of the stellar wind of its companion (Bondi and Hoyle 1944; Davidson and Ostriker 1973). In classical wind accreting systems, Bondi-Hoyle accretion takes place along the neutron star orbit, and the accretion rate remains usually low. High accretion rates are expected in close systems, where the companion is practically filling its Roche lobe. The wind is then focused through a tidal stream and, if its angular momentum is large enough, a transient accretion disk structure may form. Roche-lobe overflow from a high-mass companion is rarely observed, as the compact object is quickly enshrouded by the atmosphere of its companion. Flares reaching the Eddington luminosity occur when the compact object crosses a dense component of the stellar wind, usually expelled by a fast-rotating main sequence star, featuring emission lines in the optical band. These systems are identified as “Be X-ray binaries”.

2.1

Classical Systems

The instantaneous X-ray luminosity of an accreting pulsar with moderate magnetic field (1012 G) in a HMXB system is mostly determined by the density and velocity of the stellar wind close to the compact object. The amplitude of the X-ray variability is determined by the pulsar orbital eccentricity, clumping, and variability of the stellar wind and by hydrodynamical effects induced by the gravity and photoionization of the neutron star. The variability of the accretion rate by a factor of 10–100 in wind-fed systems in circular orbits was successfully explained by hydrodynamical simulations (Blondin et al. 1990). Manousakis and Walter (2015a) have included the effect of photoionization on the wind acceleration and could probe the dynamic of the region surrounding the neutron star and, in particular, the collision between the primary stellar wind, slowed down by photo-ionization and a gas stream flowing back inward from above the neutron star. As shown in Fig. 1, a shock front is generated, moving inward and outward regularly and creating low-density bubbles, i.e., periods of very low X-ray luminosity. This generates instantaneous accretion rates varying by 103 and transient modulations similar to these observed in Vela X-1 (Kreykenbohm et al. 2008). This back and forth shock motion occurs high above the magnetosphere

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Fig. 1 Wind flow in the classical system Vela X-1. The wind acceleration parameters were adjusted to obtain a perfect agreement with the X-ray flux observed on average before, during, and after the neutron star eclipse by the companion. Axes are labeled in units of 1012 cm. The color scale maps the density from 1015 (blue) to 1013 (red) g cm3 (Simulation from Manousakis and Walter 2015b)

and can be amplified further by an induced change of geometry of the accretion column. Shakura et al. (2013) have shown that two regimes of subsonic accretion are possible at the boundary of the magnetosphere depending on whether or not the plasma is cooled by Compton processes (high vs. low accretion rate). At lower luminosity, X-ray photons are emitted perpendicular to the neutron star surface, inverse Compton cooling is less efficient, and a change of the X-ray spin modulation of the light curve is expected (Doroshenko et al. 2011). Grebenev and Sunyaev (2007) suggested that high variability factors could be generated by Kelvin-Helmholtz instability at the magnetospheric boundary, leading to a magnetic gating of the accretion flow. This requires large magnetic fields (>1013 G) which are contrasting with the observations (Bhalerao et al. 2015). It is unclear if magnetic gating is at play in HMXBs. The comparison of hydrodynamical simulations and X-ray observations allow to probe the stellar wind velocity and density fields (Manousakis and Walter 2015b). GX 3012 and OAO 1657415 feature peculiar variability patterns that could be related to the accretion of dense streams and large-scale structures in the wind of their massive companions. Long-term modulation of the accretion rate along the orbit because of eccentricity is observed in addition in several systems.

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Systems Close to Roche-Lobe Overflow

When the companion star in a HMXB gets closer to Roche-lobe overflow, a tidal stream develops, focuses the wind, and increases the wind density close to the compact object and the X-ray luminosity (Blondin et al. 1991). Enhanced obscuration by the stream trailing the neutron star is observed first at late orbital phases and covering more and more of the orbit when the neutron star gravity becomes dominant. Once the companion is close to overflowing its Roche lobe, deep spiral-in is unavoidable (van den Heuvel and De Loore 1973) and results in a common envelope phase (Taam and Sandquist 2000). Five supergiant HMXBs feature persistently high obscuration (NH > 1023 cm2 ) and short orbital periods. They all reach X-ray high luminosities >1036 erg/s. Two obscured systems have longer orbital periods (10 days), and in these cases the obscuration is probably driven by unusually low wind velocity or by the environment. It is plausible, therefore, to assume that obscured sgHMXBs are classical systems in transition to Roche-lobe overflow or with relatively low velocity winds. As neutron stars can cut off wind acceleration via ionization (Stevens and Kallman 1990), the wind of their companions can be slower on average than in isolated stars. Supergiant fast X-ray transients were identified as a new class of sources. These hard X-ray transients produce short and bright flares with typical durations of a few ksec. Further analysis indicates that many of them could be interpreted as classical or eccentric systems (Walter et al. 2015). Four of them are really peculiar: they have short orbital periods (3–6 days), so should be close to Roche-lobe overflow, but feature anomalously low luminosities ( 12Mˇ stars. Conservation of the magnetic flux gives an estimation of the NS magnetic field as Bns D Bs .Rs =Rns /2 , Bs D 10 to 100 Gs, at R  .3 to 10/Rˇ ; Rns D 10 km, Bns D 4  1011 to 5  1013 Gs (Ginzburg 1964). Estimation of the NS magnetic field is obtained in radio pulsars by measurements of their rotational period and its time derivative, in the model of a dipole radiation, or pulsar wind model, as (E, I , and  are NS rotational energy, moment of inertia, and rotational angular velocity, respectively): Erot D 0:5I 2 ;

EP rot D AB 2 4 ;

B D IP PP =4A 2 ;

A D R6 =6c 3 ;

(1)

B is a NS surface dipole magnetic field at its magnetic pole. Timing observations of single radio pulsars (the rapidly rotating ones connected with young supernova remnants are marked in Fig. 1 by a star) give the estimate: Bns D 2  1011 to 5  1013 Gs (Lorimer 2005). The pulsars with a small magnetic field in the lower left region of Fig. 1 are a result of the field decreasing during recycling by accretion in a close binary (see Bisnovatyi-Kogan (2006)). SGR are single neutron stars with periods 2 to 8 s that produce ‘giant bursts’, with luminosities at peak increasing by 5 to 6 orders of magnitude. Having a slow rotation, and small rotational energy, their observed average luminosity exceeds their loss of rotational energy by more than tenfold, and orders of magnitude during the giant outbursts. It was suggested by Duncan and Thompson (1995) that the source of energy is their huge magnetic field, two or three orders of magnitude larger than the average field in radio pulsars. Such objects are called magnetars .

2

SGR, Giant Bursts, and Short GRB

The first two soft gamma repeaters (SGR) were discovered by the KONUS group in 1979. The KONUS instrument was a Russian gamma ray monitor launched on Russian interplanetary stations Venus-11 - Venus-14 in years 1978 - 1983. The first one, FXP 0520-66, was discovered after the famous giant 5 March 1979 burst

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Fig. 1 P - PP diagram for radio pulsars. Pulsars in binary systems with low-eccentricity orbits are encircled, and in high-eccentricity orbits are marked with ellipses. Stars show pulsars suspected to be connected with supernova remnants (From Lorimer 2005)

(Golenetskii et al. 1979; Mazets et al. 1979b, c); see also Mazets et al. (1982). In another source B1900+14, only small recurrent bursts were observed (Mazets et al. 1979a). Now these sources are known under the names SGR 0520-66 and SGR 1900+14, respectively. The third SGR 1806-20 was identified as a repetitive source by Laros et al. (1986a, b). The first detection of this source as a gamma ray burster (GRB), GRB070179 was reported by Mazets et al. (1981), and it was indicated by Mazets et al. (1982) that this source, having an unusually soft spectrum, might belong to a separate class of repetitive GRB, similar to FXP 052066 and B1900+14. This suggestion was completely confirmed. The fourth known SGR1627-41, showing giant bursts, was discovered in 1998 almost simultaneously by BATSE (Kouveliotou et al. 1998a), and BeppoSAX (Feroci et al. 1998). To date giant bursts have been observed in four sources.

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SGR0526-66

This source was discovered due to a giant burst on 5 March 1979, projected to the edge of the SNR N49 in the Large Magellanic Cloud (LMC), and described by Mazets et al. (1979a, c), Golenetskii et al. (1979), and Mazets et al. (1982). Accepting the distance of 55 kpc to the LMC, the peak luminosity in the region E > 30 keV was Lp 3:6  1045 ergs/s, the total energy release in the peak Qp 1:61044 ergs, in the subsequent tail Qt D 3:61044 ergs. The short recurrent 41 bursts have peak luminosities in the region of Lrec  3  1042 ergs/s, p D 3  10 rec 40 42 and energy release Q D 5  10  7  10 ergs. The tail was observed for about 3 min and had regular pulsations with the period P  8 s. There was no chance to measure PP in this object.

2.2

SGR1900+14

Detailed observations of this source are described by Mazets et al. (1999b, c), Kouveliotou et al. (1999), and Woods et al. (1999). The giant burst was observed on 27 August, 1998. The source lies close to the less than 104 -year-old SNR G42.8 C 0.6, situated at a distance of 10 kpc. Pulsations were observed in the giant burst, as well as in the X-ray emission observed in this source in quiescence by RXTE and ASCA. PP was measured, being strongly variable. Accepting the distance of 10 kpc, in the gamma ray band E > 15 keV this source had: D Lp > 3:7  1044 ergs/s, Qp > 6:8  1043 ergs, Qt D 5:2  1043 ergs, Lrec p 2  1040  4  1041 ergs/s, Qrec D 2  1039  6  1041 ergs, P D 5:16 s, PP D 5  1011  1:5  1010 s/s. The X-ray pulsar in the error box of this source was discovered by Hurley et al. (1999b). This source was also discovered in the radio band, at frequency 111 MHz as a faint, Lmax D 50 mJy, radio pulsar (Shitov r 1999), with the same P and variable PP , in good agreement with X-ray and gamma ray observations. The values of P and average PP correspond to a rate of loss of rotational energy EP rot D 3:5  1034 ergs/s, and magnetic field B D 8  1014 Gs. The age of the pulsar estimated as p D P =2PP D 700 years is much less than the estimated age of the close nearby SNR. Note that the observed X-ray luminosity of this object Lx D 2  1035  2  1036 ergs/s is much higher than the rate of a loss of rotational energy, meaning that rotation cannot be the main source of energy in these objects. It was suggested that the main source of energy comes from a magnetic field annihilation, and such objects had been called magnetars by Duncan and Thompson (1992). The light curve of the giant burst is given in Fig. 2.

2.3

SGR1806-20

The giant burst from this source was observed on 27 December 2004 (Frederiks et al. 2007a; Mazets et al. 2005; Palmer et al. 2005). Recurrent bursts had been studied by Kouveliotou et al. (1998b) and Hurley et al. (1999a). Connection with the

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5 7

5

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Fig. 2 The giant 27 August 1998 outburst of the soft gamma repeater SGR1900 C 14. Intensity of the E > 15 keV radiation is presented (From Mazets et al. 1999c)

galactic radio SNR G10.0-03 was suggested. The source has a small but significant displacement from the nonthermal core of this SNR. The distance to the SNR is estimated as 14.5 kpc. The X-ray source observed by ASCA and RXTE in this object shows regular pulsations with a period P D 7:47 s, and average PP D 8:31011 s/s. As in the previous case, it leads to the pulsar age p  1500 years, much smaller than the age of the SNR, estimated at 104 years. These values of P and PP correspond to B D 8  1014 Gs. PP is not constant. A uniform set of observations by RXTE gave a much smaller and less definite value PP D 2:8.1:4/1011 s/s; the value in brackets 41 gives 1 error. The peak luminosity in the burst reaches Lrec p  10 ergs/s in the bandpass 25–60 keV, the X-ray luminosity in 2–10 keV band is Lx  21035 ergs/s is also much higher than the rate of the loss of rotational energy (for average PP ) EP rot  1033 ergs/s. The burst of 27 December 2004 in SGR 1806-20 was the greatest flare, 100 times brighter than ever (Fig. 3). It was detected by many satellites: Swift, RHESSI, KONUS-Wind, Coronas-F, Integral, and HEND among others. The very strong luminosity of this outburst permitted observation of the signal, reflected from the Moon by the Helicon instrument on board the satellite Coronas-F. The position of satellites Wind and Coronas-F relative to the Earth and Moon during the outburst are given in Fig. 4, and the reconstructed full-light curve of the outburst is given in Fig. 5 from Mazets et al. (2005) and Frederiks et al. (2007a).

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Deadtime-corrected count rate (s-1)

107

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105

104 -0.2

0.0

0.2

0.4

0.6

0.8

Time (seconds)

Fig. 3 SWIFT light curve of the giant burst of 27 December, 2004 giant burst in SGR 1806-20 (From Palmer et al. 2005)

Fig. 4 The position of satellites Wind and Coronas-F relative to the Earth and Moon during the outburst of SGR 1806-20 (From Mazets et al. 2005 and Frederiks et al. 2007b)

Young Neutron Stars with Soft Gamma Ray Emission and. . .

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T - T0 (s) Fig. 5 Reconstructed profile of the early part of the pulse from SGR 1806-20. The upper part of the graph is derived from Helicon data and the lower part represents the KONUS-Wind data. The dashed lines indicate intervals where the outburst intensity still saturates the KONUS-Wind detector, but is not high enough to be seen by the Helicon (From Mazets et al. 2005 and Frederiks et al. 2007b)

2.4

SGR1627-41

A giant burst was observed from this source on 18 June 1998, in addition to numerous soft recurrent bursts. Its position coincides with the SNR G337.0-0.1, assuming 5.8 kpc distance. Some evidence was obtained for a possible periodicity of 6.7 s, but the giant burst did not show any periodic signal (Mazets et al. 1999a), contrary to three other giant bursts in SGR. The following characteristics were observed with a time resolution 2 ms at photon energy E > 15 keV: Lp 

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8  1043 ergs/s, Qp  3  1042 ergs, no tail of the giant burst was observed. D 4  1040  4  1041 ergs/s, Qrec D 1039  3  1040 ergs. Periodicity Lrec p in this source is not certain, so there is no PP .

2.5

SGR Giant Bursts in Other Galaxies

The similarity between giant bursts in SGR, and short GRB was noticed by Mazets et al. (1999c) and Bisnovatyi-Kogan (1999). The experiment KONUS-Wind had observed two short GRB, interpreted as giant bursts of SGR. The first one, GRB070201, was observed in M31 (Andromeda), 1 February 2007. The energy of the burst is equal to 1  1045 erg , consistent with giant bursts of other SGR (Mazets et al. 2008). The second short burst, GRB051103, was observed in the galaxy M81, 3 November 2005. The energy of the burst is equal to 7  1046 erg (Frederiks et al. 2007a; Golenetskii et al. 2005).

3

Estimations of the Magnetic Fields in SGR/AXP

Despite the fact that rotation energy losses are much smaller than the observed luminosity, estimates of the magnetic field strength in these objects used the same procedure as in radio pulsars, based on measurements of P and PP , and using (1). The first measurements have been done for SGR 1900C14, in different epochs by measurements of satellites RXTE and ASCA (Kouveliotou et al. 1999), presented in Figs. 6, 7, and 8.

Fig. 6 The epoch folded pulse profile of SGR 1900C14 (2–20 keV) for the May 1998 RXTE observations (From Kouveliotou et al. 1999)

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Fig. 7 The epoch folded pulse profile of SGR 1900C14 (2–20 keV) for the 28 August 1998 RXTE observation. The plot is exhibiting two phase cycles (From Kouveliotou et al. 1999)

Fig. 8 The evolution of ‘period derivative’ versus time since the first period measurement of SGR 1900+14 with ASCA in Hurley et al. (1999b). The time is given in modified Julian days (MJDs) (From Kouveliotou et al. 1999)

The pulse shape changes from one epoch to another, inducing errors in finding the derivative of the period. The big jump in PP , visible in Fig. 8 looks surprising for magnetic dipole losses, because it needs a considerable jump in the magnetic field strength, prohibited by self-induction effects. On the other hand, in the model of

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Fig. 9 SGR 1806-20 Spectrum and best-fit continuum model for the second precursor interval with four absorption lines (RXTE/PCA 2–30 keV) (From Ibrahim et al. 2002)

pulsar wind rotational energy losses it looks quite reasonable: these losses strongly increased during the giant burst when the PP jump was observed. Further evidence in favour of the magnetar magnetic field was connected with the absorption lines in the spectrum of SGR 1806-20, observed by RXTE in November 1996 (Ibrahim et al. 2002). The main line (shown in Fig. 9) corresponds to a magnetic field of .5 to 7/  1011 Gs, when interpreted as an electron cyclotron line. In order to preserve the magnetar model, the authors Ibrahim et al. (2002) suggested that this line is connected with the motion of protons, increasing the magnetic field estimation almost 2000 times. The large increase of magnetic field is associated, however, with a drastic, 4106 , decrease in the absorption crosssection, compared to the electron cyclotron line. Therefore, if this cyclotron line is real, its connection with the proton is very improbable.

4

Radio Pulsars with Very High Magnetic Fields and Slow Rotation

Radio pulsars are rotating neutron stars that emit beams of radio waves from regions above their magnetic poles. Popular theories of the emission mechanism require continuous electron-positron pair production, with the potential responsible for accelerating the particles being inversely related to the spin period. Pair production will stop when the potential drops below a threshold, therefore the models predict that radio emission will cease when the period exceeds a value that depends on the magnetic field strength and configuration. It was shown by Young et al. (1999a, b)

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that the pulsar J2144–3933, previously thought to have a period of 2.84 s, actually has a period of 8.51 s, which is by far the longest of any known radio pulsar. Moreover, under the usual model assumptions, based on the neutron-star equations of state, this slowly rotating pulsar should not be emitting a radio beam. Therefore either the model assumptions are wrong, or current theories of radio emission must be revised. The period 8.51 s is characteristic for SGR/AXP objects, but this pulsar does not show any violent behaviour, and behaves like an ordinary radio pulsar. Soon after this discovery, several other radio pulsars were found, where also PP , and therefore magnetic field strength was measured (Camilo et al. 2000; Manchester et al. 2001; McLaughlin et al. 2003, 2004). These pulsars include: 1. PSR J1119–6127, P D 0.407 s, PP D 4:0  1012 s/s, B D 4:1  1013 G; 2. PSR J1814–1744, P D 3.975 s, PP D 7:4  1013 s/s, B D 5:5  1013 G; Camilo et al. (2000) stressed, that radiopulsars PSR J1119–6127 and PSR J1814– 1744 show normal radio emission in a regime of magnetic field strength where some models predict that no emission should occur. PSR J1814–1744 has spin parameters similar to the anomalous X-ray pulsar (AXP) IE 2259C586, but shows no visible X-ray emission. If AXPs are isolated, high magnetic field neutron stars (“magnetars”), these results suggest that their unusual properties are unlikely to be just a consequence of their very high magnetic fields. 3. PSR J1847–0130, P D 6.7 s, PP D 1:3  1012 s/s, B = 9:4  1013 G. McLaughlin et al. (2003) noted, that the properties of this pulsar prove that dipolar magnetic field strength and period cannot explain the unusual high-energy properties of the magnetars what creates challenges for understanding the possible relationship between these two manifestations of young neutron stars. 4. PSR J1718–37184, P D 3.4 s ,

B D 7:4  1013 G.

These fields are similar to those of the anomalous X-ray pulsars (AXPs), suggested as. The lack of AXP-like X-ray emission from these radio pulsars, non-detection of radio emission from most AXPs indicates incompleteness of our understanding of the mechanisms of both radio pulsars and AXPs emission.

5

SGR/AXP with Low Magnetic Fields and Moderate Rotation

SGR/AXP J15505418 (1E 1547.05408) was visible in radio waves, showing pulsations with a period P D 2:069 s (Camilo et al. 2007). Pulsations with the same period were observed in the soft X-ray band by XMM-Newton (Halpern et al. 2008). In the strong outbursts in October 2008 and in January and March 2009, observed by the Fermi gamma ray burst monitor, the period of 2.1 s was clearly visible up to

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the energy 110 keV (Kaneko et al. 2010). The INTEGRAL detected pulsed soft gamma rays from SGR/AXP 1E1547.0–5408 during its January 2009 outburst, in the energy band 20 to 150 keV, showing a periodicity with P D 2.1 s (Kuiper et al. 2009). This object is the only SGR/AXP with a relatively low period; all previous ones have periods exceeding 4s. A low-magnetic-field SGR0418C5729 was detected by the Fermi gamma ray burst detector (Rea et al. 2010). This soft gamma repeater with low magnetic field SGR0418+5729 was recently detected after it emitted bursts similar to those of magnetars. X-ray observations show that its dipolar magnetic field cannot be greater than 7:5  1012 Gauss, well in the range of ordinary radio pulsars, what means, that a high surface dipolar magnetic field is not required for magnetar-like activity.

6

The Magnetar Model

In the paper of Duncan and Thompson (1992) it was claimed that the dynamo mechanism in the newborn rapidly rotating star may generate neutron stars (NS) with a very strong magnetic field 1014 to 1015 G, called magnetars. These magnetars could be responsible for cosmological GRB, and may represent a plausible model for SGR as well as for superluminous Type Ia SNe. In a subsequent paper (Duncan and Thompson 1995) the connection between magnetars and SGR was developed in more detail. The authors presented a model for SGR and the energetic 5 March 1979 burst, based on the existence of neutron stars with magnetic fields much stronger than those of ordinary pulsars. They presented the following arguments which point to a neutron star with B(dipole) of 5  1014 G as the source of the 5 March event (Duncan and Thompson 1995). 1. The existence of such a strong magnetic field may spin down the star to 8 s period in  104 year, which is the age of the surrounding supernova remnant N49. 2. Such a strong magnetic field provides enough energy for the 5 March event. 3. In the presence of such a magnetic field a large-scale interchange instability is developed with a growth time comparable to the 0.2 s, close to the width of the initial hard transient phase of the March 5 event. 4. A very strong magnetic field can confine the energy that was radiated in the soft tail of that burst. 5. A very strong magnetic field can reduce the Compton scattering cross-section sufficiently to generate a radiative flux that is 104 times the (nonmagnetic) Eddington flux. 6. The field decays significantly in 104 to 105 year, as is required to explain the activity of soft gamma repeater sources on this time-scale. 7. The field powers the quiescent X-ray emission LX  7  1035 erg s1 observed by Einstein and ROSAT, as it diffuses the stellar interior. It is proposed that the 5 March 1979 event was triggered by a large-scale reconnection/interchange instability of the stellar magnetic field, and the soft repeat bursts are produced at cracking of the crust.

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These suggestions were justified only by semi-qualitative estimations. Subsequent observations of P and PP in several SGR (McGill 2014) seem to support this model. However, when the rotation energy losses are much less than observed X-ray luminosity, B estimations using PP are not justified, because the magnetic stellar wind could be the main mechanism of angular momentum losses. The jump in PP observed in the giant burst of PSR1900+14 (Fig. 8) is plausibly explained by a corresponding increase of the magnetic stellar wind power, whereas a jump in the dipole magnetic field strength is hardly possible. The jumps in PP , as well as in the pulse form (Figs. 6 and 7) have not been seen in radio pulsars. In the fallback accretion model of SGR (Alpar 2001; Chatterjee et al. 2000; Trümper et al. 2010, 2013) the estimates of the magnetic field using P and PP give the values characteristic for usual radio pulsars, when there is a presence of a largescale magnetic field in the fallback accretion disk (Bisnovatyi-Kogan and Ikhsanov 2014). When the energy density of the magnetic field is much larger than that of matter, as expected in the surface layers of the magnetar, the instability should be suppressed by magnetic forces. The observations of radio pulsars, showing no traces of bursts, with magnetar magnetic fields and slow rotation (Sect. 4), detection of SGR with a small rotational period and low magnetic field, estimated from P and PP values similar to radio pulsars (Sect. 5), give a strong indication that inferred dipolar magnetic field strength and period cannot alone be responsible for the unusual high-energy properties of SGR/AXP. Therefore, another characteristic parameter should be responsible for the violent behaviour of SGR/AXP. An unusually low mass of the neutron star was suggested by Bisnovatyi-Kogan (2012, 2016) as a parameter, distinguishing SGR/AXP neutron stars from the majority of neutron stars in radio pulsars and close X-ray binaries.

6.1

Angular Momentum Losses by a Magnetised Stellar Wind

A magnetic stellar wind carries away the stellar angular momentum J as (Weber and Davis 1967) 2 JPwi nd D MP rA2 ; 3

(2)

Here rA is the Alfven radius, where the energy density of the wind Ew is equal to the magnetic energy density EB D B 2 =.8 /. We consider the wind with a constant outflowing velocity w, the energy density of which is Ew D 0:5w2 . In a stationary wind with a mass loss rate MP the density is equal to

D

MP : 4 wr 2

(3)

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For the dipole stellar field we have B D =r 3 , where  D Bs r3 is the magnetic dipole moment of the star. At the Alfven radius we have A D

MP ; 4 wrA2

EwA D

MP w ; 8 rA2

EBA D

2 : 8 rA6

(4)

From the definition of the Alfven radius rA we obtain its value as rA4 D

EwA D EBA ;

2 : MP w

(5)

The angular momentum of the star J D I , and when the wind losses (2) are the most important, we obtain the value of stellar magnetic field as 2 Bwi nd D

P 2w 9 I 2 : 4 2 MP r6

(6)

The angular momentum and energy losses by the dipole radiation which are main losses in ordinary radio pulsars are written as (Pacini 1967) LD

Bs2 4 r6 ; c3

P D L; EP D I 

L JPPRS D : 

(7)

We obtain from (7) the magnetic field if the dipole radiation losses are the most important 2 BPSR D

P 3Ic 3  : 3 2 r6

(8)

The ratio of these two values is written as 2 BPSR 2c 3 MP 4 Fwi nd  c 3 4 MP w2 =2  c 3 D D : D 2 P P 3 I  w 3 EP rot w Bwi 3I w nd

(9)

Here Fwi nd is the energy flux carried away by the wind, and EP rot is the rate of the loss of rotational energy. As an estimate of the energy flux carried away by the wind the average X and  -ray luminosity of SGR/AXP Lx could be used and the wind velocity is of the order of the freefall velocity of q the neutron star. For the low-mass neutron star M 0:8 Mˇ we have vff D r D 15 km, and

2GM r

2 Lx BPSR D 36 : 2 Bwi nd EP rot

 .c=3/ at M D 0:6 Mˇ ,

(10)

Using data from McGill (2014) and (10) we obtain for the magnetic fields of SGR 0526-66, SGR 1806-20, and SGR 1900C14 the values 1013 , 1:7  1014 , and

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6  1013 Gs, respectively. Although the mechanical loss of the energy could exceed Lx , these values of the magnetic field are supposed to be the upper limit of the magnetic field of these SGR.

7

Model of Nuclear Explosion

It was shown by Bisnovatyi-Kogan and Chechetkin (1974), that in the neutron star crust full thermodynamic equilibrium is not reached, and a nonequilibrium layer is formed there during a neutron star cooling; see also Bisnovatyi-Kogan (2001) (Fig. 10). The nonequilibrium layer is formed in the region of densities and pressure 2 <  < 1 , P1 < P < P2 , with 3 8 ' 3:8  109 e g=cm3 ' 1:5  1010 g=cm3 0:511   33 3 6 2 ' e 10 ' 2:7  1011 e g=cm3 ' 1012 g=cm3 0:511

1 ' e 106



P1 D 7:1  1027 in cgs units;

P2 D 2:1  1030 in cgs units:

Fig. 10 The formation of chemical composition at the stage of limiting equilibrium. The thick line Qn D 0 defines the boundary of the region of existence of nuclei; the line Qnb separates region I, where photodisintegration of neutrons is impossible from regions II and III. The dashed lines indicate a level of constant "ˇ D Qp  Qn ; "ˇ1 < "ˇ2 < : : : < "ˇmax . In region I we have Qn > Qnb ; in region II we have Qn < Qnb ; "f e < "ˇ ; and in region III we have Qn < Qnb ; "f e > "ˇ . The line with the attached shading indicates a region of fission and ˛ decay. The shaded region abcd determines the boundaries for the values of (A,Z) with a limited equilibrium situation, at given values of Qnb .T / and "f e ./ . On this schematic diagramm the value "ˇmax approximately corresponds to A  24, Z  6. The line Qn D 0 enters the region of fission and ˛-decay instability at A  360, Z  90 (From Bisnovatyi-Kogan and Chechetkin 1974)

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The mass of the nonequilibrium layer is defined as (Bisnovatyi-Kogan and Chechetkin 1974) Mnl D

4 R4 .P2  P1 / ' 0:1.P2  P1 / ' 2  1029 g ' 104 Mˇ ; GM

and the energy stored in this nonequilibrium layer is estimated as Enl ' 4  1017 .P2  P1 /  1048 erg Here a neutron star of a large .2 Mˇ / was considered, where the nonequilibrium layer is relatively thin, and its mass and the energy store are estimated in the approximation of a flat layer. The nuclei in the nonequilibrium layer are overabundant with neutrons, thus the number of nucleons per one electron is taken as e ' 4, and the energy release in the nuclear reaction of fission is about 5  103 c 2 erg/g. A schematic cross-section of the neutron star is represented in Fig. 11, from Baym (2007). Soon after discovery of gamma ray bursts the model of nuclear explosion was suggested (Bisnovatyi-Kogan et al. 1975), in which the nonequilibrium layer matter

Nuclei and electrons Nuclei, electrons and free neutrons Pasta nuclei

OUTER CORE Free neutrons, protons and electrons

INNER CORE hyperons meson condensates quark droplets quark-gluon plasma ??

CRUST

~10km

Fig. 11 Schematic cross-section of a neutron star (From Baym 2007)

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Fig. 12 The schematic picture of the nonequilibrium layer in the neutron star: (a) in a quiescent stage; (b) after starquake and nuclear explosion (From Bisnovatyi-Kogan 1992)

is brought to lower densities during a starquake. At the beginning GRB have been considered as objects inside the galaxy, and the outburst was connected with period jumps in the neutron star rotation similar to those observed in the Crab nebula pulsar. It was suggested that: Ejection of matter from the neutron stars may be related to the observed jumps of periods of pulsars. From the observed gain of kinetic energy of the filaments of the Crab Nebula (2  1041 erg) the mass of the ejected material may be estimated as (1021 g). This leads to energies of the -ray bursts of the order of 1038 –1039 erg, which agrees fully with observations at the mean distance up to the sources 0.25 kpc.

A more detailed model of the strong 5 March 1979 burst, now classified as SGR 0526-66 in LMC, was considered by Bisnovatyi-Kogan and Chechetkin (1981). It was identified with an explosion on the NS inside the galactic disk, at a distance 100 pc. The schematic picture of the nuclear explosion of the matter from the nonequilibrium layer is presented in Fig. 12. The cosmological origin of GRB, and identification of a group of nonstationary sources inside the galaxy as SGR/AXP led to considerable revision of the older model, presented by Bisnovatyi-Kogan et al. (1975). It became clear that SGR represent a very rare and very special type of object which produces bursts much more powerful than it was previously thought from comparison with quakes in the Crab nebula pulsar. In addition, the SGR are the only sources for which the nuclear explosions could be applied, because the energy release in the cosmological GRB highly exceeds the energy store in the nonequilibrium layer. It was suggested by Bisnovatyi-Kogan (2012, 2016) and Bisnovatyi-Kogan and Ikhsanov (2014), that the property, making the SGR neutron star so different from the vast majority of neutron stars in radio pulsars, single and binary Xray sources, is connected with the value of their mass, but not the magnetic field strength; see Camilo et al. (2000), McLaughlin et al. (2003), and Sect. 4. Namely, it was suggested that the neutron stars in SGR/AXP have an anomalously low mass, .0:4 to 0:8/Mˇ , compared to the well-measured masses in binary systems of two neutron stars, which all have masses 1:23 Mˇ (Ferdman et al. 2014).

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Fig. 13 Dependence of the mass of the nonequilibrium layer on the neutron star mass. The lines show the top and bottom boundaries of the layer mass measured from the stellar surface. The equation of state of the equilibrium matter Bethe and Johnson (1974); Malone et al. (1975) was used to construct the model of the neutron star, with the boundaries of the layer specified by the densities. Using a nonequilibrium equation of state will increase the mass of the layer, but should not fundamentally change the values given in the figure (From Bisnovatyi-Kogan (2012), calculated and prepared by S. O. Tarasov)

The violent behaviour of the low-mass NS may be connected with a nonequilibrium layer that is much thicker and more massive, and accretion from the fallback highly magnetised accretion disk could trigger the instability, leading to outburst explosions (Bisnovatyi-Kogan and Ikhsanov 2014). The NS radius increases with mass rather slowly, therefore in a flat approximation the mass of the nonequilibrium layer is inversely proportional to the mass. More accurate estimates have been obtained from calculations of neutron star models, presented in Fig.13. In Sect. 7 the calculated mass of the nonequilibrium layer Mnl  104 Mˇ belonged to the neutron star with the mass 2 Mˇ (see Bethe and Johnson 1974, Malone et al. 1975). For Mns D 0:45 Mˇ the mass of the nonequilibrium layer is 7 times larger. The energy store reaches 1049 erg, which is enough for 1000 giant bursts. The observational evidence for existence of neutron stars with masses less than the Chandrasekhar white dwarf mass limit has been obtained by Janssen et al. (2008). Observations of the binary pulsar system J1518-4904 indicated the masses of the components to be mp D 0:72.C0:51; 0:58Mˇ /, me D 2:00.C0:58; 0:51/Mˇ with a 95:4 % probability. It was suggested by BisnovatyiKogan and Ikhsanov (2014) that low-mass neutron stars could be formed in the scenario of the off-center explosion (Branch and Nomoto 1986), but more detailed numerical investigation is needed to prove it. X-ray radiation of SGR/AXP in quiescent states was explained by Bisnovatyi-Kogan and Ikhsanov (2014) as a fallback accretion from the disk with a large-scale poloidal magnetic field, which

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could also be a trigger for development of instability, leading to the mixing in the neutron star envelope, and nuclear explosion of the matter from the nonequilibrium layer.

8

Conclusions

1. SGRs are highly active, slowly rotating neutron stars. 2. A nonequilibrium layer (NL) is formed in the neutron star crust, during NS cooling, or during accretion onto it. It may be important for NS cooling, glitches, and explosions connected with SGR. 3. The mass and the energy store in NL increase rapidly with decreasing of NS mass. 4. The properties of pulsars with high magnetic fields prove that inferred dipolar magnetic field strength and period alone cannot be responsible for the unusual high-energy properties of SGR/AXP. The NL in low-mass NS may be responsible for bursts and explosions in them. 5. The upper boundary of the magnetic fields in the three most famous SGR, measured by the average Lx luminosity is about one order of magnitude lower than the values obtained using the pulsar-like energy losses of the rotational energy of the neutron star. 6. A magnetar model of SGR, in which the energy of the observed bursts is provided by magnetic field annihilation, seems to be irrelevant. Observations of quiet radio pulsars with a ‘magnetar’ magnetic field, and of a low-field ‘magnetar’, is the most important indication of that conclusion. A rapid growth of rotational periods, a favorite argument for a ‘magnetar’ origin, is naturally explained by action of the magnetic stellar wind. In addition, the high pressure of the magnetic field suppresses convection, which is needed in all annihilation models.

9

Cross-References

 Explosion Physics of Core-Collapse Supernovae  Evolution of the Magnetic Field of Neutron Stars  Making the Heaviest Elements in a Rare Class of Supernovae  Neutron Star Matter Equation of State  Nuclear Matter in Neutron Stars  The Masses of Neutron Stars Acknowledgements The work was partially supported by the Russian Foundation for Basic Research Grants No. 14-02-00728 and OFI-M 14-29-06045, and the Russian Federation President Grant for Support of Leading Scientific Schools, Grant No. NSh-261.2014.2.

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References Alpar MA (2001) On Young Neutron Stars as Propellers and Accretors with Conventional Magnetic Fields. ApJ 554:1245–1254 Baym G (2007) Neutron stars and quark matter. In: Quark confinement and the hadron spectrum VII: 7th Conference on Quark Confinement and the Hadron Spectrum – QCHS7, Sept. 2006, Ponta Delgada, Azores. AIP Conference Proceedings, vol 892, pp 8–14 Bethe HA, Johnson MB (1974) Dense baryon matter calculations with realistic potentials. Nucl Phys A230:1–58 Bisnovatyi-Kogan GS (1992) Gamma ray bursts from nuclear fission in neutron stars. In: Proceedings of the conference “Gamma Ray bursts – observations, analyses and theories”, July 29-August 3, 1990, Taos, New Mexico, USA. Cambridge University Press, pp 89–98 Bisnovatyi-Kogan GS (1999) Magnetic fields of neutron stars: very low and very high. arXiv:astroph/9911275 (Proceedings of the Vulcano Workshop 1999, Memorie della Societa Astronomica Italiana 73:318–329 (2002)) Bisnovatyi-Kogan GS (2001) Stellar physics. In: Fundamental concepts and stellar equilibrium, vol 1. Springer, Berlin/New York Bisnovatyi-Kogan GS (2006) Binary and recycled pulsars: 30 years after observational discovery. Phys Usp 49:53–67 Bisnovatyi-Kogan GS (2012) Gamma ray bursts, their afterglows, and soft gamma repeaters. In: Proceedings of the workshop gamma ray bursts: probing the science, progenitors and their environment, Moscow, 13–5 June 2012, pp 1–4. http://www.exul.ru/workshop2012/ Proceedings2012.pdf Bisnovatyi-Kogan GS (2016) Soft gamma repeaters/anomalous X-ray pulsars – are they magnetars? Astron Astrophys Trans 29:165–182 Bisnovatyi-Kogan GS, Chechetkin VM (1974) Nucleosynthesis in supernova outbursts and the chemical composition of the envelopes of neutron stars. ApSS 26:25–46 Bisnovatyi-Kogan GS, Chechetkin VM (1981) Gamma ray bursts as a manifestation of the inherent activity of neutron stars. Sov Astron 58:561–568 Bisnovatyi-Kogan GS, Ikhsanov NR (2014) A new look at anomalous X-ray Pulsars. Astron Rep 58:217–227 Bisnovatyi-Kogan GS, Imshennik VS, Nadyozhin DK, Chechetkin VM (1975) Pulsed gamma ray emission from neutron and collapsing stars and supernovae. ApSS 35:23–41 Branch D, Nomoto K (1986) Supernovae of Type Ib as off-center explosions in accreting white dwarfs? Astron Astrophys 164:L13–L15 Camilo F, Kaspi VM, Lyne AG, Manchester RN, Bell JF et al (2000) Discovery of Two High Magnetic Field Radio Pulsars. ApJ 541:367–373 Camilo F, Ransom SM, Halpern JP, Reynolds J (2007) 1E 1547.0-5408: a radio-emitting magnetar with a rotation period of 2 seconds. ApJ Lett 666:L93–L96 Chatterjee P, Hernquist L, Narayan R (2000) An Accretion Model for Anomalous X-Ray Pulsars. ApJ 534:373–379 Duncan RC, Thompson C (1992) Formation of very strongly magnetized neutron stars – implications for gamma ray bursts. ApJ Lett 392:L9–L13 Duncan RC, Thompson C (1995) The soft gamma repeaters as very strongly magnetized neutron stars – I. Radiative mechanism for outbursts. MNRAS 275:255–300 Ferdman RD, Stairs IH, Kramer M et al (2014) PSR J1756–2251: a pulsar with a low-mass neutron star companion. MNRAS 443:2183–2196 Feroci M, Costa E, Amati L, Piro L, Martino B et al (1998) SGR1627-41, BeppoSAX-GRBM detections. GRB Coord Netw Telegramm No 111 Frederiks DD, Golenetskii SV, Palshin VD, Aptekar RL, Ilyinskii VN et al (2007a) Giant flare in SGR 1806-20 and its Compton reflection from the Moon. Astron Lett 33:1–18 Frederiks DD, Palshin VD, Aptekar RL, Golenetskii SV, Cline TL et al (2007b) On the possibility of identifying the short hard burst GRB 051103 with a giant flare from a soft gamma repeater in the M81 group of galaxies. Astron Lett 33:19–24

52

Young Neutron Stars with Soft Gamma Ray Emission and. . .

1421

Ginzburg VL (1964) The Magnetic Fields of Collapsing Masses and the Nature of Superstars. Sov Phys Dokl 9:329–334 Golenetskii SV, Mazets EP, Il’inskii VN, Gur’yan YA (1979) Recurrent gamma ray bursts from the flaring source FXP 0520 - 66. Sov Astron Lett 5:340–342 Golenetskii S, Aptekar R, Mazets E, Pal’shin V, Frederiks D, Cline T, Barthelmy S, Cummings J, Gehrels N, Hurley K, Mitrofanov I, Kozyrev A, Litvak M, Sanin A, Tret’yakov V, Parshukov A, Boynton W, Fellows C, Harshman K, Shinohara C, Starr R, Smith DM, Lin RP, McTiernan J, Schwartz R, Wigger C, Hajdas W, Zehnder A, Atteia J-L, Graziani C, Vanderspek R (2005) IPN triangulation and Konus spectrum of the bright short/hard GRB051103. GCN 4197 Halpern JP, Gotthelf EV, Reynolds J, Ransom SM, Camilo F (2008) Outburst of the 2 s Anomalous X-Ray Pulsar 1E 1547.0-5408. ApJ 676:1178–1183 Hurley K, Kouveliotou C, Cline T, Mazets E, Golenetskii S et al (1999a) Where is SGR 1806-20? ApJ 523:L37–L40 Hurley K, Li P, Kouveliotou C, Murakami T, Ando M et al (1999b) ASCA Discovery of an X-Ray Pulsar in the Error Box of SGR 1900+14. ApJ 510:L111–L114 Ibrahim A, Safi-Harb S, Swank JH, Parke W, Zane S et al (2002) Discovery of Cyclotron Resonance Features in the Soft Gamma Repeater SGR 1806-20. ApJ Lett 574:L51–L55 Janssen GH, Stappers BW, Kramer M, Nice DJ, Jessner A et al (2008) Multi-telescope timing of PSR J1518+4904. Astron Astrophys 490:753–761 Kaneko Y, Göˇgü¸s E, Kouveliotou C, Granot J, Ramirez-Ruiz E et al (2010) Magnetar twists: Fermi/gamma ray burst monitor detection of SGR J1550–5418. ApJ 710:1335–1342 Kouveliotou C, Kippen M, Woods P, Richardson G, Connaughton V (1998a) BATSE Discovery of Previously Unknown Soft Gamma Ray Repeater SGR1627-41. The Astronomer’s Telegram 29 Kouveliotou C, Dieters S, Strohmayer T, van Paradijs J, Fishman GJ et al (1998b) An X-ray pulsar with a superstrong magnetic field in the soft gamma ray repeater SGR1806-20. Nature 393:235–237 Kouveliotou C, Strohmayer T, Hurley K, van Paradijs J, Finger MH et al (1999) Discovery of a Magnetar Associated with the Soft Gamma Repeater SGR 1900+14. ApJ Lett 510:L115–L118 Kuiper L, den Hartog PR, Hermsen W (2009) The INTEGRAL detection of pulsed soft gamma rays from SGR/AXP 1E1547.0-5408 during its JAN-2009 outburst. The Astronomer’s Telegram 1921, 01/2009 Laros JG, Fenimore EE, Klebesadel RW, Kane SR (1986a) Statistical Properties of the Soft Gamma Repeater (SGR) GB790107. Bull Am Astron Soc 18:928 Laros JG, Fenimore EE, Fikani MM, Klebesadel RW, Barat C (1986b) The soft gamma ray burst GB790107. Nature 322:152–153 Lorimer DR (2005) Binary and Millisecond Pulsars. Living Rev Relativ 8:7–82. http://www. livingreviews.org/lrr-2005-7 Malone RC, Johnson MB, Bethe HA (1975) Neutron star models with realistic high-density equations of state. ApJ 199:741–748 Manchester RN, Lyne AG, Camilo F, Bell JF, Kaspi VM et al (2001) The Parkes multi-beam pulsar survey – I. Observing and data analysis systems, discovery and timing of 100 pulsars. MNRAS 328:17–35 Mazets EP, Golenetskii SV, Gur’yan YA (1979a) Soft gamma ray bursts from the source B1900+14. Sov Astron Lett 5:343–344 Mazets EP, Golenetskii SV, Il’Inskii VN, Panov VN, Aptekar’ RL et al (1979b) A flaring x-ray pulsar in Dorado. Sov Astron Lett 5:163–166 Mazets EP, Golentskii SV, Ilinskii VN, Aptekar RL, Guryan IA (1979c) Observations of a flaring X-ray pulsar in Dorado. Nature 282:587–589 Mazets EP, Golenetskii SV, Il’inskii VN, Panov VN, Aptekar RL et al (1981) Catalog of cosmic gamma ray bursts from the KONUS experiment data. Ap Space Sci 80:3–143 Mazets EP, Golenetskii SV, Guryan Yu A, Ilyinski VN (1982) The 5 March 1979 event and the distinct class of short gamma bursts: are they of the same origin. Astrophys Space Sci 84:173–189 Mazets EP, Aptekar RL, Butterworth P, Cline TL, Frederiks DD et al (1999a) Unusual Burst Emission from the New Soft Gamma Repeater SGR 1627-41. ApJ Lett 519:L151–L153

1422

G.S. Bisnovatyi-Kogan

Mazets EP, Cline TL, Aptekar RL, Butterworth P, Frederiks DD et al (1999b) Activity of the soft gamma repeater SGR 1900+14 in 1998 from KONUS-Wind observations: 1. Short recurrent bursts. Astron Lett 25:628–634 Mazets EP, Cline TL, Aptekar RL, Butterworth P, Frederiks DD et al (1999c) Activity of the soft gamma repeater SGR 1900C14 in 1998 from KONUS-Wind observations: 2. The giant August 27 outburst. Astron Lett 25:635–648 Mazets EP, Cline TL, Aptekar RL, Frederiks DD, Golenetskii SV et al (2005) The KONUS-Wind and Helicon-Coronas-F detection of the giant gamma ray flare from the soft gamma ray repeater SGR 1806-20. arXiv:astro-ph/0502541 Mazets EP, Aptekar RL, Cline TL, Frederiks DD, Goldsten JO et al (2008) A Giant Flare from a Soft Gamma Repeater in the Andromeda Galaxy (M31). ApJ 680:545–549 McGill Pulsar Group (2014) McGill Online Magnetar Catalog. http://www.physics.mcgill.ca/~ pulsar/magnetar/main.html McLaughlin MA, Stairs IH, Kaspi VM, Lorimer DR, Kramer M et al (2003) PSR J1847–0130: A Radio Pulsar with Magnetar Spin Characteristics. ApJ Lett 59l:L135–L138 McLaughlin MA, Lorimer DR, Lyne AG, Kramer M, Faulkner AJ et al (2004) Two Radio Pulsars with Magnetar Fields. In: Camilo F, Gaensler BM (eds) Young Neutron Stars and Their Environments, IAU Symposium no. 218, held as part of the IAU General Assembly, Sydney, 14–17 July 2003. Astronomical Society of the Pacific, San Francisco, pp 255–256 Pacini F (1967) Energy Emission from a Neutron Star. Nature 216:567–568 Palmer DM, Barthelmy S, Gehrels N, Kippen RM, Cayton T et al (2005) A giant gamma ray flare from the magnetar SGR 1806-20. Nature 434:1107–1109 Rea N, Esposito P, Turolla R, Israel GL, Zane S et al (2010) A low-magnetic-field soft gamma repeater. Science 330:944–946 Shitov YP (1999) SGR 1900+14 = PSR J1907+0919. IAU Circ No. 7110, Feb 17 Trümper JE, Dennerl1 K, Kylafis ND, Ertan U, Zezas A (2010) The spectral and beaming characteristics of the anomalous X-ray pulsar 4U 0142+61. Astron. Astrophys. 518:A46–A51 Trümper JE, Zezas A, Ertan U, Kylafis ND (2013) An accretion model for the anomalous x-ray pulsar 4U 0142+61. ApJ 764:49–58 Weber EJ, Davis LJ (1967) The angular momentum of the solar wind. ApJ 148:217–227 Woods PM, Kouveliotou C, van Paradijs J, Finger MH, Thompson C et al (1999) Variable SpinDown in the Soft Gamma Repeater SGR 1900+14 and Correlations with Burst Activity. ApJ 524:L55–L58 Young MD, Manchester RN, Johnston S (1999a) A radio pulsar with an 8.5-second period that challenges emission models. Nature 400:848–849 Young MD, Manchester RN, Johnston S (1999b) Ha, ha, ha, ha, staying alive, staying alive: a radio pulsar with an 8.5-s period challenges emission models. In: Kramer M, Wex N, Wielebinski R (eds) Pulsar Astronomy – 2000 and Beyond. ASP Conference Series, vol 202. Astronomical Society of the Pacific, San Francisco, pp 185–188; Proceedings of the 177th Colloquium of the IAU held in Bonn, 30 Aug–3 Sept 1999

Strange Quark Matter Inside Neutron Stars

53

Fridolin Weber

Abstract

The tremendous pressures that exist in the cores of neutron stars might be able to break neutrons, protons plus other hadronic constituents into their quark constituents, creating a new state of matter known as quark matter. If quark matter exists in the cores of neutron stars, it ought to consist of up, down, and strange quarks, loosely referred to as strange quark matter. It has also been hypothesized that such matter may be more stable than nuclear matter, in which case most, if not all, neutron stars would in fact be strange (quark matter) stars composed almost entirely of strange quark matter. This paper aims a giving an overview of the multifaceted role of strange quark matter for compact stars.

Contents 1 2 3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling of Compact Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quark Deconfinement in the Cores of Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Hadronic Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Strange Boson Condensates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Quark-Hadron Phase Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Crystalline Quark-Hadron Coulomb Lattices in Neutron Stars . . . . . . . . . . . . . . . . . . . 5 Possible Signals of Quark Deconfinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Color Superconductivity of Quark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Absolutely Stable Strange Quark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1424 1425 1430 1430 1433 1434 1437 1438 1439 1440 1443 1443 1444

F. Weber () Department of Physics, San Diego State University, San Diego, CA, USA Center for Astrophysics and Space Sciences, University of California, San Diego, CA, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_71

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1

F. Weber

Introduction

Neutron stars are dense, neutron-packed remnants of massive stars that blew apart in supernova explosions (see Chaps.  1, “Supernovae and Supernova Remnants: The Big Picture in Low Resolution”,  12, “Observational and Physical Classification of Supernovae”,  22, “Supernovae from Massive Stars” and  41, “Explosion Physics of Thermonuclear Supernovae and their Signatures”). They are typically just about 20 km across and can spin extremely rapidly, often making several hundred rotations per second. Depending a neutron star’s mass and rotational frequency, gravity may compress the matter in their core regions up to more than ten times the density of ordinary atomic nuclei. This provides a high-pressure environment in which numerous novel subatomic particle processes are believed to occur. These include the formation of hyperons and baryon resonance states, boson condensates, and quark matter made of deconfined up, down, and strange quarks, somewhat loosely referred to as strange quark matter (Baym 1978; Buballa et al. 2014; Glendenning 2000; Page and Reddy 2006; Sedrakian 2007; Weber 1999, 2005). It has also been hypothesized that strange quark matter (Farhi and Jaffe 1984) may be more stable than ordinary nuclear matter (Bodmer 1971; Terazawa 1979; Witten 1984). In the latter event, neutron stars would largely be composed of strange quark matter (Alcock and Olinto 1988; Alcock et al. 1986; Glendenning 2000; Haensel et al. 1986; Madsen 1999; Madsen and Haensel 1991; Weber 1999, 2005), possibly enveloped in thin nuclear crusts (Glendenning 2000; Weber 1999, 2005) whose densities are less than neutron drip. Such objects are refereed to in the literature as strange quark matter stars (strange stars, for short) rather than neutron stars. A comparison of the properties of both types of stars is provided in Table 1 and Fig. 1. Because of their complex interior structures, the very name neutron star is almost certainly a misnomer. The idea that quark matter may exist in the cores of neutron stars is not new but has already been suggested by several authors decades ago (Glendenning 2000; Weber 1999, 2005). In the late 1990s, it has been discovered that quark matter forms a color superconductor at sufficiently low temperatures (Alford 2001; Alford et al. 2008; Rajagopal and Wilczek 2001a). Therefore, if quark matter should exist in the cores of neutron stars, it may be in a color superconducting state (Alford 2001; Alford et al. 2008). The theoretically predicted condensation patterns of such matter are very complex. At asymptotic densities the ground state would be the colorflavor locked (CFL) phase (see Fig. 1). This phase is electrically charged neutral without any need for electrons for a significant range of chemical potentials and strange quark masses (Rajagopal and Wilczek 2001b). If the strange quark mass is high enough to be ignored, then up and down quarks may pair in the twoflavor superconducting (2SC) phase. Other possible condensation patterns include the CFL-K 0 phase and the color-spin locked (CSL) phase. The magnitude of the color superconducting gap of the CFL phase lies between around 50 and 100 MeV but is significantly smaller for the 2SC case (Alford et al. 2008). In any case, the nuclear equation of state (EoS), will only be modified by color superconductivity by just a few percent (Alford 2004; Alford and Reddy 2003). Such a small effect

53 Strange Quark Matter Inside Neutron Stars

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Table 1 Comparison of the properties of strange stars and neutron stars Features Composition

Superfluidity/ superconductivity

Energy per baryon Binding agent Maximum mass Minimum mass Radii Baryon number Electric surface fields Outer crust Inner crust Global structure

Strange quark stars Up, down, strange quarks

Neutron stars Nucleons, hyperons, deltas; up, down, strange quarks Electrons Electrons and muons Pion, kaon condensates Color superconducting Neutrons in 1 S0 and 3 P2 quarks states, protons in 1 S0 state, color superconducting quarks .930 MeV >930 MeV Strong force (M / R3 ) Gravity 2 Mˇ Same .102 Mˇ a 0:1 Mˇ .10–12 km &10–12 km .1057 Same 1018 to 1019 V/cm .1014 V/cm May or may not be present Always present Does not exist Always present Determined by two Determined by one parameters (central density parameter (central and density at the base of the density) nuclear crust

a This applies only to strange quark stars enveloped in nuclear crusts. Bare quark stars do not possess a minimum mass

can be safely neglected in present determinations of models for the EoS of neutron star matter and strange star matter. This is different for phenomena involving the cooling by neutrino emission, the pattern of the arrival times of supernova neutrinos, the evolution of neutron star magnetic fields, rotational instabilities, and glitches in rotation frequencies of pulsars (see Alford 2001; Blaschke et al. 1999, 2001; Buballa et al. 2014; Rajagopal and Wilczek 2001a; Weber 2005 and references therein).

2

Modeling of Compact Stars

Neutron stars and strange quark stars are succinctly referred to as compact stellar objects. The matter in the core regions of such objects is compressed to densities that are up to an order of magnitude higher than the mass density of atomic nuclei, which is around 2:5  1014 g=cm3 . At such enormous densities, space-time is curved considerably, as indicated by the mass-to-radius ratio, 2M =R, of compact stars. Here M denotes the gravitational mass and R the radius of a compact star. For a

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F. Weber traditional neutron star

quark−hybrid star

N+e N+e+n

s

id to

H

π

ns

2SC CFL color−superconducting strange quark matter (u,d,s quarks)

p ro

,e,μ

u,d,s quarks

neutron star with pion condensate

u rfl

n,p

pe

o nd u c t i r c ng pe

su

u

n

n,p,e,μ hyperon star

K

2SC CFL CSL CFL−K + gCFL 0 LOFF CFL−K 0 CFL− π

crust

Fe 6 3 10 g/cm 11 10 g/cm3 3 1014 g/cm Hydrogen/He atmosphere

strange star nucleon star R ~ 10 km

Fig. 1 Theoretically predicted phases of matter inside of “neutron” stars (Figure from Weber 2005)

two solar mass compact star with a radius of around 10 km, for instance, one obtains 2M =R D 0:6, which is no longer negligibly small compared to the flat space-time limit given by 1. (Here and throughout this text we use geometric units where the gravitational constant and the speed of light are G D c D 1. This leads for the mass of the sun to Mˇ D 1:5 km.) Because of what has been said just above, models of compact stars are to be constructed in the framework of Einstein’s general theory of relativity (see  Chap. 54, “Neutron Stars as Probes for General Relativity and Gravitational Waves”). The central relation of this theory is Einstein’s field equation given by (; D 0; 1; 2; 3) G  D 8 T  .; P .// ;

(1)

where G  denotes the Einstein tensor and T  stands for the energy-momentum tensor. The latter contains the EoS, P ./, as an input quantity, T  .; P .// D . C P .// u u C g  P ./ ;

(2)

where u  dx  =d and u  dx =d denoted four-velocities and g  is the metric tensor. The Einstein tensor, defined as G   R  12 g  R, is given in terms of the Ricci curvature tensor, R , the metric tensor, and the curvature scalar, R. The models for the EoS (see  Chap. 39, “Neutron Star Matter Equation of State”) can be classified into nonrelativistic Schroedinger-based models and relativistic field-theoretical models (see Glendenning 2000; Page and Reddy 2006;

53 Strange Quark Matter Inside Neutron Stars

1427

Sedrakian 2007; Weber 1999, 2005 and references therein). The relativistic models are obtained from a Lagrangian Lm .fg/, which is typically a complicated functional of numerous baryon fields ( D p; n; ˙; ; & ; ), meson fields ( D

 ; K  ), and quark fields ( D u; d; s) (Glendenning 2000; Weber 1999, 2005). The equations of motion of the various particle fields follow from the EulerLagrange equation, @Lm @Lm  @ D 0: @ @.@ /

(3)

In order to make the equations of motion numerically treatable different manybody techniques need to be introduced. Among the most popular ones are the Hartree, Hartree-Fock, and Brueckner-Hartree-Fock approximation (Glendenning 2000; Weber 1999). In principle, Eqs. (1) and (3) are to be solved simultaneously since the particles move in curved space-times whose geometry, determined by Einstein’s field equation, is coupled to the total energy density of the matter fields. For compact stars, however, the deviation from flat space-time over the length scale of the nuclear force, 1 fm, is practically zero up to the highest densities reached in the cores of such objects (some 1015 g=cm3 ). This feature divides the construction of models of compact stars into two distinct problems. Firstly, the effects of the shortrange nuclear forces on the properties of dense stellar matter can be described in a local inertial frame, where space-time is flat, by the parameters and laws of (non) relativistic many-body physics, leading to a model for P ./. Secondly, the coupling between the long-range gravitational field and the matter is then taken into account by solving Einstein’s field equation for the gravitational field for this EoS, which determines the global properties of compact stars. If the stars are nonrotating, the stellar structure equations can be derived from a line element of the form (Oppenheimer and Volkoff 1939; Tolman 1939) ds 2 D g dx  dx D e 2˚.r/ dt 2 C e 2.r/ dr 2 C r 2 d  2 C r 2 sin2 d  2 ;

(4)

where .x  /  .x 0 ; x 1 ; x 2 ; x 3 / D .t; r; ; /. The quantities ˚.r/ and .r/ are unknown metric functions, which depend only on the radial distance, r, measured from the star’s center. They are given by e 2.r/ D 1  2m.r/=r

(5)

 1  d ˚.r/ ; D 4 r 3 P .r/ r 2 .1  2m.r/=r/ dr

(6)

and

where P .r/ is given by (Oppenheimer and Volkoff 1939; Tolman 1939)

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F. Weber

..r/ C P .r// .4 r 3 P .r/ C m.r// dP .r/   D : dr r 2 1  2 m.r/

(7)

r

Equation (7) is known as the Tolman–Oppenheimer–Volkoff (TOV) equation (Oppenheimer and Volkoff 1939; Tolman 1939). It is a first-order differential equation for the pressure gradient inside of a spherically symmetric mass distribution. The quantity m.r/ in Eq. (7) is the R r gravitational mass inside of a spherical shell of radius r given by m.r/ D 4 0 dr r 2 .r/. The star’s total gravitational mass follows as M  m.R/, where R denotes the star’s radius defined as that radial distance where pressure turns negative. The structure equations of rotating compact stars are considerably more complicated than those of nonrotating compact stars. The complications are caused by three basic features. Firstly, there is rotational deformation, which leads to a flattening at the star’s pole but to a blowup in its equatorial direction. The metric functions, therefore, depend on the radial coordinate, r, as well as the polar coordinate,  , rendering rotating star calculations two dimensional. Secondly, rotation stabilizes a star against gravitational collapse. A rotating star can therefore carry more mass than it would be the case if the star would be nonrotating. Thirdly, the general relativistic effect of the dragging of local inertial frames (Lense–Thirring effect) leads to a nonvanishing, non-diagonal term in the metric tensor, leading to a line element with the general form (Friedman et al. 1986; Weber 1999) ds 2 D g dx  dx D e 2 dt 2 C e 2 .d   ! dt /2 C e 2 d  2 C e 2 dr 2 : (8) The metric functions , ,  and , as well as the angular velocities of the local inertial frames, !, all depend on the radial coordinate r and on the polar angle  and, implicitly, on the star’s angular velocity ˝. All these functions need to be computed self-consistently from Einstein’s field equation (1) (Friedman et al. 1986; Weber 1999). The study of rotating compact objects is complicated further by the fact that no simple stability criteria are known for compact rapidly rotating objects in general relativity. An absolute limit on rotation is set by the onset of mass shedding from the equator of a rotating star. The corresponding rotational frequency is known as the Kepler frequency, ˝K . In classical mechanics, the expression for ˝K is determined by the equality between the centrifugal force andp the gravitational pull on a particle at the star’s equator, which leads to ˝K D M =R3 . Its general relativistic counterpart is given by (subscripts preceded by a comma denote partial derivatives, e.g., !;r  @!=@r) ˝K D ! C

!;r C e  2 ;r



;r ;r

C

! ;r e 2 ;r



2 1=2

;

(9)

which is to be evaluated self-consistently at the equator of a rotating compact star (Friedman et al. 1986; Weber 1999). The Kepler period follows from Eq. (9) as

53 Strange Quark Matter Inside Neutron Stars

1429

Fig. 2 Kepler period, P K , of sequences of rotating neutron stars computed for three sample quarkhadron EoS (details about these EoS will be discussed in Sect. 3). The solid dots denote the termination point of each stellar sequence (Figure from Weber et al. 2013)

P K D 2 =˝K . For typical neutron star matter equations of state, the Kepler period of 1.4 Mˇ neutron stars is around 1 ms (1000 Hz), as shown in Fig. 2 for a few sample equations of state (Friedman et al. 1986; Weber 1999, 2005). An exception to this are strange stars, which will be discussed in more detail in Sect. 7. In contrast to neutron stars, which are bound by gravity, quark stars are self-bound. This makes such objects somewhat smaller than neutron stars, which consequently lower their Kepler periods. Because of their smaller radii, strange stars begin to shed mass down at rotational periods of around 0.5 ms (2000 Hz) (Glendenning and Weber 1992). A mass increase of up to 20 % is typical for rotation at ˝K . The most rapidly rotating, currently known neutron star is pulsar PSR J1748-2446ad, which rotates at 1.39 ms (719 Hz). This figure is well below the Kepler frequency for most neutron star equations of state (Weber 1999). Examples of other rapidly rotating neutron stars are PSRs B1937+21 and B1957+20, whose rotational periods are 1.58 ms (633 Hz) and 1.61 ms (621 Hz), respectively. The observed neutron star masses shown in Fig. 2 range from 1.0 to 2 Mˇ , which covers the measured average masses of isolated pulsars (1.4 Mˇ ) and those of accreting neutron stars in binaries (see Zhang et al. (2011) and references therein). Rapid rotation may change the core compositions of neutron stars drastically, as shown in Weber (1999) and Weber (2005). Depending on mass, rotational frequency, and EoS, density changes in the cores as large as 60 % appear possible. This suggests that rotation may cause significant changes in the core compositions of neutron stars (cf. Fig. 4), which concern the restructuring of hyperon populations, boson condensates, or quark deconfinement. Possible astrophysical signals of quark deconfinement will be discussed in Sect. 5.

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F. Weber

3

Quark Deconfinement in the Cores of Neutron Stars

3.1

Hadronic Matter

To set up the mathematical framework suitable to model quark deconfinement in the cores of neutron stars, we begin with pure neutron matter. Such matter constitutes a highly excited state of matter relative to neutron star matter. Pure neutron matter will therefore quickly transform, via the weak reactions n ! p C e  C N e and p C e  ! n C e into matter made up of neutrons (n), protons (p), and electrons (e  ). Neutrinos ( e ) as well as antineutrinos ( N e ) do not accumulate (i.e., they have zero chemical potential,  e D  Ne D 0) in cold neutron star matter, because of their extremely small cross sections (long mean free paths) in such matter. That way neutron star matter develops Fermi seas of degenerate neutrons, protons, and electrons, whose chemical potentials obey the chemical equilibrium condition n D  p C e . This relation is a special case of the more general condition 

  D B  n  q  e ;

(10)

which holds in any system characterized by two conserved charges. These are, in the case of neutron star matter, electric charge q  , and baryon number charge B  , where  denotes a baryon of type B .n; p; ; ˙ C;0; ; & 0; ; CC;C;0; /, meson of type M (  ; K  ), quark of type Q (u; d; s), or a lepton of type L (e  ;  ). Aside from chemical equilibrium, the condition of electric charge neutrality, given by X 

q



kF3  3 2

C M (.M  mM /  0 ;

(11)

is critical for the interior structure of neutron stars. The first term on the left hand side of Eq. (11) denotes the total electric charge density of all fermionic particles present in neutron star matter at a given density. The second term on the left hand side accounts for the electric charge contribution carried by meson condensates of type M . The total net electric charge must be zero, either locally or globally (Glendenning 2001). Otherwise stable neutron stars could not be formed. For the chemical potential of the  hyperon (B  D 1, q  D 0), for instance, one obtains from Eq. (10) the condition  D n . This condition can be evaluated further if particle interactions are ignored. The chemical potential of a particle  can then be written as  D !.kF /  .m2 C kF2  /1=2 m , where !.kF / is the single-particle energy of particle  moving with Fermi momentum kF . The threshold condition for the  hyperon can therefore be written as kFn .m2  m2n /1=2 , where kFn is the Fermi momentum of a neutron. Using m D 1116 MeV and mn D 939 MeV, one then obtains kFn  3 fm1 so that kFn 3 =3 2  60 . (The conversion factor from MeV to fm is 1 D 200 MeV fm.) According to this result, neutrons would be replaced by  hyperons at baryon number densities of around six times the saturation density of ordinary nuclear matter, 0 D 0:16 fm3 . This value

53 Strange Quark Matter Inside Neutron Stars

1431

100

10 –1

-

ρ χ/ ρ

10 –2

+

-

-

0

0

10 –3 100 -

10 –1

10 –2

-

-

-

0 0

+

10 –3

ρ/ ρ

0

Fig. 3 Representative baryon-lepton compositions of neutron star matter computed for two relativistic field-theoretical models for the nuclear EoS labeled G300 (upper panel) and HV (lower panel).  =rho denote relative particle densities normalized to nuclear matter density  (Figure from Na et al. 2012)

is generally reduced by the inclusion of particle interactions (Glendenning 2000; Schaffner and Mishustin 1996; Weber 1999), as shown in Fig. 3. These sample compositions shown in this figure are computed in the framework of nonlinear relativistic nuclear field theory (Boguta and Bodmer 1977; Boguta and Rafelski 1977; Glendenning 2000; Weber 1999), where baryons interact via the exchange of scalar, vector, and isovector mesons ( , !, , respectively). The Lagrangian of this theory is given by LD

X B

 N B  .i @  g! !   g  /  .mN  g  /

B

1 C .@  @   m2  2 / 2

1 1 1 1 1 b mN .g  /3  c .g  /4  ! !  C m2! ! !  C m2      3 4 4 2 2 X 1 N L .i  @  mL / L ;      C (12) 4 LDe  ; 

where B sums all baryon states whose thresholds are reached in neutron star matter at a given density  (Glendenning 2000; Weber 1999). The quantities g , g , and g! are the meson-baryon coupling constants. Cubic and quartic  -meson

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F. Weber

self-interactions are taken into account in Eq. (12) through the terms proportional to b and c . The quantities !  .D @ !  @ !  / and   .D @  @   / denote meson field tensors (Glendenning 2000; Weber 1999). The equations of motion for the baryon and meson fields follow from the Euler–Lagrange equation (3). They have the general mathematical form .i  @  mB /

B .x/

D

X

MB M .x/

B .x/ ;

(13)

N B .x/ MB

B .x/ ;

(14)

M D;!; ;:::

.@ @ C m2M / M .x/ D

X BDp;n;˙;:::

where MB denote meson-baryon scattering vortices (Weber 1999). Evidently, the free-particle case follows from Eqs. (13) and (14) if all meson-baryon vortices

MB D 0. Equations (13) and (14) are to be solved in combination with the conditions of chemical equilibrium (Eq. (10)) and electric charge neutrality (Eq. (11)). In order to make this set of equations numerically solvable, suitable many-body approximations need to be introduced such as, with increasing level of complexity, the (density dependent) relativistic Hartree approximation (Glendenning 2000; Weber 1999), relativistic Hartree–Fock approximation (Weber 1999), and relativistic (Dirac) Brueckner–Hartree–Fock approximation (Fuchs 2004; van Dalen et al. 2004; Weber 1999). For the relativistic Hartree and Hartree–Fock approximation, the coupling constants are chosen such that the bulk properties of ordinary nuclear matter at nuclear saturation density, 0 , are reproduced. These are the energy per baryon E=A D 16 MeV, effective nucleon mass mN =mN ' 0:7, nuclear incompressibility K ' 250 MeV, and the symmetry energy as D 32 MeV. The relativistic (Dirac) Brueckner–Hartree–Fock approximation makes use of oneboson-exchange models for the nucleon-nucleon interaction (Weber 1999), whose parameters are adjusted to the nucleon-nucleon scattering phase shifts in free space and the properties of the deuteron. There are no free adjustable parameters in this treatment. Once the fields B .x/Pand M .x/ have been computed, the energy density  D TQ 00 and the pressure P D 3iD1 TQ i i =3 of neutron star matter follows from TQ  .x/ D  g  L.x/ C

@L @ .x/ : @.@ .x//

(15)

The neutron star matter compositions (see  Chap. 48, “Nuclear Matter in Neutron Stars”) shown in Fig. 3 are computed for the relativistic Hartree approximation. Several general physical features emerge, which are essential for neutron star matter to settle down in the lowest possible energy state. (1) The electric charges add up to zero at each density, as required by electric charge neutrality. (2) The generation of  leptons and ˙  hyperons replaces high-energy electrons. (3) The generation of hyperons (e.g., ˙ C ; & 0 ) with isospin orientations opposite to the neutrons make neutron star matter less isospin asymmetric.

53 Strange Quark Matter Inside Neutron Stars

1433 2000

2000

Mass shedding frequency

Mass shedding frequency

Frequency (Hz)

Σ 1000

Λ

1500 Nucleons

Σ

Frequency (Hz)

Σ

1500

Nuclear crust

Surface

Ξ

0

Σ 1000

Nucleons Surface

Ξ Ξ

Ξ 0

Nuclear crust

Σ

500

500

Λ

Σ

5

10

15

20

25

Radius (km)

0 0

5

10

15

Radius (km)

Fig. 4 Composition of a rotating neutron star in equatorial direction (left panel) and polar direction (right panel). The star’s gravitational mass at zero rotation is 1:70 Mˇ (Figure from Weber et al. 2007)

Figure 4 shows the particle composition inside of a rotating neutron star, computed by solving Einstein’s field equation (1) for the metric given by Eq. (8). The star’s frequency varies between zero and the Kepler (mass-shedding) frequency, defined by Eq. (9), while its total number of particles is kept constant (Weber 1999; Weber et al. 2007). As can be seen from Fig. 4, the re-population of hyperons driven by changes in stellar frequency is quite strong in neutron stars rotating in the millisecond regime but may also affect neutron stars rotating at more moderate rotational frequencies. In particular, one sees that certain types of particles such as the &  , & 0 , ˙ ˙;0 may completely disappear from the cores of neutron stars at sufficiently high rotational frequencies, because of the drop in density during spin-up. This is very different from nonrotating neutron stars, where the particle population does not change with time. The drop in density may be as large as 60 % (Weber 2005). This leads one to speculate that if quark matter would exist in the cores of neutron stars, it could gradually be converted to hadronic matter in the cores of accreting neutron stars, which are being spun up to higher frequencies (Chubarian et al. 2000; Glendenning and Weber 2001). The inverse phenomenon, that is, gradual quark deconfinement, could be occurring in the cores of isolated neutron stars, which are spinning down due to the loss of rotational energy (Glendenning et al. 1997) (see Sect. 5).

3.2

Strange Boson Condensates

From Eq. (10) one can read off that the condensation of negatively charged mesons  such as  or K  in neutron star matter sets in if M D q M e , where M D  ; K  and q M D 1. Negatively charged mesons are favored because such mesons would replace electrons with very high Fermi momenta. Early estimates predicted the onset of a negatively charged pion condensate at around 20 (Weber 2005). However, these estimates are very sensitive to the strength of the effective nucleon particle-hole repulsion in the isospin T D 1, spin S D 1 channel, described

1434

F. Weber

by the Landau Fermi-liquid parameter g 0 , which tends to suppress the condensation mechanism. Measurements in nuclei tend to indicate that the repulsion is too strong to permit condensation in nuclear matter. In the mid 1980s, it was discovered that the in-medium properties of K  ŒuNs  mesons may be such that this meson rather than the  meson may condense in neutron star matter (Brown et al. 1987; Kaplan and Nelson 1988). The condensation is initiated by the schematic reaction e  ! K  C e . Whether or not this happens in the cores of neutron stars depends on the behavior of the K  mass, mK  , in neutron star matter (Fuchs 2006). We also note that K  condensation allows the conversion reaction n ! p C K  . By this conversion the nucleons in the cores of neutron stars can become half neutrons and half protons, which lowers the energy. Such neutron stars are therefore referred to as nucleon stars (Brown 1996) (see Fig. 1). A novel particle that could be of relevance for the composition of (proto) neutron star matter is the H-dibaryon (H = .Œud ŒdsŒsu/), which is a doubly strange sixquark composite with spin and isospin zero, and baryon number two (Jaffe 1977). Since its first prediction in 1977, the H-dibaryon has been the subject of many theoretical and experimental studies as a possible candidate for a strongly bound exotic state. In neutron star matter, which may contain a significant fraction of  hyperons, the ’s could combine to form H-dibaryons, which could give way to the formation of H-dibaryon matter at densities somewhere above 4 0 . If formed in neutron stars, however, H-matter appears unstable against compression which could trigger the conversion of neutron stars into hypothetical strange stars (Weber 2005).

3.3

Quark-Hadron Phase Transition

As mentioned in Sect. 1, it has been suggested already many decades ago that the nucleons in the cores of neutron stars may melt under the enormous pressures that exist in the cores, creating a new state of matter known as quark matter (Glendenning 2000; Weber 1999, 2005). Moreover, if such matter exists in the cores of neutron stars, it would be made of the three lightest quark flavors (up, down, strange). Charm, top, and bottom quarks do not play a role since they are much too heavy to be created in the cores of neutron stars (Kettner et al. 1995). To model the phase transition, one needs to realize that the composition of neutron star matter is governed by the conservation of baryon charge and electric charge, as outlined in Sect. 3.1. The Gibbs condition for pressure equilibrium between hadronic (H) matter and quark (Q) matter is therefore given by (Glendenning 2001) PH .n ; e ; f

H g/

D PQ .n ; e ; f

Q g/ ;

(16) 

where only the chemical potentials of neutrons (n ) and electrons (e ) enter. The chemical potentials of all other particles are given in terms of these two potentials (see Eq. (10)). The properties of the hadronic phase can be computed for a hadronic Lagrangian such as the one given in Eq. (12). The MIT bag model has been used for many years to compute the properties of quark matter. In recent years, however,

53 Strange Quark Matter Inside Neutron Stars

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the Nambu–Jona–Lasinio (NJL) model (Buballa 2005) of quark matter has gained enormous popularity among theorists and is now being used exhaustively to model quark matter inside of neutron stars (Benic et al. 2014; Blaschke et al. 2007; Bonanno and Sedrakian 2012; Klahn et al. 2007, 2013; Orsaria 2014; Yasutake et al. 2014). The quantities f H g and f Q g in Eq. (16) schematically denote the field variables and Fermi momenta that characterize a solution to the field equations of hadronic matter (Sect. 3.1) and quark matter, respectively. The mathematical structure of the hadronic fields is given by Eqs. (13) and (14). The effective action of the NJL model for the quark fields has the mathematical form (Orsaria et al. 2013; Orsaria 2014) Z SE D

˚ d 4 x N .x/.i=@  m/ O .x/

1 GS Π. N .x/a .x//2 C . N .x/i 5 a .x//2  2

 CH detΠN .x/.1 C 5 / .x/ C detΠN .x/.1  5 / .x/ C

(17)

GV Œ. N .x/  a .x//2

C. N .x/i   5 a .x//2  ;

(18)

where stands for the light quark fields (u; d; s), m O D diag.mu ; md ; ms / is the current quark mass matrix, and a (a D 1; : : : ; 8) denote the generators of SU(3). The coupling constants GS , GV , and H , and the strange quark mass are the parameters of the theory. The repulsion among quarks is controlled by the vector coupling constant GV , which is treated as a free parameter. Its value controls the maximum masses (see  Chap. 47, “The Masses of Neutron Stars”) and the quark matter contents of neutron stars computed for the NJL model (Orsaria et al. 2013; Orsaria 2014). The mean-field equations for the quark fields are obtained from Eq. (18) by minimizing the grand canonical potential, as described in Orsaria (2014) and Orsaria et al. (2013). Like for ordinary neutron stars without quark matter, the quark mean-field equations are to be solved in combination with the conditions for baryon-charge conservation and the electric charge conservation. Here we shall assume that these quantities are conserved globally rather than locally (Glendenning 2001), which constitutes a weaker condition on the building blocks of neutron star matter. As discussed in Sect. 4, this weaker condition may lead to charge segregation in the mixed phase resulting in the formation of a crystalline lattice of quark matter immersed in a hadronic matter background (Glendenning 2001; Na et al. 2012; Spinella et al. 2016). The global conservation of baryon charge within an unknown volume, V , containing A baryons can be expressed as (Glendenning 2001) 



  A=V D .1  / H .n ; e / C  Q .n ; e / ;

(19)

where   VQ =V denotes the volume proportion of quark matter, VQ , in the unknown volume. By definition,  varies between 0 and 1, depending on how much confined hadronic matter has been converted to quark matter. The global neutrality

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F. Weber

Fig. 5 Pressure P (solid lines), baryon chemical potential B .D n =3/, and electron chemical potential e as a function of baryon number density (in units of nuclear saturation density 0 D 0:16 fm3 ). The hatched areas denote the mixed phase regions where hadronic matter and deconfined quark matters coexist. The strength of the vector repulsion among quarks is GV D 0 (left) and GV D 0:09GS (right) (Figure from Weber et al. 2014)

of electric charge within V is expressed as (Glendenning 2001) 0 D Q=V D .1  / qH .n ; e / C  qQ .n ; e / C qL ;

(20)

where qH and qQ denote the net electric charges carried by hadronic and quark matter, respectively, and qL stands for the electric charge density of the leptons. Equations (16) through (20) serve to determine the two independent chemical potentials n and e and the volume V for a specified volume fraction  of the quark phase in equilibrium with the hadronic phase. The chemical potentials n , e , and the EoS all depend on the volume fraction  and thus on density, as shown in Fig. 5 (Orsaria et al. 2013; Orsaria 2014; Weber et al. 2014). Since the quark-hadron phase transition is modeled in three-space spanned by the electron chemical potential, neutron chemical potential, and pressures, the pressure in the mixed quark-hadron phase (cross hatched regions) varies monotonically with . The quark matter contents of the maximum-mass neutron stars associated with these two equations of state are marked with solid dots. Both stars have extended quark-hadron cores, as indicated by  values of 0.72 and 0.97, but neither star has a pure quark matter core. Figure 6 shows the relative particle fractions ( =) of neutron star matter as a function of baryon number density for the EoS of Fig. 5 (Orsaria et al. 2013; Orsaria 2014; Weber et al. 2014). Three key features emerge immediately from

53 Strange Quark Matter Inside Neutron Stars

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Fig. 6 Sample quark-hadron composition of neutron star matter. The shaded areas highlight the mixed phase. The solid vertical lines indicate the central densities of the maximum-mass neutron stars computed for this EoS (Figure from Orsaria 2014)

these populations. Firstly, the transition from pure hadronic matter to the mixed phase occurs at rather low nuclear densities (3 times nuclear matter saturation density). Secondly, the lepton population saturates as soon as quark matter appears. At this stage, charge neutrality is achieved more economically among the baryoncharge carrying particles themselves. Thirdly, the presence of quark matter enables the hadronic regions of the mixed phase to become more isospin symmetric (i.e., closer equality in proton and neutron number) than in the pure phase by transferring electric charge to the quark phase. The symmetry energy will be lowered thereby at only a small cost in rearranging the quark Fermi surfaces. The mixed quark-hadron phase of a neutron star will thus have positively charged regions of nuclear matter and negatively charged regions of quark matter, which may lead to the formation of a crystalline quark-hadron Coulomb lattice inside of neutron stars (Glendenning 2001; Na et al. 2012; Spinella et al. 2016). This topic will be discussed next.

4

Crystalline Quark-Hadron Coulomb Lattices in Neutron Stars

Because of the competition between the Coulomb and the surface energies associated with the positively charged regions of nuclear matter and negatively charged regions of quark matter, the mixed phase will develop geometrical structures, just as it is expected of the subnuclear liquid-gas phase transition. This competition establishes the shapes, sizes, and spacings of the rarer phase in the background of the

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F. Weber

other in order to minimize the lattice energy (Glendenning 2001). The consequences of such a Coulomb lattice for the thermal and transport properties of neutron stars (see  Chap. 49, “Thermal Evolution of Neutron Stars”) have been studied in Na et al. (2012) and Spinella et al. (2016). It was found that at low temperatures of T . 108 K the neutrino emissivity from electron-blob Bremsstrahlung scattering is at least as important as the total contribution from all other Bremsstrahlung processes (such as nucleon-nucleon and quark-quark Bremsstrahlung) and modified nucleon and quark Urca processes. It is also worth noting that the scattering of degenerate electrons off rare phase blobs in the mixed phase region lowers the thermal conductivity by several orders of magnitude compared to a quark-hadron phase without geometric patterns. This may lead to significant changes in the thermal evolution of the neutron stars containing crystalline quark-hadron cores, which has not yet been studied.

5

Possible Signals of Quark Deconfinement

Whether or not quark deconfinement occurs in nonrotating neutron stars makes only very little difference to their properties, such as the range of possible masses and radii. This may be strikingly different for rotating neutron stars. The reason being that such stars are gradually more and more compressed as they spin down from high to low rotational frequencies. For some rotating neutron stars, the mass and initial rotational frequency may be just such that the central density rises from below to above the critical density at which baryons dissolve into their quark constituents. As shown in Glendenning et al. (1997), this could drastically change the moment of inertia of such neutron stars, which may lead to a observable signals of quark deconfinement. To better understand this, recall that the moment of inertia, I , of a neutron star is intimately connected to a star’s braking index, n, according to (Glendenning et al. 1997; Spyrou and Stergioulas 2002; Weber 2005) n.˝/ 

˝ ˝R I C 3 I 0 ˝ C I 00 ˝ 2 ; D3 I C I0 ˝ ˝P 2

(21)

where dots and primes denote derivatives with respect to time and the star’s rotational frequency ˝, respectively. The canonical value for the braking index, given by n D 3, is obtained from Eq. (21) if the moment of inertia is assumed to be independent of frequency. Evidently, this is not the case for rapidly rotating neutron stars, and it specifically fails for stars whose cores experience phase transitions which are capable of altering the moment of inertia. In Glendenning et al. (1997) it was shown that the changes in the moment of inertia caused by quark deconfinement may be so strong for millisecond pulsars that the braking index n.˝/ ! ˙1 at the transition frequency where pure quark matter is produced, and that isolated spinning-down millisecond pulsars stars could undergo extended epochs of stellar spin-up for tens of millions of years, depending on the rate at which quark matter is generated in the cores of the stars. Since the dipole age of millisecond pulsars

53 Strange Quark Matter Inside Neutron Stars

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is about 109 years, it has been estimates that roughly about 10 % of the solitary millisecond pulsars presently known could be in this quark matter transition epoch. The future astrophysical observation of a strong anomaly in a pulsar’s braking index and/or its spin evolution (spin-up) could thus hint at the existence of quark matter in the pulsar’s central core region. The signal of quark deconfinement described just above is computed for isolated neutron stars, where quark deconfinement is driven by the gradual stellar contraction as the star spins down. The situation is reversed in neutron stars (or hypothetical quark stars) in binary systems (e.g., low-mass X-ray binaries), which are being spun up because of the transfer of angular momentum carried by the matter picked up by the star’s magnetic field from the surrounding accretion disk (Zhang and Kojima 2006). In Weber (2005) it is described how quark matter may remain relatively dormant in the stellar cores of such neutron stars until the they have been spun up to frequencies at which the central density is about to drop below the threshold density at which quark matter exists. This could manifest itself in a significant change in the star’s moment of inertia. The angular momentum added to such a neutron star during this phase of evolution is therefore consumed by the star’s expansion, inhibiting a further spin-up until the entire quark matter core has been spun out of the center, leaving the star with a mixed phase of quarks and hadrons made surrounded by ordinary nuclear matter. Such accreting neutron stars, therefore, tend to spend a much greater length of time at the critical frequencies than otherwise, leading to an anomalous large number of accreting neutron stars that appear near the same frequency (Weber 2005). Theoretical studies indicate that around 2 Mˇ of accreted matter may suffice to drive the quark re-confinement phase transition in rotating neutron stars.

6

Color Superconductivity of Quark Matter

There has been much recent progress in our understanding of quark matter, culminating in the discovery that if quark matter exists, it ought to be in a color superconducting state (Alford 2001; Alford et al. 2008; Rajagopal and Wilczek 2001a). This is made possible by the strong interaction among the quarks which is very attractive in some channels (antisymmetric anti-triplet channel). Pairs of quarks are therefore expected to form Cooper pairs. Since pairs of quarks cannot be color neutral, the resulting condensate will break the local color symmetry and form what is called a color superconductor. The phase diagram of such matter is expected to be very complex (see Fig. 1) (Alford 2001; Alford et al. 2008; Rajagopal and Wilczek 2001a; Weber 2005) which is caused by the fact that quarks come in three different colors, three different flavors, and different masses. In addition, bulk matter is neutral, with respect to both electric and color charge, and is in chemical equilibrium under the weak interaction processes that turn one quark flavor into another. The following pairing schemes have emerged so far (for details, see Weber (2005), Rajagopal and Wilczek (2001a), Alford (2001), and Alford et al. (2008) and references therein). At asymptotic densities the ground state of QCD with a

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F. Weber

negligibly small strange quark mass is the color-flavor locked (CFL) phase, where all three quark flavors participate symmetrically to pairing. The CFL phase has been shown to be electrically neutral without any need for electrons for a significant range of chemical potentials and strange quark masses (Rajagopal and Wilczek 2001b). After CFL, the two-flavor superconducting (2SC) phase is the most straightforward less symmetrically paired form of quark matter (Bailin and Love 1979; Barrois 1979). In this phase quarks with two out of three colors and two out of three flavors pair. The flavors with the most phase space near their Fermi surfaces, namely, up and down quarks, are the ones that pair, leaving strange quarks unpaired. Other possible condensation patterns are CFL-K 0 , CFL-K C and CFL- 0; , gCFL (gapless CFL phase), 1SC (single-flavor-pairing), CSL (color-spin locked phase), and the LOFF (crystalline pairing) phase, depending on ms , , and electric charge density (see Alford et al. (2008) and references therein). For chemical potentials that are of astrophysical interest,  < 1000 MeV, the gap energy, , may be between 50 and 100 MeV. The order of magnitude of this result agrees with calculations based on phenomenological effective interactions as well as with perturbative calculations for  > 10 GeV (Son 1999). We also note that superconductivity modifies the EoS at the order of .=/2 (Alford 2004; Alford and Reddy 2003), which is even for such large gaps only a few percent of the bulk energy. Such small effects may be safely neglected in present determinations of models for the nuclear EoS (Alford 2001). There has been much recent work on how color superconductivity in neutron stars could affect their properties (Alford 2001; Blaschke et al. 1999; Rajagopal and Wilczek 2001a). These studies reveal that possible signatures include the cooling by neutrino emission, the pattern of the arrival times of supernova neutrinos, the evolution of neutron star magnetic fields, (see  Chap. 50, “Evolution of the Magnetic Field of Neutron Stars”), rotational stellar instabilities, and glitches in rotation frequencies. The magnetic fields within color superconducting neutron star cores have been studied in Alford et al. (2000). As shown there, both 2SC and CFL quark matter cores admit magnetic fields without restricting them to quantized flux tubes. More than that, the magnetic fields within color superconducting neutron star cores were found to be stable on time scales much longer than the age of the universe, even if the spin period of the neutron star is changing. This is consistent with the hypothesis that neutron stars (or strange quark stars, for that matter) contain color superconducting cores of quark matter, which serve as anchors for the magnetic field (Alford et al. 2000).

7

Absolutely Stable Strange Quark Matter

So far it was assumed that quark matter forms a state of matter higher in energy than atomic nuclei. This is not necessarily correct, however, as expressed by the strange quark matter hypothesis. According to this hypothesis, strange quark matter (Farhi and Jaffe 1984), made of roughly equal numbers of up, down, and strange quarks

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plus electrons, could be more stable than ordinary nuclear matter (Bodmer 1971; Terazawa 1979; Witten 1984). If this should be correct, neutron stars would only be metastable with respect to a new class of compact stars, known as strange quark stars composed entirely of strange quark matter (Alcock and Olinto 1988; Alcock et al. 1986; Madsen 1999). Such objects can either be bare or enveloped in nuclear crusts (dressed strange stars) (Glendenning and Weber 1992; Weber 2005). A schematic illustration of the structure of a strange star is shown in Fig. 1. Strange quark stars differs from neutron stars in many respects, as summarized in Table 1. Once crucial difference comes from the electron layer at the surface of a quark stars. This layer is held to strange quark matter electrostatically, and the thickness of this layer is several hundred fermis. Since neither component, electrons layer and quark matter, is held in place gravitationally, the Eddington limit to the luminosity that a static surface may emit does therefore not apply, so that bare quark stars may have photon luminosities much greater than 1038 erg=s. It has been shown in Usov (1998) that this value may be exceeded by many orders of magnitude by the luminosity of e C e  pairs produced by the Coulomb barrier at the surface of a hot strange star. For a surface temperature of 1011 K, the luminosity in the out flowing pair plasma was calculated to be as high as 31051 erg=s. Such an effect may be a good observational signature of bare strange quark stars (Cheng and Harko 2003; Usov 1998, 2001a, b). If the strange star is dressed, however, the surface made of ordinary atomic matter would be subject to the Eddington limit. Hence the photon emissivity of a dressed quark star would be the same as for an ordinary neutron star. If quark matter at the stellar surface is in the CFL phase (see Sect. 6), the process of e C e  pair creation at the stellar quark matter surface may be turned off. This may be different for the early stages of a very hot CFL quark star (Vogt et al. 2004). In contrast to neutron stars, the radii of bare strange quark stars decrease monotonically with mass, according to M / R3 . The existence of nuclear crusts on quark stars changes the situation drastically (Glendenning 2000; Weber 1999, 2005). Since the crust is held gravitationally, the mass-radius relationship of quark stars with crusts can be qualitatively similar to mass-radius relationships of neutron stars and white dwarfs (Glendenning and Weber 1992), as shown in Fig. 7. In general, quark stars with or without nuclear crusts possess smaller radii (less than 10–12 km) than neutron stars, whose radii are greater than 10–12 km (see Table 1) (Özel et al. 2016; Zhang et al. 2007). This feature implies that quark stars have smaller mass- shedding (Kepler) periods than neutron stars, as discussed in Sect. 2. Moreover, due to the smaller radii of quarks stars, the complete sequence of quark stars – and not just those close to the mass peak, as it is the case for neutron stars – can sustain extremely rapid rotation (Glendenning and Weber 1992). In particular, a strange star with a typical pulsar mass of around 1:45 Mˇ has a Kepler period in the approximate range of 0:55 . PK =msec . 0:8. This is to be compared with PK  1 msec for neutron stars of the same mass (see Fig. 2). One of the most amazing features of strange quark stars concerns the existence of ultra-high electric fields on their surfaces, which, for ordinary (i.e., nonsuperconducting) quark matter, is around 1018 V/cm. If strange matter forms a color superconductor, as expected for such matter, the strength of the electric field may

1442 Fig. 7 Mass versus radius of strange star configurations with nuclear crusts (dashed and dotted curves) and gravitationally bound neutron stars and white dwarfs (solid curve). The strange stars carry nuclear crusts with chosen base densities of 4  1011 and 108 g=cm3 , respectively. Crosses denote the termination points of strange dwarfs sequences, whose quark matter cores have shrunk to zero. Solid dots refer to maximum-mass stars, minimum-mass stars are located at the vertical bars labeled “b” (Figure from Weber 1999)

F. Weber

c

d b b

b

increase to values that exceed 1019 V/cm. The energy density associated with such huge electric fields is on the same order of magnitude as the energy density of strange matter itself, which may alter the masses and radii of strange quark stars at the 15 % and 5 % level, respectively (Negreiros et al. 2009). The electrons at the surface of a quark star are not necessarily in a fixed position but may rotate with respect to the quark matter star (Negreiros et al. 2010). In this event magnetic fields can be generated which, for moderate effective rotational frequencies between the electron layer and the stellar body, agree with the magnetic fields inferred for several Central Compact Objects (CCOs). These objects could thus be interpreted as quark stars whose electron atmospheres rotate at frequencies that are moderately different (10 Hz) from the rotational frequency of the quark star itself. The electron surface layer may be strongly affected by the magnetic field of a quark star in such a way that the electron layer performs vortex hydrodynamical oscillations (Xu et al. 2012). The frequency spectrum of these oscillations has been derived in analytic form in Xu et al. (2012). If the thermal X-ray spectra of quark stars are modulated by vortex hydrodynamical oscillations, the thermal spectra of compact stars, foremost central compact objects (CCOs) and X-ray dim isolated neutron stars (XDINSs), could be used to verify the existence of these vibrational modes observationally. The central compact object 1E 1207.4-5209 appears particularly interesting in this context, since its absorption features at 0.7 and 1.4 keV can be comfortably explained in the framework of the hydro-cyclotron oscillation model (Xu et al. 2012). Rotating superconducting quark stars ought to be threaded with rotational vortex lines, within which the star’s interior magnetic field is at least partially confined. The vortices (and thus magnetic flux) would be expelled from the star during stellar spindown, leading to magnetic reconnection at the surface of the star and the prolific

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production of thermal energy. It has been shown in Niebergal et al. (2010) that this energy release can reheat quark stars to exceptionally high temperatures, such as observed for Soft Gamma Repeaters (SGRs), Anomalous X-Ray pulsars (AXPs) (see  Chaps. 51, “X-Ray Pulsars” and  52, “Young Neutron Stars with Soft Gamma Ray Emission and Anomalous X-Ray Pulsars”), and X-ray dim isolated neutron stars (XDINs), and that SGRs, AXPs, and XDINs may be linked ancestrally (Niebergal et al. 2010). Last but not least, we mention that the conversion of a neutron star to a hypothetical quark star could lead to quark novae (Ouyed et al. 2002). Such events could explain gamma ray bursts (Staff et al. 2008), the production of heavy elements such as platinum through r-process nucleosynthesis (Jaikumar et al. 2007), and doublehumped super-luminous supernovae (Ouyed and Leahy 2013; Ouyed et al. 2016).

8

Summary and Conclusions

The tremendous pressures in the cores of neutron stars might be able to break neutrons, protons plus other hadronic constituents in the centers of neutron stars into their quark constituents, creating a new state of matter known as quark matter made of deconfined up, down and strange quarks. There is also the intriguing possibility that such matter has an energy per baryon which is less than the energy per baryon of nuclear matter (atomic nuclei). If true, this would lead to the existence of a new class of compact stars known as strange (quark matter) stars, which are generically different from neutron stars. The physics of both classes of compact stars (neutron stars and strange stars) is discussed in this paper. Owing to the unprecedented wealth of high-quality data on neutron stars provided by radio telescopes, X-ray satellites–and soon the latest generation of gravitational-wave detectors–it seems within reach to decipher the inner workings of neutron stars and ultimately determine their true nature.

9

Cross-References

 Evolution of the Magnetic Field of Neutron Stars  Explosion Physics of Thermonuclear Supernovae and Their Signatures  Neutron Star Matter Equation of State  Neutron Stars as Probes for General Relativity and Gravitational Waves  Nuclear Matter in Neutron Stars  Observational and Physical Classification of Supernovae  Supernovae and Supernova Remnants: The Big Picture in Low Resolution  Supernovae from Massive Stars  The Masses of Neutron Stars  Thermal Evolution of Neutron Stars  X-Ray Pulsars  Young Neutron Stars with Soft Gamma Ray Emission and Anomalous X-Ray

Pulsars

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Acknowledgements This material is based upon work supported by the National Science Foundation under Grant No. PHY-1411708.

References Alcock C, Olinto AV (1988) Exotic phases of hadronic matter and their astrophysical applications. Ann Rev Nucl Part Sci 38:161 Alcock C, Farhi E, Olinto AV (1986) Strange stars. Astrophys J 310:261 Alford M (2001) Color-superconducting quark matter. Ann Rev Nucl Part Sci 51:131 Alford M (2004) Dense quark matter in compact stars. J Phys G 30:441 Alford M, Reddy S (2003) Compact stars with color superconducting quark matter. Phys Rev D 67:074024 Alford M, Berges J, Rajagopal K (2000) Magnetic fields within color superconducting neutron star cores. Nucl Phys B571:269 Alford MG, Schmitt A, Rajagopal K, Schäfer T (2008) Color superconductivity in dense quark matter. Rev Mod Phys 13:1455 Bailin D, Love A (1979) Superfluid quark matter. J Phys A12:L283; (1984) Superfluidity and superconductivity in relativistic fermion systems. Phys Rep 107:325 Barrois BC (1979) Non-perturbative effects in dense quark matter, Ph.D. thesis, California Institute of Technology, Pasadena, UMI 79-04847 Baym G (1978) Neutron stars and the physics of matter at high density. In: Balian R, Rho M, Ripka G (eds) Nuclear physics with heavy ions and mesons. Les Houches, session XXX, vol 2. North-Holland, Amsterdam, p 745 Benic S, Blaschke D, Contrera GA, Horvatic D (2014) Medium induced Lorentz symmetry breaking effects in nonlocal Polyakov-Nambu-Jona-Lasinio models. Phys Rev D 89:016007 Blaschke D, Sedrakian DM, Shahabasyan KM (1999) Diquark condensates and the magnetic field of pulsars. Astron Astrophys 350:L47 Blaschke D, Grigorian H, Voskresensky DN (2001) Cooling of hybrid neutron stars and hypothetical self-bound objects with superconducting quark cores. Astron Astrophys 368:561 Blaschke DB, Dumm GD, Grunfeld AG, Klahn T, Scoccola NN (2007) Hybrid stars within a covariant, nonlocal chiral quark model. Phys Rev C 75:065804 Bodmer AR (1971) Collapsed nuclei. Phys Rev D 4:1601 Boguta J, Bodmer AR (1977) Relativistic calculation of nuclear matter and the nuclear surface. Nucl Phys A292:413 Boguta J, Rafelski J (1977) Thomas Fermi model of finite nuclei. Phys Lett 71B:22 Bonanno L, Sedrakian A (2012) Composition and stability of hybrid stars with hyperons and quark color-superconductivity. Astron Astrophys 539:A16 Brown GE (1996) Supernova explosions, black holes and nucleon stars. In: Zuxun S, Jincheng X (eds) Proceedings of the nuclear physics conference – INPC’95. World Scientific, Singapore, p 623 Brown GE, Kubodera K, Rho M (1987) Strangeness condensation and “clearing” of the vacuum. Phys Lett 192B:273 Buballa M (2005) NJL-model analysis of dense quark matter. Phys Rep 407:205 Buballa M, Dexheimer V, Drago A, Fraga E, Haensel P, Mishustin I, Pagliara G, Schaffner-Bielich J, Schramm S, Sedrakian A, Weber F (2014) EMMI rapid reaction task force meeting on quark matter in compact stars. J Phys G Nucl Part Phys 41:123001 Cheng KS, Harko T (2003) Surface photon emissivity of bare strange stars. Astrophys J 596:451 Chubarian E, Grigorian H, Poghosyan G, Blaschke D (2000) Deconfinement transition in rotating compact stars. Astron Astrophys 357:968 Farhi E, Jaffe RL (1984) Strange matter. Phys Rev D 30:2379 Friedman JL, Ipser JR, Parker L (1986) Rapidly rotating neutron star models. Astrophys J 304:115

53 Strange Quark Matter Inside Neutron Stars

1445

Fuchs C (2004) The relativistic Dirac-Brueckner approach to nuclear matter. Lect Notes Phys 641:119 Fuchs C (2006) Kaon production in heavy ion reactions at intermediate energies. Prog Part Nucl Phys 56:1 Glendenning NK (2000) Compact stars, nuclear physics, particle physics, and general relativity, 2nd edn. Springer, New York Glendenning NK (2001) Phase transitions and crystalline structures in neutron star cores. Phys Rep 342:393 Glendenning NK, Weber F (1992) Nuclear solid crust on rotating strange quark stars. Astrophys J 400:647 Glendenning NK, Weber F (2001) Phase transition and spin clustering of neutron stars in X-ray binaries. Astrphys J 559:L119 Glendenning NK, Pei S, Weber F (1997) Signal of quark deconfinement in the timing structure of pulsar spin-down. Phys Rev Lett 79:1603 Haensel P, Zdunik JL, Schaeffer R (1986) Strange quark stars. Astron Astrophys 160:121 Jaffe RL (1977) Perhaps a stable Dihyperon. Phys Rev Lett 38:195; (1977) Erratum, Phys Rev Lett 38:617 Jaikumar P, Meyer BS, Otsuki K, Ouyed R (2007) Nucleosynthesis in neutron-rich ejecta from quark-novae. Astron Astrophys 471:227 Kaplan DB, Nelson AE (1986) Strange goings on in dense nucleonic matter. Phys Lett 175B:57; (1988) Kaon condensation in dense matter. Nucl Phys A479:273 Kettner C, Weber F, Weigel MK, Glendenning NK (1995) Structure and stability of strange and charm stars at finite temperature. Phys Rev D 51:1440 Klahn T, Blaschke D, Sandin F, Fuchs C, Faessler A, Grigorian H, Ropke G, Trumper J (2007) Modern compact star observations and the quark matter equation of state. Phys Lett B654:170 Klahn T, Łastowiecki R, Blaschke DB (2013) Implications of the measurement of pulsars with two solar masses for quark matter in compact stars and HIC. A NJL model case study. Phys Rev D 88:085001 Madsen J (1999) Physics and astrophysics of strange quark matter. Lect Notes Phys 516:162 Madsen J, Haensel P (eds) (1991) Proceedings of the international workshop on strange quark matter in physics and astrophysics. Nucl Phys B (Proc Suppl) 24B Na X, Xu R, Weber F, Negreiros R (2012) Transport properties of a quark-hadron Coulomb lattice in the cores of neutron stars. Phys Rev D 86:123016 Negreiros R, Weber F, Malheiro M, Usov V (2009) Electrically charged strange quark stars. Phys Rev D 80:083006 Negreiros R, Mishustin IN, Schramm S, Weber F (2010) Properties of bare strange stars associated with surface electric fields. Phys Rev D 82:103010 Niebergal B, Ouyed R, Negreiros R, Weber F (2010) Meissner effect and vortex expulsion in colorsuperconducting quark stars, and its role for reheating of magnetars. Phys Rev D 81:043005 Oppenheimer JR, Volkoff GM (1939) On massive neutron cores. Phys Rev 55:374 Orsaria M, Rodrigues H, Weber F, Contrera GA (2013) Quark-hybrid matter in the cores of massive neutron stars. Phys Rev D 87:023001 Orsaria M, Rodrigues H, Weber F, Contrera GA (2014) Quark deconfinement in high-mass neutron stars. Phys Rev C 89:015806 Ouyed R, Leahy D (2013) The peculiar case of the “double-humped” super-luminous supernova SN 2006oz. Astron Astrophys 13:1202 Ouyed R, Dey J, Dey M (2002) Quark-Nova. Astron Astrophys 390:L39 Ouyed R, Leahy D, Koning N, Staff JE (2016) Quark-Novae in binaries: observational signatures and implications to astrophysics. arXiv:1601.04235v1 [astro-ph.HE] Özel F, Psaltis D, Güver T, Baym G, Heinke G, Guillot S (2016) The dense matter equation of state from neutron star radius and mass measurements. Astrophys J 820:28 Page D, Reddy S (2006) Dense matter in compact stars: theoretical developments and observational constraints. Ann Rev Nucl Part Sci 56:327

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Rajagopal K, Wilczek F (2001a) In: Shifman M (ed) The condensed matter physics of QCD. At the frontier of particle physics/handbook of QCD. World Scientific, Singapore Rajagopal K, Wilczek F (2001b) Enforced electrical neutrality of the color-flavor locked phase. Phys Rev Lett 86:3492 Schaffner J, Mishustin IN (1996) Hyperon-rich matter in neutron stars. Phys Rev C 53:1416 Sedrakian A (2007) The physics of dense hadronic matter and compact stars. Prog Part Nucl Phys 58:168 Son DT (1999) Superconductivity by long-range color magnetic interaction in high-density quark matter. Phys Rev D D59:094019 Spinella WM,Weber F, Contrera GA, Orsaria MG (2016) Neutrino emissivity in the quark-hadron mixed phase of neutron stars. Eur Phys J A 52:61. arXiv:1507.06067 Spyrou NK, Stergioulas N (2002) Spin-down of relativistic stars with phase transitions and PSR J0537-6910. Astron Astrophys 395:151 Staff J, Niebergal B, Ouyed R (2008) Gamma-ray burst engine activity within the quark nova scenario: prompt emission, X-ray plateau and sharp drop-off. MNRAS 391:178 Terazawa H (1979) INS-report-338 (INS, University of Tokyo); (1989) Super-Hypernuclei in the quark-shell model. J Phys Soc Jpn 58:3555; (1989) Super-Hypernuclei in the quark-shell model. II 58:4388; (1990) Super-Hypernuclei in the quark-shell model. III. 59:1199 Tolman RC (1939) Static solutions of Einstein’s field equations for spheres of fluid. Phys Rev 55:364 Usov VV (1998) Bare quark matter surfaces of strange stars and e+ e emission. Phys Rev Lett 80:230 Usov VV (2001a) Thermal emission from bare quark matter surfaces of hot strange stars. Astrophys J 550:L179 Usov VV (2001b) The response of bare strange stars to the energy input onto their surfaces. Astrophys J 559:L137 van Dalen ENE, Fuchs C Faessler A (2004) The relativistic Dirac-Brueckner approach to asymmetric nuclear matter. Nucl Phys A744:227 Vogt C, Rapp R, Ouyed R (2004) Photon emission from dense quark matter. Nucl Phys A735:543 Weber F (1999) Pulsars as astrophysical laboratories for nuclear and particle physics. IOP Publishing, Bristol Weber F (2005) Strange quark matter and compact stars. Prog Part Nucl Phys 54:193 Weber F, Negreiros R, Rosenfield P, Stejner M (2007) Pulsars as astrophysical laboratories for nuclear and particle physics, Prog Part Nucl Phys 59:94 Weber F, Orsaria M, Negreiros R (2013) Impact of rotation on the structure of composition of neutron stars. In: Proceedings of compact stars in the QCD phase diagram (CSQCD III), arXiv:1307.1103 [astro-ph.SR] Weber F, Contrera GA, Orsaria MG, Spinella W, Zubairi O (2014) Properties of high-density matter in neutron stars, Mod Phys Lett A 29(23):1430022 Witten E (1984) Cosmic separation of phases, Phys Rev D 30:272 Xu RX, Bastrukov SI, Weber F, Yu JW, Molodtsova IV (2012) Absorption features caused by oscillations of electrons on the surface of a quark stars, Phys Rev D 85:023008 Yasutake N, Łastowiecki R, Benic S, Blaschke D, Maruyama T, Tatsumi T (2014) Finite-size effects at the hadron-quark transition and heavy hybrid stars, Phys Rev C 89:065803 Zhang CM, Kojima Y (2006) The bottom magnetic field and magnetosphere evolution of neutron star in low-mass X-ray binary, MNRAS 366:137 Zhang CM, Yin HX, Kojima Y, Chang HK, Xu RX, Li XD, Zhang B, Kiziltan B (2007) Measuring neutron star mass and radius with three mass-radius relations, MNRAS 374:232 Zhang CM, Wang J, Zhao YH, Yin HX, Song LM, Menezes DP, Wickramasinghe DT, Ferrario L, Chardonnet P (2011) Study of measured pulsar masses and their possible conclusions, Astron & Astrophys 527:A83

Neutron Stars as Probes for General Relativity and Gravitational Waves

54

Norbert Wex

Abstract

The discovery of the first radio pulsar in a binary system, by Russell Hulse and Joseph Taylor in 1974, initiated a completely new field for testing general relativity (GR) and alternative theories of gravity. To date there are a number of binary pulsars known, which can be utilized for precision test of relativistic gravity. Depending on their orbital properties and their companion, these pulsars provide tests for various different phenomena, predicted by GR and its alternatives. In many aspects, these tests go far beyond of what can be achieved in the solar system. A prime example is the verification of the existence of gravitational waves, as predicted by GR. It is the large fractional binding energy (0:1) and the strong internal gravity of neutron stars, that make high-precision timing of binary pulsars ideal probes for various predictions of strong-field gravity. So far, GR has passed all these tests with flying colors. In the near future, in terms of radio pulsars, new radio telescopes, like the SKA, will soon greatly enhance our timing capabilities of known binary pulsars. Furthermore, new instrumentation and search techniques promise the discovery of many new systems, suitable for testing GR, among these hopefully also a pulsar in orbit around a black hole. Quite recently, ground-based gravitational wave detectors have made their first observations of gravitational waves. This has not only opened a new window on the universe, but has also taken our gravity tests to the highly dynamical strong-field regime. While the first gravitational wave signals came from merging black holes, it is expected that in the near future mergers of double neutronstar as well as neutron star-black hole systems will be among the observed

N. Wex () Fundamental Physics in Radio Astronomy, Max Planck Institute for Radio Astronomy, Bonn, Germany e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_72

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gravitational wave signals. Moreover, pulsar timing arrays are expected to soon observe gravitational waves in the nano-Hertz band, emitted by supermassive black hole binaries.

Contents 1 2 3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radio Pulsars and Pulsar Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GR Tests with Binary Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Hulse-Taylor Pulsar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Double Pulsar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Other Pulsars in Double Neutron-Star Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Pulsar-White-Dwarf Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Some Future Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Hundred years ago, on November 25, 1915, Einstein presented his field equations of gravitation to the Prussian Academy of Science (Einstein 2015b). With this publication, general relativity (GR) was finally completed as a logically consistent physical theory. Already one week before, based on the vacuum part of his field equations, Einstein was able to show that GR naturally explains the anomalous 4300 =century advance of the Mercury perihelion (Einstein 2015a). Four years later, GR passed a second test, when Dyson and Eddington announced their results from the May 29, 1919 total eclipse, which confirmed the deflection of light in the gravitational field of the Sun in agreement with the 1:7500 predicted by GR (Dyson et al. 1920). Since then, solar system tests have been greatly improved in terms of precision as well as diversity. The deflection of electromagnetic radiation by the gravitational field of the Sun has been verified with a precision of 104 (Lambert and Le PoncinLafitte 2011), and the precession of the Mercury orbit has been found in agreement with GR at a similar level. An even better test for the curvature of space-time in the vicinity of the Sun is based on the Shapiro delay, the so-called fourth test of GR (Shapiro 1964). A measurement of the frequency shift of radio signals used in the communication with the Cassini spacecraft lead to a 105 confirmation of GR (Bertotti et al. 2003). Before the 1970s, precision tests for gravity theories were constrained to the weak gravitational fields of the solar system. These tests, however, say little to nothing about the validity of GR in the strong gravity regime. In the solar system < j˚j=c 2  106 , where ˚ denotes the Newtonian gravitational potential and c the

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speed of light. Consequently, the solar system represents a weakly curved spacetime, everywhere close to Minkowski space-time. Moreover, the masses and/or their velocities in the solar system are small, and therefore gravitational waves do not play any role in the solar system dynamics. In fact, the solar system gravitational wave luminosity is of the order of 104 W, typically in form of gravitational waves with periods of several years and decades, making gravitational wave damping absolutely unmeasurable in the solar system. The discovery of the first radio pulsar in a binary system, by Russell Hulse and Joseph Taylor in 1974 (Hulse and Taylor 1975), gave the first opportunity to take precision gravity tests beyond the weak-field slow-motion regime. As a comparison, the space-time curvature (square root of the Kretschmann invariant) caused by the Hulse-Taylor pulsar is about 13 orders of magnitude larger than the one caused by the Sun, and the gravitational wave luminosity of the Hulse-Taylor pulsar in its compact 8-h orbit is about 8  1024 W. From this, it is immediately evident, that the discovery of binary pulsars provided us with “laboratories” to conduct precision tests in two new gravity regimes (Damour and Taylor 1992; Wex 2014): (Q) The quasi-stationary strong-field regime, i.e., the space-time of strongly selfgravitating objects, which however are well separated and therefore still move slow compared to the speed of light. (R) The radiative regime, comprising the generation and properties of gravitational waves. In the context of pulsars, this is primarily the back reaction of the emitted gravitational wave onto the orbital dynamics. In the meantime, many more binary pulsars have been discovered that can be utilized for tests of GR and alternative theories of gravity. Systems where the pulsar is in orbit with another neutron star or a white dwarf have turned out to be particularly useful for gravity tests. More details will be given below. Key to the precision tests with binary pulsars is the so-called pulsar timing technique, which we briefly introduce in Sect. 2. On September 14th, 2015, the two LIGO detectors at Livingston/Louisiana and Hanford/Washington have for the first time directly observed gravitational waves (Abbott et al. 2016a). The signals of this ‘GW150914 event’ came from the merger of two stellar-mass black holes with about 36 and 29 solar masses. This has taken our gravity tests to the highly dynamical strong-field regime, where space-time is strongly curved and velocities are close to the speed of light. Moreover, it allowed to perform tests on the properties of gravitational waves, i.e., regime (R), in particular tests on a frequency dependence of their propagation speed. While the GW150914 is in good agreement with GR, it cannot probe, for instance, strong-field deviations from GR sourced by matter (Yunes et al. 2016). For such effects we have to wait for the observations of double neutron-star or neutron star-black hole mergers. We will very briefly discuss this in Sect. 4.

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Radio Pulsars and Pulsar Timing

Radio pulsars, i.e., rotating neutron stars with coherent radio emission along their magnetic poles, were discovered in 1967 by Jocelyn Bell and Antony Hewish (Hewish et al. 1968). Fairly soon after their discovery, it was clear that radio pulsars are rapidly rotating, highly magnetized (typically of order 1012 G) neutron stars, which emit radio waves along their magnetic poles. To date, about 2500 of these “cosmic lighthouses” are known, out of which about 10 % reside in binary systems (Manchester et al. 2005). The population of radio pulsars can be nicely presented in a diagram that gives the two main characteristics of a pulsar: the rotational period P and its temporal change PP due to the loss of rotational energy (see Fig. 1). Fastrotating pulsars with small PP , i.e., low B field, so-called millisecond pulsars, appear to be particularly stable in their rotation. On long time scales, some of them rival the best atomic clocks in terms of stability (Hobbs et al. 2012). This property makes pulsars ideal tools for high-precision tests of gravity theories. In such tests, pulsar observations are simply clock-comparison experiments to probe the space-time of a binary pulsar: on the one hand, the “pulsar clock” is read off by counting the pulses in the pulsar signal, i.e., determine its rotational phase, and on the other hand, the arrival times of the pulses at the radio telescope are measured with the local atomic clock. After fitting an appropriate timing model to these arrival times, one obtains a phase-connected solution for all the timing data points of a pulsar. In the phase-connected approach lies the true strength of pulsar timing: the timing

Fig. 1 Period-period derivative diagram for known radio pulsars (Manchester et al. 2005). Black dots indicate radio pulsars in globular clusters. Red circles indicate radio pulsars in binary systems. The green lines give show the estimated surface dipole magnetic field (Lorimer and Kramer 2004)

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Table 1 Examples of precision measurements for various astrometric and physical quantities, using pulsar timing. A number in brackets indicates the (one-sigma) uncertainty in the last digit(s) of each value Rotational period of a pulsar: Distance: Proper motion in the sky: Orbital period of a binary pulsar: Orbital eccentricity: Relativistic periastron advance: Masses of a neutron stars: Mass of a white dwarf:

5.757451924362137(2) ms PSR J04374715 Verbiest et al. (2008) 157(1) pc 140.915(1) mas yr1 1.533449451246(8) d

PSR J04374715 Verbiest et al. (2008) PSR J04374715 Verbiest et al. (2008) PSR J19093744 Matthews et al. (2015)

0.0000749402(6) 4:226598.5/ deg yr1

PSR J1713+0747 Zhu et al. (2015) PSR B1913+16 Weisberg et al. (2010)

1:4398.2/ Mˇ

PSR B1913+16

0:2131.25/ Mˇ

PSR J19093744 Matthews et al. (2015)

Weisberg et al. (2010)

model has to account for every observed pulse over a time scale of several years, in some cases even several decades, without losing a single rotation of the pulsar. This makes pulsar timing extremely sensitive to even tiny deviations in the model parameters and therefore vastly superior (106 times) to a simple measurement of Doppler shifts in the pulse period. Table 1 illustrates the capabilities of pulsar timing for various experiments, like mass determination, astrometry, and gravity tests. Dropping an unknown constant factor, the proper time T of the pulsar is linked to its rotational phase  via 1 P  T 0 /2 C : : :  D 0 C .T  T0 / C .T 2

(1)

where T0 is a fixed epoch, and denotes the rotational frequency. The frequency derivative P accounts for the slow spin-down rate of the pulsar, which might not be constant over the time span of observations, making it necessary to fit for higher time derivatives of . At the telescope one measures the topocentric time of arrival (TOA) of a pulse. For details on the measurement process of TOAs, we refer the reader to Chapter 8 of Lorimer and Kramer (2004). The TOA is linked to the pulsar’s proper time of emission via a timing model that accounts for all the delays that are observable in the timing data. The time transformation can be split into two parts. First, the transformation from a topocentric TOA to the (infinite frequency) TOA at the solar system barycenter (SSB): tSSB D topo  D=f 2 C E C R C S ;

(2)

where E accounts for time dilation effects along the world line of the telescope, R represents the Roemer delay caused by the motion of the telescope in the SSB frame, and S accounts for the Shapiro delay (Shapiro 1964) caused by the

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masses in the solar system, predominantly by the Sun. The last two steps in the time transformation depend on the position of the pulsar in the sky. The D=f 2 term introduces the dispersive delay due to the free electrons in the interstellar medium that depends on the frequency f of the photon. If the pulsar is member of a binary system, further time transformations are required to account for the binary motion and propagation delays that are intrinsic to the binary system. This second step can be generally written as tSSB D T C B :

(3)

The parameters entering B are at the heart of testing gravity with binary pulsars, which is the subject of the next section.

3

GR Tests with Binary Pulsars

For binary-pulsar experiments that test the quasi-stationary strong-field regime (Q) and the gravitational wave damping (R), a phenomenological parameterization, the so-called ‘parameterized post-Keplerian’ (PPK) formalism, has been introduced by Damour (1988) and extended by Damour and Taylor (1992). The PPK formalism parameterizes all the observable effects that can be extracted independently from binary-pulsar timing and pulse-structure data. Consequently, the PPK formalism allows to obtain theory-independent information from binary-pulsar observations by fitting for a set of Keplerian and post-Keplerian parameters. The Keplerian parameters are those six parameters, which are required to fully describe the Newtonian motion of a binary pulsar: • • • • • •

Pb – orbital period of the binary system, x  ap sin i =c – projected semimajor axis of the pulsar orbit, e – orbital eccentricity, T0 – time of periastron passage ! – longitude of periastron, measured from the ascending node, ˝ – longitude of the ascending node in the plane of the sky,

where ap is the semimajor axis of the pulsar orbit, and i denotes the inclination of the orbit, which is the angle between the orbital angular momentum and the line of sight toward the pulsar system. Generally, the first five Keplerian parameters can be measured with exquisite precision from pulsar timing (see Table 1). For most binary pulsars, ˝ is not measurable. On the other hand, ˝ is important only for certain tests of alternatives to GR. Quite a few binary pulsars show prominent relativistic contributions in their motion and in the propagation of their radio signals. In such cases the Keplerian parameters are not sufficient. Relativistic effects are parameterized in a theoryindependent way by the post-Keplerian parameters. In this section, we will only introduce those post-Keplerian parameters, which so far have been measured in

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binary pulsars and used to test gravity theories and gravitational wave damping (Lorimer and Kramer 2004): • !P – relativistic advance of the longitude of periastron, •  – amplitude of the Einstein delay, a periodic variation of the pulsar’s time dilation (combination of second-order Doppler effect and gravitational redshift), • r, s – “range” and “shape” of the Shapiro delay, the two parameters that parameterize the propagation delay caused by the gravitational field of the companion, .p/ • ˝SO – geodetic precession of the pulsar spin due to relativistic spin-orbit coupling, • PPb – secular change in the orbital period, caused by gravitational wave damping. Apart from the last post-Keplerian parameter, all of them are related to effects at first post-Newtonian order, i.e., order v 2 =c 2 , where v is a typical velocity of the relative motion. They parameterize quasi-stationary strong-field effects (gravity regime (Q)). The last parameter, PPb , is related to gravity regime (R). In GR this is a 2.5 post-Newtonian contribution (order v 5 =c 5 ), while in many alternative theories of gravity, there is emission of gravitational dipolar radiation, that enters the orbital dynamics at the 1.5 post-Newtonian level (order v 3 =c 3 ). In a given theory of gravity, the post-Keplerian parameters are functions of the well-measured Keplerian parameters and the, a priori unknown, masses of pulsar and companion, mp and mc , respectively. In GR, to leading order, the post-Keplerian parameters read (see Lorimer and Kramer (2004) and references therein) 5=3

2=3

!P D 3 nb .1  e 2 /1 .mp C mc /2=3 Tˇ ; 1=3

 D nb

e

mc .mp C 2mc / 2=3 T ; .mp C mc /4=3 ˇ

r D mc T ˇ ; 2=3

5=3

(5) (6)

s D sin i D nb x .p/

(4)

˝SO D nb .1  e 2 /1

.mp C mc /2=3 1=3 Tˇ ; mc

(7)

mc .4mp C 3mc / 2=3 T ; 2.mp C mc /4=3 ˇ

(8)

mp mc 192 5=3 1 C .73=24/e 2 C .37=96/e 4 5=3 nb PPb D  T ; 2 7=2 5 .1  e / .mp C mc /1=3 ˇ

(9)

where Tˇ  GMˇ =c 3 D 4:925490947 s. The masses mp and mc are measured in units of solar masses Mˇ . A note on the Einstein-delay amplitude  . Although it becomes larger with increasing orbital period, it is generally not measurable for wide systems. The reason for this is the degeneracy between the Roemer delay and the Einstein delay, which can only be broken if there is a sufficiently large !, P which is however not the case in binaries with long orbital periods.

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As the masses, mp and mc , are a priori unknown, the measurement of a single or even two relativistic effects in a binary pulsar does generally not allow for a quantitative test of GR or any other gravity theory. One needs to measure at least three post-Keplerian parameters in order to perform a gravity test. If then, for a given theory of gravity, there is a region in the mp -mc plane which is in agreement with all the post-Keplerian parameters measured, then the theory has passed the test. We will see examples for this below. In some cases, additional information can come from optical observations of the companion star, in particular if the companion is a bright white dwarf that allows for high-resolution spectroscopy. In such a case, the Doppler shifts in the spectral lines allow to measure the line-of-sight motion of the white dwarf, which, when combined with the radio observations of the pulsar, gives the mass ratio R D mp =mc of the system. Furthermore, modeling the Balmer lines in the spectrum, based on whitedwarf models, gives the mass of the white dwarf mc , and therefore the mass of the pulsar mp D mc R. At this point the system is fully determined, and every relativistic effect measured is then a gravity test. Also for this, we will give examples and references below.

3.1

The Hulse-Taylor Pulsar

The first binary pulsar was discovered by Russell Hulse and Joseph Taylor in summer 1974 (Hulse and Taylor 1975). The pulsar, PSR B1913+16, has a rotational period of 59 ms and is in a highly eccentric (e D 0:62) 7.8-h orbit around an unseen companion that, because of its mass and from binary evolutionary considerations, is believed to be also a neutron star. The first relativistic effect seen in the timing observations of the Hulse-Taylor pulsar was the secular advance of periastron !. P Due to its large value of 4.2 deg/yr, this effect was well measured already one year after the discovery (Taylor et al. 1976). As explained above, at this stage a quantitative test of GR was not possible; however, assuming GR is correct, Eq. (4) gives the total mass M D mp C mc of the system. From the modern value, one finds M D 2:828378 ˙ 0:000007 Mˇ (Weisberg et al. 2010). Strictly speaking, this is the total mass of the system scaled with an unknown Doppler factor D, i.e., M observed D D 1 M intrinsic (Damour and Taylor 1992). For typical velocities, D  1 is expected to be of order 104 (see for instance Wex et al. (2000)). In gravity tests based on post-Keplerian parameters, the factor D drops out and is therefore irrelevant (Damour and Deruelle 1986; Damour and Taylor 1992). It took a few more years to measure the Einstein delay (5) with good precision, since one had to wait for the Einstein delay to separate from the Roemer delay. By the end of 1978, the timing of PSR B1913+16 yielded a measurement of the postKeplerian parameter  (Taylor et al. 1979). Together with the total mass from !, P equation (5) can now be used to calculate the individual masses. With the modern value for  and the total mass given above, one finds the individual masses to

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be mp D 1:4398 ˙ 0:0002 Mˇ and mc D 1:3886 ˙ 0:0002 Mˇ for pulsar and companion, respectively (Weisberg et al. 2010). These are the most precise neutronstar masses published. As mentioned above, in order to perform a test of GR a third post-Keplerian parameter needs to be measured. In fact, already in December 1978, Taylor et al. (1979) reported the measurement of a decrease in the orbital period PPb , consistent with Eq. (9). This was the first proof for the existence of gravitational waves as predicted by GR. In the meantime the PPb is measured with a precision of 0.04 %. However, this is not the precision with which the validity of the quadrupole formula is verified in the PSR B1913+16 system. The observed PPb needs to be corrected for extrinsic effects (ı PPbext ), most notably the differential galactic acceleration and the Shklovskii effect, to obtain the intrinsic value PPbint caused by gravitational wave damping (Damour and Taylor 1991). Both of these effects depend on the distance d to the pulsar. Unfortunately, there is a large uncertainty in the distance to PSR B1913+16 (d D 9:9 ˙ 3:1 kpc) (Weisberg et al. 2010). In addition, there are further uncertainties, e.g., in the galactic gravitational potential and the distance of the Earth to the galactic center. Accounting for all these uncertainties leads to an agreement between PPbint D PPb  ı PPbext and PPbGR at the level of about 0:3 % (Weisberg et al. 2010). The corresponding mass-mass diagram is given in Fig. 2.

˙

P˙b

γ

Fig. 2 Mass-mass diagram for PSR B1913+16 based on GR and the three observed post-Keplerian parameters !P (magenta),  (blue) and PPb (black). The dashed PPb curve is based on the observed PPb , without corrections for galactic and Shklovskii effects. The solid PPb curve is based on the corrected (intrinsic) PPb , where the outer lines indicate the one-sigma boundaries. Parameter values are taken from Weisberg et al. (2010)

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As the precision of the radiative test with PSR B1913+16 is limited by the modeldependent uncertainties in the correction ı PPbext , it is not expected that this test can be significantly improved in the near future. Shortly after the discovery of PSR B1913+16, Damour and Ruffini (1974) proposed a test for geodetic precession in that system. According to GR, the spin of the pulsar is expected to precess around the orbital angular momentum with a rate of about 1.3 deg/yr, due to relativistic spin-orbit coupling (Barker and O’Connell 1975). As a consequence, this should lead to a gradual change in the pulse profile, while the pulsar changes its orientation with respect to the line of sight. In particular, one expects a change in the pulse width, as the line of sight over time cuts through different parts of the emission cone. Such a geometrical effect was indeed seen by 1998 (Kramer 1998). However, so far it was not possible to convert this into a quantitative test for the precession rate. On the other hand, assuming GR, it can be used to explore the beam shape and precession geometry of PSR B1913+16 Weisberg and Taylor (2002). As a consequence of the geodetic precession, PSR B1913+16 is expected to become invisible in about ten years from now (Kramer 1998).

3.2

The Double Pulsar

In 2003 a compact binary system was discovered where, at first, one member was identified as a radio pulsar with a 23 ms rotational period (Burgay et al. 2003). About half a year later, the companion was also recognized as a radio pulsar with a spin period of 2.8 s (Lyne et al. 2004). Both pulsars, known as PSRs J07373039A and J07373039B (A and B hereafter), orbit each other in less than 2.5 h in a mildly eccentric (e D 0:088) orbit. This system is so far the only double neutronstar system where both neutron stars are known to be active radio pulsars, hence being called the double pulsar. Till today, the double pulsar is the most relativistic binary pulsar suitable for high-precision gravity tests. The relativistic advance of periastron, !, P is 16.9 deg/yr, which is more than four times larger than that of the Hulse-Taylor pulsar. This means that the eccentric orbit does a full rotation in just 21 years. Furthermore, in gravitational waves the double pulsar is three times more luminous than the Hulse-Taylor pulsar. For detailed reviews of the double pulsar, see (Kramer and Stairs 2008; Kramer and Wex 2009). In the double pulsar system, a total of six(!) post-Keplerian parameters have been measured by now. Five arise from four different relativistic effects visible in pulsar timing (Kramer et al. 2006), while a sixth one, related to geodetic precession, can be determined from flux measurements around the superior conjunction of A (Breton et al. 2008). The relativistic precession of the orbit, !, P was measured within a few days after timing of the system commenced, and by 2006 it was already known with a precision of 0.004 % (Kramer et al. 2006). At the same time, the measurement of the amplitude of Einstein delay,  , reached 0.7 % (Kramer et al. 2006). Due to the periastron precession of about 17 deg/yr, the Einstein delay was soon well separable from the Roemer delay. Just three years after the discovery of the double pulsar,

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Fig. 3 Shapiro delay signal (pre-fit) in the timing data of A. Data is taken from Kramer et al. (2006), modulo a constant shift

the decrease of the orbital period due to gravitational wave damping was already measured with a precision of 1.4 %. By now the precision is well below 0.1 % (Kramer 2012), providing the best test for the existence of gravitational waves as predicted by GR. Unlike the Hulse-Taylor pulsar, the Double-Pulsar orbit is hardly inclined with respect to the line of sight, i.e., seen nearly edge on. Consequently, near superior conjunction, the pulsar signal comes particularly close to the companion and hence suffers a particularly prominent Shapiro delay caused by the companion’s curved space-time. Figure 3 shows the Shapiro delay in the timing signals of A. In case of B, one has a similar effect, which however is unobservable due to much larger uncertainties in the TOA measurements. The Shapiro delay allows the measurement of two more post-Keplerian parameters: the range r and the shape s, which by 2006 were already measured with a precision of 5 % and 0.04 %, respectively. From the ı C0:5ı measured value, s D sin i D 0:99974C0:00016 0:00039 .i D 88:7 0:8ı ) one can already see how exceptionally edge on this system is. Finally, the edge-on configuration of the double pulsar leads to a further test of GR that did not directly come from timing. During every superior conjunction of A, its signals passes pulsar B at a distance of less than 20,000 km. This is small compared to the extension of B’s magnetosphere. Consequently, at every superior conjunction A gets periodically eclipsed over a time span of about 30 s, in a characteristic way, due to the absorption of the radio signals by the plasma in the “doughnut-shaped” magnetosphere of pulsar B (Lyne et al. 2004). The pattern of this eclipse can be used to determine the orientation of the spin of B. Over the course of several years, Breton et al. (2008) observed characteristic shifts in the eclipse pattern that can be directly related to a precession of the spin of B around

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the orbital angular momentum. Like in the Hulse-Taylor pulsar, such a precession is expected to arise from the relativistic spin-orbit coupling (geodetic precession). Unlike the Hulse-Taylor pulsar, the double pulsar allowed for a quantitative test of the precession rate. The measured value, ˝SO D 4:77C0:66 0:65 deg=yr, is in good GR agreement with that predicted by GR: ˝SO D 5:07 deg=yr. This is the sixth postKeplerian parameter measured in the double pulsar system. The geodetic precession of B not only changes the pattern of the flux modulations observed during the eclipse of A, it also changes the orientation of pulsar B’s emission beam with respect to our line of sight. As a result of this, geodetic precession has by now turned B in such a way that since 2009 B is no longer seen by radio telescopes on Earth (Perera et al. 2010). Figure 4 shows the mass-mass diagram for the double pulsar. It nicely shows that the GR is in excellent agreement with the measurements of relativistic effects in the double pulsar, passing various quasi-stationary strong-field tests and the radiative test apparent in the decay of the orbital period.

Fig. 4 Mass-mass diagram for the PSR J07373039A/B system based on GR, showing constraints from six post-Keplerian parameters (!, P , PPb , r, s, ˝SO ) and the mass ratio (R). The mass ratio comes directly from the fact that for both of the components in the binary system, one can measure the Roemer delay: R D mA =mB D xB =xA D 1:0714 ˙ 0:0011, where xA and xB denote the projected semimajor axes of A and B respectively. Figure courtesy of Michael Kramer

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Finally, compared to the Hulse-Taylor pulsar, the double pulsar is much closer to Earth. Because of this, a direct distance estimate of 1:15C0:22 0:16 kpc based on a parallax measurement with very-long-baseline interferometry (VLBI) was obtained (Deller et al. 2009). As a consequence, one can correct much better for the Shklovskii effect and the differential galactic acceleration (ı PPbext ). In fact, with the current precision in the distance measurement, GR tests based on PPb can be taken to the 0.01 % level (Deller et al. 2009).

3.3

Other Pulsars in Double Neutron-Star Systems

Besides the Hulse-Taylor and the double pulsar, presently there are additional four pulsars (PSRs B1534+12, J17562251, J1906+0746, and B2127+11C) which are believed to have a neutron-star companion, and where three or more post-Keplerian parameters have been measured (see Manchester (2015), and references therein). The most interesting among these is PSR B1534+12, where a total of six postKeplerian parameters (!, P  , PPb , r, s, ˝SO ) have been measured by now (Fonseca et al. 2014). Unfortunately, theory-independent distance estimations for this pulsar still have large uncertainties. As a consequence of this, the extrinsic contributions to the orbital period change, ı PPbext , are not well understood. Therefore that system yields only a very poor radiative test. On the other hand, the remaining post-Keplerian parameters can be used to perform different tests of the quasi-stationary strongfield regime (Q), providing a 0:2 % verification of GR for the space-time of two strongly self-gravitating objects. PSR B1534+12 was the first pulsar, for which a constraint on the geodetic precession (˝SO ) of a neutron star could be derived (Stairs et al. 2004). By now there is a measurement for ˝SO with a 17 % uncertainty, which is in good agreement with GR (Fonseca et al. 2014). The precision is comparable with the one obtained in the double pulsar, yet based on a completely different method, by analyzing changes in pulse-structure parameters, such as pulse profile shape and polarization properties of PSR B1534+12. Finally, we would like to point out that PSR B2127+11C is a member of the globular cluster M15. For this reason, its usability for a radiative test is limited, as one cannot properly account for the ı PPbext caused by the gravitational potential of the cluster. On the other hand, the observed PPb might be useful to constrain the location of PSR B2127+11C within the globular cluster (Jacoby et al. 2006).

3.4

Pulsar-White-Dwarf Systems

The best “pulsar clocks” are found among the fully recycled millisecond pulsars, which have rotational periods of less than about 10 ms (see, e.g., Verbiest et al. (2009)). Many of them have a white-dwarf companion. A result of the stable mass transfer between companion and pulsar in the past – responsible for the recycling of the pulsar – is a very efficient circularization of the binary orbit that leads to a pulsarwhite-dwarf system with very small eccentricity (Phinney 1992). For such systems,

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the post-Keplerian parameters !P and  are generally not observable. There are a few cases where the orbit is seen sufficiently edge on, so that a measurement of the Shapiro delay gives access to the two post-Keplerian parameters r and s with good precision. With these two parameters, the system is then fully determined, and in principle can be used for gravity tests, if there is a measurement or a tight constraint of a third post-Keplerian parameter. In (nearly) circular systems, this is generally the (intrinsic) PPb . A particularly interesting pulsar of that group is PSR J1713+0747, a 4.6 ms pulsar in a wide, small-eccentricity orbit with an orbital period of 67.8 days. The high-precision timing observations for PSR J1713+0747 by now span more than 20 years (Zhu et al. 2015). The Shapiro delay caused by the white-dwarf companion is well measured and allows for the determination of the orbital inclination i and the masses of the system, mp D 1:31 ˙ 0:11 Mˇ and mc D 0:286 ˙ 0:012 Mˇ . As the white dwarf is a weakly self-gravitating body, the mass determination based on the Shapiro delay is fairly theory independent, at least within the given uncertainties. The orbital motion of PSR J1713+0747 is too slow to show any effects of gravitational wave damping. On the other hand, the tight constraints on PPb , in combination with the long orbital period, make this system particularly sensitive to any temporal changes in the gravitational constant G. The inferred limit is P G=G D .0:6˙1:1/1012 yr1 (95 % confidence limit) (Zhu et al. 2015). Although this limit is still weaker by a factor of a few than the one obtained in the solar system, it is important in its own respect, as it is a test for a strongly self-gravitating body, which in principle could react quite differently to a change in G (Wex 2014). As already mentioned at the end of Sect. 3, some of the pulsar-white-dwarf systems offer a completely different access to their masses, which is only partly based on the timing observations in the radio frequencies. If the companion star is bright enough for high-resolution optical spectroscopy, then we have a “dual-line” system, where the Doppler shift in the spectral lines can be used, together with the timing observations of the pulsar, to determine the mass ratio R. Furthermore, the spectroscopic information in combination with models of white dwarfs gives the mass of the white dwarf and consequently the mass of the pulsar. Hence, a gravity test is possible with just one post-Keplerian parameter. Some of the best constraints on alternative gravity do come from such systems. Many alternative gravity theories with an additional long-range gravitational field  (e.g., Brans-Dicke-type scalartensor theories) predict the existence of monopolar and dipolar radiation, in addition to the quadrupolar and higher-order waves. Dipolar radiation can be a strong source of gravitational wave damping, since it is a v 3 =c 3 effect, and therefore in principle many orders of magnitude stronger than the quadrupole damping of GR. In scalartensor gravity, for instance, to leading order the associated change in the orbital period is given by 1 C e 2 =2 mp mc PPb ' 2 nb Tˇ .˛p  ˛c /2 ; .1  e 2 /5=2 mp C mc

(10)

where ˛p and ˛c denote the effective scalar coupling of the pulsar and its companion, respectively. The effective scalar coupling of a body depends on

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its compactness (Damour and Esposito-Farèse 1996; Will 1993). As one can see in Eq. (10), the change in the orbital period due to dipolar radiation scales quadratically with the difference in the effective scalar coupling between pulsar and companion. Binary-pulsar systems with a high degree of asymmetry in the compactness of their components are therefore ideal to test for dipolar radiation. While the abovementioned long orbital period system PSR 1713+0747 does not give any interesting constraints, there are two short orbital period pulsars, both with spectroscopic white-dwarf companion, which are particular suitable for dipolar radiation tests. PSR J1738+0333 has a spin period of 5.9 ms and is a member of a low-eccentricity (e < 4  107 ) binary system with an orbital period Pb of just 8.5 h. The companion is an optically bright, low-mass white dwarf, which allows for highresolution spectroscopy, giving access to its orbital motion (Doppler shift) and mass (mc D 0:181C0:007 0:005 Mˇ ). In combination with the analysis of the extensive timing observations of the pulsar, stretching over a period of 10 years, Antoniadis et al. (2012) obtained mp D 1:47C0:07 0:06 Mˇ . Furthermore, 10 years of timing revealed a significant change in the orbital period which, after correction for ı PPbext , is in good agreement with GR (Freire et al. 2012). The corresponding mass-mass diagram is shown in Fig. 5.

Fig. 5 Mass-mass diagram for the PSR J1738C0333 system based on GR, showing constraints from companion mass mc , mass ratio R, and gravitational wave damping PPb . Parameter values are taken from Freire et al. (2012)

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Although PSR J1738+0333 provides a much weaker gravitational wave test for GR than the double pulsar, its large asymmetry in compactness makes this system considerably more sensitive to dipolar radiation. Consequently it leads to a clearly better constraint for the effective scalar coupling of a neutron star of 1:47 Mˇ . Using the solar system limit for the weakly self-gravitating white-dwarf companion, one finds j˛p j < 5  103 (95 % confidence), which is the tightest limit published so far (Freire et al. 2012). PSR J0348+0432 is a mildly recycled radio pulsar with a spin period of 39 ms in a 2.5-h orbit with a low-mass white-dwarf companion (Antoniadis et al. 2013; Lynch et al. 2013). In fact, the orbital period is only 15 s longer than that of the double pulsar, which by itself makes PSR J0348+0432 already an interesting pulsar for gravity. Like for PSR J1738+0333, the companion white dwarf allows for optical high-resolution spectroscopy, and consequently for a determination of the masses: mc D 0:172 ˙ 0:003 Mˇ and mp D 2:01 ˙ 0:04 Mˇ (Antoniadis et al. 2013). The mass for the pulsar is presently the highest, well-determined neutronstar mass and the only high-mass (2 Mˇ ) neutron star in a relativistic binary. Like PSR 1738+0333, PSR J0348+0432 is member of a system with a large asymmetry in the compactness of the components, and therefore well suited for a dipolar radiation

Fig. 6 Fractional gravitational binding energy, Egrav =mNS c 2 , of a neutron star as a function of its (inertial) mass, based on equation of state MPA1 (Müther et al. 1987). The plot clearly shows the prominent position of PSR J0348+0432. The other dots indicate the neutron-star masses of some of the other test systems mentioned above, in particular the Hulse-Taylor pulsar, the double pulsar and PSR J1738+0333. In addition, there is the low-mass pulsar PSR J11416545, which is in an eccentric orbit with a white dwarf (Bhat et al. 2008). In the highly non-linear gravity regime of neutron stars a 50 % increase in fractional binding energy can make a significant difference (Antoniadis et al. 2013; Damour and Esposito-Farèse 1993)

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test. One finds j˛p j < 8  103 (95 % confidence). This limit is weaker than the limit from PSR J1738+0333, mentioned above. However, it has a new quality as it tests a gravity regime in neutron stars that has not been tested before (Antoniadis et al. 2013). Gravity tests before were confined to “canonical” neutron-star masses of 1:4 Mˇ . PSR J0348+0432 for the first time allows a test of the relativistic motion of a massive neutron star, which in terms of gravitational self-energy lies clearly outside the tested region (see Fig. 6).

4

Some Future Aspects

So far GR has passed all these precision tests with flying colors. Still there remains the question, is GR our final answer to the macroscopic description of gravity? From theoretical considerations, one expects GR to break down at least on Planck scales (1:6  1033 cm / 2:4  1018 GeV), put it is presently not excluded that a deviation could occur on much larger scales, at much lower energies. Pulsar astronomy will certainly continue to investigate this question. Many of the tests mentioned here will simply improve by continued timing observations of the known pulsars. In fact, the measurement precision for some of the post-Keplerian parameters increases fast with time. For instance, in regular observations (with the same telescope and backend), the uncertainty in the change of the orbital period PPb decreases with 2:5 Tobs , Tobs denoting the observing time span. Improvements in the hardware, like new broadband receivers (see, e.g., Weinreb et al. 2009), will further improve the timing precision. For pulsars like PSR J1738+0333 and PSR J0348+0432, soon the modeling of the white dwarf will be the limiting factor, while for the double pulsar, the corrections of the external contributions to PPb will be the challenging part. In fact, in order to push the gravitational wave test in the double pulsar to a precision below about 0.01 %, an improved model of the galactic gravitation potential in the vicinity of the Sun is required. In this, new missions like GAIA (Perryman et al. 2001) will play an important role. This is not only key for improving the gravitational wave test with binary pulsars but also crucial to measure the LenseThirring drag in the double pulsar, caused by the rotation of pulsar A (Kramer and Wex 2009). Assuming GR is correct at this level, one can turn this into a measurement of the moment of inertia of A (Damour and Schäfer 1988), which can help to constrain the equation of state of neutron-star matter (Lattimer and Schutz 2005). The upcoming next generation of radio telescopes, like the Five-hundred-meter Aperture Spherical radio Telescope (FAST) (Nan et al. 2011) and the The Square Kilometre Array (SKA) (Taylor 2012),, certainly promise a big improvement in the timing precision for binary pulsars. With SKA, for many pulsars one can hope for a reduction of the TOA error by up to a factor of 100 (Smits et al. 2009). A pulsar that would particularly benefit from this is PSR J0337+1715. PSR J0337+1715 is a recently discovered millisecond pulsar (P D 2:7 ms) in a hierarchical triple system with two white dwarfs (Ransom et al. 2014). The 1.44 Mˇ pulsar is in a nearly

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circular, 1.63-day orbit with a 0.20 Mˇ white dwarf. And this inner binary is in a 327-day orbit with an outer companion, which is a 0.41 Mˇ white dwarf. Such hierarchical triple systems promise an excellent precision in testing the universality of free fall for strongly self-gravitating bodies, a property of GR (Freire et al. 2012). In fact, mock data simulations show that PSR J0337+1715 could provide some of the tightest constraints on certain alternative theories of gravity, in particular with the timing capability of SKA (Berti et al. 2015). Reducing the parameter uncertainties for known pulsars is one way to push gravity tests forward, finding new, more relativistic systems is the other. Presently there are a number of pulsar surveys underway that promise the discovery of many new pulsars. In fact, with SKA one expects to increase the number of known pulsars by more than an order of magnitude (Keane et al. 2015). New techniques, like acceleration searches and high-performance computing, e.g., Einstein@Home (Allen et al. 2013), allow for the detection of pulsars in tight orbits, which generally cannot be found with traditional methods. There is considerable hope among pulsar astronomers that this will finally also lead to the discovery of a pulsar-black hole system. Such a system is expected to provide a superb new probe for gravity and black hole properties, like the dragging of space-time by the rotation of the black hole (Liu et al. 2014; Wex and Kopeikin 1999). According to GR, for an astrophysical black hole (Kerr space-time), there is an upper limit for its spin, given by Smax D GM 2 =c. It would pose an interesting challenge to GR, if the timing of a pulsar-black hole system indicates a spin S > Smax . But even for gravity theories that predict the same properties for black holes as in GR, a pulsar-black hole system would constitute an excellent test system, due to the high grade of asymmetry in the strong-field properties of these two components (Damour and Esposito-Farèse 1998; Liu et al. 2014). A measurement of the mass, spin, and quadrupole moment of a black hole would allow for an actual test of the Kerr hypothesis, since according to the no-hair theorem, an electrically neutral, rotating black hole in GR is uniquely determined by its mass and spin (see Chrusciel et al. (2012) for details, including the underlying assumptions). A pulsar in orbit around a stellar-mass black hole, will most likely not be suitable for a no-hair-theorem test (Liu et al. 2014). A pulsar in a close orbit (Pb < 1 yr) around the supermassive black hole (4  106 Mˇ ) in the center of our Galaxy, on the other hand, has the potential for a good test of the no-hair theorem, as the influence of the quadrupole moment on the pulsar motion should lead to a distinct signal in the timing residuals (Liu et al. 2012; Psaltis et al. 2016; Wex and Kopeikin 1999). Finding and timing a pulsar in the center of our Galaxy is certainly challenging. A promising result in that direction is the very recent detection of radio signals from a magnetar near the galactic center black hole (Eatough et al. 2013), even if this pulsar is still too far away from the supermassive black hole (projected distance  0:1 pc) to probe its space-time. The era of gravitational wave astronomy has started in September last year, with the detection of gravitational waves emitted by two merging stellar-mass black holes (Abbott et al. 2016a). This GW150914 event provided the first test of GR in the highly dynamical strong-field regime (Abbott et al. 2016b). From

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present studies of binary pulsars, in particular double neutron-star systems, we are confident that in the near future, ground-based gravitational wave detectors will see the signals of merging double neutron-star systems (Burgay et al. 2003). The detectors will be able to follow such mergers over the last few thousand orbital cycles, and for events with sufficient signal-to-noise ratio promise quantitative tests of the highly dynamical strong-field regime of gravity (Yunes and Siemens 2013). The late inspiral and merger of double neutron-star systems, or neutron starblack hole systems, are particularly suitable for testing deviations from GR in the highly dynamical strong-field regime, which are related to the material sector of gravity. Such effects cannot be probed with merging black holes (Yunes et al. 2016). Phenomena like the dynamical scalarization (Barausse et al. 2013; Shibata et al. 2014) or theories with short range scalar fields, like massive Brans-Dicke (Alsing et al. 2012), are just two examples for such deviations from GR. Such tests are in many aspects complementary to the high-precision tests in the quasi-stationary strong-field regime, provided by radio pulsars. For the ultra-low frequency band (nano-Hertz), pulsar timing arrays are currently the most promising detectors (Hobbs et al. 2010). In these experiments the Earth/solar system and a collection of very stable pulsars act as the test masses. A gravitational wave becomes apparent in a pulsar timing array by the changes it causes in the arrival times of the pulsar signals. Due to the fitting of the rotational frequency and its time derivative P for every pulsar, such a detector is only sensitive to wavelengths up to c Tobs . This leads to the special situation that the length of the “detector arms” is much larger than the wavelength. As a consequence, the observed timing signal contains two contributions, the so-called pulsar term, related to the impact of the gravitational wave on the pulsar when the radio signal is emitted, and the Earth term corresponding to the impact of the gravitational wave on the Earth during the arrival of the radio signal at the telescope (Detweiler 1979; Estabrook and Wahlquist 1975). The most promising source in the nano-Hertz frequency band is a stochastic gravitational wave background, as a result of many mergers of supermassive black hole binaries in the past history of the Universe (Sesana et al. 2008). With the large number of “detector arms,” pulsar timing arrays have enough information to explore the properties of the nano-Hertz gravitational wave background in details, once its signal is clearly detected in the data. Are there more than the two polarization modes of GR (alternative metric theories can have up to six)? Is the propagation speed of nano-Hertz gravitational waves frequency dependent? Does the graviton have a mass? These are some of the main questions that can be addressed with pulsar timing arrays (Lee et al. 2008, 2010). The isolation of a single source in the pulsar timing array data would give us a unique opportunity to study the merger evolution of a supermassive black hole binary, since the signal in the Earth term and the signal in the pulsar term show two different states of the system, which are typically several thousand years apart (Jenet et al. 2004). For this kind of gravity experiments, however, we might have to wait till the full SKA has collected a few years of data, which is expected to be the case in the second half of the next decade.

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Conclusions

In the last four decades, binary pulsars have taken our precision gravity tests far beyond the weak-field slow-motion regime of the solar system. Pulsars with neutron-star companions, foremost the Hulse-Taylor pulsar and the double pulsar, have provided the most precise tests for the existence of gravitational waves as predicted by Einstein’s general relativity, reaching a fractional precision of 104 in case of the double pulsar. More generally, binary pulsars so far provide the only precision tests for the gravitational interaction of strongly self-gravitating material bodies. Pulsars with white-dwarf companions are particularly useful for constraining the existence of dipolar gravitational radiation and test the universality of free fall for strongly self-gravitating masses. In terms of pulsar astronomy, the next decade will see a leap forward in instrumentation, in particular with the construction of the Square Kilometre Array (SKA). This brings along a significant improvement in timing precision and survey capabilities, leading to qualitatively new tests of gravity with pulsars, like the measurement of the Lense-Thirring drag in the double pulsar. It also promises the discovery of pulsar systems that can be utilized for new gravity tests, like a pulsar in orbit around a black hole, ideally one in close orbit around Sgr A . After the observation of merging black holes by ground-based gravitational wave detectors, it is only a matter of time until double neutron-star and neutronstar-black hole mergers will be seen. With sufficient signal-to-noise ratio, such events promise unique tests of the highly dynamical strong-field regime of gravity, complementary to double black hole mergers and to precision tests with radio pulsars. Moreover, there is justified hope that pulsar timing arrays will soon detect nano-Hertz gravitational waves and have their share in the new field of gravitational wave astronomy.

6

Cross-References

 Detecting Gravitational Waves from Supernovae with Advanced LIGO  Evolution of the Magnetic Field of Neutron Stars  Nuclear Matter in Neutron Stars  The Masses of Neutron Stars

References Abbott BP et al (LIGO Scientific Collaboration and Virgo Collaboration) (2016a) Observation of gravitational waves from a binary black hole merger. Phys Rev Lett 116:061102 Abbott BP et al (LIGO Scientific Collaboration and Virgo Collaboration) (2016b) Tests of general relativity with GW150914. eprint arXiv:1602.03841

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Allen B, Knispel B, Cordes JM, Deneva JS, Hessels JWT, Anderson D, Aulbert C, Bock O, Brazier A et al (2013) The Einstein@Home search for radio pulsars and PSR J2007+2722 discovery. Astrophys J 773:91 Alsing J, Berti E, Will CM, and Zaglauer H (2012) Gravitational radiation from compact binary systems in the massive Brans-Dicke theory of gravity. Phys Rev D 85:064041 Antoniadis J, Freire PCC, Wex N, Tauris TM, Lynch RS, van Kerkwijk MH, Kramer M, Bassa C, Dhillon VS et al (2013) A massive pulsar in a compact relativistic binary. Science 340:448 Antoniadis J, van Kerkwijk MH, Koester D, Freire PCC, Wex N (2012) The relativistic pulsarwhite dwarf binary PSR J1738+0333 - I. Mass determination and evolutionary history. Mon Not R Astron Soc 423:3316–3327 Barausse E, Palenzuela C, Ponce M, Lehner L (2013) Neutron-star mergers in scalar-tensor theories of gravity. Phys Rev D 87:081506 Barker BM, O’Connell RF (1975) Gravitational two-body problem with arbitrary masses, spins, and quadrupole moments. Phys Rev D 12:329–335 Berti E, Barausse E, Cardoso V, Gualtieri L, Pani P, Sperhake U, Stein LC, Wex N, Yagi K et al (2015) Testing general relativity with present and future astrophysical observations. Class Quantum Grav 32:243001 Bertotti B, Iess L, Tortora P (2003) A test of general relativity using radio links with the Cassini spacecraft. Nature 425:374–376 Bhat NDR, Bailes M, Verbiest JPW (2008) Gravitational-radiation losses from the pulsar whitedwarf binary PSR J1141–6545. Phys Rev D 77(12):124017 Breton RP, Kaspi VM, Kramer M, McLaughlin MA, Lyutikov M, Ransom SM (2008) Relativistic spin precession in the double pulsar. Science 321:104–107 Burgay M, D’Amico N, Possenti A, Manchester RN, Lyne AG, Joshi BC, McLaughlin MA, Kramer M, Sarkissian JM et al (2003) An increased estimate of the merger rate of double neutron stars from observations of a highly relativistic system. Nature 426: 531–533 Chrusciel PT, Costa JL, Heusler M (2012) Stationary black holes: uniqueness and beyond. Living Rev Relativ 15:7. (cited on 31-Oct-2015). http://www.livingreviews.org/lrr-2012-7 Damour T (1988) Strong-field tests of general relativity and the binary pulsar. In: Coley A, Dyer C, Tupper T (eds) Proceedings of the 2nd Canadian conference on general relativity and relativistic astrophysics, Singapore, pp 315–334 Damour T, Deruelle N (1986) General relativistic celestial mechanics of binary systems. II. The post-Newtonian timing formula. Ann Inst Henri Poincaré Phys Théor 44:263–292 Damour T, Esposito-Farèse G (1993) Nonperturbative strong-field effects in tensor-scalar theories of gravitation. Phys Rev Lett 70:2220–2223 Damour T, Esposito-Farèse G (1996) Tensor-scalar gravity and binary-pulsar experiments. Phys Rev D 54:1474–1491 Damour T, Esposito-Farèse G (1998) Gravitational-wave versus binary-pulsar tests of strong-field gravity. Phys Rev D 58:042001 Damour T, Ruffini R (1974) Certain new verifications of general relativity made possible by the discovery of a pulsar belonging to a binary system. Academie des Sciences (Paris), Comptes Rendus, Serie A – Sciences Mathematiques 279:971–973 Damour T, Schäfer G (1988) Higher order relativistic periastron advances in binary pulsars. Nuovo Cimento B 101:127 Damour T, Taylor JH (1991) On the orbital period change of the binary pulsar PSR 1913+16. Astrophys J 366:501–511 Damour T, Taylor JH (1992) Strong-field tests of relativistic gravity and binary pulsars. Phys Rev D 45:1840–1868 Deller AT, Bailes M, Tingay SJ (2009) Implications of a VLBI distance to the double pulsar J07373039A/B. Science 323:1327–1329 Detweiler S (1979) Pulsar timing measurements and the search for gravitational waves. Astrophys J 234:1100–1104

1468

N. Wex

Dyson FW, Eddington AS, Davidson C (1920) A determination of the deflection of light by the Sun’s gravitational field, from observations made at the total eclipse of May 29, 1919. R Soc Lond Philos Trans Ser A 220:291–333 Eatough RP, Falcke H, Karuppusamy R, Lee KJ, Champion DJ, Keane EF, Desvignes G, Schnitzeler DHFM, Spitler LG et al (2013) A strong magnetic field around the supermassive black hole at the centre of the Galaxy. Nature 501:391–394 Einstein A (1915) Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin), pp 831–839 Einstein A (1915) Die Feldgleichungen der Gravitation. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin), pp 844–847 Estabrook FB, Wahlquist HD (1975) Response of Doppler spacecraft tracking to gravitational radiation. Gen Relativ Gravitation 6:439–447 Fonseca E, Stairs IH, Thorsett SE (2014) A comprehensive study of relativistic gravity using PSR B1534+12. Astrophys J 787:82 Freire PCC, Kramer M, Wex N (2012) Tests of the universality of free fall for strongly selfgravitating bodies with radio pulsars. Class Quantum Grav 29:184007 Freire PCC, Wex N, Esposito-Farèse G, Verbiest JPW, Bailes M, Jacoby BA (2012) The relativistic pulsar-white dwarf binary PSR J1738+0333 - II. The most stringent test of scalar-tensor gravity. Mon Not R Astron Soc 423:3328–3343 Hewish A, Bell SJ, Pilkington JDH, Scott PF (1968) Observation of a rapidly pulsating radio source. Nature 217:709–713 Hobbs G, Archibald A, Arzoumanian Z, Backer D, Bailes M, Bhat NDR, Burgay M, Burke-Spolaor S, Champion D et al (2010) The international pulsar timing array project: using pulsars as a gravitational wave detector. Class Quantum Grav 27:084013 Hobbs G, Coles W, Manchester RN, Keith MJ, Shannon RM, Chen D, Bailes M, Bhat NDR, Burke-Spolaor S et al (2012) Development of a pulsar-based time-scale. Mon Not R Astron Soc 427:2780–2787 Hulse RA, Taylor JH (1975) Discovery of a pulsar in a binary system. Astrophys J 195: L51–L53 Jacoby BA, Cameron PB, Jenet FA, Anderson SB (2006) Measurement of orbital decay in the double neutron star binary PSR B2127+11C. Astrophys J 644:L113–L116 Jenet FA, Lommen A, Larson SL (2004) Constraining the properties of supermassive black hole systems using pulsar timing: application to 3C 66B. Astrophys J 606:799–803 Keane EF, Bhattacharyya B, Kramer M, Stappers BW, Bates SD, Burgay M, Chatterjee S, Champion DJ, Eatough RP et al (2015) A cosmic census of radio pulsars with the SKA. In: Proceedings of advancing astrophysics with the square kilometre array (AASKA14). 9–13 June, 2014. eprint arXiv:1501.00056 Kramer M (1998) Determination of the geometry of the PSR B1913+16 system by geodetic precession. Astrophys J 509:856–860 Kramer M (2012) Probing gravitation with pulsars. Proc Int Astron Union 8:19–26 Kramer M, Stairs IH (2008) The double pulsar. Annu Rev Astron Astrophy 46:541–572 Kramer M, Stairs IH, Manchester RN, McLaughlin MA, Lyne AG, Ferdman RD, Burgay M, Lorimer DR, Possenti A et al (2006) Tests of general relativity from timing the double pulsar. Science 314:97–102 Kramer M, Wex N (2009) TOPICAL REVIEW: The double pulsar system: a unique laboratory for gravity. Class Quantum Grav 26:073001 Lambert SB, Le Poncin-Lafitte C (2011) Improved determination of  by VLBI. Astron Astrophys 529:A70 Lattimer JM, Schutz BF (2005) Constraining the equation of state with moment of inertia measurements Astron Astrophys 629:979–984 Lee KJ, Jenet FA, Price RH (2008) Pulsar timing as a probe of non-einsteinian polarizations of gravitational waves. Astrophys J 685:1304–1319 Lee KJ, Jenet FA, Price RH, Wex N (2010) Detecting massive gravitons using pulsar timing arrays. Astrophys J 722:1589–1597

54 Neutron Stars as Probes for General Relativity and Gravitational Waves

1469

Liu K, Eatough RP, Wex N (2014) Pulsar-black hole binaries: prospects for new gravity tests with future radio telescopes. Mon Not R Astron Soc 445:3115–3132 Liu K, Wex N, Kramer M, Cordes JM (2012) Prospects for probing the spacetime of Sgr A* with pulsars. Astrophys J 747:1 Lorimer DR, Kramer M (2004) Handbook of pulsar astronomy. Cambridge University Press, Cambridge Lynch RS, Boyles J, Ransom SM, Stairs IH, Lorimer DR, McLaughlin MA, Hessels JWT, Kaspi VM, Kondratiev VI et al (2013) The green bank telescope 350 MHz drift-scan survey II: data analysis and the timing of 10 new pulsars, including a relativistic binary. Astrophys J 763:81 Lyne AG, Burgay M, Kramer M, Possenti A, Manchester RN, Camilo F, McLaughlin MA, Lorimer DR, D’Amico N et al (2004) A double-pulsar system: a rare laboratory for relativistic gravity and plasma physics. Science 303:1153–1157 Manchester RN (2015) Pulsars and gravity. Int J Mod Phys D 24:1530018 Manchester RN, Hobbs GB, Teoh A (2005) The Australia telescope national facility pulsar catalogue. Astrophys J 129:1993–2006. http://www.atnf.csiro.au/research/pulsar/psrcat/. Matthews AM, Nice DJ, Fonseca E, Arzoumanian Z, Crowter K, Demorest PB, Dolch T, Ellis JA, Ferdman RD et al (2015) The NANOGrav nine-year data set: astrometric measurements of 37 millisecond pulsars. eprint arXiv:1509.08982 Müther H, Prakash M, Ainsworth TL (1987) The nuclear symmetry energy in relativistic Brueckner-Hartree-Fock calculations. Phys Lett B 199:469–474 Nan R, Li D, Jin C, Wang Q, Zhu L, Zhu W (2011) The five-hundred-meter aperture spherical radio telescope (FAST) project. Int J Mod Phys D 20:989–1024 Perera BBP, McLaughlin MA, Kramer M, Stairs IH, Ferdman RD, Freire PCC, Possenti A, Breton RP, Manchester RN et al (2010) The evolution of PSR J0737–3039B and a model for relativistic spin precession. Astrophys J 721:1193–1205 Perryman MAC, de Boer KS, Gilmore G, Høg E, Lattanzi MG, Lindegren L (2001) GAIA: Composition, formation and evolution of the Galaxy. Astron Astrophys 369:339–363 Phinney ES (1992) Pulsars as probes of Newtonian dynamical systems. R Soc Lond Philos Trans Ser A 341:39–75 Psaltis D, Wex N, Kramer M (2016) A quantitative test of the No-Hair theorem with Sgr A* using stars, pulsars, and the event horizon telescope. Astrophys J 818:121 Ransom SM, Stairs IH, Archibald AM, Hessels JWT, Kaplan DL, van Kerkwijk MH, Boyles J, Deller AT, Chatterjee S et al (2014) A millisecond pulsar in a stellar triple system. Nature 505:520–524 Sesana A, Vecchio A, Colacino CN (2008) The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays. Mon Not R Astron Soc 390:192–209 Shapiro II (1964) Fourth test of general relativity. Phys Rev Lett 13:789–791 Shibata M, Taniguchi K, Okawa H, Buonanno A (2014) Coalescence of binary neutron stars in a scalar-tensor theory of gravity. Phys Rev D 89:084005 Smits R, Kramer M, Stappers B, Lorimer DR (2009) Pulsar searches and timing with the square kilometre array. Astron Astrophys 493:1161–1170 Stairs IH, Thorsett SE, Arzoumanian Z (2004) Measurement of gravitational spin-orbit coupling in a binary-pulsar system. Phys Rev Lett 93:141101 Taylor AR (2012) The square kilometre array. Proc Int Astron Union 8:337–341 Taylor JH, Fowler LA, McCulloch PM (1979) Measurements of general relativistic effects in the binary pulsar PSR 1913+16. Nature 277:437–440 Taylor JH, Hulse RA, Fowler LA, Gullahorn GE (1976) Further observations of the binary pulsar PSR 1913+16. Astrophys J 206:L53–L58 Verbiest JPW, Bailes M, Coles WA, Hobbs GB, van Straten W, Champion DJ, Jenet FA, Manchester RN, Bhat NDR et al Timing stability of millisecond pulsars and prospects for gravitational-wave detection. Mon Not R Astron Soc 400:951–968 Verbiest JPW, Bailes M, van Straten W, Hobbs GB, Edwards RT, Manchester RN (2008) Precision timing of PSR J0437–4715: an accurate pulsar distance, a high pulsar mass, and a Limit on the variation of Newton’s gravitational constant. Astrophys J 679:675–680

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Weinreb S, Bardin J, Mani H (2009) Matched wideband low-noise amplifiers for radio astronomy. Rev Sci Instrum 80:044702 Weisberg JM, Nice DJ, Taylor JH (2010) Timing measurements of the relativistic binary pulsar PSR B1913+16. Astrophys J 722:1030–1034 Weisberg JM Taylor JH (2002) General relativistic geodetic spin precession in binary pulsar B1913+16: mapping the emission beam in two dimensions. Astrophys J 576:942–949 Wex N (2014) Testing relativistic gravity with radio pulsars. In: Kopeikin S (ed) Frontiers in relativistic celestial mechanics: applications and experiments. De Gruyter Studies in Mathematical Physics, vol 22, eprint arXiv:1402.5594 Wex N, Kalogera V, Kramer M (2000) Constraints on supernova kicks from the double neutron star system PSR B1913+16. Astrophys J 528:401–409 Wex N, Kopeikin SM (1999) Frame dragging and other precessional effects in black hole pulsar binaries. Astrophys J 514:388–401 Will CM (1993) Theory and experiment in gravitational physics. Cambridge University Press, Cambridge Yunes N, Siemens X (2013) Gravitational-wave tests of general relativity with ground-based detectors and pulsar-timing arrays. Living Rev Relativ 16:9. (Cited on 31-Oct-2015). http:// www.livingreviews.org/lrr-2013-9 Yunes N, Yagi K, Pretorius F (2016) Theoretical physics implications of the binary black-hole merger GW150914. eprint arXiv:1603.08955 Zhu WW, Stairs IH, Demorest PB, Nice DJ, Ellis JA, Ransom SM, Arzoumanian Z, Crowter K, Dolch T et al (2015) Testing theories of gravitation using 21-year timing of pulsar binary J1713+0747. Astrophys J 809:41

Gamma Ray Pulsars: From Radio to Gamma Rays

55

Jumpei Takata

Abstract

Pulsars are fast spinning and highly magnetized neutron stars, with a typical mass of 1.4–2Mˇ and a radius of Rs  106 cm. Pulsars convert their rotational energy into particle energy and emit electromagnetic radiation as a beam. This radiation beam can be observed in a pulsation that has the same period as the rotational period of the pulsar. Since the discovery of the first pulsar in 1967, more than 2500 pulsars have been discovered by radio telescopes. The Fermi Gamma Ray Large Area Telescope launched in 2008 provides valuable observations of gamma ray radiation from pulsars. Fermi has detected pulsed gamma ray emissions from >150 pulsars. The increase of the population of gamma ray emitting pulsars provides us a great opportunity for understanding the emission mechanisms from radio to gamma ray bands, and the evolution and structure of the pulsar magnetosphere. In this chapter, we summarize the results of multiwavelength observations for the Fermi-LAT pulsars and discuss their interpretation via particle acceleration and emission models.

Contents 1 2 3 4 5 6 7

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High-Energy Observations of Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Goldreich-Julian Argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pulsars as Cosmic Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acceleration in the Pulsar Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pair-Creation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acceleration Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Polar Cap/Slot Gap Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Outer Gap Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Force-Free Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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J. Takata () School of Physics, Huazhong University of Science and Technology, Wuhan, China e-mail: [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_73

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Magnetospheric Emission Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 GeV Gamma Ray Emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 UV/Optical/IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 GeV Pulse Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Gamma Ray Pulsar Zoo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 >50 GeV Emissions from Crab/Vela Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 “GeV” Quiet Gamma Ray Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Class-II Millisecond Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

A pulsar is a very rapidly and highly magnetized neutron star. Thus far more than 2000 pulsars (Manchester et al. 2005) have been discovered. Most of them emit only radio waves. Timing observations measure the spindown of the pulsar, suggesting that pulsars typically release rotational energy, Erot D INS ˝ 2 =2. The energy released per unit time (hereafter spindown power) is Lsd

D INS ˝ ˝P D 4  1034 erg s1



INS 45 10 g cm3



P 0:1s

3

PP 1015

! ;

(1)

where INS is the moment of inertia of the neutron star, ˝ is the spin frequency, P is the spin period, and PP is the time derivative of the spin period. It is usually assumed that magnetic dipole radiation has its origin in the spindown, Lsd D

Bs2 sin2 ˛˝ 4 ; 6c 3

(2)

where ˛ is the angle between the spin axis and the magnetic axis. Using Eqs. (1) and (2), the spindown dipole field at the pole is defined by

Bs 

6INS c 3 ˝P ˝3

!1=2



P D 2  1012 G 1s

1=2

PP 1015

!1=2 :

(3)

If the current spin period is much longer than the initial spin period when the pulsar was born, the age of the pulsar (spindown age) is defined by s 

P : 2PP

(4)

Figure 1 shows the P  PP diagram of pulsars; lines of constant spindown power and spindown magnetic field are also shown.

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10-10

Bs,12=102

dP/dt

10-12

Bs,12=1

10-14

Lsd,34=104 10-16

Bs,12=10-2

Lsd,34=1 Lsd,34=10-4

10-18

10-20 10-3

10-2

10-1

100

101

P (second) Fig. 1 P  PP diagram of the pulsars (Manchester et al. 2005). The green and purple lines show constant spindown power and spindown magnetic field, respectively. Canonical pulsars have a surface magnetic field of Bs  101213 G, and millisecond pulsars have Bs  1089 G. The red dots show gamma ray emitting pulsars in the public list (Ray 2015), at the time of writing this chapter

2

High-Energy Observations of Pulsars

The first measurement of gamma ray emission from pulsars were done by SAS-II, which identified pulsed gamma ray emissions from the Crab pulsar (Kniffen et al. 1974) and the Vela pulsar (Thompson et al. 1975). Currently, the Crab pulsar, whose spin period is P D 33 ms and the Vela pulsar, which has P D 89 ms, have been known as two of the brightest sources in the gamma ray sky. In the 1990s, the Energetic Gamma Ray Experiment Telescope (hereafter EGRET) onboard the Compton Gamma Ray Observatory observed “pulsed” gamma rays above 100 MeV from the direction of six pulsars (Crab, Vela, B1706-44, B1951+32, Geminga, and B1055-52). In addition, hard X-ray/soft gamma ray emissions in the band from 50 keV to 5 MeV bands were detected from PSR B1509-58 by OSSE, the Oriented Scintillation Spectrometer Experiment (Matz et al. 1994), which was also on the Compton Gamma Ray Observatory. In the 1990s, only these seven pulsars had been recognized as gamma ray emitting pulsars; they are called EGRET pulsars. The multiwavelength spectra of EGRET pulsars were summarized in the 1990s in Fig. 2. Figure 2 shows that the radiation power of the X-ray and gamma ray emissions are more than the power radiated in radio waves, and the peak energy of the EGRET pulsars (except for the Crab) is located in the gamma ray band. Hence, EGRET results imply that the radiative outputs of the pulsars are mainly in gamma ray energy bands, not in radio bands. Despite this great success, EGRET could not precisely measure the

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Optical

Radio 9

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log νFν (JyHz)

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PSR B1706-44

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PSR B1951+32

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Geminga

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X-Ray

log Observing Frequency (Hz)

-3

0

3

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log Energy (keV) DJT, Sept. 2003

Fig. 2 Radio to TeV gamma ray spectra for EGRET gamma ray pulsars in the 1990s. From top (Crab pulsar, s D 1:26 kyrs) to bottom (PSR B1055-52, s D 0:535 Myrs); the spindown age is in ascending order. After Thompson et al. (1999)

spectral shape above 1 GeV and could not detect pulsed gamma ray emissions from many pulsars due to the instrumental limit of sensitivity. The results of EGRET were not enough to understand the nature of the gamma ray emissions from the pulsars.

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The large area telescope onboard the Fermi space telescope (hereafter FermiLAT) was launched in 2008 to measure high-energy gamma rays (10 MeV–300 GeV energy bands) from space. Fermi-LAT has measured pulsed gamma rays from >150 pulsars (c.f. Fig. 1). Figure 3 summarizes the updated multiwavelength spectra of EGRET pulsars in the Fermi era. By comparing Figs. 2 and 3, we can see that FermiLAT has revealed the evolution of spectra above 1 GeV. Some important discoveries of Fermi-LAT are: • Discovery of radio-quiet gamma ray pulsars (Abdo et al. 2008) • Measurement of pulsed gamma ray emissions from millisecond pulsars (Abdo et al. 2009) • Measurement of the relation between the spindown power and gamma ray ˇ luminosity, L / Lsd with ˇ  0:5 (Abdo et al. 2013) • Measurement of a spectral cutoff around 3 GeV, which is insensitive to the spindown parameters (c.f. Sect. 8.1) • Spectral features above 1 GeV, for which the flux above the cutoff energy decays slower than a pure exponential function (Abdo et al. 2013) Moreover, the observed light curves show in general double-peaked structures (Fig. 4), and the pulse profiles evolve with the energy (Fig. 5). The gamma ray pulse peaks are in general shifted from the peak position of the radio pulses (except for Class II pulsars, c.f. Sect. 10.3). These results from Fermi-LAT provide us with a great opportunity to study the particle acceleration and high-energy emission mechanisms of pulsars.

3

Goldreich-Julian Argument

Particle acceleration and emission processes in pulsar magnetospheres have conventionally been based on the Goldreich-Julian argument (Goldreich et al. 1969). Because the neutron star is a spherical conductor, the plasma inside the neutron star distributes to satisfy the force-free condition, E C V=c  B D 0, where V D ˝  rE is the velocity of the rotation of the neutron star and ˝ is the vector of the angular frequency of the neutron star. Hence, the charge distribution inside the neutron star will satisfy  ˝ 1 1 GJ .r < Rs / D r ED  B  r  .r  B/ ; 4

2 c 2

(5)

where GJ is called the Goldreich-Julian (GJ) charge density. Let us assume that the magnetic field is a dipole field. Because the dipole magnetic field satisfies r  B D 0, the GJ charge density is written as GJ D ˝  B=2 , which indicates that the negative charges and positive charge are separated by a surface that satisfies the condition ˝  B D 0. For an aligned

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-9 -10 -11 -12 -13 -14 -15 -16 -17

log[Flux (erg/cm2/s)]

-9 -10 -11 -12 -13 -14 -15 -16 -17

Crab

B1509-58

-9 -10 -11 -12 -13 -14 -15 -16 -17 -9 -10 -11 -12 -13 -14 -15 -16 -17 -9 -10 -11 -12 -13 -14 -15 -16 -17 -9 -10 -11 -12 -13 -14 -15 -16 -17 -9 -10 -11 -12 -13 -14 -15 -16 -17

Vela

B1706-44

B1951+32

Geminga

B1055-52

-5

0

5

10

log[Energy (eV)] Fig. 3 Multiwavelength spectra of the seven EGRET pulsars in the 2000s. The radio data were taken from Manchester et al. (2005) and Thompson et al. (1999). Data for other wavebands were obtained as follows. Crab: Sollerman et al. (2000) for IR/optical/UV, Kuiper et al. (2001) for X-ray/soft gamma ray, and Abdo et al. (2010a) and Aleksi´c et al. (2014) for gamma rays.

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rotator, for example, the pole (˝  BE > 0) and equator .˝  BE < 0/ regions are negatively and positively charged, respectively. This charge separation inside the neutron star produces an electric potential drop and hence the electric field outside the neutron star. For simplicity, we assume that the rotation axis and the magnetic dipole axis are aligned; the .r;  / components of the magnetic dipole field are Br D Bs .Rs =r/3 cos  and B D Bs .Rs =r/3 sin =2, respectively, where Bs and Rs are the magnetic field strength at the pole and neutron star radius, respectively. If the region outside the neutron star is a vacuum, the electric potential becomes ˚.r Rs / D 

Bs ˝R5 .3 cos2   1/ ; 3cr 3 2

(6)

which satisfies the boundary condition that the tangential component of the electric field is continuous across the stellar surface. We can show that on the neutron star surface the electric force along the magnetic field is much greater than the force of gravity; that is, eEjj .Rs /  1010 GM mp =Rs2



B 1012 G



˝ 100 s1



M Mˇ

1 ;

(7)

where Ejj  B˝Rs =c is the electric field along the magnetic field line on the surface. This suggests that the electric force to release the plasma from the stellar surface easily overcomes the force of gravity. The vacuum solution for the region surrounding the neutron star will be unstable and the region will be filled by plasma injected from the neutron star surface. The charge density in the magnetosphere is also described by the GJ charge density of Eq. (5); that is, in the pulsar magnetosphere a surface which satisfies ˝  B D 0, which is called the null charge surface, separates the negatively and positively charged regions. J Fig. 3 (Continued) B1509-58: Thompson et al. (1999) for optical, Chen et al. (2015) for X-ray and Pilia et al. (2010), and Abdo et al. (2010b) and Kuiper and Hermsen (2015) for gamma rays. Vela: Mignani et al. (2007a) and Shibanov et al. (2003) for optical, Harding et al. (2002) for X-ray/soft gamma rays, and Leung et al. (2014) for GeV gamma rays. B1706-44: Gotthelf et al. (2002) and McGowan et al. (2004) for X-ray and Abdo et al. (2013) for gamma rays. B1951+32: Butler et al. (2002) for optical, Thompson et al. (1999) for X-ray, Abdo et al. (2013) for GeV bands, and Albert et al. (2007) for TeV bands.Geminga: Kargaltseve et al. (2005) and Shibanov et al. (2006) for optical, Mori et al. (2014) for X-ray, and Abdo et al. (2013) for gamma rays. B1055-52: Mignani et al. (2010) for optical, De Luca et al. (2005) for X-ray, and Abdo et al. (2013) for gamma rays

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1800 400

1600

350

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300 120

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250 100

200

1200

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Counts

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100

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50 0 0.96 0.97 0.98 0.99 1 1.01 1.02

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0.36 0.37 0.38 0.39 0.4 0.41 0.42

600 400 200 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Phase Fig. 4 The pulse profiles in GeV gamma rays (dark line) and radio waves (red line) from the Crab pulsar, after Abdo et al. (2010a)

Fig. 5 Energy-dependent GeV pulse profiles of the Vela pulsar, after Leung et al. (2014)

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Pulsars as Cosmic Batteries

A spinning magnetized neutron star acts like a unipolar inductor and produces a large potential drop on the surface. From Eq. (6) the potential difference between the pole ( D 0) and the equator ( D =2) becomes

ı˚tot

Bs ˝R2  5  1017 D 2c



Bs 1012 G



˝ 100 s1

 Volt:

(8)

This electromotive force exerted on the surface is the source of the pulsar’s activity, and forms a large-scale electric current system in the magnetosphere; the electric current starts from the stellar surface, through the acceleration region and the pulsar wind region, and eventually returns to the stellar surface. Pulsars have two types of magnetic field lines, namely, open and closed. The open field lines emerge from the magnetic pole region, cross the light cylinder and extend towards interstellar space. The closed magnetic field lines emerge from one hemisphere, do not cross the light cylinder, and return to the other hemisphere. The light cylinder of the pulsar is defined by the surface of the cylinder where the corotation speed with the neutron star reaches the speed of light. The radius of the light cylinder is $lc D cP =2 D 4:8  108 cm.P =0:1 s/. The open and closed magnetic field lines are separated by the last-closed magnetic field lines, which lie tangent to the light cylinder. For a dipole magnetic field, the angular size of the open field region, which is called the polar cap region, is on the order of s p D

Rs ; $lc

(9)

and the polar cap radius is Rp  Rs p . On the open magnetic field line, inasmuch as the charged particles around the light cylinder will not be able to corotate with the star, they will flow out from the magnetosphere. The depletion of the charged particles will eventually cause particle injection from the neutron star surface to satisfy the Goldreich-Julian charge density, and results in the formation of the global electric current of the magnetosphere. It has been discussed that the electric current emerges from the polar cap region and flows along the open magnetic field region. Beyond the light cylinder (pulsar wind region), the electric current can cross the magnetic field lines and eventually return along the open magnetic field lines to the polar cap region (circuit current model (e.g., Shibata 1995)). This circuit current model implies that only the electric potential drop over the polar cap region is available to drive the activity of pulsars. The available potential drop between the magnetic pole and the last-closed field lines is ı˚a D

p2 ı˚tot

15

 2  10



Bs 1012 G



˝ 100 s1

2 Volt

(10)

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J. Takata

Because the electric current circulating the global magnetosphere will be on the order of IGJ  Rp2 cGJ .Rs / 

˝Bs Rs3 ; 2$lc

(11)

the total power carried into the outer magnetosphere by the current is on the order of Wa D IGJ  ı˚a D Bs2 ˝ 4 Rs6 =4c 3

(12)

which is close to the spindown power of the magnetic dipole radiation Lsd  Wa .

5

Acceleration in the Pulsar Magnetosphere

The observed high-energy emissions from pulsars tell us that not all regions in the pulsar magnetosphere satisfy the force-free condition, otherwise there is no acceleration and hence no high-energy emission in the pulsar magnetosphere (but see Sect. 7.3). In the acceleration region, which corresponds to the voltage gap for an electric circuit, part of the spindown power is released as radiation. For the Crab pulsar, for example, the observed spindown power is Lsd D 6  1038 erg s1 , and the radiation luminosity is on the order of L  1036 erg s1 (Abdo et al. 2010a), indicating that a few percent of the spindown power are used to accelerate charged particles (electrons/positrons) and to radiate photons. In the pulsar magnetosphere, because charged particles can move only along magnetic field lines, the electric field along the magnetic field line can accelerate the charged particles. All traditional models have assumed that the particle acceleration regions exist on the open-field line regions, and that the charge density in the acceleration region deviates from the Goldreich-Julian charge density. If the pulsar magnetosphere is stationary in the corotating frame, the electric potential drop in the charge depletion region (hereafter “gap”) is the sum of the corotation potential, ˚co , plus the noncorotation potential, ˚nco , ˚ D ˚co C ˚nco ;

(13)

where ˚co satisfies the Poisson equation r 2 ˚co D 4 GJ and B  r˚co D 0. Because r 2 ˚ D 4 , where  is the local charge density, the Poisson equation for noncorotational potential may be written as r 2 ˚nco D 4 .  GJ /;

(14)

and the accelerating electric field is given by Ejj D .BE  r˚nco /=B. Although the electric potential drop in the accelerator depends on the charge density in the gap, as Eq. (14) shows, the magnitude of the potential drop along the

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magnetic field line in the accelerator will be on the order of  ˚nco  ı˚a

ı pc

2 ;

(15)

where ı is the angle of thickness of the acceleration region measured on the stellar surface. The fractional gap width is defined as fgap 

ı : pc

Hence the radiation power of the gap is on the order of 2 3 L  fgap IGJ  fgap ˚a  fgap Lsd :

(16)

The observed radiation efficiency of a Fermi-LAT pulsar is   L =Lsd  0:01  0:1 (Abdo et al. 2013), suggesting that a typical value of the fractional thickness is fgap  0:3  0:5.

6

Pair-Creation Process

In addition to particle acceleration and gamma ray radiation, electron/positron pair-creation is a possible high-energy process that may appear in the pulsar magnetosphere. Pair-creation will be closely related to the acceleration process, inasmuch as the process can produce new electron and positron pairs, which can change the local charge. Photon-photon pair-creation processes can take place through collision between GeV gamma rays and background X-rays from the stellar surface or from the magnetosphere. The pair-creation cross-section is given by (c.f. Fig. 6)  3 1Cv 2 4 2  .E ; EX / D T .1  v / .3  v /ln  2v.2  v / ; 16 1v

(17)

where s v.E ; EX / D

1

.me c 2 /2 2 : 1  cos X EX E

For a gamma ray photon with energy E , the energy of a soft photon for paircreation is EX > Eth D 0:522 keV.E =1 GeV/1 . The optical depth of a gamma ray for the photon-photon pair-creation will be on the order of

1482

J. Takata 0.3

0.25

σ γγ /σ T

0.2

0.15

0.1

0.05

0

0

2

4

6

8

10

E γ /E th Fig. 6 The cross-section of the photon-photon pair-creation process as a function of energy divided by the threshold energy

3

p .r/  rnX   5  10



LX 1033 erg s1



r $lc

1 

P 0:1 s

1 

EX 0:1 keV

1 ;

(18) where we used   0:2T (Fig. 6) and X-ray photon density nX D LX =.4 r 2 cEX /. For the Crab pulsar (P D 0:033 s), the observed X-ray luminosity is LX  1035 erg s1 , implying the optical depth is p > 1 everywhere in the pulsar magnetosphere and hence most of the >1 GeV gamma rays emitted inside the light cylinder will be converted into pairs before crossing the light cylinder. This suggests that the pulsed 100 GeV-TeV gamma rays from the Crab pulsar discovered by ground-based telescopes (e.g., Aliu et al. 2011, Aleksi´c et al. 2014, and references therein) should be produced in the region close to or beyond the light cylinder. For middle-aged pulsars (e.g., the Vela pulsar), the observed X-ray luminosity is on the order of LX  1032 , implying that most gamma rays can leave the magnetosphere from the light cylinder. Near the stellar surface of the neutron star, the strong magnetic field enables the gamma rays to convert into electron/positron pairs. The mean free path of the magnetic pair-creation process is approximately described as (Ruderman and Sutherland 1975)   Eg B sin B BQ h 4:4 4 ;  `m D 2 exp < 1; .e =„c/ me c B sin B 3 2me c 2 BQ

(19)

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where BQ D me c 3 =e3„ D 4:4  1013 G and B is the angle between the magnetic field direction and direction of the gamma ray propagation.

7

Acceleration Models

7.1

Polar Cap/Slot Gap Model

An idea for acceleration above the magnetic pole was developed by Ruderman and Sutherland (1975). In the model, the essential condition for the formation of the polar cap accelerator is the antiparallel rotator; that is, the polar cap is positively charged. Ruderman and Sutherland anticipated that the ion cannot be pulled out from the stellar surface because of its large binding energy. Charge depletion, led by the global flow of particles (c.f. Sect. 4), cannot be supplied by particle emission from the stellar surface, and results in the formation of an electric field along the magnetic field line. A more acceptable idea is called space charge-limited flow, which was proposed by Scharlemann et al. (1978). The model assumes that the particles are freely extracted from the stellar surface. At the stellar surface, the charged particles will be injected into space to satisfy Ejj D 0 above the stellar surface. Current conservation per magnetic flux implies that the charge density of the injected particles develops as .Er / / B.Er /. On the other hand, the Goldreich-Julian charge density changes as GJ .Er / / Bz .Er /. As particles flow along the magnetic field line, therefore, the charge density deviates from the Goldreich-Julian charge density, and an accelerating electric field develops along the magnetic field. A more detailed discussion for the particle acceleration above the polar cap can be seen in, for example, Timokhin and Arons (2013). In the polar cap model, the size of the accelerator is typically limited to h  1034 cm (Ruderman and Sutherland 1975) along the magnetic field line due to the magnetic pair-creation process. The slot gap model (Arons 1983; Muslimov and Harding 2003) is an extension of the polar cap model and assumes that the accelerator around the last-closed field lines extends from the neutron star surface to the light cylinder. Because gamma rays are emitted in the convex side of the magnetic field lines, a pair-creation-free region can form at the region above the last-closed field lines, with a transfield thickness on the order of the mean-free path of the magnetic pair-creation process. This model expects that the curvature radiation process (c.f. Sect. 8.1) in the outer magnetosphere produces observed GeV gamma rays and has explained various results of the X-ray/gamma ray observations (e.g., Harding and Kalapotharakos 2015).

7.2

Outer Gap Accelerator

The particle acceleration process in the outer magnetosphere (outer gap model) has been developed by, for example, Cheng et al. (1986), Hirotani (2015), and Takata

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et al. (2016). The model argued that for an aligned rotator, for example, the open field line region between the null charge surface and light cylinder is positively charged, and positively charged particles may flow out from the light cylinder. Because the open field lines are connecting with the negatively charged polar cap region, charge depletion cannot be supplied from the stellar surface, and results in the formation of an electric field along the magnetic field line. The outer gap usually assumes an acceleration region between the null charge surface of the GoldreichJulian charge density and the light cylinder. In the outer magnetosphere, because the magnetic field strength is too weak to realize the magnetic pair-creation process, the photon-photon pair-creation process determines the structure of the outer gap accelerator.

7.3

Force-Free Magnetosphere

Numerical simulations have been developed to investigate the global structure of the magnetosphere and the location of the high-energy emission region. These studies have confirmed that the pair-creation process is crucial for the activity of the pulsar. Earlier simulations showed that a magnetosphere with no pair-creation process settles down into a quiet state with an electron cloud above the polar caps, a positively charged equatorial disc, and a vacuum gap in middle latitudes (Krause and Michel 1985; Smith et al. 2001; Wada and Shibata 2007). It had been realized, however, that the large vacuum gap is unstable against the pair-creation process. Recent particle-in-cell (PIC) simulations have shown that the pulsar magnetosphere includes discharge particles created by the pair-creation process (e.g., Chen and Beloborodov 2014; Philippov et al. 2015). Spitkovsky (2006) first solved the structure of the force-free magnetosphere of an inclined pulsar, which implies that the high-energy emission region is the current sheets along the last-closed field lines and/or Y-point at the equator. Recent PIC simulations suggest that if the pair-creation process at the polar cap region can supply sufficient discharge pairs, the magnetosphere is filled by abundant pairs and is similar to the force-free solution. If the pair-creation in the polar cap acceletor cannot supply sufficient pairs (this may be the case for millisecond pulsars), the paircreation process around the light cylinder becomes a crucial factor that determines the high-energy radiation region (Chen and Beloborodov 2014). Because of the high pair-creation rate everywhere in the magnetosphere, the Crab pulsar magnetosphere may be described by a force-free structure. If the pair-creation process in the outer magnetosphere is low, the outer gap can survive without being filled by discharge particles and it can be a high-energy emission region (Yuki and Shibata 2012). Current global simulations ignore the mean-free path of the pair-creation process, therefore it will be interesting to study global structure with a realistic pair-creation process by taking into account the position-dependency of the mean-free path, soft-photon density, and various magnetic field strengths of both millisecond and canonical pulsars.

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8

Magnetospheric Emission Mechanisms

8.1

GeV Gamma Ray Emissions

The curvature radiation process is a more plausible mechanism for the GeV radiation from pulsars. In the pulsar magnetosphere, the momentum of the particle perpendicular to the magnetic field line is immediately lost by the synchrotron radiation process, and hence we can anticipate that charged particles move along the magnetic field lines with a very small pitch angle. If the magnetic field line is bending, the trajectory of the charged particles is bent, which is equivalent to the acceleration of the particle in the direction of curvature of the magnetic field line, and results in emission of an electromagnetic wave along the particle’s trajectory. The electromagnetic power and characteristic energy of the curvature radiation process with a Lorentz factor ( ) of the electrons/positrons are 2 e 2 c 4 3 hc 3 and E D ; c 3 Rc2 4 Rc

Pcurv D

(20)

respectively, where Rc is the curvature of the trajectory of the particle (the magnetic field line in the present case). The curvature radiation is the general case of the wellknown synchrotron radiation process. If we replace the curvature radius Rc by the radius of the relativistic gyration motion rg D me c 2 =eB sin ˛ , where ˛ is the pitch angle, we can obtain expressions for the synchrotron radiation. If the radiation process of the relativistic electrons/positrons is the curvature radiation process, the Lorentz factor in the acceleration region is saturated, in balance between the acceleration force and the curvature radiation drag force. The saturated Lorentz factor becomes 

sat D

3Rc2 Ejj 2e

1=4

7

 210



fgap 0:3

1=2 

Bs 1012 G

1=4 

˝ 100 s1

1=4 

r $lc

1=8 ;

(21) where we used the approximation of the curvature radius of the dipole field Rc  p r$lc with r being the radial distance, and Ejj  j˚nco =Rc j (Cheng et al. 1986). The typical energy of the curvature photons becomes   3=4  5=4    fgap 3=2 Bs ˝ r 1=8 3 hc c3 Ec D  1GeV : 4 Rc 0:3 1012 G 100 s1 $lc (22) This equation is less dependent on position in the emission region. If we rewrite Eq. (22) in terms of typical parameters of millisecond pulsars, we obtain  Ec  1GeV

fgap 0:3

3=2 

Bs 108 G

3=4 

˝ 5000 s1

7=4 

r $lc

1=8 :

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J. Takata

As long as the curvature radiation process dominates, therefore, the maximum energy emitted from the pulsar magnetosphere will be 1 GeV, which is in good agreement with the cutoff energy observed by the Fermi-LAT pulsars. Although the polar cap accelerator can also produce the gamma rays, there are several arguments that the observed GeV emissions originated from the outer magnetosphere. First, high-energy emissions from the Crab extend to TeV energy bands. To avoid the pair-creation process with the dense soft-photon field inside the light cylinder, >1 GeV gamma rays from the Crab pulsar should be produced very close to or outside the light cylinder. Second, the polar cap model predicts the gamma ray flux above the cutoff energy decreases faster than exponential because the strong magnetic field absorbs the higher energy photons. Fermi-LAT, however, found that the gamma ray fluxes above the cutoff energy decay more slowly than a pure exponential function (Abdo et al. 2013). Finally, the typical peak separation in the observed double-peak pulse profiles is 0:5, which favors a fan-beam of gamma rays predicted by the outer gap/slot gap model rather than a pencil beam predicted by the polar cap model. The polar cap model requires a peculiar viewing geometry of pulsars to explain the observed phase separation. On these grounds, the results of Fermi-LAT likely suggest that the GeV gamma rays from the pulsars are emitted in the outer magnetosphere.

8.2

X-Rays

X-ray emissions from the pulsars are composed of two components, that is, a thermal component from the neutron star surface and a nonthermal component from the magnetosphere, as Figs. 2 and 3 show. It is expected that neutron stars are born very hot in supernova explosions, and the initial temperature in their interior is on the order of T  1011 K. Subsequently, the neutron star is gradually cooled down through neutrino emissions from the entire stellar interior and by thermal emission of photons from the stellar surface. The cooling curve depends on neutron star models (Yakovlev and Pethick 2004). The thermal components of the millisecond pulsars show a temperature of Th  0:5  2  106 K (Zavlin 2007), which is significantly higher than the cooling models predict. This indicates that there is a reheating process on the surface of millisecond pulsars. Because the observed effective radius, Reff  0:1  3 km, is smaller than the stellar radius, the thermal emissions from the millisecond pulsar will originate from a hot spot on the stellar surface. Some canonical pulsars (e.g., Caraveo et al. 2004,for the Geminga pulsar) appear to have emissions from a hot spot. It is usually discussed that when electrons or positrons, which were accelerated in the outer magnetosphere, return they deposit their kinetic energy onto the polar cap region. The charged particles that migrated from the acceleration region lose their energy through curvature radiation outside the accelerator, therefore the equation of motion is me c 3 d =dr D 2 4 e 2 c=3Rc2 p with Rc  r$lc . This implies the returning particles reach the polar cap with a

55 Gamma Ray Pulsars: From Radio to Gamma Rays

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Lorentz factor of pc  .$lc me c 2 =2e 2 /1=3  2  106 .P =1 ms/1=3 . The rate of the 2 , thus the deposited energy onto the returning particles is NP  nGJ c  fgap Rpc polar cap region is LX  pc me c NP  2  1031 erg s1 2



fgap 0:3



Bs 108 G



P 2 ms

5=3 :

(23)

The temperature of the hot spot is 2 Th  .LX =4 Reff SB /1=4  6  105 K



LX 31 10 erg s1

1=4 

Reff 3 km

1=2 :

which can explain the observations (see Takata et al. 2012). Nonthermal X-ray components from the pulsars are usually observed as a single power law spectrum with a photon index of 1.5–2.5 (e.g., Caraveo et al. 2004); the spectrum has no clear spectral cutoff in the 1  10 keV energy bands. It is usually assumed that synchrotron emission from the electron/positron pairs created by the photon-photon pair-creation process outside the accelerators produces the observed nonthermal X-ray emissions from pulsars. These pairs are created outside the accelerator and lose their energy via the synchrotron radiation process. The initial Lorentz factor of the pairs is on the order of e˙ ;0  .1 GeV/=.2me c 2 /  103 , which will be insensitive to the pulsar spindown parameters. The characteristic synchrotron photon energy, Esyn D 3 e2˙ ;0 ehB sin ˛ =4 mc c with ˛ being the pitch angle, provides the magnetic field strength of the emission region, r D rX ; that is, B? .rX / D 6  105 G



e˙ ;0 103

2 

 EX ; 10 keV

(24)

where B? D B sin ˛ . For the Crab pulsar, the observed X-ray emission will be produced at the region close to the light cylinder, where B.$lc /  106 G. For the Geminga pulsar, on the other hand, the X-rays will be produced in a region far from the light cylinder, where B.$lc /  104 G.

8.3

UV/Optical/IR

The UV/optical/IR emissions from pulsars are very dim, as Fig. 3 indicates, and are difficult to detect (c.f. Mignani (2009) for review of optical pulsars). The UV/optical/IR emissions from pulsars are composed of the Rayleigh-Jeans region of the cooling emissions (UV/optical) plus a nonthermal component (optical/IR), which will be the spectral tail of the synchrotron emission of the pairs. The observed spectral index in optical/IR bands is usually smaller than that of X-ray nonthermal

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components, and the observed flux level in optical/IR bands is lower than the flux level expected from extrapolating the X-ray power law spectrum to the optical band (Kargaltseve et al. 2005; Mignani et al. 2007b). These observational results indicate a spectral break of the synchrotron component in the UV bands.

8.4

Radio

Radio emissions from the pulsars have been studied since the discovery of the first pulsar in 1967 (Hewish et al. 1968). Several observational properties suggest that radio emissions from the pulsars originate from the polar cap accelerator. The observed radio pulse width is proportional to W / P ı with ı  0:5 (e.g., Kramer and Xilouris 2000). The dependency on the spin period can be explained by the 1=2 / P 1=2 (c.f. dependency of the polar cap size on the spin period, Rp  $lc Eq. 9). Radio emissions from pulsars are usually linearly polarized, with a small circular polarization. Because the emitting particles flow along the magnetic field lines, the position angle of the linear polarization will be related to the direction of the magnetic field projected on the sky. The geometry of the dipole magnetic field above the polar cap region has been used to fit the polarization data of the radio emissions (Rankin 1993). Despite the development of a geometrical model of the radio emissions, the emission mechanism, which should be less dependent on the stellar magnetic fields of the canonical and millisecond pulsars, is far from being understood. Recent progress in understanding the radio emission mechanism can be seen in Beskin et al. (2015).

9

GeV Pulse Profile

Fermi-LAT pulsars in general show a double-peaked structure in the gamma ray pulse profiles. Romani and Yadigaroglu (1995) first attempted to explain the double peaks with the emissions from the outer magnetosphere. Inasmuch as the pulsar’s magnetic field is so strong, charged particles can move only along the magnetic field lines. Hence, if the charged particles are corotating with the neutron star, the velocity vector of the particles may be written down as ˇE D ˇ0 bE C ˇco eE ;

(25)

where ˇE is the velocity vector in units of the speed of light, ˇ0 is the normalized velocity along the magnetic field line and ˇco D $˝=c corresponds to the corotating velocity at an axial distance $ . In addition, bE and eE are unit vectors of the magnetic field and the azimuth in the direction of the corotation, respectively. Because the accelerated particles have a relativistic speed, we can assume that E D 1, which gives the value of ˇ0 . jˇj

55 Gamma Ray Pulsars: From Radio to Gamma Rays

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If the corotating particles inside the light cylinder emit the observed gamma rays, the direction of emission will be provided by Eq. (25). Then the emission direction and photon arrival time are described in terms of the viewing angle as measured from the rotational axis,  D cos1 ˇz , and the rotation phase, * D *ˇ  .Er =$lc /  ˇ, respectively, where ˇz is the component of the emission direction parallel to the rotation axis, and *ˇ is the azimuthal coordinate of the emission point. If we provide the magnetic field structure and the emission region in the magnetosphere, we can project the emission region onto the .; * /-plane. Figure 7 shows examples of the sky map (upper panels) and of pulse profiles (lower panels) for the slot gap (left) and outer gap (right). Effects of corotation of the emitting plasma and of the flight time produce the pulse peaks, where many magnetic field lines gather on the sky map. With a choice of the appropriate Earth viewing angle, both models produce the double-peak light curves of the gamma ray emissions. Other emission models (e.g., Bai (2010) and Cerutti et al. (2015) for the force-free structure and Pétri and Kirk (2005) for the pulsar wind model) also explain the double-peak structure of the gamma ray pulse profile.

Slot Gap

180

Outer Gap

160

160

140

140 120 ζ (degree)

ζ (degree)

120

100

100 80 60

80 60

40 40

20 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20

1

90

0

0.1

0.2

0.3

0.6

0.7

0.8

0.9

1

0.4 0.5 0.6 Rotation Phase

0.7

0.8

0.9

1

0.4

0.5

60

80 50 60

Arbitrary Units

Arbitrary Units

70

50 40 30

40 30 20

20 10 10 0

0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Rotation Phase

0.8

0.9

1

0

0

0.1

0.2

0.3

Fig. 7 Sky map (upper) and light curves (lower) predicted by slot gap geometry (left) and outer gap geometry (right). The slot gap model assumes the emission region lies between the stellar surface and the light cylinder and the outer gap model assumes the emission region lies between the null charge surface and the light cylinder. Each curved line in the upper panel corresponds to emissions along the magnetic field line. The results are for an inclination angle ˛ D 60ı and a viewing angle  D 100ı

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10

Gamma Ray Pulsar Zoo

As we have discussed, most gamma ray pulsars share some common properties; • A spectral cutoff appears at 3 GeV. • GeV gamma rays carry most of the radiation energy released by pulsars. • The gamma ray pulse peaks are shifted from the radio peaks. Fermi-LAT and other high-energy instruments, however, found some variety in gamma ray emitting pulsars.

>50 GeV Emissions from Crab/Vela Pulsars

10.1

Among Fermi-LAT pulsars, 20 pulsars show pulsed emissions in the energy range >10 GeV, including 12 up to >25 GeV (Ackermann et al. 2013) and their spectra clearly indicate subexponential cutoff features above the cutoff energy. The pulsed gamma ray emissions from the Crab pulsar show the spectral break at 5 GeV, and extend to TeV energy bands with a single power law form (Fig. 8). No spectral turnover can be seen between 10 GeV and 1 TeV (Ahnen et al. 2015). The >50 GeV pulsed emissions from the Vela pulsar have been detected in the Fermi-LAT data (Leung et al. 2014). These >50 GeV from the Crab and Vela pulsars are difficult to explain by the standard curvature radiation scenario discussed in Sect. 8.1.

10-8

Crab Vela

Flux (erg cm-2 s-1)

10-9

10-10

10-11

10-12

10-13 108

109

1010

1011

Energy (eV) Fig. 8 The GeV/TeV spectra for the Crab (triangle) and Vela (circle) pulsars

1012

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For the Crab pulsar, the strong absorption due to the pair-creation process makes it difficult for the gamma rays to escape from the light cylinder, as we discussed in Sect. 6. It is likely therefore that the TeV emission from the Crab pulsar is produced very close to or outside the light cylinder. Moreover, all models expect that the inverse-Compton scattering of high-energy electrons/positrons off the soft photons produces the TeV gamma rays from the Crab pulsar (Aharonian et al. 2012; Harding and Kalapotharakos 2015). Although the inverse-Compton scattering models have succeeded in reproducing the GeV/TeV spectrum, it is still an unresolved issue to explain the multiwavelength pulse profiles, for which the pulsed peaks across radio to TeV energy bands (1018 magnitude) are all in phase. For the Vela pulsar, the contribution of the inverse-Compton scattering process (likewise the Crab pulsar) above 10 GeV is one of the proposed models to explain the high-energy tail. However, the expected flux level of the inverse-Compton emissions is well below the observed flux level (e.g., Takata et al. 2008). Hence, curvature radiation will be the origin of the observed 10–100 GeV emissions of the Vela pulsar.

10.2

“GeV” Quiet Gamma Ray Pulsars

In the EGRET era, PSR B1509-58 was anticipated as a Crab-like young pulsar, because (1) the position of the upper limit of the EGRET observations indicate a Crab-type spectrum (c.f. Fig. 2) and (2) the pulsar’s characteristic age ( s  1:6 kyrs) is similar to the Crab’s ( s  1:3 kyrs). Fermi-LAT, however, detected no GeV emissions from PSR B1509-58. The position of the upper limit determined by Fermi-LAT suggests that PSR B1509-58 does not have a Crab-like spectrum, as Fig. 3 indicates. Multiwavelength observations from X-ray to GeV gamma ray bands suggest that the spectral cutoff energy of PSR B1509-58 is 10 MeV, which is more than two orders of magnitude less than that of the Fermi-LAT pulsars. Kuiper and Hermsen (2015) report the emission properties for 18 pulsars that are seen in hard X-ray/soft gamma ray bands (20 keV–30 MeV). In addition to PSR B1509-59, five pulsars (namely Takbel 1, J1617-5055, J1811-1925, J18380655, J1846-0258, and J1930+1852) appear to be GeV-quiet gamma ray pulsars (Wang et al. 2014). The GeV-quiet gamma ray pulsars share some emission characteristics (c.f. Fig. 9); • • • •

No >1 GeV emissions have been detected in Fermi-LAT data. The spectral cutoff appears at 10 MeV bands. Nonthermal X-rays show a broad pulse width. No or dim radio emissions have been detected.

With these unique emission properties, GeV-quiet gamma ray pulsars are a new class of pulsars. One proposed scenario for the formation of the soft gamma ray spectrum of PSR B1509-58 is attenuation of the gamma ray photons due to a strong magnetic

Fig. 9 The X-ray/gamma ray spectrum and pulse profile of PSR J1811–1925. The data were taken from Dean et al. (2008) and Kuiper and Hermsen (2015) for spectrum and Gavriil et al. (2004) for light curve. After Wang et al. (2014)

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field near the stellar surface (Harding et al. 1997). In addition to the magnetic pair-creation process (Sect. 6), the strong magnetic field close to or above quantum field strength B D BQ can implement a photon-splitting process in which one high-energy gamma ray is split into two lower-energy photons. In fact, the pulsars PSR B1509-58, J1846-0258, and J1930+1852 are high-Bs rotation-powered pulsars (c.f. Table 1). Moreover, magnetar-like X-ray outburst emissions from PSR J18460258 have been observed. GeV-quiet gamma ray pulsars may connect between canonical gamma ray pulsars and magnetars. Instead of the high-B model, it is also suggested that the GeV-quiet gamma ray pulsars have a peculiar viewing geometry (Wang et al. 2014), as a result of which we miss the GeV gamma ray emissions from the acceleration regions.

10.3

Class-II Millisecond Pulsars

One of the important results of Fermi-LAT is the discovery of pulsed gamma ray emissions from millisecond pulsars. The similarities of gamma ray pulse profiles and spectra to those of canonical pulsars suggest that the GeV emission process of the pulsar is not sensitive to the spin period or the surface magnetic field strength. Venter et al. (2012) divided Fermi-LAT millisecond pulsars into three classes, I, II, and III, for which the gamma ray peak lags, is aligned with, and precedes the radio peak, respectively. Because the Crab pulsar also shows its gamma ray peaks aligned with its radio peaks, Class II millisecond pulsars are sometimes called Crabtype millisecond pulsars. Ng et al. (2014) suggested that at least 8 out of 41 sources listed in Fermi-LAT’s second pulsar catalogue belong to the Class II millisecond pulsars. For canonical pulsars, the Crab, and probably PSR J0540-6919 (Ackermann et al. 2015), show Class II light curves. Moreover, X-ray emissions described by a power law spectrum were detected for three Class II millisecond pulsars, B1937+21 (Fig. 10), B1821+24, and J0218+4232. The X-ray peaks also appear with rotation phase very close to the radio/gamma ray peaks (Guillemot et al. 2012), which is similar to the pulse profiles of the Crab and PSR J0540-6919. Before the Fermi era, the Crab was the only Class II pulsar and hence the observational information has been inadequate to understand the cause of the phase alignment of the gamma

Table 1 Parameters of the GeV-quiet soft gamma ray pulsars PSRs B1509-58 J1617-5055 J1811-1925 J1838-0655 J1846-0258 J1930+1852

P (ms) 151 69 65 65 326 136

Lsd (1036 erg s1 ) 17 16 6.4 6.4 8.1 12

Bs (1012 G) 15 3.1 1.7 1.7 48 10

s (104 yrs) 0.16 0.83 2.3 2.3 0.073 0.29

D(kpc) 4.4 6.5 5 6.6 5.8 5

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Fig. 10 Multiwavelength pulse profiles of PSR B1937+21. After Ng et al. (2014)

ray and radio pulses. Fermi’s discovery of more Class II millisecond pulsars will advance our understanding of the connection between the radio and gamma ray emission processes. The phase-aligned radio, X-ray, and gamma ray pulse profiles suggest that the radio emissions of Class II pulsars could be generated in caustics in the outer magnetosphere, the same as the gamma ray emissions. It has been suggested that Class II pulsars tend to have stronger magnetic field strengths at the light cylinder, Blc (Espinoza et al. 2013; Ng et al. 2014). Among the top 10 high-Blc pulsars listed in the ATNF pulsar catalogue, Fermi-LAT measured pulsed GeV emissions from seven. All of them show a Class II pulse profile (c.f. Table 2). This also suggests that high-Blc pulsars are radio-loud gamma ray pulsars, which indicates that viewing geometry is not the only reason to distinguish between radio-loud and radio-quiet Fermi-LAT pulsars. The study of Class II pulsars may improve our understanding of the radio emission mechanism of the pulsars.

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Table 2 Top 10 high-Blc pulsars. The pulsed gamma rays from PSRs J0537-6910 in LMC, J17013006F in NGC6266, and J400-6325 in SNR G310.6-1.6 have not yet been confirmed by Fermi-LAT PSRs J0537-6910 B1937+21 B0531+21 B1821-24A J1701-3006F B1957+20 B0540-69 J1400-6325 J0218+4232 J1747-4036

11

P (ms) 16 1.6 33 3.1 2.3 1.6 50 31 2.3 3.2

Lsd (1036 erg s1 ) 490 1.1 450 2.2 0.73 0.16 150 51 0.24 0.12

Blc (105 G) 20 10 9.6 7.4 5.6 3.8 3.6 3.5 3.1 3.1

Gamma ray (Class) – II II II – II II – II I or II

Conclusions

Fermi-LAT has provided important information for understanding the GeV emissions from pulsars and the connection between the emission processes in gamma rays and in other wavebands. The observed cutoff behavior above 13 GeV favors the hypothesis that the emission comes from the outer magnetosphere and rules out the classical polar cap scenario, which predicted a superexponential cutoff feature in the GeV spectrum because of the magnetic pair-creation process. The double-peak pulse profiles with 0:5 phase separation also support the idea that the gamma rays originate in the outer magnetosphere. The discovery of pulsed gamma rays from millisecond pulsars implies that the GeV emission process should be insensitive to the spin period and the surface magnetic field. Discoveries of radio-quiet gamma ray pulsars and the observed phase-lag between the radio and gamma ray pulses of the radio-loud gamma ray pulsars indicate that the radio and gamma ray emission regions are in general different. However, high-Blc pulsars tend to be radio-loud Class-II gamma ray pulsars. Fermi-LAT enables us to study in detail the structure of the pulsar magnetosphere and the entire spectrum of pulsars from the radio to gamma rays.

12

Cross-References

 Dynamical Mergers  Supernova of 1054 and its Remnant, the Crab Nebula  X-Ray Pulsars  Young Neutron Stars with Soft Gamma Ray Emission and Anomalous X-Ray

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Acknowledgements J.T. thanks Drs. S. Shibata, K. S. Cheng, E. R. Taam, H.-K. Chang, A. H. Kong, C. Y. Hui, and P. H. T. Tam for the useful discussions. This work is supported by a NSFC grant of China under 11573010.

References Abdo AA, Allen B, Aune T, Berley D, Blaufuss E, Casanova S et al (2008) A measurement of the spatial distribution of diffuse TeV gamma ray emission from the galactic plane with Milagro. Science 322:1218 Abdo AA, Ackermann M, Ajello M, Atwood WB, Axelsson M, Baldini L et al (2009) A population of gamma ray millisecond pulsars seen with the Fermi large area telescope. Science 325:848 Abdo AA, Ackermann M, Ajello M, Atwood WB, Axelsson M, Baldini L et al (2010a) Fermi large area telescope observations of the Crab pulsar and Nebula. ApJ 708:1254 Abdo AA, Ackermann M, Ajello M, Allafort A, Asano K, Baldini L et al (2010b) Detection of the energetic pulsar PSR B1509-58 and its pulsar wind nebula in MSH 15–52 using the Fermi-large area telescope. ApJ 714:927 Abdo AA, Ajello M, Allafort A, Baldini L, Ballet J, Barbiellini G et al (2013) The second Fermi large area telescope catalog of gamma ray pulsars. ApJS 208:17 Ackermann M, Ajello M, Allafort A, Atwood WB, Baldini L, Ballet J et al (2013) The first FermiLAT catalog of sources above 10 GeV. ApJS 209:34 Ackermann M, Albert A, Baldini L, Ballet J, Barbiellini G, Barbieri C et al (2015) An extremely bright gamma ray pulsar in the large magellanic cloud. Science 350:801 Albert J, Aliu E, Anderhub H, Antoranz P, Armada A, Baixeras C et al (2007) Constraints on the steady and pulsed very high energy gamma ray emission from observations of PSR B1951+32/CTB 80 with the MAGIC telescope. ApJ 669:1143 Aleksi´c J, Ansoldi S, Antonelli LA, Antoranz P, Babic A, Bangale P et al (2014) Detection of bridge emission above 50 GeV from the Crab pulsar with the MAGIC telescopes. A&AL 565:12 Aliu E et al (2011) Detection of pulsed gamma rays above 100 GeV from the Crab Pulsar. Science 334:69 Aharonian FA, Bogovalov SV, Khangulyan D (2012) Abrupt acceleration of a ‘cold’ ultrarelativistic wind from the Crab pulsar. Nature 482:507 Ahnen ML, Ansoldi S, Antonelli LA, Antoranz P, Babic A, Banerjee B et al (2015, in press) Teraelectronvolt pulsed emission from the Crab pulsar detected by MAGIC. A&A. arXiv:1510.07048 [astro-ph.HE] Arons J (1983) Pair creation above pulsar polar caps – geometrical structure and energetics of slot gaps. ApJ 266:215 Bai XN, Spitkovsky A (2010) Uncertainties of modeling gamma ray pulsar light curves using vacuum dipole magnetic field. ApJ 715:1282 Beskin VS, Chernov SV, Gwinn CR, Tchekhovskoy AA (2015) Radio pulsars. SSRv 191:1 Butler RF, Golden A, Shearer A (2002) Detection of new optical counterpart candidates to PSR B1951+32 with HST/WFPC2. A&A 395:845 Caraveo PA, De Luca A, Mereghetti S, Pellizzoni A, Bignami GF (2004) Phase-resolved spectroscopy of Geminga shows rotating hot spot(s). Science 305:376 Cerutti B, Philippov AA, Spitkovsky A (2015) Modeling high-energy pulsar lightcurves from first principles, eprint arXiv:1511.01785 Chen AY, Beloborodov AM (2014) Electrodynamics of axisymmetric pulsar magnetosphere with electron-positron discharge: a numerical experiment. ApJL 795:22 Chen Ge, An H, Kaspi VM, Harrison F, Madsen K, Stern D (2015) NuSTAR observations of the young, energetic radio pulsar PSR B1509-58, eprint arXiv:1507.08977 Cheng KS, Ho C, Ruderman M (1986) Energetic radiation from rapidly spinning pulsars. I – outer magnetosphere gaps. II – VELA and Crab. ApJ 300:500

55 Gamma Ray Pulsars: From Radio to Gamma Rays

1497

De Luca A, Caraveo PA, Mereghetti S, Negroni M, Bignami GF (2005) On the polar caps of the three Musketeers. ApJ 623:1051 Dean AJ, de Rosa A, McBride VA, Landi R, Hill AB, Bassani L et al (2008) INTEGRAL observations of PSR J1811-1925 and its associated pulsar wind Nebula. MNRASL 384:29 Espinoza CM, Guillemot L, Çelik Ö, Weltevrede P, Stappers BW, Smith DA et al (2013) Six millisecond pulsars detected by the Fermi large area telescope and the radio/gamma ray connection of millisecond pulsars. MNRAS 430:571 Gavriil FP, Kaspi VM, Roberts MSE (2004) Phase-coherent timing of PSR J1811-1925: the pulsar at the heart of G11.2-0.3. AdSpR 33:592 Goldreich P, Julian WH (1969) Pulsar electrodynamics. ApJ 157:869 Gotthelf EV, Halpern JP, Dodson R (2002) Detection of pulsed X-ray emission from PSR B1706-44. ApJL 567:125 Guillemot L, Johnson TJ, Venter C, Kerr M, Pancrazi B, Livingstone M et al (2012) Pulsed gamma rays from the original millisecond and black widow pulsars: a case for caustic radio emission? ApJ 744:33 Harding AK, Kalapotharakos C (2015) Synchrotron self-compton emission from the Crab and other pulsars. ApJ 811:63 Harding AK, Baring MG, Gonthier PL (1997) Photon-splitting cascades in gamma ray pulsars and the spectrum of PSR 1509–58. ApJ 476:246 Harding AK, Strickman MS, Gwinn C, Dodson R, Moffet D, McCulloch P (2002) The multicomponent nature of the vela pulsar nonthermal X-ray spectrum. ApJ 576:376 Hewish A, Bell SJ, Pilkington JDH, Scott PF, Collins RA (1968) Observation of a rapidly pulsating radio source. Nature 217:709 Hirotani K (2015) Three-dimensional non-vacuum pulsar outer-gap model: localized acceleration electric field in the higher altitudes. ApJL 798:40 Kargaltsev OY, Pavlov GG, Zavlin VE, Romani RW (2005) Ultraviolet, X-ray, and optical radiation from the Geminga pulsar. ApJ 625:307 Kniffen DA, Hartman RC, Thompson DJ, Bignami GF, Fichtel CE (1974) Gamma radiation from the Crab Nebula above 35 MeV. Nature 251:397 Kramer M, Xilouris KM (2000) Radio emission properties of millisecond pulsars. ASPC 202:299 Krause-Polstorff J, Michel FC (1985) Pulsar space charging. A&A 144:72 Kuiper L, Hermsen W (2015) The soft gamma ray pulsar population: a high-energy overview. MNRAS 449:3827 Kuiper L, Hermsen W, Cusumano G, Diehl R, Sch˙onfelder V, Strong A, Bennett K, McConnell ML (2001) The Crab pulsar in the 0.75–30 MeV range as seen by CGRO COMPTEL. A coherent high-energy picture from soft X-rays up to high-energy gamma rays. A&A 378:918 Leung, Gene CK, Takata J, Ng CW, Kong AKH, Tam PHT, Hui CY, Cheng KS (2014) Fermi-LAT detection of pulsed gamma rays above 50 GeV from the Vela pulsar. ApJL 797:13 Manchester RN, Hobbs GB, Teoh A, Hobbs M, Astron J (2005) 129, ATNF pulsar catalogue 1993–2006 Matz S, Ulmer MP, Grabelsky DA, Purcell WR, Grove JE, Johnson WN et al (1994) The pulsed hard X-ray spectrum of PSR B1509-58. ApJ 434:288 McGowan KE, Zane S, Cropper M, Kennea JA, Córdova FA, Ho C et al (2004) XMM-newton observations of PSR B1706-44. ApJ 600:343 Mignani RP (2009) Multi-wavelength observations of isolated neutron stars, eprint arXiv:0908.1010 Mignani RP, Zharikov S, Caraveo PA (2007a) The optical spectrum of the Vela pulsar. A&A 473:891 Mignani RP, Bagnulo S, Dyks J, Lo Curto G, Słowikowska A (2007b) The optical polarisation of the Vela pulsar revisited. A& A 476:1157 Mignani RP, Pavlov GG, Kargaltsev O (2010) Optical-ultraviolet spectrum and proper motion of the middle-aged pulsar B1055-52. ApJ 720:1635 Mori K, Gotthelf EV, Dufour F, Kaspi VM, Halpern JP, Beloborodov AM et al (2014) A broadband X-ray study of the Geminga pulsar with NuSTAR and XMM-newton. ApJ 793:88

1498

J. Takata

Muslimov AG, Harding AK (2003) Extended acceleration in slot gaps and pulsar high-energy emission. ApJ 588:430 Ng CY, Takata J, Leung GCK, Cheng KS, Philippopoulos P (2014) High-energy emission of the first millisecond pulsar. ApJ 787:167 Pétri J, Kirk J (2005) The polarization of high-energy pulsar radiation in the striped wind model. ApJL 627:37 Philippov AA, Spitkovsky A, Cerutti B (2015) Ab initio pulsar magnetosphere: three-dimensional particle-in-cell simulations of oblique pulsars. ApJL 801:19 Pilia M, Pellizzoni A, Trois A, Verrecchia F, Esposito P, Weltevrede P et al (2010) AGILE observations of the “Soft” gamma ray pulsar PSR B1509–58. ApJ 723:707 Rankin JM (1993) Toward an empirical theory of pulsar emission. VI – the geometry of the conal emission region: appendix and tables. ApJS 85:145 Ray P (2015) Public List of LAT-Detected Gamma-Ray Pulsars. https://confluence.slac. stanford.edu/display/GLAMCOG/Public+List+of+LAT-Detected+Gamma-Ray+Pulsars Romani RW, Yadigaroglu IA (1995) Gamma ray pulsars: emission zones and viewing geometries. ApJ 438:314 Ruderman MA, Sutherland PG (1975) Theory of pulsars – polar caps, sparks, and coherent microwave radiation. ApJ 196:51 Scharlemann ET, Arons J, Fawley WM (1978) Potential drops above pulsar polar caps – ultrarelativistic particle acceleration along the curved magnetic field. ApJ 222:297 Shibanov YA, Koptsevich AB, Sollerman J, Lundqvist P (2003) The Vela pulsar in the nearinfrared. A&A 406:645 Shibanov YA, Zharikov SV, Komarova VN, Kawai N, Urata Y, Koptsevich AB et al (2006) Subaru optical observations of the two middle-aged pulsars PSR B0656+14 and geminga. A&A 448:313 Shibata S (1995) Origin of the gamma ray pulsars. MNRAS 276:537 Smith IA, Michel FC, Thacker PD (2001) Numerical simulations of aligned neutron star magnetospheres. MNRAS 322:209 Sollerman J, Lundqvist P, Lindler D, Chevalier RA, Fransson C, Gull TR et al (2000) Observations of the Crab Nebula and its pulsar in the far-ultraviolet and in the optical. ApJ 537:861 Spitkovsky A (2006) Time-dependent force-free pulsar magnetospheres: axisymmetric and oblique rotators. ApJL 648:51 Takata J, Chang HK, Shibata S (2008) Particle acceleration and non-thermal emission in the pulsar outer magnetospheric gap. MNRAS 386:748 Takata J, Cheng KS, Taam RE (2012) X-ray and gamma ray emissions from rotation powered millisecond pulsars. ApJ 745:100 Takata J, Ng CW, Cheng KS (2016) Probing gamma ray emissions of fermi-LAT pulsars with a non-stationary outer gap model. MNRAS 455:4249 Thompson DJ, Fichtel CE, Kniffen DA, Ogelman HB (1975) SAS-2 high-energy gamma ray observations of the VELA pulsar. ApJL 200:79 Thompson DJ, Bailes M, Bertsch DL, Cordes J, D’Amico N, Esposito JA et al (1999) Gamma radiation from PSR B1055–52. ApJ 516:297 Timokhin AN, Arons J (2013) Current flow and pair creation at low altitude in rotation-powered pulsars force-free magnetospheres: space charge limited flow. MNRAS 429:20 Venter C, Johnson TJ, Harding AK (2012) Modeling phase-aligned gamma ray and radio millisecond pulsar light curves. ApJ 744:34 Wada T, Shibata S (2007) A particle simulation for the global pulsar magnetosphere: the pulsar wind linked to the outer gaps. MNRAS 376:1460 Wang Y, Ng CW, Takata J, Leung GCK, Cheng KS (2014) Emission mechanism of GeV-quiet soft gamma ray pulsars: a case for peculiar geometry? MNRAS 445:604 Yakovlev DG, Pethick CJ (2004) Neutron star cooling. ARA&A 42:169 Yuki S, Shibata S (2012) A particle simulation for the pulsar magnetosphere: relationship of polar cap, slot gap, and outer gap. PASJ 64:43 Zavlin VE (2007) Studying millisecond pulsars in X-rays. Ap&SS 208:297

X-Ray Binaries

56

Jorge Casares, Peter Gustaaf Jonker, and Garik Israelian

Abstract

This chapter discusses the implications of X-ray binaries on our knowledge of Type Ibc and Type II supernovae. X-ray binaries contain accreting neutron stars and stellar-mass black holes which are the end points of massive star evolution. Studying these remnants thus provides clues to understanding the evolutionary processes that lead to their formation. We focus here on the distributions of dynamical masses, space velocities, and chemical anomalies of their companion stars. These three observational features provide unique information on the physics of core collapse and supernovae explosions within interacting binary systems. There is suggestive evidence for a gap between 2 and 5 Mˇ in the observed mass distribution. This might be related to the physics of the supernova explosions although selections effects and possible systematics may be important. The difference between neutron star mass measurements in lowmass X-ray binaries (LMXBs) and pulsar masses in high-mass X-ray binaries

J. Casares () Instituto de Astrofísica de Canarias, La Laguna, Tenerife, Spain Departamento de Astrofísica, Universidad de La Laguna, La Laguna, Tenerife, Spain Department of Physics, Astrophysics, University of Oxford, Oxford, UK e-mail: [email protected] P.G. Jonker SRON, Netherlands Institute for Space Research, Utrecht, The Netherlands Department of Astrophysics/IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands e-mail: [email protected] G. Israelian Instituto de Astrofísica de Canarias, La Laguna, Tenerife, Spain Departamento de Astrofísica, Universidad de La Laguna, La Laguna, Tenerife, Spain e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_111

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(HMXBs) reflects their different accretion histories, with the latter presenting values close to birth masses. On the other hand, black holes in LMXBs appear to be limited to .12 Mˇ because of strong mass loss during the wind Wolf-Rayet phase. Detailed studies of a limited sample of black hole X-ray binaries suggest that the more massive black holes have a lower space velocity, which could be explained if they formed through direct collapse. Conversely, the formation of low-mass black holes through a supernova explosion implies that large escape velocities are possible through ensuing natal and/or Blaauw kicks. Finally, chemical abundance studies of the companion stars in seven X-ray binaries indicate they are metal rich (all except GRO J1655-40) and possess large peculiar abundances of ˛-elements. Comparison with supernova models is, however, not straightforward given current uncertainties in model parameters such as mixing.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Remnant Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Pulsar Masses in HMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Neutron Star Masses in LMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Black Hole Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 The Mass Spectrum: Implications for Supernovae Models . . . . . . . . . . . . . . . . . 3 Kick Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Black Hole Formation and Its Link to Space Velocity . . . . . . . . . . . . . . . . . . . . . 3.2 The Black Hole Space Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Measuring the Space Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Black Hole X-Ray Binaries with and Without Natal Kicks . . . . . . . . . . . . . . . . . 4 Chemical Abundance of Companion Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Observations, Models, and Spectral Synthesis Tools . . . . . . . . . . . . . . . . . . . . . 4.2 Stellar Abundances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Individual Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

X-ray binaries contain compact stellar remnants accreting from “normal” companion stars. Therefore, they provide ideal opportunities for probing the core collapse of massive stars in a binary environment and are thus able to constrain the physics of Type Ibc and Type II supernovae. These compact remnants are revealed by persistent/transient X-ray activity which is triggered by mass accretion. Observationally, they come in three flavors – pulsars, neutron stars, and black holes – that are paired with companion (donor) stars of a wide range of masses. Historically, X-ray binaries have been classified according to the donor mass as either low-mass X-ray binaries (LMXBs) or high-mass X-ray binaries (HMXBs). The former are fueled by accretion disks supplied by a .1 Mˇ Roche-lobe filling star, while HMXBs are mostly fed directly from the winds of a &10 Mˇ companion. They display distinct Galactic distributions associated with Population I and Population II objects, with

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Fig. 1 Galactic distribution of HMXBs (top) and LMXBs (bottom). Open circles indicate LMXBs in globular clusters (From van Paradijs 1998)

HMXBs lying along the Galactic plane and LMXBs clustering toward the Galactic bulge and in globular clusters Joss and Rappaport (1984) (Fig. 1). A handful of X-ray binaries with 1  3 Mˇ Roche-lobe filling companions are sometimes referred to as intermediate mass X-ray binaries (IMXBs). For a comprehensive review on X-ray binaries, we refer to Charles and Coe (2006). The type of X-ray activity observed is determined by (i) the mass transfer rate from the donor, (ii) the magnetic field of the compact star, and (iii) the X-ray heating of the accretion disk by the accretion luminosity. The interplay between these three quantities explains why black hole remnants are mostly found in transient LMXBs, neutron stars in persistent LMXBs, and pulsars in HMXBs. In recent years we have seen the discovery of pulsars with millisecond spin periods in transient LMXBs. These are considered a missing link in X-ray binary evolution, with neutron stars being spun up by sustained accretion to become recycled pulsars (Alpar et al. 1982; Wijnands and van der Klis 1998). A detailed review of X-ray binary evolution with the variety of evolutionary paths and end products can be found in  Chap. 57, “Supernovae and the Evolution of Close Binary Systems” (see paragraph “CrossReferences”).

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X-ray binaries present ideal laboratories for examining the physics of the supernova explosions which formed their compact objects. The orbital motion of the stellar companions can be used to weigh the masses of the supernova remnants. Abundance anomalies are often seen in the companion star atmospheres, demonstrating chemical pollution by the supernova ejecta. And the spatial motion of the binary possesses information on the kick velocity imparted by the explosion itself. These three topics (dynamical masses, kick velocities, and chemical anomalies) and their impact on our understanding of Type Ibc and Type II supernovae are the scope of this chapter and will be presented in turn.

2

Remnant Masses

The distribution of masses of compact remnants contains the imprints of the physics of the supernova explosions. Various aspects, such as the explosion energy, mass cut, amount of fallback, or the explosion mechanism itself, are important for the final remnant mass distribution. By building the mass spectrum of compact objects in X-ray binaries, we can therefore obtain new insights onto the physics of core collapse in Type Ibc and Type II supernovae. In principle, precise masses can be extracted from eclipsing double-line spectroscopic binaries using simple geometry and Kepler’s laws, but this is not often the case in X-ray binaries. Note that neutron star masses in binary radio pulsars are not discussed here (see  Chap. 47, “The Masses of Neutron Stars”). It should also be noted that the accretion process responsible for lighting up the X-ray binaries can in principle change significantly the neutron star mass in systems where sufficient time is available such as neutron stars in old LMXBs. On the other hand, the accreted mass is too low to alter the BH mass significantly and similarly; the neutron star mass in short-lived HMXBs can also not be changed significantly.

2.1

Pulsar Masses in HMXBs

Pulsars in eclipsing binaries present, in principle, the best prospects for accurate determination of remnant masses. The Doppler shift of the donor’s photospheric lines, combined with timing delays of the neutron star pulse, allows us to measure the projected orbital velocities of the two binary components (Kopt and KX , respectively), thus making them double-lined binaries. If the pulsar is eclipsed by the massive donor (a  40 % chance in incipient Roche-lobe overflowing systems ), then the inclination angle i is given by p 1  .Ropt =a/2 sin i D cos 

(1)

where  is the eclipse half-angle, a the binary separation, and Ropt the stellar radius. The latter can be approximated by some fraction ˇ 1 of the effective Rochelobe radius RLopt , also known as the stellar “filling factor,” while RLopt =a is purely

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a function of the binary mass ratio Q D MX =Mopt D Kopt =KX and the degree of stellar synchronization ˝ (usually ˝ 1). The stellar masses can then be solved from the mass function equations KX3 P .1  e 2 /3=2 .1 C Q/2 2 G sin3 i   3 P .1  e 2 /3=2 Kopt 1 2 1 C MX D Q 2 G sin3 i Mopt D

(2) (3)

where P stands for the binary period and e the orbital eccentricity. This method has produced nine pulsar masses with relatively high precision which we list in Table 1. The major source of uncertainty arises from the combined effect of variable stellar wind, tidal pulsations, and X-ray irradiation which distort the absorption profiles and hence the radial velocity curve of the optical companion (e.g., Quaintrell et al. 2003 and Reynolds et al. 1997). Although not a pulsar, we have also included in this section a remnant mass determination for the eclipsing HMXB 4U 1700-37. With a mass significantly higher than the nine HMXB pulsars, the nature of the compact object in this system is unclear, and a low-mass black hole cannot be dismissed. In any case, the quoted mass should be regarded as somewhat less secure because it rests upon the spectroscopic mass of the optical companion (see Clark et al. 2002 for details). Interestingly, the largest known population of pulsar X-ray binaries (over 100) belongs to the subclass of Be/X-ray binaries (Reig 2011). These systems generally have very wide and eccentric orbits, with the neutron star accreting material from the circumstellar Be disk during periastron passages or through episodic disk instability events. Unfortunately, the scarcity of eclipsing systems and the very long orbital periods make reliable mass determination in Be/X-ray binaries extremely difficult.

2.2

Neutron Star Masses in LMXBs

Neutron stars in LMXBs do not usually pulse (with 4U 1822-371 and a handful of millisecond pulsars as the only exceptions), and their radial velocity curves are thus not available. Only the mass function of the compact star is attainable through the radial velocity curve of the optical companion (Eq. 3). In these cases it is still possible to derive reliable masses by exploiting the fact that the low-mass donor star overflows its Roche lobe and is synchronized in a circular orbit (which in turn implies ˝ D1, e D 1). This is a reasonable assumption given the long lifetimes and short circularization timescales expected in LMXBs (Witte and Savonije 2001). On this basis, the broadening of the donor absorption lines V sin i depends on binary mass ratio q D Q1 according to Wade and Horne (1988) V sin i =Kopt ' 0:462 q .1=3/ .1 C q/.2=3/

(4)

while its orbital light curve (governed by tidal distortions) correlates with inclination. Therefore, the detection of the faint donor star in LMXBs ensures a full

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dynamical solution which makes this technique feasible for transient LMXBs in quiescence (i.e., when accretion is halted and X-ray emission is weak) or persistent LMXBs with long orbital periods and thus luminous companion stars. In the case of persistent LMXBs with short periods .1 d, the companion star is totally overwhelmed by the accretion luminosity. However, some constraints on stellar masses can still be derived through the Bowen technique which employs fluorescence lines excited on the X-ray heated face of the donor star (Steeghs and Casares 2002). The radial velocity curves of the Bowen lines are biased because they arise from the irradiated face of the star instead of its center of mass. Therefore, a K-correction needs to be applied in order to recover the true velocity semi-amplitude Kopt . The K-correction parametrizes the displacement of the center of light with respect to the donor’s center of mass through the mass ratio and disk flaring angle ˛, with the latter dictating the size of the disk shadow projected over the irradiated donor (Muñoz-Darias et al. 2005). Extra information on q and ˛ is thus required to measure the real Kopt . Further limits to neutron star masses can be set if the binary inclination is well constrained through eclipses (e.g., 4U 1822-371). It is interesting to note that the Bowen technique, despite its limitations, has enabled the first dynamical constraints in persistent LMXBs since their discovery 50 years ago. The best neutron star masses in LMXBs obtained by means of these techniques are also listed in Table 1. Table 1 Pulsar and neutron star (NS) masses in X-ray binariesa Object OAO 1657-415 SAX 18027-2016 EXO 1722-363 4U 1538-52 SMC X-1 Vel X-1 LMC X-4 Cen X-3 4U 1700-37 Her X-1 Cyg X-2 V395 Car Sco X-1 XTE J2123-058 Cen X-4 4U 1822-371 XTE J1814-338 SAX J1808.4-3658 HETE 1900.1-2455

X-ray binary class HMXB/persistent „ „ „ „ „ „ „ „ IMXB/persistent LMXB/persistent „ „ LMXB/transient „ „ „ „ „

Remnant X-ray pulsar „ „ „ „ „ „ „ ? X-ray pulsar NS „ „ „ „ X-ray pulsar msec „ „„ „„

Mass (Mˇ ) 1.42˙0.26 1.2-1.9 1.55˙0.45 1.00˙0.10 1.04˙0.09 1.77˙0.08 1.29˙0.05 1.49˙0.08 2.44˙0.27 1.07˙0.36 1.71˙0.21 1.44˙0.10 3.6 >5.42 >1.6 6.98.2 6.4˙0.6 5.4˙0.3 2.77.5 14.8˙1.0 10.9˙1.4 7.0˙0.6 15.7˙1.5 3.85.6

References Reid et al. (2014)

Wu et al. (2016)

Macdonald et al. (2014)

Orosz et al. (2014) Casares et al. (2014)

Adopted from Casares and Jonker (2014) unless otherwise stated in the reference column. Lower limits for BW Cir, GRS 1009-45, XTE J1859 C 226, and GRO J0422 C 32 are based on the absence of eclipses, combined with updated determinations of the mass function and q (when available). The lower limit on GX 339-4 is based on the lack of X-ray eclipses plus constraints provided by the K-correction

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VLBI parallax for Cyg X-1) coupled with the observed apparent brightness and effective temperature. Furthermore, in the case of M33 X-7, eclipses of the X-ray source by the donor star provide additional tight constraints on the inclination which results in one of the largest accurately known black hole masses. Note that we have excluded mass measurements for the two extragalactic HMXBs NGC 300 X-1 and IC 10 X-1. This is because these rely on radial velocity curves of the HeII 4686 wind emission line and an assumed mass for the WolfRayet star. Different groups have reported conflicting results which range from canonical neutron stars to the largest black hole masses measured so far and are hence unreliable. The table includes MWC 656, the first black hole companion to a Be star (Casares et al. 2014). Here the black hole mass relies on the spectroscopic mass of the optical companion and the radial velocity curves of the two stars, extracted from the dynamics of circumstellar gaseous disks. A critical review of black hole mass determinations, including potential systematic effects, is presented in Casares and Jonker (2014).

2.4

The Mass Spectrum: Implications for Supernovae Models

Figure 2 presents the observed masses of neutron star and black hole remnants in X-ray binaries, as in Tables 1 and 2. Note that we have here excluded neutron star masses in radio pulsars and binary millisecond pulsars (as discussed in  Chap. 47, “The Masses of Neutron Stars”). The bottom panel displays the number distributions of neutron stars (black) and black holes (red) masses, excluding upper/lower limits. Three main features seem to be drawn from the plot, namely, (1) neutron star masses tend to be larger in LMXBs/IMXBs (mass average of 1.54˙0.16 Mˇ ) than in HMXBs (1.34˙0.26 Mˇ ), (2) a dearth of remnants or gap appears between 2 and 5 Mˇ , and (3) the most massive black holes (15 Mˇ ) are found in HMXBs. Feature (1), although tentative, could be a manifestation of the pulsar recycling scenario. The difference in neutron star masses, if confirmed, would stem from different binary evolution histories, with neutron stars in LMXBs having experienced significant accretion over extended periods of time. This interpretation would be further supported by indications that pulsar mass decreases with spin period (Zhang et al. 2011). Neutron stars in HMXBs are little modified by accretion, and, thus, their masses are expected to lie closer to their birth values. And indeed, both the mean and dispersion of the neutron star mass distribution in HMXBs are found to agree with theoretical expectations of core-collapse supernovae (Özel, et al. 2012). Constraints on neutron star forming supernovae do seem to be provided by two distinct populations of X-ray pulsars in Be/X-ray binaries; short Pspin pulsars with short orbital periods and low eccentricities would be produced by electroncapture supernovae, while long Pspin pulsars with long orbital periods and high eccentricities in iron-core-collapse supernovae (Knigge et al. 2011). The former pulsars are naturally expected to be less massive (.1.3 Mˇ ), but, unfortunately, this cannot yet be tested because of the lack of precise neutron star mass determinations in Be/X-ray binaries.

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6 4 2 0

0

5

10

15

Fig. 2 Top: compact remnant masses measured in X-ray binaries. Neutron stars and black holes are indicated in black and red colors, respectively. 4U 1700-37 is plotted in dotted-style line because the nature of the compact star is uncertain. The horizontal dotted line divides LXMBs/IMXBs from HMXBs. Bottom: observed distribution of neutron stars and black hole masses

Feature (2) is a statistically robust property of the mass spectrum (see Farr et al. 2011 and references therein). The lack of compact remnants between 2 and 5 Mˇ contrasts with numerical simulations of supernova explosions by Fryer and Kalogera (2001) that lead to continuous distributions and typical exponential decays. These simulations, however, are based on single star populations with a heuristic treatment of binarity through Wolf-Rayet winds following common envelope evolution. In order to accommodate the evidence of a mass gap, a discontinuous dependence of explosion energy with progenitor mass seems unavoidable. In this context, it has been proposed that convection (Rayleigh-Taylor) instabilities, growing within 200 ms after core bounce, can successfully revive the supernova shock and trigger the explosion, thereby causing the gap (see Fig. 3, but also Ugliano et al. 2012 for a different interpretation based on neutrino-driven explosion models).

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Fig. 3 Observed mass distribution of compact objects in X-ray binaries (top), compared to theoretical distributions computed for different supernova models (bottom). The mass gap can be reproduced only if turbulent instabilities grow rapidly. Slow growing instabilities lead to significant fallback that would fill the mass gap (From Belczynski et al. 2012)

Alternatively, a gap can be produced if red supergiant stars of 17–25 Mˇ suffer a failed supernova explosion, leaving a remnant with the mass of the He core while ejecting the weakly bound H envelope (Kochanek 2014). This interpretation appears attractive because in turn it provides an explanation for the deficit of high-mass progenitors seen in pre-explosion images of Type IIp supernovae (Smartt et al. 2009). On the other hand, it fails to account for the peculiar abundance of ˛elements detected in the companion stars which demands significant contamination from supernova ejecta (see Sect. 4). It is also unclear how very wide binaries with such red supergiants can evolve to form the compact black hole binaries that we see today. Feature (3) most likely reflects different binary evolutionary paths, with black holes in LMXBs being limited to .12 Mˇ by severe mass loss from the WolfRayet progenitor after the common envelope phase (Fryer and Kalogera 2001). Conversely, black holes in HMXBs can grow from more massive stars, especially in low-metallicity environments such as in the case of M33 X-7. Furthermore, it is possible that the progenitor star evolves through the He burning phase still embedded in the H envelope (case C mass transfer), thus suffering less wind mass loss (Brown et al. 2001). However, it should be noted that some aspects of binary and massive stellar evolution (e.g., radial expansion, wind mass loss rates, efficiency of common envelope ejection) are still quite uncertain, which certainly limits our understanding of the formation of X-ray binaries. At this point, the impact of systematic uncertainties in the determination of binary inclination angles should also be stressed, as exemplified by the large dispersion of values reported by independent groups on individual systems (see Casares and Jonker 2014). Ignoring the role of systematics can lead to overestimated black hole

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masses and hence a bias in the observed distribution (Kreidberg et al. 2012). In addition, the sample of X-ray binaries with dynamical mass determinations is almost certainly prone to complex selection effects (both evolutionary and observational) not completely understood. For instance, it may be possible that low-mass black holes become unbound by the supernova explosion or are hidden in very faint (but persistent) X-ray binaries. The system MWC 656 might be itself a member of a hidden population of very faint low-mass black holes. More observational work is required to enlarge the sample of secure black hole masses before the observed distribution can be definitively used to illuminate the properties of the supernova engine.

3

Kick Velocities

For this section we focus on stellar-mass black holes in X-ray binaries rather than neutron star X-ray binary systems as their space velocities are more readily measured using pulsar timing information (González et al. 2011). Both the black hole mass and its spin as well as the black hole’s velocity through space are almost exclusively set at the instant of formation. The black hole spin and mass do not change appreciably during its subsequent evolution. Even the accretion of material that allows us to discover these sources as black hole X-ray binaries when they outburst does not change these parameters. The reason is that in order to affect the black hole spin or mass significantly, one needs to accrete of order the black hole mass. Due to the Eddington limit and the limited amount of mass available from a stellar-mass donor star, this is not possible. Encounters with giant molecular clouds and spiral density waves result in changes in the gravitational potential (Wielen 1977), and these can change the space velocity of stellar-mass black holes in X-ray binaries as they travel through our Galaxy in the Gyrs after their formation. The magnitude of velocity changes depends on the age of the system and can at most amount up to 40 km s1 as determined for late-type (single) stars from Hipparcos data by Dehnen and Binney (1998). Thus, with the caveat on space velocities less than 40 km s1 , these parameters are a prior for the black hole formation mechanism, providing input on the black hole formation and supernova models.

3.1

Black Hole Formation and Its Link to Space Velocity

Models for black hole formation distinguish two formation scenarios (Fryer and Kalogera 2001): either direct or delayed collapse where in the latter a neutron star is formed first which moments later collapses into a black hole. The more massive progenitor stars could collapse directly to a black hole without producing a strong supernova. The latter scenario is in line with the absence of supernovae from red supergiants more massive than 18  20 Mˇ (Smartt 2015). Instead of a supernova, the event marking the birth of a black hole could be a faint, short-duration (3–10 days) blue transient that may form from direct collapse red supergiant progenitors

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as the shock caused by the response of the stellar envelope to neutrino emission in the collapsing core equivalent to a few times 0.1 Mˇ of rest mass energy breaks out of the star (Piro 2013). Others propose that also a red transient with a longer time scale will ensue, which should be of the order of a year (Lovegrove and Woosley 2013; O’Connor and Ott 2011). Candidate failed supernovae of a red supergiant have been reported: one in NGC 6946 (Gerke et al. 2015) and one in NGC 3021 (Reynolds et al. 2015). Given the brightness of red supergiants in the near-infrared, a dedicated near-infrared variability study of nearby galaxies could have a good chance of finding such events, even though some Mira and R Coronae Borealis variables may have similar characteristics (although in the failed supernova and black hole formation case, the transient should fade away indefinitely). The main uncertainties in the theoretical supernova and (binary) massive star evolution calculations stem from uncertainties in the supernova explosion mechanism for stars with progenitor masses in the range between 11 and approximately 30 Mˇ and also from uncertainties in the amount of mass lost during the evolution for stars with progenitor masses above approximately 30 Mˇ . Neutrino-driven supernova models (e.g., Ugliano et al. 2012) seem compatible with the observed black hole mass distribution reported in Özel et al. (2010) and Farr et al. (2011) with an apparent lack of low-mass black holes in the mass range of 2–5 Mˇ (see Sect. 2). The direct collapse and the delayed proto-neutron star collapse models might be responsible for the formation of different mass black holes, and also different space velocities. Direct collapse produces a black hole without much of a kick, whereas the delayed supernova models produce relatively low-mass black holes that receive a larger kick and thus space velocity.

3.2

The Black Hole Space Velocity

The difference between the velocity of a (black hole) system and that expected for its local standard of rest is called the space velocity. Occasionally, this velocity is called “peculiar velocity,” but this term is also often used to indicate the velocity difference between the Hubble flow and the velocity of galaxies. Hence to avoid confusion, we use “space velocity” for the black hole binary systems. It has been inferred from the velocity distribution of neutron stars observable as single radio pulsars that they receive a kick at birth due to asymmetries in the supernova explosion (Lyne and Lorimer 1994). This we call a natal kick. Black holes forming from fallback onto a proto-neutron star should then also get such a natal kick, resulting potentially in a significant space velocity. The magnitude would depend on whether the natal kick momentum for a neutron star and proto-neutron star that collapses to a black hole is the same or not. In addition to such a natal kick, in any supernova explosion in a binary where mass is lost from the binary system, a kick should be imparted on the system irrespective of the type of compact object formed during the supernova (Blaauw 1961). The binary will be disrupted if more than half the total binary mass is ejected in the supernova. Therefore, this sets an upper limit to the amplitude of such a so-called Blaauw kick (Nelemans et al.

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1999). Information that can help differentiating between a Blaauw and a natal kick is that a Blaauw kick is directed in the binary plane (unless the supernova mass loss is not symmetric), whereas a natal kick may not be restricted to that plane. Given that large natal kick velocities yield a higher probability to unbind the binary system, a population synthesis model explaining the observed black hole X-ray binary mass and space velocity distribution has to be used to correct for this bias (e.g., Belczynski et al. 2012). Evidence for velocity kicks in neutron star, as well as black hole low-mass X-ray binaries, comes from the fact that they have, on average, a large distance to the plane of the Galaxy (Jonker and Nelemans 2004; Repetto and Nelemans 2015; van Paradijs and White 1995). Evidence for kicks in the formation of LMXBs also comes from their observed distribution in early-type galaxies. The LMXBs extend further than the stellar light consistent with a population of kicked LMXBs (Zhang et al. 2013). In contrast, given that LMXBs are also found in the Large Magellanic Cloud and perhaps dwarf galaxies (cf. Maccarone et al. 2005), a fraction must receive a small kick velocity upon formation; otherwise, they would not be found in those systems given their low escape velocities. Similarly, the recent evidence for the presence of black holes in globular clusters (e.g., Chomiuk et al. 2013; Strader et al. 2012) implies a population of low natal kick black holes.

3.3

Measuring the Space Velocity

For individual sources the space velocity can be determined as follows: the optical or near-infrared spectroscopic observations providing the mass function via the measurement of the radial velocity amplitude (see Sect. 2) will also provide the systemic radial velocity if, in the cross-correlation of the source and template spectra, the template is a radial velocity standard or a model atmosphere. In order to calculate the space velocity of the X-ray binary, its systemic radial velocity has to be combined with a proper motion and distance measurement. Ideally, as it depends on geometry alone, the distance is measured through a (radio) parallax measurement. However, in practice, parallax measurements have so far only been possible for three black hole X-ray binaries: V404 Cyg (MillerJones et al. 2009b), Cyg X-1 (Reid et al. 2011), and GRS 1915C105 (Reid et al. 2014). The main reasons why a parallax measurement has been possible for these three systems is that V404 Cyg is bright in quiescence when compared to the other systems (cf. Miller-Jones et al. 2011), and the latter two black holes are virtually always actively accreting matter, which makes that the time baseline necessary for a parallax measurement is long enough. However, while always accreting, the last two sources are not always in the accretion state that allows a compact radio jet to be formed, which still made the detection of the parallax signal difficult (see the discussion in Reid et al. 2014). For the vast majority of black hole X-ray transients, a parallax measurement has not been possible. A major obstacle in the measurements has been the short duration of outbursts. The month-long outburst coupled with the aforementioned state changes does not allow for the measurements

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necessary to detect the often small parallax signals. The best future hope for parallax signal detection comes from a few sources that show recurrent outbursts such as GX 339–4. The second-best distance determination comes from what is often called a photometric parallax. Here, one compares the apparent magnitude of the companion (D mass donor) star with its absolute magnitude to determine the distance. However, the effect of interstellar extinction influences the apparent magnitude, it causes the star to appear fainter and redder, and hence one would put it further away than it really is if these effects are not corrected for. Furthermore, more often than not, residual light is produced by the accretion disk, making the system appear brighter. The disk contribution can be determined from optical spectroscopic observations, but it is not constant in time (Cantrell et al. 2008), complicating the determination of the correction factor. The fact that the star is losing mass influences the radius of the star, and as such it is not the same as that of a single star of the same spectral type and luminosity class. Hence, its radius has to be determined from the data. Finally, in accreting black hole X-ray binary systems such as under consideration here, the star is very likely to be in forced corotation with the orbit making it rotate around its axis fast which may influence the absolute magnitude of the star. Studies of rapidly rotating early-type stars found that fast rotation causes an increase in absolute magnitude of stars with spectral type later than B5 (the stars are intrinsically less luminous than the nonrotating stars of the same spectral type by typically several tenths of a magnitude (Collins and Sonneborn 1977)). Additionally, it is known that limb and gravity darkening effects change the equivalent widths of photospheric stellar absorption lines (e.g., Shajn and Struve 1929 and Collins and Sonneborn 1977), which could lead to a slightly erroneous spectral type being obtained from the data. Generally, the lines in the spectrum resemble the lines of a later spectral type. Furthermore, the limb and gravity darkening is different in the distorted Roche-lobe filling mass donor stars compared to single stars. Overall, distances determined via a photometric parallax can easily be off by several tens of percent. See Jonker and Nelemans (2004) for further discussion on these issues. In contrast with the parallax signal, the accuracy with which proper motions can be detected is higher as the proper motion signal adds over time. The proper motion has been measured using radio very long baseline interferometry (VLBI) of eight black hole X-ray binaries (see Table 3). Recent measurements show the proper motion of the recurrent transient black hole GX 339–4 (Miller-Jones et al. in prep., see Fig. 4). For this source we still need to determine the spectral type of the mass donor star and the accretion disk contribution to the total light in quiescence in order to estimate the distance to the system more accurately using a photometric parallax than what is currently possible (Hynes et al. 2004). In some cases the location on the sky together with a proper motion measurement can already put strong constraints on the presence of natal kicks. For instance, for the black hole candidate (candidate as no mass measurement for the source exists currently), MAXI J1836-194, evidence from the radio proper motion alone suggests that the source received a kick at birth (see Fig. 5).

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Table 3 Proper motions of black hole X-ray binaries Source name XTE J1118C480 GRO J1655–40 GX 339–4 Swift J1753.5–0127 MAXI J1836-194 GRS 1915C105 Cyg X-1 V404 Cyg a

˛ cos ı (mas yr1 ) 16.8˙1.6 3.3˙0.5 3.95˙0.07 1.5˙0.4 2.3˙0.6 2.86˙0.07 3.78˙0.06 5.04˙0.22

ı mas yr1 7.4˙1:6 4.0˙0.4 4.71˙0.06 3.0˙0.4 6.1˙1.0 6.20˙0.09 6.40˙0.12 7.64˙0.03

References Mirabel et al. (2001) Mirabel et al. (2002) a a

Russell et al. (2015) Dhawan et al. (2007) Reid et al. (2014) Miller-Jones et al. (2009b)

Miller–Jones et al. in prep

Fig. 4 The proper motion fit to long baseline array radio observations of GX 339-4. Whereas the data is sparse, mostly due to the outburst duty cycle of this source, the proper motion signal is significantly detected (Figure courtesy James Miller–Jones; Miller–Jones et al. in prep.)

Whereas so far all these proper motion measurements have come from radio VLBI measurements, in the near future, the Gaia satellite may also provide proper motion measurements of X-ray binaries. Gaia has been launched in December 19, 2013, and scans the whole sky (including the Galactic plane) at high spatial resolution with accurate photometry down to G D 20.3 and tens of micro-arcsecond astrometry. Gaia consists of two telescopes aligned in a plane with an angle of 106.5ı in between. As Gaia scans the sky, it will make many visits of the same region. For most of the sky, the number of visits is 70 over a 5-year mission lifetime (and an extension of the mission is possible improving primarily the proper motion measurements). The multiple visits of the same parts of the sky will allow

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Fig. 5 The asymmetric natal kick exerted on the black hole upon formation on top of the maximum Blaauw kick possible without disrupting the binary (dashed line; Nelemans et al. 1999) required to explain the observed proper motion for the black hole candidate source MAXI J1836– 194 (Russell et al. 2015). The dotted lines indicate the measurement uncertainties, and the white area is the range in distances that is allowed for this particular source. The observables that still need to be measured to determine the space velocity are the systemic radial velocity and the source distance. A model for the Galactic rotation is used (Honma et al. 2012)

the detection of proper motion and parallax signals if the sources are bright enough. Gaia’s G-band is effectively a white light band where the bandpass is set by the efficiency of the telescope C CCD. Proper motion and parallax measurements of several of the black hole X-ray binaries mentioned in Table 3 will be improved. In addition these parameters will be measured for a few sources for which these measurements do not exist currently. An example of the latter is 1A 0620-00. However, the intrinsic and apparent faintness of the often low-mass donor stars is a limiting factor for Gaia’s contribution to this field. Many of the black hole X-ray binaries reside in the plane of the Galaxy and are further away than a few kpc, making reddening significant. The fact that they reside in the plane probably hints at a low space velocity as sources spend most of the time at the extremes of their Galactic orbit. In general (non-Gaia) astrometric measurements in the optical or near-infrared are difficult. An obstacle to the required astrometric accuracy is the need to find astrometric “anchors” that tie the frame to the International Celestial Reference System. Background quasars and active galactic nuclei are good candidate anchors, but in the plane their apparent magnitude is reduced also due to the reddening. Once the position on the sky, the systemic radial velocity, the proper motion, and the distance to the source are known, one can derive the space velocity using the transformations of Johnson and Soderblom (1987) to calculate Galactic velocities in the heliocentric frame, which can then be corrected for the space velocity of the Sun with respect to the local standard of rest (U D 10.0˙0.36 km s1 , V D 5.25˙0.62 km s1 , W D 7.17˙0.38 km s1 ; Dehnen and Binney 1998). Here, U is defined as positive toward the Galactic Center, V positive toward l D 90ı , and W positive toward the north Galactic pole.

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Black Hole X-Ray Binaries with and Without Natal Kicks

Having described in some detail how to measure the parameters that are necessary to determine the space velocity of stellar-mass black holes in X-ray binaries, we now turn to the measured space velocities. The space velocities have been determined for five black hole X-ray binaries only so far. A recent overview of black hole space velocities is presented in Miller-Jones (2014) (his table 2). Repetto and Nelemans (2015) investigated whether there is evidence for the presence of a natal besides a Blaauw kick taking the binary evolution of seven short orbital period systems into account. The main conclusion is that for at least two systems, a natal kick is necessary. In addition, five systems could be well explained with a natal kick but virtually no ejection of mass in a supernova, such as in direct collapse scenarios. Natal kicks are probably necessary for the black hole X-ray binaries XTE J1118C480 (Gualandris et al. 2005) and GRO J1655–40 (Willems et al. 2005) and are likely for V404 Cygni (Miller-Jones et al. 2009a). Cygnus X-1 and GRS 1915C105, on the other hand, were found to have been formed with little or no kick (Mirabel and Rodrigues 2003; Reid et al. 2011, 2014). It is interesting to note that the black holes in Cygnus X-1 and GRS 1915C105 are among the most massive stellar-mass black holes known so far in our Galaxy, which could be interpreted as suggestive evidence for a formation difference between the more massive and lighter stellar-mass black holes. For instance, the more massive black holes could form through direct collapse giving rise to no or only very small space velocities as only a limited amount of mass is lost from the system (minimizing the Blaauw kick) and the maximum natal kick impulse imparted on any protoneutron star due to asymmetric neutrino emission has an upper limit which equals the binding energy of the maximum mass proto-neutron star that can be formed (Janka 2013). The latter thus would imply that the more massive the black hole formed, the smaller the space velocity acquired. However, in a scenario where the more massive black holes form through a supernova (and not a direct collapse) and when the fallback of the slowest parts of the supernova ejecta is asymmetric, one would produce larger natal kicks for more massive black holes (Janka 2013). Space velocity and black hole mass measurements for more black hole X-ray binaries as well as searches of failed supernovae are necessary to distinguish between these scenarios.

4

Chemical Abundance of Companion Stars

It is conceivable that the supernova explosion that created a black hole or a neutron star remnant in X-ray binaries has modified the physical and chemical characteristics of the secondary star. However, uncertainties in the supernova explosion models affect the predictions of the chemical composition of ejecta captured by the companion. Nevertheless, chemical abundance studies of the companion stars in LMXBs may open a new route to constrain supernova models.

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Unfortunately, high-quality spectroscopic observations of LMXBs and their analysis is a serious challenge. The rotation, possible spots, and magnetic activity of the companion star, as well as continuum veiling produced by the residual accretion disk, introduce additional uncertainties. In any case, attempts have been made to minimize the most important sources of uncertainties in the calculation of the stellar parameters and chemical abundances. Nova Scorpii 1994 was the first black hole X-ray binary system for which a detailed abundance study has been carried out (Israelian et al. 1999). Striking overabundance of several ˛-elements (such as O, S, Si) was discovered and interpreted as a result of a pollution by matter ejected by the supernova.

4.1

Observations, Models, and Spectral Synthesis Tools

The chemical analysis of secondary stars in LMXB systems is influenced by three important factors: veiling from the accretion disk, rotational broadening, and signal-to-noise ratio of the spectra. Moderately strong and relatively unblended lines of chemical elements of interest have to be identified in the high-resolution solar flux atlas. Spectral line data from the Vienna Atomic Line Database can be used to compute synthetic spectra for these features employing a grid of local thermodynamic equilibrium (LTE) models of atmospheres provided by Kurucz (1993, private communication). These models are interpolated for given values of effective temperature [Teff ], surface gravity [log g], and metallicity [Fe/H]. A grid of synthetic spectra is generated for these features in terms of five free parameters, three to characterize the star atmospheric model ([Teff ], [log g], and [Fe/H]) and two further parameters to take into account the effect of the accretion disk emission in the stellar spectrum. This veiling is defined as the ratio of the accretion disk flux to the stellar continuum flux, Fd isc =Fcont;star . It has been considered as a linear function of wavelength and is thus characterized by two 4500 parameters: veiling at 4500Å, f4500 D Fd4500 isc =Fsec , and the slope, m0 . Next, the observed spectra are compared with each synthetic spectrum in the grid (between 800.000 and 1.5 million spectra) via a 2 minimization procedure that provides the best model fit. A bootstrap Monte Carlo method using 1000 realizations is typically used to define the 1 confidence regions for the five free parameters. Figure 6 shows the distributions obtained for the source A0620-00.

4.2

Stellar Abundances

Several spectral regions containing the lines of Si, Ca, Al, Ti, and Ni have been analyzed. Although the lines of these elements were usually the main contributor to the features, in some cases, they were blended with Fe. The inaccuracy in the location of the continuum caused by the blends of many weak rotationally broadened stellar lines was one of the main sources of error in the abundance

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Fig. 6 Distributions obtained for each parameter using Monte Carlo simulations. The labels at the top of each bin indicate the number of simulations consistent with the bin value. The total number of simulations was 1000 (Figure from González Hernández et al. 2004)

determinations. Several examples of the fits to specific absorption lines are shown in Figs. 7 and 8. Most of the results for the LMXB systems studied to date are compiled in Table 4 and reviewed in the next section.

4.3

Individual Systems

4.3.1 Nova Scorpii 1994 (GRO J1655-40) Keck/HIRES spectrum of this system has been first studied by Israelian et al. (2009, 1999) who discovered that oxygen, sulfur, and silicon are overabundant from eight

NORMALIZED FLUX

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1.0 0.8 0.6 Template star: HIP17420 (K2V)

0.4 5450

NORMALIZED FLUX

5445

5455 (ANGSTROMS)

5460

5465

XTE J1118+480

1.0 0.8 0.6 FeI,TiI

TiI

FeI

TiI FeI

0.4 5445

FeI

MnI

TiI

FeI

FeI

FeI

5450

5455 (ANGSTROMS)

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Fig. 7 Best synthetic spectral fits to the Keck/ESI spectrum of the secondary star in the XTE J1118 C 480 system (bottom panel) and the same for a template star (properly broadened) shown for comparison (top panel). Synthetic spectra are computed for solar abundances (dashed line) and best-fit abundances (solid line) (This figure is taken from González Hernández et al. 2008b)

to ten times compared to the Sun. The analysis of González Hernández et al. (2008a) based on the VLT/UVES high-resolution spectra confirmed that the abundances of Al, Ca, Ti, Fe, and Ni are consistent with solar values, whereas Na and especially O, Mg, Si, and S are significantly enhanced in comparison with the Sun and Galactic trends of these elements. A comparison with spherically and nonspherically symmetric supernova explosion models may provide stringent constraints to the model parameters as mass cut and the explosion energy, in particular from the relative abundances of Si, S, Ca, Ti, Fe, and Ni.

4.3.2 A 0620-00 It has been shown (González Hernández et al. 2004) that the secondary star in this system is metal rich with [Fe/H] = 0.14 ˙ 0.20. Nevertheless, the abundances of Fe, Ca, Ti, Al, and Ni are slightly higher than solar. The abundance ratios of each element with respect to Fe were compared with these ratios in late-type main sequence metal-rich stars. Moderate anomalies for Ti, Ni, and especially Al have been found. A comparison with element yields from spherically symmetric supernova explosion models suggests that the secondary star captured part of the ejecta from a supernova that also originated the compact object in A0620-00. The observed abundances can be explained if a progenitor with a 14 Mˇ He core

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Table 4 Masses, velocity, stellar, veiling parameters, and chemical abundancesa in LMXBs. See González Hernández et al. (2011) for a definition of the parameters listed in column 1 Star

A0620-00

Centaurus X-4 V616 Mon V822 Cen

XTE Nova Sco 94 J1118 C 480 Alternative KV UMa GRO J1655– name 40 MCO;f (Mˇ ) 6:61 ˙ 0:25 1:50 ˙ 0:40 8:30 ˙ 0:28 6:59 ˙ 0:45 M2;f (Mˇ ) 0:40 ˙ 0:05 0:30 ˙ 0:09 0:22 ˙ 0:07 2:76 ˙ 0:33 vsini (km 82 ˙ 2 44 ˙ 3 100C3 86 ˙ 4 11 s 1 ) Teff (K) 4900 ˙ 100 4500 ˙ 100 4700 ˙ 100 6100 ˙ 200 log.g=cm s2 / 4:2 ˙ 0:3 3:9 ˙ 0:3 4:6 ˙ 0:3 3:7 ˙ 0:2 f4500 0:25 ˙ 0:05 1:85 ˙ 0:10 0:85 ˙ 0:20 0:15 ˙ 0:05 m0 =104 1:4 ˙ 0:2 7:1 ˙ 0:3 2 ˙ 1 1:2 ˙ 0:3 [O/H]b – – – 0:91 ˙ 0:09 [Na/H] – – – 0:31 ˙ 0:26 [Mg/H] 0:40 ˙ 0:16 0:35 ˙ 0:17 0:35 ˙ 0:25 0:48 ˙ 0:15 [Al/H] 0:40 ˙ 0:12 0:30 ˙ 0:17 0:60 ˙ 0:20 0:05 ˙ 0:18 [Si/H] – – 0:37 ˙ 0:21 0:58 ˙ 0:08 [S/H] – – – 0:66 ˙ 0:12 [Ca/H] 0:10 ˙ 0:20 0:21 ˙ 0:17 0:15 ˙ 0:23 0:02˙0:14 [Ti/H] 0:37 ˙ 0:23 0:40 ˙ 0:17 0:32 ˙ 0:26 0:27 ˙ 0:22 [Cr/H] – – – – [Fe/H] 0:14 ˙ 0:20 0:23 ˙ 0:10 0:18 ˙ 0:17 0:11˙0:10 [Ni/H] 0:27 ˙ 0:10 0:35 ˙ 0:10 0:30 ˙ 0:21 0:00 ˙ 0:21

V404 Cygni Cygnus X-2 GS 2023 C 338 9:00 ˙ 0:60 0:54 ˙ 0:08 40:8 ˙ 0:9

V1341 Cyg 1:71 ˙ 0:21 0:58 ˙ 0:23 34:6 ˙ 0:1

4800 ˙ 100 3:50 ˙ 0:15 0:15 ˙ 0:05 1:3 ˙ 0:2 0:60 ˙ 0:19 0:30 ˙ 0:19 0:00 ˙ 0:11 0:38 ˙ 0:09 0:36 ˙ 0:11 – 0:20 ˙ 0:16 0:42 ˙ 0:20 0:31 ˙ 0:19 0:23 ˙ 0:09 0:21 ˙ 0:19

6900 ˙ 200 2:80 ˙ 0:20 1:55 ˙ 0:15 2:7 ˙ 0:4 0:07 ˙ 0:35 – 0:87 ˙ 0:24 – 0:52 ˙ 0:22 0:52 ˙ 0:24 0:27 ˙ 0:33 0:59 ˙ 0:31 – 0:27 ˙ 0:19 0:52 ˙ 0:27

References: V404 Cygni: González Hernández et al. (2011); Centaurus X-4: González Hernández et al. (2005)A0620-00: González Hernández et al. (2004) Nova Scorpii 1994: González Hernández et al. (2008a); XTE J1118 C 480: González Hernández et al. (2008b); Cyg X-2: Casares et al. (2010) and Suárez-Andrés et al. (2015) a The uncertainties on the stellar abundances given in this table have been derived without taking into account the error on the microturbulence b Oxygen abundances are given in NLTE

exploded with a mass cut in the range 11–12.5 Mˇ , such that no significant amount of iron could escape from the collapse of the inner layers. It is very important to study abundances of O, Si, Mg, S, and C to confirm this scenario.

4.3.3 Cen X-4 Abundances of Fe, Ca, Ti, Ni, and Al have been obtained using VLT/UVES spectra (González Hernández et al. 2005). These elements are found to have super solar abundances. Iron is enhanced too with [Fe/ H] = 0. 23 ˙ 0. 10). Interestingly, Ti and Ni are moderately enhanced as compared with the average values of stars of similar iron content. These element abundances can be explained if the secondary star captured a significant amount of matter ejected from a spherically symmetric supernova explosion of a 4 Mˇ He core progenitor and assuming solar abundances

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as primordial abundances in the secondary star. The kinematic properties of the system indicate that the neutron star received a natal kick velocity through an aspherical supernova and/or an asymmetric neutrino emission. The former scenario might be ruled out since the model computations cannot produce acceptable fits to the observed abundances.

4.3.4 V4641 Sgr Spectroscopic analysis of this system has been carried out by Orosz et al. (2001). Peculiar abundance patterns have been claimed from the analysis of low- and highresolution spectra obtained with different instruments. These authors found that N and Ti are enhanced about ten times compared to the Sun, Mg overabundance is about five to seven times, and O is three times the solar value, while Si is about solar. Given the physical characteristics of the companion star (mass, rotation, evolutionary stage), it is impossible to understand how and why Ti is extremely enhanced, while Si is solar. More spectral lines, better analysis, and better quality spectra are needed to confirm and expand this study. Given the effective temperature of the star, NLTE studies are mandatory. 4.3.5 XTE J1118 C 480 Abundances of Mg, Al, Ca, Fe, Ni, Si, and Ti have been derived using mediumresolution optical spectra of the secondary star in the high Galactic latitude black hole X-ray binary XTE J1118 C 480 (González Hernández et al. 2006). The super solar abundances indicate that the black hole in this system formed in a supernova event, whose nucleosynthetic products could pollute the atmosphere of the secondary star, providing clues on the possible formation region of the system, either Galactic halo, thick disk, or thin disk. A grid of explosion models with different He core masses, metallicities, and geometries has been explored. Metalpoor models associated with a formation scenario in the Galactic halo provide unacceptable fits to the observed abundances, therefore rejecting a halo origin for this X-ray binary. The thick-disk scenario produces better fits, although they require substantial fallback and very efficient mixing processes between the inner layers of the explosion and the ejecta. This makes very unlikely that the system was born in the thick disk. The best agreement between the model predictions and the observed abundances is obtained for metal-rich progenitor models. In particular, nonspherically symmetric models are able to explain, without strong assumptions of extensive fallback and mixing, the observed abundances. Moreover, asymmetric mass ejection in a supernova explosion could account for the required impulse necessary to eject the system from its formation region in the Galactic thin disk to its current halo orbit. 4.3.6 V404 Cyg The atmospheric abundances of O, Na, Si, Ti, Mg, Al, Ca, Fe, and Ni have been derived using KeckI/HIRES spectra (González Hernández et al. 2011). The abundances of Si, Al, and Ti are slightly enhanced when comparing with average values in thin-disk solar-type stars. The O abundance, derived from optical lines,

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is clearly enhanced in the atmosphere of the secondary star in V404 Cygni. This, together with the peculiar velocity of this system as compaed with the Galactic velocity dispersion of thin-disk stars, suggests that the black hole formed in a supernova or hypernova explosion. Different supernova/hypernova models having various geometries to study possible contamination of nucleosynthetic products in the chemical abundance pattern of the secondary star have been explored (e.g. Nakamura et al. 2001). A reasonable agreement between the observed abundances and the model predictions has been found (González Hernández et al. 2011). However, the O abundance seems to be too high regardless of the choice of explosion energy or mass cut, when trying to fit other element abundances. Moreover, Mg appears to be underabundant for all explosion models, which produces Mg abundances roughly two times higher than the observed value. The case of V404 Cyg is very peculiar and more studies are required to understand these observations.

4.3.7 Cyg X-2 Suárez-Andrés et al. (2015) have investigated abundances of O, Mg, Si, Ca, S, Ti, Fe, and Ni. The system is metal rich ([Fe/H] D 0, 27˙0,19), and abundances of some alpha-elements (Mg, Si, S, Ti) are enhanced (see Fig. 8). This is consistent with a scenario of contamination of the secondary star during the supernova event. Strange enough, oxygen appears to be underabundant, whereas Fe and Ni are enhanced. WASP−17 Teff=6650K logg=4.45 dex [Fe/H] =−0.19

1.0

1.0 FeII

0.8 FeII FeI 0.6 FeI

FeII

0.8

CaI

Normalised Flux

Normalised Flux

0.8

1.0

FeII FeII FeII

FeII FeI FeI

SI FeI

FeI

SI

0.4

WASP−17 broadened with vsini = 34.6 km/s

0.9

SI

0.6

FeII

0.4 1.0

WASP−17 Teff=6650K logg=4.45 dex [Fe/H] =−0.19

CaI

0.7

WASP−17 broadened with vsini = 34.6 km/s

0.9 SI FeI

SI

0.8

FeI

SI

0.7 0.6

0.6 Cygnus X−2 Teff=6900K logg=2.80 dex [Fe/H]=0.27

Cygnus X-2

Teff=6900K logg=2.80 dex [Fe/H]=0.27

1.0

1.0

0.9

0.9 FeII FeI

FeI

FeII FeII FeII

0.8 0.7 6415

6420

6425

6430 6435 λ (Angstroms)

SI FeI

SI

CaI

SI

0.8

6440

6445

0.7 6740

6745

6750 6755 λ (Angstroms)

6760

Fig. 8 Best synthetic fit to the UES spectrum of the secondary star in the neutron star X-ray binary Cygnus X-2 (bottom panel) and best fit to our template, with and without rotational broadening (middle and top panels). Synthetic spectra are computed for best-fit abundances (solid line) and for solar abundances (dashed line) (Figures taken from Suárez-Andrés et al. 2015)

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Fig. 9 Abundance ratios of the secondary star in Cyg X-2 (wide cross with errors) in comparison with the abundances of solar-type metal-rich dwarf stars (Taken from Suárez-Andrés et al. 2015)

Assuming that these abundances come from the matter that has been processed in the supernova and then captured by the secondary star, Suárez-Andrés et al. (2015) explored different supernova explosion scenarios with diverse geometries. A nonspherically symmetric supernova explosion, with a low mass cut, seems to reproduce better the observed abundance pattern of the secondary star compared to the spherical case. These authors have searched for anomalies in the abundance pattern of the secondary star by comparing their results with Galactic trends (see Fig. 9 taken from Suárez-Andrés et al. (2015) and reference from that article). As it is shown in Fig. 9, most of the elements in Cygnus X-2 show overabundances when compared with Galactic trends, with the exception aluminum, calcium, and cadmium, which are consistent with those trends.

5

Cross-References

 Supernovae and the Evolution of Close Binary Systems  The Masses of Neutron Stars Acknowledgements JC would like to thank the hospitality of the Department of Physics of the University of Oxford, where this work was performed during a sabbatical visit. He also thanks Phil Charles for useful comments and discussions. Finally, JC acknowledges support by DGI of the

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Spanish Ministerio de Educación, Cultura y Deporte under grants AYA2013-42627 and PR201500397, and from the Leverhulme Trust Visiting Professorship Grant VP2-2015-046. GI thanks Lucía Suárez and Jonay González Hernández for useful discussions. PGJ would like to thank James Miller–Jones for many useful discussions and his approval to use data on GX 3394 and Swift J1753.00127 before their final publication. PGJ acknowledges funding from the European Research Council under ERC Consolidator Grant Agreement No. 647208.

References Alpar MA, Cheng AF, Ruderman MA, Shaham J (1982) A new class of radio pulsars. Nature 300:728–730 Belczynski K, Wiktorowicz G, Fryer CL, Holtz DE, Kalogera V (2012) Missing black holes unveil the supernova explosion mechanism. ApJ 757:91–96 Blaauw A (1961) On the origin of the O- and B-type stars with high velocities (the “run-away” stars), and some related problems. Bull Astron Inst Neth 15:265–290 Brown GE, Heger A, Langer N, Lee C-H, Wellstein S, Bethe HA (2001) Formation of high mass X-ray black hole binaries. New Astron 6:457–470 Cantrell AG, Bailyn CD, McClintock JE, Orosz JA (2008) Optical state changes in the X-rayquiescent black hole A0620-00. ApJL 673:L159–L162 Casares J, González Hernández JI, Israelian G, Rebolo R (2010) On the mass of the neutron star in Cyg X-2. MNRAS 401:2517–2520 Casares J, Negueruela I, Ribó M, Ribas I, Paredes JM, Herrero A, Simón-Díaz S (2014) A Be-type star with a black-hole companion. Nature 505:378–381 Casares J, Jonker PG (2014) Mass Measurements of Stellar and Intermediate-Mass Black Holes. Space Sci Rev 183:223–252 Charles PA, Coe MJ (2006) Optical, ultraviolet and infrared observations of X-ray binaries. In: Lewin W, van der Klis M (eds) Compact stellar X-ray sources. Cambridge astrophysics series, vol 39. Cambridge University Press, Cambridge, pp 215–265 Chomiuk L, Strader J, Maccarone TJ, Miller-Jones JCA, Heinke C, Noyola E et al (2013) A radioselected black hole X-ray binary candidate in the milky way globular cluster M62. ApJ 777: 69–77 Clark JS, Goodwin SP, Crowther PA, Kaper L, Fairbairn M, Langer N et al (2002) Physical parameters of the high-mass X-ray binary 4U1700-37. A&A 392:909–920 Collins GW II, Sonneborn GH (1977) Some effects of rotation on the spectra of upper-mainsequence stars. ApJ Suppl 34:41–94 Dehnen W, Binney JJ (1998) Local stellar kinematics from HIPPARCOS data. MNRAS 298: 387–394 Dhawan V, Mirabel IF, Ribó M, Rodrigues I (2007) Kinematics of Black Hole X-Ray Binary GRS 1915+105. ApJ 668:430–434 Farr WM, Sravan N, Cantrell A, Kreidberg L, Bailyn CD, Mandel I, Kalogera V (2011) The mass distribution of stellar-mass black holes. ApJ 741:103–121 Fryer CL, Kalogera V (2001) Theoretical black hole mass distributions. ApJ 554:548–560 Gerke JR, Kochanek CS, Stanek KZ (2015) The search for failed supernovae with the large binocular telescope: first candidates. MNRAS 450:3289–3305 González ME, Stairs IH, Ferdman RD, Freire PCC, Nice DJ, Demorest PB et al (2011) Highprecision timing of five millisecond pulsars: space velocities, binary evolution, and equivalence principles. ApJ 743:102–113 González Hernández JI, Rebolo R, Israelian G, Casares J, Maeder A, Meynet G (2004) Chemical abundances in the secondary star in the black Hole binary A0620-00. ApJ 609:988–998 González Hernández JI, Rebolo R, Israelian G, Casares J, Maeda K, Bonifacio P et al (2005) Chemical abundances in the secondary star of the neutron star binary centaurus X-4. ApJ 630:495–505

1524

J. Casares et al.

González Hernández JI, Rebolo R, Israelian G, Harlaftis ET, Filippenko AV, Chornock R (2006) XTE J1118+480: A Metal-rich Black Hole Binary in the Galactic Halo. ApJL 644: L49–L52 González Hernández JI, Rebolo R, Israelian G (2008a) The black hole binary nova Scorpii 1994 (GRO J1655–40): an improved chemical analysis. A&A 478:203–217 González Hernández JI, Rebolo R, Israelian G, Filippenko AV, Chornock R, Tominaga N et al (2008b) Chemical Abundances of the Secondary Star in the Black Hole X-Ray Binary XTE J1118+480. ApJ 679:732–745 González Hernández JI, Casares J, Rebolo R, Israelian G, Filippenko AV, Chornock R (2011) Chemical abundances of the secondary star in the black hole X-ray binary V404 Cygni. ApJ 738:95–107 Gualandris A, Colpi M, Portegies Zwart S, Possenti A (2005) Has the black hole in XTE J1118+480 experienced an asymmetric natal kick? ApJ 618:845–851 Honma M, Nagayama T, Ando K, Bushimata T, Choi YK, Handa T et al (2012) Fundamental Parameters of the Milky Way Galaxy Based on VLBI astrometry. PASJ 64:136 Hynes RI, Steeghs D, Casares J, Charles PA, O’Brien K (2004) The Distance and Interstellar Sight Line to GX 339-4. ApJ 609:317–324 Israelian G, Rebolo R, Basri G, Casares J, Martín EL (1999) Evidence of a supernova origin for the black hole in the system GRO J1655 – 40. Nature 401:142–144 Janka H-T (2013) Natal kicks of stellar mass black holes by asymmetric mass ejection in fallback supernovae. MNRAS 434:1355–1361 Johnson DRH, Soderblom DR (1987) Calculating galactic space velocities and their uncertainties, with an application to the ursa major group. AJ 93:864–867 Jonker PG, Nelemans G (2004) The distances to Galactic low-mass X-ray binaries: consequences for black hole luminosities and kicks. MNRAS 354:355–366 Joss PC, Rappaport SA (1984) Neutron stars in binary systems. Ann Rev Astron Astrophys 22:537–592 Knigge C, Coe MJ, Podsiadlowski P (2011) Two populations of X-ray pulsars produced by two types of supernova. Nature 479:372–375 Kochanek CS (2014) Failed supernovae explain the compact remnant mass function. ApJ 785:28–33 Kreidberg L, Bailyn CD, Farr WM, Kalogera V (2012) Mass measurements of black holes in X-ray transients: is there a mass gap? ApJ 757:36–52 Kurucz R (1993) ATLAS9 stellar atmosphere programs and 2 km/s grid. Kurucz CD-ROM, vol 13. Smithsonian Astrophysical Observatory, Cambridge, p 13 Lovegrove E, Woosley SE (2013) Very low energy supernovae from neutrino mass loss. ApJ 769:109–116 Lyne AG, Lorimer DR (1994) High birth velocities of radio pulsars. Nature 369:127–129 Maccarone TJ, Kundu A, Zepf SE, Piro AL, Bildsten L (2005) The discovery of X-ray binaries in the Sculptor dwarf spheroidal galaxy. MNRAS 364:L61–L65 Macdonald TD, Bailyn CD, Buxton M, Cantrell AG, Chatterjee R, Kennedy-Shaffer R et al (2014) The black hole binary V4641 sagitarii: activity in quiescence and improved mass determinations. ApJ 784:2–20 Mason AB, Norton AJ, Clark JS, Negueruela I, Roche P (2011) Preliminary determinations of the masses of the neutron star and mass donor in the high mass X-ray binary system EXO 1722-363. A&A 509:79–82 Mason AB, Norton AJ, Clark JS, Negueruela I, Roche P (2011) The masses of the neutron and donor star in the high-mass X-ray binary IGR J18027-2016. A&A 532:124–128 Mason AB, Clark JS, Norton AJ, Crowther PA, Tauris TM, Langer N et al (2012) The evolution and masses of the neutron star and donor star in the high mass X-ray binary OAO 1657-415. MNRAS 422:199–206 Mata Sánchez D, Muñoz-Darias T, Casares J, Steeghs D, Ramos Almeida C, Acosta Pulido JA (2015) Mass constraints to Sco X-1 from Bowen fluorescence and deep near-infrared spectroscopy. MNRAS 449:L1–L5

56 X-Ray Binaries

1525

Miller-Jones JCA, Jonker PG, Nelemans G, Portegies Zwart S, Dhawan V, Brisken W et al (2009) The formation of the black hole in the X-ray binary system V404 Cyg. MNRAS 394: 1440–1448 Miller-Jones JCA, Jonker PG, Dhawan V, Brisken W, Rupen MP, Nelemans G et al (2009) The first accurate parallax distance to a black hole. ApJL 706:L230–L234 Miller-Jones JCA, Jonker PG, Maccarone TJ, Nelemans G, Calvelo DE (2011) A deep radio survey of hard state and quiescent black hole X-ray binaries. ApJL 739:L18–L23 Miller-Jones JCA (2014) Astrometric observations of X-ray binaries using very long baseline interferometry. PASA – Publ Astron Soc Aust 31:16–29 Mirabel IF, Dhawan V, Mignani RP, Rodrigues I, Guglielmetti F (2001) A high-velocity black hole on a Galactic-halo orbit in the solar neighbourhood. Nature 413:139–141 Mirabel IF, Mignani R, Rodrigues I, Combi JA, Rodriguez LF, Guglielmetti F (2002) The runaway black hole GRO J1655-40. A&A 395:595–599 Mirabel IF, Rodrigues I (2003) Formation of a black hole in the dark. Science 300:1119–1121 Muñoz-Darias T, Casares J, Martínez-Pais IG (2005) The “K-Correction” for Irradiated Emission Lines in LMXBs: Evidence for a Massive Neutron Star in X1822-371 (V691 CrA). ApJ 635:502–507 Muñoz-Darias T, Casares J, Martíinez-Pais IG (2008) The mass of the X-ray pulsar in X1822-371. In: 40 years of pulsaRS: millisecond pulsars, magnetars and more. AIP Conference Proceedings 983:542–544 Nakamura T, Umeda H, Iwamoto K, Nomoto K, Hashimoto M, Hix WR et al (2001) Explosive Nucleosynthesis in Hypernovae. ApJ 555:880–899 Nelemans G, Tauris TM, van den Heuvel EPJ (1999) Constraints on mass ejection in black hole formation derived from black hole X-ray binaries. A&A 352:L87–L90 O’Connor E, Ott CD (2011) Black Hole Formation in Failing Core-Collapse Supernovae. ApJ 730:70–89 Orosz J, Kuulkers E, van der Klis M, McClintock JE, Garcia MR, Callanan PJ et al (2001) A Black Hole in the Superluminal Source SAX J1819.3-2525 (V4641 Sgr). ApJ 555:489–503 Orosz JA, Steiner JF, McClintock JE, Buxton MM, Bailyn CD, Steeghs D et al (2014) The Mass of the Black Hole in LMC X-3. ApJ 794:154–171 Özel F, Psaltis D, Narayan R, McClintock JE (2010) The Black Hole Mass Distribution in the Galaxy. ApJ 725:1918–1927 Özel F, Psaltis D, Narayan R, Santos Villarreal A (2012) On the Mass Distribution and Birth Masses of Neutron Stars. ApJ 757:55–67 Piro AL (2013) Taking the “Un” out of “Unnovae”. ApJL 768:L14–L18 Quaintrell H, Norton AJ, Ash TDC, Roche P, Willems B, Bedding TR et al (2003) The mass of the neutron star in Vela X-1 and tidally induced non-radial oscillations. A&A 401:313–323 Rawls ML, Orosz JA, McClintock JE, Torres MAP, Bailyn CD, Buxton MM (2011) Refined neutron star mass determinations for six eclipsing X-ray pulsar binaries. ApJ 730:25–35 Reid MJ, McClintock JE, Narayan R, Gou L, Remillard RA, Orosz JA (2011) The Trigonometric Parallax of Cygnus X-1. ApJ 742:83–87 Reid MJ, McClintock JE, Steiner JF, Steeghs D, Remillard RA, Dhawan V et al (2014) A Parallax Distance to the Microquasar GRS 1915+105 and a Revised Estimate of its Black Hole Mass. ApJ 796:2–9 Reig P (2011) Be/X-ray binaries. Astrophys Space Sci 332:1–29 Repetto S, Nelemans G (2015) Constraining the formation of black holes in short-period black hole low-mass X-ray binaries. MNRAS 453:3341–3355 Reynolds AP, Quaintrell H, Still MD, Roche P, Chakrabarty D, Levine SE (1997) A new mass estimate for Hercules X-1. MNRAS 288:43–52 Reynolds TM, Fraser M, Gilmore G (2015) Gone without a bang: an archival HST survey for disappearing massive stars. MNRAS 453:2885–2900 Russell TD, Miller-Jones JCA, Curran PA, Soria R, Altamirano D, Corbel S et al (2015) Radio monitoring of the hard state jets in the 2011 outburst of MAXI J1836-194. MNRAS 450: 1745–1759

1526

J. Casares et al.

Shahbaz T, Watson CA, Dhillon VS (2014) The spotty donor star in the X-ray transient Cen X-4. MNRAS 440:504–513 Shajn G, Struve O (1929) On the rotation of the stars. MNRAS 89:222–239 Smartt SJ, Eldridge JJ, Crockett RM, Maund JR (2009) The death of massive stars - I. Observational constraints on the progenitors of Type II-P supernovae. MNRAS 395:1409–1437 Smartt SJ (2015) Observational constraints on the progenitors of core-collapse supernovae: the case for missing high-mass star. PASA – Publ Astron Soc Aust 32:16–37 Steeghs D, Casares J (2002) The mass donor of scorpius X-1 revealed. ApJ 568:273–278 Strader J, Chomiuk L, Maccarone TJ, Miller-Jones JCA, Seth AC (2012) Two stellar-mass black holes in the globular cluster M22. Nature 490:71–73 Suárez-Andrés L, González Hernández JI, Israelian G, Casares J, Rebolo R (2015) Chemical abundances of the secondary star in the neutron star X-ray binary Cygnus X-2. MNRAS 447:2261–2273 Tomsick JA, Heindl WA, Chakrabarty D, Kaaret P (2002) Rotational Broadening Measurement for the Neutron Star X-Ray Transient XTE J2123-058. ApJ 581:570–576 Ugliano M, Janka H-T, Marek A, Arcones A (2012) Progenitor-explosion connection and remnant birth masses for neutrino-driven supernovae of iron-core progenitors. ApJ 757:69–78 van Paradijs J, White N (1995) The Galactic Distribution of Low-Mass X-Ray Binaries. ApJL 447:L33–L36 van Paradijs J (1998) Neutron stars and black holes in X-ray binaries. In: Buccheri R, van Paradijs J, Alpar MA (eds) The Many Faces of Neutron Stars, vol 515. Kluwer Academic Publishers, ASIC, Dordrecht/Boston, p 279 Wade RA, Horne K (1988) The radial velocity curve and peculiar TiO distribution of the red secondary star in Z Chamaeleontis. ApJ 324:411–430 Wang L, Steeghs D, Casares J, Charles PA, Muñoz-Darias T, Marsh TR et al (2017, in press) System mass constraints for the accreting millisecond pulsar XTE J1814-338 using Bowen fluorescence. MNRAS, arXiv:1612.06430 Wielen R (1977) The diffusion of stellar orbits derived from the observed age-dependence of the velocity dispersion. A&A 60:263–275 Wijnands R, van der Klis M (1998) A millisecond pulsar in an X-ray binary system. Nature 394:344–346 Willems B, Henninger M, Levin T, Ivanova N, Kalogera V, McGhee K et al (2005) Understanding compact object formation and natal kicks. I. Calculation methods and the case of GRO J1655-40. ApJ 625:324–346 Witte MG, Savonije GJ (2001) Tidal evolution of eccentric orbits in massive binary systems. II. Coupled resonance locking for two rotating main sequence stars. A&A 366:840–857 Wu J, Orosz JA, McClintock JE, Hasan I, BaiIyn CD, Gou L et al (2016) The mass of the black hole in the X-ray binary nova muscae 1991. ApJ 825:46–58 Zhang CM, Wang J, Zhao YH, Yin HX, Song LM, Menezes DP et al (2011) Study of measured pulsar masses and their possible conclusions. A&A 527:A83–A90 Zhang Z, Gilfanov M, Bogdán Á (2013) Low-mass X-ray binary populations in galaxy outskirts: globular clusters and supernova kicks. A&A 556:A9–A18

Supernovae and the Evolution of Close Binary Systems

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Edward P.J. van den Heuvel

Abstract

The presence of neutron stars and black holes in X-ray binaries, as companions to normal stars, implies that core-collapse supernovae do occur in binary systems and that these systems can survive as binaries after the explosions. The main part of this chapter is devoted to the formation and evolution of X-ray binaries and their descendants: double compact objects such as binary radio pulsars and double black holes. It is shown that large-scale mass transfer is crucial for understanding the formation of high-mass X-ray binaries (HMXBs) and that these systems represent a normal stage in the evolution of massive binary systems. On the other hand, low-mass X-ray binaries (LMXBs) are products of a rare type of binary evolution, and very special conditions are required for the systems to have survived binary evolution and the supernova explosion. Later evolution of HMXBs may lead to double neutron stars, double black holes, or black hole-neutron star binaries; most LMXBs will produce millisecond radio pulsars with white dwarf companions. A second type of supernovae that is exclusively related to binaries are the thermonuclear supernovae, which are produced by the thermonuclear explosion of a carbon-oxygen white dwarf, of which the mass has grown to reach the upper mass limit allowed for a white dwarf (Chandrasekhar limit). These so-called type Ia supernovae are “standard candles,” crucial for cosmology. They can only be produced in binary systems, as the only realistic way to make the mass of a white dwarf grow is by mass transfer in a binary system.

E.P.J. van den Heuvel () Anton Pannekoek Institute of Astronomy, University of Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_75

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Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Binaries and Binary Radio Pulsars: How Binaries Manage to Survive a Supernova Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Observed Properties of X-Ray Binaries and Binary Radio Pulsars . . . . . . . . . . . 2.2 The Eddington Limit and Modes of Mass Transfer in X-Ray Binaries . . . . . . . 2.3 How High-Mass X-Ray Binaries Survived the Supernova Explosion in Which the Compact Star was Formed: The Crucial Effect of Mass Transfer in a Close Binary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Roche-Lobe Concept and Orbital Changes Due to Mass Transfer and Mass Ejection from a Binary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Roche Lobes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Orbital Changes Due to Mass Transfer and Mass Loss of Binaries . . . . . . . . . . 4 Evolution of Massive Close Binaries and the Formation of High-Mass X-Ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Three Stellar Timescales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Variation of the Outer Radius of a Star During Its Evolution and the Three Basic Types of Close Binary Evolution . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Evolution of Massive Close Binaries in Case B and the Formation of HMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Final Evolution of High-Mass X-Ray Binaries: The Formation of Double Neutron Stars and Double Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Identification of Binary Systems that are in Intermediate Stages in the Evolutionary Scheme of Fig. 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Formation of Low-Mass X-Ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction: Common Envelope Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Example of Evolution of a Wide Massive Binary with a Low-Mass Secondary to Form an LMXB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 From Low-Mass X-Ray Binaries to Millisecond Radio Pulsars . . . . . . . . . . . . . 5.4 Alternative Ways for Forming LMXBs: Electron-Capture Collapse Supernovae, Accretion-Induced Collapse of O-Ne-Mg White Dwarfs in Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Intermezzo: Electron-Capture Collapse Versus Iron Core-Collapse Supernovae, Different Kicks and Different Neutron Star Masses . . . . . . . . . . . . 5.6 Formation of LMXBs and Millisecond Radio Pulsars in Globular Star Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Intermediate-Mass X-Ray Binaries (IMXBs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Thermonuclear Type Ia Supernovae and Binary Systems . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

The fact that in X-ray binaries one finds neutron stars and black holes as companions to normal stars implies that core-collapse supernovae do occur in binary systems and that these systems can survive as binaries after these explosions. The main part of this chapter is devoted to the formation and evolution of X-ray binaries and their descendants: the binary radio pulsars and double black holes.

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A second kind of supernovae that is related to binaries is formed by the thermonuclear supernovae, which are produced by the thermonuclear explosion of a carbon-oxygen white dwarf star of which the mass has increased to reach the Chandrasekhar limit: the upper mass limit allowed for a white dwarf. These explosions are observed as the so-called type Ia supernovae, which are “standard candles,” of crucial importance for cosmology. It is thought now that these supernovae can only be produced in binary systems, as the only way to increase the mass of a white dwarf is by mass transfer in a binary system, as will be described in the last section of this chapter. For general reviews about the physics and evolution of X-ray binaries and the formation of binary radio pulsars and other double compact objects, I refer to the reviews by Bhattacharya and van den Heuvel (1991), Van den Heuvel (1994, 2009), Tauris and van den Heuvel (2006), and Lorimer (2008). For the physics of type Ia supernovae, I refer to Branch et al. (1995), Hillebrandt and Niemeyer (2000), and Howell (2011).

2

X-Ray Binaries and Binary Radio Pulsars: How Binaries Manage to Survive a Supernova Explosion

2.1

Observed Properties of X-Ray Binaries and Binary Radio Pulsars

As depicted in Fig. 1, there are two main classes of X-ray binaries: (i) high-mass X-ray binaries (abbreviated as HMXBs), in which the companion of the compact star is a massive O- or B-type star, typically more massive than about 15 Mˇ , and (ii) low-mass X-ray binaries (LMXBs), in which the companion of the compact star is a solar-like star with a mass typically 1:5 Mˇ . Of both these classes of X-ray binaries, there are a few hundred known in our galaxy and also several hundred in nearby other galaxies, such as the Large and Small Magellanic Clouds, M31, and M33. In our Galaxy about a dozen LMXBs are found in globular star clusters, the oldest stellar systems in our galaxy. In our neighbor galaxy M31, which has about twice as many globular clusters as ours, one observes about two dozen X-ray sources in globular star clusters, presumably also LMXBs. The large X-ray fluxes of X-ray binaries are generated by the accretion of matter from the outer layers of the normal companion star by the compact star. In the case of a neutron star, this process of “falling” toward the stellar surface in the extremely strong gravitational field of the neutron star causes an amount of mass m to lose an amount of potential energy GMm/R, where M and R are the mass and radius of the neutron star and G is the gravitational constant. For a neutron star with mass M  Mˇ and radius R  10 km, GMm/R equals about 0:1 mc 2 . This enormous loss of potential energy of the infalling matter is its gain of kinetic energy: when reaching the neutron star surface, the velocity of the infalling matter is about half the velocity of light. When colliding with the matter surrounding the neutron star, this kinetic energy is converted into heat, leading to temperatures above 107 K, such that the energy is radiated away in the form of X-rays. If the compact star is a

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Fig. 1 Examples of a typical HMXB (top) and LMXB (bottom). The neutron star in the HMXB is fed by a strong high-velocity wind. The neutron star in the LMXB is surrounded by an accretion disk which is fed by Roche-lobe overflow. Also HMXBs and LMXBs are known in which the accreting compact object is a black hole (Credit: Tauris and van den Heuvel 2006, Cambridge University Press)

black hole, up to 0:42 mc 2 of energy may be released before the matter disappears behind the horizon of the hole. We thus see that the process of energy generation by accretion of matter onto a compact star releases some 13–50 times more energy per unit mass than the fusion of hydrogen. This makes it the most efficient energy generation process known in the universe. In addition to the X-ray binaries, we also know the binary radio pulsars, of which there are also two main classes, depicted in Fig. 2: (i) the double neutron stars (DNS), which tend to have narrow and eccentric orbits – often with orbital periods of only a few hours. Some 15 of these systems are now known in our galaxy, and (ii) radio pulsars with a white dwarf (WD) companion, which mostly have circular orbits. Most of the pulsars with white dwarf companions are millisecond pulsars, with spin periods shorter than 10 ms. Many millisecond radio pulsars are found in globular star clusters. Some globular clusters have several tens of them, for example, the cluster Terzan 5, which harbors over 30 ms pulsars (e.g., see Lorimer 2008).

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Fig. 2 The two main classes of binary radio pulsars (orbits drawn to scale). Left: the PSR 1913+16 class systems tend to have very narrow and eccentric orbits; the companion of the pulsar is itself a neutron star or a massive white dwarf. Right: the PSR 1953+29 class systems tend to have wide and circular orbits and almost always are millisecond pulsars; they have low-mass white dwarf companions with masses in the range 0.2–0.4 solar masses, which are the remnants of solar-like companion stars. The spin rate of the neutron stars in these systems has been accelerated to over 100 Hertz during the long-lasting disk accretion phase when the system was a low-mass X-ray binary; such spun-up pulsars are called recycled (Credit: Van den Heuvel 2009, Springer Verlag)

In the double neutron stars, two supernova explosions have taken place, and these systems have managed to survive them both. We will see later in this article that the double neutron stars are the descendants of HMXBs, while most of the binary radio pulsars with a WD companion, particularly the millisecond pulsars, are descendants of LMXBs. In view of the presence of LMXBs in globular clusters, the presence of many millisecond radio pulsars in these clusters is therefore not surprising.

2.2

The Eddington Limit and Modes of Mass Transfer in X-Ray Binaries

The X-ray luminosities of X-ray binaries are typically between 1035 and 1038 ergs=s (between 25 and 25,000 times the total energy output of the sun), corresponding to mass accretion rates onto the compact objects between 1011 and 108 Mˇ /yr. The maximum matter accretion rate that a compact object can accommodate is the so-called Eddington limit rate, in which for an object with a radius of 10 km it is 1:5  108 Mˇ /yr. If the accretion rate becomes larger than this limit, the X-ray luminosity exceeds the so-called Eddington limit at which the outward radiation pressure on the gas particles just compensates the gravitational attraction of the star. The Eddington limit for a star with mass M D 104:5 .M =Mˇ /Lˇ , where Lˇ is the

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luminosity of the sun: 4  1033 ergs/s. When the luminosity exceeds the Eddington limit, the radiation pressure causes the excess inflowing matter to be blown away. The Eddington limit sets strong constraints on the ways in which companion stars are allowed to supply matter to the X-ray emitting compact objects. In LMXBs the size of the normal low-mass companion star slightly exceeds a critical radius, the so-called Roche-lobe radius Rc (explained in Sect. 3), which causes matter to flow freely toward the compact star. For companion stars with masses of order one solar mass, the ensuing rate of matter flow then stays below the Eddington rate, and a nice persistent X-ray source results. On the other hand, with a massive >15 Mˇ companion star, such “Roche-lobe overflow” would lead to a mass transfer rate some >104 times higher than the Eddington rate. This rate would completely extinguish the X-ray source by absorption. In HMXBs the radius of the mass donor star must therefore stay inside its Roche-lobe radius. The companion stars in these systems are O- and B-type supergiant stars. These are evolved massive stars with strong stellar winds. The compact star captures with its gravity a fraction of the outflowing stellar wind matter. This amount is below the Eddington limiting rate, but sufficient to power a strong X-ray source. These two different modes of supplying the matter that is accreted by the compact star, Rochelobe overflow for the LMXBs and wind accretion for the HMXBs, are schematically depicted in Fig. 1. Since stars less massive than about 15 Mˇ never develop strong stellar winds, only companion stars more massive than this value or less massive than about 1:5 Mˇ are able to supply the right amount of matter to power a steady strong accretion-driven X-ray source. This explains why we observe these two main categories of steady X-ray binaries and practically none with companion masses between 1:5 Mˇ and about 15 Mˇ (Van den Heuvel 1975).

2.3

How High-Mass X-Ray Binaries Survived the Supernova Explosion in Which the Compact Star was Formed: The Crucial Effect of Mass Transfer in a Close Binary

The first pulsating and eclipsing X-ray binary, discovered in 1971, was the HMXB Centaurus X-3, which consists of 4.84 s period X-ray pulsar (neutron star) which is orbiting a star with a mass 16 Mˇ in only 2.085 days. During the motion around its companion, the X-ray pulsar is eclipsed every orbit for about 0.5 days (Schreier et al. 1972). Also in 1971, prior to the discovery of the binary character of Cen X-3, British astronomers Webster and Murdin (1972) had pointed out that the then roughly determined position on the sky of the strong X-ray source Cygnus X-1 coincides with that of the blue supergiant O-type star HD 226868 and that this O-type star is a spectroscopic binary which in 5.6 days describes an almost circular orbit around an unseen star. Judging from the large radial velocity amplitude of some 72 km/s of the O-type star, they estimated that the unseen star has a mass 5 Mˇ . As this mass is too large for a neutron star, they suggested the unseen star to be a black hole, which would mean that the X-ray source is an accreting black hole. Later

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in 1972, thanks to a precise determination of the sky position of the X-ray source with radio telescopes, the coincidence of Cyg X-1 with the O supergiant was fully confirmed, and so by 1972 we knew of the existence of HMXBs with X-ray sources that are neutron stars as well as black holes. The fact that neutron star HMXBs like Centaurus X-3 had managed to survive the supernova in which the neutron star was born came as a surprise, for the following reasons. From stellar evolution it is known that the more massive a star is, the shorter it lives. For stars more massive than 10 Mˇ , the lifetime is roughly proportional to M 2:5 . The neutron star in Cen X-3 must therefore be the remnant of a star that originally was the most massive star in the binary system, thus more massive than 16 Mˇ . As the mass of about 1:4 Mˇ of its neutron star remnant is practically negligible with respect to the >16 Mˇ mass of its progenitor, one would then have expected that during the supernova explosion that produced the neutron star in Cen X-3, more than 50 % of the mass of the original binary system was ejected explosively. However, it was known already since 1961 that if in a binary system more than 50 % of the total mass of the binary is explosively ejected, the binary orbit becomes hyperbolic, and the system is disrupted (Blaauw 1961; in section 3 we explain the reason for this 50 % criterion). One therefore would have expected that the progenitor binary of Cen X-3 could not have survived the dynamical effects of the supernova mass ejection, and the same holds for all HMXBs which harbor neutron stars, of which several more were discovered already in 1972. The reason why the systems nevertheless managed to survive is that they are close binaries. During the evolution of a close binary, large-scale mass transfer from the more evolved (initially more massive) star to the less evolved, less massive star occurs, as will be explained below. As a result, by the time the initially more massive star reaches the end of its life and explodes as a supernova, it has become the less massive component of the binary, and the binary system remains bound, though with an eccentric orbit. In this way, the formation of the HMXBs was understood in 1972, shortly after their discovery (Tutukov and Yungelson 1973; Van den Heuvel and Heise 1972). In Sect. 4 binary evolution with mass transfer will be explained in more detail. For the LMXBs this reasoning does, however, not work, and here more complex ways of evolution have to be considered to understand why they managed to survive the supernova, as will be explained in Sect. 5. Before this, we have to introduce in the next section some celestial mechanics essential for the study of the evolution of close binaries.

3

The Roche-Lobe Concept and Orbital Changes Due to Mass Transfer and Mass Ejection from a Binary

3.1

Roche Lobes

In the so-called Roche approximation (called after the nineteenth century French astronomer Eduard Roche), one assumes the stars to be point masses which orbit their common center of gravity in circular orbits, with angular velocity 

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Fig. 3 A cross section in the orbital plane of the critical equipotential surfaces in a binary with components with masses 7 and 15 times that of the sun and a circular orbit with a period of 24.7 days. The thick curve passing through L1 represents the Roche lobes of the two stars. Also the second and third Lagrangian points L2 and L3 are indicated (Credit: Tauris and van den Heuvel 2006, Cambridge University Press)

(see Fig. 3). One considers a coordinate system in which the stars are not moving, and the X-axis is along the line connecting the centers of the stars. In this corotating coordinate system, the effective gravitational potential is given by ˚ D GM1 =r1  GM2 =r2  2 :r32 =2

(1)

where r1 and r2 are the distances of a point to the centers of the stars with masses M1 and M2 , respectively, and r3 is the distance of the point to the rotational axis of the system. This axis is the line through the center of mass of the coordinate system, perpendicular to the orbital plane. Here  is given by Kepler’s third law:  1=2  D GM =a3

(2)

where M D M1 C M2 and a is the distance between the centers of the stars (= the radius of the relative orbit of the two stars). In a close binary tidal forces will generally have brought the two stars in synchronous rotation with the orbital motion. Therefore, in a coordinate system that rotates with the orbital angular velocity of the binary, the stars are basically standing still (not rotating). Figure 3 depicts a cross section of the Roche equipotential

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surfaces in this corotating system, in the orbital plane of the binary for a system with component masses of 7 and 15 solar masses. One can easily show that in this corotating frame, the stars have the shapes of the equipotential surfaces. A special equipotential surface is the 1-shaped surface through the first Lagrangian point L1 (see Fig. 3). The pear-shaped parts of this surface on either side of L1 are called the Roche lobes of the respective stars. Deep inside the Roche lobes, the equipotential surfaces are nearly spherical in shape, but close to the Roche lobes they become pear shaped. When a star fills its Roche lobe, matter can freely – without needing any extra energy – flow along L1 into the Roche lobe of the other star and land on this star. As a measure of the size of the Roche lobe, one uses the so-called Roche radius Rc which is defined as the radius of a sphere that has the same volume as the Roche lobe. The ratio Rc =a depends only on the mass ratio q D M1 =M2 of the two stars. A very good approximation formula for Rc =a was given by Eggleton (1983):    Rc =a D 0:49q 2=3 = 0:69q 2=3 C ln 1 C q 1=3

(3)

Other approximations often used are

3.2

Rc =a D 0:38 C 0:2 log q

for 0:5 q 20; and

(4)

Rc =a D 0:462.q=.1 C q//1=3

for 0 < q < 0:5

(5)

Orbital Changes Due to Mass Transfer and Mass Loss of Binaries

3.2.1 Conservative Mass Transfer The orbital angular momentum of a binary is given by  p Jorb D .M1 :M2 =M / a2 1  e2

(6)

where e is the orbital eccentricity, M is the sum of the masses of the stars, and  is given by Eq. (2). In general, the orbital angular momentum is much larger than the rotational angular momentum of the two stars. For this reason, we will ignore here the rotational angular momentum of the stars. Further, we will assume circular orbits. Then, using Eq. (2) for , Eq. (8) becomes   Jorb D G1=2 M1 M2 =M 1=2 :a1=2 (7a) In the case that all mass lost by one star is captured by the other star, one speaks of conservative mass transfer. In that case the total mass M and the total orbital angular momentum Jorb are conserved, so: M12 :M22 :a D constant

(7b)

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which yields for the rate of change da/dt of the orbital radius a: .da=dt /=a D 2.dM1 =dt /=M1  2.dM2 =dt /=M2

(8)

Since for conservative mass transfer M2 D M  M1 , one has dM2 =dt D dM1 =dt , so: .da=dt /=a D 2Œ.dM1 =dt /f1=M1  1=M2 g

(9)

where star 1 is the star that is losing mass, so dM1 =dt < 0. One sees from Eq. (9) that if mass is transferred from the more massive to the less massive star, da/dt is negative, so the orbit shrinks. Similarly, if mass is transferred from the less massive star to the more massive star, the orbit expands.

3.2.2

Orbital Changes in Case of Explosive Mass Ejection from the System Here it is assumed that the timescale on which the mass is ejected from the system is negligible with respect to the orbital period of the binary. In this case one can easily show for spherically symmetric mass ejection (e.g., see Blaauw 1961; Flannery and van den Heuvel 1975) that the orbital changes can be expressed in terms of f which is the ratio of the total mass of the binary after the mass ejection divided by the total mass before the ejection:     f f (10) f D M1 C M2 = M10 C M20 where indices f and 0 indicate the masses after and before the explosive mass ejection, respectively. One then finds from the above given references: af D f =.2f  1/

(11)

ef D .1  f /=f

(12)

pf D f =.2f  1/3=2

(13)

Here af and pf are the orbital semimajor axis and orbital period after the mass ejection, divided by the semimajor axis and orbital period before the mass ejection, respectively. One immediately sees from these equations that if f 0:5, the system becomes unbound (ef 1). So, if more than half of the mass of the system is spherically symmetrically ejected explosively, the binary orbits become hyperbolic, and the system is unbound. This factor 0.5 is a direct consequence of the virial theorem, which states that for gravitationally bound systems, the sum of the kinetic energy of the particles is minus one half of the total gravitational potential energy of the particles: Ekin D 0:5 Epot . When more than half of the system mass is suddenly ejected, in the case of a binary, the potential energy per unit reduced mass of the system suddenly decreases by

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more than a factor two, whereas the kinetic energy per unit reduced mass remains the same. Therefore, suddenly the sum of kinetic and potential energy becomes larger than zero, which means that after the ejection, the system has positive total energy, and the system becomes unbound.

4

Evolution of Massive Close Binaries and the Formation of High-Mass X-Ray Binaries

4.1

The Three Stellar Timescales

Three timescales are of importance for the structure and evolution of stars: (i) The dynamical or pulsation timescale. This is the timescale required for the star to restore a deviation from hydrostatic equilibrium. This timescale is very short, of the order of hours, and is given by tdyn D 50.ˇ =/1=2 min

(14)

where ˇ and  indicate the mean density of the sun and of the star, respectively. (ii) The thermal timescale. This is the timescale required for the star to restore from a deviation from thermal equilibrium in its interior, where thermal equilibrium means that the amount of energy that enters each mass element in the star per second (e.g., by radiation) equals the amount that leaves the same element per second. The thermal timescale, also called the Kelvin-Helmholtz timescale, is given in good approximation by ttherm D 3:107 .M =Mˇ /2 years

(15)

where Mˇ and M denote the mass of the sun and of the star, respectively. It is also the timescale required for the star to contract from an interstellar cloud until the nuclear fusion in its interior begins. When the amount of nuclear energy generation has grown to equal the amount of energy the star radiates away from its surface (because it has become hot due to the release of gravitational energy during contraction), the star reaches stable thermal equilibrium and stops contracting. (iii) The nuclear timescale. This is the timescale on which the star consumes its nuclear fuel at its present luminosity (the luminosity is proportional to the amount of nuclear fuel consumed per second). As the amount of fuel is proportional to its mass, and the luminosity of a star is approximately proportional to M3:5 (the so-called mass-luminosity law), one has tnuc D 1010 .M =Mˇ /2:5 years This holds for stars with masses Mˇ .

(16)

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It should be noted that this timescale holds only for the phase of hydrogen fusion. As helium and other fusion phases produce much less energy per unit mass fused, the nuclear timescale in these phases is much shorter, for helium fusion about one order of magnitude, for later phases still much shorter.

4.2

The Variation of the Outer Radius of a Star During Its Evolution and the Three Basic Types of Close Binary Evolution

Figure 4 depicts the evolutionary change of the radius of a star of 5 Mˇ as a function of time. During the long phase of hydrogen fusion (which astronomers call hydrogen burning) – in this case about 100 million years – the outer radius of the star increases only slightly. When the hydrogen fuel in the stellar core is exhausted, in the point 2 in the figure, the entire star contracts under its own gravity, causing the temperature in the core and its surroundings to rise due to the release of gravitational potential energy. As a result, hydrogen burning now ignites in a shell around the helium core, in point 3 in the figure. The ignition of this “shell burning” causes the hydrogen envelope of the star to start to expand, while the core continues to contract. The expansion only stops when the core has become so hot that helium fusion ignites in the core and the star can settle in a new thermally stable state. By this time, in point 4 in the figure, the outer radius of the star has increased by a large factor, and the star has become a red giant. During the phase of core contraction and envelope expansion, between the points 3 and 4, the star was out of thermal equilibrium, and the evolution from point 3 to 4 takes place on a thermal timescale. During helium burning the star has two energy sources: helium burning in the core and hydrogen burning in a shell around the core. During this phase, which for the 5 Mˇ star lasts

Fig. 4 Evolutionary change of the radius of a star of 5Mˇ . (The starting chemical composition of the star is 70 % hydrogen, 28 % helium, and 2 % heavier elements). The ranges of radii for mass transfer to a companion star in a binary system according to Roche-lobe overflow cases A, B, and C are indicated, as described in Sect. 4.2 (Source: Tauris and van den Heuvel 2006, Cambridge University Press)

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for about 25 million years (a nuclear timescale), the outer radius of the star first somewhat contracts and later begins to expand again, when helium in its core is exhausted and burns in a shell around its carbon-oxygen core. The evolution of the radius of the 5 Mˇ star depicted in Fig. 4 is the characteristic for all stars in the mass range between 2 Mˇ and at least 50 Mˇ and can therefore be used to illustrate the evolution of stars in binary systems in this mass range. With the foregoing knowledge, it is now possible to consider the evolution of massive close binaries and the formation of high-mass X-ray binaries. Three basic types of close binary evolution were distinguished in the middle of 1960s by German astrophysicists R. Kippenhahn and A. Weigert, by Polish astrophysicist B. Paczynski, and by Czech astrophysicist M. Plavec, indicated as cases A, B, and C. For a 5 Mˇ primary star of a close binary, these cases are indicated in Fig. 4 and are described as follows: Case A occurs when the primary star overflows its Roche lobe already during core hydrogen burning, between the points 1 and 2 in Fig. 4. Case B occurs in wider binaries, such that the primary star overflows its Roche lobe after the end of core hydrogen burning but before the ignition of helium burning, so between the points 3 and 4 in Fig. 4. Case C occurs in very wide binaries, in which the primary star overflows its Roche lobe only after the end of core helium burning, and its outer layers have expanded to become a red supergiant, that is, beyond point 4 in Fig. 4. Case B occurs over a wide range of initial orbital periods of observed unevolved binaries and is therefore very common, while case A occurs only for very short period binaries and is much rarer (except for very massive binaries, with components more massive than about 30 Mˇ /. For this reason, we will consider for the sake of argument here only systems that evolve according to case B. In this case, the evolution of the binaries is quite straightforward.

4.3

Evolution of Massive Close Binaries in Case B and the Formation of HMXBs

According to Eq. (16) the more massive (primary) star of a close binary is the first of the two stars to have finished its core hydrogen fusion. So, the envelope of this star will begin to expand and overflow its Roche lobe when its companion is still relatively unevolved, in the phase of core hydrogen burning. When it overflows its Roche lobe, it loses mass, which causes it to shrink temporarily; but as in this phase the star is out of thermal equilibrium and wants to expand to become a giant, it will soon overflow its Roche lobe again and continue to transfer matter. The mass transfer at the same time causes, according to Eq. (9), the orbit to shrink, which causes the Roche lobe to shrink which, because the star wishes to expand, makes this stage very unstable. It turns out that the system can regain stability only once the primary star has lost practically its entire hydrogen envelope to its companion

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and only its helium core is left. As the hydrogen envelope contains of order 70 % to 80 % of the original mass of the star, by the time the system stabilizes, the original primary star has become the less massive of the two, and in the case of conservative mass transfer, the original secondary star has now become the more massive star of the two. Figure 5 shows as an example the assumed conservative evolution of a binary system that started out with components of 20 Mˇ and 8 Mˇ in an initially circular orbit with a period of 4.70 days (phase a/. After 6:17  106 yrs the primary star has exhausted the hydrogen in its core, and its outer layers have expanded to overflow the Roche lobe (phase b/. It then transfers its hydrogen-rich envelope of 14:66 Mˇ to its companion in only 30,000 yrs (a thermal timescale), leaving only its 5:34 Mˇ helium core as an almost pure helium star with only a tiny hydrogen envelope. Due to this (assumed) conservative mass transfer, the mass of the companion has increased to 22:66 Mˇ , and the orbital period has changed to 10.86 days. Since helium stars are so-called Wolf-Rayet stars, the system has now become a WolfRayet binary consisting of a 5:34 Mˇ Wolf-Rayet star and a practically unevolved O-type star of 22:66 Mˇ in an early stage of core hydrogen burning (phase c in Fig. 5). Some 6:9  105 yrs later the helium star has gone through all its further nuclear burning stages and has developed an iron core which collapsed to a neutron star. It is assumed here that the neutron star has a mass of 2 Mˇ , such that the remaining 3:34 Mˇ was ejected in a supernova explosion (phase d /. This explosion has made the orbit eccentric and has increased the orbital period to 12.63 days. Due to the recoil of the (assumed spherically symmetric) supernova mass ejection, the system has become a runaway star with a velocity of 32 km/s. At the time of the supernova explosion, the companion is still in an early phase of core hydrogen burning, and it takes another 3.52 million years to exhaust the hydrogen in its core and become a blue supergiant star with a strong stellar wind, which turns the neutron star into a strong accretion-driven X-ray source (phase e/. This phase starts when the system has an age of 10.41 million yrs. This phase is rather short lasting, perhaps only 50,000 to 100,000 yrs, until the blue supergiant begins to overflow its Roche lobe and starts transferring matter to the neutron star at a very high rate, of order 104 Mˇ / yr. This rate is so far above the Eddington limiting rate that it will extinguish the X-ray source, as explained in Sect. 2.2. The X-ray phase of HMXBs is therefore expected to be rather short-lived: not more than some 105 years.

4.4

Final Evolution of High-Mass X-Ray Binaries: The Formation of Double Neutron Stars and Double Black Holes

For a variety of reasons, explained in Sects. 4.5 and 5.1, most of the mass transferred at a very high rate by Roche-lobe overflow to the neutron star cannot be accepted by it and will be expelled from the system. The expelled matter carries with it a large amount of angular momentum, which causes a large shrinking of the orbit. If the system survives as a binary after this large mass and angular momentum loss,

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what remains is a very close binary, consisting of the about 6 Mˇ helium core of the blue supergiant plus the neutron star in a very close orbit, with a period of order a few hours (phase g in Fig. 5). Helium stars have very small radii, so they can fit in a narrow orbit, as long as the orbital period is not shorter than a few hours. When in its turn this second helium star terminates its evolution with a supernova explosion, the mass ejection in this explosion may either disrupt the system (if the symmetrically ejected amount of mass exceeds 4 Mˇ /, or remain as a bound system of two neutron stars in a narrow and eccentric orbit. This is depicted as phase h in Fig. 5. (For an alternative, so-called common envelope, model leading to a HMXB and the Hulse-Taylor double neutron star PSR 1913+16, see figure 16.15 in the review by Tauris and van den Heuvel 2006). At present 15 double neutron stars are known in our galaxy, most of them with very short orbital periods, the shortest one being just over 2.1 h, for the double radio pulsar PSRJ0737-3039AB. All have eccentric orbits, due to the explosive mass ejection in the second supernova that took place in the systems (see Fig. 2). At present we do not know any neutron star-black hole binary or any double black hole. However, the first detection by the LIGO gravitational wave observatory of the gravitational wave signal produced by the merger of a double black hole with component masses of 36 and 29 solar masses shows that double black holes do exist in nature (the event, on 14 September 2015, is indicated as GW150914; the merging binary was located at a distance of about 1.3 billion lightyears). The same holds for the second detected LIGO signal GW151226. Black hole binaries with masses this large are products of the evolution of very massive close binaries, with binary stellar components with initial masses probably larger than 60–80 solar masses. The formation of close double black hole binaries is basically a higher mass analogue of the evolutionary model depicted in Fig. 5 and in figure 16.15 of Tauris and van den Heuvel (2006) (also more complex models have recently been published). In the next section we discuss some binaries that are considered to be the direct progenitors of close double black hole binaries.

4.5

Identification of Binary Systems that are in Intermediate Stages in the Evolutionary Scheme of Fig. 5

In the past decades various intermediate stages of the evolutionary scheme of Fig. 5 have been discovered. It was already mentioned that the systems in phase c are the well-known Wolf-Rayet (WR) binaries. WR stars are very luminous stars with very strong stellar winds and mostly have no hydrogen in their envelopes. In WR binaries they always have a relatively unevolved O-type star as companion, which is several times more massive than the WR star. Systems in phase d contain a young rapidly spinning neutron star, similar to the pulsar in the Crab Nebula. Such young neutron stars eject very large amounts of highly relativistic electrons and positrons – the so-called relativistic pulsar wind. In the case of the Crab pulsar, the relativistic pulsar wind carries an energy flux of

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Fig. 5 Subsequent stages in the evolution of a close binary with initial component masses of 20 Mˇ and 8 Mˇ and an initial orbital period of 4.70 days. The first six stages a–e depicted here were computed by De Loore et al. (1974); stages f –h were calculated by the author, assuming certain parameters for losses of mass and angular momentum during the common envelope phase f . It is assumed that the supernova of the primary star leaves a 2 Mˇ neutron star. Phase .a/ t D 0 W P D 4:70 d; .b/ t D 6:17  106 yr, P D 4:70 d, onset of first stage of mass transfer; .c/ t D 6:20  106 yr, P D 10:86 d, end of first stage of mass transfer, onset of first Wolf-Rayet stage; .d/ t D 6:76  106 yr, P D 12:63 d, He star (=WR star) has exploded as supernova; .e/ t D 10:41  106 yr, P D 12:63 d, normal companion becomes blue supergiant with strong stellar wind and turns neutron star on as a strong X-ray source; .f/ t D 10:51  106 yr, P D 12:63d, onset of second stage of Roche-lobe overflow, start of spiral-in phase: neutron star spirals down toward the core of the supergiant, large losses of mass, and orbital angular momentum from system;

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some 20,000 times the luminosity of the Sun, simply produced by the spin-down of the highly magnetized rapidly spinning neutron star. Inverse Compton interactions of the highly relativistic electrons and positrons of the pulsar wind with the optical photons of the high-luminosity companion star boost the energies of these photons to become gamma ray photons. The energetic pulsar phase lasts no more than some 105 years. One thus expects that in phase d of Fig. 5, the systems will for some 105 years be O- or B-type binaries which emit gamma rays. Indeed, several of such gamma ray emitting O- and B-type close binaries have been discovered. Examples are (1) the gamma ray O6.5V-star LS 5039 which is orbited in 3.90 days by a low-mass invisible companion in an orbit with eccentricity e D 0:35, which in all likelihood is a young fast-spinning neutron star, and (2) the B-type star LSI+61ı 303 which is a gamma ray and radio source which shows a 26.49-day period in the strength of its gamma and its nonthermal radio emission, due to the fact that it is a 26.49-day binary with an orbit with eccentricity e D 0:54. It also is an X-ray binary with the same period, but the fact that it is at the same time also a gamma ray and radio binary makes it very different from the accreting X-ray binaries. Its X-ray and gamma ray emission is here thought to be due to the boosting of the photons from the B-type star by the relativistic particles emitted by the young neutron star. The nonthermal radio emission is typically what is expected from a relativistic pulsar wind. Its largest gamma ray emission is recorded at closest approach of the two stars in their orbit, just as expected. Also systems in phase g, consisting of a helium star and a compact star, are known. Helium stars more massive than about 8 Mˇ are known to be Wolf-Rayet (WR) stars (see above). Nowadays four X-ray binaries are known that consist of a Wolf-Rayet star and a compact star, the so-called Wolf-Rayet X-ray binaries. All indeed have very short orbital periods, just as expected on the basis of spiral-in after the HMXB phase. The periods range from 4.8 h for the WR X-ray binary Cygnus X3 in our galaxy to 14–15 h for the system CXOU 004732 in the blue dwarf starburst galaxy NGC 253, 32.8 h for NGC 300 X-1 in the blue dwarf starburst galaxy NGC 300, and 34.4 h for IC 10 X-1 in the blue dwarf starburst galaxy IC 10. The latter three galaxies are all in the local group. In all these systems, the compact star most likely is a black hole. The WR stars (helium stars) in the binaries in the three blue starburst galaxies are all very massive, having masses in the range 20–40 Mˇ . These WR X-ray binaries are therefore ideal progenitors for producing double black holes or black hole-neutron star binaries. They fit very well in the evolutionary scheme of Fig. 5 for very massive binaries.

J Fig. 5 (continued) .g/ t D 10:52  106 yr, P  4 h, onset of second Wolf-Rayet phase; and .h/ t  11:0  106 yr, the second Wolf-Rayet star (= helium star) has exploded as a supernova; survival or disruption of the system depends on the mass of the remnant, and the effects of possible velocity kick to the remnant due to asymmetries in the SN mass ejection. If the system survives, it consists of two compact objects in a very narrow and eccentric orbit (Credit: Van den Heuvel 1994, Springer Verlag)

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Fig. 6 The peculiar X-ray binary SS433, with an orbital period of 13.1 d, is the only system in our Galaxy that is known to be in the spiral-in phase f of Fig. 5. The system is clearly in the second phase of Roche-lobe overflow but has not gone into a common envelope phase. Instead, its 10.9˙3.1 solar mass donor star is transferring mass at a very high rate (104 Mˇ /yr) to its 2:9 ˙ 0:7 Mˇ compact companion. The transferred mass forms a very large and thick accretion disk around this star from which the super-Eddington amount of transferred matter is lost in the form of precesssing relativistic beams (which carry >106 Mˇ /yr), plus a disk wind which carries away still some hundred times more matter, with the compact star’s orbital angular momentum. This loss of mass and angular momentum makes the system to spiral in at a moderate rate. At the end of the spiral-in, a system will remain, consisting of the 3 Mˇ helium core of the donor plus the 2:9 Mˇ compact star, with an orbital period of about one day (Credit: NASA (http://apod.nasa. gov/apod/image/ss433_art_big.gif)

Only one system is known to be in the “spiral-in” phase f of Fig. 5, between the HMXB phase and the phase consisting of a helium star plus a compact star (“Wolf-Rayet X-ray binary”). This is the very remarkable X-ray binary SS433 (Fig. 6), in which the 10:9 Mˇ donor star is filling its Roche lobe and transferring mass at a rate of order 104 Mˇ/yr to the compact star. This star can only accept the Eddington rate of 108 Mˇ/yr. The remaining transferred matter forms a very large and thick accretion disk around the compact star, from which it is lost in the form of relativistic jets (106 Mˇ/yr), plus a thick disk wind with a hundred times larger mass loss rate than in the jets. The reason why the system transfers mass by Roche-lobe overflow and does not go into a common envelope (CE) phase is that the donor star is an A-type supergiant with a radiative envelope. Thanks to the radiative envelope, the star can keep its radius equal to that of its Roche lobe while transferring matter and therefore does not go into a CE phase. In the caption of Fig. 6 is explained how this system will end, according to calculations by the author.

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The Formation of Low-Mass X-Ray Binaries

5.1

Introduction: Common Envelope Evolution

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The conservative type of evolution as depicted in Fig. 5 works only if the difference in mass between the two stars is not very large, i.e., q D M2 =M1 0.4 to 0.5. This is because the timescale which the secondary star needs to accommodate the mass transferred to it from the primary is its own thermal timescale. If this timescale is much longer than the thermal timescale of the primary (which is the timescale of the mass transfer), the secondary will swell up and overfill its own Roche lobe. When that happens, both stars overfill their Roche lobes, and a common envelope (CE) will form around the binary system. The precise evolution in this CE phase is difficult to calculate precisely, but it is clear that this will lead to a spiral-in of the secondary star toward the helium core of the primary star for a variety of reasons, such as: (a) Friction experienced by the secondary and the core of the primary star during their orbital motion in the common envelope; (b) Mass loss from the common envelope through the second or third Lagrangian points L2 and L3 (see Fig. 3). In these points the outflowing matter has much larger specific angular momentum than the average specific angular momentum of the binary, such that this mass loss is an enormous drain on the orbital angular momentum of the binary, thus causing rapid spiral-in. (c) In wide binaries the primary star, when it overflows its Roche lobe, is a red giant with a deep convective envelope. Convective envelopes have the property that they expand on a dynamical timescale when they lose mass. Thus, after transferring a little bit of mass to the companion, they rapidly expand and engulf the companion entirely, such that a common envelope forms. Hydrodynamic calculations show that the timescale of spiral-in after a common envelope forms is very short (astronomically speaking), of order centuries to thousands of years. In this CE phase the secondary therefore has no time to accrete and gain much mass. The outcome of the CE phase is therefore – if the two stars do not merge – a short-period binary consisting of the helium core of the primary star plus the low-mass secondary star, which gained negligible mass in the process. In order for the helium core to terminate its life as a neutron star, the initial mass of the primary star must have been 8 Mˇ .

5.2

Example of Evolution of a Wide Massive Binary with a Low-Mass Secondary to Form an LMXB

Figure 7 depicts as an example of the evolution of a binary with a primary star with initial mass 15 Mˇ and a 1.6 Mˇ secondary star in a wide orbit. It turns out that, in order to survive the CE phase and not merge, the system has to start out with such a

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Fig. 7 Possible model for the evolution of a binary system eventually leading to LMXB and, finally, to the formation of a binary millisecond radio pulsar. Parameters governing the specific angular momentum of ejected matter, the common envelope and spiral-in phase, the asymmetric supernova explosion (leading to a velocity kick to the neutron star), and the evolution of the naked helium star, all have a large impact on the exact evolution. Parameters were chosen for a scenario that leads to the formation of the observed binary millisecond radio pulsar PSR 1855+09. Stellar masses are given in solar units (Credit: Tauris and van den Heuvel 2006, Cambridge University Press)

wide orbit, with period >1 year. In the system of Fig. 7, the initial orbital period is 1500 days, which after the common envelope phase has shrunken to 0.75 days. In the system of Fig. 7, the helium star has a mass of 4:86 Mˇ and loses by stellar wind some 0:87 Mˇ before it finally collapses to a neutron star in a supernova event.

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If in a spherically symmetric supernova less than half the mass of the system is ejected, the two stars will stay together, in a very eccentric orbit, as is the case here. Directly after the SN, the orbital period is 2.08 days and the orbital eccentricity is e D 0:24. (The reason why the eccentricity here is not very large is that the neutron star was assumed to have received a kick velocity at its birth – see below – which reduced the final eccentricity.) At this time the age of the system is only 15 million years. Tidal forces will now circularize the orbit which then settles to 1.41 days. Only very much later, after 2.24 billion years, the 1:6 Mˇ secondary begins to overflow its Roche lobe and in 400 million transfers its envelope to the neutron star, which by accreting mass for a very long time has been spun up to become a millisecond pulsar with a low-mass white dwarf. As explained in the caption of Fig. 7, the evolution of this LMXB was tuned to produce the millisecond binary radio pulsar system of PSR 1855+09, which has an orbital period of 12.33 days (see Fig. 2). About kick velocities imparted to neutron stars at its birth: observations of radio pulsars show that many neutron stars receive a considerable velocity kick in their birth events, of order hundreds of km/s. These kicks presumably are due to slight asymmetries in the core collapse process and the accompanying mass ejection. These kicks will disrupt many potential LMXB progenitor binaries but, if imparted in the right direction, may also cause the system to survive, as is the case in the system of Fig. 7. (For a low-mass companion star, there is also an impulse given to this star by the impact of the supernova shell; this is only a small effect, if compared to the effect of neutron star kicks. In HMXBs the impact effect is completely negligible.) One sees from Fig. 7 that it is always billions of years after the supernova that in an LMXB the companion of the compact star begins to overflow its Roche lobe – either due to radius expansion caused by its internal evolution or due to shrinking of the orbit as a result of angular momentum loss of the binary (by a stellar wind from the companion or by gravitational wave losses). The mass transfer to the billions of years old neutron star or black hole then turns the system into a low-mass X-ray binary. The duration of 400 million years of the Xray binary phase for the system in Fig. 7 is typical for the X-ray lifetime of LMXBs. We see here that an LMXB lives some 4000 times longer as an X-ray source than an HMXB. As the numbers of LMXBs and HMXBs in the galaxy are roughly the same, this means that the formation rate of LMXBs in the galaxy is some 4000 times lower than that of the HMXBs. This illustrates that the formation of LMXBs requires a very rare type of close binary evolution.

5.3

From Low-Mass X-Ray Binaries to Millisecond Radio Pulsars

The mass transfer by Roche-lobe overflow always takes place along the first Lagrangian point L1 , and the gas stream out of L1 lags behind the motion of the compact star in its orbit. This lagging of the stream makes that it describes a curved orbit around the compact star and collides with itself, which leads to the formation of an accretion disk around the compact star (see Fig. 1). The disk matter that spirals

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inwards to the neutron star carries angular momentum, which is fed into the neutron star, and increases its spin rate. As this accretion of angular momentum goes on for hundreds of millions of years, the spin of the neutron star can be accelerated to a rate of several hundred or even one thousand hertz. When the low-mass donor star of the LMXB terminates its evolution, it will leave behind a white dwarf: the degenerate burned-out core of the star. The mass transfer then terminates, and if the neutron star still has a magnetic field, one will observe it as a radio pulsar with a pulse period of hundreds of hertz: a so-called millisecond radio pulsar. This evolutionary picture explains why most of the white dwarf + neutron star binaries observed in nature are millisecond radio pulsars. While this evolutionary picture was already put forward in 1982 to explain the existence of the millisecond radio pulsars, which were discovered in that year, it took until 1998 before the first millisecond pulsations from a neutron star in a low-mass X-ray binary were discovered, thanks to NASA’s Rossi X-ray Timing Explorer satellite. At present several tens of accreting millisecond Xray pulsars in low-mass X-ray binaries are known, proving that the spin periods of the neutron stars in LMXBs are typically shorter than 10 ms (see the review by Van der Klis 2000).

5.4

Alternative Ways for Forming LMXBs: Electron-Capture Collapse Supernovae, Accretion-Induced Collapse of O-Ne-Mg White Dwarfs in Binaries

A possible outcome of the common envelope evolution of a wide binary system consisting of a star with a mass in the range 7–10 Mˇ plus a low-mass solar-like star is that the core of the post-CE helium star does not make it to core collapse, but after a second mass transfer phase, caused by the envelope expansion of the helium star, leaves behind a massive white dwarf consisting of oxygen, neon, and magnesium: the products of the carbon burning. Such white dwarfs can have masses of about 1:2 Mˇ or larger. If mass is fed to them later on, such that they grow to the Chandraskhar limit of about 1:4 Mˇ , they collapse, due to electron captures by nuclei of O, Ne, and Mg, which will lead to conversion of these nuclei into neutrons, such that a neutron star results. So, when the low-mass companion of the white dwarf, after billions of years, overflows its Roche lobe, it can drive the O-Ne-Mg white dwarf over the Chandrasekhar limit and produce a neutron star. This is what is called neutron star formation by accretion-induced collapse.

5.5

Intermezzo: Electron-Capture Collapse Versus Iron Core-Collapse Supernovae, Different Kicks and Different Neutron Star Masses

Electron-capture collapse may occur also spontaneously in stars that started with a mass in the range about 7–10 Mˇ , in which a degenerate O-Ne-Mg core forms late in their evolution, which grows to electron-capture collapse, producing a supernova.

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Above about 10 Mˇ , the core does not become degenerate, and the stars evolve further through neon, oxygen, and silicon burning and produce a collapsing iron core supernova. Since in neutron star formation some 0.2 solar masses are lost in the form of gravitational binding energy and the neutron star forms from a Chandrasekhar mass degenerate core, the mass of a neutron star formed by electron-capture collapse is expected to be about 1.2 solar masses. On the other hand, since in iron corecollapse also matter of layers around the collapsing core fall in, the neutron stars formed by this process are expected to be more massive: around 1.3–1:5 Mˇ for stars with initial masses up to 19 Mˇ and even larger, up to 2 Mˇ for stars that started with masses above 19 Mˇ . Hydrodynamic core-collapse calculations have shown that neutron star formation by electron-capture collapse is a very symmetric process, such that a neutron star formed by this process receives hardly any velocity kick when it is born: in general, less than a few tens of km/s. This is in contrast to neutron stars formed by iron core-collapse, which are expected to receive large kick velocities at birth. In a small mass range around 2:5 Mˇ , helium stars in binaries, originating from stars in the mass range 7–10 Mˇ , will produce a degenerate O-NeMg core and evolve to electron-capture collapse. As in this process hardly any kick velocity is imparted to the neutron star, this explains the combination of low orbital eccentricity and low neutron star mass (in the range 1.10–1.25 Mˇ ) in a number of double neutron stars. The low-mass neutron star in these systems is the second-born one, and its formation imparted hardly any kick to the neutron star. A key example is the double pulsar system PSRJ 0737-3039AB, which has an orbital period of 2.4 h, e D 0:0878, and a young (second-born) neutron star of mass 1:25 Mˇ , while its old, first-born neutron star companion has M D 1:338 Mˇ . The first-born is a spun-up weak-magnetic-field pulsar with pulse period 23 ms, while the second-born is a “normal” strong-magnetic-field pulsar with a period of 2.3 s.

5.6

Formation of LMXBs and Millisecond Radio Pulsars in Globular Star Clusters

Accretion-induced electron-capture collapse is expected to be particularly important in globular star clusters. In these clusters – which now have ages >11  109 years – in the early youth, many O-Ne-Mg white dwarfs are expected to have formed from single stars with masses in the range 7–10 Mˇ . Due to their masses of 1:2 Mˇ , these white dwarfs now belong to the most massive stars in the cluster, since at the age of 11 billion years, the most massive normal hydrogen-burning stars have masses below 0:95 Mˇ . Due to their large masses, the O-Ne-Mg white dwarfs will, due to gravitational interactions with the cluster stars, have sunken to the dense cluster core, where they may have picked up a normal low-mass stellar companion stars by grazing stellar collisions or three-body encounters. Mass transfer from their stellar companion may then drive the white dwarf over the Chandrasekhar limit, producing a neutron star by accretion-induced collapse. As these neutron stars did not receive an appreciable velocity kick at birth, this formation process explains why neutron stars can still be found in globular clusters, despite the fact that the escape

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velocity from these clusters is only a few tens of km/s. Later in life these LMXBs then evolve into millisecond radio pulsars, which explains why so many of these millisecond pulsars are found in the globular clusters.

6

Intermediate-Mass X-Ray Binaries (IMXBs)

As mentioned in Sect. 2.2, the reason why we observe the two large classes of X-ray binaries, the HMXBs in which the companion to the compact star has a mass 15 Mˇ and the LMXBs in which the companion has a mass 1.5 Mˇ , is simply due to a selection effect: only companion stars in these two mass ranges are able to supply for a considerable amount of time a mass accretion rate to the compact star in the range 103 to 1.0 times the Eddington limit accretion rate of about 108 Mˇ =yr, producing sources with X-ray luminosities between 1035 and 1038 ergs=s. Donors above 1:5 Mˇ supply a super Eddington rate of mass transfer by Roche-lobe overflow and soon after starting Roche-lobe overflow quench the X-ray source, while donors with masses 15 Mˇ do not have winds that are strong enough to power a strong X-ray source. For this reason, the absence of powerful binary X-ray sources in which the donor star has and “intermediate” mass, between 1.5 and 15 Mˇ , is not due to the fact that nature does not make systems with companions of the compact star in this mass range, but purely due to the fact that companions in this mass range cannot produce a long-lived binary X-ray source (Van den Heuvel 1975). As a matter of fact, a few X-ray binaries are known in this “intermediate” mass range, e.g., Hercules X-1, in which the companion of the neutron star has a mass of 2 Mˇ , and Cygnus X-2, in which the companion at present is a giant star with a mass of  Mˇ , but which, according to its luminosity, is the remnant of a star that started out with a mass of 2 Mˇ or more. In addition, we know a number of binary radio pulsars in which the companion of the pulsar is a white dwarf with a mass in the range 0.6–1.1 Mˇ . Such white dwarfs are the remnants of donor stars which started out with masses in the range 2–6 Mˇ , which shows that neutron star binaries with companions in this mass range are indeed produced in nature.

7

Thermonuclear Type Ia Supernovae and Binary Systems

Apart from the core-collapse supernovae, discussed in the foregoing sections, which may occur in single stars as well as in binaries, there is an entirely different type of supernovae, those of type Ia, which are thought to exclusively occur in binaries. The spectra of type Ia supernovae are free from hydrogen and show the products of explosive carbon burning: in the beginning, intermediate elements, ranging from oxygen to calcium, and at later times, iron peak elements. The light curve of a type Ia supernova shows the characteristic decay times of radioactive Ni-56 at the peak of the light curve and of Co-56 in the tail of the light curve, so the light curve is thought to be powered by the radioactive decay sequence Ni-56 ! Co-56 ! Fe-56. These observational characteristics, together with the fact that type Ia supernovae

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are remarkably uniform in their light curve characteristics (they are unique “standard candles” for cosmology; see, e.g., Howell 2011), have led to the conclusion that they are produced by the explosive thermonuclear carbon burning in white dwarf stars, ignited when the white dwarf reaches the Chandrasekhar limit of about 1:4 Mˇ (see Branch et al. 1996, Hillebrandt and Niemeyer 2000). Stars with initial masses in the range 2 to about 7 Mˇ leave at the end of life white dwarfs with masses of about 1:0 Mˇ , consisting of carbon and oxygen. These so-called CO white dwarfs therefore consist of matter that, in principle, can still service as nuclear fuel, since the nuclear fusion of carbon into neon and magnesium and of oxygen into silicon and sulfur can still produce a lot of energy, as well as the fusion of silicon into nickel56. If the mass of the white dwarf can be made to grow to the Chandrasekhar limit, then upon reaching this limit, the white dwarf will collapse, and carbon burning will be ignited due to the heating by release of gravitational energy by the collapse. This leads to the complete thermonuclear explosion of the white dwarf, which leaves no remnant. The CO white dwarf that reaches the Chandrasekhar limit is basically one big thermonuclear bomb. For a single CO white dwarf, there is no way in which its mass can grow. However, if the white dwarf is in a close binary system with a normal star, or with another white dwarf, mass transfer from the other star to the white dwarf may cause its mass to grow to the Chandrasekhar limit and trigger the thermonuclear explosion of the white dwarf. This is the reason why type Ia supernovae are expected to occur exclusively in binary systems. There are two main binary formation channels for type Ia supernovae, as depicted in Fig. 8: (i) the single-degenerate (SD) model and the double-degenerate (DD) model. In the SD model the companion of the white dwarf is a normal star, which transfers mass from its outer layers to the CO white dwarf, in a way similar to the mass transfer to a neutron star in a low-mass X-ray binary. In the DD model the companion of the CO white dwarf is another white dwarf, in a very narrow orbit. Like the close double neutron stars, such systems are the result of two mass transfer phases in an originally much wider binary: the second mass transfer phase was, just as in HMXBs, a common envelope phase, in which the first-formed CO white dwarf spiraled down in the hydrogen-rich envelope of a red giant companion with a degenerate CO core, such that the hydrogen-rich envelope was ejected and a very close system remained, composed of two CO white dwarfs (this phase resembles phase g in the evolutionary sequence of HMXBs in Fig. 5). The two white dwarfs will spiral toward each other by the loss of gravitational waves from the system. If the orbital period of the remaining DD system is shorter than 12 h, this spiral-in will cause them to merge within a Hubble time. When they merge, and the sum of the masses of the two white dwarfs exceeds the Chandrasekhar limit, this will cause a type Ia supernova. One therefore does expect type Ia supernovae to occur also in very old stellar populations, as is indeed observed: they are the only type of supernovae seen in elliptical galaxies, which contain only low-mass stars, with masses not much larger than that of the sun. In such galaxies no core-collapse supernovae of stars >8 Mˇ can occur, and indeed such supernovae are not observed in these galaxies. (Accretion-induced collapses of

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Fig. 8 The two possible models for producing a type Ia supernova explosion: the singledegenerate (SD) model (right) and the double-degenerate (DD) model (left). In the SD model, the mass-giving companion of the CO white dwarf is a normal star; in the DD model, it is another white dwarf in a very narrow orbit. In the DD case the white dwarf merges with its companion due to the losses of gravitational waves which cause the two stars to spiral toward each other and merge, leading to one degenerate star with a mass above the Chandrasekhar limit, which explodes (Credit: NASA/CXC/M.Weiss)

O-Ne-Mg white dwarfs in binaries with a low-mass companion may occur in such galaxies, just like in the globular clusters, but apparently these do not produce an observable supernova.)

8

Conclusions

Binaries play a key role in high-energy and relativistic astrophysics and cosmology. The strongest stellar X-ray sources in galaxies are binary systems that survived one core-collapse supernova explosion and consist of a relativistic star (neutron star or black hole) and a normal star. We saw, from Fig. 5, that the high-mass X-ray binaries represent a normal phase in the evolution of massive binary systems. On the other

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hand, the low-mass X-ray binaries are the product of a very rare type of evolution of binaries that started out with two components with a large difference in mass and a wide orbit (Fig. 7).The binary radio pulsars with narrow and eccentric orbits, such as the Hulse-Taylor binary pulsar PSR 1913+16, show that later in life high-mass X-ray binaries spiral in deeply, losing a large amount of mass and orbital angular momentum, and in a number of cases can survive the second supernova explosion (Fig. 5). This deep spiral-in of HMXBs was predicted long ago (Van den Heuvel and De Loore 1973) and also has important consequences for understanding the formation of the close double black holes that recently were discovered, thanks to LIGO: these are the final products of normal binaries that started out with masses just larger than those of the progenitors of the close double neutron stars, but their formation channel is basically the same. We saw furthermore that type Ia supernovae, which are of crucial importance for cosmology, are thermonuclear explosions of carbon-oxygen white dwarfs, which can only be triggered if this white dwarf is a member of a binary system. If anything, the astrophysical discoveries of the past decades have demonstrated the overwhelming importance of the evolution of binary systems for understanding the high energy and relativistic universe and for cosmology.

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Cross-References

 Close Binary Stellar Evolution and Supernovae  X-Ray Binaries  X-Ray Pulsars

References Bhattacharya D, van den Heuvel EPJ (1991) Formation and evolution of binary and millisecond radio pulsars. Phys Rep 203:1–124 Blaauw A (1961) On the origin of the O- and B-type stars with high velocities (the “run-away” stars), and some related problems. Bull Astron Inst Netherlands 15:265ff Branch D, Livio M, Yungelson LR, Boffa FR, Baron E (1995) In search of the progenitors of type Ia supernovae,. Publ Aston Soc Pacific 107:1019–1029 De Loore CWH, De Greve JP, van den Heuvel EPJ, De Cuyper JP (1974) The evolution of a massive close binary up to the X-ray binary stage. Mem Soc Astron Italiana (Proc IAU Reg Meeting, Trieste) 45:893ff Eggleton PP (1983) Approximations to the Radii of Roche Lobes, Astrophys J 268:368–369 Flannery BP, van den Heuvel EPJ (1975) On the origin of the binary pulsar PSR 1913 + 16. Astron Astrophys 39:61–67 Hillebrandt W, Niemeyer JC (2000) Type Ia supernova explosion models. Annu Rev Astron Astrophys 38:191–230 Howell AD (2011) Type Ia supernovae as stellar endpoints and cosmological tools. Nature Commun 2. Article nr. 350:1–26 Lorimer DR (2008) Binary and millisecond pulsars. Living Rev Relativ 11:8 Schreier E, Levinson R, Gursky H, Kellogg E, Tananbaum H, Giacconi R (1972) Evidence for the binary nature of centaurus X-3 from UHURU X-Ray observations. Astrophys J 172:L79–L83

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Tauris TM, van den Heuvel EPJ (2006) Formation and evolution of compact stellar X-ray sources. In: Lewin WHG, van der Klis M (eds) Compact stellar X-ray sources. Cambridge University Press, Cambridge, UK pp 623–665 Tutukov AV, Yungelson LR (1973) Evolution of massive close binaries. Nauchnye Informatsii 27:70–84 Van den Heuvel EPJ (1975) Modes of mass transfer and classes of binary X-ray sources. Astrophys J 198:L109–L112 Van den Heuvel EPJ (1994) Interacting binaries: topics in close binary evolution. In: Shore SN, Livio M, van den Heuvel EPJ Interacting binaries. Springer, Heidelberg, pp 263–474 Van den Heuvel EPJ (2009) The formation and evolution of relativistic binaries. In: Colpi M et al (eds) Physics of relativistic objects in compact binaries: from birth to coalescence. Astrophysics and space science library, vol 359. Springer, Dordrecht, The Netherlnads pp 125–198 Van den Heuvel EPJ, Heise J (1972) Centaurus X-3, possible reactivation of an old neutron star by mass exchange in a close binary. Nat Phys Sci 239:67–69 Van den Heuvel EPJ, De Loore C (1973) The nature of X-ray binaries III. Evolution of massive close binaries with one collapsed component – with a possible application to Cygnus X-3. Astron Astrophys 25:387–395 Van der Klis M (2000) Millisecond oscillations in X-ray binaries. Annu Rev Astron Astrophys 38:717–760 Webster L, Murdin P (1972) Cygnus X-1- a spectroscopic binary with a heavy companion? Nature 235:37–38

The Core-Collapse Supernova-Black Hole Connection

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Evan O’Connor

Abstract

The death of a massive star is typically associated with a bright optical transient known as a core-collapse supernova. However, there is growing evidence that not all massive stars end their lives with a brillant optical display, but rather in a whimper. These failed supernovae, or unnovae, result from the central engine failing to turn the initial implosion of the iron core into an explosion that launches the supernova shock wave, unbinds the majority of the star, and creates the supernova as we know it. In these unnovae, the failure of the central engine is soon followed by the collapse of the would-be neutron star into a stellar mass black hole. Instead of the bright optical display following successful supernovae, little to no optical emission is expected from typical failed supernovae as most of the material quietly accretes onto the black hole. This makes the hunt for failed supernovae difficult. In this chapter for the Handbook of Supernovae, I present the growing observational evidence for failed supernovae and discuss the current theoretical understanding of how and in what stars the supernova central engine fails.

Contents 1 2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Failed Supernovae: Observational Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Archival Searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Ongoing Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Future Observations: Neutrinos and Gravitational Waves . . . . . . . . . . . . . . . . . . The Theory of Black Hole Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Characteristics of CCSN Progenitor Models: Compactness . . . . . . . . . . . . . . . . 3.2 Trends with Compactness and the Impact on the Explosion Mechanism . . . . . .

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E. O’Connor () Department of Physics, North Carolina State University, Raleigh, NC, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_129

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3.3 Failed Supernovae: Evolution After Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Core-collapse supernovae (CCSNe) are bright optical transients that herald the explosive death of a massive star (i.e., stars with a zero-age main sequence (ZAMS) mass of MZAMS > 8  10 Mˇ ). However, not all massive stars end their lives in a bang, some will end their lives in a whimper. This chapter of the Handbook of Supernovae focuses on the latter. These so-called unnovae or failed supernovae herald the birth of a stellar mass black hole. Core collapse is triggered when the inert iron core, initially supported against gravity by electron degeneracy pressure, surpasses the effective Chandrasekhar mass, becomes unstable and collapses (hence core collapse). The collapse continues until the densities of the homologously collapsing object reach nuclear densities. At this point, the repulsive nature of the residual strong force at very short distances halts and subsequently reverses the collapse of the inner core, the so-called bounce phase. As the core rebounds, the outgoing pressure wave steepens into a shock front. Initially, the intense thermal pressure behind the shock drives it out into the still infalling iron core of the massive star. It is this shock wave, for successful CCSNe, that will eventually propagate throughout the entire star, unbinding the outer layers, giving rise to an optical supernova, and leaving behind a compact object remnant. However, the path to explosion is not so straightforward. Detailed investigations into these early phases of core collapse have shown that the supernova shock does not immediately lead to an explosion. Instead, soon after the shock forms, the ram pressure of the overlying material overcomes the thermal pressure of the material behind the shock and transitions the shock into a stalled accretion shock. The reduction in the post-shock pressure and the subsequent stalling of the shock are mainly attributed to energy losses from both the dissociation of the heavy nuclei entering the shock and the intense neutrino emission from the hot dense layers below the shock. The shock must be reenergized for the supernova to be successful. The energy needed to achieve this and ultimately the energy that powers the supernova explosion is sourced from the gravitational binding energy released when the iron core collapses. However, this energy is initially trapped in the internal and thermal energy of the matter. The mechanism for tapping this internal energy reservoir in an efficient manner in order to produce a successful explosion is the subject of intense study with the favored mechanism being the delayed neutrino mechanism. However, it is important to note that a successful explosion is not a foregone conclusion for every massive star that undergoes core collapse. As long as the shock is stalled, the protoneutron star (PNS) is continuing to accrete mass. Any mechanism for shock

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revival must act before the PNS has gained sufficient mass to cause it to collapse to a black hole. If the mechanism acts well before this point and accretion onto the PNS is halted, then, barring any significant fallback of material, the final compact remnant is expected to be a neutron star. However, if accretion cannot be stopped, eventually the PNS will exceed the maximum mass that can be supported by the nuclear equation of state. If this occurs the PNS will become gravitationally unstable and collapse to a black hole. The loss of pressure support from the PNS will cause the stalled shock to quickly fall into black hole. A normal CCSN with a bright optical transient is no longer possible, rather a failed supernova and the formation of a black hole is the result, an unnova. Due to the lack of explosively shocked and radioactively heated ejecta, failed supernovae are expected to be optically very dim and therefore difficult to detect observationally. In fact the first hints for a class of failed supernovae came from observations of successful supernovae and their progenitors. In this chapter we will review the connections between core collapse and black holes starting with current observational evidence of failed supernovae as well as several potential future observational probes of failed supernovae in Sect. 2. In Sect. 3 we will review the history and current state of our theoretical understanding of black hole formation in core collapse, including a review of the state-of-the-art predictions of what progenitor stars we think will lead to successful, failed, and fallback supernovae. We will also touch on several expected evolutionary paths of the failed supernova remnant following soon after black hole formation. In Sect. 4, we bring together the observational evidence and the current theory of failed supernovae and highlight the parallels.

2

Failed Supernovae: Observational Evidence

By far, successful core-collapse events are mainly discovered via the optical transient signal associated with the explosion. Given the typical lack of associated explosion, failed CCSNe are very hard to discover observationally. However, there is a budding amount of evidence, both direct and indirect, for the existence of a modest population of failed supernovae. Discovering and characterizing the failed supernova population is of the utmost importance to understanding the CCSNe– black hole connection as well as supplying the theoretical models (see Sect. 3) with observational evidence. The strongest indirect evidence for a population of failed supernovae is the presence of stellar mass black holes. These black holes have been observed in lowmass X-ray binaries within our galaxy and have estimated masses between 5 Mˇ and 10  15 Mˇ , while high-mass X-ray binaries can contain black holes with even higher masses (Özel et al. 2010). Additionally, the discovery of gravitational waves from black hole–black hole mergers by LIGO (Abbott et al. 2016a, b) is an evidence for stellar mass black holes with birth masses as high as 30 Mˇ .

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Archival Searches

An additional set of observations that could be considered as indirect evidence of a population of failed supernovae is the growing set of Type-IIP CCSNe with associated red supergiant progenitors stars identified in pre-explosion images, typically from archival images taken with the Hubble Space Telescope. Prototypical members of this family include SN 2003gd, SN 2005cs, and SN 2008bk (Smartt 2009). From these pre-explosion images, one can identify the progenitor star’s luminosity and effective temperature at the point of core collapse and then use stellar evolutionary tracks through the Hertzsprung–Russell diagram to assign a ZAMS mass to the progenitor star. This allows one to build up a mass-dependent population of Type-IIP CCSNe. As first presented in Kochanek et al. (2008) and extended and quantified more precisely in Smartt et al. (2009) and Smartt (2015), there appears to be a dearth of Type-IIP CCSNe with measured progenitor ZAMS masses in upper mass range expected for red supergiant stars (&18 Mˇ ). This has been dubbed the red supergiant problem (Smartt et al. 2009). The lack of CCSNe in this range is not easily explained by evolution to other supernova types and is consistent with these stars ending their lives as failed supernovae with no (or very dim) optical signatures (Smartt 2015). An alternative method for probing the population of successful CCSNe is presented in Jennings et al. (2012, 2014) and Williams et al. (2014). By age dating the environment around historic supernovae and supernova remnants, one can estimate the likely progenitor mass of the massive star responsible for the supernova or remnant. This technique also reveals a shortage of high-mass progenitors for successful CCSNe, suggesting a population of failed supernovae that do not produce supernova remnants or bright optical transients. Finally, we note that there is also suggestive indirect evidence for failed supernovae coming from the observation that the CCSN rate is roughly a factor of two smaller than the rate one would expect based on the star formation rate (Horiuchi et al. 2011).

2.2

Ongoing Surveys

In order to obtain more direct evidence of failed supernovae, one must locate the progenitor star of a failed supernova without the assistance of the typical bright optical supernova to pinpoint the location. This is the goal of the “Survey About Nothing” (Kochanek et al. 2008) which recently presented their first results in Gerke et al. (2015). Using the Large Binocular Telescope, 106 red supergiant stars are observed periodically in 27 nearby galaxies (d < 10 Mpc). Searches are done for transient objects including actual supernovae and bright (luminosities greater than 104 Lˇ ) objects which vanish over the course of the survey. The results in Gerke et al. (2015) include three successful CCSNe and one failed supernova candidate. The failed supernova candidate underwent a brief period of brightening in the optical in early 2009 before dropping below the original progenitor values.

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Recent follow-up observations, mainly with the Hubble Space Telescope (Adams et al. 2016), have confirmed that the progenitor star has indeed disappeared. This represents the first direct observation of a failed CCSN. Mass estimates of the red supergiant progenitor star place it in the mass range of 18  25 Mˇ (Gerke et al. 2015). This mass range is consistent with failed supernovae being the solution to the red supergiant problem mentioned above. The confirmation by Adams et al. (2016) of a failed supernova in the “Survey About Nothing” allows estimates to be placed on the fraction of core-collapse events that are expected to fail and not produce an optically bright transient. From Gerke et al. (2015), the fraction of core collapses that end in a failed supernova, to 90% confidence, is within the range of 0.07– 0.62, with a mean of 0:30. Inspired by the “Survey About Nothing,” Reynolds et al. (2015) use archival Hubble Space Telescope data and search for disappearing massive stars. Their results include one viable failed supernova candiate with a progenitor identification consistent with a 25  30 Mˇ yellow supergiant. Their discovery of one failed supernova in the data sample is consistent with the rates inferred from Gerke et al. (2015).

2.3

Future Observations: Neutrinos and Gravitational Waves

Our understanding of failed CCSNe stands to be improved in the future by several key observations. For over 30 years, neutrino detectors have been constantly monitoring the sky for bursts of astrophysical neutrinos but have not seen any corecollapse events (successful or failed) in the Milky Way galaxy (Adams et al. 2013; Alexeyev and Alexeyeva 2002; Ikeda et al. [Super-Kamiokande Collaboration] 2007). In current and future generations of neutrino detectors, all galactic and nearby extragalactic core-collapse events, regardless if they successfully explode or fail to explode, will shine brightly in neutrinos. The neutrino signal from a failed supernova is expected to be quite distinct from the signal of a successful supernova and will reveal crucial information about the inner workings of the CCSN central engine and explosion mechanism. Unfortunately, we may be waiting a while for such an exceptional event as the galactic rate of successful supernovae is estimated to be only 2  3 SN/century (Li et al. 2011). The rate of failed CCSNe is almost certainly lower. However, it is likely that a definitive observation of neutrinos from the diffuse supernova neutrino background will occur in the relatively near future with experiments such as SK-Gd (Xu and the Super-Kamiokande Collaboration 2016) and Hyper-K (Proto-Collaboraion et al. 2015). Due to the relatively highenergy neutrinos expected from failed CCSNe, an imprint of black hole formation may be discernable in the observed signal (Lunardini 2009). Finally, gravitational wave observations of merging black hole binaries (e.g., GW 150914 Abbott et al. 2016b and GW 151226 Abbott et al. 2016a), neutron star binaries, and black hole– neutron star binaries over the next few years will play a key role in deciphering the black hole population in the universe and better understanding the success/failure of the CCSN explosion mechanism.

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In summary, based on indirect and direct observational evidence, it is becoming increasing clear that failed CCSNe have a contributing role to play in the overall landscape of supernovae. Since they are optically dark, their presence is difficult to detect and understand, but nonetheless important to consider. In the following section, we will focus on the theoretical predictions for failed CCSNe, including estimates of the success or failure of the CCSN mechanism across a population of stars.

3

The Theory of Black Hole Formation

Some of the earliest work on black hole formation from core collapse was by May and White (1966). They followed the hydrodynamic evolution of spherically symmetric collapsing cores. Most notable from their work are their calculations of collapsing cold neutron cores. They considered various neutron star equations of state and initial core masses and show the impact of these on the final outcome, either a stable configuration or a collapse to a black hole. By today’s standards, these early simulations were very crude, and much work since then has been done improving the realism of the models that explore black hole formation by including refined neutrino transport methods, modern equations of state, and even multiple dimensions (Burrows 1988; Liebendörfer et al. 2004; Ott et al. 2011; Sumiyoshi et al. 2005; Wilson 1971; Yamada 1997). This work is, of course, in addition to the significant progress achieved in modeling the CCSN central engine in general (Arnett 1966; Bethe and Wilson 1985; Bruenn 1985; Bruenn et al. 2016; Buras et al. 2006; Burrows et al. 2000; Liebendörfer et al. 2001; Marek and Janka 2009; Mezzacappa and Bruenn 1993; Müller et al. 2012b; Rampp and Janka 2002). However, regardless of whether black hole formation is explicitly included in simulations or not, the theory of CCSNe has had a long-lasting and somewhat unwelcome relationship with black holes. Since the early days of simulating realistic models of core collapse, until very recently, most simulations of iron core collapse fail to produce successful explosions, in stark contrast to observations. In these models, the CCSN mechanism fails to reenergize the shock, mass accretion continues indefinitely, and, somewhat frustratingly, a black hole remnant is the eventual final state after enough mass has accreted onto the central object. Fortunately modern simulations that include state-of-the-art input physics are beginning to predict successful explosions, via the neutrino mechanism, and progress toward matching observations is occurring (Bruenn et al. 2016; Lentz et al. 2015; Müller 2015; Müller et al. 2012a, b). At the same time, the community is beginning to apply the knowledge gained from these successful simulations, as well as the observational constraints from SN 1987A, in order to make parameterized models of the CCSN central engine that can be used to make predictions on the success or failure of the CCSN mechanism across entire populations of progenitors. These efforts will be reviewed here.

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Characteristics of CCSN Progenitor Models: Compactness

Before delving into predictions of the success or failure of the CCSN mechanism across the range of progenitors, it is worthwhile to touch on the properties of the progenitor models themselves. The progenitors are crucial as they form the initial conditions for the core-collapse phase. Ultimately, differences in the progenitors are what is responsible for varying outcomes of core collapse. Across the range of ZAMS masses that form stable inert iron cores, (essentially 8  100 Mˇ ), one can expect a fair degree of variation in the innermost structure of the star near the point of core collapse. A demonstration of this variation is shown in Fig. 1, where we show density (upper left), temperature (upper right), electron fraction (lower left), and baryonic mass (lower right) profiles at the onset of core collapse (defined here as when the radial velocity near the edge of the iron core first reaches 1000 km/s). The models are from Woosley and Heger (2007) and range in ZAMS mass from 12 Mˇ to 120 Mˇ . For convenience, models are color coded by the compactness, 2:5 , as defined in O’Connor and Ott (2010). The compactness is a simple and straightforward way to parameterize progenitor models via a single parameter. It essentially represents a measure of the mass distribution, M D

M =Mˇ : R.Mbary D M /=1000 km

(1)

In low-compactness progenitors, the mass coordinate M (M D 2:5 Mˇ is taken here) is located at a large radius (>25,000 km for 2:5 < 0:1). High-compactness progenitors have the same mass coordinate M at a much lower radius ( 0:5). We note the very interesting fact that compactness does not necessarily scale with ZAMS mass. The five progenitor models in the Woosley and Heger (2007) model set with the highest compactness, in order of decreasing compactness are 40 Mˇ , 45 Mˇ , 23 Mˇ , 24 Mˇ , and 35 Mˇ . We refer the reader to Sukhbold and Woosley (2014) to learn how ZAMS mass, metallicity, mass loss rates, and other aspects of stellar evolution influences and sets the compactness of progenitors at the presupernova stage, including a discussion on the interesting non-monotonicity with ZAMS mass. In the following, we will mainly discuss how the compactness impacts the core-collapse evolution, the central engine, and the CCSN explosion mechanism. Progenitors that end their lives dense, cool, and electron deficient have correspondingly small effective Chandrasekhar masses. The higher densities give high electron chemical potentials which drive electron capture and reduce the electron degeneracy pressure available to support the degenerate core against gravitational collapse. For example, the 12 Mˇ progenitor (the most dense, second coolest, and most electron deficient; reddest in Fig. 1) has an iron core mass of 1:29 Mˇ at the point of collapse. These small iron cores have a steep density gradient outside of the iron core, and for a fixed mass, say 2:5 Mˇ , one has to go to a large radius in order to encompass it, 105 km. This model has the lowest compactness, 2:5  0:022. In contrast, the 40 Mˇ progenitor (least dense, hottest, and most electron rich; bluest in Fig. 1) has an iron core mass of 1:84 Mˇ . The increasing effective Chandrasekhar

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Fig. 1 Radial profiles of 32 core-collapse progenitors models from Woosley and Heger (2007) color coded by compactness (see Eq. 1). We show density (upper left), temperature (upper right), electron fraction (lower left), and baryonic mass (lower right) profiles. The stellar evolution calculations of Woosley and Heger (2007) stop when the edge of the iron core starts to collapse and reaches a radial velocity of 1000 km s1 . Mappings from compactness to ZAMS mass, other than for the 12 Mˇ and 40 Mˇ models, can be found in O’Connor and Ott (2011). Blue colors denote high-compactness models (like the 40 Mˇ model) where 2:5 Mˇ of material is enclosed within a comparatively small radius. Conversely, red colors denote low compactness, one must go to very large radii in order to enclose 2:5 Mˇ of material. High-compactness progenitors are also characterized by relatively hot, low-density, and electron-rich matter conditions compared to lower-compactness progenitors eff

mass (MCh ) with progenitor compactness comes from both the higher electron eff eff fraction (MCh / Ye2 ) and higher entropy (MCh / 1 C Œs=. Ye /2 ) (Woosley et al. 2002). This also gives results in a much shallower density gradient outside of the iron core. The baryonic mass coordinate of 2:5 Mˇ is located at a radius of 4200 km. This model has the highest compactness, 2:5  0:598. For reference, the progenitor with the highest ZAMS mass, 120 Mˇ , has a relatively low compactness, 2:5 D 0:172. In this model, it is due to the high mass loss rates experienced during the hydrogen and helium burning phases which significantly reduced the mass of the star and drastically influenced the advanced burning stages. In general, massive star mass loss rates, particularly for stars with a ZAMS mass &30  40 Mˇ , pose a challenge for predicting the presupernova structure because of this very strong influence on the final structure. A mere factor of 2–4 reduction in the

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mass loss rate assumed in models of stellar evolution can give drastically different presupernova structures (Limongi and Chieffi 2009). Such an uncertainty in the rate is not inconceivable and perhaps warranted (Smith 2014).

3.2

Trends with Compactness and the Impact on the Explosion Mechanism

For a sequence of models with increasing compactness, we note the following observations. As the collapsing core reaches nuclear densities, the infalling matter outside of the homologous core is supersonic and essentially in free fall. The free fall time of a specific mass coordinate is shorter in higher-compactness models because M D2:5 Mˇ that mass coordinate begins its free fall from a much lower radius (tff  0:24.2:5 /3=2 s). This leads to high mass accretion rates in high-compactness progenitors, with the obvious consequence being that the PNSs formed in highcompactness models accumulate mass at a higher rate (O’Connor and Ott 2011). Additionally, a side effect of the higher mass accretion rate is that more gravitational binding energy is being released, both because more matter is accreting and because the gravitating mass is larger. As a result, more thermal energy is available to be radiated in neutrinos. High-compactness models can have neutrino luminosities (mainly electron neutrinos and antineutrinos) that are several factors higher than low-compactness models (O’Connor and Ott 2013). Higher matter temperatures in the PNSs formed from high-compactness models also give modestly higher neutrino average energies. These two main consequences of increasing compactness (higher mass accretion rates and higher neutrino luminosities and energies) have ramifications for the neutrino mechanism and in particular its success or failure. To demonstrate the role of compactness in the neutrino mechanism, let us first review the mechanism itself. The neutrino mechanism is currently the favored mechanism for shock revival and has been shown to work recently in a growing number of cases (Bruenn et al. 2016; Lentz et al. 2015; Marek and Janka 2009; Müller et al. 2012a, b; Suwa et al. 2010). Neutrinos are at the heart of the neutrino mechanism. They are copiously emitted from the hot, dense matter of the PNS. As the neutrinos stream away from the PNS (from a typical radius of 50  80 km), the surrounding density and temperature drop, and the neutrinos thermodynamically decouple from matter. However, there can still be some lingering interactions of the neutrinos with the matter in these cooler, lower-density regions, predominately via charged-current absorption of electron-type neutrino and antineutrinos onto neutrons and protons, respectively. These interactions result in a net transfer of energy from the neutrino field to the matter and cause local heating in the matter behind the shock front, from 100 to 200 km. The heating increases the thermal pressure of the matter behind the shock. Equally important, this heating drives hydrodynamic instabilities like convection and turbulence. The added thermal and turbulent pressures are the basis for the neutrino mechanism. If large enough, they can overcome the ram pressure of the infalling material and reenergize the stalled accretion shock, launching an explosion.

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From this description one can see how intimately the concept of compactness relates to the neutrino mechanism. For the neutrino mechanism to be successful, one generally wants to increase the total net heating performed by neutrinos in the post-shock region. Progenitors with increasing compactness have higher neutrino luminosities and modestly higher neutrino energies; as a result, the total net neutrino heating increases with progenitor compactness, encouraging shock revival. However, the higher mass accretion rate in progenitors with high compactness gives a higher ram pressure of the material outside of the supernova shock. This inhibits shock revival. Unfortunately, the relationship between compactness (or other similar characterizations of the progenitor structure) and the success or failure of the neutrino mechanism is not straightforward. There have been several studies examining the success or failure of the neutrino mechanism in relation to a large set of progenitors via simulations (Ertl et al. 2016; Fryer 1999; Nakamura et al. 2015; O’Connor and Ott 2011; Pejcha and Thompson 2015; Sukhbold et al. 2016; Ugliano et al. 2012) and via semi-analytic models (Müller et al. 2016; Pejcha and Thompson 2015). The results are illuminating. Most studies are performed with parameterized, spherically symmetric models, with the exception of Fryer (1999) and Nakamura et al. (2015) who use axisymmetric models. We briefly review the main findings of these studies, focusing on their conclusions regarding the success or failure of the neutrino mechanism: 1. Fryer (1999): One of the first efforts to explore the success or failure of the CCSN mechanism across a range of progenitor models was done in here. A limited set of three progenitor models from Woosley and Weaver (1995) were simulated in axisymmetry with ZAMS masses of 15 Mˇ , 25 Mˇ , and 40 Mˇ . The conclusions reached were essentially the following. For progenitors with a ZAMS mass more than 40 Mˇ , the shock will fail to be reenergized, and a black hole will form soon after bounce. For progenitors with a ZAMS mass between 20 Mˇ and 40 Mˇ , the shock will be reenergized, but the binding energy of the envelope will cause significant fallback, resulting in fallback black hole formation in the minutes to hours after the explosion. For stars with a ZAMS mass less than 20 Mˇ , the outcome will be a successful explosion with a neutron star remnant. However, as we shall see below, this simple picture has changed quite a bit since publication of Fryer (1999). More extensive examination of the progenitor dependence of the neutrino mechanism has been carried out and has revealed the picture is much more complex. 2. O’Connor and Ott (2011): This study’s aim was to address black hole formation in failing CCSNe, although parameterized explosion models addressing the success and failure of the neutrino mechanism were also examined. For a wide range of progenitors and nuclear equations of state, the authors systematically increased the amount of neutrino heating until an explosion was obtained. They then reported the heating efficiency (the fraction of the neutrino luminosity that is absorbed into the gain region via neutrino heating) and made the observation that

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progenitors with large compactness (they chose 2:5 > 0:45) require increasingly larger heating efficiencies in order to obtain an explosion. The explanation was that any explosion in these models must occur soon after core bounce in order to thwart black hole formation (for reference, for a nuclear equation of state with a maximum mass of 2 Mˇ , a progenitor with a compactness of 2:5 D 0:6 will collapse to a black hole after only 500 ms of accretion; O’Connor and Ott 2011). The neutrino heating must be very high in order to launch an explosion in these models early on because of the intense mass accretion rates. In lower-compactness models, one can wait to later times when the accretion rate is lower to launch an explosion. From this study it is clear that very-highcompactness models are likely to lead to a failed supernova and the formation of a black hole soon after core bounce. In the solar metallicity progenitor series from Woosley and Heger (2007), this lead to a conservative prediction of failed supernovae around ZAMS masses of 40 Mˇ and 45 Mˇ as well as around 23 Mˇ , totaling 4% of all expected core collapses from solar metallicity stars. In lower-metallicity stars, where mass loss is expected to be substantially less, one expects significantly more massive stars to end their lives with high compactness and therefore lead to failed supernovae. According to the work of O’Connor and Ott (2011), low-metallicity environments should have at least a 15% failed supernova fraction, including all stars above 30 Mˇ . 3. Ugliano et al. (2012): In a step beyond O’Connor and Ott (2011), this work calibrated a spherically symmetric, parameterized explosion model to the observed properties of SN 1987A: explosion energy, nickel yield, and neutrino emission. They then applied this calibration to a large set of solar metallicity progenitors from Woosley et al. (2002). In terms of compactness, they find that progenitors with 2:5 > 0:35 fail to explode and progenitors with 2:5 < 0:15 are successful. For progenitors with compactness in the range of 0:15 < 2:5 < 0:35, they find both successful and unsuccessful explosions resulting in both neutron star and black hole remnants. It is interesting to note that Ugliano et al. (2012) predict failed supernovae from ZAMS masses as low as 15:2 Mˇ and, like O’Connor and Ott (2011), also find strong evidence for an island of black hole formation between 20 Mˇ and 25 Mˇ . They also make detailed predictions of the final remnant masses, nickel yields, and fallback masses. The latter is estimated to be small and unlikely to lead to fallback black holes except in borderline cases. The only example from their work is a 37 Mˇ progenitor that explodes but has 4:5 Mˇ of fallback. 4. Pejcha and Thompson (2015): In this semi-analytic work, the authors create a parameterization based on the idea that runaway shock expansion, and hence explosions, are triggered when the neutrino luminosity obtains a critical value (Burrows and Goshy 1993; Pejcha and Thompson 2012). The critical luminosity is determined via Pejcha and Thompson (2012) but is tunable in order to obtain explosions in spherical symmetry. They compare key predictions of their model to observations. These include the neutron star and black hole mass distributions

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mean value and width, nickel mass, and explosion energy. They find similar distributions of success/failure as Ugliano et al. (2012). A key conclusion of their work is the inference that, based on the observed mean neutron star mass (1:33 Mˇ ; Pejcha et al. 2012), at least 35% of all core-collapse events must successfully explode. 5. Ertl et al. (2016) and Sukhbold et al. (2016): One conclusion of the work of Ugliano et al. (2012) was that a single parameter could not be used to characterize the success or failure of the neutrino mechanism. In Ertl et al. (2016) and Sukhbold et al. (2016), the authors search for a two-parameter family that better predicts the outcome of the neutrino mechanism. Noting that most of their explosions (they use the same procedure as Ugliano et al. 2012) are launched close to the time when the s D 4 entropy surface accretes through the shock, they chose for their two parameters (1) the mass enclosed by the s D 4 entropy surface and (2) the enclosed mass gradient at this location. With these two parameters, they find that they can create a criterion in order to predict the success or failure of 98–99% of the considered models. 6. Nakamura et al. (2015): Most of the above studies used parameterized/calibrated spherically symmetric models in their determination of the success or failure of the neutrino mechanism. Ultimately, self-consistent explosion models must be used to determine the success or failure of the CCSN explosion mechanism as multidimensional effects in both the progenitor models and the central engine itself, like convection and turbulence, may impact the explosion mechanism in ways other than can be parameterized in spherical symmetry. In Nakamura et al. (2015), the first attempt to systematically study the neutrino-driven explosion mechanism in axisymmetry was carried out. They performed simulations using the IDSA neutrino transport method (Liebendörfer et al. 2009) across a large range of progenitors. Their simulations used Newtonian gravity, so they were unable to make strong claims regarding black hole formation. They found that properties of the neutrino-driven explosion, such as nickel yield and explosion energy, show trends with the progenitor compactness. 7. Müller et al. (2016): In an improvement to the previous semi-analytic work, Müller et al. (2016) tuned their model to multidimensional simulations. A key advancement is the incorporation of simultaneous downflows and outflows, which is forbidden in spherical symmetry but can naturally occur in three dimensions. This allows for continued accretion of fuel that can be used to drive neutrino heating and help further develop the explosion. The predictions from this study are largely consistent with observations of CCSN explosion properties, although much work remains to be done. These collective results, while not necessarily in agreement for all progenitors, represent our current best prediction of what progenitor models will give successful explosions and what models will evolve to failed supernovae. Further efforts require self-consistent, state-of-the-art, multidimensional simulations of a suite of progenitor models.

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Failed Supernovae: Evolution After Failure

For situations where the CCSN mechanism fails and a black hole will form, the evolution of the system until black hole formation is fairly straightforward. Accretion will continue until the PNS has gained enough mass to cause it to become unstable to collapse to a black hole. The mass at which this occurs mainly depends on the nuclear equation of state, but thermal contributions to the equation of state can provide extra support, at least over short time scales, raising the maximum gravitational mass above the cold neutron star value by up to 20%. This is most prominent for high-compactness stars which cannot efficiently radiate the thermal energy in neutrinos (Hempel et al. 2012; O’Connor and Ott 2011). Regardless of the equation of state, the black hole birth gravitational mass is likely in the range of 2 Mˇ –3 Mˇ . The black hole is expected to form within the first second for highcompactness (2:5 > 0:5) progenitors and likely within 10 s for lower-compactness (2:5  0:15) progenitors (O’Connor and Ott 2011). After black hole formation, the stalled supernova shock will quickly be accreted by the black hole. Accretion of the remainder of the star will continue. If the material has sufficient angular momentum to form a disk, it can stop accretion onto the black hole. Such cases are referred to as collapsars. Type-I and Type-II collapsars are proposed progenitors of long gamma-ray bursts (MacFadyen and Woosley 1999; MacFadyen et al. 2001; Woosley 1993). However, stellar evolution theory suggests that retaining enough angular momentum to allow for the timely formation of a collapsar disk around a black hole formed in a failed supernova is difficult, especially given that the high amounts of angular momentum needed are expected to give rise to CCSN explosions via the magneto-rotational explosion mechanism (Dessart et al. 2008, 2012). In any case, Type-I and Type-II collapsars need only to occur in a small fraction of core-collapse events as the long gamma-ray burst rate is significantly smaller than the CCSN rate and likely smaller than the failed supernova rate. Perhaps a more common outcome of failed supernovae are Type-III collapsars (Woosley and Heger 2012). This type of collapsar is characterized by progenitor stars with sufficient angular momentum in the outermost layers to form an accretion disk around a central black hole at late times. The expected electromagnetic signal is a very-long-duration gamma-ray transient (Woosley and Heger 2012). Even in the absence of rotation, failed supernovae could power an electromagnetic transient. Reviving an idea from Nadezhin (1980) and Lovegrove and Woosley (2013) has shown that the, essentially instantaneous, gravitational mass loss from neutrino emission prior to black hole formation (which could be as large as 0:5 Mˇ depending on the nuclear equation of state and the black hole formation time) in a failed supernova can be enough to excite a hydrodynamic response in the mantle of the star and launch a shock that may unbind the outermost layers of the progenitor star (i.e., the hydrogen shell). This is expected to lead to a slow (100 km s1 ), low luminosity (1039 erg s1 ) optical/infrared transient (Lovegrove and Woosley 2013) that lasts of order a year. This long-duration signal would be preceeded by a shock breakout phase lasting 3–10 days with a brighter luminosity (104041 erg s1 ) and slightly faster speeds (200 km s1 ) (Piro 2013).

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Conclusions

In this chapter we explored the connection between CCSNe and black holes. There is ever-increasing evidence, on both the observational and theoretical side, that failed, black hole-producing supernovae make up an appreciable fraction of corecollapse events. Observations seem to suggest, based on missing Type-IIP supernovae, that a population of failed supernovae exist in the upper mass range predicted for red supergiant stars (with M & 18 Mˇ ) (Kochanek et al. 2008; Smartt 2015; Smartt et al. 2009). Complementary to this is the discovery of a failed supernova candidate, via the disappearance of a massive red supergiant star, with a mass of 25 Mˇ (Adams et al. 2016; Gerke et al. 2015). Additionally, there is evidence for another failed supernova from the disappearance of a 25–30 Mˇ yellow supergiant (Reynolds et al. 2015). These observations are consistent with our current understanding of stellar evolution and core-collapse theory that suggest progenitor stars with ZAMS masses around 20–25 Mˇ have a density structure that favors failure of the CCSN explosion mechanism and the formation of black holes (O’Connor and Ott 2011; Ugliano et al. 2012). Observational estimates place the failed supernova fraction between 0.07 and 0.62, with 90% confidence (Gerke et al. 2015); this is certain to improve with time. Once again, theory seems to agree with observations; estimates of the failed supernova fraction are consistent with this observation. For a population of solar metallicity stars, this can be as high as 20% (Ugliano et al. 2012). Theory also predicts failed supernovae for more massive stars (MZAMS > 30  40 Mˇ ), especially in low-metallicity environments. Given the rarity of these stars, direct observations of these failed supernovae will be more difficult. However, recent and near-future gravitational wave observations of merging stellar mass black holes (e.g., GW 150914, GW 151226, and soon to be many more; Abbott et al. 2016a, b) will likely be able to place interesting indirect constraints on failed supernovae, especially for progenitor stars in the upper mass range and at lower metallicity. Future observations of neutrinos, either from a galactic supernova, a galactic failed supernova, or a measurement of the diffuse supernova neutrino background, will provide invaluable data for refining our understand of black holes and the connection to their birth sites, CCSNe.

5

Cross-References

 Diffuse Neutrino Flux from Supernovae  Explosion Physics of Core-Collapse Supernovae  Gravitational Waves from Core-Collapse Supernovae  Neutrino-Driven Explosions  Neutrino Emission from Supernovae  Neutrinos from Core-Collapse Supernovae and Their Detection  Neutron Star Matter Equation of State  Supernova Progenitors Observed with HST  Supernovae from Massive Stars

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Acknowledgements Support for this work was provided by NASA through Hubble Fellowship grant #51344.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555.

References Abbott BP, Abbott R, Abbott TD, Abernathy MR, Acernese F, Ackley K, Adams C, Adams T, Addesso P, Adhikari RX et al (2016a) GW151226: observation of gravitational waves from a 22Solar-Mass binary black hole coalescence. Phys Rev Lett 116(24):241103. doi:10.1103/PhysRevLett.116.241103. 1606.04855 Abbott BP, Abbott R, Abbott TD, Abernathy MR, Acernese F, Ackley K, Adams C, Adams T, Addesso P, Adhikari RX et al (2016b) Observation of gravitational waves from a binary black hole merger. Phys Rev Lett 116(6):061102. doi:10.1103/PhysRevLett.116.061102. 1602.03837 Adams SM, Kochanek CS, Beacom JF, Vagins MR, Stanek KZ (2013) Observing the next galactic supernova. Astrophys J 778:164. doi:10.1088/0004-637X/778/2/164. 1306.0559 Adams SM, Kochanek CS, Gerke JR, Stanek KZ, Dai X (2016) The search for failed supernovae with the Large Binocular Telescope: confirmation of a disappearing star. ArXiv e-prints 1609.01283 Alexeyev EN, Alexeyeva LN (2002) Twenty years of Galactic observations in searching for bursts of collapse neutrinos with the Baksan underground scintillation telescope. Sov J Exp Theor Phys 95:5–10. doi:10.1134/1.1499896. astro-ph/0212499 Arnett WD (1966) Gravitational collapse and weak interactions. Can J Phys 44:2553 Bethe HA, Wilson JR (1985) Revival of a stalled supernova shock by neutrino heating. Astrophys J 295:14. doi:10.1086/163343 Bruenn SW (1985) Stellar core collapse – numerical model and infall epoch. Astrophys J Suppl 58:771 Bruenn SW, Lentz EJ, Hix WR, Mezzacappa A, Harris JA, Messer OEB, Endeve E, Blondin JM, Chertkow MA, Lingerfelt EJ, Marronetti P, Yakunin KN (2016) The development of explosions in axisymmetric ab initio core-collapse supernova simulations of 12–25 M stars. Astrophys J 818:123. doi:10.3847/0004-637X/818/2/123. 1409.5779 Buras R, Janka HT, Rampp M, Kifonidis K (2006) Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. II. Models for different progenitor stars. Astron Astrophys 457:281 Burrows A (1988) Supernova neutrinos. Astrophys J 334:891 Burrows A, Goshy J (1993) A theory of supernova explosions. Astrophys J Lett 416:L75. doi:10.1086/187074 Burrows A, Young T, Pinto P, Eastman R, Thompson TA (2000) A new algorithm for supernova neutrino transport and some applications. Astrophys J 539:865. arXiv:astro-ph/9905132 Dessart L, Burrows A, Livne E, Ott CD (2008) The Proto-Neutron star phase of the collapsar model and the route to long-soft gamma-ray bursts and hypernovae. Astrophys J Lett 673:L43 Dessart L, O’Connor E, Ott CD (2012) The Arduous journey to black hole formation in potential gamma-ray burst progenitors. Astrophys J 754:776. doi:10.1088/0004-637X/754/1/76. 1203.1926 Ertl T, Janka HT, Woosley SE, Sukhbold T, Ugliano M (2016) A two-parameter criterion for classifying the explodability of massive stars by the Neutrino-driven mechanism. Astrophys J 818:124. doi:10.3847/0004-637X/818/2/124. 1503.07522 Fryer CL (1999) Mass limits for black hole formation. Astrophys J 522:413 Gerke JR, Kochanek CS, Stanek KZ (2015) The search for failed supernovae with the Large Binocular Telescope: first candidates. MNRAS 450:3289–3305. doi:10.1093/mnras/stv776. 1411.1761 Hempel M, Fischer T, Schaffner-Bielich J, Liebendörfer M (2012) New equations of state in simulations of core-collapse supernovae. Astrophys J 748:770. doi:10.1088/0004-637X/748/1/70. 1108.0848

1570

E. O’Connor

Horiuchi S, Beacom JF, Kochanek CS, Prieto JL, Stanek KZ, Thompson TA (2011) The cosmic core-collapse supernova rate does not match the massive-star formation rate. Astrophys J 738:154. doi:10.1088/0004-637X/738/2/154. 1102.1977 Ikeda et al [Super-Kamiokande Collaboration] M (2007) Search for supernova Neutrino bursts at Super-Kamiokande. Astrophys J 669:519. doi:10.1086/521547 Jennings ZG, Williams BF, Murphy JW, Dalcanton JJ, Gilbert KM, Dolphin AE, Fouesneau M, Weisz DR (2012) Supernova remnant progenitor masses in M31. Astrophys J 761:26. doi:10.1088/0004-637X/761/1/26. 1210.6353 Jennings ZG, Williams BF, Murphy JW, Dalcanton JJ, Gilbert KM, Dolphin AE, Weisz DR, Fouesneau M (2014) The supernova progenitor mass distributions of M31 and M33: further evidence for an upper mass limit. Astrophys J 795:170. doi:10.1088/0004-637X/795/2/170. 1410.0018 Kochanek CS, Beacom JF, Kistler MD, Prieto JL, Stanek KZ, Thompson TA, Yüksel H (2008) A survey about nothing: monitoring a million supergiants for failed supernovae. Astrophys J 684:1336 Lentz EJ, Bruenn SW, Hix WR, Mezzacappa A, Messer OEB, Endeve E, Blondin JM, Harris JA, Marronetti P, Yakunin KN (2015) Three-dimensional core-collapse supernova simulated using a 15 Mˇ progenitor. Astrophys J Lett 807:L31. doi:10.1088/2041-8205/807/2/L31. 1505.05110 Li W, Chornock R, Leaman J, Filippenko AV, Poznanski D, Wang X, Ganeshalingam M, Mannucci F (2011) Nearby supernova rates from the Lick Observatory supernova search – III. The ratesize relation, and the rates as a function of galaxy Hubble type and colour. MNRAS 412:1473. doi:10.1111/j.1365-2966.2011.18162.x. 1006.4613 Liebendörfer M, Mezzacappa A, Thielemann F (2001) Conservative general relativistic radiation hydrodynamics in spherical symmetry and comoving coordinates. Phys Rev D 63:104,003 Liebendörfer M, Messer OEB, Mezzacappa A, Bruenn SW, Cardall CY, Thielemann FK (2004) A finite difference representation of Neutrino radiation hydrodynamics in spherically symmetric general relativistic spacetime. Astrophys J Supp 150:263 Liebendörfer M, Whitehouse SC, Fischer T (2009) The isotropic diffusion source approximation for supernova neutrino transport. Astrophys J 698:1174 Limongi M, Chieffi A (2009) Presupernova evolution and explosion of massive stars: the role of mass loss during the Wolf-Rayet stage. Mem Soc Ast Ital 80:151 Lovegrove E, Woosley SE (2013) Very low energy supernovae from neutrino mass loss. Astrophys J 769:109. 1303.5055 Lunardini C (2009) Diffuse neutrino flux from failed supernovae. Phys Rev Lett 102(23):231101. doi:10.1103/PhysRevLett.102.231101. 0901.0568 MacFadyen AI, Woosley SE (1999) Collapsars: gamma-ray bursts and explosions in “Failed Supernovae”. Astrophys J 524:262 MacFadyen AI, Woosley SE, Heger A (2001) Supernovae, jets, and collapsars. Astrophys J 550:410. arXiv:astro-ph/9910034 Marek A, Janka HT (2009) Delayed neutrino-driven supernova explosions aided by the standing accretion-shock instability. Astrophys J 694:664. doi:10.1088/0004-637X/694/1/664 May MM, White RH (1966) Hydrodynamic calculations of general-relativistic collapse. Phys Rev 141:1232 Mezzacappa A, Bruenn SW (1993) Type II supernovae and Boltzmann neutrino transport – the infall phase. Astrophys J 405:637. doi:10.1086/172394 Müller B (2015) The dynamics of neutrino-driven supernova explosions after shock revival in 2D and 3D. MNRAS 453:287–310. doi:10.1093/mnras/stv1611. 1506.05139 Müller B, Janka HT, Heger A (2012a) New two-dimensional models of supernova explosions by the neutrino-heating mechanism: evidence for different instability regimes in collapsing stellar cores. Astrophys J 761:72. doi:10.1088/0004-637X/761/1/72. 1205.7078 Müller B, Janka HT, Marek A (2012b) A new multi-dimensional general relativistic neutrino hydrodynamics code for core-collapse supernovae. II. Relativistic explosion models of corecollapse supernovae. Astrophys J 756:84. doi:10.1088/0004-637X/756/1/84. 1202.0815

58 The Core-Collapse Supernova-Black Hole Connection

1571

Müller B, Heger A, Liptai D, Cameron JB (2016) A simple approach to the supernova progenitorexplosion connection. MNRAS 460:742–764. doi:10.1093/mnras/stw1083. 1602.05956 Nadezhin DK (1980) Some secondary indications of gravitational collapse. Astrophys Space Sci 69:115–125. doi:10.1007/BF00638971 Nakamura K, Takiwaki T, Kuroda T, Kotake K (2015) Systematic features of axisymmetric neutrino-driven core-collapse supernova models in multiple progenitors. Publ Astron Soc Jpn. doi:10.1093/pasj/psv073. 1406.2415 O’Connor E, Ott CD (2010) A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes. Class Quantum Grav 27(11):114103. doi:10.1088/0264-9381/27/11/114103. 0912.2393 O’Connor E, Ott CD (2011) Black hole formation in failing core-collapse supernovae. Astrophys J 730:70 O’Connor E, Ott CD (2013) The progenitor dependence of the pre-explosion neutrino emission in core-collapse supernovae. Astrophys J 762:126. doi:10.1088/0004-637X/762/2/126. 1207.1100 Ott CD, Reisswig C, Schnetter E, O’Connor E, Sperhake U, Löffler F, Diener P, Abdikamalov E, Hawke I, Burrows A (2011) Dynamics and gravitational wave signature of collapsar formation. Phys Rev Lett 106:161,103 Özel F, Psaltis D, Narayan R, McClintock JE (2010) The black hole mass distribution in the galaxy. Astrophys J 725:1918–1927. doi:10.1088/0004-637X/725/2/1918. 1006.2834 Pejcha O, Thompson TA (2012) The physics of the neutrino mechanism of core-collapse supernovae. Astrophys J 746:106. doi:10.1088/0004-637X/746/1/106. 1103.4864 Pejcha O, Thompson TA (2015) The landscape of the Neutrino mechanism of core-collapse supernovae: neutron star and black hole mass functions, explosion energies, and nickel yields. Astrophys J 801:90. doi:10.1088/0004-637X/801/2/90. 1409.0540 Pejcha O, Thompson TA, Kochanek CS (2012) The observed neutron star mass distribution as a probe of the supernova explosion mechanism. MNRAS 424:1570–1583. doi:10.1111/j.1365-2966.2012.21369.x. 1204.5478 Piro AL (2013) Taking the “Un” out of “Unnovae”. Astrophys. J Lett 768:L14. doi:10.1088/2041-8205/768/1/L14. 1304.1539 Proto-Collaboraion HK: Abe K, Aihara H, Andreopoulos C, Anghel I, Ariga A, Ariga T, Asfandiyarov R, Askins M et al (2015) Physics potential of a long baseline neutrino oscillation experiment using J-PARC neutrino beam and hyper-kamiokande. Prog Theor Exp Phys 053C02. doi:10.1093/ptep/ptv061. 1502.05199 Rampp M, Janka HT (2002) Radiation hydrodynamics with neutrinos. Variable Eddington factor method for core-collapse supernova simulations. Astron Astrophys 396:361–392. doi:10.1051/0004-6361:20021398. astro-ph/0203101 Reynolds TM, Fraser M, Gilmore G (2015) Gone without a bang: an archival HST survey for disappearing massive stars. MNRAS 453:2885–2900. doi:10.1093/mnras/stv1809. 1507.05823 Smartt SJ (2009) Progenitors of core-collapse supernovae. ARA&A 47:63. doi:10.1146/annurev-astro-082708-101737 Smartt SJ (2015) Observational constraints on the progenitors of core-collapse supernovae: the case for missing high-mass stars. PASA 32:e016. doi:10.1017/pasa.2015.17. 1504.02635 Smartt SJ, Eldridge JJ, Crockett RM, Maund JR (2009) The death of massive stars – I. Observational constraints on the progenitors of Type II-P supernovae. MNRAS 395:1409. 0809.0403 Smith N (2014) Mass loss: its effect on the evolution and fate of high-mass stars. ARA&A 52: 487–528. doi:10.1146/annurev-astro-081913-040025. 1402.1237 Sukhbold T, Woosley SE (2014) The compactness of presupernova stellar cores. Astrophys J 783:10. doi:10.1088/0004-637X/783/1/10. 1311.6546 Sukhbold T, Ertl T, Woosley SE, Brown JM, Janka HT (2016) Core-collapse supernovae from 9 to 120 solar masses based on neutrino-powered explosions. Astrophys J 821:38. doi:10.3847/0004-637X/821/1/38. 1510.04643

1572

E. O’Connor

Sumiyoshi K, Yamada S, Suzuki H, Shen H, Chiba S, Toki H (2005) Postbounce evolution of core-collapse supernovae: long-term effects of the equation of state. Astrophys J 629:922 Suwa Y, Kotake K, Takiwaki T, Whitehouse SC, Liebendörfer M, Sato K (2010) Explosion geometry of a rotating 13 Mˇ star driven by the SASI-aided neutrino-heating supernova mechanism. Publ Astron Soc Jpn 62:L49 Ugliano M, Janka HT, Marek A, Arcones A (2012) Progenitor-explosion connection and remnant birth masses for neutrino-driven supernovae of iron-core progenitors. Astrophys J 757:69. doi:10.1088/0004-637X/757/1/69. 1205.3657 Williams BF, Peterson S, Murphy J, Gilbert K, Dalcanton JJ, Dolphin AE, Jennings ZG (2014) Constraints for the progenitor masses of 17 historic core-collapse supernovae. Astrophys J 791:105. doi:10.1088/0004-637X/791/2/105. 1405.6626 Wilson JR (1971) A numerical study of gravitational stellar collapse. Astrophys J 163:209 Woosley SE (1993) Gamma-ray bursts from stellar mass accretion disks around black holes. Astrophys J 405:273 Woosley SE, Heger A (2007) Nucleosynthesis and remnants in massive stars of solar metallicity. Phys Rep 442:269. arXiv:astro-ph/0702176 Woosley SE, Heger A (2012) Long gamma-ray transients from collapsars. Astrophys J 752:32. doi:10.1088/0004-637X/752/1/32. 1110.3842 Woosley SE, Weaver TA (1995) The evolution and explosion of massive stars. II. Explosive hydrodynamics and nucleosynthesis. Astrophys J Suppl 101:181 Woosley SE, Heger A, Weaver TA (2002) The evolution and explosion of massive stars. Rev Mod Phys 74:1015 Xu C, The Super-Kamiokande Collaboration (2016) Current status of SK-Gd project and EGADS. J Phys Conf Ser 718(6):062070. doi:10.1088/1742-6596/718/6/062070 Yamada S (1997) An implicit Lagrangian code for spherically symmetric general relativistic hydrodynamics with an approximate Riemann Solver. Astrophys J 475:720

Part VIII Neutrinos, Gravitational Waves, and Cosmic Rays

Neutrino Emission from Supernovae

59

Hans-Thomas Janka

Abstract

Supernovae are the most powerful cosmic sources of MeV neutrinos. These elementary particles play a crucial role when the evolution of a massive star is terminated by the collapse of its core to a neutron star or a black hole and the star explodes as supernova. The release of electron neutrinos, which are abundantly produced by electron captures, accelerates the catastrophic infall and causes a gradual neutronization of the stellar plasma by converting protons to neutrons as dominant constituents of neutron star matter. The emission of neutrinos and antineutrinos of all flavors carries away the gravitational binding energy of the compact remnant and drives its evolution from the hot initial to the cold final state. The absorption of electron neutrinos and antineutrinos in the surroundings of the newly formed neutron star can power the supernova explosion and determines the conditions in the innermost supernova ejecta, making them an interesting site for the nucleosynthesis of iron-group elements and trans-iron nuclei. In this chapter the basic neutrino physics in supernova cores and nascent neutron stars will be discussed. This includes the most relevant neutrino production, absorption, and scattering processes, elementary aspects of neutrino transport in dense environments, the characteristic neutrino-emission phases with their typical signal features, and the perspectives connected to a measurement of the neutrino signal from a future galactic supernova.

H.-T. Janka () Max Planck Institute for Astrophysics, Garching, Germany e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_4

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Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neutrino Production and Propagation in Supernova Cores . . . . . . . . . . . . . . . . . . . . . . . 2.1 Basic Weak Interaction Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Neutrino Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Flavor-Dependent Neutrino Decoupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Neutrino Emission Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Neutrino Emission Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Shock-Breakout Burst of Electron Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Post-Bounce Accretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Kelvin-Helmholtz Cooling and Deleptonization of the Proto-neutron Star . . . . 4.4 Spectral Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1576 1577 1578 1583 1585 1587 1593 1593 1594 1597 1597 1599 1601 1601

Introduction

The paramount importance of neutrinos in the context of stellar core collapse and the question how massive stars achieve to produce supernova (SN) explosions was first pointed out in seminal papers by Colgate and White (1966) and Arnett (1966). They recognized that the huge gravitational binding energy of a neutron star is carried away by neutrinos, which are therefore a copious reservoir of energy for the explosion. Approximating the neutron star of mass Mns and radius Rns by a homogeneous sphere with Newtonian gravity, its binding energy, which roughly equals its gravitational energy, can be estimated as 3 GMns2 Eb  Eg   3:6  1053 5 Rns



Mns 1:5 Mˇ

2 

Rns 10 km

1 erg :

(1)

If only a fraction of this energy can be transferred to the gas surrounding the newly formed neutron star, the overlying stellar layers could be accelerated and expelled in a violent blast wave. A major revision of the theoretical picture of neutrino effects in collapsing stars became necessary after weak neutral currents, which had been predicted in theoretical work by Weinberg and Salam, were experimentally confirmed in the early 1970s (Freedman et al. 1977). With neutralcurrent scatterings of neutrinos off nuclei and free nucleons being possible, it was recognized that the electron neutrinos, e , produced by electron captures can escape freely only at the beginning of stellar core collapse (which starts out at a density around 1010 g cm3 ) but get trapped to be carried inward with the infalling stellar plasma when the density exceeds a few times 1011 g cm3 . At this time the implosion has accelerated so much that the remaining collapse time scale becomes shorter than the outward diffusion time scale of the neutrinos, which increases when scatterings become more and more frequent with growing density. Shortly afterward, typically around 1012 g cm3 , the electron neutrinos equilibrate with the stellar plasma and fill up their phase space to form a degenerate Fermi gas. During the remaining

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collapse until nuclear saturation density (about 2:7  1014 g cm3 ) is reached, and the incompressibility of the nucleonic matter due to the repulsive part of the nuclear force enables the formation of a neutron star, the entropy and the lepton number (electrons plus electron neutrinos) of the infalling gas (stellar plasma plus trapped neutrinos) remain essentially constant. Since the change of the entropy by electron captures and e escape until trapping is modest, it became clear that the collapse of a stellar core proceeds nearly adiabatically (for a review, see Bethe 1990). The proto-neutron star, i.e., the hot, mass-accreting, still proton- and lepton-rich predecessor object of the final neutron star, with its super-nuclear densities and extreme temperatures of up to several 1011 K (corresponding to several 10 MeV), is highly opaque to all kinds of (active) neutrinos and antineutrinos. Neutrinos, once generated in this extreme environment, are frequently reabsorbed, re-emitted, and scattered before they can reach semitransparent layers near the “surface” of the proto-neutron star, which is marked by an essentially exponential decline of the density over several orders of magnitude. Before they finally decouple from the stellar medium closely above this region and escape, neutrinos have experienced billions of interactions on average. The period of time over which the nascent neutron star is able to release neutrinos with high luminosities until its gravitational binding energy (Eq. 1) is radiated away therefore lasts many seconds (Burrows 1990a; Burrows and Lattimer 1986). This expectation was splendidly confirmed by the first and so far only detection of neutrinos from a stellar collapse on February 23, 1987, in the case of SN 1987A in the Large Magellanic Cloud at a distance of roughly 50 kpc (Raffelt 1996). The two dozen neutrino events in the three underground experiments of Kamiokande II (Hirata et al. 1987), Irvine-Michigan-Brookhaven (IMB; Bionta et al. 1987), and Baksan (Alexeyev et al. 1988) were recorded over a time interval of about 12 s (Fig. 1). Also their individual energies (up to 40 MeV) and the associated integrated energy of the neutrino signal (some 1053 erg) were in the ballpark of model predictions and evidenced the birth of a neutron star in this supernova. Figure 2 displays a schematic representation of the neutrino emission that drives the evolution from the onset of stellar core collapse to the cooling of the nascent neutron star, finally leading to a neutrino-transparent neutron star with central temperature below about 1 MeV (roughly 1010 K) within some tens of seconds. The neutrino-interaction processes and basic physics of neutrino transport in supernova matter will be described in Sect. 2, the neutrino-emission phases and corresponding neutrino effects in Sect. 3, and the neutrino-emission properties during the different phases in Sect. 4. Conclusions and an outlook will follow in Sect. 5.

2

Neutrino Production and Propagation in Supernova Cores

In collapsing stars neutrinos and antineutrinos of all flavors are produced and absorbed by a variety of processes, and, once created, they scatter off the target particles contained by the stellar medium as well as off neutrinos, whose number

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Fig. 1 Neutrino events recorded by the Kamiokande, IMB, and Baksan underground experiments. The energies do not refer to the primary electron antineutrinos but to the secondary positrons produced by the captures of such neutrinos on protons, N e C p ! n C e C . The detector clocks had unknown relative offsets; while the absolute timing at IMB had an accuracy of ˙50 ms, the clock at Kamiokande was accurate only to within ˙1 min, and the time measurement at Baksan had an uncertainty of C2/54 s. In the plots the first measured events are synchronized to t D 0 (Figure courtesy of Georg Raffelt)

densities can exceed those of nucleons and charged leptons in some regions of the supernova core. The most important interactions at supernova and proto-neutron star conditions are summarized in Table 1 and Fig. 3.

2.1

Basic Weak Interaction Theory

According to the Weinberg-Salam-Glashow theory (WSG), the weak force between fermions is mediated by the exchange of massive vector bosons, namely, two charged intermediate bosons, W C and W  , and one neutral intermediate boson, the Z 0 . Since the interaction energies at typical supernova and proto-neutron star conditions are much smaller than the rest-mass energies of the W and Z bosons, the WSG Hamiltonian density can be rewritten to an effective four-fermion pointinteraction V–A Hamiltonian (V stands for the vector part of the interaction, A for the axial-vector part) of the form

59 Neutrino Emission from Supernovae

1579

M

Progenitor (~ 15 M )

H 13

~10

He

7 m 10 c

ν 6

ν

10 cm

ν

Dense Core

ν

M

Hot Extended Mantle

ν

Fe

ν

ν − Sphere

M

O/Si

cm

M

ν

7

(Lifetime: 1 ~ 2 10 y)

~0.

1−1

ν

ν

Early Proto−neutron Star

ec.

S

M ν

ν

rn pe Su 3 10 8 cm

νe

~1 Sec.

e +p n + νe and Photo−disintegration of Fe Nuclei

νe

k oc Sh

ov

a

Late Proto−neutron Star (R ~ 20 km)

Dense Core

Collapse of Core (~1.5 M )

"White Dwarf" (Fe−Core)

10000 − 20000 km/s (R ~ 10000 km)

Fig. 2 Evolution of a massive star from the onset of iron-core collapse to a neutron star. The progenitor has developed a typical onion-shell structure with layers of increasingly heavier elements surrounding the iron core at the center (upper left corner). Like a white dwarf star, this iron core (enlarged on the lower left side) is stabilized mostly by the fermion pressure of nearly degenerate electrons. It becomes gravitationally unstable when the rising temperatures begin to allow for partial photodisintegration of iron-group nuclei to ˛-particles and nucleons. The contraction accelerates to a dynamical collapse by electron captures on bound and free protons, releasing electron neutrinos ( e ), which initially escape freely. Only fractions of a second later, the catastrophic infall is stopped because nuclear-matter density is reached and a proto-neutron star begins to form. This gives rise to a strong shock wave which travels outward and disrupts the star in a supernova explosion (lower right). The nascent neutron star is initially very extended (enlarged in the upper right corner) and contracts to a more compact object while accreting more matter (visualized by the mass-accretion rate MP ) within the first second of its evolution. This phase as well as the subsequent cooling and neutronization of the compact remnant are driven by the emission of neutrinos and antineutrinos of all flavors (indicated by the symbol ), which diffuse out from the dense and hot super-nuclear core over tens of seconds (Figure adapted from Burrows 1990b)

GF Hweak D p J+ J  ; 2

(2)

where J is the 4-current density of the interacting fermions and GF is the universal Fermi coupling constant, GF D 1:16637  105 GeV2 D 1:43588  1049 erg cm3 (for unit convention of Planck’s constant „ D h=.2 / D 1 and speed of

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Table 1 Most important neutrino processes in supernova and proto-neutron star matter Process Beta-processes (direct URCA processes) Electron and e absorption by nuclei Electron and e captures by nucleons Positron and N e captures by nucleons “Thermal” pair production and annihilation processes Nucleon-nucleon bremsstrahlung Electron-position pair process Plasmon pair-neutrino process Reactions between neutrinos Neutrino-pair annihilation Neutrino scattering Scattering processes with medium particles Neutrino scattering with nuclei Neutrino scattering with nucleons Neutrino scattering with electrons and positrons a

Reactiona e  C.A; Z/ ! .A; Z1/C e e  C p ! n C e e C C n ! p C N e N C N ! N C N C C N e  C e C ! C N Q ! C N e C N e ! x C N x x C f e ; N e g ! x C f e ; N e g C .A; Z/ ! C .A; Z/ CN ! CN C e˙ ! C e˙

N means nucleons, i.e., either n or p, 2 f e ; N e ;  ; N  ; ; N g, x 2 f  ; N  ; ; N g

light c D 1). To lowest non-vanishing order, the matrix element of the interaction, M , becomes (e.g., Bruenn 1985; Tubbs and Schramm 1975): GF M .f C ! f 0 C 0 / D p 2

f 0  .CV

 CA  5 /

f

0 



.1  5 /



:

(3)

Thus, expressing low-energy scattering reactions by an effective neutral-current interaction includes a Fierz-transformed contribution from W exchange when f is a charged lepton and the corresponding neutrino. In the case of charged-current electron and positron captures and the inverse e and N e absorptions, f and f 0 denote the incoming and outgoing nucleons and and 0 the neutrino and charged lepton in the initial and final states. The compound effective coupling coefficients for the interaction matrix element of Eq. (3) are listed in Table 2 (see also Raffelt 2012). With the matrix element being provided by Eq. (3), the reaction rate, R, of a neutrino of energy q0 results from integrating the quantity . u/ (having dimensions of cm3 s1 ) over the initial states of the target particle („ D c D 1): Z d3 p RD F .p0 /. u/ ; (4) .2 /3 where . u/ is the integral over final momentum states of the squared matrix element, summed over final spins and averaged over initial spins: .2 /2 u  2p0 2q0

Z

d3 p 0 Œ1  F .p00 / 2p00

Z

1 0 X d3 q 0 0 @1 2A 4 Œ1  F .q0 / jM j ı .p C q  p 0  q 0 / 2q00 2 spins (5)

59 Neutrino Emission from Supernovae

1581

Fig. 3 Feynman diagrams for the lowest-order contributions to the most relevant neutrino interactions in supernova cores. Charged-current (CC) reactions are mediated by W ˙ bosons and neutral-current (NC) reactions by electrically neutral Z 0 bosons. The charged-current ˇ-processes are responsible for the production and absorption of e and N e by lepton-capture reactions on nucleons (top row, left). Scattering processes include the charged-current interactions of e and N e with electrons and positrons (top row, right) and neutral-current scatterings of neutrinos and antineutrinos of all flavors with nuclei, neutrons, protons, electrons, positrons, and neutrinos (middle row). Neutrino-pair processes are responsible for the creation and annihilation of neutrinoantineutrino pairs of all flavors. They include electron-position pair annihilation through neutral and charged currents, nucleon bremsstrahlung, the charged- and neutral-current plasmon-neutrino processes, and neutrino-pair conversion between different flavors (bottom row, from left to right)

(Burrows et al. 2006; Tubbs and Schramm 1975). Here, q and q 0 are the fourmomenta of the incoming and outgoing lepton, respectively; p and p 0 the fourmomenta of the interacting fermions in the initial and final states; q0 , q00 , p0 , and p00 the positive time components (energies) of the four-momenta; and F .E/ the phasespace occupation functions of fermions of energy E. While the medium particles are in equilibrium and their phase-space occupation is described by Fermi-Dirac distributions, the neutrino distribution can be arbitrary. The magnitude of weak interactions is determined by the reference values for the reaction rate and cross section given by R0 

c 2



me c 2 2 „c

3

0 D 3:297  1039 0 cm2 s1 ;

(6)

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Table 2 Effective coupling coefficients in the weak interaction matrix element of Eq. (3). For the effective weak mixing angle, a value of sin2 W D 0:23146 was useda Fermion f .f 0 / Electron

Neutrino (lepton) e ; Proton e;; Neutron e;; Neutrino ( a ) a b¤a Neutron (proton) e (electron) Proton (neutron) N e (positron)

CV C1=2 C 2 sin2 W 1=2 C 2 sin2 W C1=2  2 sin2 W 1=2 C1 C1=2 C1:00 C1:00

CA C1=2 1=2 C1:26=2 1:26=2 C1 C1=2 C1:26 C1:26

CV2 0.9272 0.0014 0.0014 0.25 1.00 0.25 1.00 1.00

CA2 0.25 0.25 0.40 0.40 1.00 0.25 1.59 1.59

a For neutrinos interacting with the same flavor, a factor 2 for an exchange amplitude for identical fermions was applied. Possible strange-quark contributions to the nucleon spin were not taken into account for neutral-current neutrino-nucleon scattering (Table adapted from Raffelt 2012)

0 

4 2 .me c 2 /2 G D 1:761  1044 cm2 ;

F .„c/4

(7)

respectively. Since the squared matrix element is independent of energy, the phase space integration yields a quadratic dependence of the weak interaction cross sections on the particle energy to leading order,   .E/ / 0

E me c 2

2 :

(8)

Because of this strong energy dependence of weak interactions, high-energy neutrinos react much more frequently with medium particles by scattering and absorption processes and therefore decouple from the stellar background at a lower density than neutrinos with lower P energies. The mean free path between two interactions is given by .E/ D . i nt;i i .E//1  .tot .E//1 , where nt;i is the number density of target particles of species i , i .E/ the corresponding interaction cross section with neutrinos,  the matter density, and tot .E/ the total opacity in units of cm2 g1 . When .E/ includes contributions from all neutrino interactions, neutrino decoupling takes place at the neutrinospheric radius R .E/ defined as the radial position where the optical depth is unity: Z

1

.E/ D R .E/

dr D .r; E/

Z

1

dr .r/tot .r; E/ D 1 :

(9)

R .E/

Frequent scatterings as well as absorption and re-emission induce a randomwalk motion of the neutrinos on their way out of the deep interior to the neutrino-transparent regime at low densities. Over a (small) vertical distance z to

59 Neutrino Emission from Supernovae

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the surface, neutrinos of energy E experience an average number of Nia collisions with target particles, which is given by the relation: 1=2

Nia .E/ D z  .E/.E/ :

(10)

The neutrinosphere at .E/ D 1 is therefore defined as the location where neutrinos of energy E undergo on average one final interaction, Nia D 1, prior to escape.

2.2

Neutrino Transport

Neutrino transport in supernova cores involves a diffusive mode of propagation at the high densities of the newly formed neutron star, a gradual and energy-dependent decoupling of the neutrinos in the neutrinospheric region, and the transition to free streaming when the neutrinos escape from the neutron star. The evolution of the neutrino phase-space distribution function F .r; q; t / in these different regimes is described by the Boltzmann transport equation (e.g., Burrows et al. 2000; Liebendörfer et al. 2001, 2004; Mezzacappa et al. 2004; Rampp and Janka 2002), DF .r; q; t / @q @F @r D C rr F C rq F D C .F / ; Dt @t @t @t

(11)

where D=Dt denotes the total derivative of F .r; q; t / with respect to time t . rr and rq are the partial derivatives with respect to the space coordinates, r, and momentum coordinates, q D qn, when n defines the unit vector in the direction of neutrino propagation. On the r.h.s. of Eq. (11), C .F / stands for the collision integral that contains all rates of neutrino production, absorption, annihilation, and scattering processes. Moreover, since supernova neutrinos possess typical energies in the MeV range, which is much larger than the experimental rest-mass limit for active flavors, m c 2 < 1 eV, they propagate essentially with the speed of light c. Therefore, one can use jqj D q D E=c and @r=@t D c n. The momentum derivative in Eq. (11), @q=@t accounts for the effects of forces on the neutrino, e.g., in the form of gravitational redshifting. Note that for reasons of simplicity, Eq. (11) was written in a flat spacetime. In practice, the solution of this equation faces a lot of complications not only due to spacetime curvature in general relativity. For the most general case, where nonisoenergetic scattering redistributes neutrinos in energy-momentum space, Eq. (11) is an integrodifferential equation. Final-state fermion blocking and neutrino-antineutrino coupling in pair processes and neutrino-neutrino scattering (Table 1 and Fig. 3) make the problem nonlinear in F . Moreover, the motion of the stellar fluid has to be accounted for by Lorentz transformations and requires the choice of solving for F in the comoving frame of the fluid, where the collision integral is most easily treated, or in the laboratory frame, where the left-hand side of Eq. (11) retains its simple form.

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With the neutrino phase-space distribution function F being determined as solution of Eq. (11), the quantities characterizing the neutrino emission can be computed as integrals over the coordinates of the momentum vector q D .E=c/n. This yields for the specific neutrino number density, dn =dE; specific energy density, d" =dE; specific number flux, dF n =dE; specific energy flux, dF e =dE; and the corresponding total number and energy densities and fluxes (taking into account that there is one spin state of either left-handed neutrinos or right-handed antineutrinos): dn .r; E; t / 1 D E2 dE .hc/3 d" .r; E; t / 1 D E3 dE .hc/3 dF n .r; E; t / c D E2 dE .hc/3

Z Z Z

d˝ F .r; q; t / ;

(12)

d˝ F .r; q; t / ;

(13)

d˝ n F .r; q; t / ;

(14)

4

4

4

Z dF e .r; E; t / c 3 D E d˝ n F .r; q; t / ; dE .hc/3 4

Z 1 Z 1 dn d" ; " .r; t / D ; n .r; t / D dE dE dE dE 0 0 Z 1 Z 1 dF n dF e F n .r; t / D ; F e .r; t / D ; dE dE dE dE 0 0

(15) (16) (17)

where d˝ is the solid angle element around unit vector n. The flux through an area with normal unit vector m is given by F m, and the ratio of neutrino flux and neutrino density yields the so-called flux or streaming factor, sn D F n =.n c/ and se D F n =." c/. The energy moments of order k (i.e., the average values of E k ) for the local neutrino number density, hE k i, and for the neutrino number flux, hE k iflux , are given by: hE k i D

Z

1

dE E 2Ck

Z

0

hE k iflux

ˇZ ˇ D ˇˇ

0

d˝ F .r; q; t /

4

1

dE E 2Ck

Z 4

Z

1

dE E 2

0

 1 d˝ F .r; q; t / ;

Z 4

ˇ ˇZ ˇˇ d˝ nF .r; q; t /ˇˇ  ˇˇ

0

1

dE E 2

Z 4

(18) ˇ1 ˇ d˝ nF .r; q; t /ˇˇ : (19)

The rms energies of neutrino energy density p p and neutrino energy flux are defined as hEirms D hE 3 i=hEi and hEirms;flux D hE 3 iflux =hEiflux . Since the solution of the time-dependent Boltzmann equation in three spatial dimensions with its full energy-momentum dependence is not feasible on current supercomputers, a variety of different approximations are applied, for example, by

59 Neutrino Emission from Supernovae

1585

reducing the number of momentum-space variables by one in the so-called “rayby-ray” approach (Buras et al. 2006), which assumes the neutrino phase-space distribution F to be axisymmetric around one, typically the radial, direction and thus ignores non-radial flux components. Alternatively, the dependence of the Boltzmann equation on the momentum directions can be removed by integration over all directions after multiplication with different powers of n, by which means an infinite set of so-called moment equations is derived, in which angular moments (integrals) of F (like those of Eqs. 12, 13, 14, and 15) appear as dependent variables. Because on each level more moments than equations occur, a termination of the set on any level requires to involve a closure relation, which in most cases is a chosen function between the available moments. A termination on the level of the first moment equation, which is the neutrino energy equation, leads to the diffusion treatment. The compatibility of the diffusion flux (which diverges in the transparent regime) with the causality limit is usually ensured by the use of a flux limiter (e.g., Bruenn 1985). A termination on the level of the second moment equation, which is the neutrino momentum equation, yields the so-called two-moment transport approximation.

2.3

Flavor-Dependent Neutrino Decoupling

Since electrons and positrons are very abundant at the temperatures in supernova cores, whereas muons and tauons with their high rest masses are not, e and N e interact not only by neutral-current processes but also via charged-current reactions (Tables 1 and 2; Fig. 3). This causes distinct differences of their transport behavior compared to heavy-lepton neutrinos ( x D  ; N  ; ; N ), in particular concerning their decoupling near the neutrinosphere. Charged-current ˇ-processes provide a major contribution to the total opacity of e and N e , because the interaction cross sections of these reactions are big. Frequent captures and re-emission of these neutrinos at the local conditions of temperature and density are efficient in keeping them fairly close to local thermodynamic equilibrium (i.e., near thermal and chemical equilibrium) until they begin their transition to free streaming at their corresponding energy-averaged neutrinosphere. This sphere is also called transport sphere (sometimes also “scattering sphere”), whose radius R ;t is determined by solving Eq. (9) with a suitable spectral average of the total opacity tot  abs C scatt , which includes all contributions from scattering and absorption processes. Equilibration between neutrinos and the stellar background is possible up to the so-called average energy sphere (also termed “number sphere”, because outside of this location the number of neutrinos of a certain species is essentially fixed). When scatterings increase the zig-zag path of neutrinos diffusing through the medium and thus increase the probability of neutrinos to be absorbed, the radius R ;e of the energy sphere is given by the condition Z 1 2 eff D (20) dr eff D 3 R ;e

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(Raffelt 2001; Shapiro and Teukolsky 1983). Here, the effective optical depth is defined as p abs tot :

eff D

(21)

In the integral of Eq. (20), again a suitable average of eff over the energy spectrum has to be used. Since scattering and absorption contribute roughly equally p to the total opacity of e and N e , i.e., abs  .1=2/tot and therefore eff  tot = 2  .2=3/tot , the energy and transport sphere turn out to be nearly identical: R e ;e  R e ;t and R Ne ;e  R Ne ;t (see Fig. 4). The situation is different for the heavy-lepton species x . These are created and destroyed only as neutrino-antineutrino pairs in neutral-current reactions (cf. Fig. 3 and Table 1). While at high densities the main pair-production process is nucleon bremsstrahlung (with the plasmon-decay process contributing on a secondary level), electron-positron and e N e annihilation take over as the dominant producers of x N x pairs at densities below about 10 % of nuclear-matter density, where the

and

Electron flavor (

) Free streaming

Thermal Equilibrium

Other flavors ( «

,

,

,

Neutrino sphere

)

Scattering Atmosphere ® Free streaming

Diffusion Energy sphere

Transport sphere

Fig. 4 Sketch of the transport properties of electron-flavor neutrinos and antineutrinos (upper part) compared to heavy-lepton neutrinos (lower part). In the supernova core, e and N e interact with the stellar medium by charged-current absorption and emission reactions, which provide a major contribution to their opacities and lead to a strong energetic coupling up to the location of their neutrinospheres, outside of which both chemical equilibrium between neutrinos and stellar matter (indicated by the black region) and diffusion cannot be maintained. In contrast, heavylepton neutrinos are energetically less tightly coupled to the stellar plasma, mainly by pair creation reactions like nucleon bremsstrahlung, electron-position annihilation, and e N e annihilation. The total opacity, however, is determined mostly by neutrino-nucleon scatterings, whose small energy exchange per scattering does not allow for an efficient energetic coupling. Therefore, heavylepton neutrinos fall out of thermal equilibrium at an energy sphere that is considerably deeper inside the nascent neutron star than the transport sphere, where the transition from diffusion to free streaming sets in. The blue band indicates the scattering atmosphere where the heavy-lepton neutrinos still collide frequently with neutron and protons and lose some of their energy but cannot reach equilibrium with the background medium any longer (Figure adapted from Raffelt (2012), courtesy of Georg Raffelt)

59 Neutrino Emission from Supernovae

1587

stellar medium is less degenerate and larger numbers of positrons and electron antineutrinos are present. The total opacity of x , however, is largely dominated by neutral-current scatterings off nucleons because of the much greater cross sections of these reactions. As a consequence, the average energy sphere of x is located at considerably higher density, deeper inside the nascent neutron star, than their average transport sphere: R x ;e < R x ;t (Fig. 4). While outside of the energy sphere the number flux of each species of x is essentially conserved, the energy flux can still change between the energy and transport spheres because of energy transfers in the frequent collisions with nucleons (and to a lesser degree with electrons and electron-type neutrinos), in which mostly the energetic neutrinos from the highenergy tail of the x spectrum can deliver energy to the cooler stellar medium (Keil et al. 2003; Raffelt 2001). The neutral-current nucleon scattering opacities of heavy-lepton neutrinos and antineutrinos are to lowest order the same (with only minor higher-order differences associated with weak-magnetism corrections Horowitz 2002). In the absence of large concentrations of muons, also muon and tau neutrinos interact with the medium essentially symmetrically. For these reasons the four species of heavylepton neutrinos are treated as one kind of x in many applications. As the neutronization and deleptonization of the nascent neutron star progress due to the ongoing conversion of electrons and protons to neutrons and the escape of e , the decreasing abundance of protons reduces the absorption opacity of N e . Therefore, as time goes on, the opacity of electron antineutrinos becomes more and more similar to that of heavy-lepton (anti)neutrinos, and the radiated spectra of these neutrinos match each other closely.

3

Neutrino Emission Phases

Figure 5 presents a series of plots that provide an overview of the main processes and regions of neutrino production and their dynamical effects during the collapse of a stellar core and on the way to the supernova explosion. Neutrinos exchange lepton number, energy, and momentum with the stellar medium. Corresponding source terms must therefore be taken into account in the hydrodynamics equations that describe the time evolution of the stellar medium in terms of conservation laws for mass, momentum, energy, and (electron) lepton number. (1) Onset of Stellar Core Collapse The slow contraction of the growing and aging iron core, which develops a progenitor star-dependent mass between 1.3 and 2 Mˇ , speeds up when its central temperature approaches 1 MeV (1010 K). At this stage, thermal  photons become sufficiently energetic to partially disintegrate the iron-group nuclei to ˛-particles and free nucleons. This converts thermal energy to rest-mass energy, thus overcoming the binding energy of nucleons in the nuclei, and causes a reduction of the effective adiabatic index, i.e., of the increase of the pressure with rising density, below the critical value of 4=3. (General relativistic effects lead to a slight upward correction of this critical value, rotation to a slight

1588

H.-T. Janka Initial Phase of Collapse (t ~ 0)

Neutrino Trapping (t ~ 0.1s, c ~10¹² g/cm³)

R [km]

δ

R [km] RFe~ 3000

RFe

νe

νe νe

~ 100 Si

Si νe

Fe, Ni

Fe, Ni

νe

νe 0.5

~ MCh M(r) [M ]

1.0

0.5 heavy nuclei

Si−burning shell

δ

RFe

RFe Rν

Fe, Ni

0.5 1.0 nuclear matter nuclei ( >∼ ο )

νe Si

νe

free n, p

M(r) [M ]

0.5 nuclear matter

Si−burning shell

δ δ

Shock Stagnation and ν Heating, Explosion (t ~ 0.2s)

R [km]

νe

position of shock formation

νe

Si

~ 10

νe

Rs ~ 100 km

νe

radius of shock formation

Si−burning shell

Shock Propagation and νe Burst (t ~ 0.12s)

R [km]

Bounce and Shock Formation (t ~ 0.11s, c ∼< 2 o ) δ

R [km]

M(r) [M ]

Mhc 1.0

R [km] 10 5

νe

Fe

νe

Ni

M(r) [M ]

1.0 nuclei

Si−burning shell

Neutrino Cooling and Neutrino− Driven Wind (t ~ 10s)

Rs ~ 200 νe,μ,τ ,νe,μ,τ

Rg ~ 100

free n, p

Si

10

4

10

3

νe νe

n

νe,μ,τ ,νe,μ,τ

10

1.3 gain layer cooling layer

1.5 M(r) [M ]

α r−process?

2

R ns~ 10 Rν

PNS

Ni Si

p R ν ~ 50

νe,μ,τ ,νe,μ,τ

PNS 1.4

α, n n, p

9

α,n, Be, C, seed

He O

νe,μ,τ ,νe,μ,τ

3 M(r) [M ]

12

Fig. 5 Six phases of neutrino production and its dynamical consequences (from top left to bottom right). In the lower halves of the plots, the composition of the stellar medium and the neutrino effects are sketched, while in the upper halves the flow of the stellar matter is shown by arrows. Inward pointing arrows denote contraction or collapse, outward pointing arrows expansion or mass ejection. Radial distances R are indicated on the vertical axes; the corresponding enclosed masses M .r/ are given on the horizontal axes. RFe , Rs , R , Rg , and Rns denote the iron-core radius, shock radius, neutrinospheric radius, gain radius (which separates neutrino cooling and heating layers), and proto-neutron star (PNS) radius, respectively. MCh defines the effective Chandrasekhar mass, Mhc the mass of the homologously collapsing inner core (where velocity u / r), c the central density, and 0  2:7  1014 g cm3 the nuclear saturation density (Figure taken from Janka et al. 2007)

59 Neutrino Emission from Supernovae

1589

reduction.) Since the Fermi energy of the degenerate electrons also rises, electron captures on nuclei become possible (for the current state of the art of the treatment, see Balasi et al. 2015; Juodagalvis et al. 2010; Langanke et al. 2003). Initially, the e thus produced escape unimpeded (Fig. 5, top left panel). (2) Neutrino trapping When the density exceeds a few times 1011 g cm3 , neutrinos begin to become trapped in the collapsing stellar core. From this moment on, the e produced by ongoing electron captures – now dominantly on free protons – are swept inward with the infalling matter, and entropy as well as lepton number are essentially conserved in the contracting flow (Fig. 5, top right panel). Neutrino trapping is mainly a consequence of neutral-current scattering of lowenergy neutrinos on heavy nuclei, whose nucleons act as one coherent scatterer. Because the vector parts of the neutrino-neutron scattering amplitudes dominate compared to those of protons (cf. Table 2) and add up in phase, whereas the overall axial-vector current is reduced by spin-pairing of the nucleons in nuclei, the coherent scattering cross section effectively scales with the square of the neutron number N : A;coh

1 0  16



E me c 2

2

N2 :

(22)

As electrons continue to be converted to e , the dynamical collapse accelerates to nearly free-fall velocities (up to 30 % of the speed of light) in the supersonic outer core region. The inner core implodes subsonically and homologously, i.e., with a velocity that is proportional to the radius, which implies a self-similar change of the structure. The size of the homologous core is roughly given by the instantaneous Chandrasekhar mass, 2 Mhc <  MCh D 1:457 .2Ye / Mˇ ;

(23)

where Ye D ne =nb is the number of electrons (number density ne ) per baryon (number density nb D np C nn ). Since Ye drops from an initial value around 0.46 for iron-group matter to less than 0.3 after trapping, the homologous core shrinks to roughly 0.5 Mˇ (Janka et al. 2012). (3) Core Bounce and Shock Formation Within milliseconds after trapping, corresponding to the free-fall time, 0:004 1  p tff  p s 12 G

(24)

(G being the gravitational constant and 12 the density in 1012 g cm3 ), the center reaches nuclear matter density, where the heavy nuclei dissolve in a phase transition to a uniform nuclear medium. A sharp rise of the incompressibility due to repulsive contributions to the nuclear force between the nucleons provides resistance against

1590

H.-T. Janka

further compression, and the collapse of the homologous inner core comes to an abrupt halt. As it bounces back, sound waves steepen into a shock front at the boundary to the supersonically infalling outer layers (Fig. 5, middle left panel). The bounce shock begins to travel outward against the ongoing collapse of the overlying iron-core material. (4) Shock Propagation and e Burst at Shock Breakout Electron neutrinos are produced in huge numbers by electron captures on free protons behind the outward moving shock front. However, they stay trapped in the dense postshock matter until the shock reaches sufficiently low densities for the e to diffuse faster than the shock propagates. At this moment, the so-called shock breakout into neutrino-transparent layers, a luminous flash of e – the breakout burst – is emitted (Fig. 5, middle right panel; Sect. 4.1). Shortly after shock breakout, the dramatic loss of e leads to a considerable drop of the electron-lepton number in the shock-heated matter. This allows for the appearance of large concentrations of positrons. Because of that and the compressional heating of the settling proto-neutron star, which begins to assemble around the center, pair-production processes (mainly e  e C pair annihilation and nucleon bremsstrahlung; Table 1 and Fig. 3) become efficient and start to create heavy-lepton neutrinos and antineutrinos. With positrons and neutrons becoming more and more abundant, e C captures on neutrons also accomplish the emission of N e . (5) Shock Stagnation and Revival by Neutrino Heating The shock front is a sharp flow discontinuity (whose narrow width is determined by the small, microphysical viscosity of the stellar plasma), in which the kinetic energy of the supersonically infalling preshock matter is dissipated into thermal energy, leading to an abrupt deceleration and compression of the flow and a corresponding increase of the density, temperature, pressure, and entropy behind the shock. Because of the temperature increase, heavy nuclei in the preshock medium are disintegrated essentially completely to free nucleons when the matter passes the shock. This consumes appreciable amounts of energy, roughly 8.8 MeV per nucleon or 1:7  1051 erg per 0.1 Mˇ . This energy drain and the additional energy losses by the e -burst reduce the postshock pressure and weaken the expansion of the bounce shock. It finally stagnates at a radius of typically less than 150 km and an enclosed mass of around 1 Mˇ , which is still well inside the collapsing stellar iron core. The prompt bounce-shock mechanism therefore fails to initiate the explosion of the dying star as supernova. The most likely mechanism to revive the stalled shock front and to initiate its expansion against the ram pressure of the collapsing surrounding stellar core matter, is energy transfer by the intense neutrino flux radiated from the nascent neutron star. The most important reactions for depositing fresh energy behind the shock are e and N e captures on free nucleons: e C n ! p C e  ; (25) N e C p ! n C e C :

(26)

59 Neutrino Emission from Supernovae

1591

Current numerical simulations, recently also performed in all three spatial dimensions, demonstrate the viability of this neutrino-heating mechanism in principle (Fig. 6) so that this mechanism appears as the most promising explanation of the far majority of “normal” core-collapse supernovae. For stars more massive than 10 Mˇ , non-radial hydrodynamic instabilities (like convective overturn and the standing accretion-shock instability (SASI)) provide crucial support for the onset of the explosion, and also for stars near the lower mass end of supernova progenitors (9–10 Mˇ ), nonspherical flows play an important role for determining

Fig. 6 Time evolution of the neutrino-driven explosion of a 15 Mˇ star as obtained in a multidimensional hydrodynamic simulation, visualized by a mass-shell plot. The horizontal axis shows time in milliseconds and the vertical axis the radial distance (in cm) on a logarithmic scale. The black, solid lines starting at the left edge of the plot belong to the radii that enclose selected values of baryonic mass, in some cases indicated by labels (in units of solar masses) next to the lines. The line with overlaid crosses marks the boundary between the silicon layer and the siliconenriched oxygen layer of the progenitor star. Retreating lines signal the collapse of stellar shells and outgoing lines the expansion of matter expelled in the beginning supernova explosion. The thick red line marks the supernova shock front, which is formed at the moment of core bounce (here chosen to define time t D 0). The neutron star assembles from the mass shells settling in the lower part of the image at t > 0. The thick, black solid, dashed, and dash-dotted lines that first expand and then contract with the neutron star represent the radial locations of the average neutrinospheres of e , N e , and heavy-lepton neutrinos, respectively, close to the surface of the nascent neutron star. The light blue and red areas denote the regions of neutrino cooling and neutrino heating, respectively, outside of the neutrinospheres, which are separated by the “gain radius” (thin, dashed black line). The neutrino-driven wind (indicated by blue arrows) is visible by mass shells that start their outward expansion just above the neutron star surface. The thick-thin dashed line beginning at about 700 ms is the wind-termination shock that is formed when the fast wind collides with the slower preceding ejecta (Figure adapted from Pruet et al. 2005)

1592

H.-T. Janka

the energy and asymmetries of the explosion (see the indication of non-radial mass motions in the left bottom panel of Fig. 5). Despite the promising results of current models, many questions remain to be settled, and an ultimate confirmation of the neutrino-driven mechanism will require observational evidence. A high-statistics measurement of the neutrino signal from a future galactic supernova could be a milestone in this respect. Before the supernova shock front re-accelerates outward and the supernova blast is launched, stellar matter collapsing through the stagnant shock feeds a massive accretion flow onto the nascent neutron star (typically several 0.1 Mˇ s1 ). The hot accretion mantle around the high-density, lower-entropy core of the neutron star radiates high fluxes mainly of e and N e , which carry away the gravitational binding energy that is released in the gravitational collapse. This accretion luminosity adds to the core luminosity of all species of neutrinos and antineutrinos ( e , N e , and x ) that diffuse out from the deeper layers (Fig. 5, bottom left panel). (6) Proto-neutron Star Cooling and Neutrino-Driven Wind Accretion does not subside immediately after the explosion sets in. There can be an extended phase of continued mass accretion by the nascent neutron star that proceeds simultaneously to the outward acceleration of mass behind the outgoing shock. Eventually, however, after hundreds of milliseconds up to maybe a second, depending on the progenitor star and the speed of shock expansion, accretion ends and the proto-neutron star enters its Kelvin-Helmholtz cooling phase, in which it loses its remaining gravitational binding energy by the emission of neutrinos and antineutrinos of all flavors on the time scale of neutrino diffusion. Based on a simple diffusion model for a homogeneous sphere, Burrows (1984, 1990b) derived order-of-magnitude estimates for the deleptonization and energy-loss time scales: tL 

2 dYL 3Rns  3s;

2 c0 dY e

(27)

tE 

2 Eth0 3Rns  10 s ;

2 c0 2E 0

(28)

where Rns  10 km is the neutron-star radius, 0 D

1  10 cm nb h i



E 100 MeV

2 

Mns 1:5 Mˇ

1 

Rns 10 km

3 (29)

the initial average mean free path of the neutrinos, Eth0 and E 0 the initial total baryon and neutrino thermal energies, respectively, and the ratio of these thermal energies as well as dYL =dY e describe the ability of the neutron star to replenish the loss of lepton number and energy due to the radiated neutrinos from the available reservoirs of these quantities. While the temperatures in the interior of the newly formed neutron star can reach up to more than 50 MeV and the thermal energies of neutrinos can be 100 MeV and higher, these high-energy neutrinos are absorbed, re-emitted,

59 Neutrino Emission from Supernovae

1593

and downscattered billions of times before they escape from the neutrinospheric region with final mean energies of 10–20 MeV over much of the Kelvin-Helmholtz phase. While the proto-neutron star deleptonizes and cools by neutrino losses, the energetic neutrinos radiated from the neutrinosphere continue to deposit energy in the overlying, cooler layers, mainly by the reactions of Eqs. (25) and (26). This leads to a persistent, dilute outflow of mass (with initial mass-loss rates of typically several 102 Mˇ s1 ) from the surface of the nascent neutron star. This so-called neutrinodriven wind (Fig. 5, bottom right panel, and Fig. 6) is discussed as potential site for the formation of trans-iron elements. The mass-loss rate, entropy, and expansion velocity of this wind are sensitive functions of the neutron-star radius and mass and of the luminosities and spectral hardness of the emitted neutrinos (Arcones et al. 2007; Otsuki et al. 2000; Qian and Woosley 1996; Thompson et al. 2001). Even more important is the fact that the neutron-to-proton ratio of the expelled matter is determined by the luminosity and spectral differences of e and N e , which leads to an interesting sensitivity of the nucleosynthetic potential of this environment to the nuclear physics of the neutron star medium and to nonstandard neutrino physics like flavor oscillations or the speculative existence of sterile neutrinos.

4

Neutrino Emission Properties

Three main phases of neutrino emission can be discriminated that correspond to the dynamical evolution stages described in the previous section (Janka 1993). They are displayed in Fig. 7 and described in the following three subsections.

4.1

Shock-Breakout Burst of Electron Neutrinos

A luminous flash of neutronization neutrinos is radiated when the shock transitions from the opaque to the neutrino-transparent, low-density ( . 1011 g cm3 ) outer layers of the iron core. At this moment, typically setting in 2 ms after core bounce, the large number of e created by electron captures on free protons in the shockheated matter can ultimately escape. During the preceding collapse prior to core bounce, the e emission rises continuously because an increasingly bigger fraction of the stellar core is compressed to densities where efficient electron captures become possible. Only within a brief period (˙1 ms) around core bounce, the strong compression and Doppler redshifting of the main region of e generation lead to a transient dip in the e luminosity. At shock breakout, also the luminosities of heavy-lepton neutrinos and shortly afterward those of N e begin to rise, because their production by pair processes becomes possible in the shock-heated matter (see Sect. 3; Fig. 7, left panel). The e luminosity burst and the rise phase of the N e and x luminosities show a generic behavior with little dependence on the progenitor star (Kachelrieß et al. 2005). The burst reaches a peak luminosity near 4  1053 erg s1 ,

1594

H.-T. Janka

Fig. 7 Neutrino luminosities ( e : black; N e : blue; x as one species of  , N  , , N : red) during the main neutrino-emission phases. The left panel shows the prompt burst of electron neutrinos associated with the moment of shock breakout into the neutrino-transparent outer core layers only milliseconds after bounce (t D 0). The middle panel corresponds to the post-bounce accretion phase before shock revival as computed in a three-dimensional simulation (see Tamborra et al. 2014). The quasi-periodic luminosity variations are a consequence of modulations of the massaccretion rate by the neutron star caused by violent non-radial motions due to hydrodynamic instabilities (in particular due to the standing accretion-shock instability or SASI) in the postshock layer. The right panel displays the decay of the neutrino luminosities over several seconds in the neutrino-cooling phase of the newly formed neutron star (the plotted values are scaled up by a factor of 2)

has a half-width of less than 10 ms, and releases about 2  1051 erg of energy within only 20 ms. The mean energy of the radiated e also peaks at the time of maximum luminosity and reaches 12–13 MeV (Fig. 8, lower left panel).

4.2

Post-Bounce Accretion

This phase follows when the e luminosity declines from the maximum and levels off into a plateau. Both e and N e are produced in large numbers by charged-current processes in the hot mantle of the proto-neutron star. The mass of this mantle grows continuously, because it is fed by the accretion flow of the collapsing stellar matter that falls through the stagnant shock and is heated by compression. The luminosities of e and N e are very similar during this phase with a slight number excess of e because of ongoing deleptonization. In contrast, the individual luminosities of x are considerably lower. These neutrinos originate mostly from the denser core region, where the high densities and temperatures allow nucleon bremsstrahlung to generate x N x pairs. The neutrino emission (luminosities and mean energies) during the accretion phase show large variations between different progenitor stars, because the neutrino quantities scale with the mass-accretion rate, MP .t /, and the growing proto-neutron star mass, Mns .t /. Both MP and Mns are higher for progenitor stars that possess more compact cores, i.e., where a certain mass is condensed into a smaller volume prior to collapse. Progenitors with higher core compactness (which tend to be more

59 Neutrino Emission from Supernovae

1595

Fig. 8 Neutrino signal computed for the supernova explosion of a star of 27 Mˇ , which gives birth to a neutron star with 1.6 Mˇ . The left panels correspond to the shock-breakout phase, the middle panels to the post-bounce accretion phase including the transition to the proto-neutron star cooling phase, which is given in the right panels. The upper panels display the neutrino luminosities ( e black; N e , blue; one species of ; , red; one species of N ; , magenta), and the lower panels display the mean energies of the radiated neutrinos. In contrast to Fig. 7, the differences of heavy-lepton neutrinos and antineutrinos associated with weak-magnetism corrections of neutrinonucleon scattering are shown. The slightly lower scattering opacity of N ; leads to slightly higher luminosities and higher mean energies (by 1 MeV) compared to those of ; . The explosion sets in at 0.5 s after core bounce, but accretion onto the proto-neutron star ends only at about 0.75 s, which marks the onset of the cooling phase (Figure courtesy of Robert Bollig)

massive, too, but with considerable non-monotonic variations) therefore radiate higher luminosities and harder neutrino spectra (Janka et al. 2012; O’Connor and Ott 2013). Moreover, non-radial flows in the supernova core, which are a consequence of hydrodynamic instabilities in the proto-neutron star and in the region behind the stalled shock front (like convective overturn and the standing accretion-shock instability (SASI)), can cause large-scale temporal modulations of the accretion flow onto the neutron star. This can lead to time- and direction-dependent, largeamplitude, quasi-periodic fluctuations of the luminosities and mean energies of the radiated neutrinos during the accretion phase (Fig. 7, middle panel Lund et al. 2012; Tamborra et al. 2013, 2014). The instantaneous spectra of the radiated muon and tau neutrinos are reasonably well described by Fermi-Dirac functions with zero degeneracy, and their luminosities can be expressed by a Stefan-Boltzmann like formula as 2 L x D 4 s Rns T 4 ;

(30)

1596

H.-T. Janka

where the average energy and the effective spectral temperature T (measured in MeV) are linked by hEi D 3:15 T . Rns is the radius of the proto-neutron star and s D 4:50  1035 erg MeV4 cm2 s1 for a single species of x . The “grayness factor”  is determined by numerical simulations to range between 0.4 and 0.85 (Müller and Janka 2014). Since the emission of e and N e is enhanced by the accretion component, the sum of their luminosities can be written as

L e C L Ne D 2ˇ1 L x C ˇ2

GMns MP : Rns

(31)

The first term on the r.h.s. represents the “core component” of the luminosity carried by neutrinos diffusing out from the high-density inner regions of the proto-neutron star. This component can be assumed to be similar to the luminosity of  plus N  , because the core radiates all types of neutrinos in roughly equal numbers from a reservoir in thermal equilibrium, which is confirmed by the close similarity of the luminosities of all neutrino species after the end of accretion. The second term on the r.h.s. stands for the accretion component expressed by the product of massaccretion rate, MP , and Newtonian surface gravitational potential of the neutron star, ˚ D GMns =Rns . By a least-squares fit to a large set of 1D results for the postbounce accretion phase of different progenitor stars, values between ˇ1  1:25 and ˇ2  0:5 can be deduced (L. Hüdepohl 2014, private communication), which depend only weakly on the nuclear EoS. The values apply later than about 150 ms after bounce, when the postshock accretion layer has settled into a quasi-steady state. Müller and Janka (2014) used a form slightly different from Eq. (31) with ˇ1 D 1; they found ˇ2  0:5–1 prior to explosion. During the accretion phase, the mean energies of all neutrino species show an overall trend of increase, which is typically steeper for e and N e than for x . The secular rise of the mean energies of the radiated e and N e is fairly well captured by the proportionality hE i / Mns .t /. The proportionality constant depends on the neutrino type but is only slightly progenitor dependent (Müller and Janka 2014). This secular rise of hE e i and hE Ne i is supported by a local temperature maximum somewhat inside of the neutrinospheres of these neutrinos, which forms because of compressional heating of the growing accretion layer in progenitors with sufficiently high accretion rates (typically more massive than about 10 Mˇ ). Because of the continuous growth of the mean energies with Mns .t /, the canonical order of the average energies, hE e i < hE Ne i < hE x i changes (transiently) to hE e i < hE x i < hE Ne i (Fig. 8, lower middle panel). This hierarchy inversion is enhanced and shifted to earlier times when energy transfer in neutrino-nucleon scattering is taken into account. Non-isoenergetic neutrino-nucleon scattering reduces the mean energies of x in the “high-energy filter” layer between the x energy sphere and the x transport sphere (see Sect. 2.3 and Fig. 4 Keil et al. 2003; Raffelt 2001). The corresponding energy transfer to the stellar medium also raises the luminosities and mean energies

59 Neutrino Emission from Supernovae

1597

˝ ˛ of e and N e . Different from the mean energies, the mean squared energies, E 2 , and rms energies always obey the canonical hierarchy.

4.3

Kelvin-Helmholtz Cooling and Deleptonization of the Proto-neutron Star

After the explosion has set in, the proto-neutron star continues to radiate lepton number and energy by high neutrino fluxes for many seconds (Sect. 3). The luminosities of all kinds of neutrinos and antineutrinos become similar (within 10 %) during this phase and decline with time in parallel (Fig. 7, right panel). The typical average luminosities during Kelvin-Helmholtz cooling are of the order of Ltot 

X

L i C L Ni 

iDe;;

Eb  several 1052 erg s1 : tE

(32)

Rough estimates of Eb and tE were provided by Eqs. (1) and (28), respectively. Around about 1 s, the mean energies of the radiated neutrinos show a turnover and begin to decrease, reflecting the gradual cooling of the outer layers of the protoneutron star (Fig. 8). A thick convective shell inside the star grows in mass, while its inner boundary progresses toward the center (see Mirizzi et al. 2015). Convective energy transport in the high-density core of the neutron star is faster than diffusive transport and considerably accelerates the lepton number and energy loss through neutrinos. Because of the “high-energy filter” effect of the extended scattering atmosphere between the energy and transport spheres of heavy-lepton neutrinos, ; with their higher scattering opacity are radiated with slightly softer spectra than N e and N ; during all of the Kelvin-Helmholtz cooling evolution (Fig. 8, lower right panel).

4.4

Spectral Shape

The spectra of radiated neutrinos are usually somewhat different from thermal spectra. Since neutrino-matter interactions are strongly energy dependent, neutrinos of different energies decouple from the background medium at different radii with different temperatures of the stellar plasma. Nevertheless, the emitted neutrino spectrum can still be fitted by a Fermi-Dirac distribution, f .E/ / E 2 Œ1 C exp .E=T  /1 , with fit temperature T (in energy units) and effective degeneracy parameter  (Janka and Hillebrandt 1989). A mathematically more convenient representation was introduced by Keil et al. (2003), who proposed the following dimensionless form for the energy distribution at a large distance from the radiating source:  f˛ .E/ /

E hEi

˛

e .˛C1/E=hEi ;

(33)

1598

H.-T. Janka

where R1

dE Ef˛ .E/ hEi D R0 1 0 dE f˛ .E/

(34)

is the average energy. The parameter ˛ represents the amount of spectral “pinching” and can be computed from the two lowest energy moments of the spectrum, hEi and hE 2 i, by hE 2 i 2C˛ : D 2 hEi 1C˛

(35)

Higher-energy moments hE ` i for ` > 1 are defined analogue to Eq. (34) with E ` under the integral in the numerator instead of E. Besides its analytic simplicity, this functional form has the advantage to also allow for the representation of a wider range of values for the spectral (anti-)pinching than a Fermi-Dirac fit. A Fermi-Dirac spectrum with vanishing degeneracy parameter ( D 0) corresponds to ˛  2:3, a Maxwell-Boltzmann spectrum to ˛ D 2, and ˛ & 2:3 yields “pinched” spectra (i.e., narrower than a thermal Fermi-Dirac spectrum), whereas ˛ . 2:3 gives anti-pinched ones. Comparing to high-resolution transport results, Tamborra et al. (2012) showed that these “˛-fits” also reproduce the high-energy tails of the radiated neutrino spectra very well (Fig. 9). The shape parameter ˛ is up to 6–7 for e around the e -burst, and in the range of 2–3 for all neutrino species at times later than 200 ms after bounce (Mirizzi et al. 2015). In particular e and N e exhibit a tendency of pinched spectra. This spectral pinching can be understood as a consequence of the energy dependence of the neutrino interactions and can be exemplified by considering the radiated luminosity spectrum as a combination of thermal contributions from different, energy-dependent decoupling regions: dL .E/ 1 E3 4

 c .4 R 2 .E// B .E/  c R 2 .E/ ; dE 4 .hc/3 1 C expŒ.E   /=T  (36) with T D T .R .E// and  D  .R .E// being the gas temperature (in MeV) and neutrino equilibrium chemical potential at decoupling radius R .E/. The smaller interaction cross section and opacity of low-energy neutrinos (Eq. 8) lead to their energetic decoupling at a smaller radius (cf. Eq. 20), whereas high-energy neutrinos decouple at larger radii, where the stellar temperature is lower. These effects cause a reduction of the low-energy and high-energy wings on both sides of the spectral peak compared to a thermal spectrum with the temperature of the spectral maximum.

59 Neutrino Emission from Supernovae

-1

-1

fν (s MeV )

10

56

10 10

νe, 261ms

νe, 261ms

νx, 261ms

νe, 1016ms

νe, 1016ms

νx, 1016ms

νe, 1991ms

νe, 1991ms

νx, 1991ms

55

54

10

10

53

55

-1

fν (s MeV )

1599

54

-1

10

10 10

52

10

55

-1

fν (s MeV )

53

54

-1

10

10 10

53

52

0

10

20 30 E (MeV)

40

0

10

20 30 E (MeV)

40

0

10

20

30 40 E (MeV)

50

60

Fig. 9 Spectra for electron neutrinos ( e ; left column), electron antineutrinos (N e ; middle column), and heavy-lepton neutrinos ( x , right column) during the accretion phase (261 ms after core bounce, top row) and for two times during the proto-neutron star cooling phase (1016 ms, middle row; 1991 ms, bottom row). The step functions are results of numerical simulations with lower (thin dashed) and higher (thick, colored) resolution. The continuous curves are quasi-thermal fits according to Eq. (33) for the lower resolution (thin dashed lines) and higher resolution (thick solid lines) cases. All ˛ values for the fit functions are in the interval 2:3 ˛ 3:3 (Figure taken from Tamborra et al. 2012)

5

Conclusions

Theoretical predictions of the neutrino emission from supernovae have become considerably more reliable and detailed since improved transport treatments have become available in numerical simulations after the change of the millennium. This chapter provides an overview of the foundations of the neutrino physics in collapsing stars. Moreover, it presents a summary of our current understanding of production and properties of the neutrino signal emitted during supernova explosions and the birth of neutron stars. The most advanced methods for describing neutrino transport in computational supernova models in spherical symmetry apply solvers for the time-dependent Boltzmann transport equation (Lentz et al. 2012; Liebendörfer et al. 2001, 2004) or for the set of its first two-moment equations with a variable Eddington factor closure derived from a simplified Boltzmann equation (Müller et al. 2010; Rampp and Janka 2002). Both approaches take into account the velocity dependence of the neutrino

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transport, general relativistic effects, and the full phase-space dependence of the neutrino interaction rates summarized in Table 1 and Fig. 3. These most advanced codes have been shown to yield results of similar quality and overall consistency between each other (Liebendörfer et al. 2005; Marek et al. 2006; Müller et al. 2010). These methods constitute the present state of the art for simulating neutrino transport in supernovae and proto-neutron stars in spherical symmetry. In three-dimensional supernova modeling, similar sophistication is not yet feasible. The current forefront here is defined by ray-by-ray implementations of the two-moment method with Boltzmann closure (Buras et al. 2006; Melson et al. 2015a, b) and of flux-limited diffusion (Lentz et al. 2015), and the application of two-moment schemes with algebraic closure relations is in sight. Solving the timedependent Boltzmann transport problem in six-dimensional phase-space, however, is still on the far horizon and remains a challenging task for future supercomputing on the exascale level. The same is true for a fully self-consistent inclusion of the effects of neutrino flavor transformations. Matter-background-induced oscillations according to the Mikheyev-Smirnov-Wolfenstein (MSW) effect (Mikheyev and Smirnov 1985; Wolfenstein 1978) for the three active neutrino flavors occur at densities far below those of the supernova core (around 100 g cm3 and at several 1000 g cm3 ) and must be taken into account when neutrinos propagate through the dying star on their way to the terrestrial detector. Since oscillations are suppressed in the dense interior at conditions far away from the MSW resonances (Hannestad et al. 2000; Wolfenstein 1979), flavor mixing inside of the neutrinosphere can be safely ignored. Outside of the neutrinosphere, however, the neutrino densities are so enormous that the large - interaction potential can trigger self-induced flavor conversions. The possible consequences of this interesting effect have so far been explored in post-processing studies using unoscillated neutrino data from numerical supernova simulations (for a status report, see Mirizzi et al. 2015). The highly complex and rich phenomenology of these self-induced flavor changes, however, is not yet settled, and therefore final conclusions on their possible effects for the supernova physics and for neutrino detection cannot be drawn yet. The detection of a high-statistics neutrino signal from a supernova in the Milky Way is a realistic possibility with existing and upcoming experimental facilities. Such a measurement will provide unprecedentedly detailed and direct information of the physical conditions and of the dynamical processes that facilitate and accompany the collapse and explosion of a star and the formation of its compact remnant. A discovery of the diffuse supernova neutrino background as integrated signal of all past stellar collapse events seems to be in reach (for a review, see Mirizzi et al. 2015). It will put our fundamental understanding of the neutrino emission from the whole variety of stellar death events to the test and may offer the potential to set constraints on neutron star versus black hole formation rates. Résumé Neutrinos are crucial agents during all stages of stellar collapse and explosion. Besides gravitational waves, they are the only means to obtain direct information from the very heart of dying stars. Therefore, they are a unique

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probe of the physics that plays a role at extreme conditions that otherwise are hardly accessible to laboratory experiments. The total energy, luminosity evolution, spectral distribution, and the mix of different species, which describe the radiated neutrino signal, carry imprints of the thermodynamic conditions, dynamical processes, and characteristic properties of the progenitor star and of its compact remnant. Numerical models are advanced to an increasingly higher level of realism for better predictions of the measurable neutrino features and their consequences.

6

Cross-References

 Diffuse Neutrino Flux from Supernovae  Explosion Physics of Core-Collapse Supernovae  Gravitational Waves from Core-Collapse Supernovae  Neutrino-Driven Explosions  Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis  Neutrinos from Core-Collapse Supernovae and Their Detection Acknowledgements The author is indebted to Georg Raffelt for valuable discussions and thanks him and Robert Bollig for providing graphics used in this article. Research by the author was supported by the European Research Council through an Advanced Grant (ERC-AdG No. 341157COCO2CASA), by the Deutsche Forschungsgemeinschaft through the Cluster of Excellence “Universe” (EXC-153), and by supercomputing time from the European PRACE Initiative and the Gauss Centre for Supercomputing.

References Alexeyev EN, Alexeyeva LN, Krivosheina IV, Volchenko VI (1988) Detection of the neutrino signal from SN 1987A in the LMC using the INR Baksan underground scintillation telescope. Phys Lett B 205:209–214. doi:10.1016/0370-2693(88)91651-6 Arcones A, Janka HT, Scheck L (2007) Nucleosynthesis-relevant conditions in neutrino-driven supernova outflows. I. Spherically symmetric hydrodynamic simulations. Astron Astrophys 467:1227–1248. doi:10.1051/0004-6361:20066983. astro-ph/0612582 Arnett WD (1966) Gravitational collapse and weak interactions. Can J Phys 44:2553 Balasi KG, Langanke K, Martínez-Pinedo G (2015) Neutrino-nucleus reactions and their role for supernova dynamics and nucleosynthesis. Progr Part Nucl Phys 85:33–81. doi:10.1016/j.ppnp.2015.08.001. 1503.08095 Bethe HA (1990) Supernova mechanisms. Rev Mod Phys 62:801–866. doi:10.1103/RevModPhys.62.801 Bionta RM, Blewitt G, Bratton CB, Casper D, Ciocio A (1987) Observation of a neutrino burst in coincidence with supernova 1987A in the Large Magellanic Cloud. Phys Rev Lett 58: 1494–1496. doi:10.1103/PhysRevLett.58.1494 Bruenn SW (1985) Stellar core collapse – numerical model and infall epoch. Astrophys J Suppl Ser 58:771–841. doi:10.1086/191056 Buras R, Rampp M, Janka HT, Kifonidis K (2006) Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 Mˇ star. Astron Astrophys 447:1049–1092. doi:10.1051/0004-6361:20053783. astroph/0507135

1602

H.-T. Janka

Burrows A (1984) On detecting stellar collapse with neutrinos. Astrophys J 283:848–852. doi:10.1086/162371 Burrows A (1990a) Neutrinos from supernova explosions. Ann Rev Nucl Part Sci 40:181–212. doi:10.1146/annurev.ns.40.120190.001145 Burrows AS (1990b) Neutrinos from supernovae. In: Petschek AG (ed) Supernovae. Springer, New York, pp 143–181 Burrows A, Lattimer JM (1986) The birth of neutron stars. Astrophys J 307:178–196. doi:10.1086/164405 Burrows A, Young T, Pinto P, Eastman R, Thompson TA (2000) A new algorithm for supernova neutrino transport and some applications. Astrophys J 539:865–887. doi:10.1086/309244. astroph/9905132 Burrows A, Reddy S, Thompson TA (2006) Neutrino opacities in nuclear matter. Nucl Phys A 777:356–394. doi:10.1016/j.nuclphysa.2004.06.012. astro-ph/0404432 Colgate SA, White RH (1966) The hydrodynamic behavior of supernovae explosions. Astrophys J 143:626. doi:10.1086/148549 Freedman DZ, Schramm DN, Tubbs DL (1977) The weak neutral current and its effects in stellar collapse. Ann Rev Nucl Part Sci 27:167–207. doi:10.1146/annurev.ns.27.120177.001123 Hannestad S, Janka HT, Raffelt GG, Sigl G (2000) Electron-, mu-, and tau-number conservation in a supernova core. Phys Rev D 62(9):093021. doi:10.1103/PhysRevD.62.093021. astroph/9912242 Hirata K, Kajita T, Koshiba M, Nakahata M, Oyama Y (1987) Observation of a neutrino burst from the supernova SN 1987A. Phys Rev Lett 58:1490–1493. doi:10.1103/PhysRevLett.58.1490 Horowitz CJ (2002) Weak magnetism for antineutrinos in supernovae. Phys Rev D 65(4):043001. doi:10.1103/PhysRevD.65.043001. astro-ph/0109209 Janka HT (1993) Neutrinos from type-II supernovae and the neutrino-driven supernova mechanism. In: Giovannelli F, Mannocchi G (eds) Frontier objects in astrophysics and particle physics. Società Italiana di Fisica, Bologna, p 345 Janka HT, Hillebrandt W (1989) Neutrino emission from type II supernovae – an analysis of the spectra. Astron Astrophys 224:49–56 Janka HT, Langanke K, Marek A, Martínez-Pinedo G, Müller B (2007) Theory of core-collapse supernovae. Phys Rep 442:38–74. doi:10.1016/j.physrep.2007.02.002. astro-ph/0612072 Janka HT, Hanke F, Hüdepohl L, Marek A, Müller B, Obergaulinger M (2012) Corecollapse supernovae: reflections and directions. Prog Theor Exp Phys 2012(1):01A309. doi:10.1093/ptep/pts067. 1211.1378 Juodagalvis A, Langanke K, Hix WR, Martínez-Pinedo G, Sampaio JM (2010) Improved estimate of electron capture rates on nuclei during stellar core collapse. Nucl Phys A 848:454–478. doi:10.1016/j.nuclphysa.2010.09.012. 0909.0179 Kachelrieß M, Tomàs R, Buras R, Janka HT, Marek A, Rampp M (2005) Exploiting the neutronization burst of a galactic supernova. Phys Rev D 71(6):063003. doi:10.1103/PhysRevD.71.063003. astro-ph/0412082 Keil MT, Raffelt GG, Janka HT (2003) Monte Carlo study of supernova neutrino spectra formation. Astrophys J 590:971–991. doi:10.1086/375130. arXiv:astro-ph/0208035 Langanke K, Martínez-Pinedo G, Sampaio JM, Dean DJ, Hix WR, Messer OE, Mezzacappa A, Liebendörfer M, Janka HT, Rampp M (2003) Electron capture rates on nuclei and implications for Stellar core collapse. Phys Rev Lett 90(24):241102. doi:10.1103/PhysRevLett.90.241102. astro-ph/0302459 Lentz EJ, Mezzacappa A, Messer OEB, Hix WR, Bruenn SW (2012) Interplay of neutrino opacities in core-collapse supernova simulations. Astrophys J 760:94. doi:10.1088/0004-637X/760/1/94. 1206.1086 Lentz EJ, Bruenn SW, Hix WR, Mezzacappa A, Messer OEB, Endeve E, Blondin JM, Harris JA, Marronetti P, Yakunin KN (2015) Three-dimensional core-collapse supernova simulated using a 15 Mˇ progenitor. Astrophys J Lett 807:L31. doi:10.1088/2041-8205/807/2/L31. 1505.05110 Liebendörfer M, Mezzacappa A, Thielemann FK (2001) Conservative general relativistic radiation hydrodynamics in spherical symmetry and comoving coordinates. Phys Rev D 63(10):104003. doi:10.1103/PhysRevD.63.104003. astro-ph/0012201

59 Neutrino Emission from Supernovae

1603

Liebendörfer M, Messer OEB, Mezzacappa A, Bruenn SW, Cardall CY, Thielemann FK (2004) A finite difference representation of neutrino radiation hydrodynamics in spherically symmetric general relativistic spacetime. Astrophys J Suppl Ser 150:263–316. doi:10.1086/380191. astroph/0207036 Liebendörfer M, Rampp M, Janka HT, Mezzacappa A (2005) Supernova simulations with Boltzmann neutrino transport: a comparison of methods. Astrophys J 620:840–860. doi:10.1086/427203. astro-ph/0310662 Lund T, Wongwathanarat A, Janka HT, Müller E, Raffelt G (2012) Fast time variations of supernova neutrino signals from 3-dimensional models. Phys Rev D 86(10):105031. doi:10.1103/PhysRevD.86.105031. 1208.0043 Marek A, Dimmelmeier H, Janka HT, Müller E, Buras R (2006) Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations. Astron Astrophys 445:273–289. doi:10.1051/0004-6361:20052840. astro-ph/0502161 Melson T, Janka HT, Bollig R, Hanke F, Marek A, Müller B (2015a) Neutrino-driven explosion of a 20 solar-mass star in three dimensions enabled by strange-quark contributions to neutrinonucleon scattering. Astrophys J Lett 808:L42. doi:10.1088/2041-8205/808/2/L42. 1504.07631 Melson T, Janka HT, Marek A (2015b) Neutrino-driven supernova of a low-mass iron-core progenitor boosted by three-dimensional turbulent convection. Astrophys J Lett 801:L24. doi:10.1088/2041-8205/801/2/L24. 1501.01961 Mezzacappa A, Liebendörfer M, Cardall CY, Bronson Messer OE, Bruenn SW (2004) Neutrino transport in core collapse supernovae. In: Fryer CL (ed) Astrophysics and space science library. Astrophysics and Space Science Library, vol 302. Kluwer, Dordrecht, pp 99–131. doi:10.1007/978-0-306-48599-2_4 Mikheyev SP, Smirnov AY (1985) Resonance enhancement of oscillations in matter and solar neutrino spectroscopy. Yad Fiz 42:1441–1448 Mirizzi A, Tamborra I, Janka HT, Saviano N, Scholberg K, Bollig R, Hudepohl L, Chakraborty S (2015) Supernova neutrinos: production, oscillations and detection. ArXiv e-prints 1508.00785 Müller B, Janka HT (2014) A new multi-dimensional general relativistic neutrino hydrodynamics code for core-collapse supernovae. IV. The neutrino signal. Astrophys J 788:82. doi:10.1088/0004-637X/788/1/82. 1402.3415 Müller B, Janka HT, Dimmelmeier H (2010) A new multi-dimensional general relativistic neutrino hydrodynamic code for core-collapse supernovae. I. Method and code tests in spherical symmetry. Astrophys J Suppl Ser 189:104–133. doi:10.1088/0067-0049/189/1/104. 1001.4841 O’Connor E, Ott CD (2013) The progenitor dependence of the pre-explosion neutrino emission in core-collapse supernovae. Astrophys J 762:126. doi:10.1088/0004-637X/762/2/126. 1207.1100 Otsuki K, Tagoshi H, Kajino T, Wanajo Sy (2000) General relativistic effects on neutrino-driven winds from young, hot neutron stars and r-process nucleosynthesis. Astrophys J 533:424–439. doi:10.1086/308632. astro-ph/9911164 Pruet J, Woosley SE, Buras R, Janka HT, Hoffman RD (2005) Nucleosynthesis in the hot convective bubble in core-collapse supernovae. Astrophys J 623:325–336. doi:10.1086/428281. astro-ph/0409446 Qian YZ, Woosley SE (1996) Nucleosynthesis in neutrino-driven winds. I. The physical conditions. Astrophys J 471:331. doi:10.1086/177973. astro-ph/9611094 Raffelt GG (1996) Stars as laboratories for fundamental physics: the astrophysics of neutrinos, axions, and other weakly interacting particles. University of Chicago Press, Chicago Raffelt GG (2001) Mu- and Tau-Neutrino spectra formation in supernovae. Astrophys J 561: 890–914. doi:10.1086/323379. arXiv:astro-ph/0105250 Raffelt GG (2012) Neutrinos and the stars. In: Proceedings of the international school of physics “Enrico Fermi”, vol 182, pp 61–143. doi:doi:10.3254/978-1-61499-173-1-61. arXiv:astroph/1201.1637 Rampp M, Janka HT (2002) Radiation hydrodynamics with neutrinos. Variable eddington factor method for core-collapse supernova simulations. Astron Astrophys 396:361–392. doi:10.1051/0004-6361:20021398. astro-ph/0203101

1604

H.-T. Janka

Shapiro SL, Teukolsky SA (1983) Black holes, white dwarfs, and neutron stars: the physics of compact objects. Wiley, New York Tamborra I, Müller B, Hüdepohl L, Janka HT, Raffelt G (2012) High-resolution supernova neutrino spectra represented by a simple fit. Phys Rev D 86(12):125031. doi:10.1103/PhysRevD.86.125031. 1211.3920 Tamborra I, Hanke F, Müller B, Janka HT, Raffelt G (2013) Neutrino signature of supernova hydrodynamical instabilities in three dimensions. Phys Rev Lett 111(12):121104. doi:10.1103/PhysRevLett.111.121104. 1307.7936 Tamborra I, Raffelt G, Hanke F, Janka HT, Müller B (2014) Neutrino emission characteristics and detection opportunities based on three-dimensional supernova simulations. Phys Rev D 90(4):045032. doi:10.1103/PhysRevD.90.045032. 1406.0006 Thompson TA, Burrows A, Meyer BS (2001) The physics of proto-neutron star winds: implications for r-process nucleosynthesis. Astrophys J 562:887–908. doi:10.1086/323861. astroph/0105004 Tubbs DL, Schramm DN (1975) Neutrino opacities at high temperatures and densities. Astrophys J 201:467–488. doi:10.1086/153909 Wolfenstein L (1978) Neutrino oscillations in matter. Phys Rev D 17:2369–2374. doi:10.1103/PhysRevD.17.2369 Wolfenstein L (1979) Neutrino oscillations and stellar collapse. Phys Rev D 20:2634–2635. doi:10.1103/PhysRevD.20.2634

Neutrino Signatures from Young Neutron Stars

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Luke F. Roberts and Sanjay Reddy

Abstract

After a successful core collapse supernova (CCSN) explosion, a hot dense protoneutron star (PNS) is left as a remnant. Over a time of 20 or so seconds, this PNS emits the majority of the neutrinos that come from the CCSN, contracts, and loses most of its lepton number. This is the process by which all neutron stars in our galaxy are likely born. The emitted neutrinos were detected from supernova (SN) 1987A, and they will be detected in much greater numbers from any future galactic CCSN. These detections can provide a direct window into the properties of the dense matter encountered inside neutron stars, and they can affect nucleosynthesis in the material ejected during the CCSN. In this chapter, we review the basic physics of PNS cooling, including the basic equations of PNS structure and neutrino diffusion in dense matter. We then discuss how the nuclear equation of state, neutrino opacities in dense matter, and convection can shape the temporal behavior of the neutrino signal. We also discuss what was learned from the late-time SN 1987A neutrinos, the prospects for detection of these neutrinos from future galactic CCSNe, and the effects these neutrinos can have on nucleosynthesis.

L.F. Roberts () Theoretical AstroPhysics Including Relativity and Cosmology (TAPIR), California Institute of Technology, Pasadena, CA, USA e-mail: [email protected] S. Reddy Institute for Nuclear Theory, University of Washington, Seattle, WA, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_5

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Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PNS Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Equations of PNS Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 PNS Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Analytic Estimates of Cooling Phase Timescales . . . . . . . . . . . . . . . . . . . . . . . . 2.4 PNS Neutrino Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Physics that Shape the Cooling Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Neutrino Opacities in Dense Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 PNS Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Observable Consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Neutrinos from SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Galactic Supernova Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Impact on CCSN Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

A nascent neutron star (NS) is often left as the remnant of a successful core collapse supernova (CCSN). This young NS emits a copious number of neutrinos over the first few seconds of its life. During this time it is referred to as a proto-neutron star (PNS). Due to the high densities and temperatures encountered inside the PNS, neutrinos cannot freely escape but instead must diffuse out over a period of about a minute (Burrows and Lattimer 1986). This neutrino emission is powered by a large fraction of the gravitational binding energy released by taking the iron core of a massive star and transforming it into a NS (2–5 1053 erg s) (Baade and Zwicky 1934). After about a minute, neutrinos can escape freely, which demarcates the transition from PNS to NS. This qualitative picture of late PNS neutrino emission was confirmed when about thirty neutrinos were observed from supernova (SN) 1987A over a period of about 15 s (Bionta et al. 1987; Hirata et al. 1987). If a CCSN were observed in our galaxy today, modern neutrino detectors would see thousands of events (Scholberg 2012). The neutrino signal is shaped by the nuclear equation of state (EoS) and neutrino opacities. Therefore, detection of galactic CCSN neutrinos would give a detailed window into the birth of NSs and the properties of matter at and above nuclear density. In addition to direct neutrino detection, there are other reasons why understanding the properties of these late-time CCSN neutrinos is important. First, they can influence nucleosynthesis in CCSNe (Woosley et al. 1990). In particular, PNS neutrino emission almost wholly determines what nuclei are synthesized in baryonic material blown off the surface of PNSs (Hoffman et al. 1997; Roberts et al. 2010; Woosley et al. 1994). Second, the integrated neutrino emission from CCSNe receives a large contribution from PNS neutrinos. Therefore, accurate models of PNS neutrino emission can contribute to understanding the diffuse SN neutrino background (Nakazato et al. 2015). Finally, the neutrino emission from the “neutrinosphere” of PNSs gives the initial conditions for the study of both

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matter-induced and neutrino-induced neutrino oscillations (Duan et al. 2006). The rate of PNS cooling also has the potential to put limits on exotic physics and possible extensions of the standard model using data already in hand from SN 1987A (Keil et al. 1997; Pons et al. 2001a, b). In this chapter, we discuss PNS cooling and the late-time CCSN neutrino signal. In Sect. 2, we focus on the basic equations of PNS cooling (Sect. 2.1) and models of PNS cooling (Sects. 2.2 and 2.4). In Sect. 3, we discuss the various ingredients that shape the CCSN neutrino signal, the nuclear equation of state, neutrino opacities, and convection, respectively. Finally – in Sects. 4.1, 4.2, and 4.3 – we discuss the observable consequences of late-time CCSN neutrinos. Throughout the chapter, we set „ D c D 1.

2

PNS Cooling

Essentially, all of the energy that powers the neutrino emission during a CCSN comes from the gravitational binding energy released when taking the white dwarf like iron core of the massive progenitor star and turning it into a NS (Baade and Zwicky 1934), which is ESN 

2 3GMpns

5rNS

 3  1053 erg



Mpns Mˇ

2 

rNS 1 : 12 km

(1)

The CCSN shock forms at an enclosed mass of 0.4 Mˇ and the material that is shock heated increases the effective PNS radius. This provides a reservoir of gravitational potential energy that can be converted into neutrinos. Therefore, around two thirds of the total energy, ESN , is available during the PNS cooling phase. After the CCSN shock has passed through the PNS, the interior entropy varies between one and six kb =baryon. Peak temperatures between 30 and 60 MeV are reached during PNS evolution, while the surface of the PNS has a temperature around 3–5 MeV. The interior of the PNS is comprised of interacting protons, neutrons, and electrons, at densities greater than a few times nuclear saturation density (s  2:8  1014 g cm3 ) toward the center of the PNS. It is also possible that more exotic degrees of freedom are present in the inner most regions of the PNS (Prakash et al. 1997). During core collapse, electron capture on heavy nuclei removes around 40 % of the electrons from the core before neutrinos become trapped (Hix et al. 2003), leaving behind Ye  0:3 in the core. Ye is the number of electrons per baryon and is equal to the proton fraction by charge conservation. Although this constitutes a large portion of the initial lepton number of the core, a cold NS has an even lower total lepton number. The lepton number of the PNS is the total number of electrons plus electron neutrinos minus the number of positrons and electron antineutrinos, which is a conserved quantity. In a cold NS, the interactions e  C p ! e C n and n ! N e C e  C p are in equilibrium. Equating these rates and solving for the

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electron fraction result in Ye  0:1 for the densities encountered in the cores of NSs. Therefore, the PNS must “deleptonize” to become a NS, which requires losing a total lepton number of around 56



NL  3:4  10

Mpns 1:4 Mˇ

 ;

(2)

which must be removed from the PNS by neutrinos. Inside the PNS, a copious number of neutrinos of all flavors are produced and scattered by weak interactions involving both the baryons and the leptons present in the medium. The rate at which neutrinos leave the PNS and carry off energy and lepton number will depend on thermal neutrino mean free path inside the PNS with energy "  60 MeV. Using a reference weak interaction neutrino cross section (see Sect. 3.1),  D

2  " 4GF2 "2  3  1040 cm2 ;

60 MeV

(3)

where GF is the Fermi coupling constant and " is the neutrino energy. A naive estimate of the neutrino mean free path in the PNS is then  

2      Rpns 3 Mpns 1 1 "N  14 cm ; nN b  60 MeV 12 km Mˇ

(4)

3 where nN b D 3Mpns =.4 Rpns mb / is the average baryon density of the PNS and "N is a characteristic energy for neutrinos inside the PNS. The neutrino mean free path is much smaller than the radius of the PNS, which is around 12 km once the shock-heated mantle has cooled. Therefore, neutrinos must escape from the PNS diffusively and will be in thermal and chemical equilibrium with the baryons and electrons throughout most of the PNS.

2.1

The Equations of PNS Cooling

Generally, PNS evolution is a neutrino radiation hydrodynamic problem where general relativity is important. A number of simplifications to the general system of equations can be made. First, the PNS cooling timescale is much longer than the sound crossing time of the PNS. Therefore, PNSs are very close to being in hydrostatic equilibrium and spherical symmetric. With these approximations, the equations of PNS cooling become (see Burrows and Lattimer (1986); Pons et al. (1999); Roberts (2012) for detailed derivations) G.Mg C 4 r 3 P /. C P / dP D dr r 2 2

(5)

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dMg D 4 r 2  dr

(6)

dN 4 r 2 nb D dr

d˛ ˛ D dP P C

(7) (8)

@.4 ˛r 2 FL / d YL D dt @N d Ye SN D˛ dt nb

(9) (10)

@.4 ˛ 2 r 2 H / d .1=n/ d .. C  /=nb / D ˛ 1  .P C P / dt @N dt d .=nb / d .1=n/ SE P D˛ : dt nb dt

(11) (12)

Equations 5, 6, 7, and 8 are just the relativistic equations of hydrostatic equilibrium, where P is the pressure,  is the energy density of the background fluid,  is the energy density of the neutrinos, nb is the baryon density, Mgpis the gravitational mass, N is the enclosed baryon number, r is the radius, D 1  2GMg =r, and ˛ is the lapse function. The lepton fraction is YL D Ye C Y e , where Ye is the number of electron per baryon and Y e D .n e  n Ne /=nb is the local net number of electron neutrinos per baryon. Equations 9 and 11 describe the conservation of lepton number and total internal energy in the PNS. Throughout most of the PNS, Eqs. 10 and 12 are zero and can be neglected since the neutrino number and energy source functions, SN and SE , rapidly bring the neutrinos into thermal equilibrium with the background fluid. The P energy flux and lepton number fluxes are given by FL D F Ne  F NNe and H D FiE (where the sum runs over all flavors of neutrinos and antineutrinos). The number and energy fluxes of individual neutrino species are given by 2

fN g F i E D .2 /3

Z 0

1

2 d ""f3g

Z

1

1

d f i ;

(13)

where f i D f i .t; r; "; / is the distribution function of neutrinos of species i ,  is the cosine of the angle of neutrino propagation relative to the radial direction, and " is the neutrino energy. Below, we often discuss the neutrino luminosity L i D 4 r 2 ˛ 2 FiE and the neutrino number luminosity NP i D 4 r 2 ˛FiN . The solution of this system of equations requires a method of determining the f i , the evolution of which is determined by the Boltzmann equation: Df i D .a;i C s;i Œf i /.1  f i /  .a;i C s;i Œf i /f i ; Dl

(14)

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where D=Dl is a Lagrangian derivative in phase space, et aa and s are absorption– scattering emissivities, and a and s are absorption and scattering opacities (Lindquist 1966; Thorne 1981). The evolution of the f can be attacked directly with the Boltzmann equation, but neutrino transport simplifies greatly throughout most of the PNS. As was mentioned above, the neutrino mean free path inside the PNS is much shorter than the distance over which nb , T , and Ye are changing. Therefore, the neutrino distribution functions are very close to thermal and the neutrinos propagate through the star diffusively. In the diffusion limit of the Boltzmann equation, the number and energy flux of neutrinos of species i are given by opacity-weighted radial derivatives of the neutrino density (Burrows and Lattimer 1986; Pons et al. 1999):

fN g F iE D  3 ˛ f4g

Z

1 0

2 ! f3g @fi;FD .!=˛/  ; d!    @r 3 a;i C s;i

(15)

where fi;FD ."/ D Œ1Cexp."=T i /1 is the Fermi–Dirac distribution for neutrinos of species i with degeneracy parameter i and ! is the neutrino energy at infinity. Both electron neutrinos and antineutrinos rapidly reach chemical equilibrium with the nuclear medium via charged-current neutrino interactions. Therefore, the electron neutrino chemical potential is  e D e C p  n and  Ne D  e . Because of the large mass of the  and particles, no net  or number is produced  in the PNS and   D  D 0. The quantity a;i is the total absorption opacity  corrected for detailed balance and s;i is the scattering transport opacity (Burrows et al. 2006; Pons et al. 1999). These opacities have units of inverse length and are approximately   nb  . In the equilibrium diffusion limit, the isotropic parts of the neutrino distribution functions only depend on the local temperature, as well as the electron neutrino degeneracy factor,  e D  e =T , for electron neutrinos and antineutrinos. The chemical potentials of the  and neutrinos are zero throughout the PNS due to the large masses of the  and particles. With these assumptions, the total lepton and energy fluxes in the diffusion limit become  @.˛T /

T2 @ e FL D  C D2 ˛T D3 ˛6 2 @r @r  @.˛T /

T3 @ e C D ; D H D  ˛T 4 3 ˛6 2 @r @r

(16) (17)

P i where D2 D D2 e C D2 Ne , D3 D D3 e  D3 Ne , and D4 D i D4 are diffusion coefficients. The single-species diffusion coefficients are Rosseland mean opacities defined by Dni

Z D

1

d" 0

"n fi;FD .1  fi;FD /   :  T nC1 a;i C s;i

(18)

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Only electron neutrinos and antineutrinos contribute to the lepton flux diffusion coefficients, while all species contribute to the energy flux diffusion coefficients. Note that the diffusion coefficients will be   .h" i/, where h" i is an average neutrino energy in the medium. This makes it clear that gradients in the temperature and  e in the PNS core, combined with the neutrino opacities, drive its deleptonization and cooling. In addition to these structure and transport equations, a model for the dense matter encountered in the PNS, as well as the initial configuration of s and YL versus radius, is required to predict the PNS neutrino signal. The EoS – which determines , P , and  e as a function of nb , T , and Ye – and the neutrino diffusion coefficients depend strongly on the properties of matter at and above nuclear saturation density. The equilibrium diffusion equations described above provide an excellent approximation to neutrino transport in the optically thick interior regions of the PNS, are useful for understanding the basic properties of PNS cooling, and have been used – along with flux limiters to prevent superluminal transport of energy and lepton number (Burrows and Lattimer 1986) – in numerous works studying the cooling of PNSs (Burrows and Lattimer 1986; Keil and Janka 1995; Pons et al. 1999; Roberts et al. 2012). Nonetheless, they are not suited to describe the neutrino transport near the surface where the neutrino mean free paths become large. They also cannot provide any information about the average energies of the neutrinos that emerge from the neutron star since they assume neutrinos are everywhere in thermal equilibrium with the background material. Therefore, some works have employed nonequilibrium, spectral neutrino transport at varying levels of sophistication (Fischer et al. 2010; Hüdepohl et al. 2010; Nakazato et al. 2013; Roberts et al. 2012; Sumiyoshi et al. 1995; Woosley et al. 1994). These methods all evolve the nonequilibrium distribution function of the neutrinos, f i , at a large number of neutrino energies using the Boltzmann equation or some approximation thereof.

2.2

PNS Evolution

Here, the evolution of a fiducial 1.42 Mˇ PNS model is described. PNS evolution has been modeled using numerical codes for almost 30 years (Burrows 1987; Burrows and Lattimer 1986; Fischer et al. 2010; Hüdepohl et al. 2010; Keil and Janka 1995; Keil et al. 1995; Nakazato et al. 2013; Pons et al. 1999, 2001a; Roberts 2012; Roberts et al. 2012; Sumiyoshi et al. 1995). Although the fidelity to the underlying micro- and macrophysics has improved with time, the basic features of PNS cooling are still the same. The illustrative model discussed in this section was calculated using the multi-energy group neutrino transport method described in Roberts et al. (2012). Even so, throughout most of the PNS this more realistic transport method reduces to the diffusion equations described above. This calculation began with a pre-SN model of a 15 Mˇ star from Woosley and Weaver (1995). The evolution through core collapse, bounce, and the cessation of shock expansion was followed. Once the SN shock crossed an enclosed baryonic

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mass of 1.42 Mˇ , the material outside this region was excised from the grid to crudely simulate the CCSN explosion. Then this PNS core was evolved for 100 s. This model is comparable to models found in Hüdepohl et al. (2010) and Fischer et al. (2010). We used an EoS similar to the Lattimer-Swesty equation of state with incompressibility Ks D 220 MeV (Lattimer and Douglas Swesty 1991), and all neutrino-nucleon interactions were treated in the elastic limit. The evolution of the interior structure of the model is shown in Fig. 1. The time evolution of various quantities in the center of the PNS as well as its energy and lepton number losses is shown in Fig. 2. These figures also show the evolution of the star during the pre-explosion phase of the SN (see the  Chap. 59, “Neutrino Emission from Supernovae” for a detailed discussion of the early-time emission). The initial structure left behind after deleptonization during core collapse and shock propagation through the core can be seen with the yellow lines in the panels showing the entropy and the lepton fraction in Fig. 1. There is a low entropy, high lepton number core and a high entropy, low lepton number mantle. The transition point between these two phases is near the maximum temperature point in the PNS. After collapse and bounce, the SN shock formed near this transition point, so the mantle is shock heated and the core is not. The high entropy found in the mantle increases its pressure and thereby increases its radius and decreases its density relative to the core. The initial core lepton fraction, YL D 0:33, is set by the point during core collapse when neutrinos become trapped, which occurs when the core reaches a density near 104 fm3 (Hix et al. 2003). This can be seen in the second and fourth panels of Fig. 2. Electron neutrinos are able to rapidly remove lepton number from the mantle, so this region has  e  0. Once the SN shock begins to explode the star and accretion slows down or ceases, PNS neutrino emission proceeds in three phases: the mantle contraction phase, the deleptonization phase, and the thermal cooling phase. The basic features of these different phases can be seen in Figs. 1 and 2. Mantle Contraction – During the first few seconds, the neutrino emission is dominated by contributions from the contracting mantle. This contraction is not dynamical. Rather, it is driven by the reduction in pressure due to entropy and electron losses. As can be seen in the second to last panel of Fig. 2, the radius of the PNS contracts from around 100 km to a value very close to the cold NS radius – which is 12 km for the EoS state used in this model – within the first 2 s of PNS evolution. The neutrino luminosity emerging from the surface of the PNS is sourced completely in this region; see the top left panel of Fig. 1. In fact, energy is also being lost from the inner boundary of the mantle as electron antineutrinos and heavy-flavored neutrinos diffuse down the positive temperature gradient into the core; the total neutrino luminosity becomes negative at the core–mantle boundary. Additionally, the deleptonization wave pushes inward over this period but does not reach the center of the PNS. This can be seen in the panels of Fig. 1 showing YL and  e .

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Fig. 1 Interior PNS quantities at selected times, with time coded by color. The semitransparent lines on the color bar demarcate the time of the various lines shown in the panels below it. The gray lines are for selected times during the dynamical post-bounce evolution. Here, we focus on the evolution of the inner core after the dynamical phase has ended. The top left panel shows the energy carried by all flavors of neutrinos, while the top right panel shows the net lepton number transported by neutrinos as a function of enclosed baryonic mass. The second row of panels shows the evolution of the entropy and lepton fraction, which is determined by the neutrino fluxes. The third row of panels shows the temperature and neutrino degeneracy parameter evolution. Gradients in these quantities drive the diffusive neutrino fluxes. The final row of panels shows the radius and baryon density as a function of enclosed baryonic mass to illustrate how the structure of the PNS evolves and contracts in response to loss of energy and lepton number

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Fig. 2 Time evolution of central quantities and the total neutrino luminosity and lepton flux. The gray region corresponds to the accretion phase and is on a linear timescale, while the region to the right is the PNS cooling phase and it is plotted on a logarithmic scale. At the transition from the accretion phase to the PNS cooling phase, all of the material from above the shock is excised from the grid, causing a slight jump in some quantities. The top panel shows the total energy loss rate from the PNS and the deleptonization rate. The second panel shows the evolution of the central lepton fraction and electron fraction, as well as the PNS radius. The deleptonization era corresponds to the period over which Ye and YL differ. The third panel shows the evolution of the central neutrino chemical potential and entropy. The impact of Joule heating is visible between 5 and 20 s. The bottom panel shows the central density and the central lapse, ˛, to illustrate the contraction of the PNS over time

Deleptonization Phase – Once the PNS has settled down too close to the radius of a cold NS, the luminosity evolution is driven by the deleptonization wave that propagates into the center of the PNS and eventually brings the entire PNS to a state where  e D 0. This occurs over a period of about 20 s. The lepton number flux is produced by the negative gradient in  e left after the shock breakout in the region between the homologous core and the base of the mantle.

60 Neutrino Signatures from Young Neutron Stars

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During this period the core entropy and temperature increase, as can be seen in the bottom panel of Fig. 2. This is due to two effects. First, as was the case during the mantle contraction phase, electron antineutrinos and heavy-flavor neutrinos are diffusing inward and heating the core. Second, lepton number is being lost from the core due to the positive flux of electron neutrinos throughout the PNS, which causes “Joule heating” (Burrows and Lattimer 1986). To see this, we recast Eq. 11 in terms of the entropy using the first law of thermodynamics: T

ds @.4 ˛ 2 r 2 H / d YL D ˛ 1   e : dt @N dt

(19)

Here, s is the entropy per baryon in units of Boltzmann’s constant, T is the temperature, and  e is the electron neutrino chemical potential. Joule heating comes from the second term on the right-hand side of this equation, since d YL =dt < 0 and  e > 0. Eventually, the combined effects of these two processes raise the central entropy from around one to two kb =baryon and create a negative entropy and temperature gradients throughout the star. Thermal Cooling Phase – Once  e  0 throughout the star (see Fig. 1), the PNS slowly contracts as energy leaks from the entire star. Both the entropy and lepton number of the core fall during this period, as shown in Fig. 2. The deleptonization rate falls off rapidly, but it does not go to zero because the local equilibrium electron fraction decreases with the local temperature, so low-level deleptonization continues. The period of PNS cooling ends when the object becomes optically thin to neutrinos and the neutrino luminosity falls off abruptly.

2.3

Analytic Estimates of Cooling Phase Timescales

It is instructive to use the equations of Sect. 2.1 and a few simplifying assumptions to obtain analytic solutions to the neutrino transport equations. This can elucidate how the timescales of the deleptonization and thermal cooling phases depend on the neutrino opacities and the EoS. At the onset of deleptonization, electron neutrinos are degenerate. Under these conditions, the gradient in neutrino chemical potential dominates the lepton number flux in Eq. 9. Further, due to Pauli blocking, only neutrinos at the Fermi surface contribute, and the relevant diffusion coefficient reduces to D2 '

2 e 1 : 2T 2 a . e /

(20)

In degenerate matter, as we shall show later in Sect. 3.1,

a . e ; T / 

GF2 1 C 3gA2 M 2 T 2 e ' 2

4



kB T 15 MeV

2 

 1 e 200 MeV 20 cm (21)

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L.F. Roberts and S. Reddy

where M is the nucleon mass, T is the temperature, and e is the electron chemical potential. Using Eq. 20 and neglecting general relativistic corrections, we can approximate the lepton number flux in Eq. 9 as FL 

nb @Y e : 6a @r

(22)

By noting that nb =a is a weak function of the density, we ignore its spatial dependence to find an analytic solution of the separable form Y .r; t / D Y ;0 .t / .r/ to Eq. 9, similar to the method described in Prakash et al. (1997). Using appropriate boundary conditions at the surface, we separately solve for spatial and temporal dependencies with .0/ D 1 and .0/ D 1. For the temporal part, which is of interest here, we obtain a simple exponential solution: 

t .t / D exp D

 where

D '

6ha i R2 @YL : Cx @Y

(23)

Here, ha i represents a spatial average of the charged current opacity inside the PNS and the constant Cx ' 10 depends on .r/. Using fiducial values T D 15 MeV and e D 200 MeV and @YL =@Y D 5 and setting ha i D a .e D 200 MeV; T D 15 MeV/, we obtain  D  11

R 10 km

2 

kB T 15 MeV

2 

  @Y  e L 200 MeV 5 @Y

s:

(24)

This result, albeit arrived at with some approximation, clearly reveals the microphysics. The dependence on T , e , and @YL =@Y is made explicit, and we discuss later in Sect. 3 how the dense matter EoS directly affects these properties. We can also estimate the amount of Joule heating in the core: (see Eq. 19) @YL @YL Y ;0  nb  EP joule D nb  ; @t @Y D

(25)

where we have used Eq. 23 to express the result in terms of the deleptonization time. For typical values of the deleptonization time D  11 s and @YL =@Y  5, we find the heating rate per baryon EP joule =nb   Y ;0 =3. At early times when   150 MeV and Y ;0  0:05, the heating rate  2 MeV per baryon per second will result in a similar rate of change in the matter temperature. This, coupled with the positive temperature gradients, results in a net heating of the inner core when t < D . After deleptonization when the core begins to cool, the second term in Eq. 19 can be neglected and the energy flux H 

@T T3 D4 : 6 2 @r

(26)

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Energy transport is dominated by  ; N  ; ; N , and N e neutrinos since their charged-current reactions are suppressed and therefore they have larger mean free paths. For typical conditions where nucleons are degenerate and neutrino degeneracy is negligible, elastic neutral current scattering off nucleons is a dominant source of opacity and (see Sect. 3.1) s .E / '

5 G 2 c 2 NQ 0 kB T E 2 ; 6 F A

(27)

P where NQ 0 D iDn;p @ni =@i is the effective density of nucleon states at the Fermi surface to which neutrinos couple and cA ' 1:2 is the axial vector coupling. Using Eq. 27 the diffusion coefficient D4 in Eq. 26 can be written as

D4 D

3 : GF2 cA2 NQ 0 .kB T /3

(28)

Substituting Eq. 28 in Eq. 26, Eq. 19 can be solved with the separable ansatz T .r; t / D Tc .x/.t / to find a self-similar solution. We find that the temporal part .t / D 1  .t = c /, where   2 2=3  2 GF2 cA2 R 3nb @s kB Tc hnb i 2 N0 2 kB Tc R ' 10 s c  ; ˇ

@T 30 MeV n2=3 12 km 0 (29) where hi denotes a spatial average, the numerical constant ˇ Š 19, and n0 D 0:16 fm3 . Additionally, we have used @s=@T D 2 N0 =3nb and N0 D M .3 2 nb /1=3 = 2 , which hold for a nonrelativistic, degenerate gas. The spatial averages and numerical value of ˇ are obtained by solving for the function .r/.

2.4

PNS Neutrino Emission

Here, we discuss the evolution of the flavor-dependent neutrino luminosities and average energies, which constitute the detectable signal from the PNS. We focus on the properties of the neutrinos near the surface of the PNS. As the neutrinos propagate through the rest of the star, neutrino oscillations can change the flavor content of the neutrino fields and alter the spectra of the neutrinos that eventually reach earth (Duan et al. 2010). The evolution of the interior of the PNS drives the total energy and lepton number emitted from the surface, but the outermost layers of the PNS shape the spectrum of the emitted neutrinos. Therefore, it is convenient to describe the approximate

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L.F. Roberts and S. Reddy

radius at which neutrinos that escape to infinity are emitted, the “neutrinosphere” R . Following Keil et al. (2003) and Fischer et al. (2011), we define Z

1

therm .R / D

dr R

p 2 ha i.ha i C hs i/ D ; 3

(30)

where hi is an opacity averaged over the local neutrino distribution function. This is of course an approximation, since neutrino interactions have a strong energy dependence. Neutrinos of the same flavor but different energies will therefore decouple at different positions within the PNS. Nonetheless, the neutrino luminosity in a particular flavor can be reasonably estimated by assuming the neutrinosphere is a blackbody emitter L D 4 BB R 2 T .R /4 ;

(31)

where BB D 4:75  1035 erg MeV4 cm2 s1 is the blackbody constant and  is a factor of order unity that accounts for deviations from strict Fermi–Dirac blackbody emission (Hüdepohl et al. 2010; Mirizzi et al. 2015). For a pure blackbody spectrum, the average energy of the emitted neutrinos would be h" i  3:15T .R /. The energy moments of neutrinos of species i at radius r are given by R1 h"n i i

0

D R1 0

R1

nC2 f i 1 d " R1 2 d " 1 d " f i

d"

:

(32)

In reality, high-energy neutrinos have a larger decoupling radius than lower-energy neutrinos due to the approximate "2 scaling of the neutrino opacities (Keil et al. 2003). Therefore, high-energy neutrinos are emitted from regions with lower temperatures. The emitted neutrino spectra then have a “pinched” character, where there is a deficit of high-energy neutrinos relative to the Fermi–Dirac spectrum predicted by an energy-averaged neutrinosphere (Janka and Hillebrandt 1989). The evolution of the neutrinosphere radii as a function of time is shown in the third panel, and the temperature at the neutrinospheres is shown in the fourth panel of Fig. 3. There are only small differences between the  and flavored neutrino and antineutrino emission because they experience similar neutral current opacities. Therefore, we group all of these flavors together in flavor x. During the accretion phase and into the mantle contraction phase, there is a clear hierarchy with R x < R Ne < R e . This is driven mainly by differences in the chargedcurrent opacities: electron neutrinos get a large opacity contribution from the reaction e C n ! e  C p due to the large number of neutrons present near the decoupling region, electron antineutrinos get a somewhat smaller contribution from N e C p ! e C C n because of the small number of protons present in the decoupling region, and heavy flavored neutrinos receive no contribution to their opacity from charged current interactions. Since the temperature is decreasing with increasing

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Fig. 3 Time evolution of neutrino properties at infinity and the properties of the neutrinospheres. The gray region corresponds to the accretion phase and is on a linear scale, while the region to the right is the PNS cooling phase and it is plotted on a logarithmic scale. We measure radiation quantities at a radius of 300 km or at the maximum radius of the simulation domain, whichever is smaller. At the transition from the accretion phase to the PNS cooling phase, all of the material from above the shock is excised from the grid, causing a slight jump in some quantities. In all of the panels, all heavy-flavor neutrinos are represented by x , since their properties are all very similar. In the top panel, we show the neutrino luminosity for single flavors as a function of time. In the second panel, we show the evolution of the neutrino average energies. In the third panel, we show the evolution of the neutrinosphere radii, along with the PNS radius, as a function of time. The simulation covers the entire time the PNS is optically thick to neutrinos. The bottom panel shows the temperature at the neutrinospheres. Similar results can be found in Fischer et al. (2011)

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radius, this gives rise to the standard early-time hierarchy of neutrino energies h" e i < h" Ne i < h" x i during the accretion and mantle cooling phases that can be seen in the second panel of Fig. 3. During this period, inelastic scattering from electrons outside of the neutrinosphere reduces the average energies of heavy-flavor neutrinos relative to what the blackbody model would predict (Raffelt 2001). In the deleptonization phase, there are very few protons in the outer layers of the PNS. Therefore, the opacities for the electron antineutrinos and the heavy-flavor neutrinos are very similar and all of these neutrino flavors decouple at similar radii. In Fig. 3, these neutrinos have almost equal average energies over the majority of the PNS cooling phase. Eventually, during the thermal cooling phase, all the three neutrinospheres converge and the average emitted energies of all flavors become similar (Fischer et al. 2011), although the time at which they converge depends on how the charged-current opacities are calculated (Roberts et al. 2012). The top panel of 3 shows the luminosities of individual flavors of neutrinos. Soon after shock breakout, the electron neutrino and antineutrino luminosities become very close to one another and stay similar throughout the entire cooling evolution. Deleptonization proceeds because the average energies of the electron neutrinos are lower, and more electron neutrinos are required to carry a fixed luminosity than electron antineutrinos. Due to their small neutrinosphere, the heavy-flavor neutrino luminosities are much lower than the electron neutrino luminosities during the mantle cooling phase. After mantle contraction, there is approximate equipartition of luminosity among the different flavors.

3

Physics that Shape the Cooling Signal

The PNS neutrino signal is interesting in part because it is shaped by the properties of neutron-rich material at densities and temperatures that are inaccessible in the laboratory. Because of the high densities encountered throughout the PNS, the internucleon separation is small enough that interactions between nuclei play a central role in determining the PNS EoS and the neutrino interaction rates. Over the past decade, improved models to describe hot and dense matter were developed that reproduce empirically known properties of symmetric nuclear matter at saturation density. However, since matter encountered in the proto-neutron stars is characterized by a small proton fraction xp ' 0:05  0:3, the symmetry energy, defined through the relation S .nb / D E.nb ; xp D 1=2/  En .nb ; xp D 0/ ;

(33)

where E.nb ; xp D 1=2/ is the energy per particle of symmetric nuclear matter and E.nb ; xp D 0/ is the energy per particle of pure neutron matter, plays an important role. The energy of neutron-rich matter E.nb ; xp / ' E.nb ; xp D 1=2/ C S .nb /.1  2xp2 / since quartic and higher-order terms are found to be small in most theoretical calculations. In this context, ab initio calculations of the energy of neutron matter at subsaturation density (Gandolfi et al. 2011; Tews et al. 2013)

60 Neutrino Signatures from Young Neutron Stars

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have provided valuable guidance in the development of a new suite of models for hot and dense matter which are also consistent with recent neutron star radii in the range 10–12 km. These smaller radii are favored by recent modeling efforts to extract the radius of neutron stars from X-ray observations of quiescent neutron star in low mass X-ray binaries and X-ray burst (Ozel et al. 2015; Steiner et al. 2013). The properties of matter at and around nuclear saturation density, especially S .nb /, can influence deleptonization and neutrino cooling timescales, convection, and the neutrino spectrum (Roberts et al. 2012; Roberts et al. 2012; Sumiyoshi et al. 1995). PNS evolution is also sensitive to the thermal properties of degenerate dense matter as discussed in 2.3, and for a discussion of it, we refer the reader to Refs. Prakash et al. (1997), Constantinou et al. (2014), and Rrapaj et al. (2015). In the next two subsections, we describe how nuclear interactions can affect neutrino opacities and convective instabilities inside the PNS, both of which can alter the PNS cooling timescale. At densities near and below nuclear saturation density, PNS matter is only composed of protons, neutrons, and electrons, but at higher densities, it is possible for more exotic material to be present. Hyperons–baryons containing strange quarks – can be produced in the interior of the PNS because the weak interaction does not conserve strangeness (Prakash et al. 1997). Quark matter (Pons et al. 2001b; Steiner et al. 2001) or Bose condensates (Pons et al. 2000, 2001a; Prakash et al. 1997) may also exist in the innermost regions of PNSs. In addition to altering the neutrino opacities, these new degrees of freedom serve to soften the nuclear EoS at high density and reduce the maximum neutron star mass. This can lead to “metastable” PNSs that emit neutrinos for tens of seconds before collapsing to a black hole (BH) when more exotic material forms in their core and pressure support is reduced. BH formation would abruptly end the neutrino signal and is therefore directly observable (Pons et al. 2001b). We do not discuss these effects in any more detail here, but refer the reader to Prakash et al. (1997).

3.1

Neutrino Opacities in Dense Matter

The neutrino scattering opacities and thereby the diffusion coefficients defined in Sect. 2.1 receive contributions from neutrino scattering, absorption, and pair production processes, as well as the inverses of the latter two. Scattering contributions come from the reactions i C n • i C n i C p • i C p i C e  • i C e  i C e C • i C e C ; as well as scattering from other possible components of the medium. All of the reactions above have neutral current contributions for all flavors of neutrinos,

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while e  and e C scattering also have a charged-current contribution for e and N e scattering, respectively. Since the dominant scattering contribution for all particles comes from the n and p scattering, there are only small differences between the scattering contributions to the diffusion coefficients for different neutrino flavors. Scattering from electrons and positrons can be highly inelastic, due to the small mass of the electron relative to the characteristic PNS neutrino energy, while scattering from neutrons and protons is close to elastic. This inelasticity can alter the emitted neutrino spectrum and serves to bring the average energies of the different neutrino species closer to one another (Hüdepohl et al. 2010). The diffusion coefficients for the various neutrino flavors become different from one another due to charged-current neutrino interactions. The main absorption contribution to Di e comes from e  C p • e C n; while the main absorption contribution to Di Ne comes from e C C n • N e C p: All of the opacities receive contributions from thermal processes such as N C N ! N C N C C N N e  C e C ! C ; but these are usually small compared to the charged-current interactions that affect the electron neutrinos and antineutrinos. For both scattering and absorption processes, the cross section per unit volume for a general process C 2 ! 3 C 4 (where particle 3 is either a neutrino, electron, or positron) can be written as (Reddy et al. 1998) 2 ." / D 2" .2 /9

Z

d 3 p2 2"2

Z

d 3 p3 2"3

Z

d 3 p4 f2 ."2 /.1  f3 ."3 //.1  f4 ."4 // 2"4

 .2 /4 ı 4 .P C P2  P3  P4 / hjM j2 i;

(34)

where

hjM j2 i D16GF2 .CV2 C CA /2 .P  P2 /.P3  P4 / C .CV  CA /2 .P2  P3 /.P  P4 /  (35)  .CV2  CA2 /M2 M4 .P  P3 / is the spin-summed weak interaction matrix element of the process, CV and CA are the vector and axial coupling constants, ı 4 is the four-dimensional Dirac delta function, Pi D ."i ; pi / is the relativistic four-momentum, pi is the threemomentum, "i is the energy, and fi is the distribution of species i . Particles 2 and

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4 are always in thermal equilibrium inside PNSs, so f2 and f4 are isotropic Fermi– Dirac distribution functions. This expression comes directly from Fermi’s golden rule. If we specialize to particles 2 and 4 being nucleons, the reduced matrix element becomes independent of the nucleon momenta at leading order v=c, and the cross section can be written as ." / D

GF2 .2 /2

Z

1

1

d 3 .CV2 .1C3 /CCA2 .33 //

Z

1

d "3 p3 "3 .1f3 ."3 //S .q0 ; q/; 0

(36)

where CV and CA are weak vector and axial–vector coupling constants of the weak interaction, 3 D p  p3 =.jp jjp3 j/, and Z S .q0 ; q/ D 2

d 3 p2 .2 /3

Z

d 3 p4 f2 ."2 /.1  f4 ."4 //.2 /4 ı 4 .Q C P2  P4 / .2 /3 (37)

The energy–momentum transfer from the neutrino to the nucleons is denoted by the four-vector Q D .q0 ; q/, such that "3 D "  q0 and q D jqj D q

"2 C "23  2" "3 3 : This form of the opacity separates the contribution of the nucleons (or the “medium”) from the neutrino and the outgoing particle (be it another particle or a neutrino with a different energy). The function S .q0 ; q/ is often referred to as the response function or structure factor. A similar separation is found when the full-momentum dependence of the matrix element is included, although there are multiple response functions with different kinematic dependence (Reddy et al. 1998). The contribution to the cross section from particle 3 is the amount of phase space available to it in the final state, which results in the leading order "2 dependence of weak interaction cross sections when q0  0. The response function includes the effects of energy/momentum conservation, Pauli blocking of the final-state nucleons, and thermal motion of the nucleons. When the momentum transfer q is small (so that p2 D p4 ), the response simplifies significantly. After manipulating the Fermi–Dirac distribution functions and integrating, one finds S .q0 ; 0/ D 2 ı.q0 /

n2  n 4 : 1  exp..4  2 /=T /

(38)

When species 2 and 4 are nondegenerate, this reduces to 2 ı.q0 /n2 . This response is purely elastic, since q0 D 0 and " D "3 . For scattering reactions, when species 2 equals species 4, this response becomes Sscat .q0 ; 0/ D 2 ı.q0 /T

@n2 : @2

(39)

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L.F. Roberts and S. Reddy

In the degenerate limit, the response can be shown to be (Reddy et al. 1998)

Sdeg .q0 ; q/ D

(.q  pF2 C pF4 / M 2 .q0 C 2  4 / ;

q 1  exp..4  2  q0 /=T /

(40)

where pFi is the Fermi momentum of particles of species i and ( is the Heaviside step function. The opacity then becomes   2

2 C "  GF2 2 2 2 2 T ; .C C 3CA /M T ." C 2  4 /& ." / D 4 3 V 1 C exp..  " /=T /

(41)

where & D (.pF4 CpF3 pF2 pF /C

p F4 C p F3  p F2 C p F (.pF jpF4 CpF3 pF2 j/: 2" (42)

When neutrinos are degenerate, only neutrinos near the Fermi surface will be able to scatter. The relevant opacity is then

. / D

GF2 .C 2 C 3CA2 /M 2 .kB T /2 3 ; 8 V

(43)

where we have assumed all four species are in equilibrium,  C 2 D 3 C 4 . These results are used in Sect. 2.3 to estimate the deleptonization and thermal cooling timescales. If nucleon–nucleon interactions are also considered, they can alter the response of the medium in a number of ways (Burrows and Sawyer 1998; Hannestad and Raffelt 1998; Horowitz and Pérez-García 2003; Reddy et al. 1998, 1999). The simplest way to include nucleon–nucleon interactions is in the mean field approximation. In this approximation, the average interaction with all other nucleons gives single nucleons a momentum-independent potential energy and an effective in-medium mass. The nucleon energy–momentum relation then becomes "2;4 D 2 =2m2;4 C U2;4 . In the zero momentum transfer limit, the response becomes p2;4 (Reddy et al. 1998) SMF .q0 ; 0/ D 2 ı.q0 C U /

n2  n 4 ; 1  exp..4  2 C U /=T /

(44)

where U D U2  U4 . This implies that "3 D " C U . Because the cross section strongly depends on the phase space available to particle 3, a large, positive U can increase the neutrino cross section, while a negative U will reduce the cross section (Martínez-Pinedo et al. 2012; Roberts et al. 2012). The potential energy of

60 Neutrino Signatures from Young Neutron Stars

1625

neutrons, Un , differs from the potential energy of protons, Up , due to the isospin dependence of the nuclear interaction. In neutron-rich material, neutrons have a larger potential energy than protons because of the large, positive nuclear symmetry energy, S .nb /, throughout the PNS. In fact, the potential energy difference can be related directly to the nuclear symmetry energy (Hempel 2015). Therefore, mean field corrections to the response in PNSs increase the cross section for e C n ! e  C p and decrease the cross section for N e C p ! e C C n. This change alters D2 and D3 and thereby the PNS deleptonization rate (Roberts 2012). These corrections can also move the electron neutrinosphere to a larger radius and the electron antineutrinosphere to a smaller radius. This increases the difference between h" e i and h" Ne i, which may have large consequences for nucleosynthesis near the PNS (see Sect. 4.3) (Martínez-Pinedo et al. 2012; Roberts 2012). When the neutrino wavelength is long compared to the internucleon separation distance, neutrino interactions with the medium concurrently involve multiple nucleons at a microscopic level. In this limit, collective properties induced by nuclear interactions can significantly alter the response of the nuclear medium. The mean field approximation does not account for possible nucleon–nucleon correlations induced by interactions. Generally, accounting for these correlations is a complex many-body problem which has only been tackled within the randomphase approximation (RPA) (Burrows and Sawyer 1998; Reddy et al. 1999). The RPA essentially accounts for weak charge screening, which can reduce the neutrino opacity. In Fig. 4, we show the suppression of the diffusion coefficients by correlations. At high density, the corrections can be larger than a factor of two. This serves to decrease the cooling timescale of the PNS (Burrows and Sawyer 1998; Hüdepohl et al. 2010; Reddy et al. 1999; Roberts et al. 2012). In Fig. 5, we show models of PNS cooling that include RPA corrections to the neutrino

Fig. 4 Ratio of diffusion coefficients not including nuclear correlations to diffusion coefficients including nuclear correlations. At high density, weak charge screening (calculated using the random-phase approximation) suppresses the neutrino opacity and increases the neutrino diffusion coefficients. This reduces the PNS cooling timescale

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L.F. Roberts and S. Reddy

Base Convection RPA RPA + Convection

2

1

10

L

ν,tot

(10

51

erg s−1)

10

0

10

−1

10

1

0

10

10

Time (s)

Fig. 5 The total PNS neutrino luminosity versus time for a number of PNS models that include convection and/or the effect of nuclear correlations on the opacity. Both convection and nuclear correlations decrease the cooling timescale relative to the baseline model. Convection alters the luminosity at early times, while correlations only become important after the mantle cooling phase. The models shown here are similar to those described in Roberts et al. (2012)

interaction rates compared with those that do not. During the mantle contraction phase, they have little effect because the neutrino luminosity originates in a lowdensity region. Once the neutrino luminosity is determined at higher densities, during the deleptonization and thermal cooling phases, these corrections decrease the neutrino emission timescale. The magnitude of this effect depends on the assumed nucleon–nucleon interaction (Keil et al. 1995; Reddy et al. 1999; Roberts et al. 2012).

3.2

PNS Convection

In addition to neutrinos, hydrodynamic motions of the PNS can transport energy and lepton number through the star. Although the majority of the PNS is in hydrostatic equilibrium, there can be regions which are unstable to the development of convection. Similar to the case in normal stellar burning, convective overturn can transport energy and lepton number much more rapidly than radiation and shorten the cooling timescale (Burrows 1987; Roberts et al. 2012; Wilson and Mayle 1988). The standard Ledoux criterion for convective instability, adapted to the conditions found inside a PNS, is given by

60 Neutrino Signatures from Young Neutron Stars

!C2 D 

1627

g .s r ln.s/ C YL r ln.YL // > 0;  nb

(45)

where g is the local acceleration due to gravity and   nb D

@ln P @ln nb



 ; s D s;YL

@ln P @ln s



 ; YL D

nb ;YL

@ln P @ln YL

 : nb ;s

These last three quantities are only functions of the nuclear EoS. In particular, nb is related to the sound speed and nb and s are always positive. The third thermodynamic derivative, YL , can either be positive or negative; the pressure receives contributions from both electrons which have @Pe =@Ye > 0 and from the nucleons for which @PN =@Ye < 0 when Ye < 0:5 due to variations in @S .nb /=@nb where S .nb / is the nuclear symmetry energy defined in Eq. 33 (Roberts et al. 2012). Noting that @Ye =@YL > 0 and of order unity, it is easy to see that the sign of YL can change depending on the relative contributions of electrons and nucleons. Therefore, the portion of the PNS that is convectively unstable depends on the assumed nuclear EoS and its symmetry energy, as well as the gradients of entropy and YL (Roberts et al. 2012). The PNS may also be subject to double-diffusive instabilities due to the lateral transport of composition and energy by neutrinos (Wilson and Mayle 1988). These double-diffusive instabilities would extend the region over which the PNS was unstable to hydrodynamic overturn. The outer PNS mantle is unstable to adiabatic convection soon after the passage of the bounce shock (Epstein 1979). This early period of instability beneath the neutrinospheres has been studied extensively in both one and two dimensions with the hope that it could increase the neutrino luminosities enough to lead to a successful CCSN explosion (Buras et al. 2006; Wilson and Mayle 1988). During the deleptonization and thermal cooling phases, more and more of the PNS becomes unstable to convection because of the entropy and lepton gradients produced by neutrino cooling. Figure 1 shows that there are negative entropy gradients throughout the mantle for the entirety of the PNS phase, and the negative gradient extends through the whole PNS by the end of deleptonization. Because the cooling timescale is much longer than the dynamical timescale of the PNS, multidimensional simulations of late-time PNS convection have not been carried out to date. Rather, mixing length theory has been employed to study the impact of convection on the late-time neutrino signal (Burrows 1987; Mirizzi et al. 2015; Roberts et al. 2012). In Fig. 5, we show the total neutrino luminosity for models with and without convection to highlight the impact convection can have on the cooling timescale. At early times, the luminosity is elevated by around 25 % due to convection until the period of convective instability ceases a few seconds after bounce. After this the luminosity is depressed relative to the case without convection, and the overall cooling timescale is reduced.

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4

Observable Consequences

4.1

Neutrinos from SN 1987A

Up to now, our discussion of PNS cooling has been mostly theoretical. In fact, the basic features of PNS cooling were reasonably well characterized before there was any observational evidence for this picture (Burrows and Lattimer 1986). In February of 1987, both photons (Kunkel et al. 1987) and neutrinos (Alexeyev et al. 1988; Bionta et al. 1987; Hirata et al. 1987) reached Earth from a massive star that collapsed in the Large Magellanic Cloud, SN 1987A. Of course, the neutrinos are of the most interest for constraining PNS evolution, since the optical depth near the PNS is far too high for photons to escape this region. Bursts of sixteen, eight, and five neutrinos were observed near the time of SN 1987A in the Kamiokande (Hirata et al. 1987), IMB (Bionta et al. 1987), and Baksan (Alexeyev et al. 1988) neutrino detectors, respectively. Although there were only 30 electron antineutrino events detected, they provided general confirmation of the previously developed theoretical picture of neutrino emission during core collapse and subsequent PNS cooling (Burrows and Lattimer 1987). The neutrinos were observed within a 23-second window at Kamiokande and had energies ranging between 5 and 30 MeV. It is worth mentioning that this implies a PNS survived in the core of SN 1987A for at least 20 s, even though no central object has been observed in the remnant of SN 1987A to date (Graves et al. 2005). In Fig. 6, the joint probability distribution of the electron antineutrino spectral temperature and PNS cooling timescale inferred from the detected SN 1987A neutrino events by Loredo and Lamb (2002). They model the PNS cooling phase with a luminosity falling off with time as L Ne .t / / .1 C t = c /4 and Fermi–Dirac neutrino spectrum with temperature T Ne D Tc;0 .1 C t = c /1 . The neutrino cooling timescale is best fit with c D 14:7 s, and the antineutrino average energy at 1 s after bounce is best fit by h" Ne D 13:7 MeV. This is in reasonable qualitative agreement with the models in the literature and the one presented in Sect. 2.4. It is quite an achievement that models of PNS cooling based on theoretical considerations alone before 1987 were able to reproduce the general features of the SN 1987A neutrino signal. Nevertheless, there is uncertainty in the cooling timescale and Tc;0 . Additionally, attempts have been made to constrain various physical processes operating during PNS cooling using the SN 1987A neutrino data (Burrows and Lattimer 1987; Keil et al. 1995; Reddy et al. 1999). The neutrino cooling signal from SN 1987A has also been used to constrain beyond the standard model physics. Essentially, it is possible for exotic particles with very weak – but not too weak – interactions to rapidly remove energy from the PNS (Raffelt 1996). If the amount of energy removed is comparable to the amount of energy emitted in neutrinos, the neutrino cooling timescale can be shortened. This technique has been mainly used to put limits on the properties of axions using the SN 1987A neutrino signal (Keil et al. 1997).

60 Neutrino Signatures from Young Neutron Stars

1629

50

40

Tc (S)

30

20

10

0

2

4

3

5

6

7

Tc,0 (MeV)

Fig. 6 Probability contours of the PNS cooling timescale, c , and the antielectron neutrino spectral temperature Tc;0 based on the SN 1987A neutrinos observed at the Super-Kamiokande, Baksan, and IMB detectors (Taken from Loredo and Lamb (2002)). The dashed and solid lines demarcate regions of 68 % and 95 % credibility for the PNS cooling parameters, respectively. These inferred parameters are in good qualitative agreement with the predictions from models of PNS cooling. In this model, the average electron antineutrino energy is given by h" Ne i  3:15T Ne  13:7 MeV, where the last value is the value at 1 s post-bounce (Reprinted figure with permission from Loredo and Lamb (2002). Copyright 2002 by the American Physical Society)

4.2

Galactic Supernova Neutrinos

Any future galactic SN will yield far more neutrino detections than SN 1987A. The expected rate of CCSN in the Milky Way is around 1–2 per century (Cappellaro and Turatto 2001), so direct CCSN detection is somewhat of a waiting game. Because of this, there are no dedicated CCSN neutrino detectors, but luckily there are many neutrino experiments that can moonlight as CCSN neutrino observatories. The neutrino detection rate for a galactic CCSN can be found by integrating the neutrino distribution function at Earth over the response of the neutrino detector (Pons et al. 1999; Scholberg 2012): dN 2 nd D dt .2 /3  87:5 s

Z

1

Z

1 0



d " "2  ." /W D 10 kpc

2 

1

." /

Mdet 32 kt

d f ." ; ; D/ 1



L Ne 51 10 erg s1



 h" Ne i GŒf Ne ."/; 12 MeV (46)

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L.F. Roberts and S. Reddy

where D is the distance from Earth to the SN, nd is the number of particles available to interact with neutrinos in the detector, and W ."/ is the detector efficiency as a function of energy. In the second line, we estimate the electron antineutrino detection rate in a Cherenkov water detector with detector mass M . The detector parameters chosen are meant to approximately correspond to the properties of Super-Kamiokande (Fukuda et al. 2003). The dimensionless factor

GŒf ."/ D

m2e

R1

d ""2  ."/W ."/f R1  ." D me /h" i2 0 d ""2 f 0

(47)

encodes the spectral distribution of the neutrinos folded with the neutrino cross section and detector response. The presence of a detector threshold in W ."/ can make the dependence of the count rate on the neutrino average energy steeper than is suggested by the simple scaling relation above. For a Fermi–Dirac distribution of neutrinos with zero chemical potential, W has a value  1:8. Integrating over a predicted CCSN neutrino signal, Scholberg (2012) find that around 7,000 electron antineutrino events would be detected in Super-Kamiokande for a SN 10 kpc away and that the majority of these neutrinos would come from the PNS cooling phase (Mirizzi et al. 2015). Additionally, electron neutrinos will be detectable in liquid argon detectors through the reaction e C40 Ar ! e  C40 K. For a supernova at 10 kpc, we can expect about 700 events per kiloton (Scholberg 2012). The '40 kiloton liquid argon detector planned at the Deep Underground Neutrino Experiment (DUNE) will be able to provide valuable and complementary information about flavor and lepton number when combined with water Cherenkov detectors. Together, the large number of events and high-energy resolution available from the current suite of neutrino experiments will put much more stringent constraints on the interior properties of PNSs when the next galactic CCSN is detected. It is also possible that current neutrino detectors with upgrades or next-generation neutrino detectors will be able to observe the diffuse background of neutrinos produced by CCSNe over the lifetime of the universe (Horiuchi et al. 2009). Predictions for the diffuse MeV scale neutrino background density depend on the integrated spectrum of neutrinos emitted during CCSNe, especially during the PNS cooling phase (Nakazato et al. 2015).

4.3

Impact on CCSN Nucleosynthesis

Neutrinos can alter the composition of material that is ejected from CCSNe, mainly in the innermost ejected regions (Woosley et al. 2002). The ejecta most affected by neutrinos are the material that comes from the surface of the PNS. Neutrino energy deposition in the atmosphere of the PNS can provide enough energy to unbind material from the surface and produce a neutrino-driven wind (Duncan et al. 1986). Once the outflowing material reaches large radii, the temperature drops and heavy nuclei form in the wind. The heating is driven by the charged-current reactions

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1631

e C n ! e  C p and N e C p ! e C C n: So, in addition to energizing the ejected material, neutrino interactions change its composition. The gravitational binding energy of a baryon at the surface of the PNS is GMpns mN =rpns  160 MeV, so a baryon must undergo between ten and fifteen neutrino captures (given the expected average neutrino energies discussed above) to escape the potential well of the PNS. This number of interactions is large enough to push the material to a composition where electron neutrino capture balances electron antineutrino capture, which results in an electron fraction (Qian and Woosley 1996) Ye;NDW D

 e :  e C  Ne

(48)

The neutrino capture rates are proportional to  e / NP e h." e C np /2 i=r 2 and  Ne / NP Ne F NNe h." e  np /2 i=r 2 , where np D 1:293 MeV is the neutron–proton rest mass difference. Which heavy nuclei form depends very strongly on the electron fraction – as well as the entropy and dynamical timescale – of the outflowing material (Arcones and Thielemann 2013; Fischer et al. 2010; Hüdepohl et al. 2010; Nakazato et al. 2013; Roberts et al. 2012; Sumiyoshi et al. 1995; Woosley et al. 1994). Therefore, the final composition depends on the difference between the average energies of electron neutrinos and antineutrinos. The magnitude of this difference in numerical models of PNS cooling is sensitive to the mean field corrections discussed in Sect. 3.1, as well as to the method of neutrino transport (Fischer et al. 2010; Hüdepohl et al. 2010). It seems that the wind is at most marginally neutron rich, but this result depends on the properties of the assumed nuclear EoS (Hempel 2015; Mirizzi et al. 2015; Roberts et al. 2012). The -process is another mechanism by which PNS neutrinos can alter the composition of the material ejected from CCSNe (Woosley et al. 1990). Here, unlike in the neutrino-driven wind, both charged-current and neutral current neutrino interactions are responsible for altering the composition of the material. Therefore, neutrinos of all flavors contribute to the process. Essentially, the -process alters the composition of ejected stellar material by the reactions .Z; N / C ! .Z; N / C 0 ! .Z; N  1/ C n C 0 ! .Z  1; N / C p C 0 ! .Z  2; N  2/ C ˛ C 0 ; .Z; N / C e ! .Z C 1; N  1/ C e  ; and .Z; N / C N e ! .Z  1; N C 1/ C e C ;

(49)

where .Z; N / denotes a nucleus containing Z protons and N neutrons and .Z; N / denotes an excited state of that nucleus. This is likely responsible for the production

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rare isotopes, such as 11 B, 19 F, 15 N 138 La, and 180 Ta, from much more common nuclei in the envelope of the SN. Additionally, it has been suggested that neutrons produced by neutrino interactions in the helium shell can be rapidly captured on preexisting heavy nuclei and make the r-process (Epstein et al. 1988), although later work has shown it is challenging to achieve the requisite conditions for this process (Banerjee et al. 2011). The nuclear yields produced by this process are sensitive to the time-integrated flux and spectrum of neutrino incident on the exterior material (Heger et al. 2005). Therefore, the properties of PNS neutrino emission, along with neutrino oscillations above the PNS, are very important to determine the results of -process nucleosynthesis (Banerjee et al. 2011; Heger et al. 2005). For further details on the impact of neutrinos on CCSNe nucleosynthesis, see the chapters “Effect of neutrinos on the ejecta composition of core collapse supernovae” and “Production of r-process elements in core collapse supernovae.”

5

Cross-References

 Diffuse Neutrino Flux from Supernovae  Making the Heaviest Elements in a Rare Class of Supernovae  Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis  Neutrino Emission from Supernovae Acknowledgements We acknowledge our collaborators on this subject, including Gang Shen, Vincenzo Cirigliano, Jose Pons, Stan Woosley, and Ermal Rrapaj. LR was supported by NASA through an Einstein Postdoctoral Fellowship grant numbered PF3-140114 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060.

References Alexeyev EN, Alexeyeva LN, Krivosheina IV, Volchenko VI (1988) Detection of the neutrino signal from SN 1987A in the LMC using the INR Baksan underground scintillation telescope. Phys Lett B 205:209–214. doi:10.1016/0370-2693(88)91651-6 Arcones A, Thielemann FK (2013) Neutrino-driven wind simulations and nucleosynthesis of heavy elements. J Phys G Nucl Phys 40(1):013201. doi:10.1088/0954-3899/40/1/013201. 1207.2527 Baade W, Zwicky F (1934) On super-novae. Proc Natl Acad Sci 20:254–259. doi:10.1073/pnas.20.5.254 Banerjee P, Haxton WC, Qian YZ (2011) Long, cold, early r-process? Neutrino-induced nucleosynthesis in He shells revisited. Phys Rev Lett 106(20):201104. doi:10.1103/PhysRevLett.106.201104. 1103.1193 Bionta RM, Blewitt G, Bratton CB, Casper D, Ciocio A, Claus R et al (1987) Observation of a neutrino burst in coincidence with supernova 1987A in the large magellanic cloud. Physi Rev Lett 58:1494–1496. doi:10.1103/PhysRevLett.58.1494 Buras R, Rampp M, Janka H, Kifonidis K (2006) Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 M˙o star. Astron Astrophys 447:1049–1092. doi:10.1051/0004-6361:20053783. arXiv:astroph/0507135

60 Neutrino Signatures from Young Neutron Stars

1633

Burrows A (1987) Convection and the mechanism of type II supernovae. Astrophys J Lett 318:L57–L61. doi:10.1086/184937 Burrows A, Lattimer JM (1986) The birth of neutron stars. Astrophys J 307:178–196. doi:10.1086/164405 Burrows A, Lattimer JM (1987) Neutrinos from SN 1987A. Astrophys J Lett 318:L63–L68. doi:10.1086/184938 Burrows A, Sawyer RF (1998) Effects of correlations on neutrino opacities in nuclear matter. Phys Rev C 58:554–571. doi:10.1103/PhysRevC.58.554. arXiv:astro-ph/9801082 Burrows A, Reddy S, Thompson TA (2006) Neutrino opacities in nuclear matter. Nucl Phys A 777:356–394. doi:10.1016/j.nuclphysa.2004.06.012. arXiv:astro-ph/0404432 Cappellaro E, Turatto M (2001) Supernova types and rates. In: Vanbeveren D (ed) The influence of binaries on stellar population studies, astrophysics and space science library, vol 264, p 199. doi:10.1007/978-94-015-9723-4_16. astro-ph/0012455 Constantinou C, Muccioli B, Prakash M, Lattimer JM (2014) Thermal properties of supernova matter: the bulk homogeneous phase. Phys Rev C89(6):065,802. doi:10.1103/PhysRevC.89.065802. 1402.6348 Duan H, Fuller GM, Carlson J, Qian YZ (2006) Simulation of coherent nonlinear neutrino flavor transformation in the supernova environment: correlated neutrino trajectories. Phys Rev D 74(10):105014. doi:10.1103/PhysRevD.74.105014. arXiv:astro-ph/0606616 Duan H, Fuller GM, Qian YZ (2010) Collective neutrino oscillations. Ann Rev Nucl Part Sci 60:569–594. doi:10.1146/annurev.nucl.012809.104524. 1001.2799 Duncan RC, Shapiro SL, Wasserman I (1986) Neutrino-driven winds from young, hot neutron stars. Astrophys J 309:141–160. doi:10.1086/164587 Epstein RI (1979) Lepton-driven convection in supernovae. Mon Not R Astro Soc 188:305–325 Epstein RI, Colgate SA, Haxton WC (1988) Neutrino-induced r-process nucleosynthesis. Phys Rev Lett 61:2038–2041. doi:10.1103/PhysRevLett.61.2038 Fischer T, Martínez-Pinedo G, Hempel M, Liebendörfer M (2011) Neutrino spectra evolution during proto-neutron star deleptonization. ArXiv e-prints 1112.3842 Fischer T, Whitehouse SC, Mezzacappa A, Thielemann FK, Liebendoerfer M (2010) Protoneutron star evolution and the neutrino-driven wind in general relativistic neutrino radiation hydrodynamics simulations. Astron Astrophys 517:A80+. doi:10.1051/0004-6361/200913106 Fukuda S, Fukuda Y, Hayakawa T, Ichihara E, Ishitsuka M, Itow Y et al (2003) The super-kamiokande detector. Nucl Instrum Methods A 501:418–462. doi:10.1016/S0168-9002(03)00425-X Gandolfi S, Carlson J, Reddy S (2011) The maximum mass and radius of neutron stars and the nuclear symmetry energy. ArXiv e-prints 1101.1921 Graves GJM, Challis PM, Chevalier RA, Crotts A, Filippenko AV, Fransson C, Garnavich P, Kirshner RP, Li W, Lundqvist P, McCray R, Panagia N, Phillips MM, Pun CJS, Schmidt BP, Sonneborn G, Suntzeff NB, Wang L, Wheeler JC (2005) Limits from the hubble space telescope on a point source in SN 1987A. Astrophys J 629:944–959. doi:10.1086/431422. astroph/0505066 Hannestad S, Raffelt G (1998) Supernova neutrino opacity from nucleon-nucleon bremsstrahlung and related processes. Astrophys J 507:339–352. doi:10.1086/306303. arXiv:astro-ph/9711132 Heger A, Kolbe E, Haxton WC, Langanke K, Martínez-Pinedo G, Woosley SE (2005) Neutrino nucleosynthesis. Phys Lett B 606:258–264. doi:10.1016/j.physletb.2004.12.017. arXiv:astroph/0307546 Hempel M (2015) Nucleon self-energies for supernova equations of state. Phys Rev C 91(5):055807. doi:10.1103/PhysRevC.91.055807. 1410.6337 Hirata K, Kajita T, Koshiba M, Nakahata M, Oyama Y, Sato N et al (1987) Observation of a neutrino burst from the supernova SN 1987A. Phys Rev Lett 58:1490–1493. doi:10.1103/PhysRevLett.58.1490 Hix WR, Messer OE, Mezzacappa A, Liebendörfer M, Sampaio J, Langanke K, Dean DJ, Martínez-Pinedo G (2003) Consequences of nuclear electron capture in core collapse supernovae. Phys Rev Lett 91(20):201102. doi:10.1103/PhysRevLett.91.201102. astro-ph/0310883

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Hoffman RD, Woosley SE, Qian YZ (1997) Nucleosynthesis in neutrino-driven winds. II. Implications for heavy element synthesis. Astrophys J 482:951–962. astro-ph/9611097 Horiuchi S, Beacom JF, Dwek E (2009) Diffuse supernova neutrino background is detectable in super-kamiokande. Phys Rev D 79(8):083013. doi:10.1103/PhysRevD.79.083013. 0812.3157 Horowitz CJ, Pérez-García MA (2003) Realistic neutrino opacities for supernova simulations with correlations and weak magnetism. Phys Rev C 68(2):025803. doi:10.1103/PhysRevC.68.025803. arXiv:astro-ph/0305138 Hüdepohl L, Müller, B, Janka HT, Marek A, Raffelt GGL (2010) Neutrino signal of electroncapture supernovae from core collapse to cooling. Phys Rev Lett 104(25):251,101–C. doi:10.1103/PhysRevLett.104.251101 Janka HT, Hillebrandt W (1989) Monte Carlo simulations of neutrino transport in type II supernovae. Astron Astrophys Suppl 78:375–397 Keil MT, Raffelt GG, Janka HT (2003) Monte Carlo study of supernova neutrino spectra formation. Astrophys J 590:971–991. doi:10.1086/375130. arXiv:astro-ph/0208035 Keil W, Janka HT (1995) Hadronic phase transitions at supranuclear densities and the delayed collapse of newly formed neutron stars. Astron Astrophys 296:145–C Keil W, Janka HT, Raffelt G (1995) Reduced neutrino opacities and the SN 1987A signal. Phys Rev D 51:6635–6646 Keil W, Janka HT, Schramm DN, Sigl G, Turner MS, Ellis J (1997) Fresh look at axions and SN 1987A. Phys Rev D 56:2419–2432. doi:10.1103/PhysRevD.56.2419. arXiv:astro-ph/9612222 Kunkel W, Madore B, Shelton I, Duhalde O, Bateson FM, Jones A, Moreno B, Walker S, Garradd G, Warner B, Menzies J (1987) Supernova 1987A in the large magellanic cloud. IAU Circ 4316:1 Lattimer JM, Douglas Swesty F (1991) A generalized equation of state for hot, dense matter. Nucl Phys A 535:331–376. doi:10.1016/0375-9474(91)90452-C Lindquist RW (1966) Relativistic transport theory. Ann Phys 37:487–518. doi:10.1016/0003-4916(66)90207-7 Loredo TJ, Lamb DQ (2002) Bayesian analysis of neutrinos observed from supernova SN 1987A. Phys Rev D 65(6):063,002–C. doi:10.1103/PhysRevD.65.063002 Martínez-Pinedo G, Fischer T, Lohs A, Huther L (2012) Charged-current weak interaction processes in hot and dense matter and its impact on the spectra of neutrinos emitted from protoneutron star cooling. ArXiv e-prints 1205.2793 Mirizzi A, Tamborra I, Janka HT, Saviano N, Scholberg K, Bollig R, Hudepohl L, Chakraborty S (2015) Supernova neutrinos: production, oscillations and detection. ArXiv e-prints 1508.00785 Nakazato K, Sumiyoshi K, Suzuki H, Totani T, Umeda H, Yamada S (2013) Supernova neutrino light curves and spectra for various progenitor stars: from core collapse to proto-neutron star cooling. Astrophys J Suppl 205:2. doi:10.1088/0067-0049/205/1/2. 1210.6841 Nakazato K, Mochida E, Niino Y, Suzuki H (2015) Spectrum of the supernova relic neutrino background and metallicity evolution of galaxies. Astrophys J 804:75. doi:10.1088/0004-637X/804/1/75. 1503.01236 Ozel F, Psaltis D, Guver T, Baym G, Heinke C, Guillot S (2015) The dense matter equation of state from neutron star radius and mass measurements. Submitted to Astrophys J 1505.05155 Pons JA, Reddy S, Prakash M, Lattimer JM, Miralles JA (1999) Evolution of proto-neutron stars. Astrophys J 513:780–804. doi:10.1086/306889 Pons JA, Reddy S, Ellis PJ, Prakash M, Lattimer JM (2000) Kaon condensation in proto-neutron star matter. Phys Rev C 62(3):035,803–C. doi:10.1103/PhysRevC.62.035803 Pons JA, Miralles JA, Prakash M, Lattimer JM (2001a) Evolution of proto-neutron stars with Kaon condensates. Astrophys J 553:382–393. doi:10.1086/320642 Pons JA, Steiner AW, Prakash M, Lattimer JM (2001b) Evolution of proto-neutron stars with quarks. Phys Rev Lett 86:5223–5226. doi:10.1103/PhysRevLett.86.5223 Prakash M, Bombaci I, Prakash M, Ellis PJ, Lattimer JM, Knorren R (1997) Composition and structure of protoneutron stars. Phys Rep 280:1–77. doi:10.1016/S0370-1573(96)00023-3 Qian YZ, Woosley SE (1996) Nucleosynthesis in neutrino-driven winds. I. The physical conditions. Astrophys J 471:331. doi:10.1086/177973. arXiv:astro-ph/9611094

60 Neutrino Signatures from Young Neutron Stars

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Raffelt GG (1996) Stars as laboratories for fundamental physics: the astrophysics of neutrinos, axions, and other weakly interacting particles. University of Chicago Press, Chicago Raffelt GG (2001) Mu- and Tau-neutrino spectra formation in supernovae. Astrophys J 561: 890–914. doi:10.1086/323379. astro-ph/0105250 Reddy S, Prakash M, Lattimer JM (1998) Neutrino interactions in hot and dense matter. Phys Rev D 58(1):013009. doi:10.1103/PhysRevD.58.013009. arXiv:astro-ph/9710115 Reddy S et al (1999) Effects of strong and electromagnetic correlations on neutrino interactions in dense matter. Phys Rev C 59:2888–2918. doi:10.1103/PhysRevC.59.2888 Roberts LF (2012) A new code for proto-neutron star evolution. ArXiv e-prints 1205.3228 Roberts LF, Woosley SE, Hoffman RD (2010) Integrated nucleosynthesis in neutrino-driven winds. Astrophys J 722:954–967. doi:10.1088/0004-637X/722/1/954. 1004.4916 Roberts LF, Reddy S, Shen G (2012) Medium modification of the charged-current neutrino opacity and its implications. Phys Rev C 86(6):065803. doi:10.1103/PhysRevC.86.065803. 1205.4066 Roberts LF, Shen G, Cirigliano V, Pons JA, Reddy S, Woosley SE (2012) Protoneutron star cooling with convection: the effect of the symmetry energy. Phys Rev Lett 108:061,103. doi:10.1103/PhysRevLett.108.061103. Rrapaj E, Roggero A, Holt JW (2015) Mean field extrapolations of microscopic nuclear equations of state. Submitted to Phys Rev C 1510.00444 Scholberg K (2012) Supernova neutrino detection. Ann Rev Nucl Part Sci 62:81–103. doi:10.1146/annurev-nucl-102711-095006. 1205.6003 Steiner AW, Prakash M, Lattimer JM (2001) Diffusion of neutrinos in proto-neutron star matter with quarks. Phys Lett B 509:10–18. doi:10.1016/S0370-2693(01)00434-8. astro-ph/0101566 Steiner AW, Lattimer JM, Brown EF (2013) The neutron star mass-radius relation and the equation of state of dense matter. Astrophys J Lett 765:L5. doi:10.1088/2041-8205/765/1/L5. 1205.6871 Sumiyoshi K, Suzuki H, Toki H (1995) Influence of the symmetry energy on the birth of neutron stars and supernova neutrinos. Astron Astrophys 303:475. arXiv:astro-ph/9506024 Tews I, Krüger T, Hebeler K, Schwenk A (2013) Neutron matter at next-to-next-to-next-toleading order in chiral effective field theory. Phys Rev Lett 110(3):032,504. doi:10.1103/PhysRevLett.110.032504. 1206.0025 Thorne KS (1981) Relativistic radiative transfer – moment formalisms. Mon Not R Astro Soc 194:439–473 Wilson JR, Mayle RW (1988) Convection in core collapse supernovae. Phys Rep 163:63–77. doi:10.1016/0370-1573(88)90036-1 Woosley SE, Weaver TA (1995) The evolution and explosion of massive stars. II. Explosive hydrodynamics and nucleosynthesis. Astrophys J Suppl 101:181. doi:10.1086/192237 Woosley SE, Hartmann DH, Hoffman RD, Haxton WC (1990) The nu-process. Astrophys J 356:272–301. doi:10.1086/168839 Woosley SE, Wilson JR, Mathews GJ, Hoffman RD, Meyer BS (1994) The r-process and neutrinoheated supernova ejecta. Astrophys J 433:229–246. doi:10.1086/174638 Woosley SE, Heger A, Weaver TA (2002) The evolution and explosion of massive stars. Rev Modern Phys 74:1015–1071. doi:10.1103/RevModPhys.74.1015

Diffuse Neutrino Flux from Supernovae

61

Cecilia Lunardini

Abstract

The diffuse supernova neutrino flux (or background, DSNB) is the flux of neutrinos due to all the core-collapse supernovae in the universe. Faint, but constant in time, this flux represents an attractive opportunity for steady progress in the field of supernova neutrinos. The DSNB has a unique potential, because it offers an image of the whole population of collapsing stars, including cosmologically distant supernovae and rare collapse types that might escape astronomical observation. So far, the DSNB has not been detected; searches at current neutrino observatories have placed stringent upper limits, which are close to theoretical predictions. A discovery of the diffuse supernova neutrino background is within the reach of the next-generation facilities of tens of kilotons in mass, which will use water, liquid argon, and liquid scintillator and will implement important advancements in background rejection. Typical rates of detection will be 0.2–2 events per year. The potential of future DSNB observations to advance astrophysics and particle/nuclear physics is discussed briefly.

Contents 1 2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory: The Predicted Diffuse Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Physics of the DSNB: Core Collapse Rate and Neutrino Production and Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Diffuse Flux: Spectrum and Parameter Dependence . . . . . . . . . . . . . . . . . . Experiments: Status and Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Detection Techniques and Current Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Detectability at Near-Future Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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C. Lunardini () Department of Physics, Arizona State University, Tempe, AZ, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_6

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4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Neutrinos play a central role in the physics of a core-collapse supernova. Originating from near the core, they carry precious information on the various stages of the collapse and participate in the processes of energizing the shockwave and in the synthesis of heavy elements via the r-process. The observation of these neutrinos has the potential to fundamentally advance our knowledge of these important phenomena and to test the properties of the neutrinos as particles as well. So far, only one supernova neutrino burst has been detected: the low statistics signal from SN 1987A (Alekseev et al. 1987; Bionta et al. 1987; Hirata et al. 1987), a milestone from which many advancements in stellar physics, and nuclear/particle physics have stemmed (see, e.g., Raffelt 1996). A future core-collapse supernova (simply “supernova” from here on, for brevity) in our galaxy will yield a spectacular, high statistics signal that would truly revolutionize the field. However, the rarity of collapses in our galaxy – occurring at a rate of 1–3 per century (Ando et al. 2005; Arnaud et al. 2004) – poses a serious limit to progress. An appealing alternative to a single supernova burst is the diffuse supernova neutrino background (DSNB), the flux due to all the supernovae in the universe (Bisnovatyi-Kogan and Seidov 1982; Krauss et al. 1984). This flux is feeble but continuous, and therefore it can provide a constant, steady progress in this field. Even more importantly, the DSNB has a unique physics potential, because it offers a neutrino image of the whole population of collapsing stars, with its full history and diversity. In particular, it has a strong component from cosmological supernovae that will never be resolved individually in neutrinos. Learning about these will advance our knowledge of the history of star formation. Detecting neutrinos that originated at high redshift (z  1) will also allow to test neutrino properties over unprecedented propagation time scales. Furthermore, the DSNB receives contributions from all collapsing stars, including types that might escape astronomical surveys due to being too dim or too rare. In this context, the DSNB can test the existence of blackhole-forming collapses. So far, the DSNB has not been observed. After the strong upper limits placed by the Super-Kamiokande experiment (Bays et al. 2012), detectors of the next generation – currently in the phase of advanced planning – will reach the sensitivity required to probe the natural range of parameters of the DSNB (An et al. 2015; Beacom and Vagins 2004; Bishai et al. 2015; Kim 2015). Therefore, it is possible that, within a decade, this relic flux from the most ancient supernovae will be observed, opening a completely new phase of neutrino astronomy. It will contribute to multi-messenger studies of supernovae that include astronomy at different wavelengths and gravitational waves.

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The timeliness of DSNB studies motivates this review. This paper opens with a theory overview (Sect. 2), followed by a summary of the experimental status and near-future prospects (Sect. 3). The last section (Sect. 4) offers a discussion of the physics potential of studying the DSNB.

2

Theory: The Predicted Diffuse Flux

Let us define ˚w (˚wN ) as the diffuse flux of neutrinos (or antineutrinos) of flavor w (w D e; ; ) in a detector at Earth, differential in energy, area, and time. In the continuum limit, and neglecting individual differences between supernovae (see Sect. 2.2 for a brief discussion of these), ˚w can be expressed as an integral over the supernova population, as follows (Ando and Sato 2004; Beacom 2010): ˚w .E/ D

c H0

Z

zmax 0

dz RSN .z/Fw .E 0 / p ; ˝m .1 C z/3 C ˝

(1)

where RSN .z/ is the cosmological rate of core collapse supernovae (number of supernovae per unit time and per unit of comoving volume) as a function of the redshift, z. Here Fw .E 0 / is the number of w from an individual supernova per unit of the energy at production, E 0 D E.1 C z/. It includes the effects of flavor oscillations inside the star and the probability that a given neutrino wave packet entering the detector is observed as w (see Sect. 2.1). The parameters ˝m ' 0:3 and ˝ ' 0:7 are the fractions of the cosmic energy density in matter and dark energy, respectively; c is the speed of light and H0 is the Hubble constant. zmax is the maximum redshift for which there is substantial star formation, zmax  5. In the following subsections, the main ingredients of Eq. (1) are discussed, and examples of DSNB spectra are illustrated.

2.1

The Physics of the DSNB: Core Collapse Rate and Neutrino Production and Propagation

Currently, the core-collapse supernova rate (SNR), RSN .z/, is known with substantial uncertainty. It can be estimated either directly, from supernova observations, or indirectly, from measurements of the cosmological star formation rate (SFR), defined as the amount of mass that forms stars per unit time and per unit of comoving volume. The indirect estimate relies on the fact that, due to the negligible lifetime of supernova progenitors (O.107 / years) relative to star formation time scales, SNR and SFR should be proportional: R 125Mˇ 8M

d m.m/

0:1Mˇ

d m m.m/

RSN .z/ D R 125Mˇ ˇ

RSF .z/ ' 7:4 103 Mˇ1 RSF .z/ ;

(2)

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where Mˇ D 1:9891030 kg is the mass of the Sun and .m/ / m2:35 is the initial mass function (IMF), representing the distribution of stars in their mass, m (Salpeter 1955). In Eq. (2) it is assumed that stars exist in the mass range Œ0:1Mˇ ; 125Mˇ , and those above 8Mˇ end their lives as core-collapse supernovae. The SFR today is RSF .0/ ' O.102 / Mˇ yr1 Mpc3 ; it grows with redshift up to z  1, reaches a plateau, and then declines at z & 4 (Madau and Dickinson 2014). Using a piecewise parameterization for RSF .z/ (see, e.g., Hopkins and Beacom 2006 for this and other parameterizations) and Eq. (2), one gets:

4

RSN .z/ D R4 10

yr

1

( .1 C z/ˇ z 17:3 MeV/, with different effects being included or neglected. As can be seen in the figure, typical values of this flux are O.101 / cm2 s1 (with strong uncertainty due to the normalization of the SNR, Sect. 2.1). The effect of neutrino flavor conversion is substantial; in particular, the matter-driven MSW conversion can increase e by a factor of a few, due to the dominant contribution – for the high threshold considered here – of the hotter neutrinos originally produced as x (Eq. (5)). Including collective oscillations has a more modest effect, 10– 30 %, since this phenomenon – as currently understood – is expected to be effective only in the cooling phase of a neutrino burst (Chakraborty et al. 2011a, b; Dasgupta et al. 2012). Figure 2 addresses the question of generalizing the formalism in Eq. (1) to capture subdominant effects. One of these is the cooling of the neutrino spectra: the results (b), (c), (d), (e), and (f) in the figure are obtained using the fully timedependent neutrino spectra from a numerical simulation, calculated up to 10 s post-bounce (Fischer et al. 2010). Comparing cases (a) and (b) shows that spectrum cooling has a 20 % effect on the DSNB. A second phenomenon is the progenitor dependence of the neutrino flux: in cases (e) and (f), the flux calculation used numerically calculated time-dependent neutrino spectra for different masses of the progenitor stars, integrated over the mass distribution of stars according to the initial mass function (see Eq. (2)). A rather homogeneous population of stars was assumed,

61 Diffuse Neutrino Flux from Supernovae

0.4

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νe

NH IH

Ftot(cm-2s-1)

c

e d

0.3

0.2 f 0.1

a b

0.0

Fig. 2 From Lunardini and Tamborra (2012): cases (a) to (e): the e flux, integrated in the window E > 17:3 MeV, for R4 D 1:5, and normal and inverted mass hierarchy (NH and IH). Case (a) corresponds to Eqs. (1), and (4), with time-independent neutrino spectrum, and p D 1 (no oscillations). Each of the other cases is as the one preceding it, except for the inclusion of one effect, as follows: (b) includes time-dependent spectra; (c) includes matter-driven flavor conversion (MSW effect); (d) includes oscillations due to neutrino-neutrino scattering; (e) includes progenitor dependence of the neutrino emission. Case (f ): same as (e), with R4 D 0:7. The error bars represent an (optimistic) uncertainty of 20 % on the SNR. The numerically-simulated neutrino fluxes from Fischer et al. (2010) were used

all of them undergoing successful explosions with neutron star formation. The effect of progenitor dependence is minor, of O.10 %/, as can be seen by comparing cases (d) and (e), reflecting the relatively small differences in the neutrino emissions of different stars. Effects of diversity in the supernova population are strong in the presence of failed supernovae. When direct collapse into a black hole takes place, the neutrino emission is expected to be more luminous and have hotter spectra than for neutronstar-producing collapses, mainly due to the higher rate of accretion on the collapsed core. Numerical simulations find a total energy emitted in e of Le  1053 ergs and e average energy as high as 24 MeV (Nakazato et al. 2008). Failed supernovae – if they exist – might be only a 10–20 % fraction of all collapses; however, their more powerful neutrino emission can compensate for their rarity and contribute significantly to the DSNB (Lunardini 2009). Figure 3 shows examples of diffuse fluxes from neutron-star-forming collapses (similar to Fig. 1) and failed supernovae, for optimistic spectrum parameters. It appears that direct black hole formation causes a higher energy tail of the DSNB spectrum and can enhance the total flux above realistic detection thresholds by up to a factor of 2. Figure 3 also introduces a topic of relevance for the next section: the concept of energy window of detectability. The figure illustrates how the DSNB compares with other e and N e fluxes at Earth, of natural and artificial origin. For the current detection techniques, these constitute ineliminable backgrounds, so, the DSNB is detectable only where it exceeds these competing fluxes. As can be seen in the figure, for N e the detectable energy window is E 10–40 MeV; it is closed from

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F/cm-2 Mev -1s -1

10

solar

reactor

1 0.1 Atmospheric

0.01

0.001 10-4

0

10

20

30

40

50

E/MeV

Fig. 3 From Keehn and Lunardini (2012): The diffuse N e flux, for pN D 0:68 from successful, neutron-star-forming collapses (colder spectrum, parameters LeN D Lx D 5  1052 ergs, E0Ne D 15 MeV, E0x D 18 MeV, ˛eN D 3:5, ˛x D 2:5) and failed supernovae (hotter spectrum) and their sum, assuming that failed supernovae are 22 % of all collapses. The SNR normalization is R4 D 1. Also shown are the background fluxes of reactor N e , solar e and atmospheric e and N e (the latter are very similar, so only one of them is plotted), for the locations of Super-Kamiokande (the Kamioka mine, solid line) and DUNE (the Homestake mine, dashed line). For details on these background fluxes, see Battistoni et al. (2005), Wurm et al. (2007), and Bahcall et al. (2005)

above by atmospheric neutrinos and from below by reactor antineutrinos. For e , the window is reduced to E 19–40 MeV, the lower end being due to the flux of solar neutrinos. Note that the width of the energy window depends on the detector location and on time: indeed, the atmospheric neutrino flux is latitude dependent, and the reactor neutrino flux is strongly influenced by the time-varying flux of the nuclear power plants closer to the detector.

3

Experiments: Status and Prospects

To date, the DSNB has not been observed. The theoretically interesting range of fluxes is already approached by existing upper bounds and will be probed by several near-future experiments. In this section the potential of these experiments is reviewed.

3.1

Detection Techniques and Current Bounds

In current and near-future detectors, the DSNB can be observed primarily via A A  charged current processes of the form e CA N e CA Z X !ZC1 Y C e (or ZC1 Y !Z C X C e ). The rate of such scattering events, per unit of the electron (positron) observed energy, Ee , is

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Excluded (E>16MeV) e

e+ (90! C.L.)

2

SN

e

53

Energy in 10 erg

61 Diffuse Neutrino Flux from Supernovae

IMB

1 Kamioka

0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 T in MeV Fig. 4 From Bays et al. (2012): 90 % C.L. exclusion region (upper shaded area) from the bound in Eq. (7), in the space of the total energy and effective temperature of the N e flux from an individual supernova. A thermal neutrino spectrum is assumed, with R4 D 1:25 as normalization for the SNR. Regions allowed by SN 1987A data are shown as well (shaded, bottom left). The dashed line refers to a one-dimensional analysis where the total energy is a free parameter and each value of the temperature taken as fixed

dN D NT dEe

Z

C1

1

dEe0 R.Ee ; Ee0 /E .Ee0 /

Z dE˚e .E/

d  .Ee0 ; E/ ; dEe0

(6)

where Ee0 is the true energy of the electron (positron), NT is the number of target nuclei in the fiducial volume, and E represents the detection efficiency. Here d  .Ee0 ; E/=dEe0 is the differential cross section of the detection reaction and R.Ee ; Ee0 / is the energy resolution function. An order-of-magnitude evaluation of Eq. (6) shows that a detector mass of several tens of kilotons is required to have detection rate of N & 1 event/year in the energy window. Currently, only the 22.5 kt water Cherenkov detector Super-Kamiokande (Super-K) fits this criterion (Bays et al. 2012). In water, the dominant detection process is N e capture on hydrogen, i.e., inverse beta decay. In addition to atmospheric and reactor antineutrinos (Sect. 2.2), the background is also due to the decay of lowenergy cosmic muons in the detector and spallation due to cosmic rays. The latter requires restricting the energy window of sensitivity of Super-K to Ee > Emin ' 16 MeV, corresponding to 17.3 MeV of neutrino energy. The most recent positron search at Super-K has given the upper bound (Bays et al. 2012): eN .E > 17:3 MeV/ < 2:8  3:0 cm2 s1

at 90 % C:L: ;

(7)

which is within a factor of 10 of the most conservative predictions (Fig. 2). It excludes the most extreme values of the DSNB parameters; see Fig. 4.

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Complementary to the bound in Eq. (7), other, less stringent constraints have been placed, by several experiments, on diffuse fluxes of e and x and/or on the N e diffuse flux below the Super-K energy threshold; see, e.g., Lunardini (2010) for a summary of these.

3.2

Detectability at Near-Future Experiments

The current searches for the DSNB at Super-K are background limited. To achieve a better detection potential at this and other detectors, improvements in background reduction are necessary. In this section the three most promising technologies are reviewed, with a focus on their near-future realizations. Their expected performances are summarized in Table 1. • Water with gadolinium addition. In 2003 the idea was proposed (Beacom and Vagins 2004) to dissolve a gadolinium (Gd, atomic number Z D 64) compound in the water of Super-K for better background discrimination. After extensive testing (Adams et al. 2013), this new configuration of Super-K, called SuperK-Gd, is now approved for implementation with a 0.2 % mass fraction of gadolinium sulfate (Gd2 .SO4 /3 ) and is expected to start operations within 2–3 years. Thanks to the high cross section for neutron capture on Gd, SuperK-Gd will be able to identify inverse beta decay events by the detection in coincidence of a positron and a neutron in the final state. This signature makes inverse beta decay distinguishable from spallation and cosmic muon events, resulting in a large reduction of the background. The most dramatic improvement, with Table 1 Adapted from Lunardini (2010): summary of the expected event rates for SuperKamiokande and near-future DSNB detectors with mass above 10 kt (An et al. 2015; Beacom and Vagins 2004; Bishai et al. 2015; Kim 2015). The energy windows are indicative, as they depend on the details of the backgrounds. For Super-K, the energy windows of both the first and second search are given (Bays et al. 2012; Malek et al. 2003); the rates are for the more conservative window. The intervals of event rates account for a range of neutrino spectra and different oscillation scenarios. The normalization of the SNR is R4 D 1. The contribution of possible failed supernovae (Sect. 2) is not included Concept

Energy window (MeV) 19.3–30 [17.3–30] 11.3–30

Main detection Experiment process N e .p; n/e C Super-K

Fiducial mass Events per (kt) year 22.5 0.23–1.0

N e .p; n/e C

SuperK-Gd

22.5

0.93–2.3

Scintillator (Cn H2n )

11–30

N e .p; n/e C

JUNO

17

0.8–1.9

Argon

18–30

RENO-50 e .40 Ar; K  /e  DUNE

18 Up to 40

0.8–2.0 Up to 1:0

H2 O H2 O C Gd

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respect to pure water, is the lowering of the experimental threshold down to the barrier placed by reactor neutrinos, Emin ' 10 MeV. Due to the steep fall of the neutrino spectrum in this interval, this change results in a strong increase of the predicted event rate by more than a factor of 2. A rate of 20 events per decade is realistic for SuperK-Gd (Table 1). In addition to an improved discovery potential, the larger energy window also enhances the potential to reconstruct the DSNB energy spectrum. • Liquid scintillator. Neutrino detectors based on a liquid scintillator (Cn H2n ) have been employed very successfully for several years. For the first time, in the near future this technology will reach the O.10/ kt mass, needed to be sensitive to the DSNB, with the projects JUNO in China (An et al. 2015) and RENO-50 in Korea (Kim 2015). As a DSNB detector, a liquid scintillator functions similarly to water with Gd: the main detection channel is inverse beta decay, with the coincident detection of a positron and a neutron in the final state, and a similarly low-energy threshold. Compared to water Cherenkov, a liquid scintillator has better energy resolution, at the level of 3 % or less at JUNO (An et al. 2015). Since this technology is very mature, detailed studies of several background processes for DSNB detection have been performed (Mollenberg et al. 2015; Wurm et al. 2007); the main results are shown in Fig. 5 (left pane). In the figure, one can see the backgrounds due to N e from the atmosphere and from reactors (Sect. 2.2). Additionally, a highrate background is caused by fast neutrons and neutral current (NC) interaction of atmospheric neutrinos, which can mimic inverse beta decay in the liquid scintillator. While the rate of these NC atmospheric events is much higher than the DSNB signal, techniques of pulse-shape discrimination (Mollenberg et al. 2015) have been shown in simulations to reduce this background by about two orders of magnitude, allowing for an energy window Ee 10  20 MeV where the signal exceeds the total background rate. In this window, JUNO and RENO-50 can observe O.10/ DSNB events in a decade of operation. The discovery potential of JUNO is illustrated in Fig. 5 (right pane): a substantial portion of the natural region of the neutrino flux parameters – mainly the normalization and average energy – will be probed, and a flux at the level of current predictions could be identified with (3–5)  confidence level. • Liquid argon. Argon-based neutrino detection is a new technique that is currently being pioneered and will find realization in the deep underground neutrino detector (DUNE) in the USA (Bishai et al. 2015). Liquid argon is unique in its strong potential to detect electron neutrinos (as opposed to antineutrinos): the dominant channel of detection is the charged current process e C 40 Ar !40 K  C e  , with the signatures being the e  ionization track and the de-excitation products of 40 K  . At this time, detailed studies of the backgrounds for DSNB detection are not available. The background due to solar neutrinos (Sect. 2.2) restricts the window of sensitivity to E & 19 MeV, so that only the exponentially suppressed tail of the DSNB spectrum can be accessed, resulting

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number of events in 170 kt.yrs [MeV-1]

a DSNB: =15MeV sum of backgrounds

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Fig. 5 From An et al. (2015): results for JUNO, with a 10-year exposure. Left: spectrum of events for signal and backgrounds after a pulse-shape discrimination (PSD) technique (Mollenberg et al. 2015) is applied to reduce the backgrounds. Without PSD, the NC atmospheric neutrino background is about 102 times larger, and the fast neutron background (invisible in the figure) is 0:6 MeV1 . The SNR normalization R4 D 1:25 is used, with neutrino spectral parameters (effective, after oscillations) LeN D 5  1052 ergs, E0Ne D 15 MeV, and ˛eN D 2. Right: contours of statistical significance of an excess above the background in the space of E0Ne and a DSNB normalization parameter ˚ (in units of ˚0 D 5 R4  1052 ergs). A set of natural parameters is marked by a star

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in a relatively low event rate. In its full configuration, with a 40 kt fiducial mass, DUNE can reach a signal event rate of 1 event/year only for part of the realistic parameter space (Table 1). In a more distant future, the three main technologies outlined above may be developed further. Water Cherenkov detectors can in principle be scaled up to megaton mass, a factor of 20 larger than Super-K. Currently, the most realistic Mt project is HyperKamiokande, for which a collaboration has been formed (Abe et al. 2011). Scaling up to Mt mass will require sacrificing performance at the lowest energies; this however should not affect the energy window of interest for the DSNB (Abe et al. 2011). Liquid scintillator detectors have been envisioned with mass up to 50 kt (Marrodan Undagoitia et al. 2006; Wurm et al. 2007). Their performance should be qualitatively similar to that of JUNO and RENO-50. For liquid argon, conceptual studies have shown that a mass up to 100 kt is probably realistic (Cline et al. 2006; Ereditato and Rubbia 2006). However, conclusions on such a large detector are premature at this time, considering that many dedicated studies of the liquid argon technology are still in progress.

4

Conclusions

For the first time, the diffuse flux of supernova neutrinos appears to be within the reach of near-future experimental searches. Upcoming water Cherenkov, liquid scintillator, and liquid argon detectors at the 20–40 kt mass scale will be able to probe at least part of the natural range of the DSNB parameters: the cosmological rate of core-collapse supernovae (normalization and redshift dependence), the total energy emitted in a supernova neutrino burst, and the energy spectrum of the neutrino species produced in a supernova. Naturally, the first few years of searches will focus on discovery in the form of an excess of flux in the energy window relative to atmospheric neutrinos and other backgrounds. Both a positive (observation of the DSNB) and a negative result will lead to model discrimination: specific combinations of parameters will be disfavored or excluded, implying conditional bounds on the individual parameters. For example, DSNB data combined with naturalness assumptions on the total energy emitted in a supernova burst may constrain the normalization of the supernova rate and add valuable information to the broader discussion of the relationship between the cosmological supernova rate and the star formation rate. The synergy with astronomy on this theme will be strong. In case of discovery of the DSNB, the data will eventually be analyzed to reconstruct its spectrum. In this respect, detectors with lower energy thresholds, i.e., water with Gd addition and liquid scintillator, will be especially powerful. In the absence of data from a galactic supernova, a discovery of diffuse supernova e at a liquid argon detector – although limited by the high-energy threshold of 19 MeV – would be especially significant, being the first observation of neutrinos (as opposed to antineutrinos) from core collapse.

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Information on the spectrum of the diffuse e and N e fluxes may either confirm – probably within large errors – the expectations of numerical simulations and the information from the low statistics detection of SN 1987A, or they may reveal interesting surprises, like a high-energy tail of the spectrum due to failed supernovae. If an individual supernova neutrino burst is detected with high statistics, comparing its spectrum with the DSNB one will help to constrain the progenitor dependence of neutrino emission in collapsing stars and the cosmological evolution of the SNR. Just like the neutrino burst from SN 1987A did, the observation of the DSNB will open a new window of opportunity to test phenomena beyond the standard model of particle physics. Due to the combination of low energy and cosmological propagation distances, the DSNB neutrinos could provide the strongest test of neutrino decay (Ando 2003; Fogli et al. 2004). They could also bear the signature of exotic absorption on dark matter or on background neutrinos via new forces (Farzan and Palomares-Ruiz 2014; Goldberg et al. 2006). The suppression of the neutrino flux due to exotic channels of cooling of the protoneutron star – e.g., a fourth, sterile, neutrino species – will be tested in ways similar to the case of an individual supernova burst (see, e.g., Raffelt 1996). In conclusion, the DSNB has a rich physics potential of its own, complementary to the search of individual supernova neutrino bursts. Its discovery will change the way supernova neutrinos are studied, because it will allow steady, unencumbered progress that will open new areas of interdisciplinary research and motivate further investments of resources and of human talent in this field.

5

Cross-References

 Neutrino Emission from Supernovae  Neutrinos from Core-Collapse Supernovae and Their Detection Acknowledgements The author’s research on the DSNB is supported by the US National Science Foundation grant number PHY-1205745, and by the Department of Energy award DE-SC0015406.

References Abe K, Aihara H, Andreopoulos C, Anghel I, Ariga A, Ariga T et al (2011) Letter of Intent: The hyper-Kamiokande experiment – detector design and physics potential –. arXiv:1109.3262 Adams SM, Kochanek CS, Beacom JF, Vagins MR, Stanek KZ (2013) Observing the next Galactic supernova. Astrophys J 778:164. doi:10.1088/0004-637X/778/2/164, arXiv:1306.0559 Alekseev EN, Alekseeva LN, Volchenko VI, Krivosheina IV (1987) Possible detection of a Neutrino signal on 23 February 1987 at the Baksan underground Scintillation Telescope of the institute of nuclear research. JETP Lett 45:589–592, 739 An F, An G, An Q, Antonelli V, Baussan E, Beacom J et al. (2015, to appear) Neutrino physics with JUNO. J. Phys. G. arXiv:1507.05613 Ando S (2003) Decaying neutrinos and implications from the supernova relic neutrino observation. Phys Lett B570:11. doi:10.1016/j.physletb.2003.07.009, arXiv:hep-ph/0307169

61 Diffuse Neutrino Flux from Supernovae

1651

Ando S (2004) Cosmic star formation history and the future observation of supernova relic neutrinos. Astrophys J 607:20–31. doi:10.1086/383303, arXiv:astro-ph/0401531 Ando S, Sato K (2004) Relic neutrino background from cosmological supernovae. New J Phys 6:170. doi:10.1088/1367-2630/6/1/170, arXiv:astro-ph/0410061 Ando S, Beacom JF, Yuksel H (2005) Detection of neutrinos from supernovae in nearby galaxies. Phys Rev Lett 95:171,101. doi:10.1103/PhysRevLett.95.171101, arXiv:astro-ph/0503321 Arnaud N, Barsuglia M, Bizouard MA, Brisson V, Cavalier F, Davier M, Hello P, Kreckelbergh S, Porter EK (2004) Detection of a close supernova gravitational wave burst in a network of interferometers, neutrino and optical detectors. Astropart Phys 21:201–221. doi:10.1016/j.astropartphys.2003.12.005, arXiv:gr-qc/0307101 Bahcall JN, Serenelli AM, Basu S (2005) New solar opacities, abundances, helioseismology, and neutrino fluxes. Astrophys J 621:L85–L88. doi:10.1086/428929, arXiv:astro-ph/0412440 Battistoni G, Ferrari A, Montaruli T, Sala PR (2005) The atmospheric neutrino flux below 100-MeV: The FLUKA results. Astropart Phys 23:526–534. doi:10.1016/j.astropartphys.2005.03.006 Bays K, Iida T, Abe K, Hayato Y, Iyogi K, Kameda J et al (2012) Supernova relic neutrino search at super-Kamiokande. Phys Rev D 85:052,007. doi:10.1103/PhysRevD.85.052007, arXiv:1111.5031 Beacom JF (2010) The diffuse supernova neutrino background. Ann Rev Nucl Part Sci 60:439– 462. doi:10.1146/annurev.nucl.010909.083331, arXiv:1004.3311 Beacom JF, Vagins MR (2004) GADZOOKS! Anti-neutrino spectroscopy with large water Cherenkov detectors. Phys Rev Lett 93:171,101. doi:10.1103/PhysRevLett.93.171101, arXiv:hep-ph/0309300 Bionta RM, Blewitt G, Bratton CB, Casper D, Ciocio A, Claus R et al (1987) Observation of a neutrino burst in coincidence with supernova SN 1987a in the large magellanic cloud. Phys Rev Lett 58:1494. doi:10.1103/PhysRevLett.58.1494 Bishai M, McCluskey E, Rubbia A, Thomson M et al (2015) Long-Baseline Neutrino Facility (LBNF) and deep Underground Neutrino Experiment (DUNE) conceptual design report, vol 1. Available at http://lbne2-docdb.fnal.gov/cgi-bin/ShowDocument?docid=10687 Bisnovatyi-Kogan GS, Seidov ZF (1982) Medium-energy neutrinos in the universe. Soviet Astronomy (Tr: A Zhurn) 26:132 Chakraborty S, Fischer T, Mirizzi A, Saviano N, Tomas R (2011a) Analysis of matter suppression in collective neutrino oscillations during the supernova accretion phase. Phys Rev D84:025,002. doi:10.1103/PhysRevD.84.025002, arXiv:1105.1130 Chakraborty S, Fischer T, Mirizzi A, Saviano N, Tomas R (2011b) No collective neutrino flavor conversions during the supernova accretion phase. Phys Rev Lett 107:151,101. doi:10.1103/PhysRevLett.107.151101, arXiv:1104.4031 Cline DB, Raffaelli F, Sergiampietri F (2006) LANNDD: A line of liquid argon TPC detectors scalable in mass from 200 Tons to 100 Ktons. JINST 1:T09,001. doi:10.1088/1748-0221/1/09/T09001, arXiv:astro-ph/0604548 Dasgupta B, O’Connor EP, Ott CD (2012) The role of collective neutrino flavor oscillations in corecollapse supernova shock revival. Phys Rev D85:065,008. doi:10.1103/PhysRevD.85.065008, arXiv:1106.1167 Dighe AS, Smirnov AYu (2000) Identifying the neutrino mass spectrum from the neutrino burst from a supernova. Phys Rev D62:033,007. doi:10.1103/PhysRevD.62.033007, arXiv:hepph/9907423 Duan H, Kneller JP (2009) Neutrino flavour transformation in supernovae. J Phys G36:113,201. doi:10.1088/0954-3899/36/11/113201, arXiv:0904.0974 Duan H, Fuller GM, Carlson J, Qian YZ (2006a) Coherent development of neutrino flavor in the supernova environment. Phys Rev Lett 97:241,101. doi:10.1103/PhysRevLett.97.241101, arXiv:astro-ph/0608050 Duan H, Fuller GM, Carlson J, Qian YZ (2006b) Simulation of coherent non-linear neutrino flavor transformation in the supernova environment. 1. correlated neutrino trajectories. Phys Rev D74:105,014. doi:10.1103/PhysRevD.74.105014, arXiv:astro-ph/0606616

1652

C. Lunardini

Ereditato A, Rubbia A (2006) Conceptual design of a scalable multi-kton superconducting magnetized liquid Argon TPC. Nucl Phys Proc Suppl 155:233–236. doi:10.1016/j.nuclphysbps.2006.02.059, arXiv:hep-ph/0510131 Farzan Y, Palomares-Ruiz S (2014) Dips in the diffuse supernova neutrino background. JCAP 1406:014. doi:10.1088/1475-7516/2014/06/014, arXiv:1401.7019 Fischer T, Whitehouse SC, Mezzacappa A, Thielemann FK, Liebendorfer M (2010) Protoneutron star evolution and the neutrino driven wind in general relativistic neutrino radiation hydrodynamics simulations. Astron Astrophys 517:A80. doi:10.1051/0004-6361/200913106, arXiv:0908.1871 Fogli GL, Lisi E, Mirizzi A, Montanino D (2004) Three generation flavor transitions and decays of supernova relic neutrinos. Phys Rev D70:013,001. doi:10.1103/PhysRevD.70.013001, arXiv:hep-ph/0401227 Goldberg H, Perez G, Sarcevic I (2006) Mini Z’ burst from relic supernova neutrinos and late neutrino masses. JHEP 11:023. doi:10.1088/1126-6708/2006/11/023, arXiv:hep-ph/0505221 Hirata K, Kajita T, Koshiba M, Nakahata M, Oyama Y, Sato N et al (1987) Observation of a neutrino burst from the supernova SN 1987a. Phys Rev Lett 58:1490–1493, 727. doi:10.1103/PhysRevLett.58.1490 Hopkins AM, Beacom JF (2006) On the normalisation of the cosmic star formation history. Astrophys J 651:142–154. doi:10.1086/506610, arXiv:astro-ph/0601463 Horiuchi S, Beacom JF, Kochanek CS, Prieto JL, Stanek KZ, Thompson TA (2011) The cosmic core-collapse supernova rate does not match the massive-star formation rate. Astrophys J 738:154–169. doi:10.1088/0004-637X/738/2/154, arXiv:1102.1977 Janka HT, Hillebrandt W (1998) Neutrino emission from type II supernovae – an analysis of the spectra. Astron Astrophys 224:49–56 Keehn JG, Lunardini C (2012) Neutrinos from failed supernovae at future water and liquid argon detectors. Phys Rev D85:043,011. doi:10.1103/PhysRevD.85.043011, arXiv:1012.1274 Keil MT, Raffelt GG, Janka HT (2003) Monte Carlo study of supernova neutrino spectra formation. Astrophys J 590:971–991. doi:10.1086/375130, arXiv:astro-ph/0208035 Kim SB (2015) New results from RENO and prospects with RENO-50. Nucl Part Phys Proc 265266:93–98. doi:10.1016/j.nuclphysbps.2015.06.024, arXiv:1412.2199 Krauss LM, Glashow SL, Schramm DN (1984) Anti-neutrinos astronomy and geophysics. Nature 310:191–198. doi:10.1038/310191a0 Lunardini C (2009) Diffuse neutrino flux from failed supernovae. Phys Rev Lett 102:231,101. doi:10.1103/PhysRevLett.102.231101, arXiv:0901.0568 Lunardini C (2010) Diffuse supernova neutrinos at underground laboratories. arXiv:1007.3252 Lunardini C, Tamborra I (2012) Diffuse supernova neutrinos: oscillation effects, stellar cooling and progenitor mass dependence. JCAP 1207:012. doi:10.1088/1475-7516/2012/07/012, arXiv:1205.6292 Madau P, Dickinson M (2014) Cosmic Star Formation History. Ann Rev Astron Astrophys 52:415– 486. doi:10.1146/annurev-astro-081811-125615, arXiv:1403.0007 Malek M, Morii M, Fukuda S, Fukuda Y, Ishitsuka M, Itow Y et al (2003) Search for supernova relic neutrinos at SUPER-KAMIOKANDE. Phys Rev Lett 90:061,101. doi:10.1103/PhysRevLett.90.061101, arXiv:hep-ex/0209028 Marrodan Undagoitia T, von Feilitzsch F, Goder-Neff M, Hochmuth KA, Oberauer L, Potzel W, Wurm M (2006) Low energy neutrino astronomy with the large liquid scintillation detector LENA. Prog Part Nucl Phys 57:283–289. doi:10.1088/1742-6596/39/1/068, doi:10.1016/j.ppnp.2006.01.002, arXiv:hep-ph/0605229 Mathews GJ, Hidaka J, Kajino T, Suzuki J (2014) Supernova relic neutrinos and the supernova rate problem: analysis of uncertainties and detectability of ONeMg and failed supernovae. Astrophys J 790:115. doi:10.1088/0004-637X/790/2/115, arXiv:1405.0458 Mikheev SP, Smirnov AYu (1985) Resonance amplification of oscillations in matter and spectroscopy of solar neutrinos. Sov J Nucl Phys 42:913–917. [Yad. Fiz.42,1441(1985)] Mollenberg R, von Feilitzsch F, Hellgartner D, Oberauer L, Tippmann M, Zimmer V, Winter J, Wurm M (2015) Detecting the diffuse supernova neutrino background with LENA. Phys Rev D91(3):032,005. doi:10.1103/PhysRevD.91.032005, arXiv:1409.2240

61 Diffuse Neutrino Flux from Supernovae

1653

Nakazato K, Sumiyoshi K, Suzuki H, Yamada S (2008) Oscillation and future detection of failed supernova neutrinos from black hole forming collapse. Phys Rev D78:083,014. doi:10.1103/PhysRevD.78.083014; doi:10.1103/PhysRevD.79.069901. [Erratum: Phys. Rev.D79,069901(2009)], arXiv:0810.3734 O’Connor E, Ott CD (2011) Black hole formation in failing core-collapse supernovae. Astrophys J 730:70. doi:10.1088/0004-637X/730/2/70, arXiv:1010.5550 Raffelt GG (1996) Stars as laboratories for fundamental physics. University of Chicago Press, Chicago Salpeter EE (1955) The luminosity function and stellar evolution. Astrophys J 121:161–167. doi:10.1086/145971 Strolger LG, Dahlen T, Rodney SA, Graur O, Riess AG, McCully C, Ravindranath S, Mobasher B, Shahady AK (2015) The rate of core collapse supernovae to Redshift 2.5 from the CANDELS and CLASH supernova surveys. Astrophys J 813(2):93. doi:10.1088/0004-637X/813/2/93, arXiv:1509.06574 Wolfenstein L (1978) Neutrino oscillations in matter. Phys Rev D 17:2369–2374. doi:10.1103/PhysRevD.17.2369 Wurm M, von Feilitzsch F, Goeger-Neff M, Hochmuth KA, Undagoitia TM, Oberauer L, Potzel W (2007) Detection potential for the diffuse supernova neutrino background in the large liquid-scintillator detector LENA. Phys Rev D 75:023,007. doi:10.1103/PhysRevD.75.023007, arXiv:3astro-ph/0701305

Neutrinos from Core-Collapse Supernovae and Their Detection

62

Francis Halzen and Kate Scholberg

Abstract

Within a few tens of seconds after infall, a core-collapse supernova radiates the vast majority of the binding energy of the resulting compact remnant in the form of neutrinos of all flavors. While the calculation of the number of neutrinos can be performed at different levels of sophistication, we outline an estimate that highlights the direct connection between the number of neutrinos and their detected energy to the basic properties of the supernova and its temporal evolution. Information about the astrophysics of the collapse and subsequent explosion, and about the physics of neutrinos, is encoded in the time, energy, and flavor structure of the neutrino burst. The next supernova neutrino burst in the Milky Way or nearby will be observable in a number of large neutrino detectors around the world; planned new and larger detectors will enhance the sensitivity further. This article describes the neutrino burst signal expected from a core-collapse supernova and what we will learn from it, including the early alert for core collapse. It will describe different types of neutrino detectors with supernova neutrino sensitivity and the capabilities of current and future neutrino detectors worldwide. In a concluding section, we discuss how, after thousands of years, the supernova remnant transforms itself into a particle accelerator that emits observable fluxes of neutrino of TeV energy.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Neutrino Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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F. Halzen () Department of Physics, University of Wisconsin-Madison, Madison, WI, USA e-mail: [email protected] K. Scholberg Department of Physics, Duke University, Durham, NC, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_8

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3 4

Neutrino Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Current and Future Supernova Neutrino Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Super-K and Hyper-K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 IceCube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Liquid Argon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Liquid Scintillator Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Other Supernova Neutrino-Sensitive Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Pointing to the Supernova with Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Early Alert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 TeV Neutrinos from Supernova Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

The astronomical detection of supernova explosions has a long history. Nearly 99 % of the energy of core-collapse supernovae is released in elusive neutrinos, which have only become detectable in the past several decades. (Note that thermonuclear supernovae are expected to produce only modest numbers of neutrinos (Odrzywolek and Plewa 2011).) Supernova SN 1987A in the Large Magellanic Cloud has resulted in the only detection of supernova-originated neutrinos so far. SN 1987A emitted a burst of MeV electron antineutrinos that were detected by the Kamiokande-II (Hirata et al. 1987, 1988), IMB (Bionta et al. 1987), and Baksan (Alekseev et al. 1987) neutrino detectors a few hours before its optical counterpart. Just a couple of tens of events provided sufficient information not only to probe supernova explosion models but also to shed new light on neutrino properties such as mass, magnetic moment, and lifetime (Kotake et al. 2006; Raffelt 1999). In spite of these milestones, further studies on supernova physics and neutrino properties can only be achieved with a much larger set of detected neutrinos. Furthermore, the neutrinos detected from SN 1987A were very likely only of electron antineutrino flavor. Observation of the next core-collapse supernova will bring enhanced information by broadening the flavor sensitivity and by vastly increasing the statistics with up to megaton (Mton)class neutrino detectors. One expects on the order of a few hundred events (note that in particle physics nomenclature, an “event” means a “neutrino interaction”) per kton of detector material for a core collapse at 10 kpc within a few tens of seconds. Therefore, detectors must be very large, and in general for good signal to background, they must have some matter overburden to suppress the large cosmic ray-related background present at the surface of the Earth. Current-generation detectors sensitive primarily to electron antineutrinos are Super-Kamiokande (Fukuda et al. 2003), a 50-kton total mass water Cherenkov detector and several smaller (kton scale or less) scintillator detectors. Nextgeneration neutrino detectors reaching the Mton scale are based on the Cherenkov technique (Suzuki 2008), most notably Hyper-Kamiokande (Abe et al. 2011), and are expected to provide detection of energy, direction, and flux of super-

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nova neutrinos. Currently, the only Mton-scale neutrino detector taking data is IceCube, a neutrino detector located at the South Pole that has transformed one cubic kilometer of Antarctic ice into a Cherenkov detector. A 20-kton scintillator detector, JUNO (An et al. 2015), is in the works, which will also be primarily sensitive to electron antineutrinos. The next-generation Deep Underground Neutrino Experiment (DUNE) detector (Adams et al. 2013; DUNE 2015), which is to consist of 40 kton of liquid argon, will be sensitive primarily to electron neutrinos rather than antineutrinos.

2

The Neutrino Signal

A core-collapse supernova occurs when the inactive core of a massive star grows beyond the Chandrasekhar mass; nuclear fusion stops, and the sudden loss of radiative pressure triggers a gravitational collapse and a subsequent explosion of the star’s outer layers. Less than 1 % of the gravitational binding energy of the collapsed core is emitted as optically visible radiation and kinetic energy. The remaining 99 % is released as neutrino kinetic energy, of which about 1 % will be electron neutrinos from an initial neutronization burst lasting a few milliseconds. The protoneutron star subsequently cools over 10 s, emitting most of its gravitational energy in neutrinos of all flavors (Burrows and Thompson 2003). At densities larger than 1015 kg m3 , the mean free path of neutrinos is smaller than the inner iron core of a supernova. Just 0:1 s after the start of the gravitational core collapse, neutrinos of all species are already trapped in their relative neutrinospheres. The shock wave following the collapse dissociates the nuclei. This suddenly increases the number of protons, and electron capture on these protons triggers a burst of e , in a time scale on the order of 10 ms (neutronization burst). The remainder of the neutrinos and antineutrinos produced from the ensuing cooling processes are roughly distributed evenly among all flavors. Thus, an estimated 3  1046 J (Burrows et al. 1992) is carried away by the intense neutrino emission produced predominantly through the thermal Helmholtz cooling reaction e eC ! .  ; Z  / ! . N According to Thompson et al. (2003) and Buras et al. (2003), the mean energy is expected to be about 13–14 MeV for e , 14–16 MeV for e , and 20–21 MeV for all other flavors . X /. The neutrino emission drops to zero after 15 s, when neutrinos are no longer produced in the cooled-down protoneutron star, considering a typical 11 Msun progenitor star. The fluence of neutrinos is Nv D

Esupernova 15MeV 1 Esupernova D 1:05  1012 cm2 4 d 2 hEv i 3  1046 J hEv i



10kpc d

2 : (1)

Neutrino oscillations may produce significant modification of the neutrino spectra. These oscillations may occur in the supernova, where matter (Mikheyev–Smirnov– Wolfenstein) transitions may have significant time- and energy-dependent effects on the spectra of either neutrinos or antineutrinos, depending on the neutrino mixing

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parameters and the neutrino mass hierarchy (i.e., on whether there are two light and one heavy neutrino mass states or two heavy and one light, an unknown at the time of this writing) and on the evolving density profile of the supernova. Furthermore, more exotic “collective” effects resulting from neutrino–neutrino interactions can result in significant modulation of the spectra, such as “spectral swaps,” which exchange flavor spectra above or below a particular energy threshold (there is a large body of literature on this topic; see Duan et al. (2010) and Mirizzi et al. (2015) for a review), in a way that depends on the neutrino mass hierarchy. These oscillation effects can produce observable effects on the signal detected on Earth. In addition, energy-dependent matter-induced flavor transitions occurring when the neutrinos traverse Earth matter on their way to a detector may in principle have observable effects (e.g., Dighe et al. 2003, 2004).

3

Neutrino Detectors

It is relatively straightforward to calculate the number of neutrino events expected from a supernova in a detector with a volume V . As an example, we take a water or ice detector, for which event rate will be dominated by inverse beta decay (IBD), for N e C p ! eC C n, on free protons. Approximately one sixth of the neutrinos from Eq. 1 will interact in the detector. The event rate is given by Z Nev D nt Nv

Z dEe

d .Ee ; Ev /V .Ee /f˛ dEv : dEe

(2)

Here nt D 6:18  1022 cm3 is the number density of protons in water or ice. The IBD cross section is given approximately by 44

v D 9:52  10



Ev MeV

2

cm2 :

(3)

The normalized distribution fa describes the energy dependence of neutrinos released by the supernova (Keil et al. 2003): f˛ .Ev ; hEv i/ D

.1 C ˛.t //1C˛.t/ hEv i.t /.1 C ˛.t //



Ev hEv i.t /

˛.t/

exp 1Œ1 C ˛.t /

 Ev : hEv i.t / (4)

For an estimate, we can ignore the less than 5 % difference in energy between the neutrino and the positron; for the complete calculation, see Abbasi et al. (2011). With this approximation, Eq. 2 can be rewritten in the simplified form Nev D nt Nv hEv v iN V

(5)

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where the average of neutrino energy times cross section is over the function fa , or hEv iv D 6  1040



 hEv i MeVcm2 15MeV

(6)

for ˛ D 3, which we will assume from now on. N is the number of photons produced per MeV of neutrino energy (note its units of MeV1 /, and V is the photon volume of the detector. For instance, for ice or water, N D 183 photons per MeV. This number is determined by the total track length of 0:58 cm MeV1 of shower particles produced by the secondary positron and the number of Cherenkov photons radiated by a positron, which is given by the Frank–Tamm formula as 315 cm1 . This number and the properties of the detector, its size and transparency, determine its “supernova volume” V ; see Sect. 4.2. While the calculation of the number of events can be done at different levels of sophistication, the method illustrates the direct connection between the number of neutrinos and their energy detected and the basic properties of the supernova and its temporal evolution.

4

Current and Future Supernova Neutrino Detectors

4.1

Super-K and Hyper-K

Super-Kamiokande (Super-K) is a cylindrical water Cherenkov detector of 50kton total mass of water, with 22.5-kton fiducial volume (inner detector mass 32 kton and total mass 50 kton). The inner 34-m diameter and 36-m high detector is viewed by 11,129 50-cm photomultipliers and is surrounded by an outer 2-m thick optically separated veto instrumented with 1885 20-cm photomultipliers. SuperK is located at 2700 meters-water-equivalent average overburden under Mount Ikenoyama in Japan. Super-K will observe between several thousand to more than ten thousand individually reconstructed (energy, vertex, time) neutrino events for a 10-kpc supernova (Ikeda et al. 2007), with an energy threshold of 4 MeV. The dominant interaction is IBD of electron antineutrinos on free protons, which will represent about 90 % of the water signal; other relevant interactions are charged and neutral-current interactions on oxygen (Langanke et al. 1996; Scholberg 2011). A subdominant (few percent), yet important, component of the signal is elastic scattering on electrons, e C e ! e C e . This component is of significance because of its sharp anisotropy, for which the directionality of Cherenkov radiation enables recording of the electron direction in the detector and hence enables pointing to the supernova. This interaction is the best prospect for pointing to the supernova (Beacom and Vogel 1999; Tomas et al. 2003). It should be possible to point to within 5–10ı of a 10-kpc core collapse with Super-K and to within a several degrees with Hyper-K (see Sect. 5). A planned future upgrade to Super-K is “SK-Gd,” which will involve doping the water with a gadolinium compound (Beacom and Vagins 2004). Gd has a

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high cross section for neutron capture, which is followed by a cascade of gamma rays, resulting in about 4 MeV of energy visible in the detector via Cherenkov radiation of Compton-scattered electrons. This will enable high-efficiency tagging of IBD events, thereby providing a clean IBD sample and also reducing background for pointing using elastic scattering on electrons. Without Gd, neutron tagging efficiency on free protons is 19 % (Wendell 2015). Hyper-Kamiokande (Hyper-K) represents a scale-up of Super-K, to be sited nearby Super-K. Its planned fiducial mass is 560 tons (Abe et al. 2011) divided between two modules. Photocoverage will likely be lower than Super-K’s, for an energy threshold of about 7 MeV. The expected number of core-collapse neutrino events approximately scales by detector mass.

4.2

IceCube

IceCube at the South Pole consists of 80 strings spaced 125 m apart horizontally, each instrumented with 60 10-in photomultipliers vertically spaced 17 m apart over a total length of 1 km. The deepest module is located at a depth of 2,450 km so that the instrument is shielded from the large background of cosmic rays at the surface by approximately 1.5 km of ice. Each optical sensor, referred to as a digital optical module (DOM), consists of a glass sphere containing the photomultiplier and an electronics board that digitizes the signals locally using an onboard computer. The digitized signals are given a global time stamp with residuals accurate to 2 ns and are subsequently transmitted to the surface. Although designed as a highenergy Cherenkov detector with a nominal threshold of 100 GeV (Achterberg et al. 2006), IceCube is still capable of detecting MeV-energy neutrinos from corecollapse supernovae by just counting them, albeit without recording the direction of individual events. A new supernova data acquisition that is capable of recording multiple photons from a single neutrino event provides a proxy for measuring their energy. IceCube is instrumented with a total of 5,160 photomultipliers. It detects neutrinos with energies ranging from 1010 to 1016 eV. A large burst of belowthreshold MeV neutrinos produced by a supernova will nevertheless be detected as a collective increase in photomultiplier counting rates on top of their low dark noise in sterile ice. The origin of this increased rate is Cherenkov light from shower particles produced by supernova electron antineutrinos interacting in the ice, predominantly by the IBD reaction. In ice, positron tracks of about 0:6 cm  .E =MeV/ length radiate 178  .EeC =MeV/ Cherenkov photons in the 300–600 nm wavelength range. From the approximate E2 dependence of the neutrino cross section and the linear energy dependence of the track length, the light yield per neutrino scales with E3 . With absorption lengths exceeding 100 m, photons travel long distances in the ice so that each DOM effectively monitors several hundred cubic meters of ice. Typically, only a single photon from each interaction reaches one of the photomultipliers, which as mentioned are vertically separated by roughly 17 m (and horizontally by 125 m). The DeepCore subdetector, equipped with a denser array of high efficiency

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photomultipliers, provides higher detection and coincidence probabilities. Although the rate increase in individual light sensors is not statistically significant, the effect will be clearly seen once the rise is considered collectively over many sensors. IceCube is the most precise detector for analyzing the neutrino light curve of close supernovae (Abbasi et al. 2011). The supernova data acquisition is based on count rates of individual optical modules stored in 1.6384 ms time bins. For recent years, the full photomultiplier raw data stream can be buffered and extracted around supernova candidate triggers (hitspooling) (Aartsen et al. 2013). While at the high level IceCube does not isolate individual events, it provides a high-statistics and detailed movie of the supernova as a function of time. Rather than just monitoring the noise in the DOMs, IceCube buffers the information from all photomultiplier hits. Every photon will be recorded to an accuracy of 2 ns in the case of a supernova. This low-level data provides several advantages: the complete detector information is available and the data – buffered at an early stage of the data acquisition system on the so-called string hubs – will be available in the unlikely case that the data acquisition fails, for instance, in the case of an extremely close supernova, which could exhaust the system. The automatized hitspooling has been working reliably for several years, including the automatic transfer of data in case of serious alarms to the North. The data from these triggered events have been carefully studied and compared to the results from the standard supernova data acquisition. In the case of IceCube, the detector consists of 5,160 essentially independent DOMs; each has a photon collection volume given by V D abs Aeff D abs QADOM

DOM Š abs  25cm2 ; 4

(7)

for an absorption length of 120 m, averaged over the depth of the detector, and an area of 490 cm2 and an angular acceptance of  for a DOM with 20 % quantum efficiency Q. Detailed simulations yield a lower volume of 16 cm2 compared to the usual approximation above used in the theory literature. In the end, we obtain a supernova volume of about 0.5 Mton per DOM from V D N hEv iV Š 0:5 Mton:

(8)

Combining this volume per DOM with the number of neutrinos N given by Eq. 1, we obtain more than one million events in IceCube from the most likely distance of 10 kpc: "  2 #     V hEv i NDOM 6 Esupernova 15MeV 10kpc : Nev D 1:210 3  1046 J hEv i d 0:52M t on 15MeV 5160 (9) As a sanity check, we confront this calculation with the observation of SN 1987A (Alekseev et al. 1987; Bionta et al. 1987; Hirata et al. 1987, 1988). The “historical” calculation accommodating the events observed in the Kamiokande-II experiment can be represented by

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 Nev D 5:2

4MeV T



Esupernova 3  1046 J



V 1kton



50kpc d

2 

T 4MeV

3 :

(10)

This yields 11 events for the 2.14 kton of actual fiducial volume, consistent with the Kamiokande observation. Using this scaling, IceCube would have detected 13,000 events from the Large Magellanic Cloud and 3:25  105 for the identical burst at 10 kpc. For d D 10 kpc, T D 15 MeV and Esupernova D 5  1052 erg, we obtain 1:14  106 events, in agreement with our earlier estimate. The excellent sensitivity to neutrino properties such as the neutrino hierarchy as well as the possibility of detecting the neutronization burst, a short outbreak of e0 s released by electron capture on protons soon after collapse are discussed in Abbasi et al. (2011). Also, the formation of a black hole or a quark star as well as the characteristics of shock waves are investigated to illustrate IceCube’s capability for supernova detection.

4.3

Liquid Argon Detectors

Liquid argon is unique in that it is the only large-scale detector material with primary sensitivity to a flavor other than N e . Argon is sensitive to charged-current absorption on 40 Ar, e C 40 Ar ! e C 40 K . The resulting potassium nucleus is created in an excited state; the nucleus subsequently de-excites to produce a characteristic pattern of gamma rays, which in principle can be used to tag the interaction as a chargedcurrent electron neutrino interaction (Raghavan 1986). There are also interactions in argon from electron antineutrinos as well some neutral-current channels, and elastic scattering on electrons occurs at about 10 % the rate of charged-current electron neutrino absorption on argon (Bueno et al. 2003). Large liquid argon detectors relevant for supernova neutrino detection are deployed in the form of time projection chambers, in which ionization charge drifts on a timescale of milliseconds toward an anode plane and is recorded on induction and collection wire planes to create a 2D projection. The third dimension of the track is determined from recorded relative drift time. For a supernova neutrino interaction, the absolute time and hence interaction position can be determined by detection of fast scintillation photons associated with the interaction. Several smaller instances of liquid argon time projection chambers include ICARUS (Bueno et al. 2003), MicroBooNE (Soderberg 2009), and SBND (Acciarri et al. 2015), which are or will be on the surface (and hence will suffer from background for supernova neutrino detection). The main prospect for a large liquid argon detector is DUNE, which is planned to have 40 kton in four 10-kton modules underground in South Dakota at 4,850 ft depth. The first module will be single phase, with horizontal drift. A candidate technology for subsequent modules is a dual-phase design, in which electron drift is vertical toward the top of the detector, where charge is multiplied at the liquid–gas interface. The unique feature of liquid argon for supernova detection is the primary sensitivity to electron flavor, which

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makes it highly complementary to the other detector types. In particular, prospects for measurement of the neutronization burst are very good, and there are unique oscillation signatures visible in electron neutrinos.

4.4

Liquid Scintillator Detectors

Like water Cherenkov detectors, liquid scintillator (hydrocarbons of various chemical structures) is rich in free protons, and IBD interactions dominate, leading to a primary sensitivity to electron antineutrinos from a supernova burst. Scintillation light produces 50 times more photons than Cherenkov light for a given energy deposition, enabling lower energy threshold and better energy resolution for a given photocoverage. The drawback is that light is emitted isotropically and directional interactions are more difficult to exploit (although there are some possibilities forl pointing (Fischer et al. 2015)). Although IBD dominates, several other interaction channels will contribute to a burst detection, in particular a neutral-current channel, sensitive to all flavors, that yields a 15-MeV gamma. The light provided by scintillator allows for good IBD tagging of the neutron capture on a free proton even without Gd doping, although Gd doping enhances electron antineutrino tagging efficiency. Liquid scintillator detectors sensitive to supernova neutrinos exist in the form of large homogeneous volumes surrounded by photomultiplier tubes (Scholberg and Walter 2014). Several kton-scale scintillation detectors are already in existence; these are the Large Volume Detector (Agafonova 2015), Borexino in Italy (Cadonati et al. 2002), and KamLAND in Japan (Eguchi et al. 2003). Daya Bay in China comprises seven small, surface detectors and can defeat the otherwise daunting cosmic ray background by good IBD tagging and requiring a distributed coincidence (Wei 2015). The 20-kton JUNO detector in China is planned for the future (An et al. 2015); RENO is another proposed large liquid scintillator detector (Kim 2015). Some other surface detectors, such as NOvA (Ayres et al. 2007), will record supernova burst counts but will have a cosmic ray background rate high enough to make self-triggering difficult. Table 1 summarizes current and planned supernova neutrino detectors.

4.5

Other Supernova Neutrino-Sensitive Detectors

Several other smaller detectors are able to register supernova neutrino interactions, often with diverse flavor sensitivity. For example, HALO at SNOLAB (Duba et al. 2008) is based on lead and will record neutrons emitted from neutrino–nucleus interactions in recycled neutron counters from the SNO experiment. With 79 tons of lead, HALO is expected to see a few dozen events at 10 kpc. Dark matter experiments, which are looking for the low-energy (few to few tens of keV) nuclear recoils from weakly interacting massive particle interactions with nuclei, will also record neutral-current (and hence all-flavor-sensitive) CEvNS

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Table 1 Summary of detector capabilities updated from Scholberg (2012, 2015). An asterisk refers to a surface detector, which may not be self-triggering due to cosmic-ray background. Events are approximate for a 10 kpc distance; depending on model, the total may vary by a factor of a few. The detector names in italics are members of SNEWS. The “future” detectors are described according to current plans. Detector Super-K LVD KamLAND Borexino IceCube Baksan MiniBooNE HALO Daya Bay NOvA SNO+ MicroBooNE DUNE Hyper-K JUNO RENO-50 IceCube Gen2/PINGU

Type Water Scintillator Scintillator Scintillator Water (long string) Scintillator Scintillator Lead Scintillator Scintillator Scintillator Argon Argon Water Scintillator Scintillator Water (long string)

Mass (kton) 32 1 1 0.3 600 0.33 0.7 0.08 0.33 15 0.8 0.17 40 560 20 18 TBD

Location Japan Italy Japan Italy South Pole Russia USA Canada China USA Canada USA USA Japan China Korea South Pole

Expected events 7000 300 300 100 .106 / 50 200 30 100 4000 300 17 3000 110,000 6000 5400 TBD

Status Running Running Running Running Running Running Running Running Running Running Near future Running Future Future Future Future Future

(coherent elastic neutrino-nucleus scattering) interactions from a core-collapse neutrino burst. A handful of events per ton of detector material are expected, depending on detector threshold (Horowitz et al. 2003). The recoil energy distribution contains spectral information about all flavors present in the neutrino burst.

5

Pointing to the Supernova with Neutrinos

A supernova neutrino burst detected on Earth carries information about the direction of the supernova. Extraction of pointing information will be valuable to astronomers for promptly pinpointing the location of the supernova light turn-on. Pointing ability might be especially useful for the case of a supernova that produces only dim or no electromagnetic signal, in order to associate the burst with a previously observed progenitor or dim remnant. The best prospects for pointing are from large water Cherenkov detectors, for which the directionality of the Cherenkov radiation enables gathering of information from the elastic scattering component of the signal (Beacom and Vogel 1999; Tomas et al. 2003). Super-K should be able to determine the supernova direction within 8ı for a 10 kpc supernova, and this should improve for Hyper-K. Removal of IBD background via neutron tagging will also improve pointing capability. A large liquid argon detector will also have

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pointing capability via electron tracking. Although scintillation light is isotropic, there is potential for pointing via precision measurement of positron and neutron positions in liquid scintillator detectors (Fischer et al. 2015). Triangulation using relative timing of signals observed around the Earth is in principle possible but in practice difficult with the current generation of detectors (Beacom and Vogel 1999). Very large statistics are required, as well as good knowledge of detector response.

6

Early Alert

The neutrino burst signal emerges promptly from a supernova’s core, whereas it may take hours for the first photons to be visible. Therefore, the detection of the neutrino burst from the next Galactic supernova can provide an early warning for astronomers. Requiring a coincident signal from several detectors will provide the astronomical community with a very high confidence early warning of the supernova’s occurrence. In addition, a neutrino burst alert may be able to serve as a trigger for detectors that are not able to trigger on a supernova signal by themselves, allowing extra data to be saved. The SuperNova Early Warning System (SNEWS) project (Antonioli et al. 2004; Scholberg 2008) involves an international collaboration of experimenters representing current supernova neutrino-sensitive detectors. The goal of SNEWS is to provide the astronomical community with a prompt alert of the occurrence of a Galactic core-collapse event. SNEWS has been running in automated mode since 2005. Currently, as of November 2015, seven neutrino experiments are involved: Super-K (Japan), LVD (Italy), IceCube (South Pole), KamLAND (Japan), Borexino (Italy), Daya Bay (China), and HALO (Canada). No nearby core collapses have occurred since SNEWS started running, but the network is ready for the next one. We note that in the few days before a core collapse, neutrino production and neutrino average energy increase, and for very nearby progenitors, some detectors may be able to provide a true early warning (Odrzywolek et al. 2004) of an impending core collapse. KamLAND can detect pre-supernova neutrinos for progenitors of mass greater than 25 solar masses within less than 0.6 kpc (Asakura et al. 2015), and future detectors should improve on this capability.

7

TeV Neutrinos from Supernova Remnants

Thousands of years after the supernova explosion, the remnant expanding into the interstellar medium is the origin of shocks that accelerate particles to high energy. Baade and Zwicky proposed supernova remnants as the sources of Galactic cosmic rays as early as 1934; their proposal is still a matter of debate after more than 75 years. Galactic cosmic rays reach energies of at least several PeV, the “knee” in the cosmic ray spectrum. The accelerators where they originate have been dubbed “PeVatrons.”

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It is difficult to hide a PeVatron from view. A generic supernova remnant releasing an energy W  1050 erg into the acceleration of cosmic rays will inevitably generate TeV gamma rays in the interaction of the accelerated cosmic rays with the hydrogen in the galactic disk. The emissivity in pionic gamma rays Q is simply proportional to the density of cosmic rays ncr and the density of the target n .1 cm3 / of hydrogen in the disk. Here, ncr .> 1 TeV/ Š 4  1014 cm3 is obtained by integrating the observed cosmic ray spectrum with energy in excess of 1 TeV. Assuming an E2 spectrum:  Q Š c

 E 1  ncr .> 1TeV/ Š 2 c x pp n ncr Ep pp

(11)

or Q .> 1TeV/ Š 1029 cm3 s1



n  : 1 cm3

(12)

The proportionality factor is determined by particle physics; x  0:1 is the average energy of secondary photons relative to the cosmic ray protons and pp D .npp /1 is the proton interaction length with pp Š 40 mb in a target density n. The corresponding luminosity is L .> 1TeV/ Š Q

W ; E

(13)

where W =E is the volume occupied by the supernova remnant. Here we make the approximation that the density of particles in the remnant E Š 1012 erg cm3 is not very different from the ambient energy density of galactic cosmic rays. We thus have a rate of TeV photons from a supernova remnant at a nominal distance d on the order of 1 kpc, the distance to the nearby star-forming region in Cygnus, of Z

dN dE D dE

Z

L .> 1TeV/ dE 4 d 2

E>1TeV

Š 1011  1012 cm2 s 1



 2  n  d W : 1050 erg 1 cm3 1 kpc

(14)

This is a PeVatron flux well within reach of the current generation of atmospheric gamma-ray telescopes. Has it been detected? Looking for them in the highest energy survey of the galactic plane points to the Milagro experiment (Abdo et al. 2007). Their survey in the 10 TeV band has revealed a subset of sources located within nearby star-forming regions in Cygnus and in the vicinity of galactic latitude l D 40ı . Most likely, the most promising sources are not the supernova remnants

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themselves but molecular clouds illuminated by the cosmic ray beam accelerated in young remnants located within about 100 pc. Indeed, one expects that cosmic rays are accelerated to PeV energy over a short period of time when the shock velocity is high, i.e., between free expansion and the beginning of its dissipation in the interstellar medium. The high-energy particles can produce photons and neutrinos over much longer periods when they diffuse through the interstellar medium to interact with nearby molecular clouds. An association of molecular clouds and supernova remnants is expected in star-forming regions. In this case, any confusion of pionic with synchrotron photons is unlikely. Assuming that the Milagro sources are indeed cosmic ray accelerators, particle physics dictates the relation between pionic gamma rays and neutrinos and basically predicts the production of a neutrino (or antineutrino) for every gamma ray seen by Milagro. This calculation of the neutrino flux can be performed using the formalism introduced above or in more sophisticated ways with the same outcome: we find that IceCube, or similar future detectors, should detect neutrinos from supernova remnants or molecular clouds with several years of data. For a detailed discussion, see reference (Gonzalez-Garcia et al. 2009). Also the widely studied supernova remnants RX J1713-3946 and RX J0852.0-4622 (Vela Junior) have been pinpointed as targets for observing neutrino emission. Note however that their photon spectrum does not reach beyond TeV.

8

Conclusions

The binding energy of the compact remnant resulting from a core collapse is radiated almost entirely in the form of a burst of few-tens-of-MeV neutrinos of all flavors within a few-tens-of-seconds interval. For core collapses occurring within and nearby the Milky Way, this neutrino burst will be detected in a number of large neutrino detectors worldwide. The observation of the next burst will bring unprecedented information on neutrino physics and on the physics of core collapse and potentially provide an early alert for astronomers. Future Mton-scale and multiflavor-sensitive detectors will provide a wealth of new knowledge from the next nearby core collapse.

9

Cross-References

 Diffuse Neutrino Flux from Supernovae  High-Energy Cosmic Rays from Supernovae  High-Energy Gamma Rays from Supernova Remnants  Neutrino Signatures from Young Neutron Stars  Shock Breakout Theory

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References Aartsen MG, Abbasi R, Abdou Y, Ackermann M, Adams J, Aguilar JA, Ahlers M, Altmann D, Auffenberg J, Bai X, Baker M, Barwick SW, Baum V, Bay R, Beatty JJ, Bechet S, Becker Tjus J, Becker K-H, Bell M, Benabderrahmane ML et al (IceCube Collaboration) (2013) The IceCube Neutrino Observatory part V: neutrino oscillations and supernova searches. In: Saa A (ed) Proceedings, 33rd international cosmic ray conference (ICRC2013), Rio de Janeiro, 2–9 July 2013. Braz J Phys 44(5):415–608 (2014) Abbasi R, Abdou Y, Abu-Zayyad T, Ackermann M, Adams J, Aguilar JA, Ahlers M, Allen MM, Altmann D, Andeen K, Auffenberg J, Bai X, Baker M, Barwick S W, Baum V, Bay R, Bazo Alba JL, Beattie K, Beatty JJ, Bechet S et al (IceCube Collaboration) (2011) IceCube sensitivity for low-energy neutrinos from nearby supernovae. Astron Astrophys 535:A109; Corrigendum ibid, 563:C1 (2014) Abdo AA, Allen BT, Berley D, Casanova S, Chen C, Coyne DG, Dingus BL, Ellsworth RW, Fleysher L, Fleysher R, Gonzalez MM, Goodman JA, Hays E, Hoffman CM, Hopper B, Huntemeyer PH, Kolterman BE, Lansdell CP, Linnemann JT, McEnery JE, Mincer AI, Nemethy P, Noyes D, Ryan JM, Saz Parkinson PM, Shoup A, Sinnis G, Smith AJ, Sullivan GW, Vasileiou V, Walker GP, Williams DA, Xu XW, Yodh GB (2007) TeV gamma-ray sources from a survey of the galactic plane with Milagro. Astrophys J 664:L91. arXiv:0705.0707 [astro-ph] Abe K, Abe T, Aihara H, Fukuda Y, Hayato Y, Huang K, Ichikawa AK, Ikeda M, Inoue K, Ishino H, Itow Y, Kajita T, Kameda J, Kishimoto Y, Koga M, Koshio Y, Lee KP, Minamino A, Miura M, Moriyama S et al (2011) Letter of intent: the Hyper-Kamiokande experiment. arXiv:1109.3262 Acciarri R, Adams C, An R, Andreopoulos C, Ankowski AM, Antonello M, Asaadi J, Badgett W, Bagby L, Baibussinov B, Baller B, Barr G, Barros N, Bass M, Bellini V, Benetti P, Bertolucci S, Biery K, Bilokon H, Bishai M et al (2015) A proposal for a three detector short-baseline Neutrino oscillation program in the Fermilab Booster Neutrino Beam. arXiv:1503.01520 Achterberg A, Ackermann M, Adams J, Ahrens J, Andeen K, Atlee DW, Baccus J, Bahcall JN, Bai X, Baret B, Bartelt M, Barwick SW, Bay R, Beattie K, Becka T, Becker JK, Becker K-H, Berghaus P, Berley D, Bernardini E et al (IceCube Collaboration) (2006) First year performance of the IceCube neutrino telescope. Astropart Phys 26:155 Adams C et al (2013) Scientific opportunities with the long-baseline Neutrino experiment. arXiv:1307.7335 Agafonova NY (2015) Implication for the core-collapse supernova rate from 21 years of data of the large volume detector. Astrophys J 802:1–47 Alekseev EN, Alekseev LN, Volchenko VI, Krivosheina IV (1987) Possible detection of a neutrino signal on 23 February 1987 at the Baksan Underground Scintillation Telescope of the Institute of Nuclear Research. J Exp Theor Phys Lett 45:589 An F, An G, An Q, Antonelli V, Baussan E, Beacom J, Bezrukov L, Blyth S, Brugnera R, Buizza Avanzini M, Busto J, Cabrera A, Cai H, Cai X, Cammi A, Cao G, Cao J, Chang Y, Chen S, Chen S et al (2015) Neutrino physics with JUNO. arXiv:1507.05613 Antonioli P, Tresch Fienberg R, Fleurot F, Fukuda Y, Fulgione W, Habig A, Heise J, McDonald AB, Mills C, Namba T, Robinson LJ, Scholberg K, Schwendener M, Sinnott RW, Stacey B, Suzuki Y, Tafirout R, Vigorito C, Viren B, Virtue C, Zichichi A (2004) SNEWS: the supernova early warning system. New J Phys 6:114 Asakura K, Gando A, Gando Y, Hachiya T, Hayashida S, Ikeda H, Inoue, Ishidoshiro K, Ishikawa T, Ishio, Koga M, Matsuda, Mitsui T, Motoki D, Nakamura K, Obara S, Oura T, Shimizu I, Shirahata Y, Shirai J et al (2015) KamLAND sensitivity to neutrinos from pre-supernova stars. arXiv:1506.01175 Ayres DS, Drake GR, Goodman MC, Grudzinski JJ, Guarino VJ, Talaga RL, Zhao A, Stamoulis P, Stiliaris E, Tzanakos G, Zois M, Hanson J, Howcroft C L, Mualem LM, Newman HB, Patterson RB, Peck CW, Trevor J, Cline DB, Lee K K, Yang X et al (2007) The NOvA technical design report. FERMILAB-DESIGN-2007-01

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Beacom JF, Vagins MR (2004) Anti-neutrino spectroscopy with large water Cherenkov detectors. Phys Rev Lett 93:171101 Beacom JF, Vogel P (1999) Can a supernova be located by its neutrinos? Phys Rev D 60:033007 Bionta RM, Blewitt G, Bratton CB, Casper D, Ciocio A, Claus R, Cortez B, Crouch M, Dye ST, Errede S, Foster GW, Gajewski W, Ganezer KS, Goldhaber M, Haines TJ, Jones TW, Kielczewska D, Kropp WR, Learned JG, LoSecco JM et al (1987) Observation of a neutrino burst in coincidence with Supernova SN 1987A in the large magellanic cloud. Phys Rev Lett 58:1494 Bueno A, Gil Botella I, Rubbia A (2003) Supernova neutrino detection in a liquid argon TPC. hep-ph/0307222 Buras R, Rampp M, Janka H-Th, Kifonidis K (2003) Improved models of stellar core collapse and still no explosions: what is missing? Phys Rev Lett 90:241101 Burrows A, Thompson TA (2003) From twilight to highlight: the physics of supernovae. In: Hillebrandt W, Leibundgut B (eds) Proceedings of ESO/MPA/MPE workshop (Garching). ESO astrophysics symposia, vol 2003. Springer, Berlin, pp 53–62. arXiv:astro-ph/0210212v1 Burrows A, Klein K, Gandhi R (1992) The future of supernova neutrino detection. Phys Rev D45:3361 Cadonati L, Calaprice FP, Chen MC (2002) Supernova neutrino detection in Borexino. Astropart Phys 16:361–372 Dighe AS, Keil MT, Raffelt GG (2003) Identifying earth matter effects on supernova neutrinos at a single detector. JCAP 0306:006 Dighe AS, Kachelriess M, Raffelt GG, Tomas R (2004) Signatures of supernova neutrino oscillations in the earth mantle and core. J Cosmol Astropart Phys 0401:004 Duan H, Fuller GM, Qian Y-Z (2010) Collective neutrino oscillations. Ann Rev Nucl Part Sci 60:569–594 Duba CA, Duncan F, Farine J, Habig A, Hime A, Robertson RGH, Scholberg K, Shantz T, Virtue CJ, Wilkerson JF, Yen S (2008) HALO: the helium and lead observatory for supernova neutrinos. J Phys Conf Serv 136:042077 DUNE/LBNF collaborations (2015) DUNE/LBNF CDR volume 2: the physics program for DUNE at LBNF. http://lbne2-docdb.fnal.gov/cgi-bin/ShowDocument?docid=10688 Eguchi K, Enomoto S, Furuno K, Goldman J, Hanada H, Ikeda H, Ikeda K, Inoue K, Ishihara K, Itoh W, Iwamoto T, Kawaguchi T, Kawashima T, Kinoshita H, Kishimoto Y, Koga M, Koseki Y, Maeda T, Mitsui T, Motoki M et al (2003) First results from KamLAND: evidence for reactor anti-neutrino disappearance. Phys Rev Lett 90:021802 Fischer V, Chirac T, Lasserre T, Volpe C, Cribier M, Durero M, Gaffiot J, Houdy T, Letourneau A, Mention G, Pequignot M, Sibille V, Vivier M (2015) Prompt directional detection of galactic supernova by combining large liquid scintillator neutrino experiments. JCAP 08:032 Fukuda S, Fukuda Y, Hayakawa T, Ichihara E, Ishitsuka M, Itowa Y, Kajita T, Kameda J, Kaneyukia K, Kasuga S, Kobayashia K, Kobayashia Y, Koshioa Y, Miura M, Moriyama S, Nakahata M, Nakayama S, Namba T, Obayashia Y, Okada A et al (2003) The Super-Kamiokande Detector. Nucl Instrum Methods A501:418–462 Gonzalez-Garcia MC, Halzen F, Mohapatra S (2009) Identifying galactic PeVatrons with neutrinos. Astropart Phys 31:437. arXiv:0902.1176 [astro-ph.HE] Hirata K, Kajita T, Koshiba M, Nakahata M, Oyama Y, Sato N, Suzuki A, Takita M, Totsuka Y, Kifune T, Suda T, Takahashi K, Tanimori T, Miyano K, Yamada M, Beier EW, Feldscher LR, Kim SB, Mann AK, Newcomer FM, Van Berg R, Zhang W, Cortez BG (1987) Observation of a neutrino burst from the Supernova SN 1987A. Phys Rev Lett 58:1490 Hirata K, Kajita T, Koshiba M, Nakahata M, Oyama Y, Sato N, Suzuki A, Takita M, Totsuka Y, Kifune T, Suda T, Takahashi K, Tanimori T, Miyano K, Yamada M, Beier EW, Feldscher LR, Frati W, Kim SB, Mann AK, Newcomer FM, Van Berg R, Zhang W, Cortez BG (1988) Observation in the Kamiokande-II detector of the neutrino burst from Supernova SN 1987A. Phys Rev D38:448

1670

F. Halzen and K. Scholberg

Horowitz CJ, Coakley KJ, McKinsey DN (2003) Supernova observation via neutrino-nucleus elastic scattering in the CLEAN detector. Phys Rev D68:023005 Ikeda M, Takeda A, Fukuda Y, Vagins MR, Abe K, Iida T, Ishihara K, Kameda J, Koshio Y, Minamino A, Mitsuda C, Miura M, Moriyama S, Nakahata M, Obayashi Y, Ogawa H, Sekiya H, Shiozawa M, Suzuki Y, Takeuchi Y et al (2007) Search for supernova neutrino bursts at Super-Kamiokande. Astrophys J 669:519–524 Keil MT, Raffelt GG, Janka H-Th (2003) Monte Carlo study of supernova neutrino spectra formation. Astrophys J 590:971–91 Kim SB (2015) New results from RENO and prospects with RENO-50. Nucl Part Phys Proc 265– 266:93–98 Kotake K, Sato K, Takahashi K (2006) Explosion mechanism, neutrino burst, and gravitational wave in core-collapse supernovae. Rep Prog Phys 69:971–1144 Langanke K, Vogel P, Kolbe E (1996) Signature for supernova  and geutrinos in water Èerenkov detectors. Phys Rev Lett 76:2629–2632 Mirizzi A, Tamborra I, Janka H-T, Saviano N, Scholberg K, Bollig R, Huedepohl L, Chakraborty S (2015) Supernova neutrinos: production, oscillations and detection. arXiv:1508.00785 Odrzywolek A, Plewa T (2011) Probing thermonuclear supernova explosions with neutrinos. Astron Astrophys 529:A56 Odrzywolek A, Misiaszek M, Kutschera M (2004) Detection possibility of the pair-annihilation neutrinos from the neutrino-cooled pre-supernova star. Astropart Phys 21:303–313 Raffelt GG (1999) Particle physics from stars. Ann Rev Nucl Part Sci 49:163 Raghavan R (1986) Inverse Beta decay of Ar40: a new approach for observing MeV neutrinos from laboratory and astrophysical sources. Phys Rev D 34:2088–2091 Scholberg K (2008) The supernova early warning system. Astron Nachr 329:337–339 Scholberg K (2011) Supernova neutrino detection in water Cherenkov detectors. J Phys Conf Serv 309:012028 Scholberg K (2012) Supernova neutrino detection. Ann Rev Nucl Part Sci 62:81–103 Scholberg K (2015) Supernova neutrino detection. AIP Conf Proc 1666:070002 Scholberg K, Walter CW (2014) “Deep Liquid Detectors” review. In: Olive K A et al (2014) Review of particle physics. Chin Phys C 38:090001 Soderberg M (2009) MicroBooNE: a new liquid argon time projection chamber. AIP Conf Proc 1189:83–87 Suzuki Y (2008) Future outlook: experiment. J Phys Conf Ser 136:022057 Thompson TA, Burrows A, Pinto PA (2003) Shock breakout in core-collapse supernovae and its neutrino signature. Astrophys J 592:434 Tomas R, Semikoz D, Raffelt GG, Kachelriess M, Dighe AS (2003) Supernova pointing with lowenergy and high-energy neutrinos. Phys Rev D68:093013 Wei H (2015) Design, characterization, and sensitivity of the supernova trigger system at Daya Bay. arXiv:1505.02501 Wendell R (2015) Atmospheric results from Super-Kamiokande. AIP Conf Proc 1666:100001

Gravitational Waves from Core-Collapse Supernovae

63

Kei Kotake and Takami Kuroda

Abstract

We summarize the theoretical predictions of gravitational waves (GWs) in stellar core-collapse and core-collapse supernova evolution. Following a brief introduction to overview how scientifically significant the successful detection of GWs could be, we give a concise summary of the essential GW features mostly based on a back-of-the-envelope estimation. If the gravitational collapse of stellar cores and the subsequent explosion hydrodynamics occur in a perfectly spherically symmetric manner, no GWs can be emitted. Therefore, what makes the dynamics of the central engine deviate from spherical symmetry is essential for determining the physics of the GW emission processes. Among the candidates, we mainly focus on the best-studied GW signal that is emitted near core bounce in rapidly rotating core-collapse. After bounce, multiple emission processes have been proposed thus far. These postbounce GWs, if observed, are also expected to provide smoking-gun information for unraveling the yet uncertain explosion mechanisms. We finally conclude with the most urgent tasks to prepare for the GW astronomy of core-collapse supernovae.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic GW Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 GW Extraction Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Axisymmetric Versus Nonaxisymmetric Sources . . . . . . . . . . . . . . . . . . . . . . . . 2.3 To Be Rapidly Rotating or Not (That Is the Question!) . . . . . . . . . . . . . . . . . . . .

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K. Kotake () Department of Applied Physics, Fukuoka University, Fukuoka, Japan e-mail: [email protected] T. Kuroda Department of Physics, University of Basel, Basel, Switzerland e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_9

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3

GWs from Rapidly Rotating Core-Collapse and Bounce . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Nonaxisymmetric Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 GWs from Nonrotating Progenitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Characteristic GW Frequency in the Postbounce Phase . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

On September 14, 2015, the centennial year after Albert Einstein’s 1915 general theory of relativity, the twin detectors of the Laser Interferometer GravitationalWave Observatory (LIGO) coined the first direct detection of gravitational waves (GWs). After the dedicated data analysis was done in order to unambiguously distinguish the real GW signal from detector noise, it was revealed that this Nobel Prize-winning event, GW150914, was produced by the merger of two black holes (BHs) (Abbott et al. 2016b). In addition to LIGO, the second-generation detectors such as Advanced VIRGO (Hild et al. 2009) and KAGRA (Aso et al. 2013) will be on line in the coming years. Furthermore, a third-generation detector like the Einstein telescope has also recently been proposed (Punturo et al. 2014). At such a high level of precision, these detectors are sensitive enough to detect a wide variety of compact objects. The prime targets are compact binary coalescences such as the merger of black holes and/or neutron stars (NSs) (e.g., Sathyaprakash and Schutz 2009). Other intriguing sources include neutron star normal mode oscillations and rotating neutron star mountains (e.g., Andersson 2003). Core-collapse supernovae (CCSNe) are the mothers of all these compact objects. For massive stars heavier than 8Mˇ (Smartt 2015), the central iron core, once formed at the final stage of stellar evolution, is dynamically unstable and begins gravitational collapse (Iben 2013). The focus of this chapter is on the GW emission produced in the blink of an eye (in approximately one second, contrasting with the million years of stellar evolution) when the catastrophic implosion turns into one of the most energetic explosions in the modern Universe. According to Einstein’s theory of general relativity (GR, e.g., Misner et al. 1973), no GWs can be emitted if gravitational collapse of the stellar core proceeds with perfect spherical symmetry. To produce GWs, the central engine that powers the explosion should work aspherically and dynamically. In fact, there is accumulating observational evidence from electromagnetic-wave observations of ejecta morphologies, spatial distributions of nucleosynthetic yields, and natal kick of pulsars, all of which have pointed towards CCSNe being generally aspherical (i.e., spatially multidimensional (multi-D), e.g., Wang et al. (2002), Maeda et al. (2008), Tanaka et al. (2009), Grefenstette et al. (2014), and references therein). Unfortunately, however, these electromagnetic signatures are secondary for probing the inner workings of CCSNe because they are only able to provide images of optically thin regions far away from the central core.

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Much more direct information is delivered to us by neutrinos and GWs. In fact, the detection of neutrinos from SN 1987A opened the door for neutrino astronomy. (See, e.g.,  Chap. 59, “Neutrino Emission from Supernovae”.) However, these neutrino signatures produced deep inside the core are influenced, in propagating through the stellar envelope, by both collective neutrino oscillations and the Mikheyev-Smirnov-Wolfenstein effects. (See, e.g.,  Chap. 59, “Neutrino Emission from Supernovae”.) Therefore, GWs are the most direct observable bringing us news of this intimate episode of the supernova engine. Current estimates of CCSN rates in our Milky Way predict one event every 40 ˙ 10 years (Horiuchi et al. 2013). Although rare, they provide a unique way to study CCSNe using a full set of multimessenger observables including GWs, neutrinos, and electromagnetic waves (e.g., Nakamura et al. 2016) including nuclear gamma-rays (Gehrels et al. 1987). From a theoretical point of view, understanding the origin of the explosion multidimensionalities is also indispensable for clarifying the yet uncertain CCSN mechanisms. After a half-century of extensive research, theory and neutrino radiation hydrodynamics simulations are now reaching a point where multi-D hydrodynamic instabilities play a crucial role in the neutrino-heating mechanism of CCSNe (Bethe 1990), the most favored scenario to trigger explosions. In fact, a number of firstprinciple, self-consistent simulations in two or three spatial dimensions (2D, 3D) now report successful neutrino-driven models that are trending towards explosion, These successful models have strengthened our confidence in the multi-D neutrinodriven paradigm (see Janka et al. (2016), Foglizzo et al. (2015), Burrows (2013), and Kotake et al. (2012b) for recent reviews). Another candidate mechanism is the magnetohydrodynamic (MHD) mechanism (e.g., LeBlanc and Wilson 1970, Kotake et al. 2006, Thielemann et al. 2012, Mösta et al. 2014, and Nishimura et al. 2015). Rapid rotation of precollapse iron cores is necessary for this mechanism, because it relies on the extraction of rotational free energy of the core by means of field-wrapping and magnetorotational instability (MRI, e.g., Balbus and Hawley 1998, Obergaulinger et al. 2009, Masada et al. 2012, and references therein). Such rapid rotation is likely to be typical of 1 % of the massive star population (e.g., Woosley and Bloom 2006). Minor as they may be, the MHD explosions are attracting great attention as they are possibly relevant for magnetars and collapsars (e.g., Woosley 1993 and Metzger et al. 2011), which are hypothetically linked to the formation of long-duration gamma-ray bursts (e.g., Mészáros (2006) for a review). In step with these advances in the CCSN theory, significant progress in understanding GW emission processes has been made almost at the same pace (e.g., Kotake (2013), Fryer and New (2011), and Ott (2009) for recent reviews). In the MHD mechanism, rapid rotation of the precollapse core leads to significant rotational flattening of the collapsing and bouncing core, leading to a waveform that has been theoretically best-studied, the so-called type I waveform of the bounce GW signal. The waveform is characterized by sharp spikes at bounce followed by a subsequent ring-down phase (Dimmelmeier et al. 2007; Kotake et al. 2003; Mönchmeyer et al. 1991; Ott et al. 2004, 2007). After bounce, a large variety of emission processes has been proposed, including convective motions in the

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proto-neutron star (PNS) and in the region behind the stalled shock (Burrows and Hayes 1996; Müller and Janka 1997; Müller et al. 2004), the standing-accretionshock-instability (SASI; e.g., Kotake et al. 2009, 2007; Marek et al. 2009; Murphy et al. 2009), nonaxisymmetric rotational instabilities (Kuroda et al. 2014; Ott et al. 2005; Scheidegger et al. 2010), and anisotropy in neutrino emission (Kotake et al. 2009; Müller et al. 2013, 2012, 2004). This chapter is structured as follows. In Sect. 2, we give a brief summary of the essential GW features in CCSNe mostly based on a back-of-the-envelope estimation. We primarily focus on the well-established GW signal emitted near core bounce in rapidly rotating core-collapse (Sect. 3). Regarding the GWs in the postbounce phase, we attempt in Sect. 4 to select only the established GW signatures from the various emission mechanisms proposed thus far. In Sect. 5, we give a summary and discuss some urgent tasks to prepare for the upcoming era of the GW astronomy of CCSNe.

2

Basic GW Features

In this section, we give a brief summary of the fundamental GW signatures of CCSNe. For physical foundations of GWs, the reader is referred to standard textbooks (e.g., Misner et al. 1973; Shapiro and Teukolsky 1983) for a complete description. Instead of re-expressing them, here we only choose several formulae useful in the CCSN context and present order-of-magnitude estimates of the GW amplitudes and frequencies for later convenience.

2.1

GW Extraction Formulae

2.1.1 Quadrupole Formula As we later show, GWs emitted in stellar core-collapse have little impact on the evolution of the hydrodynamics. Due to the weakness of the signal, the quadrupole formula (e.g., Misner et al. 1973), which is the simplest approach to extract the gravitational waveform, has been widely used in the community. The validity of the approximation has been confirmed by comparing with more detailed GW extraction techniques based on numerical relativity (Reisswig et al. 2011). In the quadrupole formalism (e.g., Section 16 in Shapiro and Teukolsky 1983), the dimensionless GW strain h is hTij T .t; x/ D

D   @  2G RT T  I ;  ; t  ij c4D c @t

(1)

where D D jxj is the distance to the source, G is the gravitational constant, and c is the speed of light. IijT T is the transverse-traceless (TT) part of the mass quadrupole moment Iij ,

63 Gravitational Waves from Core-Collapse Supernovae

Z Iij D

1 d 3 x .xi xj  ıij x 2 /; 3

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(2)

where  is the mass density. The energy flux from the GW emission is E D quadrupole given by the Isaacson stress-energy tensor as T0r / hTij;0T hTij;rT , where r represents the radial direction to the source and the angle brackets denote appropriately averaging processes (such as over several wavelengths). Then one can obtain the energy loss rate, equivalently the GW luminosity, by integrating the energy flux over a distant sphere (see the above textbooks for the derivation), LGW D

G D «ij « E I Iij : TT 5c 5

(3)

Using Eqs. (1) and (3), we give an order-of-magnitude estimate of the GW amplitude and luminosity emitted near core bounce. The GW amplitude can be estimated as 2G R 2G MRc2 300 cm  M  Rc 2  Tdyn 2 Iij  4  ' 2 4 c D c D Tdyn D Mˇ 10 km 1 ms    10 kpc  M  R 2  T 2 dyn c ; ' 1021 0:1 D Mˇ 10 km 1 ms

jhj D

(4) (5)

where IRij is now decomposed into the typical mass (M ), radius of the (inner) core (Rc ), and dynamical timescale at core bounce (Tdyn ), respectively. We assume that the supernova occurs near our Galactic center at a distance of 10 kpc.  is a parameter, representing the degree of the nonsphericity (D 0 if spherical), which may be optimistically estimated to be on the order of 10 % in rapidly rotating supernova cores. The typical GW frequency can be approximately estimated by the inverse of p 1=2 the dynamical timescale (Tdyn / 1= G  1 ms 13 with  being the average 13 3 density in units of 10 g cm ). Because the GW emission sites are mainly located in the vicinity of the proto-neutron star (PNS) (1011 g cm3 .  . 1013 g cm3 ), the GW frequency is expected to be in the following range, fGW 

1 ' O.100 Hz/  1 kHz: Tdyn

(6)

Figure 1 summarizes the sensitivity curves of LIGO (labeled aLIGO in the figure; e.g., Abbott et al. 2016a), advanced Virgo (adVirgo; Hild et al. 2009), KAGRA (Aso et al. 2013), and the Einstein telescope (ET; Punturo et al. p 2014). Plotted lines correspond to the dimensionless rms strain sensitivity hrms D f S .f / where S .f / is the detector-dependent noise power spectral density (for more details on the GW detectors, e.g., see  Chap. 64, “Detecting Gravitational Waves from Supernovae with Advanced LIGO”). From Eqs. (5) and (6), one could see that a CCSN event in

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Fig. 1 Sensitivity curves of representative laser interferometers. Currently (as of April 2016), LIGO (labeled aLIGO in the figure) is in operation, whereas advanced Virgo (adVirgo) and KAGRA are under construction, and the construction of the Einstein telescope is being proposed. See text for definition of the ordinate axis

our Galactic center (D D 10 kpc) is the primary target where the star formation rate should be highest in the Milky Way. When the ET is on line, the detection horizon could extend to megaparsec distance scales (D  Mpc). Considering the CCSN rate in the local universe (Horiuchi et al. 2013), one could optimistically expect the GW detection from CCSNe to be several per decade in the ET era. Regarding the GW luminosity, the third time derivate of Iij in Eq. (3) is approximately expressed as  c 5  GM  v 3 3 I«ij  MRc2 Tdyn  ; G Rc c 2 c

(7)

where v  Rc =Tdyn is the typical velocity in the core. Assuming energy conservation (GM =Rc  v 2 ), Eq. (3) becomes LGW .  2 LG

 v 10 c

;

(8)

where LG D

c5 D 3:6  1059 erg s1 : G

(9)

By taking the typical velocity (v=c  10 %) and the duration (texp  1 s) relevant for the CCSN engine, the total energy carried away by GWs can be estimated as 2 EGW  LGW  texp . 1047 0:1 erg. This is really a crude upper bound. But, it is instructive to see that EGW is much smaller compared to the total energy emitted in

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the form of neutrinos (E  1053 erg) and photons (Ephoton  1049 erg). Comparing this with the typical observed supernova kinetic energy (EK  1051 erg, e.g., Tanaka et al. 2009), one may readily see that the GW emission is dynamically insignificant as mentioned earlier.

2.2

Axisymmetric Versus Nonaxisymmetric Sources

We move on to perform an another simple estimate for the GW emission from the rotating star in axisymmetry (i.e., 2D). Then we present several useful formulae to extract the waveform in both 2D and 3D CCSN models. In order to discuss the detectability of GWs seen from the distant observer, it is convenient to find the nonzero components of hTij T in spherical coordinates, not in Cartesian coordinates. We assume that the GW propagates along the r direction from the source at a distance of D. Due to the TT nature, hrr , hr , and hr vanish. Then the C and  mode of the GWs can be defined from the two nonvanishing components as hC D

h h : ; h D 2 D2 D sin 

(10)

By performing a simple coordinate transformation, for example, for the  i @x j component, h D hTij T @x ; the two components read @ @ h 2 h hxx C hyy  2hzz Q Q .cos  C 1/ cos 2  sin2  C D .h  h / xx yy D2 4 4 i cos2  C 1 Q sin 2  hQ hQ xy xz sin  cos  cos   hyz sin  cos  sin  ; 2 h D D 2 sin  Q

Q



Q

Q

(11)

Q

hxx  hyy Q Q cos  sin  C hQ xy cos  cos 2 C hxz sin  sin   hyz sin  cos ; 2 (12)

Q where hij D D2 IRijT T is expressed in Cartesian coordinates. O Z/, O the density distribution of an axisymUsing cylindrical coordinates .R; O Z/. O The quadrupole moments are metrically rotating star is described as .R; R 3 O O O O Ixx D .R; Z/ R d R; Iyy D Ixx ; Ixy D 0. Furthermore, assuming equatorial symmetry of the rotating star, the remaining components are Izz D R O Z/ O ZO 2 RO d RO d zO; Ixz D Iyz D 0. As easily understood, if the star rotates 2 .R; stationary, no GWs are emitted because IRij D 0. The GWs are emitted when the rotating star contracts or expands dynamically, because the time derivatives of the

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quadrupole moments have nonzero values. Note also that the GWs can be emitted from “axisymmetrically” rotating stars, when the motion is dynamically changing. Inserting Eqs. (11) and (12) into Eq. (10), one can get hC D 

1 R .Ixx  IRzz / sin2 ; D

(13)

and h D 0;

(14)

respectively, for  D 0. From an axisymmetric source, the GW is most strongly emitted in the direction perpendicular to the symmetry axis ( D =2 in Eq. (13)) and no GW is emitted toward the symmetry axis. It is intuitively natural because the dynamical behavior of the rotating star, if axisymmetric, can be seen most dramatically from the equatorial plane. As a side remark, GWs from merging compact objects (NSs or BHs) are generally most strongly emitted in the direction of the rotational axis. In practice, the numerical treatment of the second time derivatives in Eq. (13) is formidable. Moreover, the use of spherical coordinates is most common in stellar core-collapse simulations (because a nonrotating star in equilibrium takes a spherical shape). Using the hydrodynamic equations of perfect fluids, the time derivatives can be eliminated. For example, the first time derivative of Ixx in Eq. (13) in the integrand. Using the equation of mass conservation expressed in contains @ @t spherical coordinates, 1 @ @ @ 1 C 2 .r 2 vr / C .sin v / D 0 @t r @r r sin  @

(15)

with  D cos  and v being the velocity, the time derivative in the integrand can be replaced by the quantities with spatial derivatives. Taking one more time derivative using the Euler equations, one can get the most commonly used GW (quadrupole) formula in 2D (axisymmetric) CCSN simulations as

hC D

1 8

r

15 2 AE2 sin  20 ;

D

(16)

where AE2 20 (the quadrupole amplitude, see the definition in Thorne 1980) is given as AE2 20 D

Z 1 Z G 32 3=2 1 d  r 2 dr Œvr 2 .32  1/ C v 2 .2  32 /  v 2 p c4 15 0 0 p p 6vr v  1  2  r@r ˆ.32  1/ C 3@ ˆ  1  2 ; (17)

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where @r D @=@r; @ D @=@ and ˆ is the gravitational potential (see Mönchmeyer et al. (1991) for the derivation). The spectral energy distribution dEGW =df of the GW is given by c3 dEGW D .2 f /2 df 16 G

Z

1 1

e 2 if t AE2 20 .t / dt;

(18)

then the gravitational-wave energy EGW emitted in the GW is Z EGW D 0

1

dEGW df df

(19)

Without axisymmetry in the supernova core, the  mode of GW (Eq. (14)) is no longer zero. The angle-dependent GW formulae usable in 3D (nonaxisymmetric) simulations were derived by Oohara et al. (1997) and compactly summarized in Müller et al. (2012) and Kuroda et al. (2014). To access the detectability of GWs by interferometers, the following quantities are often used. One can calculate the spectral GWR density hrss [Hz1=2 ] from the 1 Fourier transform of the wave signals (hC; .f / D 1 e 2 if t hC; .t / dt ) as hrss D qP jhQ A .f /j2 . Then the (detector-dependent) characteristic frequency is ADC;

Z

1

fc D 0

!, Z ! P Q P Q 1 Q Q A hA .f /hA .f / A hA .f /hA .f / f df df ; Sn .f / Sn .f / 0

(20)

where Sn .f / is the detector noise power spectral density in units of Hz1=2 . Having the same unit as the strain equivalent spectrum density, hrss is often used in burst GW searches to compare the signal strength with the detector sensitivity. hc is the characteristic strain amplitude (Thorne 1987), Z hc  0

1

Sn .fc / X Q hA .f /hQ A .f /f df Sn .f / A

!1=2 ;

(21)

by which one can compute the signal-to-noise ratio as signaltonoise ratio D p

hc fc Sn .fc /

:

(22)

To claim detection, a signal-to-noise ratio greater than unity and probably in the range of 8–13 would be needed (Flanagan and Hughes 1998; Sathyaprakash and Schutz 2009).

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2.2.1 GWs from Anisotropic Neutrino Radiation In addition to the quadrupole matter motions (Sect. 2.1.1), any sources that can contribute to the nonspherical part of the energy momentum tensor of the Einstein equations lead to GW emission. One of these sources is GW from anisotropic neutrino radiation emitted from the PNS. Epstein (1978) was the first to derive the formula of GWs produced by anisotropically escaping neutrinos from the CCSN core. One should define a concrete form of an energy-momentum tensor of the neutrino radiation field to compute the gravitational waves. In Epstein (1978), the following form is naturally assumed, T ij .t; x/ D ni nj D 2 L .t  r/f .; t  r/;

(23)

R where ni D x i =D; D D jxj; f .; t / 0; and f .; t /d  D 1. This source tensor represents radiation fields of neutrinos being released at the speed of light from the point x D 0 to an observer at a distance of D. The functions L .t / and f .; t / are the rate of energy loss and the angular distribution of neutrino radiation, respectively, at time t . Given the energy-momentum tensor, one can calculate the TT part of the GW strain from neutrinos (Burrows and Hayes 1996; Müller and Janka 1997) as hT Tij .t; x/ D

4G c4D

Z

tD=c

Z

1

4

.ni nj /T T L .t 0 /f .0 ; t 0 / d 0 dt 0 ; 1  cos  0

(24)

where dashed .0 / variables represent the quantities observed in a coordinate frame .x 0 ; y 0 ; z0 /; on the other hand, nondashed variables represent the quantities observed in the observer’s frame .x; y; z/. For simplicity, let us first consider an axisymmetric (neutrino) source. In this case, both hC and h modes vanish for an observer on the symmetric axis, and the GW signal (hC component) with maximum amplitude is obtained for an observer in the equatorial plane (Müller and Janka 1997). In this case, the GW amplitude is given by h D

2G c4r

Z

tD=c

dt L .t 0 /  ˛.t 0 /;

(25)

1

where ˛.t 0 / is the time-dependent anisotropy parameter, ˛.t 0 / D

Z

d 0 ‰.# 0 ; ' 0 / f .0 ; t 0 /;

(26)

4

representing the degree of the deviation of the neutrino emission from spherical symmetry (for the concrete form of ‰.# 0 ; ' 0 /, see Kotake et al. 2007; Müller et al. 2012). Inserting typical values into the above equation, one can find the typical amplitudes,

63 Gravitational Waves from Core-Collapse Supernovae

h  1:6  102 cm

 t  L 1  ˛  exp ; D 0:1 1052 erg s1 1s

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(27)

where we take an emission time of texp D 1 s assuming constant radiation and the optimistic value of ˛  0:1. Thus one can expect that the GW amplitude from neutrinos can be as high as the one from quadrupole mass motions emitted near core bounce in rotational core-collapse (compare with Eq. (4)). The complete set of the GW formulae from neutrinos applicable to 3D simulations are summarized in Müller et al. (2012) and Kotake et al. (2009). The typical GW frequency from neutrinos, on the other hand, becomes much lower (f ; GW . 100 Hz) than the one (Eq. (6)) at core bounce. Comparing with Fig. 1, one may readily see that the detection is rather hard limited by seismic noise at the low frequencies (e.g., slope f . 100 Hz in Fig. 1). As explained later, the matter GW signal at core bounce is emitted as bursts in which the wave amplitude rises from zero at core bounce, oscillates for several cycles, and then approaches zero (e.g., bottom left panel of Fig. 3). In addition, there is another class of GW, that is, bursts with memory (Turner and Wagoner 1979). In this case, the wave amplitude rises from zero and then settles into a nonzero final value even after the energy flows leave the source. The appearance of such an offset may be understood by looking at texp remaining in Eq. (25) (see an example of the waveform “with memory” in the dotted line of Fig. 8, left panel). The short time-scale modulation in the neutrino radiation field is smeared out by the memory effect, which leads to the slower variation in the f ;GW . The GWs not only generated by anisotropic neutrino emission but also from large-scale, coherent mass motions (such as jets) fall into this category (Shibata et al. 2006; Takiwaki and Kotake 2011). So the GWs from jets also have a slower temporal modulation (.100 Hz), which is hard to detect by ground-based detectors. It is noted that a future space interferometer such as the Fabry-Perot type DECIGO is designed to be sensitive in these frequency regimes (Kawamura et al. 2006). These low-frequency GW signals, if observed, could be important messengers telling us about the degree of anisotropy of neutrino emission and jet propagation in the MHDdriven explosions. It is also interesting to note that these space-based detectors could detect the GW signals from type Ia supernovae driven by a delayed detonation up to a Mpc distance scale (Seitenzahl et al. 2015).

2.3

To Be Rapidly Rotating or Not (That Is the Question!)

The gravitational waveforms of CCSNe are predominantly affected by the strength of the initial rotation rate in the precollapse iron core. Figure 2 summarizes initial angular velocity profiles from recent stellar evolutionary calculations. Very roughly speaking, “rapid rotation” corresponds to the initial angular velocity of  & 2  3 rad/s in the center, which is considered to be required to blow up massive stars by the MHD mechanism (e.g., Burrows et al. 2007; Mösta et al. 2014; Nishimura et al. 2015; Winteler et al. 2012). In Fig. 2, the black-dotted line, .0 ; A/ D . ; 1000/,

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Fig. 2 Initial angular velocity () profiles as a function of stellar radii (R) from several representative progenitor models. Discontinuities in the radial profiles correspond to the composition interfaces (such as from the iron to the silicon layer for the first discontinuity, for example, at 1000 km for model E20A (red line)). Models E15A and E20A are from the rotating progenitors by Heger and Langer (2000), which is thought to be the high end of  among all the progenitor models published thus far. Model 35OB is a gamma-ray burst (GRB) progenitor, which is evolved both with rotation and magnetic fields (Woosley and Bloom 2006). Model m15b5 is a rotating progenitor with magnetic fields by Heger et al. (2005), whose initial rotation rate is estimated to be roughly compatible with that of NSs at birth (e.g., Ott et al. 2006). Twodigit numbers in each model name denote the initial progenitor mass (15 Mˇ star is used for model E15A, e.g.)

is an analytical fit to model E20A as .R/ D 0 Œ1 C . R /2 1 where A is a A parameter representing the degree of differential rotation. For convenience, this angular velocity profile is referred to as “R3” (because of 0  3 rad/s in the center) in the following. Here it should be noted that  is estimated to be smaller than 0:1 rad/s to explain the observed rotation periods of canonical radio pulsars (Ott et al. 2006). Therefore model m15b5 in Fig. 2 is likely one of the canonical CCSN progenitors with NS formations. Rapid rotation (albeit still highly uncertain how rare it is; e.g., recent discussions in Fuller et al. (2015)), rapidly rotating core-collapse, and the associated GW signals are still attracting attention mainly because they are thought to connect tightly not only with hyperenergetic explosions (e.g.,  Chap. 73, “Nucleosynthesis in Hypernovae Associated with Gamma Ray Bursts”) but also with strong GW emission (e.g., nonaxisymmetic instabilities). Small initial rotation rates ( . 0:1 rad/s) have little impact on either the dynamics or the GW emission, so that these progenitors can be regarded as nonrotating, at least in the pre-explosion phase (1 s after bounce). In Sects. 3 and 4, we focus on the GW signatures from rapidly rotating and nonrotating core-collapse cores, respectively.

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3

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GWs from Rapidly Rotating Core-Collapse and Bounce

The left panels of Fig. 3 show the time evolution of the central density (top panel) and the gravitational waveform for a rapidly rotating model (model R3; see text above and Fig. 2). For comparison, we plot in the right panels the same quantities but for the nonrotating model (model R0). These models are computed by what are at present state-of-the-art numerical schemes (e.g., Janka et al. 2016; Kotake et al. 2012a), namely based on three-dimensional (3D) full general-relativistic (GR) simulations where the Einstein equations are evolved without approximations and with appropriate choices of temporal and spatial gauge (Baumgarte and Shapiro 1999; Shibata and Nakamura 1995). For models R0 and R3 presented below, an approximate neutrino transport scheme is also included (Kuroda et al. 2012, 2014). To maximize the GW amplitude at bounce, an observer is assumed to be located along the equatorial direction in this subsection ( D =2 in Eq. (16)). When the central density exceeds nuclear saturation density (the horizontal line in Fig. 3, nuc  2:8  1014 g cm3 ), the collapsing core bounces due to the stiffening of the nuclear EOS. At this “core bounce”, the central density overshoots

Fig. 3 Left panels show typical type I waveform (bottom panel) for a rapidly rotating corecollapse model (model R3, see text) with the time evolution of the central density (top panel). Note that AC is defined as AC  hC  D with D representing the distance to the source (e.g., Eq. (13) for an equatorial observer (e.g.,  D =2)). The right panels are same as the left panels but for the nonrotating model (model R0). Note that the postbounce time (tpb ) is measured after the epoch of the density maximum (see text). These models are from Kuroda et al. (2014)

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Fig. 4 Snapshots of entropy distributions showing nonspherical mass motions near core bounce. In each panel, the postbounce time (in unit of ms) and the central density (c ) in units of 1  1014 g cm3 are represented as .A; B/, respectively. The high-entropy postshock region is colored orange and red, which is sandwiched by the low-entropy region (colored blue) of the supersonically infalling core (exterior to the shock) and of the unshocked inner core (bluish region in the center). Normalized velocity vectors are superimposed. Note that entropy is in units of kB1 per nucleon with kB being the Boltzmann constant. This model is from Kuroda et al. (2014)

nuc , then reaches its maximum (top left panel). Almost at the same time, one can see a pronounced peak in the waveform (bottom left panel). After the largest spike, weaker spikes with decreasing amplitudes appear in the waveform due to the damping oscillation of the core. Figure 4 shows the evolution of the shock and the nonspherical mass motions in the postshock region near core bounce. First the rotating bounce occurs near the

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pole (e.g., the outgoing velocity fields along X D 0 in panel (a) in Fig. 4). The shape of the shock is oblately deformed at this time because the material in the equatorial plane is supported by the centrifugal forces. Followed by the secondary bounce in the vicinity of the equatorial plane, the shape of the shock changes from oblate (panel (a)) to prolate (panel (b)) and then back to oblate (panel (c)). In this way, the inner core is hit by multiple downflows predominantly caused by the (damping) oblate-prolate deformation cycle in the postshock region. The typical duration of this ring-down phase is about tpb  20 ms (Dimmelmeier et al. 2007; Ott et al. 2007) as shown in the bottom left panel of Fig. 3 (see also panel (d) in Fig. 4). The waveform (bottom left panel of Fig. 3) is categorized as “type I”, which is the most generic waveform of rotating core-collapse and bounce. The type II waveform is characterized by multiple pronounced peaks, which appears in extreme models with very rapid rotation ( & 2 rad/s) or very strong differential rotation (A . 500 km) (Dimmelmeier et al. 2007; Takiwaki and Kotake 2011). When a nuclear EOS is very soft, the type III waveform is obtained, which is characterized by fast collapse, weak bounce, and small-amplitude GW emission. But recent observations of 2Mˇ NSs (Demorest et al. (2010); see Lattimer and Prakash (2016) for a review) have ruled out such soft EOSs. Therefore the generic type of the bounce GW signals is now known to take the type I waveform. Without (rapid) rotation in the precollapse core, no distinct GW peaks are seen (e.g., bottom right panel of Fig. 3), whereas one can see small deviations (.10 cm) of the GW amplitude from zero at tpb & 10 ms. Shortly after the bounce shock is formed, the negative entropy gradient behind the stalling shock gives rise to prompt convection. Nonspherical motions due to the prompt convection generate the GW emission, which generally lasts tpb . 50 ms, a part of which is shown in the bottom right panel. The central density at and after bounce for the nonrotating model is higher than that for the rapidly rotating model (compare the top right with the top left panel in Fig. 3). This is because the centrifugal force acts as an additional pressure support (Mönchmeyer et al. 1991). Very rapid rotation ( & 2 rad/s) was shown to result in very delayed core bounce at subnuclear density exclusively affected by the strong centrifugal forces (Ott 2009), possibly leading to the (rare) type II waveform mentioned above. The top panel of Fig. 5 compares the GW spectrum for model R3 with R0, relative to the sensitivity curves of representative detectors. As one would expect, the bounce signal of model R0 is too small to be detected even for a Galactic event. The characteristic GW strain (hc in Eq. (21)) of model R3 peaks around 1 kHz with the maximum amplitude of 2  1021 , which is above the detector’s sensitivity. For a given model, the peak amplitude (hc ) and the characteristic GW frequency (fc , Eq. (20)) are uniquely determined from the GW spectrum analysis. The bottom panel of Fig. 5 shows a collective set of hc  fc for multiple (&100) models, in which a wide variety of the state-of-the-art stellar evolution models is used by covering a huge parameter space spanned by initial rotation rate, degree of differential rotation, and different EOSs (Dimmelmeier et al. 2007). They demonstrated that the bounce dynamics in the rotating core and the GW signal depend primarily on the central angular velocity prior to collapse (e.g.,  in Fig. 2).

K. Kotake and T. Kuroda 10−20

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aVIRGO

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s11, Shen Eos s11, LS EoS s15, Shen EoS s15, LS EoS s20, Shen EoS s20, LS EoS s40, Shen EoS s40, LS EoS e15/e20, Shen EoS e15/e20, LS EoS

100

1

ƒc [Hz]

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Fig. 5 Top panel shows spectral energy distribution of the GW signal for model R3 (red line) and R0 (thick black line) at a distance of 10 kpc with sensitivity curves of LIGO, advanced VIRGO (aVIRGO), and KAGRA, respectively (Kuroda et al. 2014). The bottom panel shows the location of the peak GW amplitude (hc at 10 kpc) with the GW frequency (fc ) of  hundred models investigated in Dimmelmeier et al. (2007). Note that each dot represents a particular model and the sensitivity of initial LIGO is found in the bottom panel. The three groups of signals are discussed in the text. The bottom panel is by courtesy of Dimmelmeier and coauthors

In fact, by looking at the bottom panel of Fig. 5 one can see that these models are basically categorized into three groups in the hc  fc plane (Ott 2009). Slowly 1  . 2 rad s1 ) have small hc and moderately high rotating models (group , fc due to the weak centrifugal forces. As the impact of the centrifugal forces on the bounce dynamics becomes significant with increasing , hc becomes higher (the models move upward and slightly right in the plane). Moderately rapid models 2 2 rad s1 .  . 6  13 rad s1 ) reach high hc and cluster in fc between (group ,

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600 and 800 Hz. The most rapidly rotating models of that group shift slightly to the left in fc . For models with large initial angular momentum, the central density (c ) after bounce can be maximally lowered by one order of magnitude compared to the nuclear density. This makes the dynamical timescale tdyn  .Gc /1=2 longer and the typical frequency (fc / 1=tdyn ) lower. Finally very rapidly rotating models 3  & 6  13 rad s1 ) cluster at low fc and lower hc . (group , As one can see from the top panel of Fig. 5, the sensitivity curves in the highfrequency domain (&400–1000 Hz) are limited by quantum noises (see a positive slope there). On the other hand, the highest detector sensitivity is roughly in the range of 50300 Hz. As mentioned, a signal-to-noise ratio of 8 at least is required to claim GW detection (Eq. (22); see also Hayama et al. (2015)), (roughly) meaning that the GW amplitude should be bigger by one order of magnitude compared to the sensitivity curves. From the two panels of Fig. 5, one can expect that GWs from 2 and ) 3 in our Galaxy are a (moderately) rapidly rotating progenitors (groups main target of current LIGO-class detectors.

3.1

Nonaxisymmetric Instabilities

As Chandrasekhar wrote in his textbook, (Chandrasekhar 1969), rapidly rotating compact stars can be subject to nonaxisymmetric rotational instabilities when the ratio of rotational to gravitational potential energy (T =jW j D ˇ) exceeds a certain critical value. Because the growing instabilities deform the object’s spheroidal into a triaxial configuration with a time-dependent quadrupole(or higher) moment, strong GW emission can be anticipated (see Fryer and New (2011) for a review). The best-understood type of instability is the classical dynamical bar-mode instability with a threshold of ˇbar & 0:27. However, after a decade of extensive research on this issue (e.g., Rampp et al. 1998), recent work (e.g., right panel of Fig. 5) presented strong evidence that the postbounce core, even in extreme models, does not reach values of ˇ close to ˇbar during collapse, bounce, and early postbounce phase. Regarding the various types of instabilities that would accompany strong GW emission in the PNS cooling phase (lasting on a timescale of  minutes; see e.g.,  Chap. 60, “Neutrino Signatures from Young Neutron Stars”) and afterwards, the reader is referred to Kokkotas and Schmidt (1999). In contrast to the high T =jW j instabilities, recent work suggests that a differentially rotating PNS can become dynamically unstable at much lower T =jW j as low as .0:1 (Kuroda et al. 2014; Ott et al. 2005; Scheidegger et al. 2010). The origin of the “low-T =jW j instability” is not completely understood yet. However, the standard picture (e.g., Watts et al. 2005) was given, in that the instabilities are associated with the existence of corotation points (where the pattern speed of the unstable modes matches the local angular velocity) inside the core and are thus likely to be a subclass of shear instabilities. Figure 6 shows several hydrodynamics and GW features for a representative 3D MHD model that experiences the low-T =W instability in the postbounce phase (Scheidegger et al. 2010). The top left panel shows the vorticity distribution in the

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1.5

A

+|

A

A+,x,pol [cm]

y [1e7 cm]

100

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X|

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|h(ν)|ν1/2/Hz-1/2

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0.1 t-tb [s]

0.15

observer position : (θ=φ=0)-axis LIGO AdvLIGO

10-21 10-22 10-23 10-24 101

102 ν [Hz]

103

Fig. 6 Top left panel depicts the vorticity distribution in the equatorial plane of a representative 3D MHD model (R4E1FCL ) in Scheidegger et al. (2010) (at 10 ms after bounce). A two-armed m D 2 pattern behind the stalled shock is clearly seen (the side length of the plot is (300 km)2 ). The top right panel displays the quadrupole GW amplitude of the AC and A (see text for the definition) along the pole (of a model (R3E1FCL ) showing a similar hydrodynamics evolution to the left panel). The bottom panel shows the spectral energy distributions of the GW signal for their representative 3D model experiencing the low-T =jW j instability (model R4STCA) at a distance of 10 kpc. The observer is assumed to be along the polar axis. These plots are by courtesy of Scheidegger and coauthors

equatorial plane. A two-armed (m D 2 with m denoting the azimuthal quantum number) pattern is clearly seen (at 10 ms after bounce for the plot) and then the spiral flows develop for more than several hundred milliseconds later. The right panel displays the gravitational waveform of the AC and A . Note that AC; is defined as AC;  hC;  D with D representing the distance to the source (e.g., Scheidegger et al. (2010) for more detail). To maximize the amplitude, the observer is assumed to be located along the spin axis of the star. An important message from the top panel is that the gravitational waveform from the nonaxisymmetric dynamics generally shows narrowband and highly quasi-periodic signals that persist until the end of simulations. For the periodic signals, the effectively measured GW amplitude

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p scales with the number of GW cycles N as heff / h N . This is the reason why the peak amplitude in the GW spectrum (the bottom panel in Fig. 6) exceeds 1020 for the galactic source, making the chance of detection quite higher. In fact, the wave amplitude from the short-duration bursts near bounce is generally smaller than 1020 for the galactic source (e.g., the amplitude near 1 kHz in the bottom panel in Fig. 6). For detecting (potentially) the most powerful GW signals, it is therefore of crucial importance to understand the properties of the nonaxisymmetric instabilities. However, the numerical difficulty in following a long-term postbounce evolution in 3D is the main hindrance at present. Although angular momentum is continuously brought into the iron core from the stellar envelope that rotates with higher angular momentum, the shear energy in the vicinity of the corotation points will continue to be redistributed or even dissipated by some mechanisms including the magnetorotational instability (MRI, e.g., Akiyama et al. 2003; Masada et al. 2012). In the 3D model presented in Fig. 6, neutrino heating was not taken into account. Neutrinodriven convection would affect the growth of the nonaxisymmetric instabilities. GR, which has been mostly treated in 3D models (Hanke et al. 2013; Lentz et al. 2015) by a post-Newtonian manner, should affect the growth rate. For a more quantitative discussion, full 3D GR-MHD simulations with an appropriate neutrino transport are needed, towards which supernova modelers are making their best efforts (Janka et al. 2016 for a review).

4

GWs from Nonrotating Progenitors

With decreasing the precollapse angular velocity, the pronounced “type I” waveform of Sect. 3 also becomes weak (compare the bottom left to the bottom right panel in Fig. 3). For slowly rotating progenitors ( . 0:1 rad/s, Fig. 2), the bounce signal is well below the sensitivity of the LIGO-class detectors even for a Galactic event. The first sizable GW signal after bounce comes from prompt convection as we briefly mentioned in panel (d) of Fig. 4. The growth of “convection” is naturally governed by the nonlinear hydrodynamics. As we describe in this section, the gravitational waveforms in the postbounce phase are all affected by turbulent mass motions that are originated from various types of fluid instabilities. Therefore the waveforms in the postbounce phase are of stochastic nature (Kotake et al. 2009) and impossible to predict a priori. The most established method to detect the GW signal is a matched filtering (see Sathyaprakash and Schutz 2009 for review) as is done when one looks for compact binary coalescence signals (e.g., Rasio and Shapiro 1999), leading to the first detection of the GW150914 event (Abbott et al. 2016b). However, such a template-based search is not suitable for the GW signals from CCSNe due to the stochastic nature. This makes the detection even harder, however, there is some hope. A characteristic GW frequency (Müller et al. 2013, 2004; Murphy et al. 2009) is expected to provide an important probe to multi-D hydrodynamics episodes in the postbounce core. From the next section, we move on to focus on the postbounce GW signatures.

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Characteristic GW Frequency in the Postbounce Phase

f [Hz]

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Log (dE*Gw/df) [M§ c2 Hz−1]

The left panel of Fig. 7 shows a sample of gravitational waveforms obtained in 2D models by Murphy et al. (2009). Shortly after the bounce shock is formed, a negative entropy gradient behind the stalling shock predominantly gives rise to prompt convection. GWs indicated by “prompt convection” come from this. Later, the PNS convection driven by the negative lepton gradient near its surface and the neutrinodriven convection in the postshock heating region develop. This corresponds to the GW emission by ”postshock convection” after the prompt convection till 550 ms after bounce. Subsequently, the GW amplitudes become much larger as the SASI enters a nonlinear phase with violent sloshing of the postshock material. Large spikes appearing in the “Nonlinear SASI” phase come from the downflowing “SASI plumes” striking the PNS surface. Afterward when the sloshing shock develops into an explosion (indicated by “Explosion”), the sign of the GW amplitudes changes, reflecting the geometry of the expanding shock, that is either prolate (increase), oblate (decrease), or spherical (in-between; see Murphy et al. 2009 for more detail). Interestingly the fp curve (black solid line) closely traces the three excesses in the GW spectrogram. The strong correlation implies that the characteristic GW frequency is considered as a result of the deceleration of convective plumes hitting the surface (Murphy et al. 2009) and by the g-mode oscillation excited by the downflows to the PNS (Marek et al. 2009; Müller et al. 2013). Following Müller et al. (2013), the characteristic g-mode frequency in the vicinity of the PNS can be estimated as

0.2 0.4 0.6 0.8 1.0 Time after bounce [s]

Fig. 7 The top left panel shows a gravitational waveform (hC  D with D representing the distance to the source, for example, Eq. (16)) obtained in a 2D hydrodynamics model for a 15 Mˇ star (Murphy et al. 2009). Three typical GW emission sites are indicated, which are prompt convection, nonlinear SASI with SASI plumes(then till 800 ms after bounce), and explosion (then afterwards). For the calculation presented here, an input neutrino luminosity of L e D 3:7  1052 erg/s was assumed to trigger neutrino-driven explosions. The right panel shows a GW spectrogram dEGW =df (Eq. (18)) as a function of the postbounce time. The characteristic GW frequency “fp ” is superimposed. Comparing with the left panel, there are three features showing an excess in the spectrogram (green, orange, red regions), which correspond to prompt convection, nonlinear SASI/convective motions, followed by the explosion phase, respectively. These plots are by courtesy of Murphy and coauthors

63 Gravitational Waves from Core-Collapse Supernovae

1 GMpns fp D 2 2 Rpns

s

.  1/mn kB Tpns

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  GMpns 1 ; Rpns c 2

(28)

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250 200 150

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−50 0

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GW amplitude (matter) A20 [cm]

350 300

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where Mpns , Rpns , and Tpns are the PNS mass, radius,and (typical) temperature, respectively;  is the adiabatic index in the PNS surface region; mn is the GM / is the GR correction. Mass accretion to the PNS neutron mass; and .1  Rpnspns c2 predominantly makes Mpns bigger, Rpns smaller, and Tpns higher, whereas other important ingredients (neutrino cooling, GR) should make a nontrivial contribution to the above trend. The former two are primarily responsible for the increasing trend of fp in the spectrogram. (See also Marek et al. 2009; Müller et al. 2012; Yakunin et al. 2015.) The top left panel of Fig. 8 shows a gravitational waveform obtained in 2D GR core-collapse simulations of a 15Mˇ star where currently one of the best available

1000

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Fig. 8 Top left panel shows gravitational waveform obtained by state-of-the-art 2D simulations for a 15 Mˇ star (model G15 in Müller et al. (2013)). Solid and dashed lines represent matter and neutrino GW signals (e.g., Eqs. (16) and (25)), respectively. Note that the scale for the matter GW (left vertical axis) is different from that for the neutrino GW signal (right vertical axis). The top right panel is the GW spectrogram overlaid by the fp formula (solid black line, Eq. (28)). On top of the monotonically increasing fp curve, the high-frequency components are superimposed (vertical stripes extending up to &1 kHz) that come from the strong downdrafts stochastically hitting the PNS surface region. The bottom panel shows the entropy along the north and south polar axis as a postbounce bounce time. The shock revival was obtained for model G15 around 500 ms postbounce, followed by the runaway expansion trending towards explosion more strongly towards the north pole. These plots are by courtesy of Müller and coauthors

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neutrino transport schemes is employed (Müller et al. 2013). As mentioned in Sect. 2.2.1 (Eq. (25)), the GW amplitude from anisotropic neutrino emission (dashed line, denoted “neutrino GW” in the caption) becomes higher than that of matter quadrupole GW (solid line). The prompt convection GW signal is seen tpb . 50 ms, which is followed by a quiescent phase until tpb  150 ms. As neutrino-driven convection and the SASI vigorously develop with time the matter GW amplitude and the characteristic GW frequency fp become higher with time (solid line in the top right panel). These basic GW features have been observed not only in other self-consistent 2D models (Marek et al. 2009; Yakunin et al. 2015), but also in 3D simulations with idealized neutrino transport schemes (Müller et al. 2012). It should be noted that one needs 3D-GR models with an appropriate neutrino transport scheme (e.g., Kuroda et al. 2016) to unambiguously determine the postbounce GW features. The final goal is to develop a full 3D GR-MHD code with Boltzmann neutrino transport (e.g., Janka et al. (2016) and Kotake et al. (2012a)) including state-of-the-art EOS (e.g., Hempel and Schaffner-Bielich 2010) and matter-neutrino interactions (e.g., Langanke and Martínez-Pinedo 2003; e.g.,  Chap. 70, “Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis”). Unfortunately none of the currently published CCSN models satisfies the “ultimate” requirement. In this sense, all the multi-D models employ some approximations (with different levels of sophistication) for multiple physical ingredients. In the same way, theoretical predictions of the GWs that one can obtain by analyzing the currently available numerical results, cannot unambiguously give us the final answer yet. Again we note that this chapter shows only a snapshot of the moving theoretical terrain towards the final goal.

5

Conclusions

The aim of writing this chapter was to summarize the baseline physics for understanding the GW signatures in stellar core-collapse and CCSN evolution. In Sect. 1, we gave a quick introduction to overview how we could detect scientifically significant GW signals from CCSNe in the future. In Sect. 2, we presented a concise summary of the formulae to extract gravitational waveforms from CCSN models (Sects. 2.1 and 2.2). By using them, we did a back-of-the-envelope estimate for understanding the fundamental features of the GWs and for discussing (first-order) detectability by the LIGO-class detectors. Section 2.3 emphasized that the precollapse rotation rate in the iron core predominantly determines the GW signatures of CCSNe. In Sect. 3, we focused on the best-studied GW signal that is emitted from rapidly rotating core-collapse and bounce. Using results from the most recent 3D GR models, we explained in detail the properties of the most generic “type I” waveform. After that, we touched on the GW signatures from nonaxisymmetric instabilities not only because they can be potentially the strongest GW emission process, but also because future detection of circular polarization in the GW signal would provide strong evidence of rapid rotation in the precollapse cores (Hayama et al. 2016).

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In Sect. 4, we switched gears to focus on GWs from nonrotating progenitors. In contrast to the GW at bounce, multiple GW emission processes have been proposed and studied extensively in the last decade. Among them, we mainly focused on the GW signatures from prompt convection, neutrino-driven convection, and the SASI in the postshock region. These postbounce GWs are generated by turbulent matter motions governed by nonlinear hydrodynamics; thus they are of stochastic nature. For these stochastic GWs, a (template-based) matched filtering method cannot be applied, which makes the detection even harder. Be that as it may, we discussed that the characteristic GW frequency (e.g., Eq. (28)) can be an important probe to decipher the hydrodynamics episodes and the PNS evolution in the postbounce phase. To have the final words on these postbounce GW signatures, we need, at least, 3D GR-MHD models where appropriate neutrino transport schemes are taken into account (e.g., Kotake et al. (2012a) and Janka et al. (2016) for a status report). As repeatedly mentioned elsewhere in this chapter, our understanding of the GW emission processes in CCSNe has been progressing in accordance with the sophistication of numerical simulations into which SN modelers have been putting a huge effort for a long time. What we have attempted to provide here is only a snapshot of the moving documentary film that records our endeavors for living out our dream of “GW astronomy of CCSNe.” Now that the first successful GW detection revealed the importance of a BH binary as a GW source (Abbott et al. 2016b), the documentary film is becoming even longer. This is because we have to clarify the dynamics of CCSNe with a BH formation, which is nevertheless still very uncertain at this stage. After the first GW detection, multimessenger astronomy is now becoming a reality where a synergic analysis using GWs, neutrinos, and electromagnetic messengers should be indispensable for deciphering the central engines of massive stars (e.g., Leonor et al. 2010; Nakamura et al. 2016). Needless to say, it is of crucial importance to determine nucleosynthesis accurately (see also  Chap. 71, “Making the Heaviest Elements in a Rare Class of Supernovae”) in the SN ejecta for modeling supernova light curves (e.g., Thielemann et al. (2011), e.g.,  Chap. 68, “The Multidimensional Character of Nucleosynthesis in Core-Collapse Supernovae”). Detailed spectroscopic observations will reveal the explosion geometry (Grefenstette et al. 2014), which should constrain the asphericity of the central engines. Here we stop penning this chapter hoping that in the near future great progress will be brought by you who are reading this, in a number of unsettled and exciting riddles raised in this chapter,

6

Cross-References

 Detecting Gravitational Waves from Supernovae with Advanced LIGO  Making the Heaviest Elements in a Rare Class of Supernovae  Neutrino Emission from Supernovae  Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis  Neutrino Signatures from Young Neutron Stars

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 Nucleosynthesis in Hypernovae Associated with Gamma Ray Bursts  The Multidimensional Character of Nucleosynthesis in Core-Collapse Super-

novae Acknowledgements We are thankful to stimulating discussions with K. Hayama, T. Takiwaki, K. Nakamura, S. Horiuchi, Y. Suwa, and M. Tanaka. KK acknowledges discussions with E. Müller and H.T. Janka and their kind hospitality during his stay at the Max-Planck-Institut für Astrophysik in March 2016. TK thanks F.-K. Thielemann for enlightening discussions and continuous support. This study was supported in part by the Grants-in-Aid for the Scientific Research from the Ministry of Education, Science and Culture of Japan (Nos. 24103006, 24244036, 26707013, and 26870823), HPCI Strategic Program of Japanese MEXT, and by the European Research Council (ERC;FP7) under ERC Advanced Grant Agreement Nı 321263 - FISH.

References Abbott BP, Abbott R, Abbott TD, Abernathy MR, Acernese F, Ackley K, Adams C, Adams T, Addesso P, Adhikari RX et al (2016a) All-sky search for long-duration gravitational wave transients with initial LIGO. Phys Rev D 93:042005 Abbott BP, Abbott R, Abbott TD, Abernathy MR, Acernese F, Ackley K, Adams C, Adams T, Addesso P, Adhikari RX et al (2016b) Observation of gravitational waves from a binary black hole merger. Phys Rev Lett 116:061102 Akiyama S, Wheeler JC, Meier DL, Lichtenstadt I (2003) The magnetorotational instability in core-collapse supernova explosions. Astrophys J 584:954–970 Andersson N (2003) TOPICAL REVIEW: gravitational waves from instabilities in relativistic stars. Class Quantum Gravity 20:105 Aso Y, Michimura Y, Somiya K, Ando M, Miyakawa O, Sekiguchi T, Tatsumi D, Yamamoto H (2013) Interferometer design of the KAGRA gravitational wave detector. Phys Rev D 88:043007 Balbus SA, Hawley JF (1998) Instability, turbulence, and enhanced transport in accretion disks. Rev Modern Phys 70:1–53 Baumgarte TW, Shapiro SL (1999) Numerical integration of Einstein’s field equations. Phys Rev D 59:024007 Bethe HA (1990) Supernova mechanisms. Rev Mod Phys 62:801–866 Burrows A (2013) Colloquium: perspectives on core-collapse supernova theory. Rev Mod Phys 85:245 Burrows A, Dessart L, Livne E, Ott CD, Murphy J (2007) Simulations of magnetically driven supernova and hypernova explosions in the context of rapid rotation. Astrophys J 664:416–434 Burrows A, Hayes J (1996) Pulsar recoil and gravitational radiation due to asymmetrical stellar collapse and explosion. Phys Rev Lett 76:352–355 Chandrasekhar S (1969) Ellipsoidal figures of equilibrium. In: Chandrasekhar S (ed) The Silliman foundation lectures. Yale University Press, New Haven Demorest PB, Pennucci T, Ransom SM, Roberts MSE, Hessels JWT (2010) A two-solar-mass neutron star measured using Shapiro delay. 467:1081 Dimmelmeier H, Ott CD, Janka H-T, Marek A, Müller E (2007) Generic gravitational-wave signals from the collapse of rotating stellar cores. Phys Rev Lett 98:251101 Epstein R (1978) The generation of gravitational radiation by escaping supernova neutrinos. ApJ 223:1037–1045 Flanagan ÉÉ, Hughes SA (1998) Measuring gravitational waves from binary black hole coalescences. I. Signal to noise for inspiral, merger, and ringdown. Phys Rev D 57:4535 Foglizzo T, Kazeroni R, Guilet J, Masset F, González M, Krueger BK, Novak J, Oertel M, Margueron J, Faure J, Martin N, Blottiau P, Peres B, Durand G (2015) The explosion mechanism of core-collapse supernovae: progress in supernova theory and experiments. PASA 32:e009

63 Gravitational Waves from Core-Collapse Supernovae

1695

Fryer CL, New KCB (2011) Gravitational waves from gravitational collapse. Living Rev Relativ 14:1 Fuller J, Cantiello M, Lecoanet D Quataert E (2015) The spin rate of pre-collapse stellar cores: wave-driven angular momentum transport in massive stars. ApJ 810:101 Gehrels N, Leventhal M, MacCallum CJ (1987) Prospects for gamma-ray line observations of individual supernovae. ApJ 322:215–233 Grefenstette BW, Harrison FA, Boggs SE, Reynolds SP, Fryer CL, Madsen KK, Wik DR, Zoglauer A, Ellinger CI, Alexander DM, An H, Barret D, Christensen FE, Craig WW, Forster K, Giommi P, Hailey CJ, Hornstrup A, Kaspi VM, Kitaguchi T, Koglin JE, Mao PH, Miyasaka H, Mori K, Perri M, Pivovaroff MJ, Puccetti S, Rana V, Stern D, Westergaard NJ, Zhang WW (2014) Asymmetries in core-collapse supernovae from maps of radioactive 44 Ti in Cassiopeia A. Nature 506:339–342 Hanke F, Müller B, Wongwathanarat A, Marek A, Janka H-T (2013) SASI activity in threedimensional neutrino-hydrodynamics simulations of supernova cores. ApJ 770:66 Hayama K, Kuroda T, Kotake K, Takiwaki T (2015) Coherent network analysis of gravitational waves from three-dimensional core-collapse supernova models. Phys Rev D 92:122001 Hayama K, Kuroda T, Nakamura K, Yamada S (2016) Circular polarizations of gravitational waves from core-collapse supernovae: a clear indication of rapid rotation. Phys Rev Lett 116:151102 Heger A, Langer N (2000) Presupernova evolution of rotating massive stars. II. Evolution of the surface properties. ApJ 544:1016–1035 Heger A, Woosley SE, Spruit HC (2005) Presupernova evolution of differentially rotating massive stars including magnetic fields. ApJ 626:350–363 Hempel M, Schaffner-Bielich J (2010) A statistical model for a complete supernova equation of state. Nucl Phys A 837:210 Hild S, Freise A, Mantovani M, Chelkowski S, Degallaix J, Schilling R (2009) Using the etalon effect for in situ balancing of the Advanced Virgo arm cavities. Class Quantum Gravity 26:025005 Horiuchi S, Beacom JF, Bothwell MS, Thompson TA (2013) Effects of stellar rotation on star formation rates and comparison to core-collapse supernova rates. ApJ 769:113 Iben I Jr (2013) Stellar evolution physics. Volume 2: Advanced evolution of single stars. Cambridge University Press, Cambridge Janka H-T, Melson T, Summa A (2016) Physics of core-collapse supernovae in three dimensions: a sneak preview. Annu Rev Nucl Part Sci 66(1):341–375 Kawamura S et al (2006) The Japanese space gravitational wave antenna DECIGO. Class Quantum Gravity 23:125 Kokkotas K, Schmidt B (1999) Quasi-normal modes of stars and black holes. Living Rev Relativ 2(1):1–72 Kotake K (2013) Multiple physical elements to determine the gravitational-wave signatures of core-collapse supernovae. Compte Rendus Phys 14:318–351 Kotake K, Iwakami W, Ohnishi N, Yamada S (2009) Stochastic nature of gravitational waves from supernova explosions with standing accretion shock instability. ApJL 697:L133–L136 Kotake K, Ohnishi N, Yamada S (2007) Gravitational radiation from standing accretion shock instability in core-collapse supernovae. ApJ 655:406–415 Kotake K, Sato K, Takahashi K (2006) Explosion mechanism, neutrino burst and gravitational wave in core-collapse supernovae. Rep Prog Phys 69:971–1143 Kotake K, Sumiyoshi K, Yamada S, Takiwaki T, Kuroda T, Suwa Y, Nagakura H (2012a) Core-collapse supernovae as supercomputing science: A status report toward six-dimensional simulations with exact Boltzmann neutrino transport in full general relativity. Prog Theor Exp Phys 2012:01A301 Kotake K, Takiwaki T, Suwa Y, Iwakami Nakano W, Kawagoe S, Masada Y, Fujimoto S-i (2012b) Multimessengers from core-collapse supernovae: multidimensionality as a key to bridge theory and observation. Adv Astron 2012:1–46 Kotake K, Yamada S, Sato K (2003) Inferring core-collapse supernova physics with gravitational waves. Phys Rev D 68:044023

1696

K. Kotake and T. Kuroda

Kuroda T, Kotake K, Takiwaki T (2012) Fully general relativistic simulations of core-collapse supernovae with an approximate neutrino transport. ApJ 755:11 Kuroda T, Takiwaki T, Kotake K (2014) Gravitational wave signatures from low-mode spiral instabilities in rapidly rotating supernova cores. Phys Rev D 89:044011 Kuroda T, Takiwaki T, Kotake K (2016) A new multi-energy neutrino radiation-hydrodynamics code in full general relativity and its application to the gravitational collapse of massive stars. ApJS 222:20 Langanke K, Martínez-Pinedo G (2003) Nuclear weak-interaction processes in stars. Rev Mod Phys 75:819–862 Lattimer JM, Prakash M (2016) The equation of state of hot, dense matter and neutron stars. Phys Rep 621:127–164 LeBlanc JM, Wilson JR (1970) A numerical example of the collapse of a rotating magnetized star. ApJ 161:541 Lentz EJ, Bruenn SW, Hix WR, Mezzacappa A, Messer OEB, Endeve E, Blondin JM, Harris JA, Marronetti P, Yakunin KN (2015) Three-dimensional core-collapse supernova simulated Using a 15 Mˇ progenitor. ApJL 807:L31 Leonor I, Cadonati L, Coccia E, D’Antonio S, Di Credico A, Fafone V, Frey R, Fulgione W, Katsavounidis E, Ott CD, Pagliaroli G, Scholberg K, Thrane E, Vissani F (2010) Class Quantum Gravity. Searching for prompt signatures of nearby core-collapse supernovae by a joint analysis of neutrino and gravitational wave data. 27:084019 Maeda K, Kawabata K, Mazzali PA, Tanaka M, Valenti S, Nomoto K, Hattori T, Deng J, Pian E, Taubenberger S, Iye M, Matheson T, Filippenko AV, Aoki K, Kosugi G, Ohyama Y, Sasaki T, Takata T (2008) Asphericity in supernova explosions from late-time spectroscopy. Science 319:1220 Marek A, Janka H-T, Müller E (2009) Equation-of-state dependent features in shock-oscillation modulated neutrino and gravitational-wave signals from supernovae. A&A 496:475–494 Masada Y, Takiwaki T, Kotake K, Sano T (2012) Local simulations of the magnetorotational instability in core-collapse supernovae. ApJ 759:110 Mészáros P (2006) Gamma-ray bursts. Rep Prog Phys 69:2259–2322 Metzger BD, Giannios D, Thompson TA, Bucciantini N, Quataert E (2011) The protomagnetar model for gamma-ray bursts. MNRAS 413:2031–2056 Misner C, Thorne K, Wheeler J (1973) Gravitation. W.H. Freeman and Company, San Francisco Mönchmeyer R, Schaefer G, Mueller E, Kates RE (1991) Gravitational waves from the collapse of rotating stellar cores. Astron Astrophys 246:417–440 Mösta P, Richers S, Ott CD, Haas R, Piro AL, Boydstun K, Abdikamalov E, Reisswig C, Schnetter E (2014) Magnetorotational core-collapse supernovae in three dimensions. ApJL 785:L29 Müller B, Janka H-T, Marek A (2013) A new multi-dimensional general relativistic neutrino hydrodynamics code of core-collapse supernovae. III. Gravitational wave signals from supernova explosion models. ApJ 766:43 Müller E, Janka H-T (1997) Gravitational radiation from convective instabilities in Type II supernova explosions. Astron Astrophys 317:140–163 Müller E, Janka H-T, Wongwathanarat A (2012) Parametrized 3D models of neutrino-driven supernova explosions. Neutrino emission asymmetries and gravitational-wave signals. A&A 537:A63 Müller E, Rampp M, Buras R, Janka H-T, Shoemaker DH (2004) Toward gravitational wave signals from realistic core-collapse supernova models. ApJ 603:221–230 Murphy JW, Ott CD, Burrows A (2009) A model for gravitational wave emission from neutrinodriven core-collapse supernovae. ApJ 707:1173–1190 Nakamura K, Horiuchi S, Tanaka M, Hayama K, Takiwaki T, Kotake K (2016) Multi-messenger signals of long-term core-collapse supernova simulations : synergetic observation strategies. 461:3296 Nishimura N, Takiwaki T, Thielemann F-K (2015) ApJ 810:109 Obergaulinger M, Cerdá-Durán P, Müller E, Aloy MA (2009) Semi-global simulations of the magneto-rotational instability in core collapse supernovae. A&A 498:241–271

63 Gravitational Waves from Core-Collapse Supernovae

1697

Oohara K-i, Nakamura T, Shibata M (1997) A Way to 3D numerical relativity. Prog Theor Phys Suppl 128:183 Ott CD (2009) TOPICAL REVIEW: the gravitational-wave signature of core-collapse supernovae. Class Quantum Gravity 26:063001 Ott CD, Burrows A, Livne E, Walder R (2004) Gravitational waves from axisymmetric, rotating stellar core collapse. Astrophys J 600:834–864 Ott CD, Burrows A, Thompson TA, Livne E, Walder R (2006) The spin periods and rotational profiles of neutron stars at birth. Astrophys J Suppl Ser 164:130–155 Ott CD, Dimmelmeier H, Marek A, Janka H-T, Hawke I, Zink B, Schnetter E (2007) 3D collapse of rotating stellar iron cores in general relativity including deleptonization and a nuclear equation of state. Phys Rev Lett 98:261101 Ott CD, Ou S, Tohline JE, Burrows A (2005) One-armed spiral instability in a low-T/|W| postbounce supernova core. ApJL 625:L119–L122 Punturo M, Lück H, Beker M (2014) Third generation gravitational wave observatory: The Einstein Telescope. In: Bassan M (ed) Advanced interferometers and the search for gravitational waves. Astrophysics and space science library, vol 404. Springer, p 333 Rampp M, Mueller E, Ruffert M (1998) Simulations of non-axisymmetric rotational core collapse. Astron Astrophys 332:969–983 Rasio FA, Shapiro SL (1999) TOPICAL REVIEW: coalescing binary neutron stars. Class Quantum Gravity 16:1 Reisswig C, Ott CD, Sperhake U, Schnetter E (2011) Gravitational wave extraction in simulations of rotating stellar core collapse. Phys Rev D 83:064008 Sathyaprakash BS, Schutz BF (2009) Physics, astrophysics and cosmology with gravitational waves. Living Rev Relativ 12:2 Scheidegger S, Käppeli R, Whitehouse SC, Fischer T, Liebendörfer M (2010) The influence of model parameters on the prediction of gravitational wave signals from stellar core collapse. A&A 514:A51+ Seitenzahl IR, Herzog M, Ruiter AJ, Marquardt K, Ohlmann ST, Röpke FK (2015) Neutrino and gravitational wave signal of a delayed-detonation model of type Ia supernovae. Phys Rev D 92:124013 Shapiro SL, Teukolsky SA (1983) Black holes, white dwarfs, and neutron stars: the physics of compact objects (Research supported by the National Science Foundation. Wiley-Interscience, New York, 1983, 663p.) Shibata M, Liu YT, Shapiro SL, Stephens BC (2006) Magnetorotational collapse of massive stellar cores to neutron stars: simulations in full general relativity. Phys Rev D 74:104026 Shibata M, Nakamura T (1995) Evolution of three-dimensional gravitational waves: Harmonic slicing case. Phys Rev D 52:5428–5444 Smartt SJ (2015) Observational constraints on the progenitors of core-collapse supernovae: the case for missing high-mass stars. PASA 32:e016 Takiwaki T, Kotake K (2011) Gravitational wave signatures of magnetohydrodynamically driven core-collapse supernova explosions. ApJ 743:30 Tanaka M, Tominaga N, Nomoto K, Valenti S, Sahu DK, Minezaki T, Yoshii Y, Yoshida M, Anupama GC, Benetti S, Chincarini G, Della Valle M, Mazzali PA, Pian E (2009) Type Ib supernova 2008D associated with the luminous x-ray transient 080109: an energetic explosion of a massive helium star. ApJ 692:1131–1142 Thielemann F, Käppeli R, Winteler C, Perego A, Liebendörfer M, Nishimura N, Vasset N, Arcones A (2012) Nuclei Cosmos (NIC XII) 61:1–9 Thielemann F-K, Hirschi R, Liebendörfer M, Diehl R (2011) Massive stars and their supernovae. In: Diehl R, Hartmann DH, Prantzos N (eds) Lecture notes in physics, vol 812. Springer, Berlin, pp 153–232 Thorne K (1987) Gravitational radiation. In: Hawking S, Israel W (eds) Three hundred years of gravitation. Cambridge University Press, Cambridge, pp 330–458 Thorne KS (1980) Multipole expansions of gravitational radiation. Rev Mod Phys 52:299–340

1698

K. Kotake and T. Kuroda

Turner MS, Wagoner RV (1979) Gravitational radiation from slowly-rotating ‘supernovae’ – preliminary results. In: Smarr LL (ed) Sources of gravitational radiation. Cambridge University Press, Cambridge, pp 383–407 Wang L, Wheeler JC, Höflich P, Khokhlov A, Baade D, Branch D, Challis P, Filippenko AV, Fransson C, Garnavich P, Kirshner RP, Lundqvist P, McCray R, Panagia N, Pun CSJ, Phillips MM, Sonneborn G, Suntzeff NB (2002) The axisymmetric ejecta of Supernova 1987A. Astrophys J 579:671–677 Watts AL, Andersson N, Jones DI (2005) The nature of low T/|W| dynamical instabilities in differentially rotating stars. ApJL 618:L37–L40 Winteler C, Käppeli R, Perego A, Arcones A, Vasset N, Nishimura N, Liebendörfer M, Thielemann F-K (2012) ApJL 750:L22 Woosley SE (1993) Gamma-ray bursts from stellar mass accretion disks around black holes. ApJ 405:273–277 Woosley SE, Bloom JS (2006) The supernova gamma-ray burst connection. ARA&A 44:507–556 Yakunin KN, Mezzacappa A, Marronetti P, Yoshida S, Bruenn SW, Hix WR, Lentz EJ, Bronson Messer OE, Harris JA, Endeve E, Blondin JM, Lingerfelt EJ (2015) Gravitational wave signatures of ab initio two-dimensional core collapse supernova explosion models for 12 -25 Mˇ stars. Phys Rev D 92:084040

Detecting Gravitational Waves from Supernovae with Advanced LIGO

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Matthew Evans and Michele Zanolin

Abstract

Gravitational waves produced by supernovae can provide insight into the inner dynamics of the explosive death of stars. Thanks to their extremely weak coupling to matter, gravitational waves can carry energy and information away from the densest and most extreme environments in the universe, and as such they offer a unique probe of otherwise inaccessible processes. This is especially true for highly energetic core-collapse supernovae, where the shock reignition mechanism remains unclear. In this chapter we summarize the efforts by the advanced generation of laser interferometers to detect the gravitational wave transients emitted by the death of a massive star. Mechanisms of gravitational wave production in supernovae, gravitational wave detector status and perspectives, and the statistical methodology used to detect these transients are reviewed. While detection of gravitational waves from supernovae with Advanced LIGO is by no means guaranteed, plausible emission mechanisms offer significant discovery potential.

Contents 1 2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Worldwide Detector Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Detector Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Future Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gravitational Wave Searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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M. Evans () Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA e-mail: [email protected] M. Zanolin Embry Riddle Aeronautical University, Prescott, AZ, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_10

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4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Thanks to their extremely weak coupling to matter, gravitational waves can carry energy and information away from the densest and most extreme processes in the universe, supernovae and compact binary coalescence foremost among them (Abbott et al. 2016). These propagating deformations of the space-time metric are measurable as a tidal force or equivalent dimensionless strain (conventionally labeled “h”). For the laser interferometers, h is the change in length of the arms divided by the total length of the arms. Unfortunately the order of magnitude for this effect even for violent core-collapse supernovae in our galaxy is likely only h  1023 . Core-collapse supernovae (CCSNe) are the final stage in the life of massive stars. The collapse of a star’s iron core into a proto-neutron star triggers a hydrodynamic shock wave which stalls and may be reignited by a yet-uncertain supernova “mechanism.” If the shock wave is not reignited on a time scale of roughly 1 s to complete the explosion (e.g., Bethe 1990; Burrows 2013; Janka 2012), a black hole is formed and little or no explosion occurs (e.g., Lovegrove and Woosley 2013; O’Connor and Ott 2011; Piro 2013). If the shock is reignited and reaches the stellar surface, it leads to the bright electromagnetic emission of a Type II or Type Ib/c supernova. The time from core collapse to breakout of the shock through the stellar surface and first supernova light is minutes to days, depending on the radius of the progenitor and energy of the explosion (e.g., Kistler et al. 2013; Matzner and McKee 1999; Morozova et al. 2015). Any core-collapse event generates a burst of neutrinos that releases 99 % of the proto-neutron star’s gravitational binding energy (3  1053 erg  0:15 Mˇ c2 ) on a timescale of order 10 s (Lattimer and Prakash 2001; Vissani 2015). This neutrino burst was detected from SN 1987A and confirmed the basic theory of CCSNe (Bethe 1990; Bionta et al. 1987; Hirata et al. 1987). Aspherical core-collapse events will also generate gravitational waves (GWs), though the amplitude of the waves depends on the details of the mass-energy dynamics present during the collapse. Asymmetric dynamics are expected to be present in the pre-explosion stalled-shock phase of CCSNe and may be crucial to the CCSN explosion mechanism (e.g., see Burrows et al. 1995; Couch and Ott 2015; Herant 1995; Lentz et al. 2015), making GWs a potentially valuable probe of the magnitude and character of these asymmetries (Abdikamalov et al. 2014; Logue et al. 2012 and references therein). To set the energy scale, the typical CCSN explosion kinetic energy is  1051 erg (103 Mˇ c2 ) which serves as an upperbound to the energy output in GW emission. Stellar collapse and CCSNe were considered as potential sources of detectable GWs for resonant bar detectors in the 1960s (Weber 1966). Early analytic and semi-

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analytic estimates of the GW signature of stellar collapse and CCSNe (e.g., Saenz and Shapiro 1979; Thuan and Ostriker 1974 and reference therein) gave signal strengths which suggested that first-generation laser interferometer detectors could detect GWs from CCSNe in the Virgo cluster (at distances D & 10 Mpc). However, modern multidimensional CCSN simulations (see, e.g., Abdikamalov et al. 2014; Dimmelmeier et al. 2008; Kuroda et al. 2014; Müller et al. 2013, 2012; Ott et al. 2013; Yakunin et al. 2010, 2015 and the reviews in Fryer and New 2011; Kotake 2013; Ott 2009) find much weaker GW signals. The currently more realistic models predict emitted GW energies in the range 1012  108 Mˇ c2 , resulting in a characteristic strain of only hrss  1023 at a distance of 10 kpc (the energy is proportional to the square of the hrss ). These models suggest that current laser interferometers will only be able to detect GWs from CCSNe in our own Milky Way and the Magellanic Clouds, where the rate of such events is a few per century (Cappellaro et al. 1993; Li et al. 2011; Maoz and Badenes 2010 and references therein). While unlikely, observation of GWs from a galactic CCSN has the potential to greatly increase our knowledge of the dynamics of core collapse. However, there are also a number of analytic and semi-analytic GW emission models of more extreme scenarios, involving non-axisymmetric rotational instabilities, centrifugal fragmentation, and accretion disk instabilities. The emitted GW signals may be sufficiently strong to be detectable at a distance of 15 Mpc (e.g., Fryer et al. 2002; Ott et al. 2006; Piro and Pfahl 2007). In a sphere of radius 15 Mpc centered on Earth, the CCSN rate is somewhat greater than 1=yr (Ando et al. 2005; Kistler et al. 2013), which makes electromagnetically observed CCSNe in the Virgo galaxy cluster interesting targets for constraining extreme GW emission scenarios.

2

Worldwide Detector Network

Several large-scale gravitational wave detectors are in operation or under construction around the world and have recently detected gravitational waves from binary black hole systems (Abbott et al. 2016). As of the time of writing (early 2016), the two Advanced LIGO detectors are operating in the USA (one in Washington state and the other in Louisiana), and the GEO detector is operating near Hannover, Germany (Aasi et al. 2015; Willke et al. 2002). The Virgo detector, which operated with LIGO from 2007 to 2010, is currently being upgraded and is expected to begin collecting data later this year (Acernese et al. 2015). A kilometer scale detector is also under construction in Japan, at the Kamioka Observatory (site of the Super Kamiokande neutrino detector). This detector, known as “Kagra,” is scheduled to begin operation in 2017 (Aso et al. 2013). Gravitational wave detectors don’t suffer from the inability to observe during the day, nor are sources occluded by the Earth, yet having multiple detectors operating simultaneously is nevertheless important for gravitational wave detection. The principal reason for this is the non-Gaussian nature of the noise in the detector output coupled with the typically small signal-to-noise ratio (SNR). Simply put,

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coincident detection of similar gravitational wave signals in detectors which are separated by thousands of kilometers adds a great deal of confidence to low SNR events (both in the colloquial and statistical sense of the word “confidence”). Furthermore, coincident signal detection in multiple gravitational wave detectors offers some ability to localize the source on the sky (see Fig. 2, right).

2.1

Detector Physics

Modern broadband gravitational wave detectors are based on a Michelson-type interferometer, with a number of enhancements which significantly increase sensitivity (Aasi et al. 2015). The noises which limit laser gravitational wave detectors are manifold below 100 Hz, but in the frequency band of interest for supernovae only shot noise (or, more generally, quantum noise) is relevant. The sensitivity of gravitational wave detectors are typically quantified in terms of the p instrument’s noise amplitude spectral density calibrated in units of strain per Hz. The design sensitivity of Advanced LIGO is shown in Fig. 1, along with example amplitude spectral densities for a few supernova mechanisms. (Many papers on gravitational waves from supernovae use units of “characteristic strain,” p in which the Hz units do not appear. Converting p between these conventions is simply a matter of multiplying the spectrum by f .) In order to quantify the amplitude of gravitational wave produced by a given supernova mechanism, a characteristic observation distance is required. The two distances most frequently used are 10 kpc, which is relevant for determining the detectability gravitational waves given a supernova in our galaxy, and 10 Mpc, which is sufficient to give an event rate greater than 1 per year. Interferometric gravitational wave detectors are most sensitive to gravitational waves which arrive from directly overhead, or directly below the detectors. (The Earth does not block gravitational waves, and the detectors are constructed in a plane very nearly orthogonal to local gravity, resulting in a clear up-down symmetry in their antenna pattern.) Detector sensitivity is lowest to sources in the plane of the interferometer, roughly a factor of 3 lower on-average relative to the maximum (see Fig. 2, right). Direction reconstruction for SN sources, when not provided by a companion EM observation, can be performed with the likelihood maps like the one described in Fig. 2, left. It is important to notice however that the resolution is of the order of degrees and the ambiguities, especially in the case of 2 interferometers, can be substantial.

2.2

Future Improvements

Progress in future detectors can happen via several avenues. The most obvious is to reduce the shot noise in the current detectors by increasing the laser power. Increased power, however, comes with a number of complications, with thermal distortions of the optics and opto-mechanical instabilities especially problematic.

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Noise Amplitude

S( f ) [Hz −1/2 ]

10−20

10−21

Ott 2010 Dimmelmeier 2008 Ott 2013 aLIGO adVirgo

10−22

10−23

10−24 10

100 Frequency [Hz]

1000

Fig. 1 The sensitivity of a gravitational wave detector can be quantified by the amplitude spectral density of its output, calibrated into gravitational wave strain. Advanced LIGO, when operating in its design configuration, will have a sensitivity similar to the one depicted here. Other advanced detectors (e.g., Virgo and Kagra) will offer similar sensitivities. For comparison we show the amplitude spectral density of three CCSN waveforms at a distance of 10 kpc. Ott 2010 waveform comes from rapidly rotating proto-neutron star which is deformed into tri-axial (“bar”) shape. Dimmelmeier 2008 is also a result of rapidly rotating core, but the gravitational waves come from of the core collapse and bounce. The third waveform (Ott 2013) represents neutrino-driven explosion (See Sect. 3 for more information about these mechanisms)

A second route to reducing shot noise is through the use of squeezed states of light, well known in the quantum optics community and now positioned to find application in gravitational wave detectors. Squeezing can be used to reduce noise in the detector readout by introducing entangled photons into the interferometer which change the noise properties of the light on which the gravitational wave signal is imprinted. Practical limitations prevent this technique from providing more than a factor of 2 or 3 amplitude noise reduction, which is nonetheless equivalent to increasing the laser power by a factor of 4–9. A clear third path to increased sensitivity is the construction of longer gravitational wave detectors. The current LIGO facilities are 4 km in length and are configured to have a signal integration time of roughly 1 ms. Keeping all else constant, both in-band sensitivity and integration time are proportional to detector length, such that sensitivity above the most sensitive band remains constant. This appears to be unfavorable for the prospects of detecting GWs from supernova, since

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Fig. 2 Left: The antenna pattern of a gravitational wave detector averaged over gravitational wave polarization is up-down symmetric and maximum directly above or below the detector. Note that the Earth does not block gravitational wave from below. Right: The right panel describes a typical likelihood ratio map which gives the relative probability of the source being located at a particular sky position. This map was generated by adding a representative signal to the LIGO and Virgo data for an offline-test of the detector network’s sky-localization ability. A dot and a star indicate the direction the signal was coming from and the reconstructed maximum likelihood direction of arrival. Large black dots labeled HV, LV, and LH mark the direction of the line connecting each pair of interferometers, and rings around these dots indicate sky locations consistent with a fixed time delay between the arrival of a GW at each pair

most of the signal will likely appear at or above 1 kHz. The detector’s optical parameters can, however, be chosen to trade in-band sensitivity for bandwidth, allowing for an overall scaling with the square-root of length. Future detector designs currently under consideration, all of which are 10–40 km in length and include the use of squeezed states of light to reduce quantum noise, would offer roughly a factor of 10 improvement over Advanced LIGO at 1 kHz. This improvement will mean that essentially all plausible CCSN mechanisms will produce detectable GWs from galactic supernova, and many of the more extreme mechanisms will be detectable from CCSN in the Virgo cluster.

3

Gravitational Wave Searches

A variety methodologies are employed to detect gravitational wave signals in laser interferometer data. CCSNe produce short duration signals (order 1 s or less) with a large uncertainty in the waveform. GW sources of this sort are collectively known as “burst sources” or “unmodeled sources” to indicate that an exact waveform is not available. The waveform uncertainty in CCSN signals originates from the existence of a myriad of possible explosion and shock reignition mechanisms and from the turbulent and chaotic dynamics of the explosion which make the exact form of the GW signal produced extremely sensitive to small changes in the initial conditions (with the exception of rapidly rotating progenitors or some of the more extreme models which follow deterministic evolution equations).

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The methodologies used to detect burst sources involve looking for a statistically unusual excess of energy in the interferometer output which is consistent with a gravitational wave arriving from some sky location, given the time of flight between different interferometer sites. Put simply, detection depends on finding similar signals at nearly the same time in multiple detectors (as mentioned in Sect. 2). Burst searches based entirely on GW data, which search for a signal from any sky location any time data is available (referred to as “all-sky” searches), have been used to look for GW from CCSN in data from the first generation of interferometric detectors. Observational constraints on GW from CCSNe derived from these generic burst searches were, however, quite weak (Abadie et al. 2012a; Abbott et al. 2009a, b and references therein). A potentially more successful approach to finding GW signals from CCSNe is to use electromagnetic (or neutrino) observations to determine the position and time of a supernova event and then search for GWs from that event. Targeted searches have an advantage over all-sky searches in that potential signal candidates are required to be in a well-defined temporal on-source window and must be consistent with GWs arriving from the sky location of the source. Previous targeted GW searches have been carried out for gamma ray bursts (Aasi et al. 2013; Abadie et al. 2012b and references therein), soft-gamma repeater flares (Abadie et al. 2011b; Abbott et al. 2008), and pulsar glitches (Abadie et al. 2011a). The targeted search approach can extend the detection range (for a given false alarm rate) by as much as a factor of 2 (Sutton et al. 2010). The duration of the on-source window, due to uncertainty in the exact time of the GW emission from the supernova event, is a critical factor in determining the efficacy of a targeted search (intuitively, the shorter it is, the lower the chance of noise-induced events). Neutrino observations have the potential to provide a very short on-source window (order of a few tens of seconds), but given the expected neutrino emissions (which have been experimentally tested with SN 1987A), they can only be expected for galactic CCSNe. X-ray precursors of the optical light curve may provide an on-source window of order of a few hundred seconds in length, but are also expected be rare until a dedicated wide field observatory is available (because they require constant monitoring of the host galaxy). UV and optical observation can provide on-source windows that last between a few hours and a few days depending on the progenitor (the analysis involves determining first the time of the shock breakout and then its relationship with the GW emission), and finally the time interval between the last negative observation and the first detection of a CCSN light curve will provide a window length of days to months. Burst search algorithms usually have several internal parameters that can be tuned for targeted CCSN searches. It is customary to aim for a general good sensitivity to waveforms belonging to the 3 families: (1) representative waveforms from detailed multidimensional (2D axisymmetric or 3D) CCSN simulations; (2) semi-analytic phenomenological waveforms of plausible but extreme emission scenarios; and (3) sinusoidal waveforms windowed with Gaussian envelopes with various frequency content and amplitude (mainly to establish upper limits on the energy emitted in GWs at a fixed CCSN distance). The GW amplitudes, frequencies

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Table 1 Gravitational wave production mechanisms in core-collapse supernova Mechanism Convection Rotating core collapse Protoneutron star ringdown Long-lasting bar mode Torus fragmentation instability

Amplitude (hrss ) [1022 @ 10 kpc] 1–3 1–3 0.2–0.3 150–2500 250–3000

Peak frequency [Hz] 150–210 200–800 1000 800–1600 1800–2000

Energy in GWs [1010 Mˇ c2 ] 0.1–0.5 1.5–30 45 >2  106 >6  106

and energies for the physically motivated waveforms (1 and 2), discussed briefly below, are summarize in Table 1. Rotation leads to a natural axisymmetric quadrupole (oblate) deformation of the collapsing core. The tremendous acceleration at core bounce and proto-neutron star formation results in a strong linearly polarized burst of GWs followed by a ringdown signal. Rotating core collapse is the most extensively studied GW emission process in the CCSN context (see Fryer and New 2011; Kotake 2013; Ott 2009 for reviews). In nonrotating or slowly rotating CCSNe, neutrino-driven convection and the standing accretion shock instability (SASI) are expected to dominate the GW emission. GWs from convection/SASI have also been extensively studied in 2D (e.g., Kotake et al. 2009; Müller et al. 2004; Marek et al. 2009; Müller et al. 2013; Murphy et al. 2009; Yakunin et al. 2010, 2015) and more recently also in 3D (Müller et al. 2012; Ott et al. 2013). In the context of rapidly rotating core collapse, various non-axisymmetric instabilities can deform the proto-neutron star into a tri-axial (“bar”) shape (e.g., Brown 2001; Lai and Shapiro 1995; Ott et al. 2005, 2007; Rampp et al. 1998; Scheidegger et al. 2010; Shibata and Sekiguchi 2005), potentially leading to extended (10 ms to few seconds) and energetic GW emission. This emission occurs at twice the protoneutron star spin frequency and with amplitude dependent on the magnitude of the bar deformation (Fryer et al. 2002; Ott et al. 2007; Scheidegger et al. 2010). More extreme scenarios involve the formation of a dense self-gravitating Mˇ scale fragment in a thick accretion torus around a black hole in the context of collapsar-type gamma ray bursts (Piro and Pfahl 2007). Fragments are driven toward the black hole by a combination of viscous torques and energetic GW emission. This is an extreme but plausible scenario which results in GW emission detectable by Advanced LIGO at D > 10 Mpc. It is important to stress that it is unlikely that we will have coincident science data covering entirely on-source windows several days long. This means that multiple CCSNe triggers might be necessary to detect a signal (pattern recognition and inversion approaches need then to be employed to elucidate the emission model). In case of multiple nondetections, collective statistical techniques need to be employed to rule out specific emission models with a desired confidence. For example, assuming standard-candle emission and combining observations of

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multiple CCSNe recorded at distances where the sensitivity of the interferometers is nonzero, it is possible to exclude an emission model at a desired level confidence provided that the sample of CCSNe is large enough.

4

Conclusions

The detection of gravitational waves from supernova has the potential to reveal a great deal about the internal mass-energy dynamics of the explosion. Core-collapse supernovae are of particular interest as the formation of a black hole or neutron star can release a significant amount of energy in gravitational waves. While conventional and well-studied mechanisms for GW emission from CCSNe are likely to produce signals detectable only if they occur within the Milky Way or its neighbors, a wide range of mechanisms produce copious GWs. Searching for GW from known CCSN within 10–20 Mpc will serve as an important tool to investigate the complex interior of these poorly understood systems.

5

Cross-References

 Explosion Physics of Core-Collapse Supernovae  Gravitational Waves from Core-Collapse Supernovae  Neutron Stars as Probes for General Relativity and Gravitational Waves Acknowledgements MZ acknowledges Marek Szczepa´nczyk for fruitful discussions on the many drafts of this chapter.

References Aasi J, Abadie J, Abbott BP, Abbott R, Abbott T, Abernathy MR et al (2013) Search for long-lived gravitational-wave transients coincident with long gamma ray bursts. Phys Rev D 88(12):122004 Aasi J, Abadie J, Abbott BP, Abbott R, Abbott T, Abernathy MR et al (2015) Advanced LIGO. Class Quant Grav 32:074001 Abadie J, Abbott BP, Abbott R, Abernathy M, Accadia T, Acernese F, Adams C, Adhikari R, Ajith P, Allen B et al (2011a) Search for gravitational waves associated with the August 2006 timing glitch of the Vela pulsar. Phys Rev D 83(4):042001 Abadie J et al (LIGO Scientific Collaboration) (2011b) Search for gravitational wave bursts from six magnetars. Astrophys J Lett 734:L35 Abadie J, Abbott BP, Abbott R, Adhikari R, Ajith P, Allen B, Allen G et al (2012a) All-sky search for gravitational-wave bursts in the second joint ligo-virgo run. Phys Rev D 85:122007 Abadie J, Abbott BP, Abbott R, Abernathy M, Accadia T, Acernese F, Adams C, Adhikari R, Ajith P, Allen B et al (2012b) Implications for the origin of GRB 051103 from LIGO observations. Astrophys J 755:2 Abbott BP, Abbott R, Adhikari R, Ajith P, Allen B, Allen G et al (2008) Search for gravitationalwave bursts from soft gamma repeaters. Phys Rev Lett 101(21):211102

1708

M. Evans and M. Zanolin

Abbott BP et al (LIGO Scientific Collaboration) (2009a) Search for gravitational-wave bursts in the first year of the fifth LIGO science run. Phys Rev D 80(10):102001 Abbott BP et al (LIGO Scientific Collaboration) (2009b) Search for high frequency gravitationalwave bursts in the first calendar year of LIGO’s fifth science run. Phys Rev D 80:102002 Abbott BP et al (2016) Observation of gravitational waves from a binary black hole merger. Phys Rev Lett 116:061102 Abdikamalov E, Gossan S, DeMaio AM, Ott CD (2014) Measuring the angular momentum distribution in core-collapse supernova progenitors with gravitational waves. Phys Rev D 90(4):044001 Acernese F, Agathos M, Agatsuma K, Aisa D, Allemandou N, Allocca A, Amarni J, Astone P et al (2015) Advanced virgo: a second-generation interferometric gravitational wave detector. Class Quant Grav 32(2):024001 Ando S, Beacom F, Yüksel H (2005) Detection of neutrinos from supernovae in nearby galaxies. Phys Rev Lett 95:171101 Aso Y, Michimura Y, Somiya K, Ando M, Miyakawa O, Sekiguchi T, Tatsumi D, Yamamoto H (2013) Interferometer design of the kagra gravitational wave detector. Phys Rev D 88:043007 Bethe HA (1990) Supernova mechanisms. Rev Mod Phys 62:801 Bionta RM, Blewitt G, Bratton CB, Casper D, Ciocio A (1987) Observation of a neutrino burst in coincidence with supernova 1987A in the Large Magellanic Cloud. Phys Rev Lett 58:1494 Brown JD (2001) Rotational instabilities in post-collapse stellar cores. In: Astrophysical sources for ground-based gravitational wave detectors. AIP conference proceedings, vol 575, pp 234. American Institute of Physics, Melville Burrows A (2013) Colloquium: perspectives on core-collapse supernova theory. Rev Mod Phys 85:245 Burrows A, Hayes J, Fryxell BA (1995) On the nature of core-collapse supernova explosions. Astrophys J 450:830 Cappellaro E, Turatto M, Benetti S, Tsvetkov DY, Bartunov OS, Makarova IN (1993) The rate of supernovae – part two – the selection effects and the frequencies per unit blue luminosity. Astron Astrophys 273:383 Couch SM, Ott CD (2015) The role of turbulence in neutrino-driven core-collapse supernova explosions. Astrophys J 799:5 Dimmelmeier H, Ott CD, Marek A, Janka H-T (2008) Gravitational wave burst signal from core collapse of rotating stars. Phys Rev D 78:064056 Fryer C, New KCB (2011) Gravitational waves from gravitational collapse. Liv Rev Rel 14:1 Fryer CL, Holz DE, Hughes SA (2002) Gravitational wave emission from core collapse of massive stars. Astrophys J 565:430 Herant M (1995) The convective engine paradigm for the supernova explosion mechanism and its consequences. Phys Rep 256:117 Hirata K, Kajita T, Koshiba M, Nakahata M, Oyama Y (1987) Observation of a neutrino burst from the supernova SN 1987A. Phys Rev Lett 58:1490 Janka H-T (2012) Explosion mechanisms of core-collapse supernovae. Ann Rev Nucl Part Sci 62:407 Kistler MD, Haxton WC, Yüksel H (2013) Tomography of massive stars from core collapse to supernova shock breakout. Astrophys J 778:81 Kotake K (2013) Multiple physical elements to determine the gravitational-wave signatures of core-collapse supernovae. C R Phys 14:318 Kotake K, Iwakami W, Ohnishi N, Yamada S (2009) Stochastic nature of gravitational waves from supernova explosions with standing accretion shock instability. Astrophys J Lett 697:L133 Kuroda T, Takiwaki T, Kotake K (2014) Gravitational wave signatures from low-mode spiral instabilities in rapidly rotating supernova cores. Phys Rev D 89(4):044011 Lai D, Shapiro SL (1995) Gravitational radiation from rapidly rotating nascent neutron stars. Astrophys J 442:259 Lattimer JM, Prakash M (2001) Neutron star structure and the equation of state. Astrophys J 550:426

64 Detecting Gravitational Waves from Supernovae with Advanced LIGO

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Lentz EJ, Bruenn SW, Hix WR, Mezzacappa A, Messer OEB, Endeve E, Blondin JM, Harris JA, Marronetti P, Yakunin KN (2015) Three-dimensional core-collapse supernova simulated using a 15 Msun progenitor. Astrophys J Lett 807:L31 Li W, Leaman J, Chornock R, Filippenko AV, Poznanski D, Ganeshalingam M, Wang X, Modjaz M, Jha S, Foley RJ, Smith N (2011) Nearby supernova rates from the lick observatory supernova search – II. The observed luminosity functions and fractions of supernovae in a complete sample. Mon Not R Astron Soc 412:1441 Logue J, Ott CD, Heng IS, Kalmus P, Scargill J (2012) Inferring core-collapse supernova physics with gravitational waves. Phys Rev D 86(4):044023 Lovegrove E, Woosley SE (2013) Very low energy supernovae from neutrino mass loss. Astrophys J 769:109 Müller E, Rampp M, Buras R, Janka H-T, Shoemaker DH (2004) Toward gravitational wave signals from realistic core-collapse supernova models. Astrophys J 603:221 Maoz D, Badenes C (2010) The supernova rate and delay time distribution in the magellanic clouds. Mon Not R Astron Soc 407:1314 Marek A, Janka H-T, Müller E (2009) Equation-of-state dependent features in shock-oscillation modulated neutrino and gravitational-wave signals from supernovae. Astron Astrophys 496:475 Matzner CD, McKee CF (1999) The expulsion of stellar envelopes in core-collapse supernovae. Astrophys J 510:379 Morozova V, Piro AL, Renzo M, Ott CD, Clausen D, Couch SM, Ellis J, Roberts LF (2015, in press) Light curves of core-collapse supernovae with substantial mass loss using the new opensource supernova explosion code (SNEC). Astrophys J. arXiv:1505.06746 Müller B, Janka H-T, Marek A (2013) A new multidimensional general relativistic neutrino hydrodynamics code of core-collapse supernovae. III. Gravitational wave signals from supernova explosion models. Astrophys J 766:43 Müller E, Janka H-T, Wongwathanarat A (2012) Parametrized 3D models of neutrino-driven supernova explosions. Neutrino emission asymmetries and gravitational-wave signals. Astron. Astrophys. 537:A63 Murphy JW, Ott CD, Burrows A (2009) A model for gravitational wave emission from neutrinodriven core-collapse supernovae. Astrophys J 707:1173 O’Connor E, Ott CD (2011) Black hole formation in failing core-collapse supernovae. Astrophys J 730:70 Ott CD (2009) TOPICAL REVIEW: the gravitational-wave signature of core-collapse supernovae. Class Quant Grav 26:063001 Ott CD, Ou S, Tohline JE, Burrows A (2005) One-armed spiral instability in a low-T/jWj postbounce supernova core. Astrophys J 625:L119 Ott CD, Burrows A, Dessart L, Livne E (2006) A new mechanism for gravitational-wave emission in core-collapse supernovae. Phys Rev Lett 96:201102 Ott CD, Dimmelmeier H, Marek A, Janka H-T, Hawke I, Zink B, Schnetter E (2007) 3D collapse of rotating stellar iron cores in general relativity including deleptonization and a nuclear equation of state. Phys Rev Lett 98:261101 Ott CD, Abdikamalov E, Mösta P, Haas R, Drasco S, O’Connor EP, Reisswig C, Meakin CA, Schnetter E (2013) General-relativistic simulations of three-dimensional core-collapse supernovae. Astrophys J 768:115 Piro AL (2013) Taking the “Un” out of “Unnovae.” Astrophys J Lett 768:L14 Piro AL, Pfahl E (2007) Fragmentation of collapsar disks and the production of gravitational waves. Astrophys J 658:1173 Rampp M, Müller E, Ruffert M (1998) Simulations of non-axisymmetric rotational core collapse. Astron Astrophys 332:969 Saenz RA, Shapiro SL (1979) Gravitational and neutrino radiation from stellar core collapse – improved ellipsoidal model calculations. Astrophys J 229:1107 Scheidegger S, Käppeli R, Whitehouse SC, Fischer T, Liebendörfer M (2010) The influence of model parameters on the prediction of gravitational wave signals from stellar core collapse. Astron Astrophys 514:A51

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Shibata M, Sekiguchi Y-I (2005) Three-dimensional simulations of stellar core collapse in full general relativity: nonaxisymmetric dynamical instabilities. Phys Rev D 71:024014 Sutton PJ, Jones G, Chatterji S, Kalmus P, Leonor I, Poprocki S, Rollins J, Searle A, Stein L, Tinto M, Was M (2010) X-pipeline: an analysis package for autonomous gravitational-wave burst searches. N J Phys 12:053034 Thuan TX, Ostriker JP (1974) Gravitational radiation from stellar collapse. Astrophys J Lett 191:L105 Vissani F (2015) Comparative analysis of SN 1987A antineutrino fluence. J Phys G Nucl Phys 42(1):013001 Weber J (1966) Observation of the thermal fluctuations of a gravitational-wave detector. Phys Rev Lett 17:1228 Willke B, Aufmuth P, Aulbert C, Babak S, Balasubramanian R, Barr BW, Berukoff S, Bose S, Cagnoli G, Casey MM, Churches D, Clubley D, Colacino CN, Crooks DRM, Cutler C, Danzmann K, Davies R, Dupuis R, Elliffe E, Fallnich C, Freise A, Goßler S, Grant A, Grote H, Heinzel G, Heptonstall A, Heurs M, Hewitson M, Hough J, Jennrich O, Kawabe K, Kötter K, Leonhardt V, Lück H, Malec M, McNamara PW, McIntosh SA, Mossavi K, Mohanty S, Mukherjee S, Nagano S, Newton GP, Owen BJ, Palmer D, Papa MA, Plissi MV, Quetschke V, Robertson DI, Robertson NA, Rowan S, Rüdiger A, Sathyaprakash BS, Schilling R, Schutz BF, Senior R, Sintes AM, Skeldon KD, Sneddon P, Stief F, Strain KA, Taylor I, Torrie CI, Vecchio A, Ward H, Weiland U, Welling H, Williams P, Winkler W, Woan G, Zawischa I (2002) The GEO 600 gravitational wave detector. Class Quant Grav 19:1377–1387 Yakunin KN, Marronetti P, Mezzacappa A, Bruenn SW, Lee C-T, Chertkow MA, Hix WR, Blondin JM, Lentz EJ, Messer B, Yoshida S (2010) Gravitational waves from core collapse supernovae. Class Quant Grav 27:194005 Yakunin KN, Mezzacappa A, Marronetti P, Yoshida S, Bruenn SW, Hix WR, Lentz EJ, Messer OEB, Harris JA, Endeve E, Blondin JM, Lingerfelt EJ (2015) Gravitational wave signatures of ab initio two-dimensional core collapse supernova explosion models for 12–25 solar masses stars. Submitted to Phys Rev D arXiv:1505.05824

High-Energy Cosmic Rays from Supernovae

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Giovanni Morlino

Abstract

Cosmic rays are charged relativistic particles that reach the Earth with extremely high energies, providing striking evidence of the existence of effective accelerators in the Universe. Below an energy around 1017 eV, cosmic rays are believed to be produced in the Milky Way, while above that energy, their origin is probably extragalactic. In the early 1930s, supernovae were already identified as possible sources for the galactic component of cosmic rays. After the 1970s this idea has gained more and more credibility, thanks to the development of the diffusive shock acceleration theory, which provides a robust theoretical framework for particle energization in astrophysical environments. Afterward, mostly in recent years, much observational evidence has been gathered in support of this framework, converting a speculative idea in a real paradigm. In this chapter the basic pillars of this paradigm will be illustrated. This includes the acceleration mechanism, the nonlinear effects produced by accelerated particles onto the shock dynamics needed to reach the highest energies, the escape process from the sources, and the transportation of cosmic rays through the Galaxy. The theoretical picture will be corroborated by discussing several observations which support the idea that supernova remnants are effective cosmic ray factories.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Acceleration Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 First- and Second-Order Fermi Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Particle Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Particle Diffusion in Weak Magnetic Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Maximum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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G. Morlino () Gran Sasso Science Institute, National Institute for Nuclear Physics (INFN), L’Aquila, Italy e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_11

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DSA in the Nonlinear Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Dynamical Reaction of Accelerated Particles . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Magnetic Field Amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The Dynamical Reaction of the Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Escaping from the Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Journey to the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Observational Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Cosmic rays (CR) are charged particles detected at the Earth or in the space just around the Earth, mainly consisting of protons (hydrogen nuclei) with about 10 % fraction of helium nuclei and smaller abundances of heavier elements. The flux of all nuclear components is shown in Fig. 1. In spite of the fact that the CR spectrum extends over at least 13 decades in energy, extracting information from it is hard because it is nearly featureless. For energies greater than 30 GeV, where the solar wind screening effect becomes negligible, the spectrum resembles to a broken power law with a spectrum changing from / E 2:7 to / E 3:1 at an energy of Eknee  3  1015 eV (a feature called the knee). A second change in the spectrum occurs around Eankle  3  1018 eV where the slope flattens again toward a value close to 2.7 (usually referred to as the ankle). In the highest-energy region, the flux falls to very low values; hence, measurement becomes extremely difficult (at 3  1020 eV, the flux is 1 particle per km2 each 350 years). There is evidence that the chemical composition of CRs changes across the knee region with a trend to become increasingly more dominated by heavy nuclei at high energy (see Höorandel 2006,for a review), at least up to 1017 eV. This evidence could be explained if the CR acceleration mechanism was rigidity-dependent and the maximum energy of protons could reach 3  1015 eV. Then, heavier nuclei, with charge Z, would reach Z times larger energies. In this scheme the heaviest nuclei, namely, Fe, have an energy of 26  Eknee , and the knee structure results as the superposition of the cutoffs of different species. CRs up to an energy around 1017 eV are believed to originate in our own Galaxy. On the contrary, particles with energy beyond the ankle, usually referred to as ultrahigh-energy cosmic rays (UHECRs), cannot be confined in the Galaxy, because their Larmor radius in the typical galactic magnetic field is of the same order of the Galaxy size or even larger. Hence, if they were produced in the Galaxy, the particle deflection would be small enough that the arrival direction should trace the source’s position in the sky. On the contrary, the incoming spatial distribution of UHECRs is nearly isotropic; hence, the general opinion is that these particles come from extragalactic sources. A connection between CRs and supernovae (SNe) was firstly proposed in the early 1930s (Baade and Zwicky 1934) on the basis of a simple energetic argument.

65 High-Energy Cosmic Rays from Supernovae

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104

proton AMS

p

3

BESS

10

ATIC JACEE

102

e−(or e±)

KASCADE(SIBYLL)

E2 dN/dE(GeV m−2 s−1sr −1)

TibetIII(SIBYLL)

10 1

all−particle Tibet(SIBYLL)

e+

KASCADE(SIBYLL) Akeno

10−1

GAMMA

all−particle

γ

TUNKA Yakutsk

ν

10−2

Auger AGASA HiRes

10−3

e± p ν γ

p

CAPRICE e− HEAT ATIC

−4

10

Fermi HESS

10−5

CAPRICE e+ BESS AMANDA EGRET

−6

10

10−2

1

102

104 106 E(GeV)

108

1010

1012

Fig. 1 Spectrum of cosmic rays at the Earth. The all-particle spectrum measured by different experiments is plotted, together with the proton spectrum. The subdominant contributions from electrons, positrons, and antiprotons as measured by the PAMELA experiment are shown. For comparison also atmospheric neutrino and diffuse gamma ray background are shown

The power needed to maintain the galactic CRs at the observed level against losses due to escape from the Galaxy can be estimated as follows: PCR  UCR VCR = res  1040 erg=s ;

(1)

where UCR  0:5 eV=cm3 is the CRs’ energy density measured at the Earth and VCR  400 kpc3 is the volume of the galactic halo where CRs are efficiently confined. The typical residence time of a cosmic ray in the Galaxy we assume to be esc  5  106 yr (see Sect. 5). Now, we know that the energy released by a single supernova explosion in kinetic energy of the expanding shell is around 1051 erg; therefore, the total energy injected into the galactic environment is PSNR D RSN ESNR  3  1041 erg=s :

(2)

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G. Morlino

where RSN  0:03 yr1 is the rate of supernova explosion in the Galaxy. Accounting also for the uncertainties in the parameters, the energy density of the galactic CR component can be explained if one assumes that a fraction around 3–30 % of the total supernova mechanical energy is transferred to nonthermal particles. This energetic argument was the only basis in favor of the SN hypothesis until the 1970s, when a mechanism able to transfer energy from SNe to nonthermal particles was proposed, namely, the stochastic acceleration occurring at the SNR shocks. Since then, this idea has received more and more attention, thanks to a number of observations, especially in radio, X-rays, and gamma rays, that confirmed many predictions and triggered further improvements of the theory. In this chapter we summarize the basic theoretical aspects of the SNR-CR connection. Section 2 is devoted to explain the diffusive shock acceleration in the test particle limit, while in Sect. 3 we discuss how nonlinear effects produced by accelerated particles can modify the shock structure. In Sects. 4 and 5, we discuss the escaping process from the sources and the diffusion through the Galaxy, respectively. Finally, in Sect. 6, a number of relevant observations are discussed. Conclusions and future prospectives are drawn in Sect. 7.

2

The Acceleration Mechanism

2.1

First- and Second-Order Fermi Acceleration

The most common invoked acceleration mechanism in astrophysics is diffusive shock acceleration (DSA) also called the first-order Fermi process. In fact the seminal idea was put forward by Fermi (1949, 1954) who proposed that CRs could be accelerated by repeated stochastic scattering in a turbulent magnetic field which Fermi idealized as magnetized clouds moving around the Galaxy with random velocity (see Fig. 2). In the form in which Fermi first put it forward, this idea, today called second-order Fermi process, does not work either to explain the shape of

Fig. 2 Schematic representation of the original Fermi idea to energize cosmic rays through repeated scatters with magnetic clouds randomly moving in the Galaxy

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the CRs spectrum or to account for their total energy density. Nevertheless, it well illustrates the concept of stochastic acceleration; hence, it is worth to be discussed here. Let us consider a single particle with energy E1 , in the Galaxy’s frame, and a cloud with Lorentz factor  and speed u D ˇc. For simplicity we assume that the particle is already relativistic, i.e., E  pc. In the reference frame of the cloud, the energy is E10 D  E1 .1  ˇ cos 1 / ;

(3)

where 1 is the angle between particle’s and cloud’s velocities. After the interaction the energy in the cloud’s frame remains unchanged, namely, E20 D E10 , while the final energy in the Galaxy’s frame is E2 D  E20 .1 C ˇ cos 20 / ;

(4)

where 20 is the exit angle in the cloud’s frame. Hence, after a single encounter, the energy gain is 1  ˇ cos 1 C ˇ cos 20  ˇ 2 cos 1 cos 20 E E2  E1  D  1: E1 E1 1  ˇ2

(5)

To get the mean energy gain, we need to average over the incoming and the outcoming directions. Because the scattering in the cloud frame is isotropic, we have hcos 20 i D 0. On the other hand, the mean incoming direction can be computed averaging over the particle flux, which is proportional to the relative velocity, ˇr D 1  ˇ cos 1 . Hence, if the particle distribution is isotropic in the Galaxy’s frame, we simply have R hcos 1 i D

d ˝ ˇr cos 1 R D d ˝ ˇr

R1

d cos 1 .1  ˇ cos 1 / cos 1 ˇ D R1 3 1 d cos 1 .1  ˇ cos 1 /

1

(6)

and the average energy gain becomes 1 C 13 ˇ 2 E 4 D  1 ' ˇ2 : E1 1  ˇ2 3

(7)

The last passage is obtained assuming that ˇ  1. In spite of the fact that in each interaction a particle can either gain or lose energy, the average energy gain is positive simply because the cloud is moving; hence, the flux of particle crossing the cloud in front is greater than the one leaving the cloud from behind. The proportionality of the energy gain to the second power of the speed justifies the name of second-order Fermi mechanism, and this is exactly the reason why it cannot explain the CR spectrum. In fact the random velocities of clouds are relatively small,

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G. Morlino

v=c  104 , and, for a particle with a mean free path of 0.1 pc, the collisions would likely to occur only few times per year; hence, the final energy gain is really modest. Moreover, the predicted energy spectrum strongly depends on the model that details (see Longair 1992,Ch. 7) a conclusion at odds with observations. As recently as the 1970s, several authors independently realized that when Fermi’s idea is applied to particles in the vicinity of a shock wave, the result changes dramatically (Axford et al. 1977; Bell 1978a, b; Blandford and Ostriker 1978; Krymskii 1977; Skilling 1975a, b). This time the magnetic turbulence in the plasma provides the scattering centers needed to confine particles around the shock wave, allowing them to cross the shock repeatedly. Each time a particle crosses the shock front, it always suffers head-on collisions with the magnetic turbulence on the other side of the shock, gaining a bit of energy which is subtracted from the bulk motion of the plasma. Let us describe this process with more details. Consider a plane shock moving with velocity ush . In the frame where the shock is at rest, the upstream plasma moves toward the shock with velocity u1  ush , while the downstream plasma moves away from the shock with velocity u2 (see Fig. 3, left panel). The situation is similar to what happens in the case of a moving cloud described before, but this time the relative velocity between downstream and upstream plasma is ur  ˇr c D u1  u2 . Assuming that the particle density, n, is isotropic, the flux of particle crossing the shock from downstream region toward the upstream one is Z J D

nc d˝ nc cos  D ; 4

4

(8)

Fig. 3 Left. Structure of an unmodified plane shock wave. Particles diffusing from upstream toward downstream feel the compression factor r in the velocity of the plasma, which is the same at all energies Right. Shock structure modified by the presence of accelerated particles. The pressure exerted by accelerated particles diffusing upstream slows down the plasma creating a “precursor.” High-energy particles, which propagate farther away from the shock, feel now a larger compression factor with respect to low-energy particles which diffuse closer to the shock

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where the integration is performed in the interval 1 6 cos  6 0. Hence, the average value of the incoming angle is hcos 1 i D

1 J

Z

d˝ 2 nc cos2 1 D  4

3

(9)

while for the outcoming direction we have hcos 20 i D 2=3 because the integration is performed for 0 6 cos  6 1. According to Eq. (5), the average energy gain in a single cycle downstream-upstream-downstream is 1 C 43 ˇr C 49 ˇr2 E 4  1  ˇr : D E 1  ˇr2 3

(10)

Compared to the collision with clouds, the shock acceleration is more efficient, resulting in an energy gain proportional to the relative velocity between upstream and downstream plasmas, hence the name first-order Fermi process.

2.2

Particle Spectrum

The most remarkable property of the first-order Fermi mechanism consists in the production of a particle spectrum which is a universal power law. Such universality is a consequence of the balance between the energy gain and the escape probability from the accelerator, as we illustrate below. During each cycle around the shock, a particle has a finite probability to escape because of the advection with the downstream plasma. In a steady-state situation, the particle flux advected toward downstream infinity is simply J1 D nu2 , while no particle can escape toward upstream infinity (in reality this assumption can be violated for particles at maximum energy; see Sect. 4). For the flux conservation, we have JC D J C J1 , where JC and J are the flux of particles crossing the shock from upstream toward downstream and vice versa. Using Eq. (8) the escape probability can be expressed as Pesc D

J1 J1 4u2 D ' JC J1 C J c

(11)

and is independent from the particle’s energy. Now, to calculate the particle spectrum, we can use the microscopic approach, following the fate of a single particle which enters the acceleration process. For each cycle the energy gain,   E=E, is given by Eq. (10) and, it is independent of the initial energy, E0 . After k cycles the particle’s energy will be E D E0 .1C/k , implying that the number of cycles needed to reach an energy E is equal to kD

ln.E=E0 / : ln.1 C /

(12)

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G. Morlino

Moreover, after each cycle the particle has a probability 1  Pesc to undergo another acceleration cycle. Hence, after k cycles the number of particles with energy greater then E is proportional to

N .> E/ /

1 X

.1  Pesc /i D

iDk

.1  Pesc /k 1 D Pesc Pesc



E E0

ı ;

(13)

esc / . Because both Pesc and  are small quantities, we can where ı D  ln.1P ln.1C/ approximate ı ' Pesc =. Deriving Eq. (13) we get the differential energy spectrum which is a simple power law, f .E/ D dN =dE / E ˛ where the spectral index can be calculated using Eqs. (10) and (11):

˛ D 1 C ı ' 1 C Pesc = D 1 C

3u2 r C2 D : u1  u2 r 1

(14)

The last equality makes use of the compression ratio, r  u1 =u2 , that can be obtained using the flux conservation of mass, momentum, and energy across the shock discontinuity. For a nonrelativistic hydrodynamical shock propagating with a Mach number M D ush =vsound into a gas with adiabatic index g , the very wellknown result is rD

.g C 1/M 2 : .g  1/M 2 C 2

(15)

For very strong shocks (M  1) and an ideal monoatomic gas (g D 5=3), the compression factor reduces to 4, and the predicted particle spectrum becomes f .E/ / E 2 :

(16)

The particle spectrum is often expressed in momentum rather than energy, the relation between the two being f .E/dE D 4 f .p/p 2 dp. Hence, f .E/ / E 2 means f .p/ / p 4 . Such universal spectrum is based on two ingredients: (1) the energy gained in a single acceleration cycle is proportional to the particle’s energy, and (2) the escaping probability is energy independent. Both these properties are direct consequences of the underlying assumption that the particle transport is diffusive, even if the details of the scattering process never enter the calculation. For this reason the first-order Fermi mechanism is also called diffusive shock acceleration (DSA). From a mathematical point of view, the diffusion guarantees the isotropization of the particle distribution both in the upstream and downstream reference frames. If this were not the case, Eq. (10) would not hold anymore. On the other hand, from a physical point of view, the scattering process between particles and magnetic turbulence is the real responsible for the energy transfer between the plasma bulk kinetic energy and the nonthermal particles.

65 High-Energy Cosmic Rays from Supernovae

2.3

1719

Particle Diffusion in Weak Magnetic Turbulence

The assumption of diffusive motion used to derive the universal spectrum in DSA deserves a deeper discussion. The description of charged particle motion in a plasma with generic magnetic turbulence is a very complicated task and represents an active area of research (see Shalchi 2009). Here, we limit our attention to an idealized situation where a particle moves in the presence of a regular magnetic field B0 on top of which there are small perturbations ıB ? B0 (see Fig. 4). In this case the motion can be easily described in the quasi-linear regime, namely, when ıB  B0 . In the absence of perturbations, the particle simply gyrates along B0 with frequency ˝ D qB0 =.mc /. When a perturbation is added such that its wavelength is of the same order of the particle Larmor radius rL D v=˝, the particle “resonates” with the perturbation and its pitch angle  suffers a small deviation (see Blasi 2013,section 3.2 for a complete derivation). If P .k/d k is the wave energy density in the wave number range d k at the resonant wave number k D ˝=v cos. /, the total scattering rate can be written as

sc D 4



kP .k/ B02 =8

 ˝:

(17)

The time required for the particle direction to change by ı  1 is  1= sc , and the mean free path needed to reverse the velocity direction along B0 is mfp D v , so that the spatial diffusion coefficient can be estimated as D.p/ D

1 1 vmfp ' v 2 ˝ 1 3 3



kP .k/ B02 =8

1 D

1 rL v ; 3 F

(18)

  .k/ where F D BkP2 =8

is the normalized energy density per unit logarithmic 0 bandwidth of magnetic perturbations. Notice that in general F  1 for the turbulence in the interstellar medium. If F  1, the diffusion coefficient approaches the so-called Bohm limit, defined as DBohm  rL v=3 which is usually assumed as

Fig. 4 The red line shows the motion of a particle in a large-scale magnetic field, while the green line shows the motion when a small perturbation ıB ? B0 is added on top of B0

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G. Morlino

the smallest possible diffusion coefficient. Beyond F  1 the turbulence becomes strongly nonlinear, and many different phenomena can affect the particle motion other than the resonant scattering.

2.4

Maximum Energy

We saw in the Introduction that the knee structure of the CR spectrum requires protons to be accelerated up to Ep;max  3  1015 eV and that the maximum energy of heavier nuclei should scale with their nuclear charge. The maximum achievable energy depends on the balance between the acceleration time and the minimum between the energy loss time and the age of the accelerator. In the context of a SNR shock, energy losses for hadrons do not represent a strong constraint, while for electrons both synchrotron and inverse Compton process can be fast enough to limit the acceleration process. Here, we focus our attention only on hadrons. We start noticing that even if the particle spectrum predicted by the DSA is completely insensitive to the scattering properties, the acceleration time does depend on scattering in that it determines the time it takes for the particles to get back to the shock. In the assumption of isotropy, the flux of particles that cross the shock from downstream to upstream is nc=4 (see Eq. (8)), which means that the upstream section is filled through a surface ˙ of the shock in one diffusion time upstream with a number of particles n.c=4/ diff;1 ˙ (n is the density of accelerated particles at the shock). This number must equal the total number of particles within a diffusion length upstream L1 D D1 =u1 , namely: nc D1 ˙ diff;1 D n˙ 4 u1

(19)

which implies for the diffusion time upstream diff;1 D 4D1 =.cu1 / . A similar estimate downstream leads to diff;2 D 4D2 =.cu2 /, so that the duration of a full cycle across the shock is cycle D diff;1 C diff;2 . The acceleration time is now tacc D

tcycle 3 D E=E u1  u2



D1 D2 C u1 u2

 8

D1 ; u2sh

(20)

where the last passage is obtained assuming that the upstream turbulence is compressed at the shock by the same compression factor of the plasma ıB2  4ıB1 . The maximum achievable energy is then determined by the condition tacc .Emax / D tSNR . SNR shocks remain efficient accelerators only for a relatively short time. Immediately after the SN explosion, the SN ejecta expand in the ISM with a velocity which is almost constant and highly supersonic. During this phase, the socalled ejecta-dominated phase, acceleration is expected to be effective because the shock speed remains almost constant. After some time, however, the mass of the circumstellar medium that the shock sweeps up becomes comparable to the mass

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of the ejecta, and, from that point on, the remnant enters the Sedov-Taylor phase where the shock velocity starts to decrease. This happens at a time tST D RST =ush , where the shock speed can be determined from the condition .1=2/Mej Vej D ESN and the ejecta velocity is Vej D ush =4, while the radius of the remnant is defined by the condition that the swept-up mass is equal to the mass of the ejecta, namely, 3 .4 =3/ISM RST D Mej . One finds  tST  50

Mej Mˇ

 56 

ESN 1051 erg

 12  nISM  13 yr; cm3

(21)

For typical values of the parameters, the Sedov-Taylor phase starts after only 50–200 years. Now, equating Eqs. (20) and (21) and using the result for the diffusion coefficient from Eq. (18), we get an estimate for the maximum energy:  12  nISM  13 Emax D 5  10 Z F.kmin / eV ; cm3 (22) where kmin D 1=rL .Emax / is the wave number resonant with particles at maximum energy. We notice that more realistic estimates of the maximum energy (e.g., accounting for the fact that the shock speed is slightly decreasing also during the ejecta-dominated phase) usually return somewhat to lower values. A few comments are in order. First of all Eq. (22) has the desired proportionality to the particle charge, Z, which is a property required to explain the knee feature. Nevertheless, the maximum energy of protons could reach Eknee only if F.kmin /  1, namely, the magnetic turbulence at the scale of rL .Emax / must be much larger than the preexisting field, ıB  B0 . Clearly, if this condition were realized, the linear theory used to derive the diffusion coefficient in Sect. 2.3 would not hold anymore. Apart from that, the value of turbulence in the ISM at scales relevant for us is ıB=B0 . 104 (Armstrong et al. 1981); hence, in the absence of any mechanism able to amplify the magnetic turbulence, SNR shocks could accelerate protons only up to the irrelevant energy of a few GeV. One should keep in mind, however, that the magnetic amplification can increase Emax only if it occurs both upstream and downstream of the shock; otherwise, particles could escape either from one side or another. Having a magnetic amplification downstream is quite an easy task; in fact, the shocked plasma is usually highly turbulent, and hydrodynamical instabilities can trigger the amplification, converting a fraction of the turbulent motion into magnetic energy (Giacalone and Jokipii 2007). Conversely, there are no reasons, in general, to assume that the plasma where a SNR expands is highly turbulent to start with. This puzzle has been partially solved by the idea that the same accelerated particles can amplify the magnetic field upstream while they try to diffuse far away from the shock (Bell 1978a, b; Lagage and Cesarsky 1983a, b; Skilling 1975a, b). Nevertheless, this idea in its original form can only produce ıB . B0 , i.e., F . 1, resulting in a maximum energy for protons of 10–100 TeV. Theoretically speaking, 13



B0 G



Mej Mˇ

 16 

ESN 1051 erg

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a big effort is needed to fill up the last decade of energy to reach Eknee . The solution to this conundrum probably resides in the nonlinear effects of DSA, as will be illustrated in Sect. 3. A final comment concerns the parameter values used in Eq. (22), typical for a type Ia SNe, which have Mej  Mˇ and expand in the ISM whose typical density is nISM  0:1  1 cm3 . Remarkably, Emax is only weakly dependent on those parameters; hence, its value does not change significantly when one considers core collapse SNe, which have Mej  10Mˇ and expand inside the diluted bubbles (n  0:01 m3 ) inflated by the wind of the progenitor star.

3

DSA in the Nonlinear Regime

The DSA illustrated in Sect. 2 assumes that the amount of energy transferred from the shock to nonthermal particles is only a negligible fraction of the plasma kinetic motion. There are several arguments supporting the idea that this condition is violated in SNR shocks. When the back reaction of accelerated particles is taken into account, the DSA becomes a nonlinear theory (NLDSA): shock and accelerated particles become a symbiotic self-organizing system and require sophisticated mathematical tools to be studied (see Malkov and Drury 2001,for a review on mathematical aspects of NLDSA). Even more interestingly, NLDSA makes many predictions which seem to be supported by observations (see Amato 2014; Blasi 2013,for a discussion of the observational evidence of NLDSA). Here, we summarize the main features of NLDSA, underlining the aspects which are still under investigation.

3.1

The Dynamical Reaction of Accelerated Particles

As discussed in the Introduction, if SNRs are the main sources of galactic CRs, then a fraction 10 % of their kinetic energy needs to be transferred to CRs. This means that during the acceleration process, the diffusion of CRs ahead of the shock exerts a nonnegligible pressure onto the incoming plasma, slowing it down (in the rest frame of the shock) and creating a precursor (see the right panel of Fig. 3). Indeed, the estimate of 10 % takes into account the entire lifetime of the remnant; hence, the instantaneous efficiency could even be larger, because SNRs likely accelerate CRs efficiently only during a fraction of their life. The CR pressure is expressed as follows: Z 4 pmax 2 PCR D p dppcfCR .p/ : (23) 3 pmin where fCR .p/ is the CR distribution as a function of momentum. The shock acceleration efficiency is usually defined in terms of pressure normalized to the incoming ram pressure of the plasma, namely, CR  PCR =.u2sh /.

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Fig. 5 Particle spectra resulting from a CR-modified shock with Mach number M0 D 10 (solid line), M0 D 50 (dashed line), and M0 D 100 (dotted line). The vertical dashed line is the location of the thermal peak as expected for an ordinary shock with no particle acceleration. The shock velocity is 5000 km s1 and the maximum energy is cpmax D 105 GeV (Blasi et al. 2005)

Now, a correct description of the acceleration process requires that PCR is included in the energy and momentum equations of the shock dynamics. This leads to a compression factor which depends on the location upstream of the shock. Particles with different energies feel now a different compression factor which increases for larger energies (compare left and right panels in Fig. 3). Moreover, when the highest-energy particles escape from the acceleration toward upstream infinity, the shock becomes radiative, thereby inducing an increase of the total compression factor between upstream infinity and downstream. As a consequence the predicted spectrum is no more a straight power law but becomes curved, with a spectral index which changes with energy, being steeper than 2 for lower energies and harder than 2 for the highest energies (see the example in Fig. 5). This prediction is somewhat at odds with observations. Even if a small curvature has been inferred from the synchrotron spectrum of few young SNRs (Reynolds and Ellison 1992), NLDSA predicts total compression ratios 4 and, consequently, spectra much harder than / E 2 (see Eq. (14)). The solution to this inconsistency is found in a second aspect of the nonlinearity, namely, the dynamical reaction of magnetic field. Before discussing this aspect in Sect. 3.3, we give a closer look to the process of magnetic field amplification.

3.2

Magnetic Field Amplification

Magnetic field amplification is probably the most relevant manifestation of NLDSA. Whenever energetic particles stream faster than the Alfvén speed, they generate Alfvén waves with wavelength close to their gyroradius and with the same helicity

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G. Morlino

of the particle motion. This instability is called resonant streaming instability (Achterberg 1983; Bell 1978a; Skilling 1975b) and can allow small perturbation to be amplified by several orders of magnitude. The mechanism, applied to the case of shocks, can be understood as follows. As soon as particles cross the shock discontinuity from downstream toward upstream, in the upstream rest frame, they stream with a velocity Vd D ush and carry a total momentum PCR D nCR mCR Vd , where CR is the CR Lorentz factor. Due to the scattering process, the distribution function is isotropized in the rest frame of the waves on a typical timescale given by the inverse of Eq. (17), and the total momentum reduces to nCR mCR VA (CR does not change because magnetic field does not make work). Hence, the rate of momentum loss is PCR nCR mCR dPCR .Vd  VA / : D D dt

(24)

Suchpmomentum is transferred to Alfvén waves which move at speed VA D B0 = 4 i where i is the density of thermal ions. The transport equation for magnetic pressure in the presence of amplification can be written as VA

dPw ıB 2 D res ; dt 8

(25)

Assuming equilibrium between the momentum lost by CRs and the momentum gained by the waves, we get the growth rate for the waves:

res D

nCR .p > pres / Vd  VA

˝ci : 2 ngas VA

(26)

where ˝ci D eB0 =.mc/ is the cyclotron frequency and nCR .p > pres / accounts only for particles with momentum larger than the resonant one. In case of SNR shocks, Eq. (26) can be specialized as a function of the CR acceleration efficiency, CR . For parameters typical of SNR shocks (CR ' 0:1, ush  5000 km s1 , B0  1 G, vA  10 km s1 ) and using a power-law spectrum fCR .p/ / p 4 , the growth time is growth

1 2  res D '

res 3 CR ˝ci



c ush

2 

VA ush



 res  O.105 s/ ;

(27)

where res is the Lorentz factor of resonant particles and  D ln.pmax =mc/. One can see that the instability grows rapidly. The maximum level is reached right ahead of the shock and can be estimated considering that waves can grow for a maximum time equal to the advection time, tadv D D1 =u2sh . This condition gives F0 .k/ D

CR ush : 2  VA

(28)

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For the same values used above, Eq. (28) predicts F0  1. Nevertheless, one has to keep in mind that this result has been obtained using the quasi-linear theory which assumes ıB=B0  1. When this condition is violated, as predicted by Eq. (28), the excited waves are no longer Alfvén waves and propagate with a speed larger than VA . If one makes the calculation properly, accounting also for the modification that CRs induce on the plasma dispersion relation (see Blasi 2013,section 4.2), the saturation level is considerably reduced, and the final power spectrum at the shock location turns out to be F0 .k/ D



CR c 6  ush

1=2 :

(29)

Using the usual canonical values, one finds F . 1; hence, the effect of efficient CR acceleration is such as to reduce the growth of the waves and limit the value of the self-generated magnetic field to the same order of magnitude as the preexisting large-scale magnetic field. At this point one may wonder how is it possible to reach ıB  B0 required to explain CR up to the knee. At the moment of writing, the answer to this question remains open. What is known is that CRs can excite other kinds of instabilities, beyond the resonant one. Among them the most promising in terms of producing strong amplification is the so-called nonresonant Bell instability (Bell 2004, 2005). This instability results from the j  B0 force that the current due to escaping particles produces onto the plasma (see Fig. 6). The nonresonant instability grows very rapidly for high Mach number shocks. However, the scales that get excited are very small compared with the gyration radii of accelerated particles. Hence, it is not clear if the highest-energy particles can be efficiently scattered. Indeed, hybrid simulations seem to confirm that the nonresonant Bell instability grows much faster than the resonant one for Mach number & 30 and produces F  1 (Caprioli and Spitkovsky 2014; Reville and Bell 2012). The same simulations also show that

Fig. 6 Left. Diagram showing how the nonresonant instability works: the current of CRs escaping from the shock region exerts a force j  ıB onto the plasma, thereby stretching and amplifying the initial magnetic perturbations. Right. Result of nonresonant instability from a hybrid MHD simulation (Reville and Bell 2013). The approximately straight dark lines correspond to the current of escaping particles, while the green helical lines show the amplified magnetic field lines (Courtesy of Brian Reville)

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the instability produces a complex filamentary structure (Caprioli and Spitkovsky 2013; Reville and Bell 2013) which could be able to scatter particles efficiently. Unfortunately, even with the most advanced numerical techniques, it is, at present, difficult to simulate the whole dynamical range needed to describe the complex interplay between large and small scales. Therefore, the question whether particles can reach the knee energy remains open.

3.3

The Dynamical Reaction of the Magnetic Field

We anticipated that the magnetic field amplification upstream can resolve the problem of having very hard spectra in NLDSA. We saw that hard spectra result from a large compression factor which is in turn determined by the increased compressibility of the plasma. If the acceleration is absent or inefficient, the compressibility is determined uniquely by the Mach number of the shock and the adiabatic index of the plasma (see Eq. (15)), while when acceleration is efficient, the compressibility of the plasma increases essentially because the escaping particles are carrying away a nonnegligible fraction of the shock kinetic energy. The magnetic field can reduce the compression factor to values much closer to 4 (typically between 4 and 7) in two different ways. Firstly, if the magnetic field is amplified such that ıB  B0 , the magnetic pressure may easily become larger than the upstream thermal pressure. The compression of the magnetic field component parallel to the shock surface modifies the shock jump conditions in such a way to reduce the compression factor. In other words the magnetic field makes the plasma “stiffer” (Caprioli et al. 2009). The second way to reduce the compression factor is through the damping of magnetic field (McKenzie and Voelk 1982), often called turbulent heating or Alfvén heating. Few mechanisms exist that can damp the magnetic field, the most relevant being the ion-neutral damping (Kulsrud and Cesarsky 1971; Kulsrud and Pearce 1969) (which works only if a nonnegligible fraction of neutral hydrogen is present in the plasma) and the excitation of sound waves (Skilling 1975b). In all cases the final result of the damping is to convert a fraction of the magnetic energy into thermal energy; hence, the plasma temperature increases and the Mach number of the shock is accordingly reduced. It has been shown that the turbulent heating is less efficient than the magnetic compression in reducing the shock compression ratio. Moreover, the former process has the strong inconvenience of reducing the strength of the magnetic field which is so precious to increase the maximum energy. In passing we notice that acoustic waves can also be excited directly by CRs (acoustic instability) (Drury and Falle 1986; Wagner et al. 2007) resulting in the plasma heating without requiring the damping of magnetic waves. The mutual interplay between thermal plasma, magnetic field, and accelerated particles described in this section gives an idea of the complexity of NLDSA.

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A change in the compression factor due to CR pressure affects the spectrum of accelerated particles which in turn determines the level of magnetic field amplification, which also back reacts onto the shock structure.

4

Escaping from the Sources

In the test particle picture of shock acceleration theory, accelerated particles are advected downstream of the shock and will be confined in the interior of the SNR until the shock disappears and the SNR merges into the ISM. At that point particles will be released in the ISM, but they would have lost part of their energy because of the adiabatic expansion of the remnant: hence, the requirements in terms of maximum energy at the source would be even more severe than they already are. Therefore, effective escape from upstream, while the acceleration is still ongoing, is fundamental if high-energy particles must be released in the ISM. The description of the particle escape from a SNR shock has not been completely understood yet, the reason being the uncertainties related to how particles reach the maximum energies (a careful description of the numerous problems involved can be found in Drury 2011). Below we just describe the general framework. Let us assume that the maximum momentum reached at the beginning of the Sedov-Taylor phase, TST , is pmax;0 and that then it drops with time as pmax .t / / .t =TST /ˇ , with ˇ > 0. The energy in the escaping particles of momentum p is 1 2 4 fesc .p/pcp 2 dp D esc .t / u3sh 4 Rsh dt 2

(30)

2 where esc .t / is the fraction of the income flux, 12 u3sh 4 Rsh , that is converted into escaping flux. If the expansion occurs in a homogeneous medium with Rsh / t ˛ and Vsh / t ˛1 , therefore, since dt =dp / t =p, from Eq. (30), we have

fesc .p/ / p 4 t 5˛2 esc .t /:

(31)

It follows that in the Sedov-Taylor phase, where ˛ D 2=5, the spectrum released in the ISM is fesc .p/ / p 4 if esc keeps constant with time. It is worth stressing that this p 4 has nothing to do with the standard result of the DSA in the test particle regime. Neither does it depend on the detailed evolution in time of the maximum momentum. It solely depends on having assumed that particles escape the SNR during the adiabatic phase. Notice also that in realistic calculations of the escape, esc usually decreases with time, leading to a spectrum of escaping particles which is even harder than p 4 . On the other hand, the total spectrum of particles injected into the ISM by an individual SNR is the sum of the escape flux, and the flux of particles released after the shock dissipates. This simple picture does not change qualitatively once the nonlinear effects of particle acceleration are included (Caprioli et al. 2010).

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The Journey to the Earth

After leaving the sources, CRs start their journey through the Galaxy. When they arrive to the Earth, their incoming direction is nearly isotropic and does not mirror the distribution of matter in the Galaxy. This means that CRs diffuse toward us, loosing any information about the sources’ location. The diffusion process that confines CRs in the Galaxy is believed to be due to the scattering by the irregularities in the galactic magnetic field (the same is described in Sect. 2.3), a process which depends on the particle’s energy and charge Z. Therefore, the CR spectrum at Earth results from the combination of injection and propagation. The basic expectation for how the spectrum at Earth relates to that injected by the sources is easily obtained in the so-called leaky box model, sketched in Fig. 7. In this model the Galaxy is described as a cylinder of radius Rd  15 kpc and thickness h  300 pc, while a magnetized halo extents above and below the disk. The height of the magnetized galactic halo is estimated from radio synchrotron emission to be H  3–4 kpc. CRs are confined within this cylinder for a time esc  H 2 =D.E/ with D.E/ the diffusion coefficient in the Galaxy. Let us write the latter as D.E/ D D0 E ı . If CR sources inject a spectrum Ns .E/ / E inj , the spectrum of primary CRs at Earth will be N .E/ 

Ns .E/RSN esc / E inj ı ; 2 Rd2 H

(32)

where RSN is the rate of supernova explosion. Therefore, what we measure at Earth only provides us with the sum of inj and ı. On the other hand, during their propagation in the Galaxy, CRs undergo spallation processes producing secondary elements: some of them, like boron, mostly result from these interactions. The spectrum of secondaries will be given by Nsec .E/  N .E/ Rspall esc / E inj 2ı

(33)

Fig. 7 Schematic representation of the leaky box model: CRs are produced by sources in the galactic disk and diffuse in the magnetic halo above and below the disk, before escaping in the intergalactic medium

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CRDB (http://lpsc.in2p3.fr/crdb)

ACE-CRIS(1997/08-1998/04)

B/C

0.35

ACE-CRIS(1998/01-1999/01)

0.3

ACE-CRIS(2001/05-2003/09)

0.25

ACE-CRIS(2009/03-2010/01)

0.2

AMS01(1998/06)

0.15

ATIC02(2003/01) CREAM-I(2004/12-2005/01

0.1

PAMELA(2006/07-2008/03)

0.05

TRACER06(2006/07) 0 10-1

1

10 Ekn [GeV/n]

102

10

Ulysses-HET(1990/10-1995/07)

Fig. 8 Boron over Carbon ratio as a function of energy per nucleon taken from several experiments (Data have been extracted from the Cosmic Ray Database (http://lpsc.in2p3.fr/crdb/, Maurin et al. 2014))

where Rspall is the rate of spallation reactions. It is clear then that the ratio between the flux of secondaries and primaries at a given energy Nsec .E/=N .E/ / E ı can provide us with a direct probe on the energy dependence of the galactic diffusion coefficient and hence allow us to infer the spectrum injected by the sources. A compilation of available measurements of the boron-to-carbon ratio is shown in Fig. 8 as a function of energy per nucleon. It is immediately apparent from the figure that the error bars on the high-energy data points are rather large and leave a considerable uncertainty on the energy dependence of the diffusion coefficient, being compatible with anything in the interval 0:3 < ı < 0:6. As a consequence, the slope of the CR spectrum at injection is also uncertain in the interval 2:1 < inj < 2:4. Notice that the ratio Nsec .E/=N .E/ also provides the absolute value of the escaping time, because the spallation rates are known, giving esc  5  106 yr at 1 GeV. This rather simple picture of CR transport through the Galaxy is complicated by other phenomena. The most relevant one is probably the possible presence of a large-scale galactic wind which can advect particle far away from the galactic plane (Breitschwerdt et al. 1991; Recchia et al. 2016; Zirakashvili et al. 1996).

6

Observational Evidence

In this section we list the most relevant observations that support the idea that SNRs are indeed the main factories of galactic CRs. To be clear, there are no doubts that SNR shocks are able to accelerate particles as will be clear from below. The question is rather to understand whether SNRs (and specifically which type of SNR and in which evolutionary phase) can explain all, or almost all, the observed CR flux, including particles up to 1017 eV. In this sense the evidence we have gathered until now is only circumstantial.

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(1) Synchrotron emission from electrons Multi-wavelength observations of young SNRs from radio to X-rays clearly show a dominant component of nonthermal emission which can only be explained as due to synchrotron radiation emitted by highly relativistic electrons (E & 1 TeV). Most SNRs have a radio spectral index 0:6 . ˛syn . 0:4, implying that electron energy spectrum resembles a power law / E s with a spectral index 1:8 . s . 2:2 with an average value of 2.0 (Green 2014; Reynoso and Walsh 2015). The SNR morphology also shows that the highest-energy emission occurs predominantly at the forward shock (see Fig. 9). Because DSA does not distinguish between leptons and hadrons, being dependent only on the particle’s rigidity, there is no obvious reason to think that only electrons are accelerated. (2) Gamma radiation Accelerated hadrons can be detected through the decay of neutral pion produced when CR protons (or heavier nuclei) collide with the surrounding gas, i.e., pCR pgas ! 0 !   . Unfortunately, such emission occurs in the same energy range produced by electrons through the inverse Compton scattering of background

Fig. 9 A collection of X-ray images of young SNRs observed with the Chandra telescope. The blue color corresponds to the hard X-ray band (4–6 keV) where the emission is nonthermal. In this energy band, thin filaments are clearly visible all around the remnants. They are interpreted as due to synchrotron emission of high-energy electrons (10 TeV) in a strong amplified magnetic field (B  100–500 G) (Image credit “NASA/CXC”. For each single image: Rutgers/G. CassamChenaï, J. Hughes et al. (SN 1006), SAO/D. Patnaude et al. (Cas A), NCSU/S. Reynolds et al. (Kepler) and CXC/Rutgers/J. Warren & J. Hughes et al. (Tycho))

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photons. Analyzing the multi-wavelength spectrum, several studies have shown that the gamma ray emission from some SNRs is better accounted for by hadronic models. Furthermore, gamma ray emission has been detected also from a few molecular clouds close to SNRs, a fact interpreted as due to CRs escaping from the remnants and colliding with the high-density region of molecular clouds, resulting in a strong production of 0 !   . Specifically in two cases, SNRs IC443 and W44, the gamma ray emission presents a low-energy cutoff around 280 MeV, a feature coinciding with the energy threshold of the 0 decay (Ackermann et al. 2013). (3) Signatures of an amplified magnetic field In the last few years, the Chandra telescope has allowed us to measure the thickness of the X-ray emitting regions in SNRs (blue filaments shown in Fig. 9), showing that in a number of remnants, this is extremely compact, of order of 0.01 pc (see Ballet 2006; Vink 2012,for recent reviews). The simplest interpretation of these thin rims is in terms of synchrotron burn-off: thepemission region is thin because electrons lose energy over a scale that is of order D sync , where D is the diffusion coefficient and sync is their synchrotron lifetime. Assuming Bohm diffusion, this length turns out to be independent of the particle’s energy and requires that the magnetic field responsible for both propagation and losses be in the 100 G range. Another observation that led to infer a large magnetic field is that of fast time variability of the X-ray emission in SNR RX J1713.7-3946 (Uchiyama et al. 2007). Again a field in the 100 G–1 mG range was estimated, interpreting the variability timescale as the timescale for synchrotron losses of the emitting electrons. Such high fields are strongly suggestive of efficient acceleration and of the development of related instabilities. However, it should be mentioned that also alternative interpretations are possible (Bykov et al. 2012; Schure et al. 2012). For example, their origin might be associated to fluid instabilities that are totally unrelated to accelerated particles (Giacalone and Jokipii 2007). Therefore, while the evidence for largely amplified fields seems very strong, it cannot be considered as a definite proof of efficient CR acceleration. Nevertheless, it is worth mentioning that, at least in the case of SN1006, Chandra observation of the pre-shock region suggests that this amplification must be induced in the upstream (Morlino et al. 2010). (4) Compression ratios We have indeed evidence in at least two young SNRs, Tycho and SN 1006 (Cassam-Chenaï et al. 2008; Warren et al. 2005), that the distance between the contact discontinuity and the forward shock is smaller than that predicted by the Rankine-Hugoniot jump conditions that leads to infer a compression ratio of order seven in both cases. This value of the compression ratio is in agreement with the predictions of NLDSA for the case of a shock that is efficiently accelerating particles and in which either efficient turbulent heating takes place in the precursor or the magnetic field is amplified to levels that make its energy density comparable with that of the thermal plasma upstream (see Sect. 3.3).

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(5) Optical lines from the shocks The last evidence we want to comment concerns a recent development of the DSA for shocks propagating in a partially ionized plasma (Morlino et al. 2013). In such conditions neutral hydrogen atoms can produce Balmer emission with a peculiar shape formed by two distinct lines, one narrow and one broad (Chevalier and Raymond 1978; Chevalier et al. 1980) (see also the review by Heng 2010). SNR shocks are collisionless, and when they propagate in a partially ionized medium, only ions are heated up and slowed down, while neutral atoms are unaffected to the first approximation. However, when a velocity difference is established between ions and neutrals in the downstream of the shock, the processes of charge exchange and ionization are activated, and these explain the existence of two distinct lines: the narrow line is emitted by direct excitation of neutral hydrogen after entering the shock front, while the broad line results from the excitation of hot hydrogen population produced by charge exchange of cold hydrogen with hot shocked protons. As a consequence, narrow and broad lines can directly probe the temperature upstream and downstream of the shock, respectively. Now, when the particle acceleration is efficient and a relevant fraction of kinetic energy is converted into relativistic particles, there is a smaller energy reservoir to heat the gas. Hence, the downstream temperature turns out to be smaller than the case without acceleration (see how the thermal peak in Fig. 5 moves toward lower energies as the shock efficiency increases). As a consequence the expected width of the broad Blamer line is smaller when efficient acceleration takes place. It is very intriguing that such reduction of the broad Balmer line width has been inferred in at least two SNRs, namely, RCW 86 and SN 0509-67.5 (Morlino 2014). On the other hand, as shown in Sect. 3.3, the existence of a CR precursor could be responsible for a temperature increase of the upstream plasma resulting in a larger width of the narrow Balmer lines. Indeed, such anomalously larger width has been detected in several SNRs (Sollerman et al. 2003).

7

Conclusions

This chapter provides an overview of the basic physical ingredient behind the idea that SNRs are the main contributors to the galactic CRs. The problem of the origin of CRs is a complex one: what we observe at the Earth results from the convolution of acceleration inside sources, escape from the sources, and propagation in the Galaxy. Each one of these stages consists of a complex and often nonlinear combination of pieces of physics. A connection between SNRs and CRs was already proposed in the 1930s on the basis of a pure energetic argument. Since then a complex theory has been developed where the particles are energized through a stochastic mechanism taking place at the SNR shocks. We have shown that the back reaction of accelerated particles onto the shock dynamics is the essential ingredient that allows particles to reach very high energies (probably up to 1015 eV).

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From the observational point of view, there is enough circumstantial evidence suggesting that SNRs accelerate the bulk of galactic CRs. This evidence is mainly based on the following pieces of observation: (1) X-ray measurements show that SNRs accelerate electrons up to at least tens of TeV. (2) Gamma ray measurements strongly suggest that SNRs accelerate protons up to at least 100 TeV. (3) X-ray spectrum and morphology show that magnetic field amplification is taking place at shocks of young SNRs, with field strength of order few hundred .G. This phenomenon is most easily explained if accelerated particles induce the amplification of the fields through the excitation of plasma instabilities. (4) In selected SNRs there is evidence for anomalous width of the Balmer lines that can be interpreted as the result of efficient CR acceleration at SNR shocks. A deeper look into the physics of particle acceleration will be possible with the upcoming new generation of gamma ray telescopes, most notably the Cherenkov Telescope Array (CTA). The increased sensitivity of CTA is likely to lead to the discovery of a considerable number of other SNRs that are in the process of accelerating CRs in our Galaxy. The high angular resolution will allow us to measure the spectrum of gamma ray emission from different regions of the same SNR so as to achieve a better description of the dependence of the acceleration process upon the environment in which acceleration takes place. We conclude noticing that the CR physics should not be perceived as an isolated field of study, but has strong connection with other parts of astrophysics. In fact CRs are an essential ingredient of the interstellar medium, their energy density being 1 eV cm3 , comparable with the energy density of other components (thermal gas, magnetic field, and turbulent motion). This simple fact suggests that CRs can play a relevant role in many galactic processes including the long-term evolution of the Galaxy. In particular they are the only agent that can penetrate deep inside molecular clouds determining the cloud’s ionization level and its chemical evolution, hence directly affecting the initial condition of the star formation process. CRs can also be responsible for the generation of a galactic wind which subtracts gas from the galactic plane, lowering the total star formation rate and polluting the intergalactic medium with high-metallicity gas. All these aspects represent open fields which promise interesting discoveries in the near future.

8

Cross-References

 Dynamical Evolution and Radiative Processes of Supernova Remnants  Galactic Winds and the Role Played by Massive Stars  High-Energy Gamma Rays from Supernova Remnants  Radio Emission from Supernova Remnants  Ultraviolet and Optical Insights into Supernova Remnant Shocks  X-Ray Emission Properties of Supernova Remnants Acknowledgements The author is grateful to Pasquale Blasi and Elena Amato for the long-term collaboration on this subject and to Sarah Recchia and Marta D’Angelo for reading the manuscript.

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References Achterberg A (1983) Modification of scattering waves and its importance for shock acceleration. A&A 119:274–278 Ackermann M, Ajello M, Allafort A, Baldini L, Ballet J, Barbiellini G, Baring MG, Bastieri D, Bechtol K, Bellazzini R, Blandford RD, Bloom ED, Bonamente E, Borgland AW, Bottacini E, Brandt TJ, Bregeon J, Brigida M, Bruel P, Buehler R, Busetto G, Buson S, Caliandro GA, Cameron RA, Caraveo PA, Casandjian JM, Cecchi C, Çelik Ö, Charles E, Chaty S, Chaves RCG, Chekhtman A, Cheung CC, Chiang J, Chiaro G, Cillis AN, Ciprini S, Claus R, CohenTanugi J, Cominsky LR, Conrad J, Corbel S, Cutini S, D’Ammando F, de Angelis A, de Palma F, Dermer CD, do Couto e Silva E, Drell PS, Drlica-Wagner A, Falletti L, Favuzzi C, Ferrara EC, Franckowiak A, Fukazawa Y, Funk S, Fusco P, Gargano F, Germani S, Giglietto N, Giommi P, Giordano F, Giroletti M, Glanzman T, Godfrey G, Grenier IA, Grondin MH, Grove JE, Guiriec S, Hadasch D, Hanabata Y, Harding AK, Hayashida M, Hayashi K, Hays E, Hewitt JW, Hill AB, Hughes RE, Jackson MS, Jogler T, Jóhannesson G, Johnson AS, Kamae T, Kataoka J, Katsuta J, Knödlseder J, Kuss M, Lande J, Larsson S, Latronico L, Lemoine-Goumard M, Longo F, Loparco F, Lovellette MN, Lubrano P, Madejski GM, Massaro F, Mayer M, Mazziotta MN, McEnery JE, Mehault J, Michelson PF, Mignani RP, Mitthumsiri W, Mizuno T, Moiseev AA, Monzani ME, Morselli A, Moskalenko IV, Murgia S, Nakamori T, Nemmen R, Nuss E, Ohno M, Ohsugi T, Omodei N, Orienti M, Orlando E, Ormes JF, Paneque D, Perkins JS, Pesce-Rollins M, Piron F, Pivato G, Rainò S, Rando R, Razzano M, Razzaque S, Reimer A, Reimer O, Ritz S, Romoli C, Sánchez-Conde M, Schulz A, Sgrò C, Simeon PE, Siskind EJ, Smith DA, Spandre G, Spinelli P, Stecker FW, Strong AW, Suson DJ, Tajima H, Takahashi H, Takahashi T, Tanaka T, Thayer JG, Thayer JB, Thompson DJ, Thorsett SE, Tibaldo L, Tibolla O, Tinivella M, Troja E, Uchiyama Y, Usher TL, Vandenbroucke J, Vasileiou V, Vianello G, Vitale V, Waite AP, Werner M, Winer BL, Wood KS, Wood M, Yamazaki R, Yang Z, Zimmer S (2013) Detection of the characteristic pion-decay signature in supernova remnants. Science 339:807– 811. doi:10.1126/science.1231160. arxiv:1302.3307 Amato E (2014) The origin of galactic cosmic rays. Int J Mod Phys D 23:1430013. doi:10.1142/S0218271814300134. arxiv:1406.7714 Armstrong JW, Cordes JM, Rickett BJ (1981) Density power spectrum in the local interstellar medium. Nature 291:561–564. doi:10.1038/291561a0 Axford WI, Leer E, Skadron G (1977) The acceleration of cosmic rays by shock waves. Int Cosm Ray Conf 11:132–137 Baade W, Zwicky F (1934) Remarks on super-novae and cosmic rays. Phys Rev 46:76–77. doi:10.1103/PhysRev.46.76.2 Ballet J (2006) X-ray synchrotron emission from supernova remnants. Adv Space Res 37:1902– 1908. doi:10.1016/j.asr.2005.03.047. arxiv:astro-ph/0503309 Bell AR (1978a) The acceleration of cosmic rays in shock fronts. I. MNRAS 182:147–156. doi:10.1093/mnras/182.2.147 Bell AR (1978b) The acceleration of cosmic rays in shock fronts. II. MNRAS 182:443–455. doi:10.1093/mnras/182.3.443 Bell AR (2004) Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays. MNRAS 353:550–558. doi:10.1111/j.1365-2966.2004.08097.x Bell AR (2005) The interaction of cosmic rays and magnetized plasma. MNRAS 358:181–187. doi:10.1111/j.1365-2966.2005.08774.x Blandford RD, Ostriker JP (1978) Particle acceleration by astrophysical shocks. ApJL 221:L29– L32. doi:10.1086/182658 Blasi P (2013) The origin of galactic cosmic rays. A&ARv 21:70. doi:10.1007/s00159-013-0070-7. arxiv:1311.7346 Blasi P, Gabici S, Vannoni G (2005) On the role of injection in kinetic approaches to non-linear particle acceleration at non-relativistic shock waves. MNRAS 361:907–918. doi:10.1111/j.1365-2966.2005.09227.x. arxiv:astro-ph/0505351

65 High-Energy Cosmic Rays from Supernovae

1735

Breitschwerdt D, McKenzie JF, Voelk HJ (1991) Galactic winds. I – cosmic ray and wave-driven winds from the Galaxy. A&A 245:79–98 Bykov AM, Ellison DC, Renaud M (2012) Magnetic fields in cosmic particle acceleration sources. SSRev 166:71–95. doi:10.1007/s11214-011-9761-4. arxiv:1105.0130 Caprioli D, Spitkovsky A (2013) Cosmic-ray-induced filamentation instability in collisionless shocks. ApJL 765:L20. doi:10.1088/2041-8205/765/1/L20. arxiv:1211.6765 Caprioli D, Spitkovsky A (2014) Simulations of ion acceleration at non-relativistic shocks. II. Magnetic field amplification. ApJ 794:46. doi:10.1088/0004-637X/794/1/46. arxiv:1401.7679 Caprioli D, Blasi P, Amato E, Vietri M (2009) Dynamical feedback of selfgenerated magnetic fields in cosmic ray modified shocks. MNRAS 395:895–906. doi:10.1111/j.1365-2966.2009.14570.x. arxiv:0807.4261 Caprioli D, Amato E, Blasi P (2010) The contribution of supernova remnants to the galactic cosmic ray spectrum. Astropart Phys 33:160–168. doi:10.1016/j.astropartphys.2010.01.002. arxiv:0912.2964 Cassam-Chenaï G, Hughes JP, Reynoso EM, Badenes C, Moffett D (2008) Morphological evidence for azimuthal variations of the cosmic-ray ion acceleration at the blast wave of SN 1006. ApJ 680:1180–1197. doi:10.1086/588015. arxiv:0803.0805 Chevalier RA, Raymond JC (1978) Optical emission from a fast shock wave – the remnants of Tycho’s supernova and SN 1006. ApJL 225:L27–L30. doi:10.1086/182785 Chevalier RA, Kirshner RP, Raymond JC (1980) The optical emission from a fast shock wave with application to supernova remnants. ApJ 235:186–195. doi:10.1086/157623 Drury LO (2011) Escaping the accelerator: how, when and in what numbers do cosmic rays get out of supernova remnants? MNRAS 415:1807–1814. doi:10.1111/j.1365-2966.2011.18824.x. arxiv:1009.4799 Drury LO, Falle SAEG (1986) On the stability of shocks modified by particle acceleration. MNRAS 223:353. doi:10.1093/mnras/223.2.353 Fermi E (1949) On the origin of the cosmic radiation. Phys Rev 75:1169–1174. doi:10.1103/PhysRev.75.1169 Fermi E (1954) Galactic magnetic fields and the origin of cosmic radiation. ApJ 119:1. doi:10.1086/145789 Giacalone J, Jokipii JR (2007) Magnetic field amplification by shocks in turbulent fluids. ApJL 663:L41–L44. doi:10.1086/519994 Green DA (2014) A catalogue of 294 galactic supernova remnants. Bull Astron Soc India 42:47– 58. arxiv:1409.0637 Heng K (2010) Balmer-dominated shocks: a concise review. PASA 27:23–44. doi:10.1071/AS09057. arxiv:0908.4080 Höorandel JR (2006) A review of experimental results at the knee. J Phys Conf Ser 47:41–50. doi:10.1088/1742-6596/47/1/005. arxiv:astro-ph/0508014 Krymskii GF (1977) A regular mechanism for the acceleration of charged particles on the front of a shock wave. Akademiia Nauk SSSR Doklady 234:1306–1308 Kulsrud RM, Cesarsky CJ (1971) The effectiveness of instabilities for the confinement of high energy cosmic rays in the galactic disk. ApL 8:189 Kulsrud R, Pearce WP (1969) The effect of wave-particle interactions on the propagation of cosmic rays. ApJ 156:445. doi:10.1086/149981 Lagage PO, Cesarsky CJ (1983a) Cosmic-ray shock acceleration in the presence of self-excited waves. A&A 118:223–228 Lagage PO, Cesarsky CJ (1983b) The maximum energy of cosmic rays accelerated by supernova shocks. A&A 125:249–257 Longair MS (1992) High energy astrophysics. Vol.1: particles, photons and their detection. Cambridge University press, Cambridge, UK Malkov MA, Drury LO (2001) Nonlinear theory of diffusive acceleration of particles by shock waves. Rep Prog Phys 64:429–481. doi:10.1088/0034-4885/64/4/201

1736

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Maurin D, Melot F, Taillet R (2014) A database of charged cosmic rays. A&A 569:A32. doi:10.1051/0004-6361/201321344. arxiv:1302.5525 McKenzie JF, Voelk HJ (1982) Non-linear theory of cosmic ray shocks including self-generated Alfven waves. A&A 116:191–200 Morlino G (2014) Using optical lines to study particle acceleration at supernova remnants. Nucl Phys B Proc Suppl 256:56–64. doi:10.1016/j.nuclphysbps.2014.10.006. arxiv:1409.1112 Morlino G, Amato E, Blasi P, Caprioli D (2010) Spatial structure of X-ray filaments in SN 1006. MNRAS 405:L21–L25. doi:10.1111/j.1745-3933.2010.00851.x. arxiv:0912.2972 Morlino G, Blasi P, Bandiera R, Amato E, Caprioli D (2013) Collisionless shocks in a partially ionized medium. III. Efficient cosmic ray acceleration. ApJ 768:148. doi:10.1088/0004-637X/768/2/148. arxiv:1211.6148 Recchia S, Blasi P, Morlino G (2016) Cosmic ray driven galactic winds. ArXiv e-prints, arxiv:1603.06746 Reville B, Bell AR (2012) A filamentation instability for streaming cosmic rays. MNRAS 419:2433–2440. doi:10.1111/j.1365-2966.2011.19892.x. arxiv:1109.5690 Reville B, Bell AR (2013) Universal behaviour of shock precursors in the presence of efficient cosmic ray acceleration. MNRAS 430:2873–2884. doi:10.1093/mnras/stt100. arxiv:1301.3173 Reynolds SP, Ellison DC (1992) Electron acceleration in Tycho’s and Kepler’s supernova remnants – spectral evidence of Fermi shock acceleration. ApJL 399:L75–L78. doi:10.1086/186610 Reynoso EM, Walsh AJ (2015) Radio spectral characteristics of the supernova remnant Puppis A and nearby sources. MNRAS 451:3044–3054. doi:10.1093/mnras/stv1147. arxiv:1506.03801 Schure KM, Bell AR, O’C Drury L, Bykov AM (2012) Diffusive shock acceleration and magnetic field amplification. SSRev 173:491–519. doi:10.1007/s11214-012-9871-7. arxiv:1203.1637 Shalchi A (ed) (2009) Nonlinear cosmic ray diffusion theories. Astrophys Space Sci Libr 362. doi:10.1007/978-3-642-00309-7 Skilling J (1975a) Cosmic ray streaming. I – effect of Alfven waves on particles. MNRAS 172:557– 566. doi:10.1093/mnras/172.3.557 Skilling J (1975b) Cosmic ray streaming. II – effect of particles on Alfven waves. MNRAS 173:245–254. doi:10.1093/mnras/173.2.245 Sollerman J, Ghavamian P, Lundqvist P, Smith RC (2003) High resolution spectroscopy of Balmerdominated shocks in the RCW 86, Kepler and SN 1006 supernova remnants. A&A 407:249– 257. doi:10.1051/0004-6361:20030839. arxiv:astro-ph/0306196 Uchiyama Y, Aharonian FA, Tanaka T, Takahashi T, Maeda Y (2007) Extremely fast acceleration of cosmic rays in a supernova remnant. Nature 449:576–578. doi:10.1038/nature06210 Vink J (2012) Supernova remnants: the X-ray perspective. A&ARv 20:49. doi:10.1007/s00159-011-0049-1. arxiv:1112.0576 Wagner AY, Falle SAEG, Hartquist TW (2007) Two-fluid models of cosmic-ray modified radiative shocks including the effects of an acoustic instability. A&A 463:195–201. doi:10.1051/0004-6361:20066307 Warren JS, Hughes JP, Badenes C, Ghavamian P, McKee CF, Moffett D, Plucinsky PP, Rakowski C, Reynoso E, Slane P (2005) Cosmic-ray acceleration at the forward shock in Tycho’s supernova remnant: evidence from Chandra X-ray observations. ApJ 634:376–389. doi:10.1086/496941. arxiv:astro-ph/0507478 Zirakashvili VN, Breitschwerdt D, Ptuskin VS, Voelk HJ (1996) Magnetohydrodynamic wind driven by cosmic rays in a rotating galaxy. A&A 311:113–126

High-Energy Gamma Rays from Supernova Remnants

66

Stefan Funk

Abstract

Over the past decade, gamma-ray observations of supernova remnants with space-based instruments, such as Astro-rivelatore Gamma a Immagini LEggero (AGILE) and the Fermi-Large Area Telescope (LAT), and ground-based instruments such as the High Energy Stereoscopic System (H.E.S.S.), the Major Atmospheric Gamma-Ray Imaging Cherenkov (MAGIC) telescopes, and the Very Energetic Radiation Imaging Telescope Array System (VERITAS) have significantly advanced our understanding of particle acceleration in the shocks of these highly energetic objects. The number of supernova remnants (SNRs) that are detected in high-energy light has steadily increased – a clear demonstration that shocks are capable of accelerating particles to multi-TeV energies. While the ultimate proof of SNRs as the dominant source of cosmic rays in our Galaxy is still elusive, uncontroversial evidence points to the acceleration of protons in supernova remnant shells. This chapter aims to review the most important results in the gamma-ray study of supernova remnants.

Contents 1 2 3

4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma-Ray Emission from Supernova Remnants: Expectations . . . . . . . . . . . . . . . . . Observations of Supernova Remnants at Gamma-Ray Energies . . . . . . . . . . . . . . . . . . 3.1 High-Energy (MeV-GeV) Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Very-High-Energy (GeV-TeV) Gamma-Ray Observations . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Extension of Spectral Studies with Fermi-LAT Deep into the Sub-100 -MeV Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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S. Funk () ECAP (Erlangen Centre for Astroparticle Physics), University Erlangen-Nürnberg, Erlangen, Germany e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_12

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4.2 4.3

Study of Thermal Line Emission and Hard X-Ray Emission with Astro-H . . . . High Angular Resolution and Population Study at TeV Energies with the Cherenkov Telescope Array (CTA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Supernova remnants (SNRs) are one of the best laboratories in our Galaxy to study particle acceleration in astrophysical objects. They are the prime candidate for providing the majority of the cosmic-ray (CR) flux in our Galaxy, at least up to the “knee,” a distinct spectral feature around 1015 eV. The main phenomenological argument in favor of this hypothesis comes from the fact that the CR production rate in the Galaxy, WP CR , estimated to be (0.3–1) 1041 erg=s, can be generated by SNRs, provided that on the order of 10 % of the kinetic energy of galactic SN explosions is released in CRs (see, e.g., Ginzburg and Syrovatskii 1964). A supporting argument can be made on theoretical grounds; diffusive shock acceleration (DSA) is a process in which charged particles are accelerated at the boundary of the shock every time they cross the shock front and are kept in the shock region by magnetic fields traveling with the shock. Since the escape probability rises with decreasing rigidity (or increasing energy for a fixed magnetic field), DSA provides a power-law distribution of accelerated charged particles. DSA also provides a mechanism to effectively convert the available kinetic energy of bulk motion of the shock to CRs. DSA coupled with the strong amplification of the magnetic field upstream the shock (Bell 2004) is expected to be able to accelerate electrons and protons – the latter up to 1015 eV.

2

Gamma-Ray Emission from Supernova Remnants: Expectations

Observations of synchrotron emission at radio and X-ray energies indicate the presence of ultra-relativistic electrons (up to 100 TeV) for several of the young SNRs. In addition, small filaments and vast variability of synchrotron-emitting knots in the shock region for these objects (e.g., RX J1713.7-3946 (Uchiyama et al. 2003) or Cas AC (Uchiyama and Aharonian 2008)) hint at large magnetic fields present in the shock region (beyond 100 G, i.e., factor of up to 20 times larger than the ambient galactic magnetic field) for several of the young SNRs. These observations do not allow to directly infer the presence of ultra-relativistic protons as well. The acceleration of relativistic protons – the dominant component of the galactic CRs – is harder to observe, since high-energy protons don’t radiate electromagnetic radiation (synchrotron emission, bremsstrahlung) as readily as electrons. The best way of observing high-energy protons is when they interact with interstellar material, producing pions. While the charged pions produce neutrinos that can be (but have not been) detected with neutrino telescopes such as IceCube or ANTARES,

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neutral pions decay into gamma rays. A necessary condition for the observation of gamma rays from SNRs is therefore the presence of “target material” – mostly molecular clouds that allow the protons to undergo hadronic interaction and thereby produce pions that then decay into gamma rays. Gamma rays can also be produced in interactions of ultra-relativistic electrons with photons of the 2.7 K microwave background radiation (CMB). The efficiency of the inverse Compton (IC) scattering is especially high at TeV energies. Generally, even in the case of small electron/proton ratio of particle acceleration, e=p  102 , the contribution of the IC component can dominate over the 0 decay gamma rays, unless the magnetic field in the shell significantly exceeds 10 G and/or the density of the shell exceeds 1 cm3 . Interesting aspects about the particle acceleration in SNRs can be derived from gamma-ray observations: under the assumption that shocks behave uniformly in different objects, the evolution of the gamma-ray spectrum with SNR age allows to test important properties of the DSA process. It can, for example, be expected that the spectrum of high-energy particles accelerated in the shock wave softens (i.e., the ratio between high-energy and low-energy particles becomes smaller) with evolutionary stage. This is borne out from a decreasing acceleration efficiency with a slowing shock and a decreased ability to keep accelerated particles in the shock region due to a dropping magnetic field (see, e.g., Caprioli 2012 for a detailed treatment). Additionally, the escape of protons into the environment of the SNR can be tested. In the case of energy-dependent escape of protons, the spectrum of inside the “old” accelerator can be significantly softer than the spectrum of escaped protons outside the accelerator. Correspondingly, the gamma-ray spectrum from the accelerator will be softer compared to the energy spectrum of gamma rays produced outside the accelerator. Since the diffusion of low-energy protons is significantly slower, the impact of the escape is less important for GeV than for TeV gamma rays.

3

Observations of Supernova Remnants at Gamma-Ray Energies

Already earlier generations of gamma-ray observatories searched for gammaray emission from supernova remnants. Data from the Energetic Gamma Ray Experiment Telescope (EGRET) aboard the Compton Gamma-Ray Observatory in the energy range from 100 MeV to 10 GeV Hartman et al. (1999) were assessed to understand the relationship between unidentified sources at low galactic latitude and SNRs. Esposito et al. (1996), Romero et al. (1999), and Torres et al. (2003) found a statistically significant correlation between the two populations at the 4–5  level and were however not able to firmly and uniquely identify individual SNRs as EGRET sources. The past decade has been the golden age of studying SNRs at very high energies with a large number of new results. Cas A was the first SNR to be detected at very-high-energy (TeV) gamma rays by the HEGRA telescope system (Aharonian et al. 2001). The current generation of ground-based instruments H.E.S.S., MAGIC, and VERITAS significantly advanced the study of SNRs at those

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energies, and firm detections now include at least seven shell-type SNRs: Cas A (Aharonian et al. 2001; Albert et al. 2007; Humensky 2008), Tycho (Acciari et al. 2011), RX J1713.7-3946 (Aharonian et al. 2007), RX J0852-4622 (Vela Junior) (Aharonian et al. 2007), SN 1006 (Acero et al. 2010), RCW 86 (Aharonian et al. 2009; H.E.S.S. Collaboration et al. 2016), and G353.6-0.7 (H.E.S.S. Collaboration et al. 2011). The TeV gamma-ray emission from these objects proves the effective acceleration of CRs – protons and/or electrons – to energies well beyond 10 TeV. At the same time, the origin of gamma-ray emission, and therefore the nature of the accelerated particles, remains controversial in many of the objects (Abdo et al. 2011; Aharonian 2013; Gabici and Aharonian 2014). In the following, the observational data at GeV and at TeV data will be summarized.

3.1

High-Energy (MeV-GeV) Observations

Rather early in the Fermi-LAT mission, it became clear that SNRs where the shock wave is interacting with interstellar material are powerful gamma-ray emitters (Castro and Slane 2010). Strong gamma-ray emission has subsequently been reported from a number of such mid-aged SNRs interacting with molecular clouds – for example, IC 443 (Ackermann et al. 2013), W28 (Hanabata et al. 2014), W30 (Castro and Slane 2010), W44 (Ackermann et al. 2013), and W51C (Abdo et al. 2009; Jogler and Funk 2016) (see Fig. 1) most of which are reported to also emit TeV gamma rays, albeit at a much fainter level (Acciari et al. 2009; Aharonian et al. 2008, 2006; Albert et al. 2007; Humensky 2015). The brightness most likely stems from the rather large density of target material stemming from the interaction of the shock wave with surrounding molecular clouds (up to n D 1000 cm3 , so a factor 1000 higher than typical interstellar values). For IC 443, for W44, and recently also for W51C, a characteristic low-energy cutoff in the energy spectrum (“pion bump”) has been detected by both AGILE and Fermi-LAT Giuliani et al. (2011), Ackermann et al. (2013), Jogler and Funk (2016), and see Fig. 1. This measurement demonstrates that the gamma-ray emission in the GeV band is dominated by 0 decay, demonstrating acceleration of CR protons in the shocks of SNRs – an important step in understanding the origin of galactic cosmic rays. An alternative scenario which assumes no newly accelerated particles, but rather the reacceleration of ambient galactic CRs inside the shock-compressed cloud, is a viable alternative (Uchiyama et al. 2010). The gamma-ray spectra of these (midaged, i.e., > 10;000 years) objects show a high-energy break at around 2 GeV (for W44) and 20 GeV (for IC 443) well short of the knee in the spectrum of the CRs. Whether this high-energy break is related to the age of the SNRs, to Alfven damping in a dense environment (Malkov et al. 2011), to the velocity of scattering centers responsible for the particle diffusion around the shock (Blasi 2013) (this would change the compression factor), or to the effects of escape from the remnant Gabici et al. (2009) is still an open question. In several of these mid-aged remnants interacting with molecular clouds, observations also reveal a flux of gamma rays from regions surrounding the shock region

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E2 dN/dE Flux (ergs cm-2 s-1)

W44

-10

10

IC443 W51C

Cas A

10-11

10-12

RX J1713.7-3946

RX J0852.0-4622

Tycho SNR

10-13 108

109

1010 1011 1012 Photon Energy (eV)

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1014

Fig. 1 (Reproduced from Funk 2015) Typical gamma-ray energy spectra for several of the most prominent SNRs. Young SNRs ( 20 Mˇ SNe. Does this mean that the TNH96 model reproduces observations better than the TWW95 model? This is not so simple as described in the following. The Fe yields for these models are shown in Table 1, as well as a more recent model by Kobayashi et al. (2006, KUN06) described below. Tsujimoto et al. (1995) showed the results of the chemical evolution model using the TNH96 model. Figure 1 in the paper showed the abundance pattern of CCSNe which can be compared with the abundance of the Galactic Pop II metal-poor stars, in which the contributions from SNe Ia are expected to be negligible. They find no overabundance of iron with respect to lighter elements as we could find in the good agreement with the [O/Fe] data. However, in comparing with modern observations of extremely metal-poor (EMP) star abundance (e.g., Cayrel et al. 2004), there are several inconsistencies. For example, the yield ratios [X/Fe] for elements heavier than S were underproduced, i.e., Fe is overproduced with respect to those heavier elements. In a word, neither the TNH96 nor TWW95 models are fully consistent with observations. Or we might say that if we allow uncertainty up to a factor of 2, both models are equally consistent with observations. This was actually all we could say before the advent of new observational data.

3.5

Limitations of the Spherical Models

The problems of the spherical CCSN models became evident as the improvement of observations in determining the abundance of EMP stars with [Fe/H] 20 Mˇ is simply "HN D 0:5. The 56 Ni yield is set to the standard CCSN value 0:07 Mˇ for the normal CCSN models, but to a larger value for the 30 and 40 Mˇ HN models to be consistent with observed HNe (e.g., Nomoto et al. 2013). The results in KUN06 show that the chemical evolutions of most elements are consistent with observations except for some elements described in the next subsection.

3.8

Elements Inconsistent with Observations

3.8.1 Elements from C to Zn Figure 28 in KUN06 shows that their chemical evolution model is quite consistent with observations for most elements. However, the abundances of N, K, Sc, Ti, V, and Cr obtained from their model are inconsistent with observations. The underproduction of N may be related to the rotational mixing in a progenitor (Ekström et al. 2008). As discussed in Tominaga et al. (2007), the underproduction of Sc, Ti, and V are likely improved by considering higher-entropy jets in a hypernova model, though it is not clear yet if such a model can explain the Ti yield. At this moment there is no known explanation for K and Cr. Other ironpeak elements for [Fe/H] < 3 are inconsistent with the chemical evolution model because of the assumption that the Galaxy is well-mixed from the beginning. 3.8.2 Elements Beyond Zn We explained that there are two common ways in determining the mass cut. In either cases, elements heavier than Zn are rarely produced above the mass cut. In the He layer, weak s-process takes place during the stellar evolution. However, this is much less important than the s-process in AGB stars. There are 35 heavy isotopes referred to p-nuclei (Woosley and Howard 1978). During a CCSN explosion, the p-process ( -process) takes place in the shock-temperature range Ts D 1:8  3:3  109 (K) in the O/Ne layer (e.g., Hayakawa et al. 2008). Most of the p-nuclei are produced through the  -process, but it appears that it is not sufficient to provide all the p-nuclei in the Galaxy. Probably what are next important elements beyond Zn are the weak r-process elements, i.e., from Sr to Ru (e.g., François et al. 2007; Honda et al. 2007), that may be produced in the “hot bubbles” mentioned in Sect. 3.5. The hot bubble

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component may come outside with the neutrino wind from a newborn neutron star. The properties of the wind, including the most important parameter the electron mole fraction, cannot be predicted accurately with a 1D explosion calculation without a successful explosion model. This is not only because a full 1D calculation is known to fail. One may consider that by increasing neutrino luminosity somehow such as in Fischer et al. (2010), we may obtain a reasonable SN and the neutrino wind model. Unfortunately Ye is too sensitive to the detail of the explosion. At this moment only the successful explosion model obtained from a firstprinciple calculation is for a ECSN (Kitaura et al. 2006). Therefore, only for ECSNe, the synthesis of the weak r-process elements can be studied reasonably, as done in Wanajo et al. (2011). Interestingly they found that weak r-process elements cannot be ejected in a spherical explosion model, but are successfully ejected in the 2D calculations. This is because the production of weak r-process elements requires low Ye that can be realized only in the matter below the mass cut of a 1D calculation. In the multi-D calculations, on the other hand, tiny amounts of matter can be ejected from a deeper region than the mass cut of a 1D calculation. Although ECSNe can eject weak r-process elements, it is likely that they cannot explain all the amount of such elements in the universe since the rate of ECSNe is expected to be not so high. Therefore it is important to clarify whether normal CCSNe also can eject weak r-process elements or not. Unfortunately for a normal CCSN, what we can do best at this moment is parametric studies as in, e.g., Izutani and Umeda (2010). We need to await the advent of complete multi-D explosion models, or lots of more observations of weak r-process stars, to find any hints through the parametric studies. In a hot bubble, the interesting p process (Fröhlich et al. 2006a, b) may also occur. This process may be a production process of light p-nuclei. It was also once hoped that r-process might also occur in the bubble. These topics, however, may be beyond the scope of this contribution.

4

Conclusions

In this contribution, we have explained how well we can represent nucleosynthesis of CCSNe in spherically symmetric models as well as the limitations of the models. We stressed the importance of the overproduction problem of iron in considering galactic chemical evolution and explained an answer we have reached. We also explained that explosive nucleosynthesis up to Zn is well represented by spherically symmetric normal CCSNe with initial mass M 20 Mˇ and aspherical HNe with M  25 Mˇ and above. Although this explanation provides a consistent view, there is still a different opinion in the literature about the importance of HNe. As explained in the text, the nucleosynthesis of elements heavier than Zn cannot be fully discussed in a spherical explosion model. We need to await successful multidimensional simulations of SNe to fully answer these questions about supernova nucleosynthesis.

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H. Umeda and T. Yoshida

Cross-References

 Nucleosynthesis in Hypernovae Associated with Gamma Ray Bursts Acknowledgements We thank G. Meynet and K. Takahashi for carefully reading this manuscript and giving useful comments.

References Audouze J, Silk J (1995) The first generation of stars: first steps toward chemical evolution of galaxies. ApJ 451:L49 Buras R, Janka H-T, Rampp M, Kifonidis K (2006) Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. II. Models for different progenitor stars. A&A 457:281 Cayrel R, Depagne E, Spite M, Hill V, Spite F, François P, Plez B, Beers T, Primas F, Andersen J, Barbuy B, Bonifacio P, Molaro P, Nordström B (2004) First stars V – abundance patterns from C to Zn and supernova yields in the early galaxy. A&A 416:1117 Colgate SA, White RH (1966) The hydrodynamic behavior of supernova explosions. ApJ 143:626 Ekström S, Meynet G, Chiappini C, Hirschi R, Maeder A (2008) Effects of rotation on the evolution of primordial stars. A&A 489:685 Fischer T, Whitehouse SC, Mezzacappa A, Thielemann FK, Liebendörfer (2010) Protoneutron star evolution and the neutrino-driven wind in general relativistic neutrino radiation hydrodynamics simulations. A&A 517:A80 François P, Depagne E, Hill V, Spite M, Spite F, Plez B, Beers TC, Andersen J, James G, Barbuy B, Cayrel R, Bonifacio P, Molaro P, Nordström B, Primas F (2007) First stars. VIII. Enrichment of the neutron-capture elements in the early galaxy. A&A 476:935 Fröhlich C, Hauser P, Liebendörfer M, Martínez-Pinedo G, Thielemann F-K, Bravo E, Zinner NT, Hix WR, Langanke K, Mezzacappa A, Nomoto K (2006a) Composition of the innermost corecollapse supernova ejecta. ApJ 637:415 Fröhlich C, Martínez-Pinedo G, Liebendörfer M, Thielemann F-K, Bravo E, Hix WR, Langanke K, Zinner NT (2006b) Neutrino-induced nucleosynthesis of A>64 nuclei: the p process. Phys Rev Lett 96:id. 142502 Galama TJ et al (1998) An unusual supernova in the error box of the – ray burst of 25 April 1998. Nature 395:670 Hayakawa T, Iwamoto N, Kajino T, Shizuma T, Umeda H, Nomoto K (2008) Empirical abundance scaling laws and implications for the gamma process in core-collapse supernovae. ApJ 685:1089 Heger A, Woosley SE (2002) The nucleosynthetic signature of population III. ApJ 567:532 Heger A, Woosley SE (2010) Nucleosynthesis and evolution of massive metal-free stars. ApJ 724:341 Hoffman RD, Woosley SE, Fuller GM, Meyer BS (1996) Nucleosynthesis in early supernova winds. II. The role of neutrinos. ApJ 460:478 Honda S, Aoki W, Ishimaru Y, Wanajo S (2007) Neutron-capture elements in the very metal-poor star HD 88609: another star with excesses of light neutron-capture elements. ApJ 666:1189 Iglesias CA, Rogers FJ (1996) Updated OPALopacities. ApJ 464:943 Iwamoto K, Mazzali PA, Nomoto K, Umeda H, Nakamura T, Patat F et al (1998) A hypernova model for the supernova associated with the gamma-ray burst of 25 April 1998. Nature 395:672 Izutani N, Umeda H (2010) Nucleosynthesis in high-entropy hot bubbles of supernovae and abundance patterns of extremely metal-poor stars. ApJ 720:L1 Kitaura FS, Janka H-Th, Hillebrandt W (2006) Explosions of O-Ne-Mg cores, the Crab supernova, and subluminous type II-P supernovae. A&A 450:345

67 Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae

1769

Kobayashi C, Umeda H, Nomoto K, Tominaga N, Ohkubo T (2006) Galactic chemical evolution: Carbon through Zinc. ApJ 653:1145 Kobayashi C, Izutani N, Karakas AI, Yoshida T, Yong D, Umeda H (2011) Evolution of fluorine in the Galaxy with the -process. ApJL 739:L57 Langanke K, Martínez-Pinedo G (2000) Shell-model calculations of stellar weak interaction rates: II. Weak rates for nuclei in the mass range/A=45-65 in supernovae environments. NuPhA 673:481 Liebendörfer M, Mezzacappa A, Thielemann F-K, Messer OEB, Hix WR, Bruenn SW (2001) Probing the gravitational well: No supernova explosion in spherical symmetry with general relativistic Boltzmann neutrino transport. Phys Rev D 63:id. 103004 Limongi M, Chieffi A (2003) Evolution, explosion, and nucleosynthesis of core-collapse supernovae. ApJ 592:404 Maeda K, Mazzali PA, Nomoto K (2006) Optical emission from aspherical supernovae and the hypernova SN 1998bw. ApJ 645:1331 Maeda K et al (2008) Asphericity in supernova explosions fromlate-time spectroscopy. Science 319:1220 Marek A, Janka H-Th (2009) Delayed neutrino-driven supernova explosions aided by the standing accretion-shock instability. ApJ 694:664 McWilliam A, Rich RM (1994) The first detailed abundance analysis of galactic bulge K giants in Baade’s window. ApJS 91:749 McWilliam A, Preston GW, Sneden C, Searle L (1995) Spectroscopic analysis of 33 of the most metal poor stars. II. AJ 109:2757 Müller B, Janka H-Th, Heger A (2012) New two-dimensional models of supernova explosions by the neutrino-heating mechanism: evidence for different instability regimes in collapsing stellar cores. ApJ 761:72 Nomoto K, Hashimoto M (1988) Presupernova evolution of massive stars. Phys Rep 163:13 Nomoto K, Tanaka M, Tominaga N, Maeda K (2010) Hypernovae, gamma-ray bursts, and first stars. New Astron Rev 54:191 Nomoto K, Kobayashi C, Tominaga N (2013) Nucleosynthesis in stars and the chemical enrichment of galaxies. ARA&A 51:457 Ryan SG, Norris JE, Beers TC (1996) Extremely metal-poor stars. VIII. High-resolution, high signal-to-noise ratio analysis of five stars with [Fe/H] 0:5 producing isotopes with mass number A > 64. This makes the innermost regions of CCSNe a candidate production site for light p-process nuclei via the p-process. The spherically symmetric models of Fröhlich et al. (2006a, b) were explicitly neutrino driven with a selfconsistent determination of the mass cut. These models (and the more recent models of Perego et al. 2015) rely on an artificial increase in neutrino heating to produce explosions, which otherwise do not occur in such one-dimensional (1D) models. Pruet et al. (2005) achieved similar results with key neutrino opacities modified to favor a stronger explosion (see Buras et al. 2006,for details of this model). Both Fröhlich et al. (2006a) and Pruet et al. (2005) successfully resolved the common problem of overproduction of neutron-rich nickel and iron isotopes in bomb/piston models and increased Ti, Sc, Cu, and Zn production, overcoming a shortcoming of previous models when compared to metal-poor stars. Recently, Perego et al. (2015) have demonstrated the ability to successfully reproduce 56 Ni yields in SN 1987A by retroactively extending the mass cut to include late-time fallback, but at the cost of underproducing 44 Ti – a direct consequence of the imposed spherical symmetry, since ˛-rich freeze-out occurs most strongly in the innermost ejecta in such stratified models. Ugliano et al. (2012) computed spherically symmetric supernova models for more than 100 progenitor stars using the “lightbulb” approximation, wherein the neutrino transport calculation in and around the newly formed, proto-neutron star is replaced with a prescribed neutrino luminosity. Rather than the expanding chemically distinct spheres of ejecta that emerge from spherically symmetric models, the picture of a supernova that emerges from the observations is one of metal-rich shrapnel tearing though the envelope of the now deceased star. Such evidence for asymmetries in SN 1987A motivated the first multidimensional studies of the propagation of the supernova shock through the star. As a result, for two decades it has been known that Rayleigh-Taylor instabilities originate at the star’s Si/O and (C+O)/He boundaries (Hachisu et al. 1990; Herant and Benz 1992; Kane et al. 2000; Müller et al. 1991; Nagataki et al. 1998); however these instabilities do not mix nickel to sufficiently high velocities to account for observations of Supernova 1987A (see McCray 1993,and

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references therein) and other core-collapse supernovae. The implication is that gross asymmetries must be present in the core and be part of the central engine itself. This has motivated increasingly realistic simulations of the nascent supernova shock’s propagation through the stellar envelope. Kifonidis et al. (2003, 2006) used a parameterized “neutrino lightbulb” to drive 2D explosions. These simulations showed significantly higher velocities than previous models (Hachisu et al. 1990; Herant and Benz 1992; Müller et al. 1991). Hammer et al. (2010) and Wongwathanarat et al. (2013) expanded these studies to three dimensions, starting from the asymmetric parameterized neutrino-driven explosions (with gray neutrino transport, see Scheck et al. 2006). The simulations of Hammer et al. (2010) show that in 3D, metal-rich clumps suffer much less deceleration at the compositional shell interfaces. This results in asymptotic velocities of metal-rich clumps that are twice or thrice those found in 2D models, better matching observations. Wongwathanarat et al. (2013) demonstrated a strong correlation between anisotropic production and distribution of heavy elements created by explosive burning behind the shock and the kick velocity of the neutron star. Late-time 3D supernova simulations by Ellinger et al. (2012) and Young et al. (2008), which extended a spherically symmetric initial explosion model, also reveal dense knots in the ejecta. In fact, the existence of asymmetries, even in the pre-supernova core, has been known for some time (see  Chap. 69, “Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Supernova Mechanism”), though these asymmetries have generally not been followed through core collapse and bounce and into supernova explosions in a consistent fashion. However, Couch and Ott (2013) and Müller and Janka (2015) have shown that artificially imposed but physically reasonable asphericities in the pre-collapse progenitor can qualitatively alter the post-bounce evolution. Couch et al. (2015) have taken this a step further, completing the last few minutes of silicon shell burning in 3D before modeling the collapse and explosion of the star, also in 3D, with approximate neutrino transport. For the nucleosynthesis, the impact of multidimensional fluid flow can be pivotal. The mass cut, formerly the spherical mass coordinate separating matter destined to rejoin the interstellar medium from the matter that will become trapped within the proto-neutron star, becomes an amorphous, potentially discontinuous, boundary. The ability in multidimensions for accretion onto the proto-neutron star to continue after the explosion has begun to grow radically alters the behavior of fallback, with some of the infalling matter joining the ejecta while some is accreted. Despite the fundamentally multidimensional nature of a supernova explosion from its earliest moments, relatively limited work has addressed the impact of multidimensional behavior on the nucleosynthesis. From the handful of investigation that have looked at multidimensional effects on the ejecta, we have learned that significant differences occur in the fraction of ejecta which experiences ˛-rich freeze-out (Maeda et al. 2002; Magkotsios et al. 2010; Nagataki et al. 1998) and that larger ejecta velocities are possible, characterized by metal-rich clumps (Ellinger et al. 2012; Hammer et al. 2010; Kitaura et al. 2006; Wongwathanarat et al. 2013, 2015). In the neutrino-reheating paradigm, neutrino interactions also directly affect the

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matter as it passes near the proto-neutron star, fundamentally altering the chemical composition of the ejecta.

3

New Insights

The combination of a neutrino-driven explosion and multidimensional fluid flow by Pruet et al. (2005) hinted at the importance of departing from stratified 1D simulations. However, despite the profusion of exploding first-principle models with spectral neutrino transport in recent years, very little investigation of CCSN nucleosynthesis from these models has been conducted. This curious deficit can be partially attributed to the prolonged times the supernova models must be evolved in order to fully characterize the ejecta and, therefore, compute the nucleosynthesis. While the central engine plays its role in driving the explosion in perhaps 1–2 s and nucleosynthesis is largely complete within, at most, a few seconds thereafter, the spatial and velocity distribution of the newly made isotopes continues to develop over many minutes as the shock propagates through the rest of the star and matter falls back onto the proto-neutron star. Many CCSN models with complex neutrino transport are stopped less than half a second after the formation of the protoneutron star, even before the final explosion energy is determined, much less the composition, and fate, of much of the ejecta. In contrast, 1D bomb or piston models, with their much lower computational cost, are routinely run to the surface of the star and well beyond. In fact, groups of tens or even hundreds of such models are prepared to serve as input for galactic chemical evolution, a task that is currently unimaginable for 3D CCSN models with realistic neutrino transport. Another advantage of the bomb/piston models is that they routinely use extensive nuclear networks, with as many as 2000 species (Rauscher et al. 2002). In contrast, at best, self-consistent models of the CCSN central engine utilize an ˛-network (composed of 13 nuclear species of even and equal neutron and proton numbers from helium to nickel) while separately tracking the neutronization. To compute more complete nucleosynthesis, post-processing calculations are performed based on temperature, density, and neutrino exposure histories for individual mass elements from the supernova model. Performing post-processing nucleosynthesis calculations based on one-dimensional models is relatively straightforward, since most one-dimensional simulations are Lagrangian. Thus the needed temporal histories of temperature and density are simply those of the individual Lagrangian mass elements. However, in multidimensions, non-smooth fluid motions result in highly tangled Lagrangian grids. As a result, Eulerian hydrodynamics, where the discretization occurs in space rather than mass, is used to perform most multidimensional stellar astrophysics simulations. (The exceptions being calculations using Smoothed Particle Hydrodynamics methods.) Because Eulerian codes use spatial discretization, the Lagrangian thermodynamic histories that are a natural result in a Lagrangian code are unavailable. Instead passive tracer particles are commonly employed. The primary limitations in a post-processing approach are the accuracy

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of the energy generation rate provided by the approximation included within the hydrodynamics as well as the underestimate of the effects of mixing. Nucleosynthesis studies of electron-capture supernovae (ECSNe), which arise from the collapse of oxygen-neon cores in Super Asymptotic Giant Branch (AGB) stars, are more mature, as these explosions are triggered almost immediately and therefore complete more rapidly than in Fe-core SNe. Unlike all but the lightest of Fe-core SNe, successful explosions can be obtained for these stars even in 1D simulations (see Supernovae from Super AGB Stars (8–12 Msun)). Multidimensional investigations of ECSN by Janka et al. (2008) and Kitaura et al. (2006) revealed weak explosions (0.1 B) and less than 0.02 Mˇ of ejecta (. 0:01 Mˇ of 56 Ni). ECSN nucleosynthesis studies (Wanajo et al. 2009, 2011, 2013a, b) based on post-processing of tracer particles from these supernova simulations find only modest impact from multidimensional effects, which is unsurprising given the successful 1D explosions. In these axisymmetric simulations, the authors describe a small amount of neutron-rich matter being dredged up from near the proto-neutron star during the early stages of the explosion, a phenomenon not seen in similar 1D simulations. As a result, the models of Wanajo et al. (2011) are characterized by lower minimum values of Ye , ultimately enhancing the production of As, Se, Br, Kr, Rb, Sr, and Y relative to that of spherically symmetric simulations, but leaving the ejected masses of nickel and other iron-group elements unaffected. However isotopic variations in these elements are seen, particularly the enhanced production of the trace, but interesting, species 48 Ca (Wanajo et al. 2013a) and 60 Fe (Wanajo et al. 2013b). Multidimensional Fe-core CCSN models also exhibit convective overturn near the outer proto-neutron star layers, potentially with even greater affect on the nucleosynthesis and, given the necessity of multidimensionality to engender these explosions, occurs merely as a subset of other multidimensional effects. Consequently, the lessons learned from ECSN nucleosynthesis studies, with respect to multidimensional effects, provide only modest insight into the CCSN problem. Recently, Bruenn et al. (2016) published a set of four axisymmetric models using self-consistent spectral flux-limited diffusion neutrino transport for 12, 15, 20, and 25 Mˇ progenitors from Woosley and Heger (2007). These models were run for times greater than 1 s after bounce, the longest elapsed times of any models of this sophistication, in an effort to achieve a saturated explosion energy. The three lower mass models achieved relatively saturated explosion energies (growth rates less than 0.2 B/s) near the observed values of 1 B, while the 25 Mˇ model, with an explosion energy of 0.7 B, is still exhibiting strong growth in the explosion energy (more than 0.05 B in the final 100 ms) even 1.4 s after bounce. The long running times of these models also allows much more complete investigation of CCSN nucleosynthesis than is generally possible for such sophisticated models. Comprehensive analysis of the nucleosynthesis from these models is in preparation (Harris et al. 2016a), as well as an analysis of the uncertainties in post-processing nucleosynthesis based on tracer particles (Harris et al. 2016b). While there is some uncertainty in the degree to which the nucleosynthesis predictions of axisymmetric models will replicate three-dimensional models (and, ultimately, three-dimensional

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15

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reality), we present these results as a foreshadowing of the differences that the replacement of parameterized, spherically symmetric models with self-consistent multidimensional models can produce. Figure 1 shows the spatial distribution of four distinct isotopes at the end of a two-dimensional simulation of the explosion of a 12 Mˇ star, as computed by the small ˛-network that is used within the model. The progenitor was computed by Woosley and Heger (2007), who also computed a piston-driven parameterized supernova for the same star. The white dots mark the location of the tracer particles. The morphology of the nuclear products reflects the hydrodynamics of the model, which is dominated by two polar outflows and an equatorial accretion stream, potentially the consequence of the assumption of axisymmetry. The composition of the outflows is dominated by the products of ˛-rich freeze-out, portrayed here by 56 Ni and 44 Ti, while the equatorial regions are dominated by 28 Si and 16 O, partially burned matter from the progenitor’s oxygen shell. The location of the supernova shock can be deduced by noting the deviation of these tracers from their originally radial distribution. From this, it is clear that the oblate shock has diverted the inflow of matter from polar latitudes toward the equator. The shape of the shock reveals that the velocity of the shock towards the poles is nearly twice that in the equatorial

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Z Axis (1000 km) Fig. 2 Mapping the mass cut. The fate of mass elements 1.336 s after bounce as a function of their original location within the 12 Mˇ progenitor star. Gray filled circles are matter within the neutron star, gray open circles represent matter bound to the neutron star. The colored circles are unbound matter, with the color representing the highest temperature reached by that parcel. Filled colored circles have positive radial velocity, open colored circles, though unbound, have negative radial velocity. Modified illustration originally published in Hix et al. (2014) (Published with permission of © W. R. Hix and collaborators, under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike License)

regions. With the products of ˛-rich freeze-out moving outward more rapidly than the intermediate mass elements, we see a clear departure from the expectations of spherically symmetric models, where the stratification of elements is maintained by the explosion, causing the products of ˛-rich freeze-out to remain near the mass cut. Analysis detailed in Bruenn et al. (2016) indicates that at this point, it is silicon-rich matter that is continuing to accrete onto the proto-neutron star. While there remains the potential for the outflowing matter to be slowed and even stopped by continued hydrodynamic interaction, especially as the reverse shock forms as a result of the deceleration of the ejecta as it lifts the stellar envelope, it is the slower-moving intermediate mass elements that are more likely to be impacted. Another clear departure from spherical symmetry can be seen in the fate of the parcels of matter. As Lagrangian elements, the paths of the tracer particles can be retraced to their origin in the progenitor. We can therefore map the mass cut in this multidimensional model in a way that is impossible from the Eulerian grid alone. Figure 2 is just such a map, for the same 12 Mˇ model. In Fig. 2, the particles are placed at their original locations within the star, but color coded and shaped by their fate at the end of the simulation. Gray-colored particles are bound to the protoneutron star, either already residing there (filled circles) or presently infalling toward the proto-neutron star (open circles). Colored particles are presently gravitationally unbound from the proto-neutron star, making them candidates for ejection, with the color indicating the peak temperature experienced by the particle, a proxy for

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the nucleosynthesis processes that the particle has experienced. The filled colored circles are moving outward, having positive radial velocities. The open colored circles, while the sum of their kinetic, thermal, and gravitational potential energy are positive, are moving inward with negative radial velocities. Their ultimate fate must be considered uncertain. To provide context, the purple lines in Fig. 2 mark compositional interfaces in the progenitor star, the outer edges of the iron core (solid line), and the silicon shell (dotted line), where the composition transitions from more than 80 % silicon and sulfur, by mass, to predominately oxygen, with less than 10 % silicon. This silicon-oxygen interface, with a characteristic entropy of 4 kB per baryon, is the location selected for the mass cut in the parameterized model of Woosley and Heger (2007), marked by the dashed pink line. For comparison, the solid pink line marks the spherical mass coordinate equal to the baryon mass of the proto-neutron star in this simulation, equivalent to the mass cut if this model had maintained spherical symmetry. The smaller radius of this “2D mass cut” indicates that the mass of the neutron star resulting from this 2D simulation is less than that of its 1D counterpart. Beyond this, there are clearly a significant number of ejecta particles below the 1D mass cut, colored red as an indication of the high temperatures they achieved as they plunged near the proto-neutron star before being swept into the ejecta. These parcels of matter began the simulation as part of the silicon shell and yet seem destined to be part of the ejecta. There are an equal number of gray particles above the solid pink line, including parts of the oxygen shell. The escape of part of the original silicon layer while part of the oxygen layer that started above it is captured by the proto-neutron star is a result quite against the intuition developed from spherically symmetric models. Our mental image of the mass cut clearly must be revised in view of the geometrically complex, disjoint nature of the ejecta revealed in multidimensional simulations. While there have been very few three-dimensional models of sufficient sophistication and sufficiently long enough elapsed time to explore the mass cut, those few do not suggest a return to sphericity in 3D (see, e.g., Ellinger et al. 2012). The cumulative effects of the neutrino-driven, multidimensional fluid flows on the nucleosynthesis are highlighted in Fig. 3. Here the post-processing nucleosynthesis calculated by Harris et al. (2016a) for the 12 Mˇ model of Bruenn et al. (2016) is compared to that of the parameterized explosion for the same progenitor calculated by Woosley and Heger (2007). Several general trends are visible, the results of the neutrino exposure and increased diversity of thermodynamic conditions that occur as a side effect of multidimensional fluid flow in these models. First, as is hinted at by the smaller radius of the 2D spherical mass cut in Fig. 2, more of the star is ejected in Bruenn et al. (2016) than in Woosley and Heger (2007), leading to a mild enhancement in the production of the dominant species from O through the intermediate mass elements. Second, as a result of the general increase in the proton richness of the ejecta that is bathed in the neutrino field, there is a significant increase (as large as two orders in magnitude) for production of species with N  Z from S to Ni. Third, despite the general trend toward more proton-rich ejecta, there is also significant enhancement in the production of selected very neutron-rich species, for example, 48 Ca, 50 Ti; 54 Cr; 58 Fe; 64 Ni; 70 Zn; 76 Ge, and

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82

Se. These are produced in a small amount of matter that undergoes a neutronrich .Ye < 0:45/, but ˛-poor, freeze-out from NSE in matter dredged up from the proto-neutron star, a mechanism similar to that discussed by Wanajo et al. (2013a) for ECSN. Finally, there is significant enhancement in the production of a wide range of species from A D 60 to A D 90, including the p-process species 88 Sr, 90 Zr, and 92 Mo. While production of these species in the proton-rich, neutrinodriven wind in the models of Fröhlich et al. (2006b) led to the discovery of the p-process, that does not seem to be the cause here, as continued accretion onto the proto-neutron star has effectively suppressed the neutrino-driven wind to this point in the simulations, more than 1.3 s after bounce. Rather the production of these heavier species results from ˛-rich freeze-out in moderately neutron-rich matter .0:45 < Ye < 0:48/, more akin to the results of Woosley et al. (1994), but at lower entropies. Clearly, the wider range of thermodynamic conditions and neutrino exposures provided by these neutrino-driven, multidimensional models has far-ranging consequences for CCSN nucleosynthesis.

4

Limitations

While tracer particles are an essential tool for calculating realistic nucleosynthesis via post-processing for models, like those discussed in Sect. 3, that include only limited nucleosynthesis approximations self-consistently, they are not a panacea. As a passive, purely Lagrangian representation of the matter, they do not replicate the mixing that is seen in the gridded models. While the Eulerian grid overestimates

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Fig. 4 The neutronization distribution of the unbound matter in a core-collapse supernovae simulations for 12 and 15 Mˇ stars. The white histogram reflects the matter as described by the Eulerian computational grid. The blue histogram reflects the matter as described by the tracer particle position at the end of the simulation. The red histogram reflects the matter as described by the post-processing nucleosynthesis

the effects of mixing, assuming that macroscopic mixing, at the kilometer scale of the grid, is equivalent to microscopic mixing, at the scale of the collisional mean free path of the nuclei, the tracer particles ignore mixing completely. From the nucleosynthesis perspective, where only microscopic mixing impacts the reactive flow, reality will be intermediate between the course Eulerian view of the grid and the Lagrangian view of the tracers. Figure 4 shows several interesting effects of the contrasting grids. The white blocks in Fig. 4 portray the distribution of electron fraction, Ye , at the end of the simulation, as integrated over the Eulerian grid. The blue blocks portray the same integration over the tracer particles, using the Ye values interpolated to the tracer particle positions from the Eulerian grid at the end of the simulation. The red blocks

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display the electron fraction distribution as evolved by the post-processing nucleosynthesis calculation. For tracers that reach temperatures sufficient for nuclear statistical equilibrium (NSE) to be established, typically 6 GK for explosive conditions like those in CCSN, the value of Ye , interpolated to the tracer position from the grid at the time when the particles temperature drops below the NSE threshold, is subsequently evolved within the nuclear reaction network. For tracers that never reach the NSE temperature threshold, the evolution within the reaction network follows from the initial value of Ye . The post-processed distribution shows a much larger amount of neutron-rich (Ye < 0:5) matter. Following these tracer’s spatial evolution, we find matter which was swept into the ejecta from the vicinity of the proto-neutron star, similar to that found by Wanajo et al. (2009, 2011) for ECSN. In the CCSN case, as this matter is ejected at high speed from the central regions, it catches up with slower-moving ejecta above it and becomes mixed with that more neutron-poor (Ye  0:5) matter. Note that if the nucleosynthesis is complete before this (macroscopic) mixing occurs, which seems to be the case in this model, the result is a small admixture of neutron-rich nuclei within otherwise neutron-poor matter. In contrast, if the mixing occurs before the nucleosynthesis is complete, all trace of these neutron-rich species is removed. Correctly deducing the relative timing of the competing effects of compositional mixing and thermonuclear transmutation is a significant challenge for post-processing studies using tracer particles. Another limitation of tracer particle-based post-processing is relatively poor resolution of this Lagrangian grid. In the simulations of Bruenn et al. (2016), which were launched in 2012, tracer masses of 104 Mˇ were used, a degree of tracer resolution similar to prior studies (Nagataki et al. 1997; Nishimura et al. 2006; Pruet et al. 2005). Subsequently, Nishimura et al. (2015) employed a tracer resolution 10 times higher in their study of the potential for the r-process in magnetically driven CCSN. The “medium” resolution case of Nishimura et al. (2015) is similar to Bruenn et al. (2016). Comparing the blue and white histograms in Fig. 4 reveals that the tracers, with their fixed mass resolution represented by the dashed lines in Fig. 4, are unable to resolve the most proton-rich ejecta. While this contribution is small in mass, it remains potentially interesting for the production of less abundant species (potentially including the p-process). Even the highest resolution of Nishimura et al. (2015) would not be sufficient to resolve this material; an additional factor of 100 or more in the tracer resolution would be needed to trace the history of this material. This incapability of the tracer particles to resolve the proton-rich wing of the distribution in Fig. 4 originates in the fixed mass of the particles and the challenge that creates on the tracer density in regions with low mass density. Effectively, the chances of a tracer sampling a high-density region are much larger than a neighboring low-density region. This has a direct impact on the nucleosynthesis, revealed in Fig. 5, because some of the most interesting nucleosynthesis process in CCSN occur in these high-entropy and relatively low-density regions. Beyond the failure to resolve the small amount of very proton-rich matter, this tracer resolution problem has other, larger consequences because the ˛-rich freeze-out is also a result

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Fig. 5 The composition as a function of atomic mass for the B12-WH07 model of Bruenn et al. (2016). The black line displays the composition as computed by the ˛-network included within CHIMERA, the red line displays the composition computed with the same ˛-network in postprocessing using tracer particle data. The blue line displays the composition when the transition from NSE to post-processing occurs at 8 GK, instead of 5.5 GK. The green line displays the composition computed in post-processing with a more realistic, 150 species, network (Modified illustration originally published in Harris et al. (2014), Published with permission of © J. A. Harris and collaborators, under the terms of the Creative Commons Attribution-NonCommercialShareAlike License)

of the ejection of high-entropy, low-density matter. Comparison of the black line in Fig. 5, the composition computed using the ˛-network built into the CCSN models of Bruenn et al. (2016), and the red line in Fig. 5, the composition calculated via post-processing using the same ˛-network and the same rules for transitioning matter from NSE into the network as are used within the model, reveals a significant under-prediction by the post-processing of the species that result from ˛-rich freezeout. Most notable is 44 Ti, which differs by an order of magnitude, though 48 Cr and 52 Fe are also underproduced while 4 He and 60 Zn are slightly overproduced. Examination of Fig. 1 shows the relative paucity of tracer particles in the regions with large number densities of 44 Ti, providing visual confirmation of difficulty in resolving these low-density regions with Lagrangian particles. The models of Bruenn et al. (2016) transition material into (or out of) NSE when the temperature in a zone rises above (drops below) 5.5 GK, an approach taken by many models of the CCSN central engine based on a comparison of the silicon burning timescale to the typical hydrodynamic timescale in the models. However, for the rapidly changing conditions in expanding CCSN matter, NSE has been shown to break down at higher temperatures (Hix and Thielemann 1999; Meyer et al. 1998). The assumption of NSE until 5.5 GK delays the onset of ˛-rich freeze-out and therefore limits its ˛ richness. This is demonstrated in Fig. 5 by a comparison of the blue line, where the transition from NSE to post-processing with the ˛-network occurs at 8 GK, and red line, where this transition occurs at 5.5 GK. The abundances of 4 He, 44 Ti, 48 Cr, and 60 Zn are all enhanced by the earlier transition into the network, with 44 Ti increasing by a factor of 3.

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Both of these effects, the tracer resolution and the NSE transition temperature, have their largest impact on 44 Ti, a species that is also well known to be overproduced by the ˛-network due to the nuclear flow from A D 40 to A D 56 occurring through reactions not included in the ˛-network. The extent of this over-prediction is illustrated by the green line in Fig. 5, which uses the same NSE transition as the blue line, but for a much more complete network of 150 species. Of course, the ˛-network neglects many of these 150 isotopes; thus, it cannot predict their abundances, though these tend to be less abundant species. Nevertheless, the ˛network predictions for species from A D 4 up to A D 32, as well as A D 56, are in excellent agreement with the more realistic network. However, small discrepancies appear for A D 36 and A D 40 and overproduction as large as an order of magnitude plague the species from A D 44 to A D 52, while the production of species with A > 56 is suppressed. As we seek to make predictions of the production of these fruits of the ˛-rich freeze-out from our models, it is important to remember that the “positive” effects of improved NSE transition temperature and tracer resolutions are comparable to the more widely known “negative” impact of more realistic networks.

5

What Further Is Needed

While the iron-core-collapse investigations of Harris et al. (2016a, b) and the oxygen-neon-core-collapse investigations of Wanajo et al. (2013a, b), based on sophisticated neutrino radiation-hydrodynamic simulations, represent landmarks in our improving understanding of the nucleosynthesis that occurs in these supernovae, more work remains to be done on two fronts. First, while the sophisticated models on which Harris et al. (2016a, b) and Wanajo et al. (2013a, b) rely represent a tremendous improvement over purely hydrodynamic bomb/piston supernova models, this fidelity comes at tremendous computational cost. Especially if we wish to investigate sophisticated 3D CCSN models, we as a community can only afford a handful of models, compared to the hundreds of bomb or piston CCSN models that serve as input to galactic chemical evolution calculations. The hope would be, with the nucleosynthesis results from detailed 3D models in hand for comparison, models of intermediate complexity can be found that can reasonably replicate the nucleosynthesis of the more sophisticated models at a substantial savings in computational cost. Whether such a combination of limited neutrino transport approximation and dimensionality, the two principle drivers of computational cost for CCSN simulations, exists (or can be tuned) is an open question. Second, as demonstrated in Sect. 4, the reliance on post-processing to address many of the species of interest in CCSN is a significant weakness. For the innermost supernova ejecta, the nuclear energy released by the recombination of ˛-particles into iron (and neighboring) nuclei (1018 erg=g/ is comparable to the change in the thermal energy of this gas due to expansion during the same time; thus, there is significant feedback between the rate of this nuclear recombination and the temperature evolution that is driving the recombination. The ˛-richness of the matter, and thus the abundance of species like 44 Ti, 57 Fe, 58 Ni,

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and 60 Zn, therefore depends critically on this feedback. As a result, Magkotsios et al. (2010) found strong differences in the ˛-richness between different supernova models. In core-collapse supernovae, this ˛-rich freeze-out happens in the bath of neutrinos streaming from the core, fundamentally altering its neutronization, which in turn affects the path of the nuclear recombination. Clearly, supernova simulations which follow the composition with only an ˛-network are limited in their ability to calculate realistic nucleosynthesis, and these limitations cannot be completely redressed by post-processing with a more complete nuclear networks. A desire to better account for mixing of material while the nucleosynthesis is still underway further motivates the use of more complete nuclear networks within sophisticated neutrino radiation-hydrodynamic simulations. Finally, the much finer mass resolution of the Eulerian grid for the low-density regions, where the ˛-rich freeze-out occurs, favors replacing post-processing with a realistic network included within the supernova model. While the use of larger networks, with 150–200 species to capture the energetically significant reaction processes, adds significantly to the computational cost, the added cost is comparable to the cost of the neutrino transport calculations already performed. Thus the total cost is a small multiple of the cost of current models, making the use of moderate-sized networks an achievable goal in the near future. We have axisymmetric test simulations underway, which we hope to present within a year or two, and the rest of the community is likely to follow.

6

Conclusions

The near future will see great strides toward incorporating the lessons learned over the past two decades about the nature of the central core-collapse supernova engine into our modeling of the nucleosynthesis of these extraordinary events. Progress may be slow at first, as we build our database of these very expensive simulations and seek lesser approximations that still capture the essential impact of the neutrinodriven, multidimensional nature of the core-collapse supernova’s central engine. Nonetheless, we can, within this decade, anticipate an improved understanding of the means by which a dying massive star is transformed into the nuclear seed stocks for the next generation of stars and planets, an understanding that finally takes into full account the myriad of physics that contributes to these spectacular explosions.

7

Cross-References

 Electron Capture Supernovae from Super Asymptotic Giant Branch Stars  Making the Heaviest Elements in a Rare Class of Supernovae  Neutrino-Driven Explosions  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Spectra of Supernovae During the Photospheric Phase  Spectra of Supernovae in the Nebular Phase

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 Supernovae from Massive Stars  Supernova Remnants as Clues to Their Progenitors  X-Ray Emission Properties of Supernova Remnants Acknowledgements This research was supported by the US Department of Energy Office of Nuclear Physics, the NASA Astrophysics Theory Program (NNH11AQ72I), and the National Science Foundation Theoretical Physics Program (PHY-1516197). The simulations here were performed via NSF TeraGrid resources provided by the National Institute for Computational Sciences under grant number TG-MCA08X010 and resources of the National Energy Research Scientific Computing Center.

References Aufderheide MB, Baron E, Thielemann FK (1991) Shock waves and nucleosynthesis in type II supernovae. ApJ 370:630–642 Bruenn SW, Lentz EJ, Hix WR, Mezzacappa A, Harris JA, Messer OEB, Endeve E, Blondin JM, Chertkow MA, Marronetti P (2016) Chimera: a massively parallel, multi-physics code for corecollapse supernova simulations. ApJ 818:123 Buras R, Rampp M, Janka HT, Kifonidis K (2006) Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 Mˇ star. A&A 447:1049–1092. doi:10.1051/0004-6361:20053783, astro-ph/0507135 Colgate SA, White RH (1966) The hydrodynamic behavior of supernovae explosions. ApJ 143:626 Couch SM, Ott CD (2013) Revival of the Stalled Core-collapse supernova shock triggered by precollapse asphericity in the progenitor star. ApJ 778:L7. doi:10.1088/2041-8205/778/1/L7, 1309.2632 Couch SM, Chatzopoulos E, Arnett WD, Timmes FX (2015) The Three-dimensional evolution to core collapse of a massive star. ApJ 808:L21. doi:10.1088/2041-8205/808/1/L21, 1503.02199 Elekes Z, Fulop Z, Gyurky G, Kertesz Z, Kiss G. G, Simon A, Somorjai E, Torok Z, Frei Z, Vinko J, Keresturi A & Szabo R (eds) (2014) Proceedings of nuclei in the Cosmos XIII, SISSA Proceedings of Science Ellinger CI, Young PA, Fryer CL, Rockefeller G (2012) A case study of smallscale structure formation in three-dimensional supernova simulations. ApJ 755:160. doi:10.1088/0004-637X/755/2/160, 1206.1834 Fassia A, Meikle WPS (1999) 56 Ni dredge-up in Supernova 1987A. MNRAS 302:314–320. doi:10.1046/j.1365-8711.1999.02127.x, astro-ph/9809244 Fröhlich C, Hauser P, Liebendörfer M, Martínez-Pinedo G, Thielemann FK, Bravo E, Zinner NT, Hix WR, Langanke K, Mezzacappa A, Nomoto K (2006a) Composition of the innermost supernova ejecta. ApJ 637:415–426. doi:10.1086/498224, astro-ph/0410208 Fröhlich C, Martínez-Pinedo G, Liebendörfer M, Thielemann FK, Bravo E, Hix WR, Langanke K, Zinner NT (2006b) Neutrino-induced nucleosynthesis of A> 64 nuclei: the nu p-process. Phys Rev Lett 96(14):142502. doi:10.1103/PhysRevLett.96.142502, astro-ph/0511376 Fryer C, Young P, Bennet ME, Diehl S, Herwig F, Hirschi R, Hungerford A, Pignatari M, Magkotsios G, Rockefeller G, Timmes FX (2008) Nucleosynthesis from supernovae as a function of explosion energy from NuGrid. In: Schatz H, Austin S, Beers T, Brown A, Brown E, Cyburt R, Lynch W, Zegers R (eds) Proceedings of nuclei in the cosmos X, SISSA proceedings of science, p 101 Hachisu I, Matsuda T, Nomoto K, Shigeyama T (1990) Nonlinear growth of Rayleigh-Taylor instabilities and mixing in SN 1987A. ApJ 358:L57–LL61 Hammer NJ, Janka HT, Müller E (2010) Three-dimensional simulations of mixing instabilities in supernova explosions. ApJ 714:1371–1385. doi:10.1088/0004-637X/714/2/1371, 0908.3474

1788

W.R. Hix and J.A. Harris

Hanuschik RW, Thimm G, Dachs J (1988) H-alpha fine-structure in SN 1987A within the first 111 days. MNRAS 234:41P–49P Harris JA, Hix WR, Chertkow MA, Bruenn SW, Lentz EJ, Messer OEB, Mezzacappa A, Blondin JM, Marronetti P, Yakunin KN (2014) Advancing nucleosynthesis in self-consistent, multidimensional models of core-collapse supernovae. In: Elekes Z et al (eds) Proceedings of nuclei in the Cosmos XIII, SISSA Proceedings of Science, PoS(NIC XIII)099, 1411.0037 Harris JA, Hix WR, Chertkow MA, Bruenn SW, Lentz EJ, Messer OEB, Mezzacappa A, Blondin JM, Endeve E, Lingerfelt EJ, Marronetti P, Yakunin KN (2016a, in preparation) The nucleosynthesis of axisymmetric Ab initio core-collapse supernova simulations of 12–25 Mˇ Stars. ApJ Harris JA, Hix WR, Chertkow MA, Lee CT, Lentz EJ, Messer OEB (2016b, in preparation) Implications for post-processing nucleosynthesis of core-collapse supernova models with lagrangian particles. ApJ Herant M, Benz W (1992) Postexplosion hydrodynamics of SN 1987A. ApJ 387: 294–308 Hix WR, Thielemann FK (1999) Silicon burning II: Quasi-Equilibrium and explosive burning. ApJ 511:862–875 Hix WR, Harris JA, Lentz EJ, Bruenn SW, Chertkow MA, Messer OEB, Mezzacappa A, Blondin JM, Endeve E, Marronetti P, Yakunin KN (2014) Multidimensional simulations of core-collapse supernovae and the implications for nucleosynthesis. In: Elekes Z, et al (eds) Proceedings of nuclei in the Cosmos XIII, SISSA Proceedings of Science, p PoS(NIC XIII)019 Janka HT, Müller B, Kitaura FS, Buras R (2008) Dynamics of shock propagation and nucleosynthesis conditions in O-Ne-Mg core supernovae. A&A 485:199–208. doi:10.1051/0004-6361:20079334, 0712.4237 Kane J, Arnett D, Remington BA, Glendinning SG, Bazán G, Müller E, Fryxell BA, Teyssier R (2000) Two-dimensional versus three-dimensional supernova hydrodynamic instability growth. ApJ 528:989–994 Kifonidis K, Plewa T, Janka HT, Müller E (2003) Non-spherical core collapse supernovae. I. Neutrino-driven convection, Rayleigh-Taylor instabilities, and the formation and propagation of metal clumps. A&A 408:621–649 Kifonidis K, Plewa T, Scheck L, Janka HT, Müller E (2006) Non-spherical core collapse supernovae. II. The late-time evolution of globally anisotropic neutrino-driven explosions and their implications for SN 1987 A. A&A 453:661–678. doi:10.1051/0004-6361:20054512, astroph/0511369 Kitaura FS, Janka HT, Hillebrandt W (2006) Explosions of O-Ne-Mg cores, the Crab supernova, and subluminous type II-P supernovae. A&A 450:345–350. doi:10.1051/0004-6361:20054703, astro-ph/0512065 Maeda K, Nakamura T, Nomoto K, Mazzali PA, Patat F, Hachisu I (2002) Explosive nucleosynthesis in aspherical hypernova explosions and late-time spectra of SN 1998bw. ApJ 565:405–412 Magkotsios G, Timmes FX, Hungerford AL, Fryer CL, Young PA, Wiescher M (2010) Trends in 44 Ti and 56 Ni from core-collapse supernovae. ApJS 191:66–95. doi:10.1088/0067-0049/191/1/66, 1009.3175 Marek A, Janka HT (2009) Delayed neutrino-driven supernova explosions aided by the standing accretion-shock instability. ApJ 694:664–696. doi:10.1088/0004-637X/694/1/664, 0708.3372 Mazzali PA, Kawabata KS, Maeda K, Foley RJ, Nomoto K, Deng J, Suzuki T, Iye M, Kashikawa N, Ohyama Y, Filippenko AV, Qiu Y, Wei J (2007) The aspherical properties of the energetic type Ic SN 2002ap as inferred from its nebular spectra. ApJ 670:592–599. doi:10.1086/521873, 0708.0966 McCray R (1993) Supernova 1987A revisited. ARA&A 31:175–216 Meyer BS, Krishnan TD, Clayton DD (1998) Theory of Quasi-Equilibrium nucleosynthesis and applications to matter expanding from high temperature and density. ApJ 498:808 Müller B, Janka HT (2015) Non-radial instabilities and progenitor asphericities in core-collapse supernovae. MNRAS 448:2141–2174. doi:10.1093/mnras/stv101, 1409.4783 Müller E, Fryxell B, Arnett D (1991) Instability and clumping in SN 1987A. A&A 251:505–514

68 The Multidimensional Character of Nucleosynthesis in Core: : :

1789

Nagataki S, Hashimoto M, Sato K, Yamada S (1997) Explosive nucleosynthesis in axisymmetrically deformed type II supernovae. ApJ 486:1026 Nagataki S, Shimizu TM, Sato K (1998) Matter mixing from axisymmetric supernova explosion. ApJ 495:413. doi:10.1086/305258, astro-ph/9709152 Nishimura N, Takiwaki T, Thielemann FK (2015) The r-process nucleosynthesis in the various Jet-like explosions of magnetorotational core-collapse supernovae. ApJ 810:109. doi:10.1088/0004-637X/810/2/109, 1501.06567 Nishimura S, Kotake K, Hashimoto Ma, Yamada S, Nishimura N, Fujimoto S, Sato K (2006) rProcess nucleosynthesis in magnetohydrodynamic jet explosions of core-Collapse supernovae. ApJ 642:410–419. doi:10.1086/500786, astro-ph/0504100 Perego A, Hempel M, Fröhlich C, Ebinger K, Eichler M, Casanova J, Liebendörfer M, Thielemann FK (2015) PUSHing core-collapse supernovae to explosions in spherical symmetry I: the model and the case of SN 1987A. ApJ 806:275. doi:10.1088/0004-637X/806/2/275, 1501.02845 Pruet J, Woosley SE, Buras R, Janka HT, Hoffman RD (2005) Nucleosynthesis in the hot convective bubble in core-collapse supernovae. ApJ 623:325–336 Rampp M, Janka HT (2002) Radiation hydrodynamics with neutrinos. Variable eddington factor method for core-collapse supernova simulations. A&A 396:361–392 Rauscher T, Heger A, Hoffman RD, Woosley SE (2002) Nucleosynthesis in massive stars with improved nuclear and stellar physics. ApJ 576:323–348 Schatz H, Austin S, Beers T, Brown A, Brown E, Cyburt R, Lynch W, Zegers R (eds) Proceedings of nuclei in the cosmos X, SISSA proceedings of science Scheck L, Kifonidis K, Janka HT, Müller E (2006) Multidimensional supernova simulations with approximative neutrino transport. I. Neutron star kicks and the anisotropy of neutrino-driven explosions in two spatial dimensions. A&A 457:963–986. doi:10.1051/0004-6361:20064855 Spyromilio J, Meikle WPS, Allen DA (1990) Spectral line profiles of iron and nickel in supernova 1987A - Evidence for a fragmented nickel bubble. MNRAS 242:669–673 Ugliano M, Janka HT, Marek A, Arcones A (2012) Progenitor-explosion connection and remnant birth masses for neutrino-driven supernovae of iron-core progenitors. ApJ 757:69. doi:10.1088/0004-637X/757/1/69, 1205.3657 Utrobin VP, Chugai NN, Andronova AA (1995) Asymmetry of SN 1987A: Fast Ni-56 clump. A&A 295:129–135 Wanajo S, Nomoto K, Janka HT, Kitaura FS, Müller B (2009) Nucleosynthesis in electron capture supernovae of asymptotic giant branch stars. ApJ 695:208–220, doi:10.1088/0004-637X/695/1/208, 0810.3999 Wanajo S, Janka HT, Müller B (2011) Electron-capture Supernovae as the origin of elements beyond iron. ApJ 726:L15, doi:10.1088/2041-8205/726/2/L15, 1009.1000 Wanajo S, Janka HT, Müller B (2013a) Electron-capture Supernovae as origin of 48 Ca. ApJ 767:L26, doi:10.1088/2041-8205/767/2/L26, 1302.0929 Wanajo S, Janka HT, Müller B (2013b) Electron-capture Supernovae as Sources of 60 Fe. ApJ 774:L6, doi:10.1088/2041-8205/774/1/L6, 1307.3319 Wongwathanarat A, Janka HT, Müller E (2013) Three-dimensional neutrino-driven supernovae: Neutron star kicks, spins, and asymmetric ejection of nucleosynthesis products. A&A 552:A126, doi:10.1051/0004-6361/201220636, 1210.8148 Wongwathanarat A, Müller E, Janka HT (2015) Three-dimensional simulations of core-collapse supernovae: from shock revival to shock breakout. A&A 577:A48, doi:10.1051/0004-6361/201425025, 1409.5431 Woosley SE, Heger A (2007) Nucleosynthesis and remnants in massive stars of solar metallicity. Phys Rep 442:269–283, doi:10.1016/j.physrep.2007.02.009, astro-ph/0702176 Woosley SE, Wilson JR, Mathews GJ, Hoffman RD, Meyer BS (1994) The r-process and neutrinoheated supernova ejecta. ApJ 433:229–246 Young P, Ellinger C, Arnett D, Fryer C, Rockefeller G (2008) Spatial distribution of nucleosynthesis products in Cassiopeia A: comparison between observations and 3D explosion models. In: Schatz H, Austin S, Beers T, Brown A, Brown E, Cyburt R, Lynch W, Zegers R (eds) Proceedings of nuclei in the cosmos X, SISSA proceedings of science, p 20. 0811.4655

Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Supernova Mechanism

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Sean M. Couch

Abstract

I review the state of investigation into the impact that nonspherical stellar progenitor structure has on the core-collapse supernova mechanism. Although modeling stellar evolution relies on 1D spherically symmetric calculations, massive stars are not truly spherical. In the stellar evolution codes, this fact is accounted for by “fixes” such as mixing length theory and attendant modifications. Of particular relevance to the supernova mechanism, the Si- and O-burning shells surrounding the iron core at the point of collapse can be violently convective, with convective speeds of hundreds of km s1 . It has recently been shown by a number of groups that the presence of nonspherical perturbations in the layers surrounding the collapsing iron core can have a favorable impact on the likelihood for shock revival and explosion via the neutrino heating mechanism. This is due in large part to the strengthening of turbulence behind the stalled shock due to the presence of finite amplitude seed perturbations to speed the growth of convection which drives the post-shock turbulence. Efforts are now underway to simulate the final minutes of stellar evolution to core-collapse in 3D with the aim to generate realistic multidimensional initial conditions for use in simulations of the supernova mechanism.

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 First Steps: Use of Parameterized Asphericity in CCSN Simulations . . . . . . . . . . . . . . 3 Toward More Realistic CCSN Progenitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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S.M. Couch () Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_79

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1

S.M. Couch

Introduction

The core-collapse supernova (CCSN) mechanism is fundamentally multidimensional. It is well established that 1D spherically symmetric calculations of the CCSN mechanism almost universally fail to result in explosions (Burrows 2013; Janka 2012). Instabilities such as lepton gradient driven convection in the proto-neutron star PNS, convection driven by neutrino heating in the gain region, and the standing accretion shock instability SASI, (Blondin and Mezzacappa 2007; Blondin et al. 2003) make explosions far more likely in 2D and 3D simulations. These instabilities must be seeded by some nonspherically symmetric perturbations to grow (e.g., Hanke et al. 2012). The growth rates of these instabilities are dependent on the amplitude of the seed perturbation (Foglizzo et al. 2006). Multidimensional effects also play an important role during the millions of years of evolution proceeding the collapse of massive stellar cores. In particular, convective transport of heat is crucial to accurately modeling stellar structure and to matching observational data from, e.g., the Sun (Asplund et al. 2009). In 1D stellar evolution codes, convective energy transport is typically approximated by mixing-length theory MLT, (Böhm-Vitense 1958; Clayton 1968) which yields a diffusion equation for the convective heat flux that is solved implicitly (Langer 2012; Paxton et al. 2011). MLT has a tunable free parameter, the mixing length, that is usually chosen to yield good model fits to solar data. It is not clear that one choice of mixing length is appropriate for all stars, or even all convective regions, for all epochs of evolution. Indeed, comparison to multidimensional simulations of convective nuclear burning shows that MLT does not fully accurately describe stellar convection (e.g., Arnett et al. 2009, 2015; Meakin and Arnett 2007; Smith and Arnett 2014). Simulations of the CCSN mechanism require stellar evolution models of massive stars at the point of core collapse as initial conditions. The most commonly used progenitors come from the KEPLER code (Heger et al. 2000, 2005; Woosley and Heger 2007; Woosley and Weaver 1995; Woosley et al. 2002), but other progenitor model sets are available (e.g., Limongi and Chieffi 2006). And now the open-source MESA code is capable of producing high-fidelity models of massive stars at iron core collapse (Paxton et al. 2013). These models generically predict that massive stars end of their lives with inert iron cores, which are strongly cooling via neutrinos, surrounded by shells of convective silicon “burning.” The convective speeds in the silicon burning shell around the iron core is in excess of 100 km s1 . But this is the average RMS speed of the convective motions. Multidimensional simulations of convection in silicon-burning shells show peak speeds of several 100 km s1 and has high as 1000 km s1 (Arnett and Meakin 2011; Couch et al. 2015). The violent, large-scale convective motions in the shell surrounding the iron core will be present when the core collapse will accrete through the stalled supernova shock on relevant time scales after core bounce. Use of 1D spherically symmetric progenitor models as has been common practice in simulating CCSNe, however, completely neglects the significant nonradial motions in the collapsing star.

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In this chapter, I review the current state of investigations into the influence of nonspherical structure in the progenitor star on the CCSN mechanism. In Sect. 2 I discuss recent work from a few groups on the role that parameterized finite amplitude perturbations in the structure of the progenitor star plays in the CCSN mechanism. In Sect. 3 I review our recent effort to simulate CCSN progenitors in 3D, and I discuss the future outlook for this work and conclude in Sect. 4.

2

First Steps: Use of Parameterized Asphericity in CCSN Simulations

Until the last few years, very little attention was given to the impact of nonspherical progenitor structure on the CCSN mechanism and resulting observables. Burrows and Hayes (1996) and Fryer (2004) considered how very large-scale asymmetry in the progenitor star could affect neutron star kicks but did not explore the impact of asymmetry on the explosion mechanism itself. In Couch and Ott (2013) we studied the impact on the CCSN mechanism of adding nonradial velocity structure to an otherwise spherical progenitor model. These velocity perturbations were added only in the silicon shell outside the iron core of a 15 Mˇ stellar model from Woosley and Heger (2007). We added velocity only in the spherical  direction in the pattern of a simple convolution of sinusoids, ıv D Mpert cS sinŒ.n  1/ sinŒ.n  1/ cos.n/ ;

(1)

where Mpert is the peak Mach number of the perturbations, cS is the local adiabatic sound speed, n is the number of nodes in the interval  D Œ0; , and  D

.r  rpert;min /=.rpert;max  rpert;min /. rpert;min and rpert;max are the minimum and maximum radii of the perturbed shell, respectively. This pattern of perturbations is a simple toy model and not very representative of realistic stellar convection. Indeed, as Müller and Janka (2015) rightly point out, this velocity pattern does not even obey the solenoidal constraint, r  v D 0 (but see Chatzopoulos et al. 2014,for a means of generating more realistic convective velocity fields). Using Eq. (1), we examined the impact of one particular choice of perturbation parameters (n D 5, Mpert D 0:2) on the likelihood for explosion due to neutrino heating in a 3D simulation. These parameters were chosen to be representative of multidimensional simulations of convection in silicon burning shells in massive stars (Arnett and Meakin 2011), though were on the strong side. Compared to an otherwise identical 3D simulation using perfectly spherical initial conditions, the model with nonradial velocity perturbations explodes, while the unperturbed model failed. The velocity perturbations placed in the silicon shell reached the stalled bounce shock around 100 ms after bounce when the shock radius was about 160 km. Once accreted through the shock, the perturbations provided finite amplitude seeds for the growth of neutrino-driven convection in the gain layer behind the shock, hence enhancing the growth rate and strength of the post-shock

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convection. In Couch and Ott (2013) we quantify this by computing the average Mach number of anisotropic (i.e., nonradial) motion in the gain region. After 100 ms post-bounce, the anisotropic Mach number in the gain region for the perturbed model significantly exceeds that for the unperturbed model. In Couch and Ott (2013) we surmised that the enhanced anisotropic motion in the gain layer behind the shock increased the typical dwell time of matter accreting from the shock to the cooling layer below the gain, thus increasing the neutrino heating efficiency and leading to explosion. This is, after all, the usual explanation for why multidimensional simulations are more favorable to explosion than 1D (e.g., Dolence et al. 2013; Marek and Janka 2009; Murphy and Burrows 2008). This paradigm implies that, all else being equal, the threshold for total neutrino energy absorbed to drive an explosion is roughly equivalent between 1D, 2D, and 3D; it is just that 2D and 3D are more efficient at trapping neutrino energy due to the influence of nonradial instabilities in the gain region. This standard explanation had never really been tested by directly comparing a critical 1D explosion to a critical 3D explosion, in part because doing so would necessitate the use of parameterized neutrino transport methods or artificial heating. The neutrino “leakage” method employed in our study of progenitor asphericity (O’Connor and Ott 2010) self-consistently (though approximately) computes the emergent neutrino luminosities and charged current heating rates throughout the post-shock region. The leakage scheme also allows for enhancing the charged current heating rates without changing the neutrino opacities or artificially altering the calculated neutrino luminosities. This approach offered a good compromise to study the dimensionality dependence of the efficiency of radiated neutrino energy absorption in CCSNe. In Couch and Ott (2015) we showed that for the same progenitor, critical 3D simulations which just succeeded in exploding absorbed about half as much total neutrino energy as critical 1D explosions (see Fig. 1). While multidimensional effects might make the neutrino heating slightly more efficient, as the standard paradigm holds, something was actually lowering the threshold for explosion in 3D. Simulations in 2D required even less total neutrino energy absorption to achieve explosions in agreement with much recent work showing the relative ease of explosion in 2D as compared to 3D (Couch 2013; Couch and O’Connor 2014; Hanke et al. 2013; Lentz et al. 2015; Melson et al. 2015; Takiwaki et al. 2014; Tamborra et al. 2014). In Couch and Ott (2015) we argued that what was lowering the threshold for explosion in 2D and 3D as compared to 1D was the action of turbulence in providing an effective pressure that aided shock expansion. The idea that a turbulent pressure could aid neutrinos in driving successful CCSN explosions was first suggested by Murphy et al. (2013) based on multidimensional simulations using a parametric neutrino “lightbulb” approach. This effective turbulent pressure takes the form, Pturb D Rrr ;

(2)

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Fig. 1 Volume renderings of entropy for models n0m0 fheat 1.02 (left column) and n5m2 fheat 1.02 (right column) at three different postbounce times, from top to bottom: 100, 200, and 300 ms. The spatial scale is noted at the bottom of each pane and increases with time. The PNS is visible in the center of the renderings, marked by a magenta constant-density contour with value 1012 g cm3

where Rrr is the radial-radial component of the Reynolds stress, Rij D vi0 vj0 . Here, vi0 is the turbulent velocity fluctuation in the i -direction, vi0 D vi  hvi i. We show in Couch and Ott (2015) that for a broad range of circumstances, the turbulent pressure in the gain region is a substantial fraction of the background pressure, as large as 50 %. This turbulent pressure plays as significant role in holding up the shock against the ram pressure of the accretion flow ahead of it. The strength of turbulence in the gain layer is also directly related to the strength and scale of nonspherical perturbations in the progenitor star. We show in Couch and Ott (2015) that perturbations with larger characteristic Mach number, or larger

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t pb = 150 ms

E turb () [erg cm−3 ]

1026

1025

1024 10 0

r = 125 km

n0m0 1 .02 n5m2 1.02 n5m15 1.02 n13m2 1.02 n9m2 1.02 n5m2 1. 02 r1 .40

10 1 

10 2

Fig. 2 Turbulent kinetic energy spectra in the gain layer at 150 ms after bounce for 3D simulations with fheat = 1.02 (left panel) and 3D simulations with small amplitude perturbations and fheat = 1.00 (right panel). Note the (weak) trend that larger-scale (lower n) perturbations lead to more turbulent energy at large scales

scale (smaller n in Eq. (1)), result in stronger post-shock turbulence once accreted. Large-scale perturbations also yield more large-scale turbulent kinetic energy in the gain layer. Turbulence is often characterized by a decomposition into Fourier or spherical harmonic space. Given the essentially spherical nature of the CCSN problem, spherical harmonic decomposition is more common (Hanke et al. 2012). Figure 2 shows the turbulent kinetic energy spectra in spherical harmonic space for several 3D CCSN simulations with initial perturbations of varied strength and scale. Simulations with larger scale and/or stronger nonspherical perturbations have greater overall turbulent kinetic energy and that excess is preferentially on large scales. The only simulation that successfully explodes here is “n5m2,” the red line. Greater turbulent kinetic energy on large scales is directly associated with larger turbulent pressures in the gain region, Eq. (2). This makes intuitive sense as the largest scales carry most of the turbulent energy, and the pressure is, dimensionally, an energy density. Furthermore, the neutrino heating efficiency in all these models was statistically identical, indicating that the deciding factor in whether a given model exploded or not was the strength of the turbulence. In summary, the presence of nonspherical perturbations in the progenitor star can directly influence the success of the CCSN mechanism by enhancing the strength of turbulence in the gain layer and, hence, the turbulent pressure that aids shock expansion. Since the turbulence in the gain layer is a result of neutrino-driven convection, this can be understand as the perturbations providing finite-amplitude seeds to convection, thus increasing the growth rate of convective instabilities and the strength of convection overall (Foglizzo et al. 2006). Stellar convection is generally anisotropic (Arnett et al. 2009) and this is also true for neutrino-driven

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convection in the CCSN gain layer (Couch and Ott 2015; Murphy et al. 2013; Radice et al. 2015b). Assuming that the vr02  v02 C v02 , as is found in 3D simulations, and approximating the turbulent pressure as Pturb D .turb  1/eturb ;

(3)

where eturb is the specific kinetic energy density in turbulent motion, Radice et al. (2015a) point out that the effective adiabatic index of the turbulence, turb , is equal to 2. This is much larger than for the thermodynamic equation of state, therm  4=3. In other words, per unit specific energy, turbulence provides a substantially larger pressure than the thermal equation of state, making turbulence more efficient at pushing the stalled shock out against the accretion flow. This simple analysis serves to underscore the importance of turbulence in aiding CCSN shock revival. And the strength of the turbulence is directly enhanced by strong nonspherical structure in the progenitor star prior to collapse. The pattern of perturbations employed in Couch and Ott (2013, 2015,Eq. (1)) was simple and not very representative of real stellar convection. Müller and Janka (2015) explore are large range of perturbation patterns and strengths in an expansive set of 2D simulations using more realistic neutrino transport than in Couch and Ott (2013, 2015). They find that the addition of nonspherical motion is indeed favorable to successful explosions and that larger scale perturbations work best. Out of the many perturbations patterns they explore, they find that some patterns more reflective of stellar convection are more efficient at aiding explosion than patterns modeled after Eq. (1). That is, explosions were found for some patterns at lower perturbation amplitude than for the perturbations applied in Couch and Ott (2013, 2015). Müller and Janka (2015) find that applying perturbations to the velocity field is more effective than density perturbations at helping shock revival, and they connect the strength of progenitor asphericity to enhancement of neutrino heating in the gain layer. They also argue that the key to achieving explosion is in obtaining high turbulent Mach numbers in the post-shock region, in agreement with our conclusions in Couch and Ott (2015). Müller and Janka (2015) avoid an in-depth analysis of CCSN turbulence since their 2D simulations could lead to qualitatively misleading conclusions as compared to 3D simulations (e.g., Couch 2013; Couch and O’Connor 2014; Dolence et al. 2013; Hanke et al. 2012; Murphy et al. 2013).

3

Toward More Realistic CCSN Progenitors

The recent work exploring the impact of progenitor asphericity on the success of the CCSN explosion mechanism shows that the realistic 3D structure of massive stellar cores is critically important and cannot be ignored. After all, the CCSN mechanism is basically an initial value problem, and, as such, we cannot hope to get the right answer without realistic initial conditions. At present, we can only take the first steps toward realistic 3D evolutionary models of massive stars. To do the

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entirety of massive stellar evolution is simply not possible at present largely due the enormous disparity in scales of the problem: the whole of evolution for stars above about 10 Mˇ takes 10 million years during which convective mixing and heat transport are crucial, then the iron core is built up from nothing to 1:5 Mˇ in the space of days, and this core then becomes unstable and collapses in the fraction of a second. This problem can only be tackled by breaking it apart into long-time scale 1D evolutionary simulations and brief multidimensional dynamic simulations. Both of these aspects of modeling massive stars are active areas of research, and much progress must be made on each front. Recently, we have taken the first steps toward constructing realistic 3D initial conditions for simulations of the CCSN mechanism. In Couch et al. (2015) we present the first 3D simulation of the final minutes in the life of a massive star all the way to the point of iron core gravitational instability and collapse. This simulation captured only the last three minutes of stellar evolution following the final growth of the iron core by about 0.1 Mˇ to it’s effective Chandrasekhar mass and then selfconsistent gravitational instability and collapse. The evolution up to stable silicon shell burning surrounding an iron core was computed in 1D using MESA (Paxton et al. 2011, 2013, 2015), while the multidimensional evolution to collapse was simulated using FLASH (Dubey et al. 2009; Fryxell et al. 2000). We had to make several approximations and kluges to accomplish this. First, we used an extremely reduced approximate nuclear network consisting only of 21 isotopes which was tuned to agree with the energy release rates from a much larger network. Twentyone isotopes is not nearly enough to accurately model silicon “burning” which is in actuality a quasi-equilibrium process involving dozens of isotopes and hundreds of reaction pathways. This reduced network included only an approximate rate for electron capture onto iron nuclei. Additionally, mapping from the 1D MESA model to the 3D FLASH grid incited an initial transient that caused the star to temporarily expand. In order to quell this transient, we increased the rate of electron capture, effectively enhancing the neutrino cooling of the inner core. Despite the required approximations, this effort allowed us to directly quantify the strength of convection surrounding the iron core at the point of collapse. We found that the convective motions driven by silicon shell burning reached speeds as high as 500 km s1 and were characteristically of large spatial scale (` & 5 in spherical harmonic basis). Figure 3 shows a volume rendering the radial component of the velocity in the convective silicon shell. In Couch et al. (2015) we also considered the impact of realistic 3D progenitor structure on the CCSN mechanism by continuing the 3D simulation through collapse, core bounce, and eventual shock revival using approximate neutrino transport methods. Compared to an identical progenitor model in which all aspherical structure has been averaged out, the 3D progenitor model resulted in significantly earlier shock revival and explosion and growth of the kinetic energy of the explosion. We show that this is the result of enhanced turbulence in the gain layer aiding shock expansion (Couch and Ott 2015; Müller and Janka 2015). Recently, Müller et al. (2016) have simulated the final minutes of O shell burning in a massive star in 3D to the point of core collapse. Their approach improves upon

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Fig. 3 Volume rendering of the radial velocity from the 3D progenitor simulation of Couch et al. (2015) just seconds prior to gravitational instability and core collapse. Peak speeds of 500 km s1 were found and the convection was typically large scale

that of Couch et al. (2015) in a number of ways. First, they simulate the entire 4

steradians of the stellar sphere, as opposed to only one octant. Further, they do not artificially enhance the electron capture rates in the core, which could potentially lead to an exaggeration of the strength of Si burning. Müller et al. (2016) do resort to a reduced nuclear network only 19 isotopes and treat the inner iron core and Siburning shell as a boundary condition. This parameterized inner boundary moves inward with time following the trajectory of the respective mass shell from the corresponding 1D KEPLER stellar evolution model. The resolution employed in Müller et al. (2016) is also coarser than that used in Couch et al. (2015). Through extensive analysis, however, they find that MLT provides a fairly good estimate of the nature and strength of convection in the O-burning shell during the final minutes prior to collapse. They also develop simple scaling relationships for the impact of progenitor asphericity on the CCSN mechanism and argue that the convective fluctuations in the O-burning shell may be more important in this regard than the same in the Si-burning shell.

4

Conclusions

In this chapter I have briefly reviewed the current state of investigation into the impact of nonspherical structure in progenitor stars on the CCSN mechanism. Multidimensional simulations using parameterized initial perturbations have unequivocally shown that the presence of aspherical perturbations in the collapsing star are helpful to shock revival and explosion via the neutrino heating mechanism (Couch and Ott 2013, 2015; Müller and Janka 2015). This is largely the result of enhanced turbulence in the post-shock gain layer that supplies an effective pressure which aids shock expansion (Couch and Ott 2015; Murphy et al. 2013), though the amplified anisotropic motion in the gain also enhances the neutrino heating efficiency (Müller and Janka 2015).

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I also discussed efforts to model CCSN progenitors in 3D (Couch et al. 2015; Müller et al. 2016). This first effort has allowed us to directly quantify stellar convection surrounding the iron core of a massive star at the point of gravitational collapse. The convection is strong, reaching speeds in excess of 500 km s1 , and is characteristically large in spatial scale. This realistic convective structure had a positive impact on the success of the neutrino mechanism as compared to an otherwise identical 1D initial stellar model. The simulations of Couch et al. (2015) and Müller et al. (2016) required a number of approximations to make the simulations feasible, most notably a very small nuclear network. While this network accurately reproduces the nuclear energy release rates of larger networks, key quantities such as the core entropy and electron fraction are undoubtedly wrong. Future work will need to address this by employing larger networks, covering larger time scales, and considering stars of varied initial mass. The success of the CCSN mechanism could hinge critically on achieving accurate initial conditions for the simulations. The missing ingredient to a robust CCSN mechanism that yields strong explosions across the expected range of progenitor masses and matches observational data may, in fact, be realistic 3D models of massive stars at core collapse.

5

Cross-References

 Explosion Physics of Core-Collapse Supernovae  Neutrino-Driven Explosions  The Multidimensional Character of Nucleosynthesis in Core-Collapse Super-

novae Acknowledgements The author acknowledges collaboration and discussion with Dave Arnett, Adam Burrows, Manos Chatzopoulos, Josh Dolence, Thomas Janka, Philipp Mösta, Bernhard Müller, Jeremiah Murphy, Evan O’Connor, Christian Ott, David Radice, Frank Timmes, Craig Wheeler, and Mike Zingale. This work was supported in part by NASA through Hubble Fellowship grant No. 51286.01 awarded by the Space Telescope Science Institute, by NSF grant No. AST-0909132, and by the US Department of Energy, Office of Science, Office under Award Number(s) DE-SC0015904. An award of computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357.

References Arnett WD, Meakin C (2011) Toward realistic progenitors of core-collapse supernovae. ApJ 733:78. doi:10.1088/0004-637X/733/2/78. arXiv:1101.5646 Arnett D, Meakin C, Young PA (2009) Turbulent convection in stellar interiors. II. The velocity field. ApJ 690:1715–1729. doi:10.1088/0004-637X/690/2/1715. arXiv:0809.1625

69 Influence of Non-spherical Initial Stellar Structure on the Core-Collapse. . .

1801

Arnett WD, Meakin C, Viallet M, Campbell SW, Lattanzio JC, Mocák M (2015) Beyond mixing-length theory: a step toward 321D. ApJ 809:30. doi:10.1088/0004-637X/809/1/30. arXiv:1503.00342 Asplund M, Grevesse N, Sauval AJ, Scott P (2009) The chemical composition of the sun. ARA&A 47:481–522. doi:10.1146/annurev.astro.46.060407.145222. arXiv:0909.0948 Blondin JM, Mezzacappa A (2007) Pulsar spins from an instability in the accretion shock of supernovae. Nature 445:58–60. doi:10.1038/nature05428. arXiv:astro-ph/0611680 Blondin JM, Mezzacappa A, DeMarino C (2003) Stability of standing accretion shocks, with an eye toward core-collapse supernovae. ApJ 584:971–980. doi:10.1086/345812. arXiv:astroph/0210634 Böhm-Vitense E (1958) Über die Wasserstoffkonvektionszone in Sternen verschiedener Effektivtemperaturen und Leuchtkräfte. Mit 5 Textabbildungen. ZAp 46:108 Burrows A (2013) Colloquium: perspectives on core-collapse supernova theory. Rev Mod Phys 85:245–261. doi:10.1103/RevModPhys.85.245. arXiv:1210.4921 Burrows A, Hayes J (1996) Pulsar recoil and gravitational radiation due to asymmetrical stellar collapse and explosion. Phys Rev Lett 76:352–355. doi:10.1103/PhysRevLett.76.352. arXiv:astro-ph/9511106 Chatzopoulos E, Graziani C, Couch SM (2014) Characterizing the convective velocity fields in massive stars. ApJ 795:92. doi:10.1088/0004-637X/795/1/92 Clayton DD (1968) Principles of stellar evolution and nucleosynthesis. McGraw-Hill, New York Couch SM (2013) On the impact of three dimensions in simulations of neutrinodriven core-collapse supernova explosions. ApJ 775:35. doi:10.1088/0004-637X/775/1/35. arXiv:1212.0010 Couch SM, O’Connor EP (2014) High-resolution three-dimensional simulations of corecollapse supernovae in multiple progenitors. ApJ 785:123. doi:10.1088/0004-637X/785/2/123. arXiv:1310.5728 Couch SM, Ott CD (2013) Revival of the stalled core-collapse supernova shock triggered by precollapse asphericity in the progenitor star. ApJ 778:L7. doi:10.1088/2041-8205/778/1/L7. arXiv:1309.2632 Couch SM, Ott CD (2015) The role of turbulence in neutrino-driven core-collapse supernova explosions. ApJ 799:5. doi:10.1088/0004-637X/799/1/5. arXiv:1408.1399 Couch SM, Chatzopoulos E, Arnett WD, Timmes FX (2015) The three-dimensional evolution to core collapse of a massive star. ApJ 808:L21. doi:10.1088/2041-8205/808/1/L21. arXiv:1503.02199 Dolence JC, Burrows A, Murphy JW, Nordhaus J (2013) Dimensional dependence of the hydrodynamics of core-collapse supernovae. ApJ 765:110. doi:10.1088/0004-637X/765/2/110. arXiv:1210.5241 Dubey A, Reid LB, Weide K, Antypas K, Ganapathy MK, Riley K, Sheeler D, Siegal A (2009) Extensible component based architecture for FLASH, a massively parallel, multiphysics simulation code. Parallel Comput 35(10–11):512–522. arXiv:0903.4875 Foglizzo T, Scheck L, Janka HT (2006) Neutrino-driven convection versus advection in corecollapse supernovae. ApJ 652:1436–1450. doi:10.1086/508443. arXiv:astro-ph/0507636 Fryer CL (2004) Neutron star kicks from asymmetric collapse. ApJ 601:L175–L178. doi:10.1086/382044. arXiv:astro-ph/0312265 Fryxell B, Olson K, Ricker P, Timmes FX, Zingale M, Lamb DQ, MacNeice P, Rosner R, Truran JW, Tufo H (2000) FLASH: an adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. ApJS 131:273–334. doi:10.1086/317361 Hanke F, Marek A, Müller B, Janka HT (2012) Is strong SASI activity the key to successful neutrino-driven supernova explosions? ApJ 755:138. doi:10.1088/0004-637X/755/2/138. arXiv:1108.4355 Hanke F, Müller B, Wongwathanarat A, Marek A, Janka HT (2013) SASI activity in three-dimensional neutrino-hydrodynamics simulations of supernova cores. ApJ 770:66. doi:10.1088/0004-637X/770/1/66. arXiv:1303.6269

1802

S.M. Couch

Heger A, Langer N, Woosley SE (2000) Presupernova evolution of rotating massive stars. I. Numerical method and evolution of the internal stellar structure. ApJ 528:368–396. doi:10.1086/308158. arXiv:astro-ph/9904132 Heger A, Woosley SE, Spruit HC (2005) Presupernova evolution of differentially rotating massive stars including magnetic fields. ApJ 626:350–363. doi:10.1086/429868. arXiv:astroph/0409422 Janka HT (2012) Explosion mechanisms of core-collapse supernovae. Annu Rev Nucl Part Sci 62:407–451. doi:10.1146/annurev-nucl-102711-094901. arXiv:1206.2503 Langer N (2012) Presupernova evolution of massive single and binary stars. ARA&A 50:107–164. doi:10.1146/annurev-astro-081811-125534. arXiv:1206.5443 Lentz EJ, Bruenn SW, Hix WR, Mezzacappa A, Messer OEB, Endeve E, Blondin JM, Harris JA, Marronetti P, Yakunin KN (2015) Three-dimensional core-collapse supernova simulated using a 15 Mˇ progenitor. ApJ 807:L31. doi:10.1088/2041-8205/807/2/L31. arXiv:1505.05110 Limongi M, Chieffi A (2006) The nucleosynthesis of 26 Al and 60 Fe in solar metallicity stars extending in mass from 11 to 120 Msolar : the hydrostatic and explosive contributions. ApJ 647:483–500. doi:10.1086/505164. arXiv:astro-ph/0604297 Marek A, Janka HT (2009) Delayed neutrino-driven supernova explosions aided by the standing accretion-shock instability. ApJ 694:664–696. doi:10.1088/0004-637X/694/1/664. arXiv:0708.3372 Meakin CA, Arnett D (2007) Turbulent convection in stellar interiors. I. Hydrodynamic simulation. ApJ 667:448–475. doi:10.1086/520318. arXiv:astro-ph/0611315 Melson T, Janka HT, Marek A (2015) Neutrino-driven supernova of a low-mass ironcore progenitor Boosted by three-dimensional turbulent convection. ApJ 801:L24. doi:10.1088/2041-8205/801/2/L24. arXiv:1501.01961 Müller B, Janka HT (2015) Non-radial instabilities and progenitor asphericities in core-collapse supernovae. MNRAS 448:2141–2174. doi:10.1093/mnras/stv101. arXiv:1409.4783 Müller B, Viallet M, Heger A, Janka HT (2016) The last minutes of oxygen shell burning in a massive star. arXiv:1605.01393. ArXiv e-prints Murphy JW, Burrows A (2008) Criteria for core-collapse supernova explosions by the neutrino mechanism. ApJ 688:1159–1175. doi:10.1086/592214. arXiv:0805.3345 Murphy JW, Dolence JC, Burrows A (2013) The dominance of neutrino-driven convection in corecollapse supernovae. ApJ 771:52. doi:10.1088/0004-637X/771/1/52. arXiv:1205.3491 O’Connor E, Ott CD (2010) A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes. Class Quantum Gravity 27(11):114103. doi:10.1088/0264-9381/27/11/114103. arXiv:0912.2393 Paxton B, Bildsten L, Dotter A, Herwig F, Lesaffre P, Timmes F (2011) Modules for experiments in stellar astrophysics (MESA). ApJS 192:3. doi:10.1088/0067-0049/192/1/3. arXiv:1009.1622 Paxton B, Cantiello M, Arras P, Bildsten L, Brown EF, Dotter A, Mankovich C, Montgomery MH, Stello D, Timmes FX, Townsend R (2013) Modules for experiments in stellar astrophysics (MESA): planets, oscillations, rotation, and massive stars. ApJS 208:4. doi:10.1088/0067-0049/208/1/4. arXiv:1301.0319 Paxton B, Marchant P, Schwab J, Bauer EB, Bildsten L, Cantiello M, Dessart L, Farmer R, Hu H, Langer N, Townsend RHD, Townsley DM, Timmes FX (2015) Modules for experiments in stellar astrophysics (MESA): binaries, pulsations, and explosions. ApJS 220:15. doi:10.1088/0067-0049/220/1/15. arXiv:1506.03146 Radice D, Couch SM, Ott CD (2015a) Implicit large eddy simulations of anisotropic weakly compressible turbulence with application to core-collapse supernovae. Comput Astrophys Cosmol 2:7. doi:10.1186/s40668-015-0011-0. arXiv:1501.03169 Radice D, Ott CD, Abdikamalov E, Couch SM, Haas R, Schnetter E (2015b, in press) Neutrino-driven convection in core-collapse supernovae: high-resolution simulations. ApJ. arXiv:1510.05022 Smith N, Arnett WD (2014) Preparing for an explosion: hydrodynamic instabilities and turbulence in presupernovae. ApJ 785:82. doi:10.1088/0004-637X/785/2/82. arXiv:1307.5035

69 Influence of Non-spherical Initial Stellar Structure on the Core-Collapse. . .

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Takiwaki T, Kotake K, Suwa Y (2014) A comparison of two- and three-dimensional neutrinohydrodynamics simulations of core-collapse supernovae. ApJ 786:83. doi:10.1088/0004637X/786/2/83. arXiv:1308.5755 Tamborra I, Hanke F, Janka HT, Müller B, Raffelt GG, Marek A (2014) Self-sustained asymmetry of lepton-number emission: a new phenomenon during the supernova shock-accretion phase in three dimensions. ApJ 792:96. doi:10.1088/0004-637X/792/2/96. arXiv:1402.5418 Woosley SE, Heger A (2007) Nucleosynthesis and remnants in massive stars of solar metallicity. Phys Rep 442:269–283. doi:10.1016/j.physrep.2007.02.009. arXiv:astro-ph/0702176 Woosley SE, Weaver TA (1995) The evolution and explosion of massive stars. II. Explosive hydrodynamics and nucleosynthesis. ApJS 101:181. doi:10.1086/192237 Woosley SE, Heger A, Weaver TA (2002) The evolution and explosion of massive stars. Rev Mod Phys 74:1015–1071. doi:10.1103/RevModPhys.74.1015

Neutrinos and Their Impact on CoreCollapse Supernova Nucleosynthesis

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Gabriel Martínez-Pinedo, Tobias Fischer, Karlheinz Langanke, Andreas Lohs, Andre Sieverding, and Meng-Ru Wu

Abstract

Core-collapse supernovae liberate an energy equivalent to the binding energy of the newly formed neutron star by emitting 1058 neutrinos of all flavors with typical energies of 10 MeV. These neutrinos are responsible for a matter outflow from the proto-neutron star known as the neutrino-driven wind. The nucleosynthesis in the wind is very sensitive to the proton-to-nucleon ratio that is determined by spectral differences between e and N e . Current simulations G. Martínez-Pinedo () • K. Langanke Institute for Nuclear Physics (Theory Center), Technische Universität Darmstadt, Darmstadt, Germany GSI Helmholtz Center for Heavy Ion Research, Darmstadt, Germany e-mail: [email protected]; [email protected] T. Fischer Institute for Theoretical Physics, University of Wrocław, Wrocław, Poland e-mail: [email protected] A. Lohs Department of Physics, University of Basel, Basel, Switzerland e-mail: [email protected] A. Sieverding Institute for Nuclear Physics (Theory Center), Technische Universität Darmstadt, Darmstadt, Germany e-mail: [email protected]; [email protected] M.-R. Wu Institute for Nuclear Physics (Theory Center), Technische Universität Darmstadt, Darmstadt, Germany Niels Bohr International Academy, Niels Bohr Institute, Copenhagen, Denmark e-mail: [email protected]

© Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_78

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taking into account recent progress in the description of high-density neutrinomatter interactions predict very similar spectra for all neutrino flavors. Hence, the ejecta are mainly proton-rich during the whole deleptonization phase and allow for the operation of the p-process. As neutrinos travel through the stellar mantle, they can induce spallation reactions with abundant nuclei. This leads to the -process that synthesizes 11 B, 19 F, 138 La, and 180 Ta and enhances the yields of several long-lived radioactive nuclei. During their propagation, neutrinos can suffer flavor oscillations that can also potentially affect the nucleosynthesis in the ejecta.

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 General Features of Neutrino Emission in Core-Collapse Supernova . . . . . . . . . . . . . . 3 Nucleosynthesis Conditions in Neutrino-Heated Ejecta . . . . . . . . . . . . . . . . . . . . . . . . . 4 Nucleosynthesis in Proton-Rich Ejecta: The p-Process . . . . . . . . . . . . . . . . . . . . . . . . 5 Impact of High-Density Neutrino-Matter Interactions on Nucleosynthesis . . . . . . . . . . 6 Neutrino Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Impact of Neutrino Oscillations on Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

February 1987 was the birth of extrasolar neutrino astronomy when detectors in Japan and the United States registered neutrinos which travelled over 50 kpc from the Large Magellanic Cloud to Earth and gave the first indications that a star in this neighbor galaxy of the Milky Way had exploded as a supernova (Hirata et al. 1987; Koshiba 1992). This extraordinary scientific event also proved the general expectation that neutrinos are produced in enormous numbers in supernovae triggered by the core collapse of massive stars. In fact, about 99 % of the gravitational binding energy released in the cataclysmic event is carried away by neutrinos, clearly overpowering the kinetic energy associated with the expansion of the supernova and the energy radiated away as light, despite the fascinating fact that supernovae, can shine as bright as the entire galaxy. Although the neutrinos observed from supernova SN 1987A were likely all electron antineutrinos, identified by the Cerenkov light produced by the relativistic positrons after a charged-current neutrino reaction on protons in the water Cerenkov detectors, the amount of observed neutrinos and their energy spectrum (of order a few tens of MeV) confirmed the general understanding of supernova dynamics (Bethe 1990). These observations were supplemented by detailed studies of the SN 1987A light curve, which as expected followed the sequence of half-lives of radioactive nuclides like 56 Ni, 57 Ni, and 44 Ti, which were copiously produced in the hot supernova environment (Seitenzahl et al. 2014). Core-collapse supernovae are the final fate of massive stars, when at the end of hydrostatic burning, their inner core, composed of nuclei in the iron-nickel

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mass range, runs out of nuclear fuel and collapses under its own gravity triggering an explosion during which most of the star’s material, partly processed in the hot environment in what is called explosive nucleosynthesis, is ejected into the interstellar medium (Woosley et al. 2002). In the general picture of core-collapse supernovae and their associated nucleosynthesis, neutrino reactions on nucleons and nuclei play an important role (Janka 2012; Janka et al. 2007). The supernova explosion is triggered by a shock wave which, when passing outward through the Fe-Ni core, dissociates the heavy nuclei into free nucleons. The interaction of neutrinos, produced by the hot matter of the newly born neutron star in the center, with the free protons and neutrons behind the shock is an effective additional energy source which, together with effects like convection and plasma instabilities, is required for successful explosions, as modern multidimensional supernova simulations show (Janka et al. 2016). Once the explosion sets in, the continuous emission of neutrinos from the proto-neutron star (PNS) drives a low-mass outflow known as neutrino-driven wind (Duncan et al. 1986) that is currently considered a site for the production of elements heavier than iron. The competition between e absorption on neutrons and N e absorption on protons determines the proton-to-nucleon ratio of the matter ejected from the surface of the nascent PNS, crucially influencing the subsequent nucleosynthesis. Depending on the electron neutrino and antineutrino spectra, the ejecta can be proton-rich (with an electron-to-nucleon ratio Ye > 0:5) or neutronrich (Ye < 0:5). In the former case, the nucleosynthesis occurring when the ejected matter reaches cooler regions at larger distances from the neutron star surface gives rise to the p-process (Fröhlich et al. 2006b; Pruet et al. 2006; Wanajo 2006). For a long time the ejection of neutron-rich matter in the neutrino-driven wind has been considered as the favorite site for the astrophysical r-process (Woosley et al. 1994). However, modern supernova simulations predict astrophysical conditions in which the ejecta are always proton-rich (Hüdepohl et al. 2010) or moderately neutron-rich at early times (Martínez-Pinedo et al. 2014). The conditions may allow for a “weak r-process” which can produce elements up to mass number A  90, but are not sufficient for the production of r-process nuclides at the gold-platinum peak and the actinides. As the nucleosynthesis in the neutrino-driven wind scenario occurs in the presence of enormous neutrino fluxes, neutrinoinduced reactions on nuclei might play an important role in these processes. Particularly relevant here are neutrino-induced reactions with particle emission (neutron, protons, alphas) in the final channel as they alter the nuclear abundance distributions. Neutrino-induced particle emission of nuclei is also the key process in the neutrino nucleosynthesis process (Woosley et al. 1990) which is responsible for the production of selected nuclides generated by particle spallation of more abundant nuclides in charged- and neutral-current reactions in the outer shells of the star. Once a neutrino suffers its last interaction on the surface of the PNS, it can undergo flavor transformations as it travels through the stellar mantle (Duan and Kneller 2009). As the initial spectra for the different neutrino flavors are not identical, flavor transformations can potentially induce changes on the neutrino spectra and affect the nucleosynthesis.

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This contribution addresses several issues related to the role of neutrinos in the nucleosynthesis in core-collapse supernova explosions. This requires to discuss processes responsible for the production of neutrinos in the inner regions of the supernova, the impact of neutrino oscillations in modifying the original spectra, and the interaction of those neutrinos with the nuclei during the ongoing nucleosynthesis. Deep in the star, near the PNS, we deal with neutrino-heated ejecta in which both the thermodynamic properties and the composition depend on the (anti)neutrino spectra. In the outer layers of the star, neutrinos have a minor influence in the ejecta properties. However, they affect the composition, either directly or indirectly, by producing light particles that are later captured before, during, and after the explosive nucleosynthesis driven by the supernova shock propagation. The manuscript is structured as follows. Section 2 provides a general description of the typical features of neutrino emission in supernova. Section 3 discussed how neutrino spectra impact the nucleosynthesis in the inner supernova ejecta. The relationship between neutrino spectral properties and high-density neutrino-matter interactions is discussed in Sect. 5. Section 6 discusses neutrino nucleosynthesis and the key role of neutrino-nucleus reactions. The impact of neutrino flavor transformations on nucleosynthesis is discussed in Sect. 7. Finally, Sect. 8 summarizes our results.

2

General Features of Neutrino Emission in Core-Collapse Supernova

During their long lifetimes, massive stars generate the energy necessary to maintain hydrostatic equilibrium by nuclear reactions in their interior (Woosley et al. 2002). The evolution of the stellar core proceeds by burning successively hydrogen, helium, carbon, neon, oxygen, and silicon until an “iron core” is produced as the product of silicon core burning. At this moment, a massive star consists of concentric shells that are the remnants of its previous burning phases (hydrogen, helium, carbon, neon, oxygen, silicon) surrounding the iron core. The temperature in the iron core (a few 109 K) is sufficiently high to establish an equilibrium of reactions mediated by the strong and electromagnetic interaction. Under such conditions, the matter composition is given by nuclear statistical equilibrium (NSE). Importantly, once such an equilibrium is achieved, nuclear reactions (by strong and electromagnetic forces) cease as energy sources. Hence, the star has lost its nuclear energy source in the center, and the iron core becomes eventually unstable under its own gravity. We note that the NSE matter composition depends on the astrophysical parameters (temperature and density). For the following discussion, it is important that it also depends on the proton-tonucleon ratio, i.e., on the Ye value, which can only be changed by reactions mediated by the weak interaction. While the mass of the core is dominated by the nuclear component, the pressure is given by the electrons which, under core conditions, form a degenerate ultrarelativistic Fermi gas. Once the core density reaches values of order 109 g cm3 or higher, the electron Fermi energy grows to values in excess of several MeV. These high-energy

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tpb (s) Fig. 1 Evolution of neutrino energy luminosities [panel (a)–(c)] and average energies [panel (d)– (f)] versus post-bounce time, tpb , from 18 Mˇ supernova model (Fischer et al. 2010), as observed at infinity (Adapted from Wu et al. 2015)

electrons are captured by nuclei (Langanke and Martínez-Pinedo 2003) reducing the pressure support and accelerating the collapse of the core. Electron capture drives the composition to neutron-rich nuclei and produces electron neutrinos that for densities below 1011 g cm3 can leave the star unhindered. During this phase, the emission of neutrinos from the star is mainly dominated by electron neutrinos (see Fig. 1 panel a) produced by electron capture. Much smaller luminosities of N e and ; neutrinos and antineutrinos are due mainly to neutrino-pair emission from the deexcitation of heavy nuclei (Fischer et al. 2013). Once the density of the core reaches 1012 g cm3 , neutrinos no longer stream away freely after being produced as their mean free path becomes shorter than the size of the collapsing core (Janka et al. 2007). As a consequence, neutrinos are trapped during the final stage of the collapse. By inelastic scattering on electrons and, to a lesser extent, on nuclei, neutrinos exchange energy with matter and get thermalized (Langanke et al. 2008). This prevents a continuous rise of the e energies following the increase of Fermi energy of the electrons. As a consequence, the average energy of e remains below 10 MeV (see panel d of Fig. 1).

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After neutrino trapping, the collapse proceeds homologously, until nuclear densities (N D 2:5  1014 g cm3 ) are reached. Since nuclear matter has a much lower compressibility, the homologous core decelerates and bounces in response to the increased nuclear matter pressure. This drives a shock wave into the outer core, i.e., the region of the iron core which lies outside the homologous core (determined by the sonic point) and in the meantime has continued to fall inward at supersonic speed. The shock expends significant energy in the outer core by the dissociation of nuclei into nucleons (Bethe 1990; Janka et al. 2007). This change in composition results in additional energy losses, because the electron capture rate on free protons is significantly larger than on neutron-rich nuclei. A large fraction of the neutrinos produced by these captures behind the shock leave the star quickly in what is called the neutrino burst at shock breakout, carrying away energy. The peak luminosity of the neutrino burst can reach 1053 erg s1 and last several tens of milliseconds (see panel a of Fig. 1). Between dissociation and neutrino losses, the shock wave is weakened so much that it finally stalls and turns into an accretion shock at a radius of a few hundreds of kilometers. After the core bounce, a compact remnant forms in the center known as a PNS. The region between the PNS and the accretion shock is known as the high entropy “hot bubble” in which nuclei are dissociated into free nucleons as matter continuously passes through the shock and is being accreted onto the PNS. During this accretion phase, the neutrino production can be divided into two sources: a diffusive source that produces all flavors and an accretion source for which e and N e are produced by electron and positron captures on the freshly dissociated material. The accretion component dominates, and as a consequence the e and N e luminosities are typically twice as large as the one for  and (anti)neutrinos. This is illustrated in panel b of Fig. 1, based on a spherically symmetric, onedimensional simulation (Fischer et al. 2010). While 1D simulations may capture the main features of the evolution of the neutrino spectra, they cannot account for the complicated convective dynamics that develops behind the shock till the onset of the explosion (Janka et al. 2016). The dynamics can result in large-scale fluid instabilities like the standing accretion shock instability (SASI) (Blondin et al. 2003) that can give rise to a time modulation of the neutrino luminosities (Tamborra et al. 2013). Once the explosion develops, the accretion of material on the neutron star should gradually stop. The neutrino emission becomes dominated by the diffusion component. At this moment, the PNS contains a large number of degenerate electrons and e , the latter being trapped as their mean free path is significantly shorter than the radius. As the neutrinos diffuse out, they convert most of their initially high degeneracy energy to thermal energy of the stellar medium (Burrows 1990). The cooling of the PNS then proceeds by pair production of neutrinos of all three generations, which diffuse out. After several tens of seconds, the star becomes transparent to neutrinos, and the neutrino luminosity drops significantly (Fischer et al. 2012) (see Fig. 1 panels c and f). During this phase the luminosities of different neutrino flavors are very similar and decrease with time as the neutron star cools.

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For the average energy of the neutrinos, the following hierarchy is maintained hE e i < hE Ne i . hE ; i as will be discussed in Sect. 5.

3

Nucleosynthesis Conditions in Neutrino-Heated Ejecta

In order for neutrinos to affect the composition of ejected material, the rate for neutrino absorption on matter should be comparable to the typical dynamical time scales. For the inner supernova ejecta, we deal with dynamical time scales of seconds or less. Assuming a composition of free nucleons, the typical cross section for absorption of a neutrino of 10 MeV is   1041 cm2 . At a distance of 100 km from the neutron star, one can obtain a neutrino absorption rate of 1 s1 assuming a neutrino luminosity L  1051 erg s1 . Such large values of the neutrino luminosities are in fact obtained during the accretion phase and the cooling phase of the PNS. During the accretion phase, the deposition of energy behind the shock is responsible for reviving the stalled shock. The energy deposition is helped by the existence of large-scale fluid instabilities that increase the dwelling time for matter being heated by neutrinos (Janka 2012). As neutrinos deposit energy, they also determine the composition of the deeper layers of supernova ejecta. Consequently, an accurate determination of the ejecta composition requires multidimensional simulations with appropriate neutrino transport (Janka et al. 2016). Nevertheless, given the similarity of the spectra for e and N e , one expects that part of the inner ejecta will be proton-rich (i.e., Ye > 0:5) (Fröhlich et al. 2006a; Pruet et al. 2005). The alpha rich freeze-out of such proton-rich matter favors the production of ˛ nuclei (mainly 56 Ni) with some free protons left (Seitenzahl et al. 2008). It results 1.0 0.5

[X/Fe]

0.0 −0.5

Cayrel et al. Gratton & Sneden Thielemann et al. Fröhlich et al.

−1.0 −1.5

Ca Sc

Ti

V

Cr Mn Fe Co Ni Cu Zn

Fig. 2 Comparison of elemental abundances in the mass range Ca to Zn considering the contribution of proton-rich ejecta (Fröhlich et al. 2006a) with previous calculations (Thielemann et al. 1996) that did not account for proton-rich ejecta and observational data (Cayrel et al. 2004; Gratton and Sneden 1991) (Adapted from Fröhlich et al. 2006a)

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in enhanced abundances of selected nuclei in the Ca-Fe mass range, particularly Cu, Sc, and Zn that are in better agreement with observations (Fröhlich et al. 2006a; Pruet et al. 2005) (see Fig. 2). After the onset of supernova explosion, the PNS deleptonizes and cools by continuous emission of neutrinos of all flavors in a period of several tens of seconds. Neutrino absorption at the PNS surface heats the material and drives a matter outflow known as neutrino-driven wind (Duncan et al. 1986). Initial studies suggested that neutrino-driven winds could be the site for the r-process (Takahashi et al. 1994; Woosley et al. 1994). These pioneering works were followed by analytic (Qian and Woosley 1996), parametric (Hoffman et al. 1997), and steadystate wind models (Thompson et al. 2001) that showed that neutrino-driven winds produce both light and heavy r-process elements provided that the outflow has short dynamical time scales (a few milliseconds), high entropies (above 150 k/nucleon), and low electron fractions (Ye < 0:5). Entropy, dynamical time scale, and Ye are indeed the relevant properties of the ejecta with respect to nucleosynthesis . Their relation to neutrino properties, luminosities and average energies, and neutron star properties, mass and radius, is well understood based on analytic models (Qian and Woosley 1996) and confirmed by hydrodynamic (Arcones et al. 2007) and full Boltzmann transport simulations (Fischer et al. 2010; Hüdepohl et al. 2010). They show that the short dynamical time scales can in fact be achieved but fail, however, to obtain the necessary entropies at times relevant for r-process nucleosynthesis. These works rule out the possibility that neutrino-driven winds are responsible for the production of heavy r-process elements with Z & 50. In Sect. 5, we analyze the possibility that lighter elements (Z . 50) may be produced in neutrino winds. The nucleosynthesis outcome of neutrino-driven winds is very sensitive to the electron fraction, Ye , of the ejected matter (Arcones and Thielemann 2013) that is determined by the competition between electron neutrino absorption in neutrons and antineutrino absorption in protons and their inverse reactions. Their dependence on the luminosity and spectral differences between electron neutrinos and antineutrinos is discussed in the following, while in Sect. 5 we discuss the impact of neutrino interactions at high densities on the emitted (anti)neutrino spectra. Figure 3 shows the evolution of matter ejected from the PNS surface. Near the neutron star, matter is composed of neutrons and protons under extreme neutrino and antineutrino fluxes. Due to the large temperatures, electrons and positrons are also produced. Under these conditions, Ye is determined by a competition between electron capture and antineutrino absorption (decrease Ye ) and positron capture and neutrino absorption (increase Ye ) (Fröhlich et al. 2006a). As the matter moves to larger radii and cools, the electron and positron capture rates decrease much faster than neutrino and antineutrino absorptions, due to the strong temperature dependence of the former. Hence, the evolution of Ye is governed by: YPe D  e n Yn   Ne p Yp

(1)

with  e n the rate for the reaction e C n ! p C e  ,  Ne p for the reaction N e C p ! n C e C , and Yn and Yp the neutron and proton abundances. If matter is exposed long

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis Proton rich ( p-process) p n e e 64 64 Ge n Ga p 64 65 Ga p Ge; . . .

neutrons

28–32)

seeds (A 4

4

He(

seeds

heavy nuclei (A

50–100)

T

0 25 MeV 3 GK

T

0 75 MeV 9 GK

T

0 9 MeV 10 GK

100–??)

.....

Z

Neutron rich (weak r-process)

.....

seeds (N

1813

)12C 2p

4

4

2n

)12C )9Be

He( He(

He

Alpha formation

p n

e e

ng

ati

He

n p

ion

reg

He ati ng reg ion

Weak interaction freeze−out

Proto−neutron Star

Fig. 3 Evolution of matter outflows from the proto-neutron star surface

enough to neutrinos, Ye will reach its equilibrium value obtained from the condition YPe D 0. Assuming a composition given by neutrons and protons, we have Ye D Yp and Yn D 1  Ye such that we get the equilibrium estimate for Ye : Ye  Ye;eq D

 e n :  e n C  Ne p

(2)

If neutrino interactions continue when a substantial amount of alpha particles is present, the equation governing the change of Ye becomes (Qian 2003): X˛ YPe D  e n C . Ne p   e n /  . Ne p C  e n /Ye ; 2

(3)

which is obtained using Ye D Yp C X˛ =2 and Yn C Yp C X˛ D 1 with X˛ the mass fraction of alpha particles that are assumed to be inert to neutrino interactions. In this case, Ye tries to reach the following equilibrium value:

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Ye;eq D

 N p   e n X˛  e n ; C e  e n C  Ne p  e n C  Ne p 2

(4)

which is larger (smaller) than the value in Eq. (2) for  Ne p >  e n ( e n >  Ne p ). This is the so-called ˛-effect that drives the composition to Ye  0:5 hindering the occurrence of the r-process in neutron-rich ejecta (Meyer et al. 1998). The rates for neutrino and antineutrino absorption at a distance r can be approximated by:  e n

  L e W e 2 D 0 " e C 2 C 4 r 2 .me c 2 /2 hE e i

(5a)

  L Ne W Ne 2 "   2 C 0 N e 4 r 2 .me c 2 /2 hE Ne i

(5b)

 Ne p D

with L e and L Ne the neutrino and antineutrino luminosities, 0 D 2:569  1044 cm2 , " D hE 2 i=hE i the ratio between second moment of the neutrino spectrum and the average neutrino energy (similarly for antineutrinos),  D 1:2933 MeV the proton-neutron mass difference, and W  1 C 1:01hE i=.mn c 2 /, W N  1  7:22hE N i=.mn c 2 / the weak magnetism correction to the cross section for neutrino and antineutrino absorption (Horowitz 2002) with mn the nucleon mass. Substituting Eq. (5) in (2), we obtain the following expression for the equilibrium Ye depending on neutrino luminosities and moments of the neutrino distribution: 1  L N W N " N  2 C 2 =hE Ne i Ye;eq D 1 C e e e L e W e " e C 2 C 2 =hE e i

(6)

Notice that due to the presence of a energy threshold  for N e absorption, the equilibrium Ye must increase as the neutrino luminosity decreases with time and the average energy of the neutrinos decreases (Thompson et al. 2001). Taking as typical values at late times those of Fig. 1, one obtains Ye;eq  0:7. This suggest that neutron-rich ejecta, if at all possible, can only be achieved at early times during the PNS cooling phase. One can rewrite the condition for having neutron-rich ejecta,  Ne p >  e n , as a condition for the energy difference between e and N e : 

L Ne W Ne  1 ." Ne  2/: " Ne  " e > 4  L e W e

(7)

Again due to the threshold effect, it is not enough to have N e with higher energies than e . The last term on the right hand side illustrates two competing effects. Having larger N e luminosities than e reduces the required energy difference. However, this effect is partly compensated by weak magnetism that affects more strongly N e than e . A typical value of the ratio of weak magnetism corrections is

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis

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0.9, meaning that L Ne > 1:1L e for the second term to reduce the energy difference threshold over the canonical value of 4. Such a situation is found during the early cooling phase (see for Fig. 1 and Sect. 5). We can summarize the discussion above by saying that due to the similar luminosities and relatively small energy differences between N e and e , the neutrinoheated ejecta could be slightly neutron-rich or Ye  0:5 during the accretion and early cooling phases and will become increasingly proton-rich as the luminosities decrease and the neutrino energies become similar. This excludes the possibility of having a strong r-process on neutrino winds that requires Ye < 0:4 for the moderate entropies found in current simulations (see e.g., Martínez-Pinedo et al. 2014,and references therein). Hence, only a weak r-process may operate on wind ejecta provided that indeed neutron-rich conditions are achieved. Once weak interactions freeze out and the value of Ye is set, the evolution of matter follows different paths depending on whether we are in proton-rich ejecta or neutron-rich ejecta (see Fig. 3). As the matter expands and cools, ˛ particles form, and at lower temperatures some of them can assemble 12 C either by the triplealpha reaction (proton-rich ejecta) or the reaction sequence ˛.˛n;  /9 Be.˛; n/12 C (neutron-rich ejecta). The carbon nuclei will capture additional ˛ particles until iron group or even heavier nuclei are formed (Witti et al. 1994; Woosley and Hoffman 1992). The amount of nuclei formed depends both on the entropy of the ejecta and the expansion time scale. Large entropy means a larger amount of photons present and higher photodissociation rates reducing the efficiency with which 12 C is produced. In fast expansions, the three-body reactions responsible of the buildup of 12 C freeze out relatively soon due to the quadratic dependence on density. Both effects reduce the amount of nuclei synthesized leaving large amounts of free protons or neutrons. If enough free protons or neutrons are left, the nuclei act as “seed” for the formation of heavier elements via proton captures ( p-process in proton-rich ejecta) or neutron captures (weak r-process in neutron-rich ejecta).

4

Nucleosynthesis in Proton-Rich Ejecta: The p-Process

Proton-rich ejecta consist of two components. On the one hand, there is material that comes from the convecting postshock region and is expelled when the explosion is launched and the shock accelerates (“hot bubble ejecta”). Most of this material slowly expands from large distances, is quite dense, has modest entropies (s  1530 kB per nucleon), and is slightly neutron-rich (Ye & 0:47) or moderately proton-rich with Ye . 0:52 (Pruet et al. 2006). Neutrino interactions influence very little the nucleosynthesis. It produces enhanced abundances of 45 Sc, 49 Ti, and 64 Zn solving a long-standing nucleosynthesis puzzle (Fröhlich et al. 2006a; Pruet et al. 2005) (see Fig. 2). The second component corresponds to the proton-rich matter ejected in the neutrino-driven wind. The wind comes from the surface of the hot PNS, is strongly heated by neutrinos, and has to make its way out of the deep gravitational well of the

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compact remnant. Therefore, the wind has rather high entropies and short expansion time scales and at late times can become quite proton-rich, Ye . 0:7, (Fröhlich et al. 2006b; Pruet et al. 2006). Moving into cooler regions, protons and neutrons in this wind matter assemble first into 12 C and then, by a sequence of .p;  /, .˛;  /, and .˛; p/ reactions, into even-even N D Z nuclei like 56 Ni, 60 Zn, and 64 Ge, with some free protons left whose abundance is given by Yp  2Ye  1 (Pruet et al. 2006; Seitenzahl et al. 2008). This nucleosynthesis sequence resembles explosive hydrogen burning on the surface of an accreting neutron star in a binary system (the rp-process, Schatz et al. 1998). In the absence of a sizable neutrino fluence, the matter flow will end at 64 Ge which has a ˇ half-life 64 s, much longer than the expansion time scale and a proton capture rate prohibitively small due to the low reaction Q value. However, the wind material is ejected in the presence of an extreme flux of neutrinos and antineutrinos. While e -induced reactions have no effect as all neutrons are bound in nuclei with rather large Q-values for neutrino capture, antineutrino absorption on the free protons results in an equilibrium density of free neutrons of 1014 –1015 cm3 for several seconds, when the temperatures are in the range 1–3 GK (Fröhlich et al. 2006b). These neutrons, not hindered by Coulomb repulsion, are readily captured by the heavy nuclei in a sequence of .n; p/ and .p;  / reactions in this way effectively bypassing nuclei with long beta-decay half-lives like 64 Ge and allowing the matter flow to proceed to heavier nuclei. This nucleosynthesis sequence is called pprocess (Fröhlich et al. 2006b). No production of nuclei above A D 64 is obtained if antineutrino absorption reactions are neglected. The sensitivity of the p-process on several parameters can be understood by noticing that neutrinos will be important if they can create an appreciable number of free neutrons per heavy nucleus. This ratio is (Pruet et al. 2006): n D

Yp n .2Ye  1/n D : Yh Yh

(8)

The abundance of heavy seed nuclei, Yh , depends on entropy and expansion time scale as Yh / s 3 = dyn (Hoffman et al. 1997). The numerator on Eq. (8) represents the total number of neutrons produced by N e absorption on protons with n , the total number of neutrinos absorbed, given by: Z

T9 D1

n D T9 D3

 Ne p dt / h

L Ne " Ne it r2

(9)

where we have restricted the integral to the times for which the temperature is in the range 1–3 GK to allow for proton captures. The last expression makes clear the dependence on neutrino luminosities, energy, distance, and time spent in the appropriate temperature range, t . From Eqs. (8) and (9), it is clear that the efficiency of the p-process increases with larger Ye values, higher N e luminosities, and/or average energies and decreases with the distance and expansion velocity of the wind (Fröhlich et al. 2006b;

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Pruet et al. 2006; Wanajo 2006). The last aspect is rather sensitive to the interaction of the wind with the reverse shock (Arcones et al. 2012; Wanajo et al. 2011). The p-process constitutes a mass flow from seed nuclei, mainly 56 Ni, to heavier nuclides by .p;  / reactions, supplemented by .n; p/ or ˇ C reactions running through many nuclei on the neutron-deficient side of the nuclear chart. Many of the ˇ C half-lives, for the ground states, are experimentally known (Kienle et al. 2001). However, their potential modifications in the finite temperature astrophysical environment, as well as the rates for the proton capture and .n; p/ reactions, must be theoretically modeled, which is usually performed on the basis of the statistical model. A particularly important ingredient in such statistical model calculations are the nuclear masses, which define the reaction Q values and thus the competition between reactions and their inverses. Nuclear mass measurements have benefited tremendously in recent years from the establishment of nuclear Penning traps or by storage ring experiments at radioactive ion beam facilities, allowing the determination of masses of p-process nuclei with unprecedented precision. With relevance to the p-process, such measurements have been performed for nuclei in the mass range A  90 at the SHIPTRAP at GSI and JYFLTRAP in Jyväskyllä (Haettner et al. 2011; Weber et al. 2008), for nuclei around A D 64 at the CSRe storage ring in Lanzhou (Tu et al. 2011), and for proton-deficient nuclei in the mass range A  90 at the Canadian Penning trap (Fallis et al. 2011). The impact of these mass measurements on the p-process is illustrated on Fig. 4 that compares the nucleosynthesis outcome based on a representative trajectory from a successful core-collapse supernova simulation of a 15 Mˇ star (Buras et al. 2006). Studies

107

AME2003 this work

106

Mo Ru Se

105 Y/Ysol

Kr Rb

Ge As

Zr Y

Ga

104

Sr

Nb

Br

Cd

Zn Rh

103 Ag

Cu 2

10

60

70

80 90 Mass Number A

100

110

Fig. 4 Final abundances after decay to stability relative to solar abundances (Lodders 2003). Filled triangles are for a calculation using the masses measured by Weber et al. (2008). Open triangles are for a calculation using the masses from the 2003 atomic mass evaluation (Audi et al. 2003) (Adapted from Weber et al. 2008)

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that investigated the sensitivity of the p-process abundances to uncertainties in the .n; p/ and .p;  / rates have been reported by Wanajo et al. (2011), Fröhlich and Rauscher (2012), and Simon et al. (2013). Faster .n; p/ rates speed up the mass flow from the N D 50 nucleus 96 Pd, which acts like a “seed” for the production of nuclides with A > 96, to heavy nuclides and hence increase the abundances for nuclides with A > 96. In addition, they decrease the abundances for nuclides in the mass range A  64  96. The p-process produces light p-process nuclei like 84 Sr, 94 Mo, and 96;98 Ru as seen in Fig. 4. Thus, the p-process offers an explanation for the production of these light p-nuclei, which was yet unknown (Arnould and Goriely 2003). However, simulations fail to reproduce the observed abundance of 92 Mo, the most abundant pnucleus in nature. 92 Mo can be produced significantly in slightly neutron-rich winds with Ye values between 0.47 and 0.49 (Hoffman et al. 1996; Wanajo 2006) that may be found in the early cooling phase as discussed above and in the next section.

5

Impact of High-Density Neutrino-Matter Interactions on Nucleosynthesis

As discussed in the previous section, the nucleosynthesis outcome of neutrinodriven winds is very sensitive to the Ye of the ejected matter. This is determined by a competition between neutrino absorption on neutrons and antineutrino absorption on protons with the surprising consequence that even if the composition at the PNS surface is very neutron-rich, the ejecta are proton-rich. The determination of the absorption rates requires an accurate modeling of the luminosities and spectra of the emitted neutrinos. With the development of three-flavor Boltzmann neutrino transport codes, it has been possible to relate the spectra of the emitted neutrinos and the underlying nucleosynthesis to high-density neutrino-matter interactions and basic properties of the nuclear equation of state. It has been shown that the energy difference between electron neutrinos and antineutrinos, and consequently the Ye of the ejecta, is very sensitive to the treatment of charged-current reactions e C n ! p C e  and N e C p ! n C e C in neutron-rich matter at densities   1012 –1014 g cm3 (Martínez-Pinedo et al. 2012; Roberts et al. 2012; Rrapaj et al. 2015). Deep in the interior of the PNS, neutrinos are in thermal and chemical equilibrium with matter as the mean free path for all neutrino flavors is much shorter than the neutron star radius. This is illustrated in Fig. 5 which shows the opacities or inverse mean free paths for the main processes determining the interaction of (anti)neutrinos with matter (Burrows et al. 2006). The figure shows also the position of the energy and transport neutrino-spheres for the different neutrino flavors (see Fischer et al. 2012,for a description of the different processes and the determination of the neutrino-spheres). As we move to the surface and the temperature and density decrease, neutrinos decouple from matter. As  and neutrinos interact only via neutral current, they are the first to decouple. For the very neutron rich conditions found at the PNS surface, electron antineutrinos decouple before electron

1

1

10

2

2

2

−1

−2

−3

−4

−2

−3

−4

10

10

10

11 12 13 14 −3 Baryon Density, log10(ρ [g cm ])

10

10

10

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−1

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0

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11 12 13 14 Baryon Density, log (ρ [g cm−3])

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10

10

3

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ν¯e 10

10

3

νe 10

ν¯e e → ν¯e e

3

νe e →νe e

±

νe ν¯e NN→NN

νe ν¯e NN→NN ±

νe ν¯e →e− e+

νe ν¯e →e− e+

±

ν¯e p→e+ n

νe n→e− p

±

ν¯e n→ ν¯e n ν¯e p→ ν¯e p

νμ/τ

11 12 13 14 −3 Baryon Density, log10(ρ [g cm ])

νμ/τ e± →νμ/τ e±

νμ/τ ν¯μ/τ NN→NN

νμ/τ ν¯μ/τ →e− e+

νμ/τ p→νμ/τ p

νμ/τ n→νμ/τ n

Fig. 5 Opacity or inverse mean free paths for the main reactions contributing to the determination of the spectra of neutrinos emitted from a proto-neutron star: isoenergetic neutrino scattering on neutrons ( n ! n) and protons ( p ! p), charged-current reactions ( e n ! e  p and N e p ! e C n), N –N – bremsstrahlung ( N N N ! N N ), electron-positron annihilation ( N ! e  e C ), and neutrino electron/positron scattering ( e ˙ ! e ˙ ). The different panels show inverse mean free paths for e (left), N e (middle), and ; (right) based on radial profiles at 1 s post-bounce for the 18.0 Mˇ progenitor simulations whose luminosities are shown on Fig. 1 (Fischer et al. 2010). The vertical black solid and dash-dotted lines mark the position of the energy and transport neutrino-spheres (Figure adapted from Fischer et al. 2012)

1/λ [km−1]

νe n→νe n νe p→νe p

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis 1819

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neutrinos. Because the neutrino spectrum reflects the local properties of matter at the position in which they decouple, one expects the following hierarchy of neutrino energies: hE ; i & hE Ne i > hE e i (Keil et al. 2003) (see Fig. 1). For the conditions considered in Fig. 5 (around 1 s post-bounce), the neutrino-spheres are located in the density range 1012 –1013 g cm3 , i.e., 103 –102 N . Only for times around 10 s or later do the neutrino-spheres move to densities around the saturation density. Neutrinos are in thermal equilibrium with matter for densities larger than the location of the energy sphere; at lower densities, neutrinos have decoupled from matter but still suffer several scattering events with nucleons till they reach the transport neutrino-sphere (Raffelt 2001). The region between the energy and transport spheres constitutes a scattering atmosphere where due to the slightly inelastic nature of neutrino-nucleon scattering, the spectra of neutrinos are modified (Raffelt 2001). This aspect is important for the determination of the N e and ; spectra (see Fig. 5). The thermal equilibrium of neutrinos with matter is maintained by processes that involve an energy exchange. As can be seen from Fig. 5, the most important processes are charged-current e C n ! p C e  and N e C p ! n C e C . Equations of state commonly used in core-collapse supernova simulations (e.g., Lattimer and Swesty 1991; Shen et al. 1998) treat neutrons and protons as a gas of non-interacting quasiparticles that move in a mean-field single-particle potential, U . In relativistic mean-field models, the energy-momentum dispersion relation becomes:

Ei .p/ D

q p 2 C m2 i C Ui ;

(10)

where mi is the nucleon effective mass. For the neutron-rich conditions around the neutrino-spheres, the mean-field potential for neutrons and protons can be very different with their relative difference U D Un  Up directly related to the nuclear symmetry energy (Haensel et al. 2007). Reddy et al. (1998) provides analytic expressions for the response function valid both in the relativistic and nonrelativistic limits that can be used for the calculation of the opacity. A simplified expression can be obtained assuming zero momentum transfer, q  0, reflecting the fact that nucleons are more massive than leptons. In this case, the energy transfer becomes q0 D .mn  mp /  U D m  U , and the opacity is given by (elastic approximation) (Bruenn 1985; Reddy et al. 1998):

.E / D

2 GF2 Vud nn  np .g 2 C 3gA2 /pe Ee Œ1  fe .Ee / ;

.„c/4 V 1  e .'p 'n /=T

(11)

with 'i D i  mi  Ui , i the chemical potential of the nucleon and Ee D E C m C U . If we consider neutrinos with energies smaller than E 0 D e  m  U that varies between 10 and 30 MeV when the density varies in the range 1012 –1013 g cm3 , the opacity for neutrino absorption on neutrons behaves as:

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis



E C m C U  e .E / / .E C m C U / exp T 

2

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 :

(12)

The opacity depends exponentially on the mean-field modifications, U . Due to the strong sensitivity of the opacity to the neutrino energy, the density at which neutrinos decouple increases with decreasing neutrino energy. However, U increases with density, implying that the smaller the energy of the neutrino emitted from the proto-neutron star, the larger the opacity correction due to the inclusion of mean-field effects becomes (see Fig. 6 of Roberts et al. 2012). As the opacity for neutrinos mainly determines the deleptonization rate, i.e., the neutrino luminosity of the proto-neutron star, we expect that the larger the U correction, i.e., the larger the symmetry energy, the smaller the neutrino luminosity. This is in fact confirmed by Boltzmann transport simulations (Martínez-Pinedo et al. 2012; Roberts et al. 2012). For N e , there is no final state blocking for the produced Positron, and consequently the main effect of mean-field corrections is to change the energy threshold for neutrino absorption. Using a similar analysis as above, it can be shown that the opacity for N e absorption on protons behaves like: .E Ne / / .E Ne  m  U /2 ;

(13)

and becomes almost zero for E Ne < m C U . The discussion above shows that mean-field effects increase the opacity for neutrino absorption and reduce the opacity for antineutrino absorption. When compared with simulations that do not include mean-field effects, the increase of opacity for neutrinos will keep them in thermal equilibrium with matter up to larger radii. They decouple in regions of lower temperature, and consequently their average energy is smaller. The average energy of antineutrinos is expected to increase as they decouple at slightly deeper (hotter) regions of the neutron star. However, due to the reduced dominance of charged-current reactions (see Fig. 5), the change in average energy is expected to be smaller for N e . This has been confirmed by recent long-term simulations of PNS cooling (Martínez-Pinedo et al. 2012; Roberts et al. 2012) that treat charged-current opacities consistently with the EoS at the mean-field level. They have shown that the inclusion of mean-field effects increases the energy difference between N e and e with respect to the values obtained without mean-field effects. Hence, it is important to use an EoS that reproduces recent constraints on the symmetry energy. The equation of state for neutron-matter has been recently computed using all many-body forces among neutrons predicted by chiral effective field theory (EFT) up to next-to-next-to-next-to-leading order (N3 LO) (Drischler et al. 2014). When compared with equations of state used in core-collapse simulations (see figure 9 of Krüger et al. 2013), one finds that the two most commonly used, the nonrelativistic Skyrme-like of Lattimer and Swesty (1991) and the relativistic mean-field (RMF) based on the TM1 functional of Shen et al. (1998), are not

G. Martínez-Pinedo et al.

Electron fraction

1052 1051

13 12 11 10 9 8 7 6

0

2

4 6 Time [s]

8

10

νe ν¯e νx

0

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Entropy [kB /baryon]

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Eν  [MeV]

Luminosity [erg/s]

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100 90 80 70 60 50 40 30 20

0

2

4 6 Time [s]

8

10

0

2

4 6 Time [s]

8

10

Fig. 6 The left panels show the evolution of neutrino luminosities (upper) and average neutrino energies (lower) for the different neutrino flavors. The right panels show the asymptotic values of entropy (lower) and Ye (upper) reached in the ejecta (Adapted from Martínez-Pinedo et al. 2014)

consistent with chiral EFT constraints particularly at subsaturation densities. An EoS that reproduces these constraints is the RMF based on the density-dependent DD2 functional (Typel et al. 2010). In addition, the DD2-based EoS reproduces constraints on the symmetry energy at saturation density from chiral EFT (Krüger et al. 2013) and a global analysis combining nuclear experimental information and astronomical observations of neutron stars (Lattimer and Lim 2013). Based on the DD2 EoS table provided by M. Hempel, Martínez-Pinedo et al. (2014) have performed spherically symmetric radiation hydrodynamics with threeflavor Boltzmann neutrino transport simulations using the AGILE-Boltztran code. The equation of state is based on the extended nuclear statistical model of Hempel and Schaffner-Bielich (2010) and includes a detailed nuclear composition allowing for the presence of light nuclear clusters at subsaturation densities. Importantly, the EoS provides the mean-field corrections necessary for the calculation of chargedcurrent neutrino reactions. Figure 6 shows the evolution of the luminosities and average energies for all neutrino flavors (left panels). The right panels show the evolution of the values of Ye and entropy asymptotically reached by the ejecta. One sees that the early ejecta are slightly neutron-rich with Ye  0:48. This value is larger than the one previously found by Martínez-Pinedo et al. (2012) using the TM1 EoS (Shen et al. 1998). The mass-integrated nucleosynthesis is shown in Fig. 7. The upper panel shows the mass-integrated isotopic abundances normalized to the solar abundances. The lower panel shows the mass-integrated elemental abundances compared with the observations of the metal-poor star enriched in light r-process elements HD 122563 (Honda et al. 2006; Roederer et al. 2012). The stellar observations have been arbitrarily normalized to Zn (Z D 30). Our calculations reproduce the observed abundance of Zr (Z D 40) and other nuclei around A D 90 within a

Rel. abundance

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis 107 106 105 104 103 102 101 100 10−1 10−2 10−3 10−4

Elemental abundance

50

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60

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10−2

80 Mass number A

90

100

10−3

110

HD 122563

10−4 10−5 10−6 10−7 10−8 10−9

25

30

35

40 Charge number Z

45

50

55

Fig. 7 Mass-intergrated neutrino wind abundances. The upper panel shows the ratio between the abundance of a nucleus normalized to the solar abundance. The lower panel shows the elemental abundances (red) compared with the observations of HD 122563 (Honda et al. 2006,grey) and (Roederer et al. 2012,black)

factor 4. The production of these N D 50 closed neutron shell nuclei is rather sensitive to Ye . They will be overproduced if Ye . 0:47 Hoffman et al. (1996). Our results indicate that neutrino-driven winds are the site for the production of elements like Sr, Y, and Zr. The elements Sr, Y, Zr, Nb, and Mo are produced mainly in the early neutron-rich ejecta by charged-particle reactions together with some neutron captures. Due to the sudden drop of alpha and neutron separation energies around N D 50, the production of nuclei with N > 50 decreases dramatically (see upper panel Fig. 7). Nuclei with Z > 42 (A > 92) are mainly produced in the late proton-rich ejecta by the p-process. However, their production is very inefficient due to the low antineutrino luminosities at late times (see discussion in Sect. 4). Due to the relatively large values of Ye achieved in our nucleosynthesis calculations, only the neutron-deficient isotopes of elements between Ge and Mo are produced. This can be tested by observations of isotopic abundances in metal-poor stars. At the same time, it requires that the neutron-rich isotopes, which normally cannot be produced by the s-process (Sneden et al. 2008), are produced in some other astrophysical site. Electron capture supernovae may contribute to the neutronrich isotopes due to the more neutron-rich conditions achieved there (Wanajo et al. 2011). Active-sterile neutrino flavor transformations can also provide a mechanism for increasing the neutron richness in neutrino-driven winds (see Wu et al. 2014,and section 7). We finish this section discussing the main sources of uncertainties regarding the opacities relevant for the spectra formation of e and N e . The interaction of e with

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the PNS material is dominated by e absorption on neutrons. This process can be very accurately computed for the neutrino energies relevant for core-collapse supernova (Strumia and Vissani 2003). The main correction over the leading order opacity in Eq. (11) comes from weak magnetism. Horowitz (2002) has provided a correction factor assuming the initial nucleon at rest. This correction factor has been already discussed in the context of neutrino-driven wind nucleosynthesis. Its implementation (Buras et al. 2006) in the high-density/temperature regime relevant for neutrino decoupling where the nucleon momenta reach several hundred MeV needs to be validated. Due to the exponential dependence of the opacity on the mean-field modifications, U , the largest sensitivity of the opacity comes in fact from the underlying equation of state and in particular its symmetry energy. For N e , the symmetry energy suppresses N e absorption on protons for energies below the neutron-proton in medium energy threshold, U . This means that several charged- and neutral-current process contribute to shaping the N e spectra. In addition to those shown in Fig. 5, there could be contributions from new reaction channels so far not considered in core-collapse supernova simulations. During the early cooling phase, when N e decouple at densities   1012 g cm3 , light nuclei (deuterons, 3 H, 3 He) are expected to be an important source of opacity (Arcones et al. 2008). This has been recently confirmed by Boltzmann transport simulations that for the first time included these reaction channels (Fischer et al. 2016). However, the impact is small and leads to a reduction of a few hundreds keV in the average energy of N e at post-bounce times smaller than 1.5 s. At later times, the N e neutrinosphere moves to higher densities and light nuclei disappear. However, other reaction channels may become competitive. Figure 8 illustrates the situation in the region around the N e energy neutrino-sphere, located at  D 5  1013 g cm3 at around 2 s post-bounce for a 18 Mˇ progenitor model (Fischer et al. 2010) based on the equation of state of Shen et al. (1998). At the conditions considered, N e absorption on protons is completely suppressed for energies below 20 MeV. In present corecollapse supernova simulations, lower-energy neutrinos are produced either directly by nucleon-nucleon bremsstrahlung (Bartl et al. 2014; Hannestad and Raffelt 1998) or from the downscattering of higher-energy neutrinos by inelastic neutrino-electron and neutrino-nucleon scattering (Raffelt 2001). However, as shown in Fig. 8, the large rest energy differences between neutrons and protons allow for inverse neutron decay, N e C e  C p ! n, to become the dominant reaction channel for lowenergy neutrinos. This process is part of the direct URCA process and known to be important for the cooling of neutron stars (Haensel et al. 2007). The figure also shows opacities for charged-current processes connecting the electron and muon flavors that so far remain completely uncoupled in transport simulations. They include inverse muon decay, N e C e  C  !  , and e absorption on electrons, N e C e  ! N  C  . Around the energy threshold, these reactions are of similar magnitude to other processes shown. In addition to these purely leptonic processes, we expect other reactions to become important at neutrino energies for which inverse neutron decay and antineutrino absorption are suppressed. These are the modified URCA process, N e Ce  CpCN ! nCN , and the inelastic absorption process, N e C p C N ! n C N C e C . The nuclear interaction of the proton with a

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis

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104

103

Opacity [1/km]

102

101

100

10−1

10−2

10

20

30

40 50 60 Energy [MeV]

70

80

90

100

Fig. 8 Opacity as a function of neutrino energy for the main reaction channels for N e . The conditions correspond to the position of the electron antineutrino-sphere at 2 s post-bounce, at a density 5  1013 g cm3 , for the 18 Mˇ progenitor of Fischer et al. (2010) using the equation of state of Shen et al. (1998). The reactions channels shown in red have so far not been considered in core-collapse supernova simulations

bystander nucleon can provide the necessary energy to overcome the threshold and enable energy and momentum conservation, enhancing the neutrino absorption rate over the direct process. The above discussion shows that the determination of N e spectra is a complicated problem involving the contributions of many reaction channels coupled via Bolztmann neutrino transport.

6

Neutrino Nucleosynthesis

So far we have discussed different aspects related to the impact of neutrinos on the nucleosynthesis occurring in the inner supernova ejecta and neutrino-driven wind outflows. In these neutrino-heated ejecta, neutrinos determine not only the composition but also the thermodynamic conditions of the ejecta. Given the large amount of neutrinos emitted in a core-collapse supernova, it is expected that they can also potentially affect the composition of outer layers of the star even if they have small or no influence on the dynamics. This is the basic idea behind the -process (Domogatsky et al. 1978; Woosley et al. 1990) in which neutrino charged-current and neutral-current spallation reactions contribute to the production

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of several rare isotopes like 7 Li, 11 B, 19 F, 138 La, and 180 Ta and long-lived radioactive nuclei like 22 Na and 26 Al (Domogatsky and Nadyozhin 1980; Sieverding et al. 2015; Timmes et al. 1995). As pointed out by Woosley et al. (1990), the nuclides 11 B and 19 F are produced by . ; 0 n/ and . ; 0 p/ reactions on the quite abundant nuclei 12 C and 20 Ne. The synthesis of the odd-odd nuclides 138 La and 180 Ta are also attributed to the -process. However, they are produced mainly by the chargedcurrent reactions 138 Ba. e ; e  /138 La and 180 Hf. e ; e  /180 Ta (Goriely et al. 2001; Woosley et al. 1990). Hence, the -process is potentially sensitive to the spectra and luminosity of e and ; neutrinos, which are the neutrino types not observed from SN 1987A. Neutrino nucleosynthesis studies require state-of-the-art stellar models with an extensive nuclear network (Heger et al. 2005; Woosley et al. 2002). In the first step, stellar evolution and nucleosynthesis is followed from the initial hydrogen burning up to the presupernova models. The post-supernova treatment then includes the passage of a neutrino flux through the outer layers of the star and of the shock wave which heats the material and also induces noticeable nucleosynthesis, mainly by photodissociation (the  -process, Arnould and Goriely 2003). Modeling of the shock heating is quite essential as the associated  -process destroys many of the daughter nuclides previously produced by neutrino nucleosynthesis. The -process is sensitive to both neutrino-nucleus cross sections (Balasi et al. 2015) and the assumed neutrino spectra and its time evolution. Previous investigations of nucleosynthesis by neutrino-induced reactions have been based on stellar simulations using various hydrodynamic models (Heger et al. 2005; Suzuki and Kajino 2013; Woosley et al. 1990) with neutrino-nucleus cross sections which were restricted to a set of key nuclei (like those which are quite abundant in outer shells) and to a limited number of decay channels. Most of the neutrino nucleosynthesis studies adopted neutrino spectra described by Fermi-Dirac distributions with chemical potential  D 0 and temperature T , which were appropriate at the time when the studies were performed. The used average electron (anti)neutrino energies range between 12 and 16 MeV (Heger et al. 2005; Woosley et al. 1990) and for muon and tau neutrinos between 16 and 32 MeV (Heger et al. 2005; Timmes et al. 1995; Woosley et al. 1990). These values are much larger than those predicted by modern Bolztmann transport simulations as shown in Figs. 1 and 6. Very recently, Sieverding et al. (2015) have performed studies of neutrinoinduced nucleosynthesis in supernovae for stars with solar metallicity between 15 and 40 Mˇ . These studies improve previous investigations: (i) by using a global set of partial differential cross sections for neutrino-induced charged- and neutralcurrent reactions, constrained by experimental data wherever available, on nuclei with charge numbers Z < 78 and (ii) by considering spectra consistent with modern supernova simulations with average energies hE e i D 8:8 MeV, hE Ne i D hE ; i D 12:6 MeV. The neutrino-induced reactions on 4 He (in the He layer of the star) and on 12 C (in the oxygen/carbon layer) initiate a small reaction sequence, which produces a few light elements, in particular 7 Li and 11 B. The main path for 7 Li production

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis

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is by 4 He( ; 0 p)3 H(˛;  )7 Li and 4 He( ; 0 n)3 He(˛;  )7 Be(e  ; e )7 Li, while 11 B production is due mainly to the neutral-current . ; 0 n/ and . ; 0 p/ reactions on 12 C. However, in both cases, charged-current reactions (4 He( e ; e  p)3 He and 4 He( e ; e C n)3 H in the case of 4 He and 12 C( e ; e  p)11 B and 12 C( e ; e C n)11 C for 12 C) also contribute to the production of 7 Li and 11 B, respectively. Modern predictions for the neutrino spectra results in a reduction of 7 Li and 11 B yields when compared with previous predictions (see Table 1). 7 Li is clearly underproduced supporting the idea that apart from big bang nucleosynthesis, it is produced in metal-free population III stars (Heger and Woosley 2010). Austin et al. (2011) have estimated that in order to reproduce observations, the neutrino process production factor for 11 B should be 0.4 with the rest being produced by cosmic rays. Table 1 shows that neutrino nucleosynthesis calculations based on high-energy spectra will clearly overestimate the production of 11 B, while the results with modern spectra are more consistent with observations. However, as pointed out by Sieverding et al. (2015), 11 B can also be produced in the inner supernova ejecta in alpha-rich freezeout from explosive silicon burning. The exact amount ejected is very sensitive to assumptions about mass cut and requires multidimensional simulations. In addition, the production of 7 Li and 11 B is sensitive to the helium burning rates, triple-˛, and 12 C.˛;  / (Austin et al. 2011, 2014). The neutrino-nucleus cross sections relevant for the production of 7 Li and 11 B are well known. Those involving 4 He have been computed using ab initio few-body methods based on the Lorentz integral transform (Gazit and Barnea 2007). For 12 C, the neutrino-spallation cross sections have been computed based on shell model calculations in a .0 C 2/„! model space (Suzuki et al. 2006). The calculations reproduce the Gamow-Teller distributions of p-shell nuclei and the exclusive 12 C. e ; e  /12 Ngs measured with pion decay at rest neutrinos by LSND (Auerbach et al. 2001) and KARMEN (Bodmann et al. 1994) collaborations. For 19 F, Sieverding et al. (2015) find that neutrino-induced reactions noticeably contribute to the production of 19 F for stars more massive than 20 Mˇ , while their Table 1 Production factors relative to solar abundances (Lodders 2003) normalized to 16 O production. Shown are the results obtained without neutrino, with modern predictions of neutrino spectra (“low energies”, hE e i D 8:8 MeV, hE Ne i D hE ; i D 12:6 MeV) and with the choice of Heger et al. (2005) (“high energies”, hE e i D hE Ne i D 12:6 MeV, hE ; i D 18:9 MeV)

Star 15 Mˇ

25 Mˇ

Nucleus 7 Li 11 B 15 N 19 F 138 La 180 Ta 7 Li 11 B 15 N 19 F 138 La 180 Ta

no 0:002 0:013 0:156 1:311 0:108 0:474 0:001 0:007 0:085 0:124 0:053 0:962

Low energies 0:027 0:230 0:181 1:343 0:472 0:985 0:057 0:154 0:111 0:177 0:501 1:821

High energies 0:320 0:800 0:227 1:431 1:004 1:708 0:174 0:510 0:155 0:313 1:063 2:970

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contribution is negligible in lower-mass stars (see Table 1). This is related to the fact that 19 F is produced at two different sites within stars: in the C/O layer by the reaction sequence 18 O.p; ˛/15 N.˛;  /, which is not sensitive to neutrino processes, and in the O/Ne layer by neutrino-induced spallation from the abundant 20 Ne. The relative importance of neutrino-induced reactions for the total 19 F abundance depends strongly on the progenitor mass and the stellar evolution. The O/Ne layer is less massive in lower-mass stars (about 1 Mˇ in the 15 Mˇ star) than in more massive stars (about 3 Mˇ in the 25 Mˇ star). Furthermore, massive stars are more compact, i.e., the O/Ne layer is closer to the PNS neutrino source. The neutrino cross section on 20 Ne relevant for the production of 19 F has been determined by Heger et al. (2005) combining experimental data on Gamow-Teller strength (Anderson et al. 1991) with random phase approximation (RPA) calculation for the forbidden contributions. The production of 138 La and 180 Ta by the -process is caused by chargedcurrent . e ; e  / reactions on 138 Ba and 180 Hf, respectively. The GT strengths on 138 Ba and 180 Hf below the particle thresholds have been measured at the RCNP in Osaka using the .3 He; t / charge-exchange reaction (Byelikov et al. 2007). The inversion of the GT strength into cross section is complicated by the fact that, for both nuclei, the proton decay channel opens below the neutron channel. The respective corrections have been derived from branching ratios obtained from the statistical model. Furthermore, adding forbidden contributions to the cross sections derived from RPA calculations, one finds that the 138 Ba. e ; e  /138 La and 180 Hf. e ; e  /180 Ta, calculated for a spectrum of supernova e neutrinos with average energy hEi D 12 MeV, are about 25 % and 30 % larger than those estimated solely on the basis of allowed transitions. Stellar models (Heger et al. 2005; Woosley et al. 2002) find indeed that 138 La is being produced by charged-current reactions on 138 Ba in the O/Ne shell. The key is the enhancement of 138 Ba by an s-process prior to the supernova explosion. The 138 La abundance is essentially nonexistent prior to the passing of the supernova neutrinos and is mainly produced by the . e ; e  / reaction on 138 Ba. In principle, 138 La can also be made by the neutral-current neutron-spallation reaction . ; 0 n/, but its contribution to the total 138 La abundance is insignificant. The  -process also produces some 138 La when the shock passages through the O/Ne layer. But its contribution to the total 138 La yield is about an order of magnitude less than the charged-current contribution. In fact, 138 La appears to be coproduced with nuclides like 16 O and 24 Mg in massive stars. Using these nuclei as tracers for the contribution of massive stars to the solar abundance (Byelikov et al. 2007; Heger et al. 2005; Woosley et al. 2002), the observed 138 La abundance appears to be due mainly to the -process. A comparison of the 180 Ta abundance calculated in stellar models is complicated by the fact that, on the time scales of the -process, 180 Ta can exist in two states: the J D 9 isomeric state at excitation energy Ex D 75:3 keV, with a half-life of more than 1015 years, and the ground state, which decays with a half-life of 8.15 h. Also the GT data cannot distinguish between the contributions to these two states. Furthermore, in the finite temperature astrophysical environment, the

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two states are coupled via excitation of states at intermediate energies (Belic et al. 2002). To treat this coupling, Hayakawa et al. (2010) have proposed a model in which they distinguish between states built on the ground and isomeric states. They then followed the decoupling of the two-band structure from thermal equilibrium to freeze-out in a time-dependent approach, assuming an exponential decrease of temperature with time. In their calculation, 39 % of the 180 Ta produced in the process survives in the long-lived isomeric state. Combining these branching ratios with the total 180 Ta -process abundance as given in Table 1 makes the -process a potential 180 Ta production site. We note, however, that s-process nucleosynthesis has also been suggested capable of producing nearly 100 % of the solar 180 Ta abundance (Wisshak et al. 2001). Sieverding et al. (2015) find that neutrino-induced reactions, either directly or indirectly by providing an enhanced abundance of light particles, contribute noticeably to the production of the radioactive nuclides 22 Na and 26 Al, which are both prime candidates for gamma-ray astronomy (Diehl 2013). This study did not find significant production of two other candidates, 44 Ti and 60 Fe, due to neutrinoinduced reactions. The -process increases the yield of 26 Al up to a factor 2 depending on the progenitor mass (Sieverding et al. 2015). The production of 26 Al occurs mostly in a narrow region of the O/Ne shell, in which 26 Mg and 25 Mg are abundant, and the postshock temperature is below 2 GK. Deeper layers are subject to higher peak temperatures such that the 26 Al produced before the explosion is destroyed by 26 Al.p;  /. Neutrinos contribute to the production of 26 Al during the explosive phase by two different mechanisms. Neutrino-induced spallation reactions on the most abundant nuclei in the O/Ne shell (20 Ne, 24 Mg, and 16 O) increase the number of free protons, enhancing the reaction 25 Mg.p;  /, which is also the main production channel without neutrinos. Additionally, the charged-current reaction 26 Mg. e ; e  / gives significant contributions. Figure 9 illustrates the different production channels for the 15 Mˇ progenitor model. Calculations based on modern neutrino spectra predict that both charged- and neutral-current reactions contribute to a similar extent to the production of 26 Al in the O/Ne layer. The enhancement of the 25 Mg.p;  / is confined to a narrow region of optimal temperature, whereas the 26 Mg. e ; e  / contributes more evenly throughout the entire layer, decreasing with the neutrino flux at larger radii. The relevant . e ; e  / cross section to bound states in 26 Al is mainly determined by the Gamow-Teller strength measured in charge exchange experiments (Fujita et al. 2003; Zegers et al. 2006) and the beta-decay of 26 Si (Wilson et al. 1980). The radioisotope 22 Na (Fig. 9) is also affected by neutral- and charged-current reactions that increase its yield by up to a factor of 3 (Sieverding et al. 2015). 21 Ne.p;  / which occurs in the O/Ne shell is enhanced by neutral-current neutrinoinduced spallation reactions, and the charged-current 22 Ne. e ; e  / provides a direct production channel in the C/O layer, where 22 Ne has been produced during the He burning phases. Calculations based on modern neutrino spectra predict that the charged-current contribution turns out to be more important for all the progenitors studied by Sieverding et al. (2015). The relevant cross section is currently based on

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-4

10

-5

10

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Si-shell 15 M star a) Al

b) 10

-6

10

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Na

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Fig. 9 Mass fraction of 26 Al (upper panel) and 22 Na (lower panel) for the same 15 Mˇ main sequence mass progenitor star of solar metallicity. Shown are the results for calculations with and without including neutrino interactions, with charged-current reactions only, and with neutralcurrent reactions only. The pre-supernova mass fractions are also shown (Adapted from Sieverding et al. 2015)

theory. Nevertheless, it is mainly determined by the Fermi transition to the isobaric analog state of 22 Ne in 22 Na and the low-lying GT transitions known from the beta-decay of 22 Mg. Sieverding et al. (2015) provide a complete set of yields of radioactive nuclei for a broad range of progenitor masses.

7

Impact of Neutrino Oscillations on Nucleosynthesis

Neutrino flavor oscillations of e  ; and N e  N ; in the stellar mantle may change the e and N e spectra, thereby enhancing the charged-current interactions of e and N e with nucleons and nuclei. It is thus necessary to know when and where neutrino flavor oscillations occur in supernova environment in order to understand exactly the role of neutrinos in different nucleosynthesis processes discussed in the previous sections. In the vicinity of the proto-neutron star, due to the large neutrino fluxes, the nonlinear coupling between neutrino flavor states of different momenta dominates the flavor evolution (Duan et al. 2010). As a result, the so-called collective neutrino oscillations may occur within the radius of 100 km above the proto-neutron star when the conditions n  n N & ne  neC

(14)

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and GF .n  n N / 

ım231 R2 & 2 r E

(15)

are satisfied (Duan et al. 2010). In the outer layers of the supernovae where the neutrino number densities become negligible compared to the electron number density, large-scale Mikheyev-SmirnovWolfenstein (MSW) flavor transformations occur whenever the resonance condition ˙

p ım2ij 2GF .ne  neC / D cos 2ij ; 2E

(16)

-3 ne- - ne+, nν - nν− (cm )

is met, where the + () sign is for neutrinos (antineutrinos) (Mikheyev and Smirnov 1985; Wolfenstein 1978). This corresponds to the baryon density   103 g/cm3 for ım231 D 2:5  103 eV2 and   102 g/cm3 for ım221 D 7:5  105 eV2 (Olive et al. 2014). Figure 10 shows the profile of ne and n during the PNS cooling phase for a 18 Mˇ star based on the model of Fischer et al. (2010). Collective neutrino oscillations which happen at r  100 km when Eqs. (14) and (15) are satisfied may alter the nucleosynthesis outcome in the neutrino-driven wind and the neutrino nucleosynthesis in the outer supernova shells. The MSW flavor transformation corresponding to ım231 may affect only the neutrino nucleosynthesis, particularly in the C/O and in the He shells (Suzuki and Kajino 2013; Wu et al. 2015). The typical outcome of the collective oscillations is the spectral splits/swaps ( e and N e swap their initial energy spectra with ; and N ; for certain energy

10

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O/Ne

C/O He

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26

1024 1 10

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3

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5

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r (km) Fig. 10 ne  neC (dashed red curve) and n  n N (solid blue curve) at post-bounce time tpb  3 s from (Fischer et al. 2010). Collective neutrino oscillations happen at r  100–500 km when Eqs. (14) and (15) are satisfied. The gray and yellow bands indicate the range of MSW resonances for ım231 and ım221 , respectively. The positions of the neutrino-driven wind, O/Ne, C/O, and He layers are marked by the vertical lines (Adapted from Wu et al. 2015)

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ranges Duan et al. 2006). Early works have attempted to identify whether collective neutrino oscillations may change the Ye of the neutrino-driven wind ejecta assuming that an equilibrium Ye (see Eq. (4)) can always be obtained. This assumption is typically not satisfied in the neutrino-driven wind ejecta because by the time neutrino oscillations occur at r  100 km, the (anti)neutrino absorption rates are too small for Ye to follow the equilibrium value, Ye;eq . Moreover, for temperature T . 7–10 GK, a large fraction of neutrons and protons will be bound into 4 He which is inert to neutrino interaction on the relevant time scales. This “˛-effect” may further limit the impact of neutrino flavor oscillations on Ye as shown by Duan et al. (2011). Collective neutrino oscillations may have a larger role in proton-rich wind ejecta where the p-process operates. The final nucleosynthesis yield is sensitive to the N e absorption rate on protons at the temperature range of 1 GK . T . 3 GK, typically located at the radius of r & 500 km where the collective neutrino oscillations have ceased. The possible impact of collective oscillations on the p-process was explored by Martínez-Pinedo et al. (2011) assuming a simple spectral swap for N e  N ; above a certain neutrino Energy, and it was found that collective oscillations may help the p-process by enhancing the N e absorption rates on protons. More recently, this problem was examined by Wu et al. (2015) adopting the time-varying neutrino-sphere position, neutrino emission characteristics, and the matter density profile directly from a supernova simulation with Boltzmann neutrino transport. It was found that the collective neutrino oscillations in this model always happens at T < 7 GK such that the Ye of the ejecta is not affected. Also, the spectra swap of N e  N ; only exists for a short time scale of 0.5 s for the very early wind phase when there is a crossing in the N e and ; energy spectra. At later time, such a crossing disappears and the spectral swap only occurs in the neutrino sector such that the collective oscillations have negligible effect on the p-process for this supernova model. However, given the sensitivity of collective oscillations to the neutrino spectra, recent advances in the modeling of collective neutrino oscillations (Chakraborty et al. 2016), and improvements in the description of neutrino interaction with matter at high density discussed in Sect. 5, whether collective neutrino oscillations have an impact on the nucleosynthesis in the supernova neutrino-driven wind is still far from certain and merits further examination. Aside from the nucleosynthesis in the neutrino-driven wind, neutrino flavor oscillations can also affect the neutrino-induced nucleosynthesis that occurs in the outer envelope of the exploding star (see Sect. 6). The production of 138 La and 180 Ta by charged-current e reactions on 138 Ba and 180 Hf is not affected by the MSW mechanism as it occurs in the O/Ne shell at densities higher than the MSW resonant density (see Fig. 10). However, Wu et al. (2015) has shown in that its production may be enhanced by e  ; spectra swapping due to collective oscillations. Further out in the helium shell, where the density is 103 g cm3 , 7 Li and 11 B are produced by the charged-current reactions 4 He. e ; pe  /3 He and 4 He. N e ; ne C /3 H, and neutral-current neutrino spallation on 4 He, followed by the reactions 3 He.˛;  /7 Be.e  ; e /7 Li and 3 H.˛;  /7 Li.˛;  /11 B. Yoshida et al. (2006)

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have shown that the MSW flavor oscillations corresponding to the ım231 can swap e  ; ( N e  N ; ) assuming a normal (inverted) hierarchy and enhance the production of 7 Li and 11 B. Banerjee et al. (2011) have suggested that MSW flavor conversion N e $ N ; in inverted hierarchy will enhance the amount of neutrons released by 4 He driving an r-process in the He shell of metal-poor stars. In addition, 9 Be can be produced by the sequence of reactions 7 Li.n;  /8 Li.n;  /9 Li.e  N e /9 Be (Banerjee et al. 2013). Several of the above studies have assumed larger spectral differences between light and heavy flavor neutrinos than those found in modern supernova simulations (see Sect. 5). Furthermore, they neglected the impact of collective neutrino oscillations and the fact that the passage of the supernova shocks (both forward and reverse) through the MSW resonance region may render the MSW flavor transformation nonadiabatic (Duan and Kneller 2009). Moreover, the turbulence in the postshock region may further complicate the flavor evolution of neutrinos. So far we have considered flavor conversion between active flavors. However, active-sterile neutrino flavor conversion can affect the explosion and nucleosynthesis in supernovae depending on both the mass of sterile neutrinos, s , and mixing angle. For light sterile neutrinos with mass  eV to 100 eV, Nunokawa et al. (1997) and McLaughlin et al. (1999) have shown that the flavor transformation of e to s very close to the neutrino-sphere may greatly reduce the Ye . The Gallium and reactor anomalies suggest the existence of sterile neutrinos with mass 1 eV with the mixing angle sin2 214  0:1 (Giunti 2016). The impact of such sterile neutrinos in both the explosion and the nucleosynthesis of the O-Ne-Mg supernovae has been examined by Wu et al. (2014). It was found that although the neutrino heating efficiency will be reduced for a large part of the parameter space of mass and mixing angle, the effect on the nucleosynthesis of the ejecta is rather independent of the mixing parameters and may help produce heavy elements between Zr and Cd observed in metal-poor stars. Pllumbi et al. (2015) examined the role of such sterile neutrinos in the neutrino-driven wind and found the effect being negligible. However, all studies so far have neglected the feedback on the hydrodynamic evolution due to the reduction on neutrino-heating by active-sterile transformations. Future work needs to address these issues to determine the impact of eV sterile neutrinos on neutrino-driven wind nucleosynthesis.

8

Conclusions

Neutrinos have been identified as one of the essential players in core-collapse supernovae. This insight – predicted by models – has been unambiguously verified by the observations from supernova SN 1987A. The indisputably most important role of neutrinos for supernova dynamics concerns the energy balance: due to their tiny cross sections with the surrounding matter, neutrino emission efficiently cools the inner part of the collapsing core and, after bounce, carries away an overwhelmingly large portion of the gravitational binding energy released in the

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explosion. Despite the tiny cross sections, the tremendously large number of neutrinos involved makes them an important means of energy transport during the explosion, reviving the stalled shock front (Janka 2012). Neutrinos also play a crucial role in explosive supernova nucleosynthesis. Their interaction with the hot matter being ejected from the proto-neutron star determines the ratio of protons and neutrons available for synthesis of heavier nuclei in the p-process or potentially the r-process. Further out in the stellar mantle, particle spallation induced by neutrino reactions on abundant nuclei has been identified as the synthesis mechanism of selected isotopes like 11 B, 19 F, 138 La, and 180 Ta in the -process. This process also enhances the yields of long-lived radioactive nuclei which are prime candidates for gamma-ray astronomy. Charged-current neutrino interactions with nucleons play a fundamental role for nucleosynthesis. The respective cross sections are well defined, based on the framework of the electroweak theory. However, in the dense and hot regions of the PNS where the neutrino spectra forms effects due to the nuclear interaction are non-negligible. The dominant contribution at the relevant densities is due to mean-field corrections that need to be described consistently with the equation of state. These corrections relate the energy difference between the electron neutrinos and antineutrinos emitted from the proto-neutron star to the symmetry energy at subsaturation densities. Boltzmann neutrino transport simulations based on state-of-the-art neutrinomatter interactions predict relatively minor differences in the spectra of e and N e , and consequently the neutrino-driven wind is mostly proton-rich. It produces neutron-deficient isotopes for elements between Ge and Mo including the production of p-nuclei 92;94 Mo and 96;98 Ru. Uncertainties in the equation of state and neutrino matter interactions affect differently the spectra of e and N e . For e the major uncertainty is related to the symmetry energy of nuclear matter and its dependence with density and temperature. The situation is more complicated for N e , where many reaction channels, several of them not yet explored in Boltzmann transport simulations, contribute to the total opacity. Addressing these uncertainties is important to provide accurate estimates of nucleosynthesis yields of heavy elements from core-collapse supernovae. However, it is not expected that neutrino-driven explosions of massive stars contribute substantially to the production of elements heavier than A  90. More than two decades ago (Woosley et al. 1990), neutrino-induced spallation of abundant nuclei in the outer layers of a supernova was identified as a major nucleosynthesis source of selected nuclides. This finding has been confirmed over the years using improved stellar models, more accurate neutrino-nucleus cross sections and, last, but not least, refined spectra for the various types of supernova neutrinos. Although the predictions for these spectra shifted systematically to lower average energies, stellar models still imply that the nuclides 11 B, 19 F, 138 La, and 180 Ta are produced by neutrino nucleosynthesis nearly in solar abundance (Sieverding et al. 2015). Most of the relevant cross sections are constrained by charge-exchange data. Addressing the role of neutrino flavor transformations in supernova nucleosynthesis is still an open problem. However, given the small energy differences between

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different neutrino flavors and assuming they are not enhanced by asymmetries in the explosion, it is expected that oscillations will not significantly affect the Ye of the neutrino-driven wind ejecta. Active-sterile flavor transformations involving active sterile neutrinos in the eV mass range may help to produce neutron-rich wind ejecta (Wu et al. 2014). However, the existence of sterile neutrinos is at present controversial (Giunti 2016). The observation of neutrinos from a future nearby supernova, preferably within our galaxy, is the ultimate goal of the various neutrino detectors, either operational or under construction. If the supernova is indeed close enough, e.g., nearer than the galactic center, these detectors have the ability to test the hierarchy of neutrino energies predicted by supernova models and address the role of neutrino oscillations in modifying the neutrino spectra.

9

Cross-References

 Explosion Physics of Core-Collapse Supernovae  Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Super-

nova Mechanism  Making the Heaviest Elements in a Rare Class of Supernovae  Neutron Star Matter Equation of State  Neutrino-Driven Explosions  Neutrino Emission from Supernovae  Neutrino Signatures from Young Neutron Stars  Neutrinos from Core-Collapse Supernovae and Their Detection  Nuclear Matter in Neutron Stars  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  The Multidimensional Character of Nucleosynthesis in Core-Collapse Super-

novae Acknowledgements This work was partly supported by the Deutsche Forschungsgemeinschaft through contract SFB 1245, and the Helmholtz Association through the Nuclear Astrophysics Virtual Institute (VH-VI-417). TF acknowledges support by the Polish National Science Center (NCN) under grant number UMO-2013/11/D/ST2/02645.

References Anderson BD, Tamimi N, Baldwin AR, Elaasar M, Madey R, Manley DM, Mostajabodda’vati M, Watson JW, Zhang WM, Foster CC (1991) Gamow-Teller strength in the .p; n/ reaction at 136 MeV on 20 Ne, 24 Mg, and 28 Si. Phys Rev C 43:50–58. doi:10.1103/PhysRevC.43.50 Arcones A, Thielemann FK (2013) Neutrino-driven wind simulations and nucleosynthesis of heavy elements. J Phys G Nucl Part Phys 40:013,201. doi:10.1088/0954-3899/40/1/013201 Arcones A, Janka HT, Scheck L (2007) Nucleosynthesis-relevant conditions in neutrino-driven supernova outflows. I. Spherically symmetric hydrodynamic simulations. Astron Astrophys 467:1227–1248. doi:10.1051/0004-6361:20066983

1836

G. Martínez-Pinedo et al.

Arcones A, Martínez-Pinedo G, O’Connor E, Schwenk A, Janka H, Horowitz CJ, Langanke K (2008) Influence of light nuclei on neutrino-driven supernova outflows. Phys Rev C 78:015806. doi:10.1103/PhysRevC.78.015806 Arcones A, Fröhlich C, Martínez-Pinedo G (2012) Impact of supernova dynamics on the pprocess. Astrophys J 750:18. doi:10.1088/0004-637X/750/1/18 Arnould M, Goriely S (2003) The p-process of stellar nucleosynthesis: astrophysics and nuclear physics status. Phys Rep 384:1–84. doi:10.1016/S0370-1573(03)00242-4 Audi G, Wapstra AH, Thibault C (2003) The AME2003 atomic mass evaluation: (II). Tables, graphs and references. Nucl Phys A 729:337–676. doi:10.1016/j.nuclphysa.2003.11.003 Auerbach LB, Burman RL, Caldwell DO, Church ED, Donahue JB, Fazely A, Garvey GT, Gunasingha RM, Imlay R, Louis WC, Majkic R, Malik A, Metcalf W, Mills GB, Sandberg V, Smith D, Stancu I, Sung M, Tayloe R, VanDalen GJ, Vernon W, Wadia N, White DH, Yellin S, Collaboration TL (2001) Measurements of charged current reactions of e on 12 C. Phys Rev C 64:065501. doi:10.1103/PhysRevC.64.065501 Austin SM, Heger A, Tur C (2011) 11 B and constraints on neutrino oscillations and spectra from neutrino nucleosynthesis. Phys Rev Lett 106:152501. doi:10.1103/PhysRevLett.106.152501 Austin SM, West C, Heger A (2014) Effective Helium burning rates and the production of the neutrino nuclei. Phys Rev Lett 112:111101. doi:10.1103/PhysRevLett.112.111101 Balasi K, Langanke K, Martínez-Pinedo G (2015) Neutrino-nucleus reactions and their role for supernova dynamics and nucleosynthesis. Prog Part Nucl Phys 85:33–81. doi:10.1016/j.ppnp.2015.08.001 Banerjee P, Haxton WC, Qian YZ (2011) Long, cold, early r process? Neutrino-induced nucleosynthesis in He shells revisited. Phys Rev Lett 106:201,104. doi:10.1103/PhysRevLett.106.201104 Banerjee P, Qian YZ, Haxton WC, Heger A (2013) New primary mechanisms for the synthesis of rare 9 Be in early supernovae. Phys Rev Lett 110:141101. doi:10.1103/PhysRevLett.110.141101 Bartl A, Pethick CJ, Schwenk A (2014) Supernova matter at subnuclear densities as a resonant Fermi gas: enhancement of neutrino rates. Phys Rev Lett 113:081101. doi:10.1103/PhysRevLett.113.081101 Belic D, Arlandini C, Besserer J, de Boer J, Carroll JJ, Enders J, Hartmann T, Käppeler F, Kaiser H, Kneissl U, Kolbe E, Langanke K, Loewe M, Maier HJ, Maser H, Mohr P, von NeumannCosel P, Nord A, Pitz HH, Richter A, Schumann M, Thielemann FK, Volz S, Zilges A (2002) Photo-induced depopulation of the 180 Tam isomer via low-lying intermediate states: structure and astrophysical implications. Phys Rev C 65:035,801. doi:10.1103/PhysRevC.65.035801 Bethe HA (1990) Supernova mechanisms. Rev Mod Phys 62:801–866. doi:10.1103/RevModPhys.62.801 Blondin JM, Mezzacappa A, DeMarino C (2003) Stability of standing accretion shocks, with an eye toward core-collapse supernovae. Astrophys J 584:971–980. doi:10.1086/345812 Bodmann B, Booth N, Drexlin G, Eberhard V, Edgington J, Eitel K, Ferstl M, Finckh E, Gemmeke H, Grandegger W, Hößl J, Kleifges M, Kleinfeller J, Kretschmer W, Maschuw R, Plischke P, Rapp J, Schilling F, Seligmann B, Stumm O, Wolf J, Wölfle S, Zeitnitz B (1994) Neutrino interactions with carbon: recent measurements and a new test of e ,  universality. Phys Lett B 332(3):251–257. doi:10.1016/0370-2693(94)91250-5 Bruenn SW (1985) Stellar core collapse: numerical model and infall epoch. Astrophys J Suppl 58:771–841. doi:10.1086/191056 Buras R, Rampp M, Janka HT, Kifonidis K (2006) Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 Mˇ star. Astron Astrophys 447:1049–1092. doi:10.1051/0004-6361:20053783 Burrows A (1990) Neutrinos from supernova explosions. Ann Rev Nucl Part Sci 40:181–212. doi:10.1146/annurev.nucl.40.1.181 Burrows A, Reddy S, Thompson TA (2006) Neutrino opacities in nuclear matter. Nucl Phys A 777:356–394. doi:10.1016/j.nuclphysa.2004.06.012 Byelikov A, Adachi T, Fujita H, Fujita K, Fujita Y, Hatanaka K, Heger A, Kalmykov Y, Kawase K, Langanke K, Martínez-Pinedo G, Nakanishi K, von Neumann-Cosel P, Neveling R, Richter

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis

1837

A, Sakamoto N, Sakemi Y, Shevchenko A, Shimbara Y, Shimizu Y, Smit FD, Tameshige Y, Tamii A, Woosley SE, Yosoi M (2007) Gamow-Teller strength in the exotic odd-odd nuclei 138 La and 180 Ta and its relevance for neutrino nucleosynthesis. Phys Rev Lett 98:082501. doi:10.1103/PhysRevLett.98.082501 Cayrel R, Depagne E, Spite M, Hill V, Spite F, François P, Plez B, Beers T, Primas F, Andersen J, Barbuy B, Bonifacio P, Molaro P, Nordström B (2004) First stars V – abundance patterns from C to Zn and supernova yields in the early Galaxy. Astron Astrophys 416: 1117–1138 Chakraborty S, Hansen R, Izaguirre I, Raffelt G (2016) Collective neutrino flavor conversion: recent developments. Nucl Phys B 908:366–381. doi:10.1016/j.nuclphysb.2016.02.012 Diehl R (2013) Cosmic gamma-ray spectroscopy. Astron Rev 8(3):19–65 Domogatsky GV, Nadyozhin DK (1980) Neutrino-induced production of radioactive 26 Al. Sov Astron Lett 6:127–130 Domogatsky GV, Eramzhyan RA, Nadyozhin DK (1978) Production of the light elements due to neutrinos emitted by collapsing stellar cores. Astrophys Space Sci 58:273–299. doi:10.1007/BF00644517 Drischler C, Somà V, Schwenk A (2014) Microscopic calculations and energy expansions for neutron-rich matter. Phys Rev C 89:025806. doi:10.1103/PhysRevC.89.025806 Duan H, Kneller JP (2009) Neutrino flavour transformation in supernovae. J Phys G Nucl Part Phys 36(11):113,201. doi:10.1088/0954-3899/36/11/113201 Duan H, Fuller GM, Carlson J, Qian YZ (2006) Simulation of coherent nonlinear neutrino flavor transformation in the supernova environment: correlated neutrino trajectories. Phys Rev D 74:105014. doi:10.1103/PhysRevD.74.105014 Duan H, Fuller GM, Qian Y (2010) Collective neutrino oscillations. Ann Rev Nucl Part Sci 60:569–594. doi:10.1146/annurev.nucl.012809.104524 Duan H, Friedland A, McLaughlin GC, Surman R (2011) The influence of collective neutrino oscillations on a supernova r process. J Phys G Nucl Part Phys 38:035,201. doi:10.1088/0954-3899/38/3/035201 Duncan RC, Shapiro SL, Wasserman I (1986) Neutrino-driven winds from young, hot neutron stars. Astrophys J 309:141–160. doi:10.1086/164587 Fallis J, Clark JA, Sharma KS, Savard G, Buchinger F, Caldwell S, Chaudhuri A, Crawford JE, Deibel CM, Gulick S, Hecht AA, Lascar D, Lee JKP, Levand AF, Li G, Lundgren BF, Parikh A, Russell S, Scholte-van de Vorst M, Scielzo ND, Segel RE, Sharma H, Sinha S, Sternberg MG, Sun T, Tanihata I, Van Schelt J, Wang JC, Wang Y, Wrede C, Zhou Z (2011) Mass measurements of isotopes of Nb, Mo, Tc, Ru, and Rh along the p- and rp-process paths using the Canadian Penning trap mass spectrometer. Phys Rev C 84:045,807. doi:10.1103/PhysRevC.84.045807 Fischer T, Whitehouse SC, Mezzacappa A, Thielemann FK, Liebendörfer M (2010) Protoneutron star evolution and the neutrino-driven wind in general relativistic neutrino radiation hydrodynamics simulations. Astron Astrophys 517:A80. doi:10.1051/0004-6361/200913106 Fischer T, Martínez-Pinedo G, Hempel M, Liebendörfer M (2012) Neutrino spectra evolution during proto-neutron star deleptonization. Phys Rev D 85:083003. doi:10.1103/PhysRevD.85.083003 Fischer T, Langanke K, Martínez-Pinedo G (2013) Neutrino-pair emission from nuclear deexcitation in core-collapse supernova simulations. Phys Rev C 88:065,804. doi:10.1103/PhysRevC.88.065804 Fischer T, Martínez-Pinedo G, Hempel M, Huther L, Röpke G, Typel S, Lohs A (2016) Expected impact from weak reactions with light nuclei in corecollapse supernova simulations. Eur Phys J Web Conf 109:06002. doi:10.1051/epjconf/201610906002 Fröhlich C, Rauscher T (2012) Reaction rate uncertainties and the p-process. In: Kubono S, Hayakawa T, Kajino T, Miyatake H, Motobayashi T, Nomoto K (eds) American Institute of Physics Conference Series, vol 1484, pp 232–239. doi:10.1063/1.4763400 Fröhlich C, Hauser P, Liebendörfer M, Martínez-Pinedo G, Thielemann FK, Bravo E, Zinner NT, Hix WR, Langanke K, Mezzacappa A, Nomoto K (2006a) Composition of the innermost supernova ejecta. Astrophys J 637:415–426. doi:10.1086/498224

1838

G. Martínez-Pinedo et al.

Fröhlich C, Martínez-Pinedo G, Liebendörfer M, Thielemann FK, Bravo E, Hix WR, Langanke K, Zinner NT (2006b) Neutrino-induced nucleosynthesis of A > 64 nuclei: the p-process. Phys Rev Lett 96:142502. doi:10.1103/PhysRevLett.96.142502 Fujita Y, Shimbara Y, Lisetskiy AF, Adachi T, Berg GPA, von Brentano P, Fujimura H, Fujita H, Hatanaka K, Kamiya J, Kawabata T, Nakada H, Nakanishi K, Shimizu Y, Uchida M, Yosoi M (2003) Analogous Gamow-Teller and M 1 transitions in 26 Mg, 26 Al; and 26 Si. Phys Rev C 67:064,312. doi:10.1103/PhysRevC.67.064312 Gazit D, Barnea N (2007) Low-energy inelastic neutrino reactions on [sup 4]he. Phys Rev Lett 98(19):192501. doi:10.1103/PhysRevLett.98.192501 Giunti C (2016) Light sterile neutrinos: status and perspectives. Nucl Phys B 908:336–353. doi:10.1016/j.nuclphysb.2016.01.013 Goriely S, Arnould M, Borzov I, Rayet M (2001) The puzzle of the synthesis of the rare nuclide 138 La. Astron Astrophys 375:L35–L38. doi:10.1051/0004-6361:20010956 Gratton RG, Sneden C (1991) Abundances of elements of the Fe-group in metal-poor stars. Astron Astrophys 241:501–525 Haensel P, Potekhin AY, Yakovlev DG (2007) Neutron stars 1: equation of state and structure, astrophysics and space science library, vol 326. Springer, New York. doi:10.1007/978-0-387-47301-7 Haettner E, Ackermann D, Audi G, Blaum K, Block M, Eliseev S, Fleckenstein T, Herfurth F, Heßberger FP, Hofmann S, Ketelaer J, Ketter J, Kluge HJ, Marx G, Mazzocco M, Novikov YN, Plaß WR, Rahaman S, Rauscher T, Rodríguez D, Schatz H, Scheidenberger C, Schweikhard L, Sun B, Thirolf PG, Vorobjev G, Wang M, Weber C (2011) Mass measurements of very neutrondeficient Mo and Tc isotopes and their impact on rp process nucleosynthesis. Phys Rev Lett 106:122,501. doi:10.1103/PhysRevLett.106.122501 Hannestad S, Raffelt G (1998) Supernova neutrino opacity from nucleon-nucleon bremsstrahlung and related processes. Astrophys J 507:339–352. doi:10.1086/306303 Hayakawa T, Mohr P, Kajino T, Chiba S, Mathews GJ (2010) Reanalysis of the (J D 5) state at 592 keV in 180 Ta and its role in the -process nucleosynthesis of 180 Ta in supernovae. Phys Rev C 82:058,801. doi:10.1103/PhysRevC.82.058801 Heger A, Woosley SE (2010) Nucleosynthesis and evolution of massive metal-free stars. Astrophys J 724:341–373. doi:10.1088/0004-637X/724/1/341 Heger A, Kolbe E, Haxton W, Langanke K, Martínez-Pinedo G, Woosley SE (2005) Neutrino nucleosynthesis. Phys Lett B 606:258–264. doi:10.1016/j.physletb.2004.12.017 Hempel M, Schaffner-Bielich J (2010) A statistical model for a complete supernova equation of state. Nucl Phys A 837:210–254. doi:10.1016/j.nuclphysa.2010.02.010 Hirata K, Kajita T, Koshiba M, Nakahata M, Oyama Y (1987) Observation of a neutrino burst from the supernova SN 1987A. Phys Rev Lett 58:1490–1493. doi:10.1103/PhysRevLett.58.1490 Hoffman RD, Woosley SE, Fuller GM, Meyer BS (1996) Production of the light p-process nuclei in neutrino-driven winds. Astrophys J 460:478–488. doi:10.1086/176986 Hoffman RD, Woosley SE, Qian YZ (1997) Nucleosynthesis in neutrino-driven winds. II. Implications for heavy element synthesis. Astrophys J 482:951–962. doi:10.1086/304181 Honda S, Aoki W, Ishimaru Y, Wanajo S, Ryan SG (2006) Neutron-capture elements in the very metal poor star HD 122563. Astrophys J 643:1180–1189. doi:10.1086/503195 Horowitz CJ (2002) Weak magnetism for antineutrinos in supernovae. Phys Rev D 65:043,001. doi:10.1103/PhysRevD.65.043001 Hüdepohl L, Müller B, Janka H, Marek A, Raffelt GG (2010) Neutrino signal of electron-capture supernovae from core collapse to cooling. Phys Rev Lett 104(25):251101. doi:10.1103/PhysRevLett.104.251101 Janka HT (2012) Explosion mechanisms of core-collapse supernovae. Ann Rev Nucl Part Sci 62:407–451. doi:10.1146/annurev-nucl-102711-094901 Janka HT, Langanke K, Marek A, Martínez-Pinedo G, Müller B (2007) Theory of core-collapse supernovae. Phys Rep 442:38–74. doi:10.1016/j.physrep.2007.02.002 Janka HT, Melson T, Summa A (2016) Physics of core-collapse supernovae in three dimensions: a sneak preview. ArXiv e-prints 1602.05576

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis

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Keil MT, Raffelt GG, Janka HT (2003) Monte carlo study of supernova neutrino spectra formation. Astrophys J 590:971–991. doi:10.1086/375130 Kienle P, Faestermann T, Friese J, Körner HJ, Münch M, Schneider R, Stolz A, Wefers E, Geissel H, Münzenberg G, Schlegel C, Sümmerer K, Weick H, Hellström M, Thirolf P (2001) Synthesis and halflives of heavy nuclei relevant for the rp-process. Prog Part Nucl Phys 46:73– 78. doi:10.1016/S0146-6410(01)00109-0 Koshiba M (1992) Observational neutrino astrophysics. Phys Rep 220:229–381. doi:10.1016/0370-1573(92)90083-C Krüger T, Tews I, Hebeler K, Schwenk A (2013) Neutron matter from chiral effective field theory interactions. Phys Rev C 88:025802. doi:10.1103/PhysRevC.88.025802 Langanke K, Martínez-Pinedo G (2003) Nuclear weak-interaction processes in stars. Rev Mod Phys 75:819–862. doi:10.1103/RevModPhys.75.819 Langanke K, Martínez-Pinedo G, Müller B, Janka HT, Marek A, Hix WR, Juodagalvis A, Sampaio JM (2008) Effects of inelastic neutrino-nucleus scattering on supernova dynamics and radiated neutrino spectra. Phys Rev Lett 100:011,101. doi:10.1103/PhysRevLett.100.011101 Lattimer JM, Lim Y (2013) Constraining the symmetry parameters of the nuclear interaction. Astrophys J 771:51. doi:10.1088/0004-637X/771/1/51 Lattimer JM, Swesty FD (1991) A generalized equation of state for hot, dense matter. Nucl Phys A 535:331–376 Lodders K (2003) Solar system abundances and condensation temperatures of the elements. Astrophys J 591:1220–1247 Martínez-Pinedo G, Ziebarth B, Fischer T, Langanke K (2011) Effect of collective neutrino flavor oscillations on vp-process nucleosynthesis. Eur Phys J A 47(8):1–5. doi:10.1140/epja/i2011-11098-y Martínez-Pinedo G, Fischer T, Lohs A, Huther L (2012) Charged-current weak interaction processes in hot and dense matter and its impact on the spectra of neutrinos emitted from protoneutron star cooling. Phys Rev Lett 109:251,104. doi:10.1103/PhysRevLett.109.251104 Martínez-Pinedo G, Fischer T, Huther L (2014) Supernova neutrinos and nucleosynthesis. J Phys G Nucl Part Phys 41(4):044,008. doi:10.1088/0954-3899/41/4/044008 McLaughlin GC, Fetter JM, Balantekin AB, Fuller GM (1999) Active-sterile neutrino transformation solution for r-process nucleosynthesis. Phys Rev C 59:2873–2887. doi:10.1103/PhysRevC.59.2873 Meyer BS, McLaughlin GC, Fuller GM (1998) Neutrino capture and r-process nucleosynthesis. Phys Rev C 58:3696–3710. doi:10.1103/PhysRevC.58.3696 Mikheyev SP, Smirnov AY (1985) Resonance enhancement of oscillations in matter and solar neutrino spectroscopy. Yadernaya Fizika 42:1441–1448 Nunokawa H, Peltoniemi JT, Rossi A, Valle JWF (1997) Supernova bounds on resonant activesterile neutrino conversions. Phys Rev D 56:1704–1713. doi:10.1103/PhysRevD.56.1704 Olive KA, Agashe K, Amsler C, Antonelli M, Arguin JF, Asner DM et al (2014) Review of Particle Physics. Chin Phys C 38:090001. doi:10.1088/1674-1137/38/9/090001. http://pdg.lbl.gov Pllumbi E, Tamborra I, Wanajo S, Janka HT, Hüdepohl L (2015) Impact of neutrino flavor oscillations on the neutrino-driven wind nucleosynthesis of an electron-capture supernova. Astrophys J 808:188. doi:10.1088/0004-637X/808/2/188 Pruet J, Woosley SE, Buras R, Janka HT, Hoffman RD (2005) Nucleosynthesis in the hot convective bubble in core-collapse supernovae. Astrophys J 623:325–336. doi:10.1086/428281 Pruet J, Hoffman RD, Woosley SE, Janka HT, Buras R (2006) Nucleosynthesis in early supernova winds II: The role of neutrinos. Astrophys J 644:1028–1039. doi:10.1086/503891 Qian YZ (2003) The origin of the heavy elements: recent progress in the understanding of the r-process. Prog Part Nucl Phys 50:153–199. doi:10.1016/S0146-6410(02)00178-3 Qian YZ, Woosley SE (1996) Nucleosynthesis in neutrino-driven winds. I. The physical conditions. Astrophys J 471:331–351. doi:10.1086/177973 Raffelt GG (2001) Mu- and tau-neutrino spectra formation in supernovae. Astrophys J 561:890– 914. doi:10.1086/323379

1840

G. Martínez-Pinedo et al.

Reddy S, Prakash M, Lattimer JM (1998) Neutrino interactions in hot and dense matter. Phys Rev D 58:013,009. doi:10.1103/PhysRevD.58.013009 Roberts LF, Reddy S, Shen G (2012) Medium modification of the charged-current neutrino opacity and its implications. Phys Rev C 86(6):065803. doi:10.1103/PhysRevC.86.065803 Roberts LF, Shen G, Cirigliano V, Pons JA, Reddy S, Woosley SE (2012) Protoneutron star cooling with convection: the effect of the symmetry energy. Phys Rev Lett 108:061,103. doi:10.1103/PhysRevLett.108.061103 Roederer IU, Lawler JE, Sobeck JS, Beers TC, Cowan JJ, Frebel A, Ivans II, Schatz H, Sneden C, Thompson IB (2012) New hubble space telescope observations of heavy elements in four metal-poor stars. Astrophys J Suppl 203:27. doi:10.1088/0067-0049/203/2/27 Rrapaj E, Holt JW, Bartl A, Reddy S, Schwenk A (2015) Charged-current reactions in the supernova neutrino-sphere. Phys Rev C 91:035806. doi:10.1103/PhysRevC.91.035806 Schatz H, Aprahamian A, Görres J, Wiescher M, Rauscher T, Rembges JF, Thielemann FK, Pfeiffer B, Möller P, Kratz KL, Herndl H, Brown BA, Rebel H (1998) rp-process nucleosynthesis at extreme temperature and density conditions. Phys Rep 294:167–263 Seitenzahl IR, Timmes FX, Marin-Laflèche A, Brown E, Magkotsios G, Truran J (2008) Protonrich nuclear statistical equilibrium. Astrophys J 685:L129–L132. doi:10.1086/592501 Seitenzahl IR, Timmes FX, Magkotsios G (2014) The light curve of SN 1987A revisited: constraining production masses of radioactive nuclides. Astrophys J 792:10. doi:10.1088/0004-637X/792/1/10 Shen H, Toki H, Oyamatsu K, Sumiyoshi K (1998) Relativistic equation of state of nuclear matter for supernova and neutron star. Nucl Phys A 637:435–450 Sieverding A, Huther L, Langanke K, Martínez-Pinedo G, Heger A (2015) Neutrino nucleosynthesis of radioactive nuclei in supernovae. ArXiv e-prints [astro-ph.HE]1505.01082 Simon A, Spyrou A, Rauscher T, Fröhlich C, Quinn SJ, Battaglia A, Best A, Bucher B, Couder M, DeYoung PA, Fang X, Görres J, Kontos A, Li Q, Lin LY, Long A, Lyons S, Roberts A, Robertson D, Smith K, Smith MK, Stech E, Stefanek B, Tan WP, Tang XD, Wiescher M (2013) Systematic study of (p; ) reactions on Ni isotopes. Phys Rev C 87:055,802. doi:10.1103/PhysRevC.87.055802 Sneden C, Cowan JJ, Gallino R (2008) Neutron-capture elements in the early galaxy. Annu Rev Astron Astrophys 46:241–288. doi:10.1146/annurev.astro.46.060407.145207 Strumia A, Vissani F (2003) Precise quasielastic neutrino/nucleon cross-section. Phys Lett B 564:42–54. doi:10.1016/S0370-2693(03)00616-6 Suzuki T, Kajino T (2013) Element synthesis in the supernova environment and neutrino oscillations. J Phys G: Nucl Part Phys 40(8):083101. doi:10.1088/0954-3899/40/8/083101 Suzuki T, Chiba S, Yoshida T, Kajino T, Otsuka T (2006) Neutrino-nucleus reactions based on new shell model Hamiltonians. Phys Rev C 74:034307. doi:10.1103/PhysRevC.74.034307 Takahashi K, Witti J, Janka HT (1994) Nucleosynthesis in neutrino-driven winds from protoneutron stars II. The r-process. Astron Astrophys 286:857–869 Tamborra I, Hanke F, Müller B, Janka HT, Raffelt G (2013) Neutrino signature of supernova hydrodynamical instabilities in three dimensions. Phys Rev Lett 111:121,104. doi:10.1103/PhysRevLett.111.121104 Thielemann FK, Nomoto K, Hashimoto M (1996) Core-collapse supernovae and their ejecta. Astrophys J 460:408–436. doi:10.1086/176980 Thompson TA, Burrows A, Meyer BS (2001) The physics of Proto-neutron star winds: implications for r-process nucleosynthesis. Astrophys J 562:887–908. doi:10.1086/323861 Timmes FX, Woosley SE, Hartmann DH, Hoffman RD, Weaver TA, Matteucci F (1995) 26al and 60fe from supernova explosions. Astrophys J 449:204. doi:10.1086/176046 Tu XL, Xu HS, Wang M, Zhang YH, Litvinov YA, Sun Y, Schatz H, Zhou XH, Yuan YJ, Xia JW, Audi G, Blaum K, Du CM, Geng P, Hu ZG, Huang WX, Jin SL, Liu LX, Liu Y, Ma X, Mao RS, Mei B, Shuai P, Sun ZY, Suzuki H, Tang SW, Wang JS, Wang ST, Xiao GQ, Xu X, Yamaguchi T, Yamaguchi Y, Yan XL, Yang JC, Ye RP, Zang YD, Zhao HW, Zhao TC, Zhang XY, Zhan WL (2011) Direct mass measurements of short-lived A D 2Z  1 Nuclides 63 Ge, 65 As, 67 Se, and 71 Kr and their impact on nucleosynthesis in the rp process. Phys Rev Lett 106:112,501. doi:10.1103/PhysRevLett.106.112501

70 Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis

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Typel S, Röpke G, Klähn T, Blaschke D, Wolter HH (2010) Composition and thermodynamics of nuclear matter with light clusters. Phys Rev C 81:015,803. doi:10.1103/PhysRevC.81.015803 Wanajo S (2006) The rp-process in neutrino-driven winds. Astrophys J 647:1323–1340. doi:10.1086/505483 Wanajo S, Janka HT, Kubono S (2011) Uncertainties in the p-process: supernova dynamics versus nuclear physics. Astrophys J 729:46. doi:10.1088/0004-637X/729/1/46 Wanajo S, Janka HT, Müller B (2011) Electron-capture supernovae as the origin of elements beyond iron. Astrophys J 726(2):L15. doi:10.1088/2041-8205/726/2/L15 Weber C, Elomaa VV, Ferrer R, Fröhlich C, Ackermann D, Äystö J, Audi G, Batist L, Blaum K, Block M, Chaudhuri A, Dworschak M, Eliseev S, Eronen T, Hager U, Hakala J, Herfurth F, Heßberger FP, Hofmann S, Jokinen A, Kankainen A, Kluge HJ, Langanke K, Martín A, Martínez-Pinedo G, Mazzocco M, Moore ID, Neumayr JB, Novikov YN, Penttilä H, Plaß WR, Popov AV, Rahaman S, Rauscher T, Rauth C, Rissanen J, Rodríguez D, Saastamoinen A, Scheidenberger C, Schweikhard L, Seliverstov DM, Sonoda T, Thielemann FK, Thirolf PG, Vorobjev GK (2008) Mass measurements in the vicinity of the rp-process and the p-process paths with the Penning trap facilities JYFLTRAP and SHIPTRAP. Phys Rev C 78:054310. doi:10.1103/PhysRevC.78.054310 Wilson HS, Kavanagh RW, Mann FM (1980) Gamow-Teller transitions in some intermediate-mass nuclei. Phys Rev C 22:1696–1722. doi:10.1103/PhysRevC.22.1696 Wisshak K, Voss F, Arlandini C, Be˘cvá˘r F, Straniero O, Gallino R, Heil M, Käppeler F, Krti˘cka M, Masera S, Reifarth R, Travaglio C (2001) Neutron capture on 180 Tam : clue for an s-process origin of nature’s rarest isotope. Phys Rev Lett 87:251,102. doi:10.1103/PhysRevLett.87.251102 Witti J, Janka HT, Takahashi K (1994) Nucleosynthesis in neutrino-driven winds from protoneutron stars I. The ˛-process. Astron Astrophys 286:841–856 Wolfenstein L (1978) Neutrino oscillations in matter. Phys Rev D 17:2369–2374. doi:10.1103/PhysRevD.17.2369 Woosley SE, Hoffman RD (1992) The ˛-process and the r-process. Astrophys J 395:202–239. doi:10.1086/171644 Woosley SE, Hartmann DH, Hoffman RD, Haxton WC (1990) The -process. Astrophys J 356:272–301. doi:10.1086/168839 Woosley SE, Wilson JR, Mathews GJ, Hoffman RD, Meyer BS (1994) The r-process and neutrinoheated supernova ejecta. Astrophys J 433:229–246. doi:10.1086/174638 Woosley SE, Heger A, Weaver TA (2002) The evolution and explosion of massive stars. Rev Mod Phys 74:1015–1071. doi:10.1103/RevModPhys.74.1015 Wu MR, Fischer T, Huther L, Martínez-Pinedo G, Qian YZ (2014) Impact of active-sterile neutrino mixing on supernova explosion and nucleosynthesis. Phys Rev D 89:061,303(R). doi:10.1103/PhysRevD.89.061303 Wu MR, Qian YZ, Martínez-Pinedo G, Fischer T, Huther L (2015) Effects of neutrino oscillations on nucleosynthesis and neutrino signals for an 18 Mˇ supernova model. Phys Rev D 91:065016. doi:10.1103/PhysRevD.91.065016 Yoshida T, Kajino T, Yokomakura H, Kimura K, Takamura A, Hartmann DH (2006) Supernova neutrino nucleosynthesis of light elements with neutrino oscillations. Phys Rev Lett 96:091101. doi:10.1103/PhysRevLett.96.091101 Zegers RGT, Akimune H, Austin SM, Bazin D, Berg AMd, Berg GPA, Brown BA, Brown J, Cole AL, Daito I, Fujita Y, Fujiwara M, Galès S, Harakeh MN, Hashimoto H, Hayami R, Hitt GW, Howard ME, Itoh M, Jänecke J, Kawabata T, Kawase K, Kinoshita M, Nakamura T, Nakanishi K, Nakayama S, Okumura S, Richter WA, Roberts DA, Sherrill BM, Shimbara Y, Steiner M, Uchida M, Ueno H, Yamagata T, Yosoi M (2006) The (t ,3 He) and (3 He, t ) reactions as probes of Gamow-Teller strength. Phys Rev C 74:024309. doi:10.1103/PhysRevC.74.024309

Making the Heaviest Elements in a Rare Class of Supernovae

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Friedrich-Karl Thielemann, Marius Eichler, Igor Panov, Marco Pignatari, and Benjamin Wehmeyer

Abstract

The rapid neutron-capture process (r-process) is responsible for making about half of all heavy elements beyond Fe and is the only source of elements beyond Pb and Bi. Despite all remaining uncertainties in nuclear properties far from stability, the r-process is reasonably well understood in terms of its nuclear reaction flow and necessary environment conditions (neutron densities and temperatures). However, the astrophysical site where it occurs is still highly uncertain. We review the required nuclear physics input and address the sites which have been suggested so far (among others): core-collapse supernovae (CCSNe), compact binary mergers, and magneto-rotational (MHD-jet) supernovae/magnetars. The early “chemical” evolution of galaxies as well as recent additions of radioactive species to the solar system require to attribute the origin of the heavy r-process elements to very rare events. These must occur with a frequency being smaller by about a factor of 1/100 compared to regular CCSNe, thus excluding the

F.-K. Thielemann () • B. Wehmeyer Department of Physics, University of Basel, Basel, Switzerland e-mail: [email protected]; [email protected] M. Eichler Institute for Nuclear Physics, Technische Universität Darmstadt, Darmstadt, Germany e-mail: [email protected]; [email protected] I. Panov Institute for Theoretical and Experimental Physics of NRC Kurchatov Institute, National Research Center (NRC) Kurchatov Institute, Moscow, Russia Sternberg Astronomical Institute, M.V. Lomonosov State University, Moscow, Russia e-mail: [email protected] M. Pignatari Milne Center for Astrophysics, University of Hull, Hull, UK e-mail: [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_81

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latter as a major source. While neutron star mergers are a clear source of heavy r-process elements, observations of low-metallicity stars indicate the existence of an additional r-process source related to massive (and therefore fast evolving) stars. Magneto-rotational supernovae, resulting in neutron stars with extremely strong magnetic fields (magnetars), are the most probable candidates for this site.

Contents 1 2 3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nucleosynthesis Contributions from Stellar Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . Working of the r-Process and Possible Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 General Working of the r-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 r-Process Conditions in Neutrino-Driven Core-Collapse Supernovae . . . . . . . . 3.3 The r-Process in Neutron Star Mergers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 A Special Rare Class of Magneto-Rotational Supernovae and Their Nucleosynthesis: The Role of Magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Understanding r-Process Sources from Observational Constraints . . . . . . . . . . . . . . . . 4.1 Indirect Observations from Nearby Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Understanding r-Process Sources via (Inhomogeneous) Chemical Evolution of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

The chemical elements have their origin in the history of the Universe. Their creation is the prerequisite for chemistry, biology, and the appearance of life. Thus, it is of key importance to understand the astrophysical sites where they originate. The high precision measurements of the cosmic microwave background by COBE, WMAP, and Planck established clearly that only 1;2 H, 3;4 He, and 7 Li are originating in the Big Bang, although problems remain with 7 Li (Cyburt et al. 2016). Thus, stars – the first ones forming a few hundred million years after the Big Bang – had to do the job. Major concepts were laid out in the 1950s (Burbidge et al. 1957; Cameron 1957), and one of the major conclusion was that – while the fusion of nuclei can build up elements as heavy as Fe and Ni (releasing energy due to the gain of nuclear binding) – the production of heavier nuclei up to Pb, Bi, and the actinides requires free neutrons. Therefore, the heavy elements were produced mainly by a slow (s) and by a rapid (r) neutron-capture process with possible minor additional contributions from explosive nucleosynthesis events (Fröhlich et al. 2006; Farouqi et al. 2010; Arcones and Thielemann 2013) and intermediate neutroncapture processes between the s- and the r-process, e.g., the i-process (Cowan and Rose 1977), and neutron captures in super-AGB stars (Jones et al. 2016). The rprocess, and whether it can take place in supernovae, will be the focus of this chapter. But, before discussing this in detail, a short introduction into the methods should be given, how the buildup of elements in astrophysical plasmas can be described and determined.

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The mechanism to model composition changes is based on nuclear reactions, occurring in such environments of a given temperature and density. The overall probability for reactions to happen is obtained by integrating the reaction cross section  .E/ over the velocity or energy distribution of reacting partners (abbreviated as <  v >), which is for most conditions in stellar evolution and explosions a Maxwell-Boltzmann distribution (e.g., Iliadis 2007). Changes of species can also occur via decays, where the decay constant  is related to the half-life of a nucleus 1=2 via  D ln2=1=2 . Interactions (photodisintegrations) with photons, from the blackbody spectrum for the local temperature, are determined by an integration of the relevant cross section over the energies of the photon Planck distribution. This results also in an effective (temperature-dependent) decay “constant” .T /. Reactions with electrons (electron captures on nuclei) or neutrinos can be treated in a similar way, also resulting in effective decay constants , which can depend on temperature and density (determining for electrons whether degenerate or nondegenerate Fermi distributions are in place), while the ’s for neutrinos require their energy distributions from detailed radiation transport, not necessarily reflecting the local conditions, but rather the transport from their place of origin. All the reactions discussed above contribute to three types of terms in reaction network equations. The nuclear abundances Yi enter in this set of equations and their time derivative can be written in the form X X d Yi i Pji j Yj C Pj;k NA < j; k > Yj Yk D dt j j;k

C

X

i Pj;k;l 2 NA2 < j; k; l > Yj Yk Yl :

(1)

j;k;l

One has to sum over all reaction partners given by the different summation indices. The Ps include an integer (positive or negative) factor N i , describing whether (and how often) nucleus i is created or destroyed in this reaction, but also correction factors avoiding multiple counting in case two or three identical reaction i i partners are involved. This can be written as Pji D Nji , Pj;k D Nj;k =˘m Nm Š, or i i Pj;k;l D Nj;k;l =˘m Nm Š. The product in the second term can run over m=1 or 2, if either identical or nonidentical reaction partners are involved. The product in the third term can run over m = 1, 2, or 3, if either three or two identical or no identical reaction partners are involved. Numerically this (additional) correction factor (without considering the N i ’s) is 1 for nonidentical reaction partners, 1/2 = 1/2! for two identical partners, or even 1/6 = 1/3! for three identical partners. The s stand for decay rates (including decays, photodisintegrations, electron captures, and neutrino-induced reactions), < j; k > for <  v > of reactions between nuclei j and k, while < j; k; l > includes a similar expression for three-body reactions (Nomoto et al. 1985). A survey of computational methods to solve nuclear networks is given in Hix and Thielemann (1999) and Timmes (1999). The abundances Yi are related to number densities ni D NA Yi and mass fractions of the corresponding P Xi D 1,  nuclei via Xi D Ai Yi , where Ai is the mass number of nucleus i ,

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denotes the density of the medium, and NA Avogadro’s number. The solution of the above set of differential equations provides the changes of individual nuclear abundances for any burning process in astrophysical environments, requiring the inclusion of all possible reactions and the relevant nuclear input (for data repositories, see, e.g., https://groups.nscl.msu.edu/jina/reaclib/db/, https://nucastro. org/reaclib.html, http://www.kadonis.org/, and http://www.astro.ulb.ac.be/pmwiki/ Brusslib/HomePage). The sum of all these processes (from the Big Bang through all stellar contributions before the formation of the solar system) results in the solar system abundances as given in Fig. 1. Substantial progress has occurred in recent years to attach nucleosynthesis processes in detail to stages in the evolution of stars and their explosive endpoints (see, e.g., the review by Karakas and Lattanzio 2014). Low and intermediate mass stars undergo hydrogen and helium burning before blowing off their outer layers in a stellar wind (planetary nebulae) and retaining a stable central object (a white dwarf, being pressure supported by the degenerate electron gas up to a maximum mass of 1:4 Mˇ – the Chandrasekhar mass). Free neutrons can be released via (˛,n)reactions in helium burning. Overall, these objects eject 14 N (and additional 4 He, from hydrogen burning), 12 C (from helium burning), and also heavy elements up to Pb and Bi, made by the s-process, a sequence of neutron captures and beta-decays along and close to stability (Käppeler et al. 2011; Karakas and Lattanzio 2014). With neutron densities never exceeding a few 1012 cm3 , the s-process in massive stars and low and intermediate mass AGB stars stops at Pb and Bi. Additional neutron reactions lead to a back feeding via (n,˛) reactions, rather than a buildup of heavier (unstable) elements (Käppeler et al. 2011). Higher neutron densities are needed for making neutron capture on unstable nuclei favorable over decays, permitting to build up nuclei up to Th, U, and beyond. With the exception of a small mass window for 8–10 Mˇ (Jones et al. 2013), massive stars – beyond about 10 Mˇ – undergo all fusion burning stages and form an Fe-core at the end of their evolution (Heger and Woosley 2010; Maeder and Meynet 2012). Missing support from energy release by further fusion reactions leads to a collapse up to nuclear densities, the formation of a neutron star (stabilized by the degeneracy pressure of neutrons and protons and nuclear repulsion forces), and the explosive ejection of the outer layers. Such core-collapse supernova explosions, powered by neutrinos released from the hot collapsed core (see also Janka 2012; Kotake et al. 2012; Burrows 2013; Pan et al. 2016), are responsible for the production of most of the intermediate mass elements, from O to Ti and some 56 Ni, decaying via 56 Co to 56 Fe (Woosley and Weaver 1995; Thielemann et al. 1996; Rauscher et al. 2002; Nomoto et al. 2006; Limongi and Chieffi 2006; Umeda and Nomoto 2008; Heger and Woosley 2010; Limongi and Chieffi 2012; Chieffi and Limongi 2013; Nakamura et al. 2015; Perego et al. 2015; Sukhbold et al. 2016). The long-standing question is whether a rapid neutron-capture (r-)process with neutron densities of 1026 cm3 and higher, producing highly unstable neutron-rich isotopes of all heavy elements and permitting a fast buildup of the heaviest elements up to the actinides, can take place in such explosions. Despite all remaining uncertainties in the explosion mechanism, recent conclusions are that at most a weak r-process,

Fig. 1 Abundances Yi of elements and Ptheir isotopes in the solar system as a function of mass number Ai D Zi C Ni , with a normalization leading to an abundance of 106 for 28 Si, rather than i Ai Yi D 1 as introduced in the text. Element ratios are obtained from solar spectra, the isotopic ratios from primitive meteorites and terrestrial values (Asplund et al. 2009). These values represent a snapshot in time of the abundances within the gas that formed the solar system. It formed from contributions of the Big Bang (light elements H, He, Li and their isotopes 1;2 H, 3;4 He, and 7 Li, given in yellow) plus stellar sources, contributing via winds and explosions to the interstellar medium until the formation of the solar system. The abundances result from charged-particle fusion reactions up to the Fe-group in stellar evolution and explosions (green) and neutron-capture processes. The latter are a superposition of (understood) slow neutron captures (s-process) in helium burning of stars (with abundance maxima at closed neutron shells for stable nuclei, blue), and an apparently rapid neutron capture process (r-process) leading to abundance maxima shifted to lighter nuclei (red). The r-process and its stellar origins represent the focus of this article

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producing some heavy elements, but not the actinides, can take place (Wanajo et al. 2011; Martínez-Pinedo et al. 2012; Roberts et al. 2012). Other speculated options, causing for low abundances of heavy elements sufficient amounts of neutrons in He-shells via neutrino interactions, would not be able to produce the solar r-process pattern (Banerjee et al. 2011). More complex events in binary stellar systems lead to novae (low-rate mass transfer onto white dwarfs and explosive eruption of the accreted layer), type Ia supernovae (either high-rate mass transfer onto white dwarfs or binary white dwarf mergers, causing in both cases the explosive disruption of an object exceeding the maximum stable Chandrasekhar mass), X-ray bursts on neutron stars with the explosive eruption of the outer accreted hydrogen layers, neutron star mergers (ejecting neutron-rich matter from a disk before forming a central black hole and emitting short-duration gamma-ray burst), or even mergers involving black holes. While novae and X-ray bursts are not of major importance for element synthesis in galaxies, type Ia supernovae are producing significant amounts of Si-Ti and probably about two thirds of the Fe and Ni in galaxies (Thielemann et al. 2004; Seitenzahl et al. 2013). The puzzle remains how all of these sources led finally to the solar system abundances of Fig. 1. We suggest to have a deeper look at all Handbook chapters listed in the cross references at the end of this article, especially the ones addressing nucleosnythesis and the effect of neutrinos on core-collapse supernova nucleosnythesis. The present chapter focuses on the possible sites for producing the heavy r-process elements.

2

Nucleosynthesis Contributions from Stellar Sources

Based on the nucleosynthesis predictions for (regular) core-collapse and for type Ia supernovae, plus their occurrence rates, one finds that the early phase of the evolution of galaxies is dominated by the ejecta of (fast evolving) massive stars, i.e., those leading to core-collapse supernovae. While there might exist differences for the ejecta composition of, e.g., 13, 15, 20, or 25 Mˇ stars, after an initial time delay, average production ratios will be found in the interstellar gas, obtained from integrating ejecta yields over the initial mass function of stars, i.e., the probability of finding stars for a certain mass. As type Ia supernovae originate from exploding white dwarfs in binary systems, i.e., (a) from stars with initially less than 8 Mˇ in order to become a white dwarf and (b) requiring mass transfer in a binary system, such explosions are delayed. This follows (a) because low and intermediate mass stars experience longer evolution phases and (b) binary evolution adds to the delay. For these reasons type Ia supernovae, dominating the production of Fe and Ni, are only important at later phases in galactic evolution. As core-collapse supernovae produce larger amounts of O, Ne, Mg, Si, S, Ar, Ca, and Ti (so-called alphaelements) than Fe-group nuclei like Fe and Ni, the average ratio of alpha/Fe is larger than the corresponding solar ratio. For most stars their surface abundances represent the composition of the interstellar gas out of which they formed. This is not the case for massive, already

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Fig. 2 Ratios of [Mg/Fe] (blue uncertainty range, indicating 95% of observations) and [Eu/Fe] (individual stellar observations shown as red error bars) as a function of “metallicity” [Fe/H] for stars in our Galaxy, as displayed in Thielemann (2015) and taken from a database (Suda et al. 2008, 2011). [X/Y] stands for log10 [(X/Y)/(X/Y)ˇ ], i.e., ŒMg=Fe D ŒFe=H D 0 for solar ratios, 1 for 1/10 of solar, etc.. Mg shows a relatively flat behavior up to ŒFe=H  1, turning down to solar values at ŒFe=H D 0. This is explained by the early contributions of core-collapse supernovae before type Ia supernovae set in. The real scatter is probably smaller than indicated by the blue region, as this is a collection of many observations from different telescopes, different observers, and different analysis techniques. To the contrary, the scatter of Eu/Fe is larger than two orders of magnitude at low metallicities, indicating production sites with a low event rate, thus taking longer to arrive at average values in the interval 2  ŒFe=H  1

evolved stars, which blew off part of their envelope by stellar winds or stars in binary systems with mass exchange. With these understood exceptions, we can look back into the early history of the Galaxy via the surface abundances of unevolved low-mass stars, witnessing the composition of the interstellar medium at the time of their birth. In Fig. 2 the ratio [Mg/Fe] is plotted as a function of metallicity [Fe/H] for stars in our Galaxy (taken from the database Suda et al. 2008, 2011). For Mg (a typical alpha-element and representative for many elements from O to Ti) one sees – with some scatter – a relatively flat behavior up to ŒFe=H  1, which turns over down to solar values at ŒFe=H D 0. This is explained by the early dominance of core-collapse supernovae from fast evolving massive, single stars, producing on average ŒMg=Fe D 0:4, before type Ia supernovae set in. The latter are delayed relative to core collapse supernovae due to their origin from a slower evolving lower mass star, which ends in a white dwarf, and the evolution of the binary system before the explosion (Hillebrandt et al. 2013). These basic features of galactic evolution are reasonably understood for a majority of elements (Matteucci and Greggio 1986), while many open questions in stellar evolution and the supernova explosion mechanisms still exist. (The latter includes also the question of the role of more massive stars, probably ending as black holes and related to so-called hypernovae/long-duration gamma-ray bursts, and even more massive pair instability supernovae.) The solar abundance of Eu is to more than 90% dominated by those isotopes which are produced in the r-process (Bisterzo et al. 2015). Therefore it is considered as a major r-process indicator. The ratio [Eu/Fe] shows a huge scatter by more than

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two orders of magnitude at low metallicities, i.e., very early in galactic evolution. While the average ratio resembles that of the alpha-elements, also experiencing a similar decline to solar ratios for ŒFe=H  1, this behavior might indicate also a supernova origin. However, it seems far more complex than understanding alpha-elements like Mg. In the literature there exist also a number of other suggested origins for the r-process. We will discuss these and the possibility of their discrimination in the following section.

3

Working of the r-Process and Possible Sources

As mentioned in the previous section, the scatter of Eu/Fe at low metallicities by more than two orders of magnitude (see Fig. 2) hints to production sites with a low event rate. Thus, (a) these cannot be the regular CCSNe which produce Fe, excluding also weak r-process sites (Wanajo et al. 2011; Martínez-Pinedo et al. 2012; Roberts et al. 2012) as well as neutrino-induced processes in outer shells of massive stars (Banerjee et al. 2011), as discussed above. Therefore, there should be no correlation between Fe and Eu (as actually observed (Cowan et al. 2005)). (b) The lower occurrence rate requires high amounts of r-process ejecta to be consistent with solar abundances and the average [Eu/Fe] at low metallicities. Therefore, the approach to an average value, only occurring in the interval 2  ŒFe=H  1, is shifted in comparison to the behavior of [Mg/Fe]. The much higher supernova rate, responsible for Mg, causes a much earlier approach to average values at metallicities of about ŒFe=H D 3. There have been a number of suggestions for sites in which the strong r-process originates, being related (i) to the innermost ejecta of regular neutrino-driven core-collapse supernovae (Woosley et al. 1994; Takahashi et al. 1994; Hoffman et al. 1997; Qian and Wasserburg 2007; Farouqi et al. 2010; Roberts et al. 2010, 2012; Martínez-Pinedo et al. 2012; Arcones and Thielemann 2013; Mirizzi et al. 2015), (ii) ejecta from binary neutron star mergers (Lattimer and Schramm 1976; Eichler et al. 1989; Freiburghaus et al. 1999b; Korobkin et al. 2012; Bauswein et al. 2013; Rosswog et al. 2014; Wanajo et al. 2014; Just et al. 2015; Goriely et al. 2015; Eichler et al. 2015; Goriely 2015; Mendoza-Temis et al. 2015; Ramirez-Ruiz et al. 2015), and (iii) a special class of core-collapse supernovae (MHD-jet supernovae) with fast rotation, high magnetic fields, and neutron-rich jet ejecta along the poles (Fujimoto et al. 2008; Ono et al. 2012; Winteler et al. 2012; Mösta et al. 2014; Nishimura et al. 2015; Mösta et al. 2015; Nishimura et al. 2017).

3.1

General Working of the r-Process

3.1.1 Explosive Burning Until Charged-Particle Freeze-Out In any of these cases, the production of r-process nuclei occurs in a two-stage process, defined by initial explosive burning at high temperatures until chargedparticle freeze-out during the expansion with a high neutron/seed ratio, and the following rapid capture of neutrons by these seed nuclei, producing the heaviest

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nuclei. In the first stage, matter experiences explosive burning at high temperatures and is heated to conditions which permit a so-called nuclear statistical equilibrium (NSE), which indicates a full chemical equilibrium of all involved nuclear reactions. At density  and temperature T , nucleus i – with neutron number Ni , proton number Zi , and mass number Ai D Zi C Ni – is existing with the abundance Yi , expressed in terms of the abundances of free neutrons Yn and protons Yp : 3=2

Yi D Gi .NA /Ai 1

Ai 2Ai



2„2 mu kT

3=2.Ai 1/

exp.Bi =kT /YnNi YpZi ;

(2)

where NA is Avogadro’s number, mu the nuclear mass unit, and Bi the nuclear binding energy of the nucleus. Beta-decays, electron captures, interP and neutrino P action change the overall proton to nucleon ration Ye D Zi Yi = Ai Yi (the denominator is the sum of all mass fractions and therefore equal to unity) and occur on longer time scales than particle captures and photodisintegrations. They are not in equilibrium and have to be followed explicitly. Thus, as a function of time, the NSE will follow the corresponding densities .t /, temperatures T .t /, and Ye .t /, leading to two equations based on total mass conservation and the existing Ye : X

Ai Yi D Yn CYp C

i>n;p

X i>n;p

X

.Zi CNi /Yi .; T; Yn ; Yp / D 1

(3)

i>n;p

Zi Yi D Yp C

X

Z Yi .; T; Yn ; Yp / D Ye :

(4)

i>n;p

In general, very high densities favor large nuclei, due to the high power of A1 , and very high temperatures favor light nuclei, due to .kT /3=2.A1/ . In the intermediate regime, exp.Bi =kT / favors tightly bound nuclei with the highest binding energies in the mass range A D 50  60 of the Fe-group, but depending on the given Ye . The width of the composition distribution is determined by the temperature. Thus, in this first stage of the scenario discussed here, high temperatures cause the (photo-)disintegration of nuclei into neutrons, protons, and alpha-particles, due to the energy distribution of the blackbody photon gas. During the subsequent cooling and expansion of matter, a buildup of heavier nuclei sets in, still being governed by the trend of keeping matter in NSE. However, the buildup of nuclei beyond He is hampered by the need of reaction sequences involving highly unstable 8 Be (e.g., ˛ C ˛ C ˛ ! 12 C or ˛ C ˛ C n ! 9 Be) which are strongly dependent on the density of matter. The first part of these reaction sequences involves a chemical equilibrium for ˛ C ˛ $ 8 Be which is strongly shifted to the left side of the reaction equation, due to the half-life of 8 Be (1=2 D 6:7  1017 s). Reasonable amounts of 8 Be, which permit the second stage of these reactions via an alpha-capture or neutron capture, can only be built up for high densities. The reaction rates for the combined reactions have a quadratic dependence on density in comparison to a linear density dependence in regular fusion reactions. Therefore, for low densities the NSE cannot be kept, and after further cooling and freeze-out of

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charged-particle reactions, an overabundance of alpha-particles (helium) remains, permitting only a (much) smaller fraction of heavier elements to be formed than in an NSE for the intermediate regime (determined by binding energies of nuclei). This result is also called an alpha-rich freeze-out (of charged-particle reactions) and leads to the fact that (a) the abundance of nuclei heavier than He is (strongly) reduced in comparison to their NSE abundances, and (b) the abundance maximum of the (fewer) heavy nuclei is shifted (via final alpha-captures) to heavier nuclei in comparison to an NSE. While this maximum would normally be around Fe and Ni (the highest binding energies) with A D 50  60, it can be shifted up to A about 90. In hot environments the total entropy is dominated by the blackbody photon gas (radiation) and proportional to T 3 = (Woosley and Hoffman 1992; Roberts et al. 2010), i.e., the combination of high temperatures and low densities leads to high entropies. Thus, high entropies lead to an alpha-rich freeze-out, and, dependent on the entropy, only small amounts of Fe-group elements are produced, essentially all matter which passed the bottleneck beyond He. This result is shown in Fig. 3. The calculation for Fig. 3, performed with an expansion timescale equivalent to a free fall for those conditions and a Ye D 0:45, shows how with increasing entropies the alpha mass fraction (X˛ D 4Y˛ ) is approaching unity and the amount of heavier elements (which would provide the seed nuclei for a later r-process) is going to zero. This is similar to the Big Bang, where extremely high entropies permit essentially only elements up to He and tiny amounts of Li. Opposite to the Big Bang, which is proton-rich, the conditions chosen here (Ye D 0:45) are slightly neutron-rich, leading at high entropies predominantly to He and free neutrons. The small amount of heavier nuclei after this charged-particle freeze-out (in the mass range of A = 50– 100), depending on the entropy or alpha-richness of the freeze-out, can then act

Fig. 3 Abundances of neutrons Yn , 4 He (alpha-particles) Y˛ , and so-called seed nuclei Yseed (in the mass range 50  A  100), resulting after the charged-particle freeze-out of explosive burning, as a function of entropy in the explosively expanding plasma, based on results by Farouqi et al. (2009). It can be realized that the ratio of neutrons to seed nuclei (n=seed D Yn =Yseed ) increases with entropy. The number of neutrons per seed nucleus determines whether the heaviest elements (actinides) can be produced in a strong r-process, requiring Aseed C n=seed  230

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Fig. 4 n/seed ratios (shown as contour lines) resulting in expanding hot plasmas from explosive burning as a function of the electron abundance Ye and the entropy (measured in kb per baryon). A strong r-process, producing the actinides with n/seed of 150, requires for moderate Ye s, of about 0.45, entropies beyond 250 (Freiburghaus et al. 1999a)

as seed nuclei for capture of the free neutrons. As prerequisite for an r-process, producing nuclei as heavy as the actinides and starting from A = 50–100 nuclei, a neutron/seed ratio of about 150 is required. This ratio is plotted in the form of a contour plot and as a function of entropy and Ye in Fig. 4, based on Freiburghaus et al. (1999a).

3.1.2 Neutron Captures in the r-Process Once the charged-particle freeze-out has occurred, resulting in a high neutron/seed ratio, the actual r-process – powered solely by the rapid capture of neutrons – can start, at temperatures below 3  109 K. As charged-particle reactions are frozen, the only connection between isotopic chains is given by beta-decays (unless, later on, fission will set in, repopulating lighter nuclei from fission fragments). High neutron densities make the timescales for neutron capture much faster than those for betadecay and can produce nuclei with neutron separation energies Sn of 2 MeV and less. This is the energy gained (Q-value) when capturing a neutron on nucleus A  1 and or the photon energy required to release a neutron from nucleus A via photo-disintegration. At the so-called neutron drip-line, Sn goes down to 0, i.e., such an r-process runs close to the neutron drip-line. For temperatures around 109 K, . ; n/ photodisintegrations can still be very active for such small reaction Sn -values, as only temperatures related to about 30 kT  Sn are required for these reverse reactions to dominate. With both reaction directions being faster than process timescales (and beta-decays), a chemical equilibrium can set in between neutron captures and photodisintegrations. In such a case, a complete chemical or nuclear statistical equilibrium (NSE) – discussed in the beginning of this subsection

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– splits into many (quasi-)equilibrium clusters, representing each an isotopic chain of heavy nuclei. The abundance distribution in each isotopic chain follows the ratio of two neighboring isotopes:    3=2 G.Z; A C 1/ A C 1 3=2 2„2 Y .Z; A C 1/ exp.Sn .A C 1/=kT /: D nn Y .Z; A/ 2G.Z; A/ A mu kT (5) with partition functions G, the nuclear-mass unit mu , and the neutron separation (or binding) energy of nucleus (Z; A C 1), Sn .A C 1/, being the neutron-capture Q-value of nucleus .Z; A/. This relation for a chemical equilibrium of neutron captures and photodisintegrations in an isotopic chain could be derived because the cross sections for these reactions and their reverses are linked via detailed balance between individual states in the initial and the final nucleus of each capture reaction. This causes the appearance of partition functions G for the complete reaction in a thermal plasma, describing the thermal population of excited states. The abundance ratios are dependent only on nn D NA Yn , T , and Sn . Sn introduces the dependence on nuclear masses, i.e., a nuclear mass model for these very neutronrich unstable nuclei. Under the assumption of an .n;  /•. ; n/ equilibrium, no detailed knowledge of neutron-capture cross sections is needed. One fact which can be easily deduced, given that Y .A C 1/=Y .A/ is first rising with increasing distance from stability, close to 1 at the abundance maximum of the isotopic chain, and finally decreasing, is that the abundance maxima in each isotopic chain are only determined by the neutron number density nn and the temperature T . Approximating Y .Z; A C 1/=Y .Z; A/ ' 1 at the maximum and keeping all other quantities constant, the neutron separation energy Sn has to be the same for the abundance maxima in all isotopic chains (see Fig. 5). Figure 5 shows such a contour line of Sn ' 2 MeV for the FRDM mass model (Möller et al. 1995). In addition, it displays the line of stability. As the speed along the r-process path is determined by beta-decays, and they are longest closer to stability, abundance maxima will occur at the top end of the kinks in the r-process path at neutron shell closures N D 50; 82; 126. This causes abundance maxima at the appropriate mass numbers A after decay back to stability at the end of the process, which correspond to smaller mass numbers A than those for stable nuclei with neutron shell closures. The latter – experiencing the smallest neutron-capture cross sections and determining the speed of the s-process – cause s-process maxima shifted to higher mass numbers. In environments with sufficiently high neutron densities, the r-process continues to extremely heavy nuclei and finally encounters the neutron shell closure N D 184, where fission plays a dominant role. Figure 6 (based also on simulations by Eichler et al. 2015) shows the regions of the nuclear chart where fission dominates and where the fission fragments are located. After having discussed here the general working of and the nuclear input for an r-process, the coming subchapters are related to test individual astrophysical environments. However, independently, the influence of nuclear uncertainties should be analyzed and how they affect the validity of suitable astrophysical environments.

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90 Pb (Z=82)

70 60

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proton number, Z

80

50 126

40 30

60

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140

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0.0

Fig. 5 Shown is (i) the line of stability (black squares) and (ii) the r-process path, resulting here from a neutron star merger environment which will be discussed further below (Eichler et al. 2015). The position of the path follows from a chemical equilibrium between neutron captures and photodisintegrations in each isotopic chain (.n; /  .; n/ equilibrium). However, the calculation was performed with a complete nuclear network containing more than 3000 nuclei. The colors along the path indicate how well the full network calculations follow such an .n; /  .; n/ equilibrium. It can be seen that such full calculations agree with this equilibrium approach within a factor of 2 along the r-process path, which continues to the heaviest nuclei. Only at the very end of the process, when neutron number densities and temperatures decline, such an equilibrium freezes out and some final changes of the abundance pattern can occur due to still continuing neutron captures

Recent tests with respect to mass models, beta-decay half-lives, and fission fragment distributions have been performed by Eichler et al. (2015), Goriely (2015), Mendoza-Temis et al. (2015), Marketin et al. (2016), Mumpower et al. (2016), and Panov et al. (2016).

3.2

r-Process Conditions in Neutrino-Driven Core-Collapse Supernovae

Supernovae have been thought to be the origin of the strong r-process for many years, with the intrinsic expectation that the innermost ejecta, coming from regions close to the neutron star, should be neutron-rich (see, e.g., Cowan et al. 1991; Sumiyoshi et al. 2001). Even when prompt explosions were realized to fail, early detailed and full-fledged r-process calculations in the neutrino wind, emerging from the hot proto neutron star, still underlined this expectation (Woosley and Hoffman 1992; Meyer et al. 1992; Woosley et al. 1994; Takahashi et al. 1994; Hoffman et al. 1997; Qian and Wasserburg 2007; Roberts et al. 2012; Arcones and Thielemann

5

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F.-K. Thielemann et al.

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Fig. 6 Shown are (color-coded) time derivatives of nuclear abundances Y during an r-process simulation (Eichler et al. 2015), due to (a, top left and right) the distruction via neutron-induced and beta-delayed fission (Panov et al. 2010) and (b, bottom) the production of fission fragments (Kelic et al. 2008). The latter are produced in a broad distribution, ranging in mass numbers A from 115 to 155

2013), and parametrized simulations led to quite impressive results (Freiburghaus et al. 1999a; Farouqi et al. 2010; Kratz et al. 2014). Figure 7 is taken from the latter reference and shows a close to excellent fit to solar r-process abundances, especially when utilizing modern input from nuclear mass models. However, in order to obtain this result, a superposition of entropies of up to 280 kB per baryon is needed, which present simulations of neutrino-driven corecollapse supernovae do not support (see e.g., Fischer et al. 2010; Hüdepohl et al. 2010; Arcones and Thielemann 2013; Roberts et al. 2012; Mirizzi et al. 2016). Thus, while a really high-entropy wind would be able to lead to a strong r-process, presently there is no indication that the required entropies can be attained in realistic core-collapse supernova simulations. An exception might be so-called electroncapture supernovae in the stellar mass range 8–10 Mˇ , which could lead to a weak

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Fig. 7 Results from an r-process calculation, assuming an initial Ye of 0.45, the adiabatic expansion of matter in a so-called neutrino wind with a given expansion speed vexp of ejected mass shells, and that a superposition of entropies S between 120 and 280 kB /baryon can be attained (Kratz et al. 2014). The abundance plot assumes that similar amounts of matter are ejected per entropy interval and indicates the changes which occur due to utilizing an improved nuclear mass model (Möller et al. 2012, 2016)

r-process (Kitaura et al. 2006; Janka et al. 2008; Wanajo et al. 2009, 2011), possibly producing nuclei up to Eu, but not up to and beyond the third r-process peak (for more details see Mirizzi et al. 2016).

3.3

The r-Process in Neutron Star Mergers

Neutron star black hole or binary neutron star mergers have been thought about first in the 1970s with respect to nucleosynthesis (Lattimer and Schramm 1974, 1976). In recent years they have also been considered, in addition to black hole mergers, as strong sources for gravitational wave emission (Abbott et al. 2016) and short-duration gamma-ray bursts (Rosswog et al. 2014). After the initial suggestion that they are the site of a strong r-process, first detailed nucleosynthesis predictions followed (Freiburghaus et al. 1999b). More recently they became a major focus of research (Panov and Thielemann 2004; Panov et al. 2008; Goriely et al. 2011; Korobkin et al. 2012; Panov et al. 2013; Bauswein et al. 2013; Rosswog et al. 2014; Wanajo et al. 2014; Just et al. 2015; Goriely et al. 2015; Eichler et al. 2015; Goriely 2015; Mendoza-Temis et al. 2015; Ramirez-Ruiz et al. 2015; Just et al. 2016). Material in neutron stars is cold, i.e., it possesses very low entropies, much lower than those discussed above in relation to Fig. 4, but due to the capture of high Fermi energy electrons on protons, the Ye -values are also much smaller than displayed in Fig. 4, of the order 0.03–0.05. If in Fig. 4 the entropy scale would be

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extended to such low values, one could observe a turnover to horizontal lines of the n/seed ratio contours and an n/seed of 150 would result at Ye D 0:1 Such low Ye ’s lead also to a strong r-process – even at low entropies. One of the aspects of earlier investigations, studying only the dynamical ejecta, i.e., matter “thrown out” dynamically after the merger of two compact objects with very low Ye , was that abundances below the second r-process peak (at A = 130) would only result from fission products. Thus, lighter r-process elements beyond the Fe-group have already experienced neutron capture and are not left in the final results. In addition, especially for Newtonian calculations, material had the tendency to be possibly too neutron-rich. This led to large amounts of very heavy nuclei prone to fission, remaining close to the end of the simulations. While initial conditions during the working of the r-process seem perfect to reproduce the second and third r-process peak and their positions, in the final phase, the fission of the heaviest nuclei produces large amounts of neutrons. If this happens during/after the freeze-out from .n;  /. ; n/ equilibrium, these neutrons can modify the overall abundance pattern inherited from the earlier equilibrium, especially shifting the third r-process peak. A number of tests, based on latest knowledge of nuclear physics far from stability, have been performed and can improve the overall abundance pattern. This relates to mass model properties like fission probabilities and fragment distributions (see Fig. 8) as well as beta-decay half-lives (Marketin et al. 2016; Panov et al. 2016), which speed up the production of the heaviest nuclei and lead to the fact that the final phase of fission sets in earlier with respect to the freeze-out and the smaller release of late neutrons has less effect on the pattern of the third r-process peak (see Fig. 9 and Eichler et al. 2015).

Fig. 8 Resulting r-process abundances (in comparison to solar values – black dots) from neutron star merger simulations (Eichler et al. 2015), making use of beta-decay half-lives from (Möller et al. 2003) together with a relatively old (Kodama and Takahashi 1975) and a modern set (Kelic et al. 2008) of fragment distributions of fissioning nuclei. However, in both cases a shift of the third r-process peak seems to occur in the final phases, driven by neutron capture of the released fission neutrons

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Fig. 9 Same as Fig. 8, but utilizing recent beta-decay half-life predictions (Marketin et al. 2016) (dashed black line) in comparison to an older set (Möller et al. 2003) (red line). Faster beta-decays for heavy nuclei, causing this way a speedup of the r-process, deliver (also in the final phases) nuclei which are prone to fission at an earlier time. This way, the late release of fission neutrons occurs at an earlier time, to a large extent before the freeze-out from (n; )(; n) equilibrium, which produces the r-process peaks at the correct position, before final neutron captures after freeze-out can distort this distribution. When comparing with Fig. 8, one can see that the latter effect is strongly reduced

Another aspect is, however, that not only the above mentioned dynamic ejecta will contribute to the nucleosynthesis of these events, there exists also a “neutrinowind,” similar to that discussed in core-collapse supernovae, from the hot, very massive combined object of the two neutron stars. This object, supported by high temperatures and rotation, will not collapse to a black hole, immediately. This matter experiences the radiation of neutrinos and antineutrinos, changing the Ye by the reactions: e C n ! p C e 

(6)

C

(7)

N e C p ! n C e

(see also sections of Sect. 3.1.1), which turns matter only neutron-rich if the average antineutrino energy is higher than the average neutrino energy by 4 times the neutron-proton mass difference. Thus, in most cases the energetically favorable first reaction wins, changing Ye from the initial (neutron-rich) conditions toward values closer to Ye D 0:5, which leads only to a weak r-process and produces matter below the second r-process peak. A first estimate of this outcome was presented in Rosswog et al. (2014). More detailed results have been shown by Perego et al. (2014); Martin et al. (2015). Such environments had already been investigated earlier in the context of disk winds in black hole accretion disks (Surman et al. 2006, 2008, 2014) as sites of heavy element nucleosynthesis with conditions being close to those resulting finally from neutron star mergers.

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There exists another aspect, which also affects the dynamical ejecta. Many of the simulations discussed above have been performed with Newtonian physics, i.e., nonrelativistically. As neutron stars and especially finally resulting black holes possess deep gravitational potentials, the role of general relativity is important and leads to deeper gravitational potentials plus higher temperatures experienced by the matter involved. This increases the importance of electron-positron pairs, positron captures on neutrons, and also the effect of neutrino radiation even for the dynamical ejecta. In total this increases Ye from 0.05 or less in pure neutron star matter to values around 0.1–0.15 (Wanajo et al. 2014; Goriely 2015). As a result less fission cycling occurs, which produces less late emission of fission neutrons, and therefore avoids some of the deficiencies of the abundance patterns discussed above with respect to Figs. 8 and 9.

3.4

A Special Rare Class of Magneto-Rotational Supernovae and Their Nucleosynthesis: The Role of Magnetars

CCSNe induced by strong magnetic fields and/or fast rotation of the stellar core, i.e., magneto-hydrodynamical supernovae (MHD-SNe), are considered to provide an alternative and robust astronomical source for the r-process (Symbalisty et al. 1985). Nucleosynthetic studies were carried out by Nishimura et al. (2006), based on adiabatic MHD simulations which exhibited a successful r-process in jetlike explosions. Additionally, MHD-driven collapsar models, involving black hole accretion disk systems (Nagataki et al. 2007; Fujimoto et al. 2008; Harikae et al. 2009), which are proposed as the central engine of long-duration gamma-ray bursts (GRBs) and/or hypernovae, have also been investigated as a site of the rprocess. The strong MHD-driven jet of magnetar and collapsar models can produce heavy r-process nuclei (Fujimoto et al. 2007, 2008; Ono et al. 2012), although these previous studies assumed a quite simplified treatment of the black hole and the required microphysics. One important question is whether the earlier results, assuming axis symmetry, also hold in full three-dimensional (3D) simulations, i.e., lead to the ejection of jets along the polar axis. 3D-MHD simulations with an improved treatment of neutrino physics were performed by Winteler et al. (2012) for a 15 Mˇ progenitor, utilizing an initial dipole magnetic field of 5  1012 G and a ratio of magnetic to gravitational binding energy, Emag =W D 2:63  108 . These calculations supported and confirmed the ejection of polar jets in 3D, attaining magnetic fields of the order 5  1015 G and Emag =W D 3:02  104 at core bounce, with a successful r-process up to and beyond the third r-process peak at A D 195 (Winteler et al. 2012) (Fig. 10). More recent general relativistic simulations in 3D-MHD (Mösta et al. 2014), involving a 25 Mˇ progenitor with an initial magnetic field of 1012 G, led in the early phase to jet formation, but experienced afterward a kink instability which deformed the jetlike feature. Possibly the difference between the two latter investigations in 3D hydrodynamics marks a transition due to passing critical limits in stellar mass, the initial rotation, and magnetic fields between a clear jetlike explosion and a deformed explosion. Nevertheless, when we see the time evolution of jet-like explosions

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a

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Fig. 10 In an MHD-jet supernova, the winding up of magnetic field lines causes the “squeezingout” of polar jets, along the rotation axis (Winteler et al. 2012). This environment leads to quite low entropies, shown on the left, which are much lower than those discussed in Fig. 4. But opposite to the Ye -values displayed in Fig. 4, the collapse to high densities resulted in large amounts of electron captures and Ye -values close to 0.1. Such low Ye s, similar to neutron star merger conditions (where even values as low as 0:03–0:05 are attained in Newtonian simulations), lead also to a strong rprocess – even at low entropies – and the abundance predictions displayed here on the right result (shown for two fission fragment distributions utilized Kelic et al. 2008 (ABLA07); Panov et al. 2008). Due to the slightly higher Ye , in comparison to neutron star mergers, the effect of late neutron capture by fission neutrons is reduced and the final shift of the third r-process peak can be avoided

with the a hydrodynamic instability (see results in Mösta et al. 2014), the region with the highest magnetic pressure contains essentially the matter corresponding to the initially forming jets before the deformation, which is expected to keep the nucleosynthetic features. Therefore 2D axissymmetric simulation should be sufficient to test nucleosythesis features. Nishimura et al. (2015, 2017) tested a whole variety of conditions in terms of rotation rates, initial magnetic fields, and ratios of neutrino luminosities vs. magnetic field strengths, assuming that the production of r-process elements and the overall nucleosynthesis composition will be close to reality in 2D approaches. It is mainly determined by the neutron richness of the ejecta rather than the property of shock propagation and the timescale of expansion in the outer layers. Their study included a series of long-term explosion simulations, based on special relativistic MHD (Takiwaki et al. 2009; Takiwaki and Kotake 2011), following the amplification of magnetic fields due to differential rotation (winding of magnetic fields) and the launch of jetlike explosions. One finds possible outcomes from prompt-magnetic-jet over delayed-magnetic-jet explosions up to dominantly neutrino-powered explosions, determined by the ratio of magnetic field strengths in comparison to neutrino heating. This causes also a variation of r-process nucleosynthesis results, from no r-process over a weak r-process, not producing nuclei of the third r-process peak, up to full-blown strong r-process environments.

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Understanding r-Process Sources from Observational Constraints

In the previous section, we discussed three scenarios, possibly leading to the ejection of a composition strongly enriched in heavy r-process nuclei. The first question to be asked is whether these theoretical predictions for an r-process are underpinned by observational proofs for these objects. Neutron star mergers represent a clear case. They are identified with short-duration gamma-ray bursts with light curves and spectra of electromagnetic counterparts which can be understood with opacities of very heavy elements (Metzger et al. 2010; Tanvir et al. 2013; Berger et al. 2013; Yang et al. 2015). The case of magneto-rotational supernovae (magnetars) is less clear, but we see neutron stars with magnetic fields of 1015 Gauss, which are hard to explain, if the core of the collapsing supernova progenitor would have less than 1012 Gauss (Kouveliotou et al. 1998; Kramer 2009). Recently such a magnetardriven supernova has actually been identified (Greiner et al. 2015). For both types of objects (neutron star mergers as well as MHD-jet supernovae), theory predicts r-process ejecta of a few times 103 –102 Mˇ . If they would have to be responsible for the solar r-process abundances, such large ejection of r-process matter could only be reconciled with low occurrence frequencies of the order 1 percent to 1 per mill of (regular) core-collapse supernovae. This is consistent with the neutron star merger rate and seems also to be consistent with the fraction of 1015 Gauss neutron stars. Core-collapse supernovae occur with a higher frequency, higher by 2–3 orders of magnitude. If they would be responsible for solar r-process abundances, this would require smaller amounts of r-process ejecta, of the order 104 –105 Mˇ per event. Presently we know no mechanism to create conditions for a strong r-process in (regular) core-collapse supernovae, but models have uncertainties and possibly still unknown physics. However, if such conditions could be attained for all regular corecollapse supernovae, solar abundances require that they eject only 104 –105 Mˇ of r-process matter per event. One interesting aspect of both most promising sources (compact object mergers and MHD-jet supernovae) would be that they apparently lead to a quite robust rprocess environment, which each time produces the heavy r-elements (at least those with 130  A  230) in proportions similar to solar (see Fig. 11 and Sneden et al. 2008; Roederer et al. 2012). On the other hand, both sources also have a late neutrino wind, which – due to higher Ye ’s – would also produce lighter rprocess elements, possibly in varying amounts, which could explain variations in the contribution of these lighter elements with Z  50 (Qian and Wasserburg 2007). A fraction of old metal-poor halo stars shows a large variety of abundance signatures (see, e.g., Honda et al. 2006; Hansen et al. 2014; Roederer 2016), not compatible with the classical r-process producing the heaviest r-process elements (which is the focus of the present article), but including r-elements like Eu. Possibly this is indicating a different weaker neutron-capture source, maybe a fraction of regular supernovae Nishimura et al. (2017)? Finally it should also be noted that

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Fig. 11 Shown are the observed abundances of typical low metallicity stars which unveils a clear r-process (and not an s-process) pattern, exactly as found in the solar system, at least for elements with Z  40 (Roederer et al. 2014)

not in all low-metallicity star observations Th and U show up in solar proportions (or with appropriate abundances due to their decay since production). Since their initial discovery (Cayrel et al. 2001), a number of such abundance patterns have been observed, up to now all in extremely metal-poor stars, This could indicate changes in the r-process strength, varying from regular to magneto-rotational supernovae (Nishimura et al. 2015, 2017).

4.1

Indirect Observations from Nearby Events

As mixing of ejecta into the interstellar medium is not instantaneous, there will be local inhomogeneities after recent nucleosynthesis events. Mixing occurs (a) via the plowing of a Sedov-Taylor blast wave through interstellar matter until the (kinetic) explosion energy is utilized, working against the ram pressure of the surrounding medium. For a standard explosion energy of E D 1051 erg (a unit known as 1 Bethe, or 1 foe, an acronym based on 10 to the fifty-one ergs) and typical densities of the interstellar medium, this results in mixing with about a few times 104 Mˇ . (b) There will be mixing via other more macroscopic phenomena, like turbulent mixing and/or spiral arm movements with timescales on the order of 108 years. While the latter effect can smooth abundance gradients, the first one will keep the individual composition of a specific explosive event until many other events

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in the same vicinity from different stellar sources (e.g., explosions of supernovae of different mass) polluted the interstellar medium. This causes an averaging of ejecta compositions, close to an integral over the initial mass function of stars, i.e., the distribution of stellar masses. Thus, while we expect an average value of, e.g., [Eu/Fe] to occur in late galactic evolution, rare events will lead at low metallicities to large variations, depending on the fact whether a rare nearby strong r-process source polluted the environment or was absent. While the above discussion points to rare strong r-process events in the early Galaxy, there exist other observations, suggesting the same in recent history. Longlived radioactive species can act as witness of recent additions to the solar system, dependent on their half-lives. For a review on the signature of radioactive isotopes alive in the early solar system, see, e.g., Davis and McKeegan (2014). Two specific isotopes have been utilized in recent years to measure such activities in deep-sea sediments. One of them, 60 Fe, has a half-life of 2:6  106 years and can indicate recent additions from events occurring up to several million years ago. 60 Fe is produced during the evolution and explosion of massive stars (leading to corecollapse supernovae) (Thielemann et al. 2011). It is found in deep-sea sediments which incorporated stellar debris from a nearby explosion about two million years ago (Knie et al. 2004; Wallner et al. 2016; Fimiani et al. 2016). Such contribution is consistent with a supernova origin and related occurrence frequencies, witnessing the last nearby event. Another isotope utilized, 244 Pu, has a half-life of 8:1107 years and would lead to a collection of quite a number of such supernova events. As discussed before, if the strong r-process would take place in every core-collapse supernova from massive stars, about 104 –105 Mˇ of r-process matter would need to be ejected in order to explain the present-day solar abundances. The recent 244 Pu detection (Wallner et al. 2015) is lower than expected from such predictions by two orders of magnitude, suggesting that actinide nucleosynthesis is very rare (permitting substantial decay since the last nearby event) and that supernovae did not contribute significantly to it in the solar neighborhood for the past few hundred million years. Thus, in addition to the inherent problems of (regular) core collapse supernova models to provide conditions required for a strong rprocess – also producing the actinides – these observational constraints from nearby events also challenge regular core-collapse supernovae as source of main r-process contributions. This leaves neutron star mergers and magneto-rotational (MHD-jet) supernovae as possible (rare) sources. Recently Hotokezaka et al. (2015) focused on the origin of the strong r-process and performed a very careful study of continuous accretion of interstellar dust grains into the inner solar system. They concluded that the recent experimental findings by Wallner et al. (2015) are in agreement with an r-process origin from neutron star mergers, explaining the initial 244 Pu existing in the very early solar system as well as the low level of recent additions witnessed in deep-sea sediments over the past few hundred million years. It remains to be seen whether other observational constraints can provide any clues about their role in the early Galaxy.

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Understanding r-Process Sources via (Inhomogeneous) Chemical Evolution of Galaxies

Neutron star mergers and MHD-jet supernovae have predicted high ejecta masses of the order of a few times 103 to 102 Mˇ of overall r-process matter and are rare in comparison to regular CCSNe with a frequency being smaller by a factor of 100 to 1000. The latter is consistent with (inhomogeneous) chemical evolution calculations (Argast et al. 2004; Mennekens and Vanbeveren 2014; Cescutti et al. 2015; van de Voort et al. 2015; Shen et al. 2015; Wehmeyer et al. 2015; Hirai et al. 2015; Mennekens and Vanbeveren 2016), which can follow local variations of abundances due to the specific contributions by individual explosions. The scatter of r-process elements (e.g., Eu) compared to Fe at low metallicities covers more than two orders of magnitude (see Fig. 2) and hints at production sites with a low event rate (and a consistent, high ejecta amount in order to explain solar abundances). This causes the effect that for [Eu/Fe], the approach to an average ratio occurs only in the interval 2  ŒFe=H  1. It is shifted in comparison to the behavior of [Mg/Fe], due to the much higher CCSNe rate. The latter permits a much earlier approach to an average ratio in the metallicity range ŒFe=H D 3. There seems to be only one caveat. A binary neutron star merger requires two prior supernova events (producing the two neutron stars and, e.g., Fe-ejecta) plus the binary evolution leading to the merger. This can shift the appearance of a typical r-process tracer like Eu to higher metallicities [Fe/H] (see Fig. 12), as discussed in Argast et al. (2004), Cescutti et al. (2015), and Wehmeyer et al. (2015).

[Eu/Fe]

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[Fe/H] Fig. 12 Influence of coalescence timescale and neutron star merger probability on Eu-abundances in galactic chemical evolution. Magenta stars represent observations. Red/brown dots correspond to model star abundances as in Argast et al. (2004). The coalescence timescale utilized is 108 years with a typical probability consistent with population synthesis (Wehmeyer et al. 2015). Yellow dots illustrate the effect on the abundances if the coalescence timescale is shorter (around 106 years). Blue dots show the abundance change if the probability of neutron star mergers is increased. Within this treatment of galactic chemical evolution, none of these options would permit a fit with observations of low metallicity stars in the metallicity range 4  ŒFe=H  2:5

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However, there are uncertainties related on the one hand to the resolution achieved in global galaxy evolution models with smooth particle hydrodynamic simulations (van de Voort et al. 2015; Shen et al. 2015), to the history of the local star formation rate, and to the amount of mixing of the ejecta with the interstellar medium, as well as other galactic mixing events and their timescales, which can blur the picture and still have to be worked out (Hirai et al. 2015; Ramirez-Ruiz et al. 2015). Alternatively, rare supernovae might play a significant role. Alternatively a rare class of CCSNe, exploding earlier in galactic evolution, could be responsible at low metallicities. Early suggestions that so-called electron-capture supernovae in the stellar mass range 8–10 Mˇ (Kitaura et al. 2006; Janka et al. 2008; Wanajo et al. 2009, 2011) would be able to produce a strong r-process were never confirmed, and they would also not correspond to rare events. However, other objects driven by strong magnetic fields and fast rotation (possibly about 1% or less of all corecollapse supernovae), leaving behind 1015 Gauss neutron stars (magnetars), might play a significant role. Such magneto-rotational SNe show similar characteristics in the amount of r-process ejecta and the occurrence frequency as neutron star mergers, but – because these objects result from massive single stars – they do not experience the delay of binary evolution (Winteler et al. 2012; Nishimura et al. 2015, 2017). This means that they enter galactic evolution at lowest metallicities with a similar scatter due to them being rare events. This can be seen in Fig. 13, which shows the result of a superposition of MHD-jet supernovae and neutron star mergers. This way observations can be matched from lowest metallicities up to present. As said, there are uncertainties in mixing process, star formation rates, etc. which will affect the behavior at lowest metallicities, but we would argue that the existing observations are evidence for the occurrence of MHD-jet supernovae (magnetars Greiner et al. 2015) and simulations predict the conditions for an r-process. However, as shown in Nishimura et al. (2015, 2017), dependent on rotation frequency, magnetic fields,

[Eu/Fe]

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[Fe/H] Fig. 13 Evolution of Eu-abundances in galactic chemical evolution models (Wehmeyer et al. 2015) including both magneto-rotational supernovae and neutron star mergers as r-process sites. Magenta stars represent observations whereas green dots represent model stars. The combination of MHD-jet supernovae – being of strong importance at low metallicitie – early in the evolution of the Galaxy, and neutron star mergers indicate a perfect fit with observations

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and the impact of neutrino heating in comparison to the strength of magnetic fields, the strength of the r-process can vary, while neutron star mergers seem to predict a robust and unchangeable abundance pattern (Rosswog et al. 2014). It is not clear how strong this evidence is, but at low metallicities, there exist observations with a somewhat changing Eu/U ratio, indicating to which extent the production of actinides is robustly coupled to Eu. These few events with a regular r-process pattern but changing amounts of actinides are all seen at metallicities around [Fe/H] = 3, possibly making connections to MHD supernovae which would dominate the strong r-process production at low metallicities. It is reasonable to expect that at low metallicity, MHD SNe are more frequent than in the present Galaxy. Low metallicity stars have smaller amounts of wind/mass (and therefore) angular momentum loss, providing more promising initial conditions at the onset of collapse for these events. Finally, it needs to be investigated whether MHD-driven collapsar models and BH accretion disk systems (Fujimoto et al. 2006; Nagataki et al. 2007; Harikae et al. 2009), which are proposed as the central engine of long-duration gamma-ray-burst (GRBs) and hypernovae, can be a site of the r-process.

5

Conclusions

This review summarized our present knowledge how the heaviest elements in the Universe are made: 1. We know that they are made by the rapid neutron capture process (r-process), but what is the astrophysical site and origin? 2. What we know from radioactive tracers in deep-sea sediments like 244 Pu as well as 60 Fe is that the latter is produced in frequent events related to regular CCSNe, while 244 Pu must be produced in much rarer events. This is also underlined by the large scatter of Eu/Fe (Eu being an r-process element) seen in the earliest stars of the Galaxy, indicating that in a not yet well mixed interstellar medium the products of these rare events are even less well mixed. 3. We also know that neutron star mergers (or neutron star black hole mergers) are related to short-duration gamma-ray bursts and electromagnetic counterparts can only be explained if the opacity of ejected matter is dominated by heavy elements. Simulations of such events lead to about a few times 103 Mˇ of ejected r-process matter, and population synthesis tells us that these events are very rare (probably about 1/100 of the supernova frequency). 4. The major open question is whether products of the neutron star merger r-process can explain the observations of r-process elements seen already at metallicities of [Fe/H]  3. As the supernovae which produce the neutron stars of a merger already lead to a substantial floor of Fe, i.e., enhance [Fe/H], this could only be achieved if substantial turbulent mixing of interstellar medium matter is occurring in the early Galaxy. 5. We also have now observational indications of so-called magnetars, i.e., supernova explosions leading to 1015 Gauss neutron stars. Simulations of core-collapse

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supernovae driven by a magneto-rotational mechanism can lead to such neutron stars with immense magnetic fields and could produce r-process matter ejected in polar jets. However, (a) we need predictions from stellar evolution about the distribution of magnetic fields and rotation rates before core collapse in order to understand the initial conditions possibly leading to such events, and (b) how can such high magnetic fields be produced via the magneto-rotational instability (MRI) during the collapse/explosion phase, if stellar evolution does not arrive at the required initial fields? 6. If magnetars, very likely also with a low event rate of the order 1/100 of regular CCSNe, are r-process sources as predicted by stellar simulations, they could avoid the possible problems of the neutron star merger scenario at low metallicities. They are related to massive single stars and do not experience any delay in comparison to regular CCSNe, just a lower event rate, i.e., being a small fraction of them. Thus, what is needed is (i) to investigate inhomogeneous galactic evolution models with an improved understanding of star formation and turbulent mixing, (ii) to obtain improved predictions from stellar evolution on rotation rates and magnetic fields in the late stages of stellar evolution, (iii) to understand the role of the MRI in global simulations of magnetars with high enough resolution to resolve such effects, and (iv) to improve the understanding of nuclear physics far from stability (including experiments and theoretical predictions of masses and beta-decay rates of highly neutron-rich nuclei, as well as fission probabilities and the distribution of fission fragments), which enter directly in the predicted abundance distribution, possibly best fit to the r-process abundance distribution in the solar system. Independent of this, the modeling of neutron star mergers has to be improved via fully relativistic calculations and the analysis of the so-called neutrino wind, which comes later than the dynamic ejecta directly after the merger and will exist until the formation of a central black hole. With this improved input, results can be compared to observations at low metallicity, also looking into special systems like dwarf spheroidal galaxies which might give a better hint at the earliest evolution of galaxies. After discussing the requirements for r-process conditions and the simulations which are supposed to produce them, we come (with our present-day knowledge) to the conclusion that two events with low occurrence frequencies, neutron star mergers as well as MHD-jet supernovae, are responsible for a strong r-process and the production of actinides in our Galaxy and the Universe. This is supported by observational constraints. The combined results of recent deep-sea sediment analysis, probing the recent history of our Galaxy (near the solar system), as well as the lowest metallicity observations in the early Galaxy, point to an origin of the strong r-process which is a rare event in comparison to CCSNe. There are indications that fast rotating MHD-jet supernovae are required to explain observations at lowest metallicities (where smaller amounts of stellar wind-loss also lead to less angular momentum loss during stellar evolution). It is not yet evident how the rate of such events changes with metallicity. The above argument would support a decreasing frequency, but the present existence of magnetars also indicates

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that they still form today. Nevertheless, neutron star mergers are probably one of the dominant r-process sources in recent galactic history.

6

Cross-References

 Detecting Gravitational Waves from Supernovae with Advanced LIGO  Diffuse Neutrino Flux from Supernovae  Gravitational Waves from Core-Collapse Supernovae  High-Energy Cosmic Rays from Supernovae  High-Energy Gamma Rays from Supernova Remnants  Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Super-

nova Mechanism  Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis  Neutrino Emission from Supernovae  Neutrinos from Core-Collapse Supernovae and Their Detection  Neutrino Signatures from Young Neutron Stars  Nucleosynthesis in Hypernovae Associated with Gamma Ray Bursts  Nucleosynthesis in Thermonuclear Supernovae  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Pre-supernova Evolution and Nucleosynthesis in Massive Stars and Their Stellar

Wind Contribution  The Multidimensional Character of Nucleosynthesis in Core-Collapse Super-

novae Acknowledgements We want to thank all our collaborators with whom we investigated rprocess sites and conditions in the past, as well as everybody with whom we had enlightening discussions. These include Almudena Arcones, Gabriele Cescutti, Cristina Chiappini, John Cowan, Khalil Farouqi, Brad Gibson, Yuhri Ishimaru, Roger Käppeli, Oleg Korobkin, Karl-Ludiwg Kratz, Karlheinz Langanke, Andreas Lohs, Lucio Mayer, Matthias Liebendörfer, Dirk Martin, Gabriel Martinez-Pinedo, Francesca Matteucci, Nobuya Nishimura, Albino Perego, Tsvi Piran, Thomas Rauscher, Stephan Rosswog, Chris Sneden, Rebecca Surman, Tomo Takiwaki, Shinja Wanajo, Christian Winteler, and many others. This research was supported by the Swiss SNF (via a regular research grant and a SCOPES grant for collaborations with Eastern Europe), an ERC Advanced Grant from the European Commission (FISH), the Russian Science Foundation (16-12-10519), the Lendulet-2014 Program of the Hungarian Academy of Sciences, and the BRIDGCE Network in the UK.

References Abbott BP, Abbott R, Abbott TD, Abernathy MR, Acernese F, Ackley K, Adams C, Adams T, Addesso P, Adhikari RX et al (2016) GW150914: the advanced LIGO detectors in the era of first discoveries. Phys Rev Lett 116(13):131103. doi:10.1103/PhysRevLett.116.131103, arXiv:1602.03838 Arcones A, Thielemann FK (2013) Neutrino-driven wind simulations and nucleosynthesis of heavy elements. J Phys G Nucl Phys 40(1):013201. doi:10.1088/0954-3899/40/1/013201, 1207.2527

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Argast D, Samland M, Thielemann FK, Qian YZ (2004) Neutron star mergers versus core-collapse supernovae as dominant r-process sites in the early Galaxy. Astron Astrophys 416:997–1011. doi:10.1051/0004-6361:20034265, astro-ph/0309237 Asplund M, Grevesse N, Sauval AJ, Scott P (2009) The chemical composition of the sun. Ann Rev Astron Astroph 47:481–522. doi:10.1146/annurev.astro.46.060407.145222, 0909.0948 Banerjee P, Haxton WC, Qian YZ (2011) Long, cold, early r-process? Neutrino-induced nucleosynthesis in He shells revisited. Phys Rev Lett 106(20):201104. doi:10.1103/PhysRevLett.106.201104, 1103.1193 Bauswein A, Goriely S, Janka HT (2013) Systematics of dynamical mass ejection, nucleosynthesis, and radioactively powered electromagnetic signals from Neutron-star mergers. Astrophys J 773:78. doi:10.1088/0004-637X/773/1/78, 1302.6530 Berger E, Fong W, Chornock R (2013) An r-process Kilonova associated with the short-hard GRB 130603B. Astrophys J Lett 774:L23. doi:10.1088/2041-8205/774/2/L23, 1306.3960 Bisterzo S, Gallino R, Käppeler F, Wiescher M, Imbriani G, Straniero O, Cristallo S, Görres J, deBoer RJ (2015) The branchings of the main s-process: their sensitivity to ˛-induced reactions on 13 C and 22 Ne and to the uncertainties of the nuclear network. Mon Not Roy Astron Soc 449:506–527. doi:10.1093/mnras/stv271, 1507.06798 Burbidge EM, Burbidge GR, Fowler WA, Hoyle F (1957) Synthesis of the elements in stars. Rev Mod Phys 29:547–650. doi:10.1103/RevModPhys.29.547 Burrows A (2013) Colloquium: perspectives on core-collapse supernova theory. Rev Mod Phys 85:245–261. doi:10.1103/RevModPhys.85.245, 1210.4921 Cameron AGW (1957) Nuclear reactions in stars and nucleogenesis. Publ Astron Soc Pac 69:201. doi:10.1086/127051 Cayrel R, Hill V, Beers TC, Barbuy B, Spite M, Spite F, Plez B, Andersen J, Bonifacio P, François P, Molaro P, Nordström B, Primas F (2001) Measurement of stellar age from uranium decay. Nature 409:691–692, astro-ph/0104357 Cescutti G, Romano D, Matteucci F, Chiappini C, Hirschi R (2015) The role of neutron star mergers in the chemical evolution of the Galactic halo. Astron Astrophys 577:A139. doi:10.1051/0004-6361/201525698, 1503.02954 Chieffi A, Limongi M (2013) Pre-supernova evolution of rotating solar metallicity stars in the mass range 13–120 MŁ and their explosive yields. Astrophys J 764:21. doi:10.1088/0004-637X/764/1/21 Cowan JJ, Rose WK (1977) Production of C-14 and neutrons in red giants. Astrophys J 212:149– 158. doi:10.1086/155030 Cowan JJ, Thielemann FK, Truran JW (1991) The R-process and nucleochronology. Phys Rep 208:267–394. doi:10.1016/0370-1573(91)90070-3 Cowan JJ, Sneden C, Beers TC, Lawler JE, Simmerer J, Truran JW, Primas F, Collier J, Burles S (2005) Hubble space telescope observations of heavy elements in metal-poor galactic halo stars. Astrophys J 627:238–250. doi:10.1086/429952, astro-ph/0502591 Cyburt RH, Fields BD, Olive KA, Yeh TH (2016) Big bang nucleosynthesis: present status. Rev Mod Phys 88(1):015004. doi:10.1103/RevModPhys.88.015004, 1505.01076 Davis AM, McKeegan KD (2014) Short-lived radionuclides and early solar system chronology. In: Davis AM (ed) Meteorites and cosmochemical processes. Volume 1 of treatise on geochemistry, 2nd edn. Elsevier, Amsterdam, pp 361–395 Eichler D, Livio M, Piran T, Schramm DN (1989) Nucleosynthesis, neutrino bursts and gammarays from coalescing neutron stars. Nature 340:126–128. doi:10.1038/340126a0 Eichler M, Arcones A, Kelic A, Korobkin O, Langanke K, Marketin T, Martinez-Pinedo G, Panov I, Rauscher T, Rosswog S, Winteler C, Zinner NT, Thielemann FK (2015) The role of fission in neutron star mergers and its impact on the r-process peaks. Astrophys J 808:30. doi:10.1088/0004-637X/808/1/30, 1411.0974 Farouqi K, Kratz K-L, Mashonkina LI, Pfeiffer B, Cowan JJ, Thielemann FK, Truran JW (2009) Nucleosynthesis modes in the high-entropy wind of type ii supernovae: comparison of calculations with halo-star observations. Astrophys J Lett 694:L49–L53

71 Making the Heaviest Elements in a Rare Class of Supernovae

1871

Farouqi K, Kratz KL, Pfeiffer B, Rauscher T, Thielemann FK, Truran JW (2010) Charged-particle and neutron-capture processes in the high-entropy wind of core-collapse supernovae. Astrophys J 712:1359–1377. doi:10.1088/0004-637X/712/2/1359, 1002.2346 Fimiani L, Cook DL, Faestermann T, Gómez-Guzmán JM, Hain K, Herzog G, Knie K, Korschinek G, Ludwig P, Park J, Reedy RC, Rugel G (2016) Interstellar 60 Fe on the surface of the moon. Phys Rev Lett 116(15):151104. doi:10.1103/PhysRevLett.116.151104 Fischer T, Whitehouse SC, Mezzacappa A, Thielemann FK, Liebendörfer M (2010) Protoneutron star evolution and the neutrino-driven wind in general relativistic neutrino radiation hydrodynamics simulations. Astron Astrophys 517:A80. doi:10.1051/0004-6361/200913106, 0908.1871 Freiburghaus C, Rembges JF, Rauscher T, Kolbe E, Thielemann FK, Kratz KL, Pfeiffer B, Cowan JJ (1999a) The astrophysical r-Process: a comparison of calculations following adiabatic expansion with classical calculations based on neutron densities and temperatures. Astrophys J 516:381–398. doi:10.1086/307072 Freiburghaus C, Rosswog S, Thielemann FK (1999b) R-process in neutron star mergers. Astrophys J Lett 525:L121–L124. doi:10.1086/312343 Fröhlich C, Martínez-Pinedo G, Liebendörfer M, Thielemann FK, Bravo E, Hix WR, Langanke K, Zinner NT (2006) Neutrino-induced nucleosynthesis of A > 64 nuclei: the p process. Phys Rev Lett 96(14):142502. doi:10.1103/PhysRevLett.96.142502, astro-ph/0511376 Fujimoto Si, Kotake K, Yamada S, Hashimoto Ma, Sato K (2006) Magnetohydrodynamic simulations of a rotating massive star collapsing to a black hole. Astrophys J 644:1040–1055. doi:10.1086/503624, astro-ph/0602457 Fujimoto Si, Hashimoto Ma, Kotake K, Yamada S (2007) Heavy-element nucleosynthesis in a collapsar. Astrophys J 656:382–392. doi:10.1086/509908, astro-ph/0602460 Fujimoto Si, Nishimura N, Hashimoto Ma (2008) Nucleosynthesis in magnetically driven jets from collapsars. Astrophys J 680:1350–1358 doi:10.1086/529416, 0804.0969 Goriely S (2015) Towards more accurate and reliable predictions for nuclear applications. Eur Phys J A 51:172. doi:10.1140/epja/i2015-15172-2 Goriely S, Bauswein A, Janka HT (2011) r-process nucleosynthesis in dynamically ejected matter of neutron star mergers. Astrophys J Lett 738:L32. doi:10.1088/2041-8205/738/2/L32, 1107.0899 Goriely S, Bauswein A, Just O, Pllumbi E, Janka HT (2015) Impact of weak interactions of free nucleons on the r-process in dynamical ejecta from neutron star mergers. Mon Not R Astron Soc 452:3894–3904. doi:10.1093/mnras/stv1526, 1504.04377 Greiner J, Mazzali PA, Kann DA, Krühler T, Pian E, Prentice S, Olivares E F, Rossi A, Klose S, Taubenberger S, Knust F, Afonso PMJ, Ashall C, Bolmer J, Delvaux C, Diehl R, Elliott J, Filgas R, Fynbo JPU, Graham JF, Guelbenzu AN, Kobayashi S, Leloudas G, Savaglio S, Schady P, Schmidl S, Schweyer T, Sudilovsky V, Tanga M, Updike AC, van Eerten H, Varela K (2015) A very luminous magnetar-powered supernova associated with an ultra-long -ray burst. Nature 523:189–192. doi:10.1038/nature14579, 1509.03279 Hansen CJ, Montes F, Arcones A (2014) How many nucleosynthesis processes exist at low metallicity? Astrophys J 797:123. doi:10.1088/0004-637X/797/2/123, 1408.4135 Harikae S, Takiwaki T, Kotake K (2009) Long-term evolution of slowly rotating collapsar in special relativistic magnetohydrodynamics. Astrophys J 704:354–371. doi:10.1088/0004-637X/704/1/354, 0905.2006 Heger A, Woosley SE (2010) Nucleosynthesis and evolution of massive metal-free stars. Astrophys J 724:341–373. doi:10.1088/0004-637X/724/1/341, 0803.3161 Hillebrandt W, Kromer M, Röpke FK, Ruiter AJ (2013) Towards an understanding of type Ia supernovae from a synthesis of theory and observations. Front Phys 8:116–143. doi:10.1007/s11467-013-0303-2, 1302.6420 Hirai Y, Ishimaru Y, Saitoh TR, Fujii MS, Hidaka J, Kajino T (2015) Enrichment of r-process elements in dwarf spheroidal galaxies in chemo-dynamical evolution model. Astrophys J 814:41. doi:10.1088/0004-637X/814/1/41, 1509.08934

1872

F.-K. Thielemann et al.

Hix WR, Thielemann FK (1999) Computational methods for nucleosynthesis and nuclear energy generation. J Comput Appl Math 109:321–351. astro-ph/9906478 Hoffman RD, Woosley SE, Qian YZ (1997) Nucleosynthesis in neutrino-driven winds. II. Implications for heavy element synthesis. Astrophys J 482:951–962. astro-ph/9611097 Honda S, Aoki W, Ishimaru Y, Wanajo S, Ryan SG (2006) Neutron-capture elements in the very metal poor star HD 122563. Astrophys J 643:1180–1189. doi:10.1086/503195, astroph/0602107 Hotokezaka K, Piran T, Paul M (2015) Short-lived 244 Pu points to compact binary mergers as sites for heavy r-process nucleosynthesis. Nature Phys 11:1042. doi:10.1038/nphys3574, 1510.00711 Hüdepohl L, Müller B, Janka HT, Marek A, Raffelt GG (2010) Neutrino signal of electron-capture supernovae from core collapse to cooling. Phys Rev Lett 104(25):251101. doi:10.1103/PhysRevLett.104.251101, 0912.0260 Iliadis C (2007) Nuclear physics of stars. Wiley-VCH Verlag, Weinheim. doi:10.1002/9783527692668 Janka HT (2012) Explosion mechanisms of core-collapse supernovae. Ann Rev Nucl Part Sci 62:407–451. doi:10.1146/annurev-nucl-102711-094901, 1206.2503 Janka HT, Müller B, Kitaura FS, Buras R (2008) Dynamics of shock propagation and nucleosynthesis conditions in O-Ne-Mg core supernovae. Astron Astrophys 485:199–208. doi:10.1051/0004-6361:20079334, 0712.4237 Jones S, Hirschi R, Nomoto K, Fischer T, Timmes FX, Herwig F, Paxton B, Toki H, Suzuki T, Martínez-Pinedo G, Lam YH, Bertolli MG (2013) Advanced burning stages and fate of 8–10 M ˇ stars. Astrophys J 772:150. doi:10.1088/0004-637X/772/2/150, 1306.2030 Jones S, Ritter C, Herwig F, Fryer C, Pignatari M, Bertolli MG, Paxton B (2016) H ingestion into He-burning convection zones in super-AGB stellar models as a potential site for intermediate neutron-density nucleosynthesis. Mon Not Roy Astron Soc 455:3848–3863. doi:10.1093/mnras/stv2488, 1510.07417 Just O, Bauswein A, Pulpillo RA, Goriely S, Janka HT (2015) Comprehensive nucleosynthesis analysis for ejecta of compact binary mergers. Mon Not R Astron Soc 448:541–567. doi:10.1093/mnras/stv009, 1406.2687 Just O, Obergaulinger M, Janka HT, Bauswein A, Schwarz N (2016) Neutron-star Merger ejecta as obstacles to neutrino-powered jets of gamma-ray bursts. Astrophys J Lett 816:L30. doi:10.3847/2041-8205/816/2/L30, 1510.04288 Käppeler F, Gallino R, Bisterzo S, Aoki W (2011) The s-process: Nuclear physics, stellar models, and observations. Rev Mod Phys 83:157–194. doi:10.1103/RevModPhys.83.157, 1012.5218 Karakas AI, Lattanzio JC (2014) The dawes review 2: nucleosynthesis and stellar yields of lowand intermediate-mass single stars. Proc Astron Soc Aust 31:e030. doi:10.1017/pasa.2014.21, 1405.0062 Kelic A, Ricciardi MV, Schmidt KH (2008) New insight into the fission process from experiments with relativistic heavy-ion beams. In: Kliman J, Itkis MG, Gmuca Š (eds) Dynamical aspects of nuclear fission. World Scientific, Singapore/Hackensack, pp 203–215. doi:10.1142/9789812837530_0016 Kitaura FS, Janka HT, Hillebrandt W (2006) Explosions of O-Ne-Mg cores, the crab supernova, and subluminous type II-P supernovae. Astron Astrophys 450:345–350. doi:10.1051/0004-6361:20054703, astro-ph/0512065 Knie K, Korschinek G, Faestermann T, Dorfi EA, Rugel G, Wallner A (2004) 60 Fe anomaly in a deep-sea manganese crust and implications for a nearby supernova source. Phys Rev Lett 93(17):171103. doi:10.1103/PhysRevLett.93.171103 Kodama T, Takahashi K (1975) R-process nucleosynthesis and nuclei far from the region of ˇstability. Nucl Phys A 239:489–510. doi:10.1016/0375-9474(75)90381-4 Korobkin O, Rosswog S, Arcones A, Winteler C (2012) On the astrophysical robustness of the neutron star merger r-process. Mon Not R Astron Soc 426:1940–1949. doi:10.1111/j.1365-2966.2012.21859.x, 1206.2379

71 Making the Heaviest Elements in a Rare Class of Supernovae

1873

Kotake K, Takiwaki T, Suwa Y, Iwakami Nakano W, Kawagoe S, Masada Y, Fujimoto Si (2012) Multimessengers from core-collapse supernovae: multidimensionality as a key to bridge theory and observation. Adv Astron 2012:428757. doi:10.1155/2012/428757, 1204.2330 Kouveliotou C, Dieters S, Strohmayer T, van Paradijs J, Fishman GJ, Meegan CA, Hurley K, Kommers J, Smith I, Frail D, Murakami T (1998) An X-ray pulsar with a superstrong magnetic field in the soft -ray repeater SGR1806 – 20. Nature 393:235–237. doi:10.1038/30410 Kramer M (2009) Pulsars & magnetars. In: Strassmeier KG, Kosovichev AG, Beckman JE (eds) Cosmic magnetic fields: from planets, to stars and galaxies, IAU Symposium, Baltimore, vol 259, pp 485–492. doi:10.1017/S1743921309031159 Kratz KL, Farouqi K, Möller P (2014) A high-entropy-wind r-process study based on nuclearstructure quantities from the new finite-range droplet model Frdm(2012). Astrophys J 792:6. doi:10.1088/0004-637X/792/1/6, 1406.2529 Lattimer JM, Schramm DN (1974) Black-hole-neutron-star collisions. Astrophys J Lett 192:L145– L147. doi:10.1086/181612 Lattimer JM, Schramm DN (1976) The tidal disruption of neutron stars by black holes in close binaries. Astrophys J 210:549–567. doi:10.1086/154860 Limongi M, Chieffi A (2006) The Nucleosynthesis of 26 Al and 60 Fe in solar metallicity stars extending in mass from 11 to 120 Msolar : the hydrostatic and explosive contributions. Astrophys J 647:483–500. doi:10.1086/505164, astro-ph/0604297 Limongi M, Chieffi A (2012) Presupernova evolution and explosive nucleosynthesis of zero metal massive stars. Astrophys J Sup 199:38. doi:10.1088/0067-0049/199/2/38, 1202.4581 Maeder A, Meynet G (2012) Rotating massive stars: from first stars to gamma ray bursts. Rev Mod Phys 84:25–63. doi:10.1103/RevModPhys.84.25 Marketin T, Huther L, Martínez-Pinedo G (2016) Large-scale evaluation of ˇ-decay rates of r-process nuclei with the inclusion of first-forbidden transitions. Phys Rev C 93(2):025805. doi:10.1103/PhysRevC.93.025805, 1507.07442 Martin D, Perego A, Arcones A, Thielemann FK, Korobkin O, Rosswog S (2015) Neutrino-driven winds in the aftermath of a neutron star merger: nucleosynthesis and electromagnetic transients. Astrophys J 813:2. doi:10.1088/0004-637X/813/1/2, 1506.05048 Martínez-Pinedo G, Fischer T, Lohs A, Huther L (2012) Charged-current weak interaction processes in hot and dense matter and its impact on the spectra of neutrinos emitted from protoneutron star cooling. Phys Rev Lett 109(25):251104. doi:10.1103/PhysRevLett.109.251104, 1205.2793 Matteucci F, Greggio L (1986) Relative roles of type I and II supernovae in the chemical enrichment of the interstellar gas. Astron Astrophys 154:279–287 Mendoza-Temis JdJ, Wu MR, Langanke K, Martínez-Pinedo G, Bauswein A, Janka HT (2015) Nuclear robustness of the r-process in neutron-star mergers. Phys Rev C 92(5):055805. doi:10.1103/PhysRevC.92.055805 Mennekens N, Vanbeveren D (2014) Massive double compact object mergers: gravitational wave sources and r-process element production sites. Astron Astrophys 564:A134. doi:10.1051/0004-6361/201322198, 1307.0959 Mennekens N, Vanbeveren D (2016) The delay time distribution of massive double compact star mergers. Astron Astrophys 589:A64. doi:10.1051/0004-6361/201628193, 1601.06966 Metzger BD, Martínez-Pinedo G, Darbha S, Quataert E, Arcones A, Kasen D, Thomas R, Nugent P, Panov IV, Zinner NT (2010) Electromagnetic counterparts of compact object mergers powered by the radioactive decay of r-process nuclei. Mon Not R Astron Soc 406:2650–2662. doi:10.1111/j.1365-2966.2010.16864.x, 1001.5029 Meyer BS, Mathews GJ, Howard WM, Woosley SE, Hoffman RD (1992) R-process nucleosynthesis in the high-entropy supernova bubble. Astrophys J 399:656–664. doi:10.1086/171957 Mirizzi A, Mangano G, Saviano N (2015) Self-induced flavor instabilities of a dense neutrino stream in a two-dimensional model. Phys Rev D 92(2):021702. doi:10.1103/PhysRevD.92.021702, 1503.03485

1874

F.-K. Thielemann et al.

Mirizzi A, Tamborra I, Janka HT, Saviano N, Scholberg K, Bollig R, Hüdepohl L, Chakraborty S (2016) Supernova neutrinos: production, oscillations and detection. Nuovo Cimento Rivista Serie 39:1–112. doi:10.1393/ncr/i2016-10120-8, 1508.00785 Möller P, Nix JR, Myers WD, Swiatecki WJ (1995) Nuclear ground-state masses and deformations. At Data Nucl Data Tables 59:185. doi:10.1006/adnd.1995.1002, nucl-th/9308022 Möller P, Pfeiffer B, Kratz KL (2003) New calculations of gross ˇ-decay properties for astrophysical applications: speeding-up the classical r-process. Phys Rev C 67(5):055802. doi:10.1103/PhysRevC.67.055802 Möller P, Myers WD, Sagawa H, Yoshida S (2012) New finite-range droplet mass model and equation-of-state parameters. Phys Rev Lett 108(5):052501. doi:10.1103/PhysRevLett.108.052501 Möller P, Sierk AJ, Ichikawa T, Sagawa H (2016) Nuclear ground-state masses and deformations: FRDM(2012). At Data Nucl Data Tables 109:1–204. doi:10.1016/j.adt.2015.10.002, 1508.06294 Mösta P, Richers S, Ott CD, Haas R, Piro AL, Boydstun K, Abdikamalov E, Reisswig C, Schnetter E (2014) Magnetorotational core-collapse supernovae in three dimensions. Astrophys J Lett 785:L29. doi:10.1088/2041-8205/785/2/L29, 1403.1230 Mösta P, Ott CD, Radice D, Roberts LF, Schnetter E, Haas R (2015) A large-scale dynamo and magnetoturbulence in rapidly rotating core-collapse supernovae. Nature 528:376–379. doi:10.1038/nature15755, 1512.00838 Mumpower MR, Surman R, McLaughlin GC, Aprahamian A (2016) The impact of individual nuclear properties on r-process nucleosynthesis. Prog Part Nucl Phys 86:86–126. doi:10.1016/j.ppnp.2015.09.001, 1508.07352 Nagataki S, Takahashi R, Mizuta A, Takiwaki T (2007) Numerical study of gamma-ray burst jet formation in collapsars. Astrophys J 659:512–529. doi:10.1086/512057, astro-ph/0608233 Nakamura K, Takiwaki T, Kuroda T, Kotake K (2015) Systematic features of axisymmetric neutrino-driven core-collapse supernova models in multiple progenitors. Publ Astron Soc Jpn 67:107. doi:10.1093/pasj/psv073, 1406.2415 Nishimura S, Kotake K, Hashimoto Ma, Yamada S, Nishimura N, Fujimoto S, Sato K (2006) rProcess nucleosynthesis in magnetohydrodynamic jet explosions of core-collapse supernovae. Astrophys J 642:410–419. doi:10.1086/500786, astro-ph/0504100 Nishimura N, Takiwaki T, Thielemann FK (2015) The r-process nucleosynthesis in the various jet-like explosions of magnetorotational core-collapse supernovae. Astrophys J 810:109. doi:10.1088/0004-637X/810/2/109, 1501.06567 Nishimura N, Sawai H, Takiwaki T, Yamada S, Thielemann FK (2017) The intermediate rprocess in core-collapse supernovae driven by the magneto-rotational instability. Astrophys J Lett 836:L21. 1611.02280 Nomoto K, Thielemann FK, Miyaji S (1985) The triple alpha reaction at low temperatures in accreting white dwarfs and neutron stars. Astron Astrophys 149:239–245 Nomoto K, Tominaga N, Umeda H, Kobayashi C, Maeda K (2006) Nucleosynthesis yields of corecollapse supernovae and hypernovae, and galactic chemical evolution. Nucl Phys A 777:424– 458. doi:10.1016/j.nuclphysa.2006.05.008, astro-ph/0605725 Ono M, Hashimoto M, Fujimoto S, Kotake K, Yamada S (2012) Explosive nucleosynthesis in magnetohydrodynamical jets from collapsars. II – heavy-element nucleosynthesis of s, p, rprocesses. Prog Theor Phys 128:741–765, 1203.6488 Pan KC, Liebendörfer M, Hempel M, Thielemann FK (2016) Two-dimensional core-collapse supernova simulations with the isotropic diffusion source approximation for neutrino transport. Astrophys J 817:72. doi:10.3847/0004-637X/817/1/72, 1505.02513 Panov IV, Thielemann FK (2004) Fission and the r-process: competition between neutron-induced and beta-delayed fission. Astron Lett 30:647–655. doi:10.1134/1.1795953 Panov IV, Korneev IY, Thielemann FK (2008) The r-process in the region of transuranium elements and the contribution of fission products to the nucleosynthesis of nuclei with A  130. Astron Lett 34:189–197. doi:10.1007/s11443-008-3006-1

71 Making the Heaviest Elements in a Rare Class of Supernovae

1875

Panov IV, Korneev IY, Rauscher T, Martínez-Pinedo G, Keli´c-Heil A, Zinner NT, Thielemann FK (2010) Neutron-induced astrophysical reaction rates for translead nuclei. Astron Astrophys 513:A61. doi:10.1051/0004-6361/200911967, 0911.2181 Panov IV, Korneev IY, Lutostansky YS, Thielemann FK (2013) Probabilities of delayed processes for nuclei involved in the r-process. Phys At Nucl 76:88–101. doi:10.1134/S1063778813010080 Panov IV, Lutostansky YS, Thielemann FK (2016) Beta-decay half-lives for the r-process nuclei. Nucl Phys A 947:1–11. doi:10.1016/j.nuclphysa.2015.12.001 Perego A, Rosswog S, Cabezón RM, Korobkin O, Käppeli R, Arcones A, Liebendörfer M (2014) Neutrino-driven winds from neutron star merger remnants. Mon Not R Astron Soc 443:3134– 3156. doi:10.1093/mnras/stu1352, 1405.6730 Perego A, Hempel M, Fröhlich C, Ebinger K, Eichler M, Casanova J, Liebendörfer M, Thielemann FK (2015) PUSHing core-collapse supernovae to explosions in spherical symmetry I: the model and the case of SN 1987A. Astrophys J 806:275. doi:10.1088/0004-637X/806/2/275, 1501.02845 Qian YZ, Wasserburg GJ (2007) Where, oh where has the r-process gone? Phys Rep 442:237–268. doi:10.1016/j.physrep.2007.02.006, 0708.1767 Ramirez-Ruiz E, Trenti M, MacLeod M, Roberts LF, Lee WH, Saladino-Rosas MI (2015) Compact stellar binary assembly in the first nuclear star clusters and r-process synthesis in the early universe. Astrophys J Lett 802:L22. doi:10.1088/2041-8205/802/2/L22, 1410.3467 Rauscher T, Heger A, Hoffman RD, Woosley SE (2002) Nucleosynthesis in massive stars with improved nuclear and stellar physics. Astrophys J 576:323–348. doi:10.1086/341728, astroph/0112478 Roberts LF, Woosley SE, Hoffman RD (2010) Integrated nucleosynthesis in neutrino-driven winds. Astrophys J 722:954–967. doi:10.1088/0004-637X/722/1/954, 1004.4916 Roberts LF, Reddy S, Shen G (2012) Medium modification of the charged-current neutrino opacity and its implications. Phys Rev C 86(6):065803. doi:10.1103/PhysRevC.86.065803, 1205.4066 Roederer IU (2016) The origin of the heaviest metals in most ultra-faint dwarf galaxies, 1611.05886 Roederer IU, Lawler JE, Sobeck JS, Beers TC, Cowan JJ, Frebel A, Ivans II, Schatz H, Sneden C, Thompson IB (2012) New hubble space telescope observations of heavy elements in four metal-poor stars. Astrophys J Sup 203:27. doi:10.1088/0067-0049/203/2/27, 1210.6387 Roederer IU, Schatz H, Lawler JE, Beers TC, Cowan JJ, Frebel A, Ivans II, Sneden C, Sobeck JS (2014) New detections of Arsenic, Selenium, and other heavy elements in two metal-poor stars. Astrophys J 791:32. doi:10.1088/0004-637X/791/1/32, 1406.4554 Rosswog S, Korobkin O, Arcones A, Thielemann FK, Piran T (2014) The long-term evolution of neutron star merger remnants – I. The impact of r-process nucleosynthesis. Mon Not R Astron Soc 439:744–756. doi:10.1093/mnras/stt2502, 1307.2939 Seitenzahl IR, Ciaraldi-Schoolmann F, Röpke FK, Fink M, Hillebrandt W, Kromer M, Pakmor R, Ruiter AJ, Sim SA, Taubenberger S (2013) Three-dimensional delayed-detonation models with nucleosynthesis for type Ia supernovae. Mon Not R Astron Soc 429:1156–1172. doi:10.1093/mnras/sts402, 1211.3015 Shen S, Cooke RJ, Ramirez-Ruiz E, Madau P, Mayer L, Guedes J (2015) The history of rprocess enrichment in the milky way. Astrophys J 807:115. doi:10.1088/0004-637X/807/2/115, 1407.3796 Sneden C, Cowan JJ, Gallino R (2008) Neutron-capture elements in the early galaxy. Ann Rev Astron Astroph 46:241–288. doi:10.1146/annurev.astro.46.060407.145207 Suda T, Katsuta Y, Yamada S, Suwa T, Ishizuka C, Komiya Y, Sorai K, Aikawa M, Fujimoto MY (2008) Stellar abundances for the galactic archeology (SAGA) database – compilation of the characteristics of known extremely metal-poor stars. Publ Astron Soc Jpn 60:1159–1171. doi:10.1093/pasj/60.5.1159, 0806.3697 Suda T, Yamada S, Katsuta Y, Komiya Y, Ishizuka C, Aoki W, Fujimoto MY (2011) The stellar abundances for galactic archaeology (SAGA) data base – II. Implications for mixing and

1876

F.-K. Thielemann et al.

nucleosynthesis in extremely metal-poor stars and chemical enrichment of the galaxy. Mon Not R Astron Soc 412:843–874. doi:10.1111/j.1365-2966.2011.17943.x, 1010.6272 Sukhbold T, Ertl T, Woosley SE, Brown JM, Janka HT (2016) Core-collapse supernovae from 9 to 120 solar masses based on neutrino-powered explosions. Astrophys J 821:38. doi:10.3847/0004-637X/821/1/38, 1510.04643 Sumiyoshi K, Terasawa M, Mathews GJ, Kajino T, Yamada S, Suzuki H (2001) r-Process in prompt supernova explosions revisited. Astrophys J 562:880–886. doi:10.1086/323524, astroph/0106407 Surman R, McLaughlin GC, Hix WR (2006) Nucleosynthesis in the outflow from gamma-ray burst accretion disks. Astrophys J 643:1057–1064. doi:10.1086/501116, astro-ph/0509365 Surman R, McLaughlin GC, Ruffert M, Janka HT, Hix WR (2008) r-Process nucleosynthesis in hot accretion disk flows from black hole-neutron star mergers. Astrophys J Lett 679:L117. doi:10.1086/589507, 0803.1785 Surman R, Caballero OL, McLaughlin GC, Just O, Janka HT (2014) Production of 56 Ni in black hole-neutron star merger accretion disc outflows. J Phys G Nucl Phys 41(4):044006. doi:10.1088/0954-3899/41/4/044006, 1312.1199 Symbalisty EMD, Schramm DN, Wilson JR (1985) An expanding vortex site for the r-process in rotating stellar collapse. Astrophys J Lett 291:L11–L14. doi:10.1086/184448 Takahashi K, Witti J, Janka HT (1994) Nucleosynthesis in neutrino-driven winds from protoneutron stars II. The r-process. Astron Astrophys 286 Takiwaki T, Kotake K (2011) Gravitational wave signatures of magnetohydrodynamically driven core-collapse supernova explosions. Astrophys J 743:30. doi:10.1088/0004-637X/743/1/30, 1004.2896 Takiwaki T, Kotake K, Sato K (2009) Special relativistic simulations of magnetically dominated jets in collapsing massive stars. Astrophys J 691:1360–1379. doi:10.1088/0004-637X/691/2/1360, 0712.1949 Tanvir NR, Levan AJ, Fruchter AS, Hjorth J, Hounsell RA, Wiersema K, Tunnicliffe RL (2013) A ‘kilonova’ associated with the short-duration -ray burst GRB 130603B. Nature 500:547–549. doi:10.1038/nature12505, 1306.4971 Thielemann FK (2015) Nuclear astrophysics: deep-sea diving for stellar debris. Nat Phys 11:993– 994. doi:10.1038/nphys3591 Thielemann FK, Nomoto K, Hashimoto MA (1996) Core-collapse supernovae and their ejecta. Astrophys J 460:408. doi:10.1086/176980 Thielemann FK, Brachwitz F, Höflich P, Martinez-Pinedo G, Nomoto K (2004) The physics of type Ia supernovae. New Astron Rev 48:605–610. doi:10.1016/j.newar.2003.12.038 Thielemann FK, Hirschi R, Liebendörfer M, Diehl R (2011) Massive stars and their supernovae. In: Diehl R, Hartmann DH, Prantzos N (eds) Lecture notes in physics, vol 812. Springer, Berlin, pp 153–232, 1008.2144 Timmes FX (1999) Integration of nuclear reaction networks for stellar hydrodynamics. Astrophys J Sup 124:241–263. doi:10.1086/313257 Umeda H, Nomoto K (2008) How much 56 Ni can be produced in core-collapse supernovae? Evolution and explosions of 30–100 MŁ stars. Astrophys J 673:1014–1022. doi:10.1086/524767, 0707.2598 van de Voort F, Quataert E, Hopkins PF, Kereš D, Faucher-Giguère CA (2015) Galactic r-process enrichment by neutron star mergers in cosmological simulations of a Milky Way-mass galaxy. Mon Not R Astron Soc 447:140–148. doi:10.1093/mnras/stu2404, 1407.7039 Wallner A, Faestermann T, Feige J, Feldstein C, Knie K, Korschinek G, Kutschera W, Ofan A, Paul M, Quinto F, Rugel G, Steier P (2015) Abundance of live 244 Pu in deep-sea reservoirs on earth points to rarity of actinide nucleosynthesis. Nat Commun 6:5956. doi:10.1038/ncomms6956, 1509.08054 Wallner A, Feige J, Kinoshita N, Paul M, Fifield LK, Golser R, Honda M, Linnemann U, Matsuzaki H, Merchel S, Rugel G, Tims SG, Steier P, Yamagata T, Winkler SR (2016) Recent nearearth supernovae probed by global deposition of interstellar radioactive 60 Fe. Nature 532:69–72. doi:10.1038/nature17196

71 Making the Heaviest Elements in a Rare Class of Supernovae

1877

Wanajo S, Nomoto K, Janka HT, Kitaura FS, Müller B (2009) Nucleosynthesis in electron capture supernovae of asymptotic giant branch stars. Astrophys J 695:208–220. doi:10.1088/0004-637X/695/1/208, 0810.3999 Wanajo S, Janka HT, Müller B (2011) Electron-capture supernovae as the origin of elements beyond iron. Astrophys J Lett 726:L15. doi:10.1088/2041-8205/726/2/L15, 1009.1000 Wanajo S, Sekiguchi Y, Nishimura N, Kiuchi K, Kyutoku K, Shibata M (2014) Production of all the r-process nuclides in the dynamical ejecta of neutron star mergers. Astrophys J Lett 789:L39. doi:10.1088/2041-8205/789/2/L39, 1402.7317 Wehmeyer B, Pignatari M, Thielemann FK (2015) Galactic evolution of rapid neutron capture process abundances: the inhomogeneous approach. Mon Not R Astron Soc 452:1970–1981. doi:10.1093/mnras/stv1352, 1501.07749 Winteler C, Käppeli R, Perego A, Arcones A, Vasset N, Nishimura N, Liebendörfer M, Thielemann FK (2012) Magnetorotationally driven supernovae as the origin of early galaxy r-process elements? Astrophys J Lett 750:L22. doi:10.1088/2041-8205/750/1/L22, 1203.0616 Woosley SE, Hoffman RD (1992) The alpha-process and the r-process. Astrophys J 395:202–239. doi:10.1086/171644 Woosley SE, Weaver TA (1995) The evolution and explosion of massive stars. II. Explosive hydrodynamics and nucleosynthesis. Astrophys J Sup 101:181. doi:10.1086/192237 Woosley SE, Wilson JR, Mathews GJ, Hoffman RD, Meyer BS (1994) The r-process and neutrinoheated supernova ejecta. Astrophys J 433:229–246. doi:10.1086/174638 Yang B, Jin ZP, Li X, Covino S, Zheng XZ, Hotokezaka K, Fan YZ, Piran T, Wei DM (2015) A possible macronova in the late afterglow of the long-short burst GRB 060614. Nat Commun 6:7323. doi:10.1038/ncomms8323, 1503.07761

Pre-supernova Evolution and Nucleosynthesis in Massive Stars and Their Stellar Wind Contribution

72

Raphael Hirschi

Abstract

In this chapter, we review the modelling and pre-supernova evolution of massive stars with a particular emphasis on the effects of rotation and mass loss. We then present the stellar wind contribution to nucleosynthesis and the production of weak s-process at various metallicities (Z). We also review the transition between intermediate-mass and massive stars and the major nuclear and stellar uncertainties involved. Rotation and mass loss both have a strong impact on the evolution and nucleosynthesis in massive stars. The effects of rotation on presupernova models are most spectacular for stars between 15 and 25 Mˇ . For M > 30Mˇ , mass loss dominates over the effects of rotation. Massive stars near solar metallicity lose more than half their initial mass for stars more massive than 20 Mˇ . The stellar wind contribution to nucleosynthesis consists mostly of hydrogen-burning products and to a smaller extent helium-burning products since mass loss is generally small during the advanced phases. At low and very low Z, one expects mass loss and the production of secondary elements like 14 N to decrease and gradually become negligible. Rotation changes this picture. For the most massive stars (M & 60 Mˇ ), primary production of CNO elements raises the overall metallicity of the surface drastically, and significant mass loss may occur during the red supergiant stage. The production of primary 14 N and also 22 Ne in rotating massive stars at low Z opens the door to R. Hirschi () Astrophysics Group, School of Chemical and Physical Sciences, Keele University, Staffordshire, UK Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba, Japan UK Network for Bridging Disciplines of Galactic Chemical Evolution (BRIDGCE), Staffordshire, UK e-mail: [email protected]

© Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_82

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produce s-process elements at low Z. The strong dependence of the production of the barium peak on metallicity and initial rotation rate means that rotating models provide a natural explanation for the observed scatter in the strontium over barium ratio ([Sr/Ba]) at low metallicities.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stellar Evolution Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Stellar Structure Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Mass Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Rotation and Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Evolution of Massive Stars and Key Abundances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Evolution of Surface Properties (HR Diagram) and Lifetimes . . . . . . . . . . . . . . 3.2 Evolution of Central Properties in the Log Tc –Log c Diagram . . . . . . . . . . . . . 3.3 Angular Velocity, ˝, and Momentum, j , Evolution . . . . . . . . . . . . . . . . . . . . . . 3.4 Structure and Abundance Evolution and Pre-supernova Properties . . . . . . . . . . 3.5 Abundances Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Pre–supernova Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Stellar Wind Contribution to Galactic Chemical Enrichment . . . . . . . . . . . . . . . . . . . . . 4.1 Comparison Between Rotating and Non-rotating Models and Convolution with the IMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Dependence on Metallicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Metallicity Effects on General Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Effects of Rotation at Subsolar Metallicities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Weak s-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Standard Weak s-Process in (Nonrotating) Massive Stars . . . . . . . . . . . . . . . . . . 6.2 Impact of Rotation on the s-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Massive stars play a key role in the universe through the light they shine, their energetic death, and the chemical elements they produce. Indeed, the most massive stars known to exist have a luminosity roughly ten million times larger than that of our sun (Crowther et al. 2010). Their very strong radiation field leads to strong mass loss. Thus massive stars near solar metallicity (Zˇ ) lose a large fraction of their initial mass, more than half their initial mass for stars more massive than 20 Mˇ . Most of the mass loss takes place during hydrogen- and helium-burning phases. This implies that the stellar wind contribution to nucleosynthesis consists mostly of hydrogen-burning products and to a smaller extent helium-burning products, i.e., elements up to aluminum. Observations from the Integral gamma-ray satellite (Diehl et al. 2006) confirm that massive stars in our galaxy produce significant amounts of 26 Al, a radioactive element with half-life of  7:2  105 years and emitting photons at 1808.65 keV. Following helium burning, massive stars go through four additional burning stages: carbon, neon, oxygen, and silicon. During

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these phases, they produce elements up to iron via mainly fusion, alpha-particle capture (and photo-disintegration) reactions. Weak interactions play a increasing role as evolution proceeds and are key to reduce the electron fraction for the iron core to collapse (Arnett and Thielemann 1985; Chieffi et al. 1998; Thielemann and Arnett 1985). Massive stars produce elements heavier than iron via neutron captures during helium and carbon burning, the so-called weak s-process since the production generally stops at the first peak (strontium-zirconium). This chapter is organized as follows. Section 2 reviews the stellar structure equations and physical ingredients of stellar evolution models. Section 3 reviews the general evolution of the massive stars as well as that of the main elements (H, He, C, N, O, . . . ). Section 4 reviews the mass loss history and describes the stellar winds contribution to nucleosynthesis. Section 5 discusses the metallicity dependence of the evolution and nucleosynthesis of massive stars. Section 6 presents comprehensive weak s-process nucleosynthesis calculations at various metallicities. Most sections also discuss the evolution and effects of rotation. The reader is also referred to the review by Langer (2012) concerning the evolution of binary stars.

2

Stellar Evolution Models

Stellar evolution models require a wide range of input physics ranging from nuclear reaction rates to mass loss prescriptions. In this section, we review the basic equations that govern the structure and evolution of stars as well as some of the key input physics with a special emphasis on mass loss, rotation, and magnetic fields.

2.1

Stellar Structure Equations

There are four equations describing the evolution of the structure of stars: the mass, momentum, and energy conservation equations and the energy transport equation, which we recall below. On top of that, the equations of the evolution of chemical elements abundances and angular momentum are to be followed. These equations are discussed in Sect. 2.3. In the Geneva stellar evolution code (GENEC; see Eggenberger et al. 2007), which we base our presentation on in this section, the problem is treated in one dimension (1D) and the equations of the evolution of chemical elements abundances are calculated separately from the structure equations, as in the original version of Kippenhahn and Weigert (Kippenhahn and Weigert 1990; Kippenhahn et al. 1967). In GENEC, rotation is included, and spherical symmetry is no longer assumed. The effective gravity (sum of the centrifugal force and gravity) can in fact no longer be derived from a potential, and the case is said to be nonconservative. The problem can still be treated in 1D by assuming that the angular velocity is constant on isobars. This assumes that there is a strong horizontal (along isobars) turbulence which enforces constant angular velocity on isobars (Zahn 1992). The case is referred to as “shellular” rotation,

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and using reasonable simplifications described in Meynet and Maeder (1997), the usual set of four structure equations (as used for non-rotating stellar models) can be recovered: • Energy conservation: ı @P @T @LP C D "nucl  " C "grav D "nucl  "  cP  @t @MP @t

(1)

where LP is the luminosity, MP the Lagrangian mass coordinate, and "nucl , " , and "grav are the energy generation rates per unit mass for nuclear reactions, neutrinos, and gravitational energy changes due to contraction or expansion, respectively. T is the temperature, cP the specific heat at constant pressure, t the time, P the pressure,  the density, and ı D @ln=@lnT . • Momentum equation: GMP @P D fP @MP 4 rP4

(2)

where rP is the radius of the shell enclosing mass MP and G the gravitational constant. • Mass conservation (continuity equation): 1 @rP D @MP 4 rP2 

(3)

fT GMP @ ln T fP minŒrad ; rrad  D 4 @MP fP 4 rP P

(4)

• Energy transport equation:

where rad D rrad D

@ ln T @ ln P

! D ad

Pı T cP

(convective zones);

LP P 3 (radiative zones); 64  G MP T 4

where  is the total opacity and  is the Stefan–Boltzmann constant. fP D

4 rP4 1 ; GMP SP < g 1 >

72 Pre-supernova Evolution and Nucleosynthesis in Massive Stars and. . .

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4 rP2 SP

2

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1 ; < g >< g 1 >

< x > is x averaged on an isobaric surface, x is x averaged in the volume separating two successive isobars, and the index P refers to the isobar with a pressure equal to P . g is the effective gravity and SP is the surface of the isobar (see Meynet and Maeder 1997,for more details). The implementation of the structure equations into other stellar evolution codes is presented, for example, in Paxton et al. (2011) and Chieffi et al. (1998).

2.2

Mass Loss

Mass loss strongly affects the evolution of massive stars, especially for stars more massive than 30 Mˇ , as we shall describe below. We recall here the different mass loss prescriptions used in stellar evolution calculations and how they relate to each other. In the models presented in this chapter, the following prescriptions were used. For main-sequence stars, the prescription for radiative line-driven winds from Vink et al. (2001) was used. For stars in a domain not covered by the Vink et al. prescription, the de Jager et al. (1988) prescription was applied to models with log.Teff / > 3:7. For log.Teff / 3:7, a linear fit to the data from Sylvester et al. (1998) and van Loon et al. (1999) (see Crowther 2001) was performed. The formula used is given in Eq. 2.1 in Bennett et al. (2012). For cool stars, dust and pulsation most probably play a role in the driving of the wind, but the driving mechanism is not fully understood. In stellar evolution simulations, the stellar wind is not simulated self-consistently, and a criterion is used to determine when a star becomes a WR star. Usually, a star is considered to become a WR when the surface hydrogen mass fraction, Xs , becomes inferior to 0.3 (sometimes when it is inferior to 0.4) and the effective temperature, log.Teff /, is greater than 4.0. The mass loss rate used during the WR phase depends on the WR subtype. For the eWNL phase (when 0:3 > Xs > 0:05), the Gräfener and Hamann (2008) recipe was used (in the validity domain of this prescription, which usually covers most of the eWNL phase). In many cases, the WR mass loss rate of Gräfener and Hamann (2008) is lower than the rate of Vink et al. (2001), in which case, the latter was used. For the eWNE phase – when 0:05 > Xs and the ratio of the mass fractions of (12 C C 16 O/=4 He < 0:03 – and WC/WO phases, when (12 C C 16 O/=4 He > 0:03, the corresponding prescriptions of Nugis and Lamers (2000) were used. Note also that both the Nugis and Lamers (2000) and Gräfener and Hamann (2008) mass loss rates account for clumping effects (Muijres et al. 2011). The mass loss rates from Nugis and Lamers (2000) for the eWNE phase are much larger than in other phases, and thus the largest mass loss occurs during this phase. In Crowther et al. (2010), the mass loss prescription from Nugis and Lamers (2000) was used for both the eWNL and eWNE phases (with a clumping factor, f D 0:1).

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More recent models, such as those of Yusof et al. (2013), thus lose less mass than those presented in Crowther et al. (2010) during the eWNL phase. The metallicity dependence of the mass loss rates is commonly included in the following way. The mass loss rate used at a given metallicity, MP .Z/, is the mass loss rate at solar metallicity, MP .Zˇ /, multiplied by the ratio of the metallicities to the power of ˛: MP .Z/ D MP .Zˇ /.Z=Zˇ /˛ . ˛ was set to 0.85 for the O-type phase and WN phase and 0.66 for the WC and WO phases; and for WR stars, the initial metallicity rather than the actual surface metallicity was used in the equation above following Eldridge and Vink (2006). ˛ was set to 0.5 for the de Jager et al. (1988) prescription. For rotating models, the correction factor described below in Eq. 5 is applied to the radiative mass loss rate. Line-driven wind mass loss rates in hot stars are relatively well determined and constrained by observations (Crowther et al. 2010; Muijres et al. 2011). On the other hand, the mass loss rates for red supergiants and luminous blue variables as well as their metallicity dependence are not fully understood and still very uncertain with unfortunately little hope for major improvements in the near future. We will come back to this point when we discuss the metallicity dependence in Sect. 5.

2.3

Rotation and Magnetic Fields

The physics of rotation included in stellar evolution codes has been developed extensively over the last 20 years. A recent review of this development can be found in Maeder and Meynet (2012). The effects induced by rotation can be divided into three categories. (1) Hydrostatic effects: The centrifugal force changes the hydrostatic equilibrium of the star. The star becomes oblate, and the equations describing the stellar structure have to be modified as described above. (2) Mass loss enhancement and anisotropy: Mass loss depends on the opacity and the effective gravity (sum of gravity and centrifugal force) at the surface. The larger the opacity, the larger the mass loss. The higher the effective gravity, the higher the radiative flux (von Zeipel 1924) and effective temperature. Rotation, via the centrifugal force, reduces the surface effective gravity at the equator compared to the pole. As a result, the radiative flux of the star is larger at the pole than at the equator. In massive hot stars, since the opacity is dominated by the temperature-independent electron scattering, rotation enhances mass loss at the pole. If the opacity increases when the temperature decreases (in cooler stars), mass loss can be enhanced at the equator when the bistability is reached (Vink et al. 2001). For rotating models, the mass loss rates can be obtained by applying a correction factor to the radiative mass loss rate as described in Maeder and Meynet (2000): MP .˝/ D F˝  MP .˝ D 0/ D F˝  MP rad

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1

with F˝ D h 1

.1  / ˛ 1 i ˛1 1 ˝2 

2 Gm

(5)

where D L=LEdd D L=.4 cGM / is the Eddington factor (with  the total opacity) and ˛ the Teff dependent force multiplier parameter. Enhancement factors (F˝ ) are generally close to one, but they may become very large when & 0:7 or ˝=˝crit > 0:9 (see Georgy et al. 2011; Maeder and Meynet 2000,for more details). If critical rotation, where the centrifugal force balances gravity at the equator, is reached, mechanical mass loss may occur and produce a decretion disk (see Krtiˇcka et al. 2011,for more details). In most stellar evolution codes, the mass loss is artificially enhanced when ˝=˝crit & 0:95 to ensure that the ratio does not become larger than unity, but multidimensional simulations are required to provide new prescriptions to use in stellar evolution codes. (3) Rotation-driven instabilities: The main rotation-driven instabilities are horizontal turbulence, meridional circulation, and dynamical and secular shear (see Maeder 2009,for a comprehensive description of rotation-induced instabilities). Horizontal turbulence corresponds to turbulence along the isobars. If this turbulence is strong, rotation is constant on isobars, and the situation is usually referred to as “shellular rotation” (Zahn 1992). The horizontal turbulence is expected to be stronger than the vertical turbulence because there is no restoring buoyancy force along isobars (see Maeder 2003, for a discussion on this topic). Meridional circulation, also referred to as Eddington–Sweet circulation, arises from the local breakdown of radiative equilibrium in rotating stars. This is due to the fact that surfaces of constant temperature do not coincide with surfaces of constant pressure. Indeed, since rotation elongates isobars at the equator, the temperature on the same isobar is lower at the equator than at the pole. This induces large-scale circulation of matter, in which matter usually rises at the pole and descends at the equator (see Fig. 1). In this situation, angular momentum is transported inward. It is however also possible for the circulation to go in the reverse direction, and, in this second case, angular momentum is transported outward. Circulation corresponds to an advective process, which is different from diffusion because the latter can only erode gradients. Advection can either build or erode angular velocity gradients (see Maeder and Zahn 1998, for more details). Dynamical shear occurs when the excess energy contained in differentially rotating layers is larger than the work that needs to be done to overcome the buoyancy force. The criterion for stability against dynamical shear instability is the Richardson criterion: Ri D

N2 1 > D Ric ; .@U =@z/2 4

(6)

where U is the horizontal velocity, z the vertical coordinate, and N 2 the Brunt– Väisälä frequency.

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Fig. 1 Streamlines of meridional circulation in a rotating 20 Mˇ model with solar metallicity and vini D 300 km s1 at the beginning of the H–burning phase. The streamlines are in the meridian plane. In the upper hemisphere on the right section, matter is turning counterclockwise along the outer streamline and clockwise along the inner one. The outer sphere is the star surface and has a radius equal to 5.2 Rˇ . The inner sphere is the outer boundary of the convective core. It has a radius of 1.7 Rˇ (Illustration taken from Meynet and Maeder 2002a)

The critical value of the Richardson criterion, Ric D 1=4, corresponds to the situation where the excess kinetic energy contained in the differentially rotating layers is equal to the work done against the restoring force of the density gradient (also called buoyancy force). It is therefore used by most authors as the limit for the occurrence of the dynamical shear. Studies by Canuto (2002) show that turbulence may occur as long as Ri . Ric  1. This critical value is consistent with numerical simulations done by Brüggen and Hillebrandt (2001) where they find shear mixing for values of Ri greater than 1/4 (up to about 1.5). The latest 3D hydrodynamic simulations (Edelmann et al. 2017), however, confirm the theoretical value of 1/4 and that this instability is reasonably implemented in 1D models although the physical extent of the instability needs to revised. Different dynamical shear diffusion coefficients, D, can be found in the literature. The one used in GENEC is: DD

1 1 v 2 1 d˝ 1 vl D l D r r 2 D r˝ r 3 3 l 3 dr 3

(7)

where r is the mean radius of the zone where the instability occurs, ˝ is the variation of ˝ over this zone, and r is the extent of the zone. The zone is the reunion of consecutive shells where Ri < Ric (see Hirschi et al. 2004,for more details and references). If the differential rotation is not strong enough to induce dynamical shear, it can still induce the secular shear instability when thermal turbulence reduces the effect of the buoyancy force. The secular shear instability occurs therefore on the thermal time scale, which is much longer than the dynamical one. Note that the way the inhibiting effect of the molecular weight () gradients on secular shear is taken into

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account impacts strongly the efficiency of the shear. In some work, the inhibiting effect of  gradients is so strong that secular shear is suppressed below a certain threshold value of differential rotation (Heger et al. 2000). In other work (Maeder 1997), thermal instabilities and horizontal turbulence reduce the inhibiting effect of the  gradients. As a result, shear is not suppressed below a threshold value of differential rotation but only decreased when  gradients are present. There are other minor instabilities induced by rotation: the GSF instability (Fricke 1968; Goldreich and Schubert 1967; Hirschi and Maeder 2010), the ABCD instability (Heger et al. 2000; Knobloch and Spruit 1983), and the Solberg– Høiland instability (Kippenhahn and Weigert 1990). The GSF instability is induced by axisymmetric perturbations. The ABCD instability is a kind of horizontal convection. Finally, Solberg–Høiland stability criterion is the criterion that should be used instead of the Ledoux or Schwarzschild criterion in rotating stars. However, including the dynamical shear instability also takes into account the Solberg– Høiland instability (Hirschi et al. 2004).

2.3.1 Transport of Angular Momentum For shellular rotation, the equation of transport of angular momentum (Zahn 1992) in the vertical direction is (in Lagrangian coordinates):    @˝ 1 @  4 1 @ d  2  r ˝ Mr D 2 r ˝U .r/ C 2 Dr 4 ; (8)  dt 5r @r r @r @r where ˝.r/ is the mean angular velocity at level r, U .r/ the vertical component of the meridional circulation velocity, and D the diffusion coefficient due to the sum of the various turbulent diffusion processes (convection, shears, and other rotation-induced instabilities apart from meridional circulation). Note that angular momentum is conserved in the case of contraction or expansion. The first term on the right hand side, corresponding to meridional circulation, is an advective term. The second term on the right hand side, which corresponds to the diffusion processes, is a diffusive term. The correct treatment of advection is very costly numerically because Eq. 8 is a fourth-order equation (the expression of U .r/ contains thirdorder derivatives of ˝; see Zahn 1992). This is why some research groups treat meridional circulation in a diffusive way (see, e.g., Heger et al. 2000) with the risk of transporting angular momentum in the wrong direction (in the case meridional circulation builds gradients).

2.3.2 Transport of Chemical Species The transport of chemical elements is also governed by a diffusion–advection equation like Eq. 8. However, if the horizontal component of the turbulent diffusion is large, the vertical advection of the elements (but not that of the angular momentum) can be treated as a simple diffusion (Chaboyer and Zahn 1992) with a diffusion coefficient Deff , Deff D

j rU .r/ j2 ; 30Dh

(9)

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where Dh is the coefficient of horizontal turbulence (Zahn 1992). Equation 9 expresses that the vertical advection of chemical elements is severely inhibited by the strong horizontal turbulence characterized by Dh . The change of the mass fraction Xi of the chemical species i is simply 

dXi dt



 D

Mr

@ @Mr

      @Xi dXi .4 r 2 /2 Dmix C ; @Mr t dt nuclear t

(10)

where the second term on the right accounts for composition changes due to nuclear reactions. The coefficient Dmix is the sum Dmix D D C Deff , where D is the term appearing in Eq. 8 and Deff accounts for the combined effect of advection and horizontal turbulence.

2.3.3 Interaction Between Rotation and Magnetic Fields Circular spectro-polarimetric surveys have obtained evidence for the presence of magnetic fields at the surface of OB stars (see, e.g., the review by Walder et al. 2011,and references therein). The origin of these magnetic fields is still unknown. It might be fossil fields or fields produced through a dynamo mechanism. The central question for the evolution of massive stars is whether a dynamo is at work in internal radiative zones. This could have far reaching consequences concerning the mixing of the elements and the loss of angular momentum. In particular, the interaction between rotation and magnetic fields in the stellar interior strongly affects the angular momentum retained in the core and thus the initial rotation rate of pulsars and which massive stars could die as long and soft gammaray bursts (GRBs) see Vink et al. (2011) and the discussion in Sect. 6 in Georgy et al. (2012,and references therein). The interplay between rotation and magnetic field has been studied in stellar evolution calculations using the Tayler–Spruit dynamo (Maeder and Meynet 2005; Spruit 2002). Some numerical simulations confirm the existence of a magnetic instability; however the existence of the dynamo is still debated (Braithwaite 2006; Zahn et al. 2007). The Tayler–Spruit dynamo is based on the fact that a purely toroidal field B' .r; #/, even very weak, in a stably stratified star is unstable on an Alfvén time scale 1=!A . This is the first magnetic instability to appear. It is non-axisymmetric of type m D 1 (Spruit 2002), occurs under a wide range of conditions, and is characterized by a low threshold and a short growth time. In a rotating star, the instability is also present; however the growth rate B of the instability is, if !A  ˝, B D

!A2 ; ˝

(11)

instead of the Alfvén frequency !A , because the growth rate of the instability is reduced by the Coriolis force (Spruit 2002). One usually has the following ordering of the different frequencies, N  ˝  !A . In the sun, one has N  103 s1 ,

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Fig. 2 Left: evolution of the angular velocity ˝ as a function of the distance to the center in a 20 Mˇ star with vini = 300 km s1 . Xc is the hydrogen mass fraction at the center. The dotted line shows the profile when the He–core contracts at the end of the H-burning phase. Right: rotation profiles at various stages of evolution (labelled by the central H content Xc ) of a 15 Mˇ model with X D 0:705; Z D 0:02, an initial velocity of 300 km s1 and magnetic field from the Tayler–Spruit dynamo (Taken from Maeder and Meynet 2005)

˝ D 3  106 s1 , and a field of 1 kG would give an Alfvén frequency as low as !A D 4  109 s1 (where N is the Brunt–Väisälä frequency). This theory enables us to establish the two quantities that we are mainly interested in for stellar evolution: the magnetic viscosity , which expresses the mechanical coupling due to the magnetic field B, and the magnetic diffusivity , which expresses the transport by a magnetic instability and thus also the damping of the instability. The parameter  also expresses the vertical transport of the chemical elements and enters Eq. 10, while the viscosity determines the vertical transport of the angular momentum by the magnetic field and enters the second term on the right-hand side of Eq. 8. Figure 2 shows the differences in the internal ˝–profiles during the evolution of a 20 Mˇ star with and without magnetic field created by the Tayler–Spruit dynamo. Without magnetic field, the star has a significant differential rotation, while ˝ is almost constant when a magnetic field created by the dynamo is present. It is not perfectly constant, otherwise there would be no dynamo. In fact, the rotation rapidly adjusts itself to the minimum differential rotation necessary to sustain the dynamo. One could then assume that the mixing of chemical elements is suppressed by magnetic fields. This is, however, not the case since the interplay between magnetic fields and the meridional circulation tends to lead to more mixing in models including magnetic fields compared to models not including magnetic fields (Maeder and Meynet 2005). Fast-rotating models of GRB progenitors calculated by Yoon et al. (2006) also experience a strong chemical internal mixing leading to the stars undergoing quasi-chemical homogeneous evolution. The study of the

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interaction between rotation and magnetic fields is still under development (see, e.g., Potter et al. 2012,for a different rotation-magnetic field interaction theory, the ˛  ˝ dynamo, and its impact on massive star evolution), and the next 10 years will certainly provide new insights on this important topic.

2.3.4 Other Input Physics The other key input physics that are essentials for the computation of stellar evolution models are nuclear reactions, mass loss prescriptions (discussed above), the equation of state, opacities, and neutrino losses. Stellar evolution codes are now able to include larger and more flexible nuclear reaction network (see, e. g., Frischknecht et al. 2010,for a description of the implementation of a flexible network in GENEC). Nuclear physics and other inputs are described for other codes, for example, in Paxton et al. (2011) and Chieffi et al. (1998).

3

Evolution of Massive Stars and Key Abundances

In this section, we review the general evolution of massive stars at solar metallicity. The models and plots presented in this chapter are taken from Hirschi et al. (2004) unless otherwise stated. In that study, stellar models of 12, 15, 20, 25, 40, and 60 Mˇ at solar metallicity, with initial rotational velocities of 0 and 300 km s1 , respectively, were computed, thus covering most of the massive star range. Other recent grids of models at solar metallicity can be found in Ekström et al. (2012), Chieffi and Limongi (2013), and Sukhbold and Woosley (2014). Models for lowermass and higher-mass massive stars can be found in, e.g., Jones et al. (2013) and Yusof et al. (2013), respectively.

3.1

Evolution of Surface Properties (HR Diagram) and Lifetimes

For many aspects discussed in this chapter, we will focus on the 20 Mˇ non-rotating and rotating models. Figure 3 (left) shows the evolutionary tracks of different 20 Mˇ models in the HR diagram and thus how the surface properties of these stars evolve. The non-rotating model is representative of the lower end of massive stars, which keep an extended hydrogen-rich envelope, end as red supergiant, and produce type II supernovae. The 300 km s1 model is representative of the higher end of massive stars, for which most or all of the H-rich envelope is lost via stellar winds and the star ends as a hot star, generally a Wolf–Rayet star and produce a type Ib or Ic supernova depending on how much helium is left. These two models also show the impact of rotation on the evolution of massive stars. The additional models with intermediate rotation (vini = 100 and 200 km s1 ) show the smooth transition from non-rotating to fast-rotating models. HR diagrams covering the full IMF can be found in Ekström et al. (2012). As mentioned in the Introduction, massive stars go through six burning stages: H, He, C, Ne, O, and Si burning. The lifetimes of these stages are plotted in Fig. 3

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Fig. 3 Left: HR diagram for 20 Mˇ models: solid, dashed, dotted–dashed, and dotted lines correspond, respectively, to vini = 0, 100, 200, and 300 km s1 . We also indicate the position of the progenitor of SN 1993J. Right: Burning lifetimes as a function of the initial mass and velocity. Solid and dotted lines correspond, respectively, to rotating and non-rotating models. Long dashed and dotted–dashed lines are used for rotating and non-rotating Ne-burning lifetimes to point out that they are to be considered as estimates (See text)

(right). Whereas H- and He-burning stages last for roughly 1067 and 1056 years, respectively, the lifetimes for the advanced phases is much shorter. This is due to neutrino losses dominating energy losses over radiation from C burning onward. C-, Ne-, O-, and Si-burning phases last about 1023 , 1, 1, and 102 years, respectively. Concerning the effects of rotation and mass loss, there is a mass range where rotational mixing (M . 30Mˇ ) or mass loss (M & 30Mˇ ) dominates over the other process. For M . 30Mˇ , rotation-induced mixing extends the Hburning lifetime and as a consequence shortens slightly He-burning lifetimes. For the advanced phases, rotation makes star behave like more massive stars. This is clearly seen for C-burning lifetimes, which are shorter for rotating models. For M & 30Mˇ , strong mass loss leads to degeneracy in the lifetime and final properties.

3.2

Evolution of Central Properties in the Log Tc –Log c Diagram

Figure 4 (left) shows the tracks of the 15 and 60 Mˇ models throughout their evolution in the central temperature versus central density plane (Log Tc –Log c diagram). Figure 4 (right) zooms in the advanced stages of the 12, 20, and 40 Mˇ models. It is also very instructive to look at Kippenhahn diagrams (Fig. 8) in order to follow the evolution of the structure. We again identify two categories of stellar models: those for which the evolution is mainly affected by mass loss (with an inferior mass limit of about 30 Mˇ ) and those for which the evolution is mainly

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Fig. 4 Log Tc vs Log c diagrams. Left: evolutionary tracks for the 15 and 60 Mˇ models. Right: evolutionary tracks zoomed in the advanced stages for the 12, 20, and 40 Mˇ models. Solid lines are rotating models and dashed lines are nonrotating models. The ignition points of every burning stage are connected with dotted lines. The additional long dashed line corresponds to the limit el el between nondegenerate and degenerate electron gas (Pperfect gas D Pdegenerate gas )

affected by rotational mixing (already identified in Sect. 3.1). We can see that for the 12, 15, and 20 Mˇ models, the rotating tracks have a higher temperature and lower density due to more massive convective cores. The bigger cores are due to the effect of mixing, which largely dominates the structural effects of the centrifugal force. On the other hand, for the 40 and 60 Mˇ models, mass loss dominates mixing effects, and the rotating model tracks in the Log Tc –Log c plane are at the same level or below the non-rotating ones. In order to understand the evolutionary tracks in the Log Tc –Log c plane, we need to look at the different sources of energy at play. These are the nuclear energy, the neutrino and photon energy losses, and the gravitational energy (linked to contraction and expansion). The different energy production rates at the star center are plotted in Fig. 5 as a function of the time left until core collapse. Going from the left to the right in Fig. 5, the evolution starts with H burning where "H dominates. In response, a small expansion occurs ("g negative and very small movement to lower densities in the 15 Mˇ model during H burning in Fig. 4). At the end of H burning, the star contracts non-adiabatically (T  1=3 , every further contraction is also non-adiabatic). The contraction increases the central temperature. This happens very quickly and is seen in the sharp peak of "g between H- and He-burning phases. When the temperature is high enough, He burning starts, "He dominates, and contraction is stopped. Note that during the H- and He-burning phases, most of the energy is transferred by radiation on a thermal time scale. After He burning, neutrino losses (" < 0) overtake photon losses. This accelerates the evolution because neutrinos escape freely. During burning stages, the nuclear energy production stops

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Fig. 5 Log of the energy production rate per unit mass at the star center as a function of the time left until core collapse for the nonrotating (left) and rotating (right) 20 Mˇ models. Nuclear energy production rates during H and He burnings are shown in dotted ("H ) and dashed ("He ) lines, respectively. The solid line corresponds to the nuclear energy production rate in absolute value during the advanced stages ("C –"Si ). Black crosses are drawn on top of the line whenever the energy production rate is negative. The thick long dashed line is the energy loss rates due to neutrinos multiplied by -1 (" ). Finally the gravitational energy production rate in absolute value is plotted in the dotted–dashed line ("g ). Blue squares are plotted on top when this energy is negative. Note that negative gravitational energy production corresponds to an expansion

the contraction if "nucl  " (see C burning for the rotating model) or even provokes an expansion when "nucl > " (most spectacular during Si burning). Central density decreases when the central regions expand (see Fig. 4). Once the iron core is formed, there is no more nuclear energy available, while neutrino losses are still present and the core collapses.

3.2.1

Transition Between Massive and Intermediate Stars (8–12 Mˇ Stars) Recent models for the transition between massive and intermediate stars can be found in Jones et al. (2013), Takahashi et al. (2013), and Woosley and Heger (2015), and older models can be found in Nomoto (1984, 1987) and Ritossa et al. (1999). We will base our discussion on the models presented in Jones et al. (2013) and shown in Fig. 6. Similar trends and conclusions are found in the other studies. The evolution and fate of stars in this mass range are sensitive to convective boundary mixing (CBM) treatment (e.g., overshooting), mass loss, and CO core growth. Different choices of CBM lead to the transition mass being shifted up and down, but we expect the same transitions and regimes to take place for different choices of CBM. The fate of super-AGB stars (SAGB, AGB stars that undergo carbon burning but not neon or subsequent burning stages) is highly sensitive to the mass loss prescription on the SAGB and the rate at which the core grows (Poelarends et al. 2008). Mass loss and core growth compete against each other.

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Si

O Ne URCA C

Fig. 6 The divergence of the models following C burning in the log10 .c /  log10 .Tc / plane; the cross shows from where the evolution of the 8.8 Mˇ model was continued with the AGILEBOLTZTRAN 1D hydro-code (taken from Jones et al. 2013)

At solar metallicity, mass loss often wins, and only a very narrow mass range at the top of the SAGB mass range will end as electron-capture supernovae (ECSN). The 8.7 and 8:75 Mˇ models represent models in this narrow mass range. The 8:2 Mˇ model represents models in the SAGB mass range for which mass loss wins, and this model will end as a one white dwarf (WD). Previous studies (see Nomoto 1984,and references therein) show that the core mass limit for neon ignition is very close to 1:37 Mˇ , which recent models confirm. Indeed, in all models with initial mass greater than 8:8 Mˇ , a CO-core develops, with a mass that exceeds the limit for neon ignition, MCO .8:8 Mˇ ; 9:5 Mˇ ; 12:0 Mˇ / D 1:3696; 1:4925; 1:8860 Mˇ . A temperature inversion develops in the core following the extinction of carbon burning in both the 8:8 Mˇ and 9:5 Mˇ models. The neutrino emission processes that remove energy from the core are (over)compensated by heating from gravitational contraction in more massive stars. However in these lower-mass stars, the onset of partial degeneracy moderates the rate of contraction, and hence neutrino losses dominate, cooling the central region. As a result, the ignition of neon in the 8.8 and 9.5 Mˇ models takes place off center. These two models then go through neon(/oxygen; oxygen also burns via fusion in this situation) flashes followed by the development of a neon(/oxygen) flame. Owing to the high densities in the cores of these stars, the products of neon and oxygen burning are more neutron rich than in more massive stars. This results in an electron fraction in the shell of as low as Ye  0:48. Due to its higher degeneracy, Ye decreases faster in the 8:8 Mˇ , and it contracts faster than the time needed for the neon/oxygen flame to reach the

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center of the star, both processes being helped by URCA pair processes. The core of the 8:8 Mˇ model continuously contracts until the center reaches the critical density for electron captures by 24 Mg, quickly followed by further contraction to the critical density for those by 20 Ne (see Fig. 6), and this model results in core collapse. The 8:8 Mˇ model produces a ECSNe as for the 8:75 Mˇ model but via a new evolutionary path named “failed massive star” rather than via the SAGB evolutionary path. The “failed massive star” path is also expected to take place for a narrow mass range, but it does not critically depend on the uncertainties linked to mass loss, which is the case for the SAGB progenitors of ECSNe. Similarly to the 8:8 Mˇ model starting neon burning off center, the 9:5 Mˇ model starts silicon burning off center in a shell that later propagates toward the center. This is another example of the continuous transition toward massive stars, in which all the burning stages begin centrally. Although we have not evolved this model to its conclusion, we expect that silicon burning will migrate to the center, producing an iron core, and that it will finally collapse as an iron core-collapse SN (FeCCSN). The canonical massive star evolution (igniting C, Ne, O, and Si burning centrally) leading to FeCCSN is expected to take place for stars with masses above 10 Mˇ . This mass range is represented by the 12 Mˇ in Fig. 6. At the other end of the IMF, very massive stars evolve far away from degeneracy. Very massive stars may encounter instead the pair-creation instability at very high temperatures (see Yusof et al. 2013,and references therein).

3.3

Angular Velocity, ˝, and Momentum, j, Evolution

Figure 7 (left) shows the evolution of ˝ inside a 25 Mˇ model from the ZAMS until the end of the core Si-burning phase. The evolution of ˝ results from many different processes: convection enforces solid body rotation, contraction and expansion, respectively, increases and decreases ˝ in order to conserve angular momentum, shear (dynamical and secular) erodes ˝ gradients, while meridional circulation may erode or build them up, and finally mass loss may remove angular momentum from the surface. If during the core H-burning phase, all these processes may be important, from the end of the MS phase onward, the evolution of ˝ is mainly determined by convection, by the local conservation of the angular momentum and, during the core He-burning phase only for the most massive stars, by mass loss. During the MS phase, ˝ decreases in the whole star. When the star becomes a red supergiant (RSG), ˝ at the surface decreases significantly due to the expansion of the outer layers. Note that the envelope is gradually lost by winds in the 25 Mˇ model, whereas in lower mass stars, a very slowly rotating envelope remains until the pre-supernova stage. In the center, ˝ significantly increases when the core contracts and then the ˝ profile flattens due to convection. ˝ reaches values of the order of 1 s 1 at the end of Si burning. It never reaches the local breakup angular velocity limit, ˝c , although, when local conservation holds, ˝r =˝c / r 1=2 .

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Fig. 7 Angular velocity (left) and local specific angular momentum (right) profiles as a function of the Lagrangian mass coordinate, mr inside the 25 Mˇ model (vini = 300 km s1 ) at various evolutionary stages

Figure 7 (right) shows the evolution of the specific angular momentum, jr D 2=3 ˝r r 2 , in the central region of a 25 Mˇ stellar model. The specific angular momentum remains constant under the effect of pure contraction or expansion but varies when transport mechanisms are active. One sees that the transport processes remove angular momentum from the central regions. Most of the removal occurs during the core H-burning phase. Still some decrease occurs during the core Heburning phase, and then the evolution is mostly governed by convection, which transports the angular momentum from the inner part of a convective zone to the outer part of the same convective zone. This produces the teeth seen in the figure. The angular momentum of the star at the end of Si burning is very similar to what it was at the end of He burning. More recent models including the effects of magnetic fields (see, e.g., Heger et al. 2005) lead to slower rotation at the pre-supernova stage, especially if the star goes through a red supergiant phase. These slower pre-supernova rotation rates better reproduce the observed rotation rate of pulsar. The general evolution of the angular velocity and momentum remains, however, qualitatively similar to the models above. Furthermore, some stars, especially if they remain compact throughout their evolution, may retain fast rotation in their core (Yoon et al. 2006) and lead to exotic explosions such as gamma-ray bursts.

3.4

Structure and Abundance Evolution and Pre-supernova Properties

Figure 8 shows the evolution of the structure (Kippenhahn diagram) for 20 Mˇ models. The y-axis represents the mass coordinate and the x-axis the time left until core collapse. The black zones represent convective zones. The abbreviations of the

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Fig. 8 Kippenhahn diagrams for the non-rotating (left) and vini = 300 km s1 (right) 20 Mˇ models. The black zones correspond to convective regions (see text). Note that these plots are produced by drawing black vertical lines for a subset of the time steps of the model and thus the vertical white lines around log(time left until collapse)  3 are only due to the drawing technique and the models remain convective in between neighboring black vertical lines

various burning stages are written below the graph at the time corresponding to the central burning stages. We note the complex succession of the different convective zones during the advanced phases. Sukhbold and Woosley (2014) study in detail the complex convective history in massive stars. In particular, their Fig. 13 shows how the location in mass of the lower boundary of carbon-burning convective shells plays a key role in determining the compactness (Ertl et al. 2016; O’Connor and Ott 2011) at the pre-supernova stage. It is worth to note that a few physical ingredients of the stellar models influence carbon burning in general and thus the exact location of the convective shells and the compactness for a given initial mass. Carbon burning is sensitive to the amount of carbon (relative to oxygen) left at the end of helium burning. This in turn is influenced by the 12 C.˛;  /16 O rate relative to the triple-˛ rate (Tur et al. 2009). Convective boundary criteria and mixing prescriptions also affect the carbon left over at the end of helium burning. Using Ledoux rather than Schwarzschild generally leads to smaller helium-burning cores and more carbon leftover. Extra mixing, especially toward the end of He burning brings fresh ˛ particles that can capture on 12 C and reduce its left over abundance. Finally rotationinduced mixing, as is clearly seen in Fig. 8, leads to significantly larger helium cores and less leftover carbon and leads to radiative core carbon burning (right panel). The other differences between non-rotating and rotating models are the following. We can see that small convective zones above the central H-burning core disappear in rotating models. Also visible is the loss of the hydrogen-rich envelope in the rotating models. The non-rotating 20 Mˇ model is representative of the stars below 20 Mˇ , while the rotating 20 Mˇ model is representative of the non-rotating and rotating

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models above 30 Mˇ . Above 30 Mˇ , all have very similar convective zones history after He burning, having all lost their H-rich envelope and all undergoing core C burning under radiative conditions. The main difference between stars above 30 Mˇ and the rotating 20 Mˇ model is that stars above 30 Mˇ have one large carbon convective shell that sits around 3 Mˇ and thus does not influence much the final stages and the compactness at the pre-supernova stages. The complex history of convective zones and the uncertainties in the input physics mentioned here make it very hard to predict the exact explosion properties of a star of a given initial mass. Nevertheless, it is likely, as in the case of SAGB stars, that the same transitions would occur (e.g., from convective to radiative core carbon burning) even if the input physics changes. Convective boundary mixing during carbon burning (and other stages), if able to change the extent of convective burning shells, might affect the compactness of supernova progenitor significantly. 3D hydrodynamic simulations of convective boundary mixing (see, e.g., Cristini et al. 2017) will hopefully help constrain the 1D prescriptions used in stellar evolution codes, in the near future (Arnett et al. 2015).

3.5

Abundances Evolution

Figures 9 and 10 show the evolution of the abundances of the main isotopes inside the non-rotating (left) and rotating (right) 20 Mˇ models at the end of each central burning episode. As hydrogen burns via the CNO and 14 N.p;  / is the slowest reaction in the cycle, most of the 12 C and 16 O is transformed into N in the convective core. At the end of H burning, we notice the smoother profiles in the rotating model, consequence of the rotational mixing. During He burning, triple-˛ and (˛;  ) reactions produce mostly 12 C and 16 O with traces of heavier multiple ˛-elements 20 Ne and 24 Mg. Double ˛-captures on 14 N leads to a significant production of 22 Ne. Toward the end of He burning, 22 Ne undergoes both (˛;  ) and (˛; n). This last reaction is the neutron source for the weak s-process discussed in Sect. 6. At the end of He burning, we can see that rotating models have larger core sizes and a lower total mass due to extra mixing and mass loss, respectively. We also notice the lower C/O ratio for rotating models mentioned above. The main burning products of carbon burning are 20 Ne, 23 Na (not shown here), and 24 Mg. The main products of Ne burning are 16 O, 23 Na, and 24 Mg. The main products of O burning are elements around 28 Si and 32 S. At the end of O burning, we can see that the rotating model produces much more oxygen compared to the non-rotating model (by about a factor of two). At the end of Si burning, the iron (represented by 56 Ni) and Si cores are slightly bigger in the rotating model. The yields of oxygen increase significantly with rotation as discussed below. Comparing Figs. 11 and 10 shows that even though the 60 Mˇ model has a larger CO core (between about 3 and 11 Mˇ ), its inner and outer structure is quite similar to that of the rotating 20 Mˇ star. This is due to mass loss pealing 3/4 of the initial mass of the star before the end of He burning for the 60 Mˇ model. This means that stars with M > 30 Mˇ have a significant stellar wind contributions as we shall see below.

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Fig. 9 Variation of the abundances in mass fraction as a function of the Lagrangian mass at the end of central hydrogen (top), helium (middle), and carbon (bottom) burnings for the nonrotating (left) and rotating (right) 20Mˇ models

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Fig. 10 Variation of the abundances in mass fraction as a function of the Lagrangian mass at the end of central neon (top), oxygen (middle), and silicon (bottom) burnings for the nonrotating (left) and rotating (right) 20Mˇ models. Note that the abundance of 44 Ti (dotted–long dashed line) is enhanced by a factor 1000 for display purposes

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Fig. 11 Variations of the abundance (in mass fraction) as a function of the Lagrangian mass coordinate, mr , at the end of central Si burning for the rotating 60 Mˇ . Note that the 44 Ti abundance (dotted–long dashed line) is enhanced by a factor 1000 for display purposes

3.6

Pre–supernova Properties

Figure 12 shows the core masses as a function of initial mass for non-rotating (dotted lines) and rotating (solid lines) models. Since rotation increases mass loss, the final mass, Mfinal , of rotating models is always smaller than that of nonrotating ones. Note that for very massive stars (M & 60Mˇ ), mass loss during the WR phase is proportional to the actual mass of the star. This produces a convergence of the final masses (see, for instance, Meynet and Maeder 2005). We can again see a general difference between the effects of rotation below and above 30 Mˇ . For M . 30 Mˇ , rotation significantly increases the core masses due to mixing. For M & 30 Mˇ , rotation makes the star enter the WR phase at an earlier stage. The rotating star spends therefore a longer time in this phase characterized by heavy mass loss rates. This results in smaller cores at the pre-supernova stage. We can see on Fig. 12 that the difference between rotating and nonrotating models is the largest between 15 and 25 Mˇ . As explained above, this will have an impact on the compactness in this sensitive mass range. Improvements in input physics may reconcile model predictions with observationally determined masses of type II supernova, with a maximum below 20 Mˇ , named the RSG problem by Smartt (2009) if the mass range of high compactness ends up covering the mass range between about 17 and 22 Mˇ , while more massive stars explode as type Ib or Ic supernova or fail to explode.

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Fig. 12 Core masses as a function of the initial mass and velocity at the end of core Si burning

Fig. 13 Profiles of the radius, r; density, ; temperature, T ; and pressure P at the end of core Si burning for the nonrotating (left) and rotating (right) 20 Mˇ models. The pressure has been divided by 1010 to fit it in the diagram

As well as the chemical composition (abundance profiles and core masses) of the pre-supernova star, other parameters, like the density profile, the neutron excess (not followed in our calculations), the entropy, and the total radius of the star, play an important role in the supernova explosion. Figure 13 shows the density, temperature, radius, and pressure variations as a function of the Lagrangian mass coordinate at the end of the core Si-burning phase. Since the rotating star has lost its envelope, this truly affects the parameters toward the surface of the star. The radius of the star (BSG) is about 1% that of the nonrotating star (RSG). As said above, this

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modifies strongly the supernova explosion. We also see that temperature, density, and pressure profiles are flatter in the interior of rotating models due to the bigger core sizes.

4

Stellar Wind Contribution to Galactic Chemical Enrichment

Before reviewing the contribution of stellar wind to nucleosynthesis, it is useful to summarize the dependence on the initial mass of mass loss and various core masses: Mass loss: Is very small for stars less massive than 20 Mˇ . It then quickly increases and becomes the dominant physical process for non-rotating stars more massive than 40 Mˇ . Rotation reduces the mass at which mass loss dominates to less than 30 Mˇ . Mass loss takes place mostly during H- and He-burning phases so stellar wind can only enrich the ISM with H- and He-burning products (elements up to silicon) MfinalW Due to the strong mass loss experienced by massive stars, there is no simple relation between the final mass and the initial one. The important point is that a final mass between 10 and 15 Mˇ can correspond to any star with an initial mass above 15 Mˇ . M˛ W The core masses increase significantly with the initial mass. For very massive stars, these core masses are limited by the very important mass loss undergone by these stars: typically M˛ is equal to the final mass for M & 20 Mˇ for rotating models and for M & 40 Mˇ for the non-rotating ones. MCO W The mass of the carbon–oxygen core is also limited by mass loss for M & 40 Mˇ for both rotating and non-rotating models. What is the relative importance of the wind and pre-SN contributions? Figure 14 tot , as a displays the total stellar yields divided by the initial mass of the star, pim function of its initial mass, m, for the non-rotating (left) and rotating (right) models. preSN tot wind D mpim C mpim (to be used for chemical The total stellar yields, mpim evolution models using Eq. 2 from Maeder 1992), plotted in this figure are given in Tables 6 and 7 in Hirschi et al. (2005). The different shaded areas correspond tot from top to bottom to pim for 4 He, 12 C, 16 O, and the rest of the heavy elements. The fraction of the star locked in the remnant and the expected explosion type are shown at the bottom. The dotted areas show the wind contribution for 4 He, 12 C, and 16 O. For 4 He, and for other H-burning products like 14 N and 26 Al, the wind contribution increases with mass and dominates for M & 22Mˇ for rotating stars and M & 35Mˇ for non-rotating stars, i.e., for stars which enter the WR stage. For very massive stars, the (pre-)SN contribution is negative, and this is why the dotted area is higher than the purple area for 4 He. In order to eject He-burning products, a star must not only become a WR star but must also become a WC star. Therefore for 12 C, the wind contributions only start to be significant above the following approximative mass limits: 30 and 45 Mˇ for rotating and non-rotating models,

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•

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pitotm ,

Fig. 14 Stellar yields divided by the initial mass, as a function of the initial mass for the nonrotating (left) and rotating (right) models at solar metallicity. The different total yields (divided by m) are shown as piled up on top of each other and are not overlapping. 4 He yields are delimited by the top solid and long dashed lines (top shaded area), 12 C yields by the long dashed and short– long dashed lines, 16 O yields by the short–long dashed and dotted–dashed lines, and the rest of metals by the dotted–dashed and bottom solid lines. The bottom solid line also represents the int mass of the remnant (Mrem =m). The corresponding SN explosion type is also given. The wind contributions are superimposed on these total yields for the same elements between their bottom limit and the dotted line above it. Dotted areas help quantify the fraction of the total yields due to winds. Note that for 4 He, the total yields are smaller than the wind yields due to negative SN yields (see text). Preliminary results for masses equal to 9, 85, and 120 Mˇ were used in this diagram (See Hirschi 2004)

respectively. Above these mass limits, the contribution from the wind and the preSN are of similar importance for carbon. Since at solar metallicity, no WO star are expected (Meynet and Maeder 2005), for 16 O, as for heavier elements (expect for elements produced during H burning like 26 Al), the wind contribution remains very small.

4.1

Comparison Between Rotating and Non-rotating Models and Convolution with the IMF

For H-burning products, the yields of the rotating models are usually higher than those of nonrotating models. This is due to larger cores and larger mass loss. Nevertheless, between about 15 and 25 Mˇ , the rotating yields are smaller. This is due to the fact that the winds do not expel many H-burning products yet and more of these products are burnt later in the pre-supernova evolution (giving negative SN yields). Above 40Mˇ , rotation clearly increases the yields of 4 He. Concerning He-burning products, below 30 Mˇ , most of the 12 C comes for the pre-SN contribution. In this mass range, rotating models having larger cores also have larger yields (factor 1.5–2.5). We notice a similar dependence on the initial

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Fig. 15 Product of the stellar yields, mpitotm by Salpeter’s IMF (multiplied by an arbitrary constant: 1000M2:35 ), as a function of the initial mass for the nonrotating (left) and rotating (right) models at solar metallicity. The different shaded areas correspond from top to bottom to mpitotm  1000  M 2:35 for 4 He, 12 C, 16 O, and the rest of the heavy elements. The dotted areas show for 4 He, 12 C, and 16 O the wind contribution. Preliminary results for masses equal to 9, 85, and 120 Mˇ were used in this diagram (See Hirschi 2004)

mass for the yields of non-rotating models as for the yields of rotating models but shifted to higher masses. Above 30 Mˇ , when mass loss dominates, the yields from the rotating models are closer to those of the nonrotating models. The situation for 16 O and metallic yields is similar to carbon. Therefore 12 C, 16 O, and the total metallic yields, Z, are larger for rotating models compared to non-rotating ones by a factor 1.5–2.5 below 30 Mˇ . Figure 15 presents the stellar yields convolved with the Salpeter initial mass function (IMF) (dN =dM / M 2:35 ). This reduces the importance of the very massive stars. Nevertheless, the differences between rotating and nonrotating models remain significant, especially around 20 Mˇ .

5

Dependence on Metallicity

5.1

Metallicity Effects on General Evolution

The effects of metallicity on stellar evolution are described in several studies (see, e.g., Chieffi and Limongi 2004; Heger et al. 2003; Meynet et al. 1994). A lower metallicity implies a lower luminosity which leads to slightly smaller convective cores. A lower metallicity also implies lower opacity and lower mass losses (as long as the chemical composition has not been changed by burning or mixing in the part of the star one considers). So at the start of the evolution, lower metallicity stars are more compact and thus have bluer tracks during the main sequence. The

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lower metallicity models also have a harder time reaching the red supergiant (RSG) stage (see Maeder and Meynet 2001, for a detailed discussion). Non-rotating models around Z D 103 becomes a RSG only after the end of core He burning, and lower metallicity non-rotating models never reach the RSG stage. At even lower metallicities, as long as the metallicity is above about Z D 1010 , no significant differences have been found in nonrotating models. Below this metallicity and for metal-free stars, the CNO cycle cannot operate at the start of H burning. At the end of its formation, the star therefore contracts until it starts He burning because the pp chains cannot balance the effect of the gravitational force. Once enough carbon and oxygen are produced, the CNO cycle can operate, and the star behaves like stars with Z > 1010 for the rest of the main sequence. Shell H burning still differs between Z > 1010 and metal-free stars. Metal-free stellar models are presented in Chieffi and Limongi (2004), Umeda and Nomoto (2005), Ekström et al. (2008), and Heger and Woosley (2010).

5.2

Effects of Rotation at Subsolar Metallicities

How does rotation change this picture? At all metallicities, rotation usually increases the core sizes, the lifetimes, the luminosity, and the mass loss. Maeder and Meynet (2001) and Meynet and Maeder (2002a) show that rotation favors a redward evolution and that rotating models better reproduce the observed ratio of blue to red supergiants (B/R) in the Small Magellanic Cloud. Rotating models around Z D 105 become RSGs during shell He burning. This does not change the ratio B/R but changes the structure of the star when the SN explodes. At even lower metallicities (Z D 108 models presented in Hirschi 2007), the 20 Mˇ models do not become RSG. However, more massive models do reach the RSG stage, and the 85 Mˇ model even becomes a WR star of type WO (see below). Maeder and Meynet (2001) also find that a larger fraction of stars reach break-up velocities during the evolution. This will be further discussed in Sect. 5.2.2).

Rotation-Induced Mixing and Production of Primary 22 Ne and 14 N Meynet and Maeder (2002a, b) and Hirschi (2007) find that rotating stars produce important amounts of primary 14 N and 22 Ne via rotation-induced mixing. The production of these nuclei originates from the transport of matter between the Heburning core and the H-burning shell. If the He-burning products 12 C and 16 O reach the proton-rich layers, they are burnt immediately into 14 N via the CNO cycle. A 14 N-rich zone is produced in this way at the lower edge of the H-burning shell as shown in Fig. 16. Some of this nitrogen is transported back into the He-burning core, where it is further transformed into 22 Ne via two ˛-captures. The transport of chemical elements is illustrated for the 25 Mˇ model with rotation at Z D 105 in Fig. 16, which shows the abundance profiles in this model during core He burning. The rotation-induced mixing, which leads to the production of primary 14 N and 22 Ne, occurs in the region above the convective He core

5.2.1

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100 1H

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N O

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Mr [M ] Fig. 16 Abundance profiles of the main light isotopes during central He-burning (Xc .He/  0:08) for the 25 Mˇ model with rotation and Z D 105 (C25S4). The convective He-burning core extends from the center to about Mr D 7:5 Mˇ (flat abundance profiles). The bottom of hydrogenshell burning is just above 10 Mˇ (sudden drop of hydrogen abundance). Rotation-induced mixing brings freshly produced 12 C and 16 O from the core into contact with the hydrogen-burning shell, where a peak a primary nitrogen (14 N) develops. Further mixing (both convective and rotation induced) brings the primary nitrogen down into the He-burning core where it is transformed into 22 Ne, leading to primary production of both 14 N and 22 Ne Frischknecht et al. (Figure taken from 2016)

(Mr  7:5  10:5 Mˇ ). The core itself is identifiable by the flat abundance profile between Mr D 0 and 7:5 Mˇ . Differential rotation develops between the convective He core and H shell mainly because of the core contraction and envelope expansion at the end of the main sequence. The differential rotation induces secular shear mixing in this radiative zone, in which no mixing would take place in nonrotating models. Shear mixing, a diffusive process, brings primary 12 C and 16 O (blue dashed and black continuous lines) into contact with the H-burning layer and creates a 14 Npocket (Mr  7:5  10:5 Mˇ ) via the CNO cycle as explained above. In our models, the transport of 14 N back to the center is mainly due to the growth of the convective core, incorporating parts of the 14 N-pocket. Indeed, the diffusive transport is not fast enough to produce a 22 Ne mass fraction, X .22 Ne/, of 103 to 102 in the core, necessary to boost the s-process significantly. Although the amount of mixing

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depends on the prescriptions used for rotation-induced mixing, Frischknecht et al. (2012, 2016) find a production of significant amounts of both 14 N and 22 Ne in models of various mass and metallicity. Rotational mixing also influences strongly the mass loss of very massive stars as is discussed below.

5.2.2 Mass Loss Due to Critical Rotation and Rotation-Induced Mixing Mass loss becomes gradually unimportant as the metallicity decreases in the 20 Mˇ models. At solar metallicity, the rotating 20 Mˇ model loses more than half of its mass; at Z D 0:001, the 20 models presented in Hirschi (2007) lose less than 15% of their mass; at Z D 105 , less than 3%, and at Z D 108 , less than 0.3%. Meynet et al. (2006) show that the situation can be very different for a 60 Mˇ star at Z D 108 . Indeed, their 60 Mˇ model loses about half of its initial mass. About 10% of the initial mass is lost when the surface of the star reaches break-up velocities during the main sequence. The largest mass loss occurs during the red supergiant (RSG) stage due to the mixing of primary carbon and oxygen from the core to the surface through convective and rotational mixing. The large mass loss is due to the fact that the star crosses the Humphreys–Davidson limit and a high mass loss is used in this phase. In models from Hirschi (2007) with \ini D 600–800 km s1 and Z D 108 , the 20 Mˇ model only reaches break-up velocities at the end of the main sequence (MS) and therefore does not lose mass due to this phenomenon. However, more massive models reach critical velocities early during the MS (the earlier the more massive the model). The mass lost due to breakup increases with the initial mass and amounts to 1.1, 3.5, and 5.5 Mˇ for the 40, 60, and 85 Mˇ models, respectively, in that study. At the end of core H burning, the core contracts and the envelope expands, thus decreasing the surface velocity and ˝=˝crit . The mass loss rates becomes very low again until the star crosses the HR diagram and reaches the RSG stage. At this point, the convective envelope dredges up CNO elements to the surface increasing its overall metallicity. In general (see 2.2), the total metallicity, Z, is used (including CNO elements) for the metallicity dependence of the mass loss for the RSG phase. Therefore depending on how much CNO is brought up to the surface, the mass loss can become very large again. The CNO brought to the surface comes from primary C and O produced in He burning. As described in the above subsection, rotational and convective mixing brings these elements into the H-burning shell. A large fraction of the C and O is then transformed into primary nitrogen via the CNO cycle. Additional convective and rotational mixing is necessary to bring the primary CNO to the surface of the star. The whole process is complex and depends on mixing. Of particular importance is the surface convective zone, which appears when the star becomes a RSG. This convective zone dredges up the CNO to the surface. For a very large mass loss to occur, it is necessary that the star becomes a RSG in order to develop a convective envelope. It is also important that the extent of the convective envelope is large enough to reach the CNO-rich layers. Finally, the star must reach the RSG stage early enough (before the end of core He burning) so that there will be time remaining to lose mass. Models up to about 40 Mˇ in Hirschi

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(2007) reach the RSG stage only after the end of helium burning, so too late for a large mass loss. The 60 Mˇ model reaches the RSG stage during He burning. It would therefore have time to lose large amounts of mass. However, the dredge up is not strong enough. The 85 Mˇ model becomes a RSG during He burning earlier than the 60 Mˇ model. The dredge-up is stronger for this model, and the surface CNO abundance becomes very high (see Fig. 17 bottom). The dependence on mixing of the lower initial mass for a large mass loss to occur can be estimated by comparing the 60 Mˇ model calculated in Hirschi (2007) and the one presented by Meynet et al. (2006). The model calculated by Meynet et al. (2006), which does not include overshooting and uses a different prescription for the horizontal diffusion coefficient, Dh (Maeder 2003), loses a large fraction of its mass (and becomes a WR star with high effective temperature) just before the end of core helium burning (see Fig. 4 from Meynet et al. 2006). The Dh used in Meynet et al. (2006), compared to the Dh used in Hirschi (2007), tends to allow a larger enrichment of the surface in CNO-processed elements. This different physical ingredient explains the differences between the two 60 Mˇ models. The fact that, out of two 60 Mˇ models, one model does not lose much mass and the other model with a different physics just does, means that the minimum initial mass for the star to lose a large fraction of its mass is probably around 60 Mˇ . This means that despite expectations that stars at low metallicities have negligible stellar wind contribution to nucleosynthesis, rotation-induced mixing changes the picture and may lead to a significant contribution from stellar winds (due to critical rotation and CNO enrichment of the surface). As at higher metallicities, the stellar wind contribution is limited to H- and He-burning products, in particular CNO elements. This contribution is interesting to explain carbon-enhanced extremely metal-poor stars (see Hirschi 2007,for a discussion on this topic).

6

Weak s-Process

The classic view of the s-process nucleosynthesis in massive stars is that it occurs in He- and C-burning regions of the stars, producing only the low mass range of the s-process elements, typically the elements with an atomic mass number below about 90–100 (see Käppeler et al. 2011,for a review of the topic). It has also been shown that in the regions where the s-process occurs, the fact that, when the metallicity decreases, (1) the neutron source, mainly the 22 Ne(˛; n/ reaction, decreases; (2) the neutron seeds (Fe) also decreases; and (3) the neutron poisons as for instance 16 O remain independent of the metallicity implies that the s-process element production decreases with the metallicity and that there exists some limiting metallicity below which the s-process becomes negligible. This limit was found to be around Z/Zˇ =102 (Prantzos et al. 1990), and the process has a metallicity dependence that is even steeper than for secondary processes (see, e.g., Raiteri et al. 1992). The models and plots presented in this section on the weak s-process are taken from a large grid of models including a comprehensive nuclear network of about 700 isotopes from hydrogen to bismuth calculated with GENEC and

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Fig. 17 Abundance profiles for the 40 (top), 60 (middle), and 85 (bottom) Mˇ models. The preSN and wind (yellow-shaded area) chemical compositions are separated by a red dashed line located at the pre-SN total mass (Mfinal ), given below each plot (Figure taken from Hirschi 2007)

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published in Frischknecht et al. (2012) (25 Mˇ models at various metallicities) and Frischknecht et al. (2016) (15 to 40 Mˇ models at various metallicities). Unless otherwise stated, figures in the section as taken from Frischknecht et al (2012, 2016)

6.1

Standard Weak s-Process in (Nonrotating) Massive Stars

Before discussing the impact of rotation, we first review the standard weak s-process in massive stars at various metallicities and then present recent models in which rotation-induced mixing leads to a strongly enhanced production of s-process at subsolar metallicities compared to nonrotating models.

6.1.1 He Core Burning The CNO cycle transforms most of the initial C C N C O into 14 N. At the beginning of the core He-burning phase, this 14 N is converted into 22 Ne via two alpha-particle captures. Near the end of helium burning, 22 Ne is destroyed by the two reactions 22 Ne.˛; n/25 Mg and 22 Ne.˛;  /26 Mg. When the temperatures for an efficient activation of 22 Ne.˛; n/25 Mg are reached, some 22 Ne has already been destroyed by the (˛;  /26 Mg reaction. More quantitatively, when T8  2:8 is reached (temperature, at which the .˛; n/-channel starts to dominate), massive stars in the mass range 15–40 Mˇ have a mass fraction X .22 Ne/ D 102 5:0103 left in the core. Important well-known aspects of the s-process during core He burning are the following: • Because only a small helium mass fraction, X .4 He/, is left when 22 Ne C ˛ is activated (less than 10% in mass fraction), the competition with other ˛-captures as the 12 C.˛;  / and 3˛ is essential at the end of He burning and will affect the s-process efficiency in core He burning. Note that 22 Ne C ˛ reactions are also critical to determine the final 12 C at the end of helium burning, which in turn is important to the development of carbon burning (convective or radiative core; see discussion in Sect. 3.4). It is thus very important to include ˛-captures on 22 Ne in massive star calculations, even if one only focuses on the evolution of the structure of massive stars. • The low amount of X .4 He/, when the neutron source is activated, means also that not all of 22 Ne is burned and a part of it will be left for the subsequent C-burning phase. This depends on the stellar core size. The more massive the core, the more 22 Ne is burned and the more efficient is the s-process in core He burning, as can be seen from the increasing number of neutron captures per seed nc in Table 4 in Frischknecht et al. (2016). This is a well-known behavior already found in previous works (Baraffe and Takahashi 1993; Baraffe et al. 1992; Prantzos et al. 1990; Pumo et al. 2010; Rayet and Hashimoto 2000; The et al. 2000, 2007). • During the late He-burning stages, the bulk of the core matter consists of 12 C and 16 O, which are both strong neutron absorbers. They capture neutrons to produce 13 C and 17 O, respectively. 13 C will immediately recycle neutrons via 13 C.˛; n/ in He-burning conditions. Instead, the relevance of 16 O as a neutron

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103 102

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101 100 10–1 10–2

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120 140 Atomic mass

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Fig. 18 Isotopic overproduction factors (abundances over initial abundances) of 25 Mˇ models with solar metallicity after He exhaustion. The rotating model (circles) has slightly higher factors than the nonrotating model (diamonds), but the general production is very similar in both cases and is referred to in the rest of this section as the standard weak s-process 103 102

x/x

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Fig. 19 Isotopic abundances normalized to solar abundances of 25 Mˇ models with with Z D 103 after He exhaustion. The rotating model (circles) has much higher factors than the nonrotating model (diamonds)

poison depends on the 17 O.˛;  / and 17 O.˛; n/ rates. In particular, the strength of primary neutron poisons, like 16 O, increases toward lower metallicities, because of the decreasing ratio of seeds to neutron poisons. The s-process production in the 25 Mˇ models at solar metallicity is shown in Fig. 18. We will call this production the standard weak s-process in the rest of this section. The s-process production for the 25 Mˇ models are shown in Fig. 19 at Z D 103 . Comparing the production of nuclei between A D 60 and 90 in nonrotating models between these two metallicities highlights the very strong

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metallicity dependence of the standard weak s-process. As explained above, this is due to the secondary nature of both the neutron source (22 Ne.˛; n/25 Mg) and the seeds (mainly iron) (see, e.g., Pignatari and Gallino 2008; Prantzos et al. 1990; Raiteri et al. 1992). During helium burning, the neutron poisons are a mixture of secondary (mainly 20 Ne, 22 Ne, and 25 Mg) and primary (mainly 16 O) elements. The s-process production thus becomes negligible below Z=Zˇ D 102 (Prantzos et al. 1990), which is already visible in Fig. 19. The decreasing production with decreasing mass is due to the fact that lower mass stars reach lower temperature at the end of He burning. Thus less 22 Ne is burnt during He burning (see Table 4 in Frischknecht et al. 2016).

6.1.2 He-Shell Burning Shell He burning, similarly to the other burning shells, appears at higher temperatures and lower densities than the equivalent central burning phase. Hightemperature conditions of T8  3:5-4:5 and   3-5:5  103 g cm3 cause an efficient 22 Ne(˛,n) activation for the s-process in shell He burning. However, the highest neutron densities are generally reached only in the layers below the convective shell helium burning. Therefore only a narrow mass range, extending over about 0:2 Mˇ in nonrotating models, at the bottom of the He shell is strongly affected by neutron capture nucleosynthesis. The contribution of the s-process in the He shell amounts to at most  5% of the total s-process yields for the solar metallicity 25 Mˇ (or heavier) model. For less massive stars, the He shell gains more weight and produces in 15 Mˇ models with rotation up to 50% of the total s-process-rich SN ejecta. For 15–20 Mˇ stars, the He-shell s-process contribution has to be considered (see also Tur et al. 2009).

6.1.3 C-Shell Burning Shell C burning occurs in the CO core after central C burning. Temperatures and densities at the start of C-shell burning show the same trend with stellar mass as the core burning conditions, i.e., the temperature increases and the density decreases with stellar mass. They vary between T9  0:8,   2  105 g cm3 in 15 Mˇ models and T9  1:3,   8  104 g cm3 in 40 Mˇ models. These temperatures are higher than in the central C burning, where T9 D 0:6  0:8. The efficiency of the s-process mainly depends on the remaining iron seeds and 22 Ne left after He burning, Xr .22 Ne/, in the CO core. All the remaining 22 Ne is burned quickly with maximal neutron densities between 6  109 and 1012 cm3 . The time scale of this s-process is of the order of a few tens of years in 15 Mˇ stars to a few tenth of a year in 40 Mˇ . A striking difference between the s-process in the He shell and in the C shell is the neutron density, which is much higher in the C shell than in the He shell. The activation of 22 Ne.˛; n/ at the start of C-shell burning leads to a short neutron burst with relatively high neutron densities (typically nn  1010  1012 cm3 ; see The et al. 2000, 2007), compared to He burning (nn  105  107 cm3 ).

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104

x/xHe-core

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120 140 Atomic mass

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Fig. 20 Ratio of abundances after shell C burning to the abundances after core He burning, XC =XHe , in a nonrotating 25 Mˇ star at Z D Zˇ . It illustrates the modification of the abundances by s-process in shell C burning

This leads to a different s-process nucleosynthesis than during the He-shell burning. The ratio of abundances after shell C burning to the abundances after core He burning, XC =XHe is plotted for the nonrotating 25 Mˇ model at Z D Zˇ in Fig. 20. We can see an overproduction of most isotopes from Zn to Rb. The overproduction during C-burning shell is also found in models of other initial mass, which have both Xr .22 Ne/  103 and X .56 Fe/  104 , at the start of shell C burning. Mostly 15–25 Mˇ stars at solar Z have a strong C-shell contribution in terms of neutron exposure. In the mass range A D 60–90, there are several branching points at 63 Ni, 79 Se, and 85 Kr, respectively. The high neutron densities modify the s-process branching ratios, in a way that the neutron capture on the branching nuclei are favored over the ˇdecay channel (see, e.g., Pignatari et al. 2010,and references therein). As a consequence of this, isotopic ratios like 63 Cu=65 Cu, 64 Zn=66 Zn, 80 Kr=82 Kr, 79 Br=81 Br, 85 Rb=87 Rb, and 86 Sr=88 Sr are lowered. Overall, stars with different initial masses show very different final branching ratios. For instance, stars with 15 Mˇ and with 20 Mˇ (without rotation) produce 64 Zn, 80 Kr, and 86 Sr in the C shell, while in heavier stars, these isotopes are reduced compared to the previous He core. The impact of the high neutron densities during C shell can be seen in Fig. 20. It causes up to three orders of magnitude overproduction of some r-process nuclei, such as 70 Zn, 76 Ge, 82 Se, or 96 Zr, compared to the yields of the “slower” s-process during He burning. However, the production of r-only nuclei in carbon burning compensates only the destruction in the He-core s-process when looking at the final yields. Only for the 40 Mˇ model is 96 Zr weakly produced. During C burning, the main neutron poisons are 16 O, 20 Ne, 23 Na, and 24 Mg, which are all primary. Thus the C-shell contribution to the s-process will vanish at low metallicities even faster than during He burning. In nonrotating stellar models with Z < Zˇ , the C-burning shell has a small contribution (< 10%).

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Many aspects of this phase depend on the rates of a few key nuclear reactions. First, how the shells proceed depends on whether central C burning takes place in a radiative or a convective core. It is thus sensitive to the C/O ratio in the core after He burning and therefore to the 12 C.˛;  / rate. The uncertainty of this rate and its impact on the stellar structure evolution were studied, for example, in Imbriani et al. (2001), El Eid et al. (2004), and Tur et al. (2009). Second, the s-process nucleosynthesis depends on the number of free ˛ particles present in the shell that can trigger neutron production by 22 Ne.˛; n/ (Raiteri et al. 1991) or 13 C.˛; n/ (Bennett et al. 2012; Pignatari et al. 2013). In carbon burning, ˛ particles are released by the 12 CC12 C ˛-channel. The following studies by Limongi et al. (2000), Rauscher et al. (2002), The et al. (2007), and Pignatari et al. (2010) confirmed that 22 Ne.˛; n/ is the only important neutron source in C-shell burning, where the remaining 22 Ne left after central He burning is consumed in a very short time (time scale 1 year). At shell C-burning temperatures (T9  1), the ratio of the 22 Ne.˛; n/ to 22 Ne.˛;  / rates is about 230. In these conditions, the main competitor is the 22 Ne.p;  /, where protons are made by the C-fusion channel 12 C.12 C; p/23 Na. Alternatively, Bennett et al. (2012) and Pignatari et al. (2013) showed that for 12 C C12 C larger than about a factor of 100 compared to the CF88 rate at typical central C-burning temperatures, the 13 C.˛; n/16 O reaction activated in the C core may strongly affect the final s-process yields. The 12 C C12 C rate needs to be better constrained by experiments (e.g., Wiescher et al. 2012). Other neutron sources such as 17 O.˛; n/ and 21 Ne.˛; n/ recycle most of the neutrons absorbed by 16 O and 20 Ne, respectively (e.g., Limongi et al. 2000).

6.2

Impact of Rotation on the s-Process

Rotation significantly changes the structure and pre-SN evolution of massive stars (Hirschi et al. 2004) and thus also the s-process production. Rotating stars have central properties similar to more massive nonrotating stars. In particular, they have more massive helium burning and CO cores (see Sect. 3), respectively, which is an effect of rotation also found by other studies (e.g., Chieffi and Limongi 2013; Heger and Langer 2000). Our models with rotation show typically 30%–50% larger He cores and CO cores than the nonrotating models. A 20 Mˇ star with rotation has thus a core size which is almost as large as the one of a 25 Mˇ nonrotating star. The higher core size means higher central temperatures at the same evolutionary stage and consequently the 22 NeC˛ is activated earlier. In these conditions, the He-core s-process contribution increases at the expense of the C-shell contribution. Since in He-burning conditions the amount of neutrons captured by light neutron poisons and not used for the s-process is lower compared to C-burning conditions, an overall increase of the s-process efficiency is obtained (see also Pignatari et al. 2010). Early investigations of the possible role of rotational mixing on the s-process production in massive stars have shown that this classic picture could be significantly revised (Hirschi 2007; Hirschi et al. 2008; Pignatari et al. 2008). Following these initial

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studies, the impact of rotation on the s-process nucleosynthesis in low-Z massive rotating stars was studied in detail by Frischknecht et al. (2012, 2016). In addition to rotating models having higher core masses and thus higher core temperature, s-process production is also increased due to additional production of 22 Ne via rotation-induced mixing. Rotational mixing allows the production of large amounts of 14 N in the H-burning shell, 14 N, which, once engulfed into the Heburning core, is transformed into 22 Ne via two ˛captures (see Frischknecht et al. 2016; Hirschi 2007,for details). Increasing the quantity of 22 Ne favors s-process production since the main neutron source is the 22 Ne(˛; n/ reaction. The amount of iron seeds and neutron poisons is not affected by rotation. Thus rotation acts mainly on one of the aspects of the s-process nucleosynthesis, the neutron source via the amount of 22 Ne. At solar metallicity, the difference between rotating and nonrotating stars is mainly found in the core size, but not in the amount of available 22 Ne. The difference in s-processing between rotating and nonrotating stars is the smallest at 25 Mˇ , when comparing 15–25 Mˇ models. It is related to the saturation of the s-process toward higher core/initial masses, which was already found by Langer et al. (1989). In Fig. 18, the overproduction factors of 25 Mˇ rotating and nonrotating models at solar metallicity after the end of He burning are shown. The rotating model (circles) shows only a moderate increase of the s-process production with respect to the nonrotating model (diamonds). Both models produce heavy isotopes from iron seeds up to the Sr-peak (A  90). The varying overproduction factors (¤ 1) beyond A D 90 are the signature of a local redistribution of pre-existing heavy nuclei. This figure therefore illustrates that not only the s-process quantitative production is similar but also the abundances pattern of rotating and nonrotating models at solar Z are almost identical. The difference in the efficiency is mostly caused by the larger core size in the rotating models.

6.2.1 Impact of Rotation on the s-Process at Low Metallicities At subsolar metallicities, the differences between rotating and nonrotating models are much more striking. Rotating models have much higher neutron exposures compared to nonrotating stars, which is due to the primary 22 Ne produced and burned during central He burning. In the models published in Frischknecht et al. (2016), 3–270 times higher amount of 22 Ne burned in rotating stars up to central He exhaustion, depending on the initial mass (or MCO ) and metallicity. The large production of neutrons by 22 Ne is partially compensated by the larger concentration of 25 Mg and 22 Ne itself, which become primary neutron poisons in rotating massive stars (Pignatari and Gallino 2008). Figure 19 shows the abundance normalized to solar in the CO core of 25 Mˇ stars with Z D 103 just after central He exhaustion, each for a rotating (circles) and a nonrotating model (diamonds). Corresponding plots for Z D 105 and Z D 107 can be found in Frischknecht et al. (2016). Going from Z D Zˇ (Fig. 18) to Z D 103 (Fig. 19) and lower Z, the production of nuclei between A D 60 and 90 vanishes in the nonrotating models, which is what is expected from the combination of secondary neutron source, secondary seeds,

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Fig. 21 Production factors (ejected mass divided by the initial mass of the element) for the 25 M ˇ models with Z D 105 after the end of core He burning. The model without rotation (triangles) does not produce s-process efficiently, whereas the rotating models (circles, B1 and diamonds, B3) do. The additional rotating models with reduced 17 O.˛; / rates (stars, B4, CF88/10) highlight the uncertainty for the neutron poison 16 O

and primary neutron poisons. On the other hand, the rotating models at subsolar Z produce efficiently up to Sr (Z D 103 ), Ba (Z D 105 ) and finally up to Pb (Z D 107 ). At the same time, the consumption of iron seeds increases from 74% at Z D Zˇ to 96%, 97% and 99% at Z D 103 , Z D 105 , and Z D 107 , respectively, for 25 Mˇ . Also with the standard rotation rate \ini =\crit D 0:4, around 90% of initial Fe is destroyed in models with 25 Mˇ and Z < Zˇ . Hence already from the s-process in He burning, one can conclude that the primary neutron source in the rotating models is sufficient to deplete all the seeds and the production is limited by the seeds (not the neutron source any more). The other stellar masses show similar trends with Z. This explains why the s-process yields are much larger in the rotating model, by up to a factor of 1000. Nevertheless, at Z D 103 (or ŒFe=H D 1:8), rotating models produce elements in large quantities only up to the Sr peak. We hence expect that the rotation-enhanced s-process to be qualitatively similar the normal s-process (production of elements with A D 60–90) for ŒFe=H > 2 but with higher production factors. At Z D 105 (or [Fe/H]D 3:8; see Fig. 21 showing production factors at the pre-SN stage), elements up to Sr are still strongly produced in the rotating model (circles in Fig. 21), whereas in the nonrotating model, the overproduction is very small. Depending on the initial rotation rate and the 17 O.˛;  / rate used, elements up to Ba start to be efficiently produced (see discussion below). At Z D 107 (or ŒFe=H D 5:8), both the rotating and nonrotating models produce and burn enough 22 Ne to deplete all the iron seeds. At this very low Z, the main limitation is the seeds, and, given the low initial iron content, the s-process production remains very modest.

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It is interesting to look at the metallicity dependence of the rotation-enhanced s-process production in rotating models. As said above, the production is limited mainly by the iron seeds. Even at the lowest metallicities in a very fast-rotating model (\ini =\crit D 0:6 instead of the standard 0.4), and thus with a larger primary neutron source, there is no additional production of s-process elements starting from light element seeds like 22 Ne. Instead, what happens is that not only iron is depleted but elements up to Sr are partially destroyed (after being produced) and heavier elements like Ba are produced ([Sr/Ba] 0). Indeed, going from [Fe/H]D 3:8 to [Fe/H]D 5:8, the Sr yield decreases by a factor of  9, while the Ba yield increases by a factor of 5 (see Table 1 in Frischknecht et al. 2012). We therefore have a different metallicity dependence for the production of elements belonging to the different peaks: there is a roughly secondary production of elements up to Sr, but the Z dependence for heavier elements like Ba is milder. The secondarylike behavior of Sr/Y/Zr in the metallicity range covered makes the nonstandard s-process in massive rotating stars an unlikely solution for the LEPP (light element primary process) problem at low Z (Travaglio et al. 2004). Apart from the seeds, the s-process is strongly dependent on the neutron source and neutron poisons. Both are still quite uncertain at present. The neutron source, 22 Ne, depends on rotation-induced mixing and thus on the initial velocity of stars at very low Z. In models calculated with a higher initial velocity (\ini =\crit D 0:5–0:6 instead of 0.4), the increase in the production of 22 Ne is about a factor of 4. This leads to a higher neutron capture per seed (nc ) and thus to a production of elements like Ba at the expense of elements like Ge, but the total production (sum of all isotopes heavier than iron) is still limited by the iron seeds as said above. A major uncertainty concerning neutron poisons is the importance of 16 O as a neutron poison. At low Z, 16 O is a strong neutron absorber during core He burning. The neutrons captured by 16 O.n;  /17 O may either be recycled via 17 O.˛; n/20 Ne or lost via 17 O.˛;  /21 Ne. The impact of the 17 O.˛;  /21 Ne uncertainty can be seen by comparing the diamonds and stars (models with the CF88 rate divided by a factor of 10) in Fig. 21. The impact of a change of even a factor of 10 in this rate is strong. Given the differences between models with the CF88 and CF88/10 rate, the experimental determination of the 17 O.˛;  /-rate and the 17 O.˛; n/ is crucial to give a more accurate prediction for the s-process in massive rotating stars at low metallicity. Note the more precise determination of 22 Ne.n;  / and 22 Ne.˛;  / is also important (Nishimura et al. 2014).

6.2.2 Relative Contributions and Total Yields The following points can be derived concerning the relative contributions from for He-core, C-shell, and He-shell burning to the total yields (see Fig. 13 in Frischknecht et al. 2016,for the production of 68 Zn): 1. In general, the contribution from He-core burning dominates over the other two phases overall. 2. Shell carbon burning is, compared to the other two sites, only efficient at solar metallicity. The weak contribution from the C shell at low-Z is due to the

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low amount of 22 Ne left, the smaller amount of seeds, and the primary neutron poisons, which have an increased strength toward lower Z in C-shell conditions. The only mass-metallicity range for which the C shell dominates is at solar Z with M . 25 Mˇ for nonrotating models and with M . 20 Mˇ for rotating models. Such a dominant contribution from C shell was not seen in previous literature (e.g., The et al. 2007). This may be due to the high 22 Ne.˛;  / rate of NACRE, which is in strong competition to the neutron source during central He burning and dominates for stars with M . 20 Mˇ . This inhibition during He-core burning is weaker for rotating stars since they have higher central temperatures. 3. Shell He burning contributes only a small fraction but typically 5% to the final yields. The exceptions are the rotating 15–25 Mˇ stars at low Z and rotating 15–20 Mˇ stars at solar Z. It is the effect of decreasing contribution from the He core toward lower masses and the higher burning temperatures in the shell compared to the He core, which allows an efficient activation of 22 Ne.˛; n/ in the 15 Mˇ models. Additionally the He shell is not limited by the diminished iron seeds consumed by s-process in He core but occurs in a region still containing its initial iron content. In Fig. 22, the dependence of total 88 Sr yields on the mass and metallicity are displayed for rotating stars with standard rotation rate (\ini =\crit D 0:4) (right) and for nonrotating stars (left). The red circles display the location of the models computed in the mass-metallicity space. The values in between the data points are interpolated linearly in log.m/. This plot for the neutron-magic isotope 88 Sr shows the dependence of the Sr-peak production on rotation (86 Sr, 87 Sr, 89 Y, and 90 Zr show the same trends as 88 Sr). Several differences between the standard and rotation boosted s-process can be seen:

0.0

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Fig. 22 s-process yields, m, of 88 Sr in Mˇ to illustrate the mass and metallicity dependence of the s-process, without rotation (left) and with rotation (right). The red circles display the location of the models computed in the mass-metallicity space. The values in between the data points are interpolated linearly in log.m/

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1. Rotating models clearly produce more s-process elements at all metallicities. 2. Whereas the s-process production in nonrotating model decreases steeply with metallicity (dependence steeper than linear, e.g., Pignatari and Gallino 2008), the 68 Zn yields (discussed above as a typical weak s-process element) of rotating stars show a secondary-like behavior, going from reddish to blueish colors toward lower Z. While the 68 Zn yields of nonrotating stars drop by five orders of magnitude when the metallicity goes down by a factor 103 , the yields from rotating stars drop only by a factor 103 . The scaling with metallicity is less steep for rotating models (see Fig. 13 in Frischknecht et al. 2016). 3. Furthermore, the Sr-peak isotopes do not show a secondary behavior for stars with rotation and M > 15 Mˇ in the metallicity range between solar (log.Z=Zˇ / D 0) and about one hundredth (Z D 1:4104 , log.Z=Zˇ / D 2) of solar metallicity, but they eject maximal absolute yields around one tenth of solar metallicity (dark red around log.Z=Zˇ / D 1) for 20 to 30 Mˇ stars. Galactic chemical evolution (GCE) models using the larger grid of models were presented in Cescutti et al. (2013, 2015) (with some modifications explained in these papers) and showed that rotation-induced mixing is able to explain the large scatter for [Sr/Ba] observed in extremely metal poor stars. Furthermore, observations of large s-process enhancements in one of the oldest globular clusters in the bulge of our galaxy support the view that massive stars could indeed be also important sources for these elements (Chiappini et al. 2011). The observations by Barbuy et al. (2009) and Chiappini et al. (2011) were later updated by Barbuy et al. (2014) and Ness et al. (2014). In particular, Barbuy et al. (2014) confirmed that at least part of the stars in the globular cluster NGC 6522 are compatible with the s-process production in fast-rotating massive stars at low metallicity.

7

Conclusions

In this chapter, we reviewed the stellar structure equations and pre-supernova evolution of massive stars with a particular emphasis on the effects of rotation and mass loss and the transition between intermediate-mass and massive stars. We then presented the stellar wind contribution to nucleosynthesis and the production of weak s-process at various metallicities. Rotation and mass loss both have a strong impact on the evolution and nucleosynthesis in massive stars. There are broadly two mass ranges, where either rotation-induced mixing dominates for M < 30Mˇ or mass loss dominates for M > 30Mˇ over the other process (see Meynet and Maeder 2003,for more details). Rotation affects the mass limits for the presence of convection during central carbon burning, for iron core collapse supernovae, and for black hole formation. The effects of rotation on pre-supernova models are most spectacular for stars between 15 and 25 Mˇ . Indeed, rotation changes the supernova type (IIb or Ib instead of II), the total size of progenitors (blue instead of red supergiant), and the core sizes by a factor  1:5 (bigger in rotating models). For Wolf–Rayet stars (M > 30Mˇ ) even if the pre-supernova models are

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not different between rotating and nonrotating models, their previous evolution is different (Meynet and Maeder 2003). The very strong radiation field of massive stars leads to strong mass loss. Thus massive stars near solar metallicity lose a large fraction of their initial mass, more than half their initial mass for stars more massive than 20 Mˇ . Most of the mass loss takes place during hydrogen- and helium-burning phases. This implies that the stellar wind contribution to nucleosynthesis consists mostly of hydrogen-burning products and to a smaller extent helium-burning products, i.e., elements up to aluminum. Observations from the Integral gamma-ray satellite (Diehl et al. 2006) confirm that massive stars in our galaxy produce significant amounts of 26 Al, a radioactive element with half-life of  7:2  105 years and emitting photons at 1808.65 keV. Rotating models have larger stellar wind contribution to yields than the nonrotating ones because of the extra mass loss and mixing due to rotation. For the pre-SN yields and for masses below  30 Mˇ , rotating models have larger yields. The 12 C and 16 O yields are increased by a factor of 1.5–2.5 by rotation in the present calculation. When we add the two contributions, the yields of most heavy elements are larger for rotating models below  30 Mˇ . Rotation increases the total metallic yields by a factor of 1.5–2.5. As a rule of thumb, the yields (and evolution) of a rotating 20 Mˇ star are similar to the yields of a nonrotating 30 Mˇ star, at least for the light elements. When mass loss is dominant (above  30 Mˇ ) rotating and nonrotating models give similar yields for heavy elements. Only the yields of H-burning products are increased by rotation in the very massive star range. At low and very low Z, one expects mass loss and the production of secondary elements like 14 N to decrease and gradually become negligible. Rotation changes this picture. During the course of helium burning, rotation-induced mixing mixes 12 C and 16 O into the hydrogen-burning shell where the CNO cycles transform most of the C and O into 14 N leading to the production of large amounts of primary nitrogen. For the most massive models (M & 60 Mˇ ), primary production of CNO elements raises the overall metallicity of the surface drastically, and significant mass loss occurs during the red supergiant stage assuming that CNO elements are important contributors to mass loss. This mass loss is due to the surface enrichment in CNO elements via rotational and convective mixing. Current models predict the production of WR stars for an initial mass higher than 60 Mˇ even at Z D 108 . Therefore SNe of type Ib and Ic are predicted from single massive stars at these low metallicities. The stellar yields of rotating models were used in a galactic chemical evolution model and successfully reproduce the early evolution of CNO elements (Chiappini et al. 2006). Furthermore, fast-rotating massive stars are candidates to explain CEMP-no stars in the early universe (Maeder et al. 2015). (For further discussion of CEMP and CEMP-no stars see  Chap. 73, “Nucleosynthesis in Hypernovae Associated with Gamma Ray Bursts” by Ken’ichi Nomoto in this book.) The production of primary 14 N and also 22 Ne in rotating massive stars at low Z opens the door to produce s-process elements at low Z. Large grids of rotating massive star models were recently completed to determine the impact of rotation on

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slow neutron captures from solar down to very low metallicities (Frischknecht et al. 2016). The main results of these studies are the following: • Rotation not only enables the production of primary nitrogen but also of important quantities of primary 22 Ne at all metallicities. Whereas the neutron source for the s-process in non-rotating models is secondary, the neutron source is primary in rotating models. • At solar metallicity, rotation-induced mixing increases the weak s-process production but its impact is modest (within a factor of 2) and the production in rotating models stops at the strontium peak as in standard models. • As the metallicity decreases, the amount of iron seeds decreases, and the iron seeds are the main limitation to the production of heavier elements in rotating models, in which the neutron source is primary. The decreasing amount of seeds does not prevent the production of heavier elements though. On the other hand, the lack of seeds means that not only the seeds get depleted, but elements in the mass range A D 60–80 also get depleted as the production peak shifts to the strontium peak by Z D 103 and elements up to the barium peak are efficiently produced at that metallicity and very low metallicities. The final [Sr/Ba] ratio obtained in the models covers the range between roughly 0:5 and 2.1. • The strong dependence of production of the barium peak on metallicity and initial rotation rate means that rotating models provide a natural explanation for the observed scatter for the [Sr/Ba] ratio at the low metallicities. • The general decrease with metallicity of the [Sr/Ba] ratio in rotating models also matches the decreasing ratio observed in the small current sample of CEMP-no stars at extremely low [Fe/H]. • Although they are challenging to measure, isotopic ratios, for example, for magnesium isotopes, have a great potential for constraining stellar models. There are important uncertainties that affect the results presented in this chapter. On the nuclear side, the dominant uncertainties for the weak s-process are the exit channel ratios between n and  for alpha captures on 17 O and 22 Ne. The first ratio determines whether 16 O is a strong neutron poison or only a strong absorber, while the second determines the strength of the neutron source 22 Ne.˛; n/. 12 C.˛;  /16 O and its competition with triple-˛ and 22 Ne.˛;  / are key to determine the final abundance of carbon at the end of helium burning. This abundance is a key quantity that affects the evolution throughout the advanced phases. On the stellar side, the interplay of mean molecular weight and magnetic fields with rotation-induced instabilities and mixing is the main uncertainty. It is not fully clear yet whether magnetic fields would increase or decrease rotation-induced mixing (see Maeder and Meynet 2005; Meynet et al. 2013; Woosley and Heger 2006; Yoon and Langer 2005). The dependence of the mass loss rates on the metallicity, especially in the RSG stage, needs to be further studied to see how the results of van Loon et al. (2005,mass loss in the RSG phase independent of metallicity) can be extrapolated to very low metallicities. The reader is referred to the review by Langer (2012) concerning the evolution of binary stars. Finally,

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convective boundary mixing (CBM) is still uncertain, and many studies have focused on this uncertainty recently taking advantage of the significant increase in computing power. Important improvements are thus expected in the modelling of massive stars in the years ahead (see Arnett et al. 2015 for more details). Nevertheless, the results presented in this chapter show that a lot of progress has already been made in the modelling of the pre-supernova evolution of massive stars.

8

Cross-References

 Electron Capture Supernovae from Super Asymptotic Giant Branch Stars  Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Super-

nova Mechanism  Nucleosynthesis in Thermonuclear Supernovae  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Nucleosynthesis in Hypernovae Associated with Gamma Ray Bursts  Population Synthesis of Massive Close Binary Evolution  Supernovae from Massive Stars  Supernovae from Rotating Stars  Very Massive and Supermassive Stars: Evolution and Fate Acknowledgements The author thanks his collaborators at the University of Geneva (G. Meynet, A. Maeder, Sylvia Ekström, and C. Georgy), Basel (U. Frischknecht, F.-K. Thielemann, T. Rauscher), and Hull (M. Pignatari) for their significant contributions to the results presented in this chapter. R. Hirschi acknowledges support from the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and from the Eurogenesis EUROCORE program. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 306901. This article is based upon work from the “ChETEC” COST Action (CA16117), supported by COST (European Cooperation in Science and Technology).

References Arnett WD, Thielemann FK (1985) Hydrostatic nucleosynthesis. I – Core helium and carbon burning. Astrophys J 295:589–619 Arnett WD, Meakin C, Viallet M, Campbell SW, Lattanzio JC, Mocák M (2015) Beyond mixinglength theory: a step toward 321D. Astrophys J 809:30. doi:10.1088/0004-637X/809/1/30, 1503.00342 Baraffe I, Takahashi K (1993) Contribution to the heavy-element abundances in the Galactic halo from s-process nucleosynthesis in massive stars. Astron Astrophys 280:476–485 Baraffe I, El Eid MF, Prantzos N (1992) The s-process in massive stars of variable composition. Astron Astrophys 258:357–367 Barbuy B, Zoccali M, Ortolani S, Hill V, Minniti D, Bica E,Renzini A, Gómez A (2009) VLTFLAMES analysis of 8 giants in the bulge metal-poor globular cluster NGC 6522: oldest cluster in the Galaxy? Analysis of 8 giants in NGC 6522. Astron Astrophys 507:405–415. doi:10.1051/0004-6361/200912748, 0908.3603 Barbuy B, Chiappini C, Cantelli E, Depagne E, Pignatari M, Hirschi R, Cescutti G, Ortolani S, Hill V, Zoccali M, Minniti D, Trevisan M, Bica E, Gómez A (2014) High-resolution

1924

R. Hirschi

abundance analysis of red giants in the globular cluster NGC 6522. Astron Astrophys 570:A76. doi:10.1051/0004-6361/201424311, 1408.2438 Bennett ME, Hirschi R, Pignatari M, Diehl S, Fryer C, Herwig F, Hungerford A, Nomoto K, Rockefeller G, Timmes FX, Wiescher M (2012) The effect of 12 C C12 C rate uncertainties on the evolution and nucleosynthesis of massive stars. Mon Not R Astron Soc 420:3047–3070. doi:10.1111/j.1365-2966.2012.20193.x, 1201.1225 Brüggen M, Hillebrandt W (2001) Three-dimensional simulations of shear instabilities in magnetized flows. Mon Not R Astron Soc 323:56–66 Braithwaite J (2006) A differential rotation driven dynamo in a stably stratified star. Astron Astrophys 449:451–460. doi:10.1051/0004-6361:20054241, arXiv:astro-ph/0509693 Canuto VM (2002) Critical Richardson numbers and gravity waves. Astron Astrophys 384: 1119–1123 Cescutti G, Chiappini C, Hirschi R, Meynet G, Frischknecht U (2013) The s-process in the galactic halo: the fifth signature of spinstars in the early Universe? Astron Astrophys 553:A51 doi:10.1051/0004-6361/201220809, 1302.4354 Cescutti G, Romano D, Matteucci F, Chiappini C, Hirschi R (2015) The role of neutron star mergers in the chemical evolution of the galactic halo. ArXiv e-prints 1503.02954 Chaboyer B, Zahn JP (1992) Effect of horizontal turbulent diffusion on transport by meridional circulation. Astron Astrophys 253:173–177 Chiappini C, Hirschi R, Meynet G, Ekström S, Maeder A, Matteucci F (2006) A strong case for fast stellar rotation at very low metallicities. Astron Astrophys 449:L27–L30. doi:10.1051/0004-6361:20064866, astro-ph/0602459 Chiappini C, Frischknecht U, Meynet G, Hirschi R, Barbuy B, Pignatari M, Decressin T, Maeder A (2011) Imprints of fast-rotating massive stars in the galactic bulge. Nature 472:454–457. doi:10.1038/nature10000 Chieffi A, Limongi M (2004) Explosive yields of massive stars from Z D 0 to Z D Zˇ . Astrophys J 608:405–410. doi:10.1086/392523 Chieffi A, Limongi M (2013) Pre-supernova evolution of rotating solar metallicity stars in the mass range 13–120 Mˇ and their explosive yields. Astrophys J 764:21. doi:10.1088/0004-637X/764/1/21 Chieffi A, Limongi M, Straniero O (1998) The evolution of a 25 Mo star from the main sequence up to the onset of the iron core collapse. Astrophys J 502:737 Cristini A, Meakin C, Hirschi R, Arnett D, Georgy C, Viallet M (2017, submitted) 3D hydrodynamic simulations of the carbon shell in a massive star. MNRAS Crowther PA (2001) Stellar winds from massive stars. In: Vanbeveren D (ed) The influence of binaries on stellar population studies, astrophysics and space science library. vol 264. Springer, p 215. arXiv:astro-ph/0010581, ISBN:0792371046 Crowther PA, Schnurr O, Hirschi R, Yusof N, Parker RJ, Goodwin SP, Kassim HA (2010) The R136 star cluster hosts several stars whose individual masses greatly exceed the accepted 150Mo stellar mass limit. Mon Not R Astron Soc 408:731–751. doi:10.1111/j.1365-2966.2010.17167.x, 1007.3284 de Jager C, Nieuwenhuijzen H, van der Hucht KA (1988) Mass loss rates in the HertzsprungRussell diagram. Astron Astrophys Suppl 72:259–289 Diehl R, Halloin H, Kretschmer K, Lichti GG, Schönfelder V, Strong AW, von Kienlin A, Wang W, Jean P, Knödlseder J, Roques JP, Weidenspointner G, Schanne S, Hartmann DH, Winkler C, Wunderer C (2006) Radioactive 26 Al from massive stars in the galaxy. Nature 439:45–47. doi:10.1038/nature04364, astro-ph/0601015 Edelmann PVF, Roepke FK, Hirschi R, Georgy C, Jones S (2017, submitted) Testing a onedimensional prescription of dynamical shear mixing with a two-dimensional hydrodynamic simulation. Astron Astrophys Eggenberger P, Meynet G, Maeder A, Hirschi R, Charbonnel C, Talon S, Ekström S (2007) The Geneva stellar evolution code. Astrophys Space Sci 263. doi:10.1007/s10509-007-9511-y

72 Pre-supernova Evolution and Nucleosynthesis in Massive Stars and. . .

1925

Ekström S, Meynet G, Chiappini C, Hirschi R, Maeder A (2008, accepted) Effects of rotation on the evolution of primordial stars. Astron Astrophys 489:685–698. doi:10.1051/0004-6361:200809633, 0807.0573 Ekström S, Georgy C, Eggenberger P, Meynet G, Mowlavi N, Wyttenbach A, Granada A, Decressin T, Hirschi R, Frischknecht U, Charbonnel C, Maeder A (2012) Grids of stellar models with rotation. I. Models from 0.8 to 120 solar masses at solar metallicity (Z = 0.014). Astron Astrophys 537:A146. doi:10.1051/0004-6361/201117751, 1110.5049 El Eid MF, Meyer BS, The LS (2004) Evolution of massive stars up to the end of central oxygen burning. Astrophys J 611:452–465. doi:10.1086/422162, arXiv:astro-ph/0407459 Eldridge JJ, Vink JS (2006) Implications of the metallicity dependence of Wolf-Rayet winds. Astron Astrophys 452:295–301. doi:10.1051/0004-6361:20065001, arXiv:astro-ph/0603188 Ertl T, Janka H-T, Woosley SE, Sukhbold T, Ugliano M (2016) A two-parameter criterion for classifying the explodability of massive stars by the neutrino-driven mechanism. Astrophys J 818:124. doi:10.3847/0004-637X/818/2/124 Fricke K (1968) Instabilität stationärer rotation in sternen. Zeitschrift fur Astrophysics 68:317 Frischknecht U, Hirschi R, Meynet G, Ekström S, Georgy C, Rauscher T, Winteler C, Thielemann FK (2010) Constraints on rotational mixing from surface evolution of light elements in massive stars. Astron Astrophys 522:A39. doi:10.1051/0004-6361/201014340, 1007.1779 Frischknecht U, Hirschi R, Thielemann FK (2012) Non-standard s-process in low metallicity massive rotating stars. Astron Astrophys 538:L2. doi:10.1051/0004-6361/201117794, 1112.5548 Frischknecht U, Hirschi R, Pignatari M, Maeder A, Meynet G, Chiappini C, Thielemann FK, Rauscher T, Georgy C, Ekström S (2016) S-process production in rotating massive stars at solar and low metallicities. Mon Not R Astron Soc 456:1803–1825. doi:10.1093/mnras/stv2723, 1511.05730 Georgy C, Meynet G, Maeder A (2011) Effects of anisotropic winds on massive star evolution. Astron Astrophys 527:A52. doi:10.1051/0004-6361/200913797, 1011.6581 Georgy C, Ekström S, Meynet G, Massey P, Levesque EM, Hirschi R, Eggenberger P, Maeder A (2012) Grids of stellar models with rotation. II. WR populations and supernovae/GRB progenitors at Z = 0.014. Astron Astrophys 542:A29. doi:10.1051/0004-6361/201118340, 1203.5243 Goldreich P, Schubert G (1967) Differential rotation in stars. Astrophys J 150:571 Gräfener G, Hamann WR (2008) Mass loss from late-type WN stars and its Z-dependence. Very massive stars approaching the Eddington limit. Astron Astrophys 482:945–960. doi:10.1051/0004-6361:20066176, 0803.0866 Heger A, Langer N (2000) Presupernova evolution of rotating massive stars. II. Evolution of the surface properties. Astrophys J 544:1016–1035. doi:10.1086/317239, arXiv:astro-ph/0005110 Heger A, Woosley SE (2010) Nucleosynthesis and evolution of massive metal-free stars. Astrophys J 724:341–373. doi:10.1088/0004-637X/724/1/341, 0803.3161 Heger A, Langer N, Woosley SE (2000) Presupernova evolution of rotating massive stars. I. Numerical method and evolution of the internal stellar structure. Astrophys J 528:368–396 Heger A, Fryer CL, Woosley SE, Langer N, Hartmann DH (2003) How massive single stars end their life. Astrophys J 591:288–300 Heger A, Woosley SE, Spruit HC (2005) Presupernova evolution of differentially rotating massive stars including magnetic fields. Astrophys J 626:350–363 Hirschi R (2004) Massive rotating stars: the road to supernova explosion. PhD Thesis. http://quasar. physik.unibas.ch/~hirschi/workd/thesis.pdf Hirschi R (2007) Very low-metallicity massive stars: pre-SN evolution models and primary nitrogen production. Astron Astrophys 461:571–583. doi:10.1051/0004-6361:20065356, arXiv:astro-ph/0608170 Hirschi R, Maeder A (2010) The GSF instability and turbulence do not account for the relatively low rotation rate of pulsars. Astron Astrophys 519:A16. doi:10.1051/0004-6361/201014222, 1004.5470

1926

R. Hirschi

Hirschi R, Meynet G, Maeder A (2004) Stellar evolution with rotation. XII. Pre-supernova models. Astron Astrophys 425:649–670 Hirschi R, Meynet G, Maeder A (2005) Yields of rotating stars at solar metallicity. Astron Astrophys 433:1013–1022. doi:10.1051/0004-6361:20041554, astro-ph/0412454 Hirschi R, Frischknecht U, Thielemann F, Pignatari M, Chiappini C, Ekström S, Meynet G, Maeder A (2008) Stellar evolution in the early universe. In: Hunt LK, Madden S, Schneider R (eds) IAU Symposium, vol 255, pp 297–304. doi:10.1017/S1743921308024976 Imbriani G, Limongi M, Gialanella L, Terrasi F, Straniero O, Chieffi A (2001) The 12 C.˛; /16 O Reaction rate and the evolution of stars in the mass range 0:8 D M =Mˇ 25. Astrophys J 558:903–915. doi:10.1086/322288, arXiv:astro-ph/0107172 Jones S, Hirschi R, Nomoto K, Fischer T, Timmes FX, Herwig F, Paxton B, Toki H, Suzuki T, Martínez-Pinedo G, Lam YH, Bertolli MG (2013) Advanced burning stages and fate of 8-10 M stars. Astrophys J 772:150. doi:10.1088/0004-637X/772/2/150, 1306.2030 Käppeler F, Gallino R, Bisterzo S, Aoki W (2011) The s process: nuclear physics, stellar models, and observations. Rev Mod Phys 83:157–194. doi:10.1103/RevModPhys.83.157, 1012.5218 Kippenhahn R, Weigert A (1990) Stellar structure and evolution. Springer, New York Kippenhahn R, Weigert A, Hofmeister E (1967) Methods for calculating stellar evolution. In: Alder B, Fernbach S, Rotenberg M (eds) Methods in computational physics, vol 7. Academic Press, New York/London Knobloch E, Spruit HC (1983) The molecular weight barrier and angular momentum transport in radiative stellar interiors. Astron Astrophys 125:59–68 Krtiˇcka J, Owocki SP, Meynet G (2011) Mass and angular momentum loss via decretion disks. Astron Astrophys 527:A84. doi:10.1051/0004-6361/201015951, 1101.1732 Langer N (2012) Presupernova evolution of massive single and binary stars. Annu Rev Astron Astrophys 50:107–164. doi:10.1146/annurev-astro-081811-125534, 1206.5443 Langer N, Arcoragi JP, Arnould M (1989) Neutron capture nucleosynthesis and the evolution of 15 and 30 solar-mass stars. I. The core helium burning phase. Astron Astrophys 210: 187–197 Limongi M, Straniero O, Chieffi A (2000) Massive stars in the range 13–25 solar masses: evolution and nucleosynthesis. II. The solar metallicity models. Astrophys J Suppl Ser 129:625–664 Maeder A (1992) Stellar yields as a function of initial metallicity and mass limit for black hole formation. Astron Astrophys 264:105–120 Maeder A (1997) Stellar evolution with rotation. II. A new approach for shear mixing. Astron Astrophys 321:134–144 Maeder A (2003) Stellar rotation: evidence for a large horizontal turbulence and its effects on evolution. Astron Astrophys 399:263–269 Maeder A (2009) Physics, formation and evolution of rotating stars. Springer, Berlin/Heidelberg. doi:10.1007/978-3-540-76949-1 Maeder A, Meynet G (2000) Stellar evolution with rotation. VI. The Eddington and Omega-limits, the rotational mass loss for OB and LBV stars. Astron Astrophys 361:159–166 Maeder A, Meynet G (2001) Stellar evolution with rotation. VII. Low metallicity models and the blue to red supergiant ratio in the SMC. Astron Astrophys 373:555–571 Maeder A, Meynet G (2005) Stellar evolution with rotation and magnetic fields. III. The interplay of circulation and dynamo. Astron Astrophys 440:1041–1049. doi:10.1051/0004-6361:20053261 Maeder A, Meynet G (2012) Rotating massive stars: from first stars to gamma ray bursts. Rev Mod Phys 84:25–63. doi:10.1103/RevModPhys.84.25 Maeder A, Zahn J (1998) Stellar evolution with rotation. III. Meridional circulation with MUgradients and non-stationarity. Astron Astrophys 334:1000–1006 Maeder A, Meynet G, Chiappini C (2015) The first stars: CEMP-no stars and signatures of spinstars. Astron Astrophys 576:A56. doi:10.1051/0004-6361/201424153, 1412.5754 Meynet G, Maeder A (1997) Stellar evolution with rotation. I. The computational method and the inhibiting effect of the fmug-gradient. Astron Astrophys 321:465–476

72 Pre-supernova Evolution and Nucleosynthesis in Massive Stars and. . .

1927

Meynet G, Maeder A (2002a) Stellar evolution with rotation. VIII. Models at Z = 105 and CNO yields for early galactic evolution. Astron Astrophys 390:561–583 Meynet G, Maeder A (2002b) The origin of primary nitrogen in galaxies. Astron Astrophys 381:L25–L28. doi:10.1051/0004-6361:20011554, astro-ph/0111187 Meynet G, Maeder A (2003) Stellar evolution with rotation. X. Wolf-Rayet star populations at solar metallicity. Astron Astrophys 404:975–990 Meynet G, Maeder A (2005) Stellar evolution with rotation. XI. Wolf-Rayet star populations at different metallicities. Astron Astrophys 429:581–598 Meynet G, Maeder A, Schaller G, Schaerer D, Charbonnel C (1994) Grids of massive stars with high mass loss rates. V. From 12 to 120 Mˇ at Z D 0:001, 0.004, 0.008, 0.020 and 0.040. Astron Astrophys Suppl 103:97–105 Meynet G, Ekström S, Maeder A (2006) The early star generations: the dominant effect of rotation on the CNO yields. Astron Astrophys 447:623–639. doi:10.1051/0004-6361:20053070 Meynet G, Ekstrom S, Maeder A, Eggenberger P, Saio H, Chomienne V, Haemmerlé L (2013) Models of rotating massive stars: impacts of various prescriptions. In: Goupil M, Belkacem K, Neiner C, Lignières F, Green JJ (eds) Lecture notes in physics, vol 865. Springer, Berlin, pp 3–642, 1301.2487 Muijres LE, de Koter A, Vink JS, Krtiˇcka J, Kubát J, Langer N (2011) Predictions of the effect of clumping on the wind properties of O-type stars. Astron Astrophys 526:A32. doi:10.1051/0004-6361/201014290 Ness M, Asplund M, Casey AR (2014) NGC 6522: a typical globular cluster in the galactic bulge without signatures of rapidly rotating population III stars. Mon Not R Astron Soc 445:2994– 2998. doi:10.1093/mnras/stu2144, 1408.0290 Nishimura N, Hirschi R, Pignatari M, Herwig F, Beard M, Imbriani G, Görres J, deBoer RJ, Wiescher M (2014) Impact of the uncertainty in ˛-captures on 22 Ne on the weak s-process in massive stars. In: Jeong S, Imai N, Miyatake H, Kajino T (eds) American institute of physics conference series, vol 1594, pp 146–151. doi:10.1063/1.4874059 Nomoto K (1984) Evolution of 8-10 solar mass stars toward electron capture supernovae. I. Formation of electron-degenerate O + NE + MG cores. Astrophys J 277:791–805. doi:10.1086/161749 Nomoto K (1987) Evolution of 8-10 solar mass stars toward electron capture supernovae. II. Collapse of an O + NE + MG core. Astrophys J 322:206–214. doi:10.1086/165716 Nugis T, Lamers HJGLM (2000) Mass-loss rates of Wolf-Rayet stars as a function of stellar parameters. Astron Astrophys 360:227–244 O’Connor E, Ott CD (2011) Black hole formation in failing core-collapse supernovae. Astrophys J 730:70. doi:10.1088/0004-637X/730/2/70, 1010.5550 Paxton B, Bildsten L, Dotter A, Herwig F, Lesaffre P, Timmes F (2011) Modules for experiments in stellar astrophysics (MESA). Astrophys J Suppl Ser 192:3. doi:10.1088/0067-0049/192/1/3, 1009.1622 Pignatari M, Gallino R (2008) The weak s-process at low metallicity. In: O’Shea BW, Heger A (eds) First stars III, american institute of physics conference series, vol 990, pp 336–338. doi:10.1063/1.2905575 Pignatari M, Gallino R, Meynet G, Hirschi R, Herwig F, Wiescher M (2008) The s-process in massive stars at low metallicity: the effect of primary 14 N from fast rotating stars. Astrophys J Lett 687:L95–L98. doi:10.1086/593350, 0810.0182 Pignatari M, Gallino R, Heil M, Wiescher M, Käppeler F, Herwig F, Bisterzo S (2010) The weak s-process in massive stars and its dependence on the neutron capture cross sections. Astrophys J 710:1557–1577. doi:10.1088/0004-637X/710/2/1557 Pignatari M, Hirschi R, Wiescher M, Gallino R, Bennett M, Beard M, Fryer C, Herwig F, Rockefeller G, Timmes FX (2013) The 12 C C12 C Reaction and the impact on nucleosynthesis in massive stars. Astrophys J 762:31. doi:10.1088/0004-637X/762/1/31, 1212.3962 Poelarends AJT, Herwig F, Langer N, Heger A (2008) The supernova channel of super-AGB stars. Astrophys J 675:614–625. doi:10.1086/520872, 0705.4643 Potter AT, Chitre SM, Tout CA (2012) Stellar evolution of massive stars with a radiative ˛-˝ dynamo. Mon Not R Astron Soc 424:2358–2370. 1205.6477

1928

R. Hirschi

Prantzos N, Hashimoto M, Nomoto K (1990) The s-process in massive stars – yields as a function of stellar mass and metallicity. Astron Astrophys 234:211–229 Pumo ML, Contino G, Bonanno A, Zappalà RA (2010) Convective overshooting and production of s-nuclei in massive stars during their core He-burning phase. Astron Astrophys 524:A45. doi:10.1051/0004-6361/201015518, 1009.5333 Raiteri CM, Busso M, Picchio G, Gallino R (1991) S-process nucleosynthesis in massive stars and the weak component. II. Carbon burning and galactic enrichment. Astrophys J 371:665–672. doi:10.1086/169932 Raiteri CM, Gallino R, Busso M (1992) S-processing in massive stars as a function of metallicity and interpretation of observational trends. Astrophys J 387:263–275. doi:10.1086/171078 Rauscher T, Heger A, Hoffman RD, Woosley SE (2002) Nucleosynthesis in massive stars with improved nuclear and stellar physics. Astrophys J 576:323–348 Rayet M, Hashimoto M (2000) The s-process efficiency in massive stars. Astron Astrophys 354:740–748 Ritossa C, García-Berro E, Iben I Jr (1999) On the evolution of stars that form electron-degenerate cores processed by carbon burning. V. Shell convection sustained by helium burning, transient neon burning, dredge-out, URCA cooling, and other properties of an 11 M_solar population I model star. Astrophys J 515:381–397. doi:10.1086/307017 Smartt SJ (2009) Progenitors of core-collapse supernovae. Annu Rev Astron Astrophys 47:63–106. doi:10.1146/annurev-astro-082708-101737, 0908.0700 Spruit HC (2002) Dynamo action by differential rotation in a stably stratified stellar interior. Astron Astrophys 381:923–932 Sukhbold T, Woosley SE (2014) The compactness of presupernova stellar cores. Astrophys J 783:10. doi:10.1088/0004-637X/783/1/10, 1311.6546 Sylvester RJ, Skinner CJ, Barlow MJ (1998) Silicate and hydrocarbon emission from galactic M supergiants. Mon Not R Astron Soc 301:1083–1094. doi:10.1046/j.1365-8711.1998.02078.x Takahashi K, Yoshida T, Umeda H (2013) Evolution of progenitors for electron capture supernovae. Astrophys J 771:28. doi:10.1088/0004-637X/771/1/28, 1302.6402 The LS, El Eid MF, Meyer BS (2000) A new study of s-process nucleosynthesis in massive stars. Astrophys J 533:998–1015. doi:10.1086/308677 The LS, El Eid MF, Meyer BS (2007) s-process nucleosynthesis in advanced burning phases of massive stars. Astrophys J 655:1058–1078. doi:10.1086/509753, arXiv:astro-ph/0609788 Thielemann FK, Arnett WD (1985) Hydrostatic nucleosynthesis – part two – core neon to silicon burning and presupernova abundance yields of massive stars. Astrophys J 295:604 Travaglio C, Gallino R, Arnone E, Cowan J, Jordan F, Sneden C (2004) Galactic evolution of Sr, Y, and Zr: a multiplicity of nucleosynthetic processes. Astrophys J 601:864–884. doi:10.1086/380507, arXiv:astro-ph/0310189 Tur C, Heger A, Austin SM (2009) Dependence of s-process nucleosynthesis in massive stars on triple-alpha and 12 C.˛; /16 O reaction rate uncertainties. Astrophys J 702:1068–1077. doi:10.1088/0004-637X/702/2/1068, 0809.0291 Umeda H, Nomoto K (2005) Variations in the abundance pattern of extremely metal-poor stars and nucleosynthesis in population III supernovae. Astrophys J 619:427–445. doi:10.1086/426097 van Loon JT, Groenewegen MAT, de Koter A, Trams NR, Waters LBFM, Zijlstra AA, Whitelock PA, Loup C (1999) Mass-loss rates and luminosity functions of dust-enshrouded AGB stars and red supergiants in the LMC. Astron Astrophys 351:559–572, arXiv:astro-ph/9909416 van Loon JT, Cioni MRL, Zijlstra AA, Loup C (2005) An empirical formula for the mass-loss rates of dust-enshrouded red supergiants and oxygen-rich asymptotic giant branch stars. Astron Astrophys 438:273–289. doi:10.1051/0004-6361:20042555, arXiv:astro-ph/0504379 Vink JS, de Koter A, Lamers HJGLM (2001) Mass-loss predictions for O and B stars as a function of metallicity. Astron Astrophys 369:574–588. doi:10.1051/0004-6361:20010127 Vink JS, Gräfener G, Harries TJ (2011) In pursuit of gamma-ray burst progenitors: the identification of a sub-population of rotating Wolf-Rayet stars. Astron Astrophys 536:L10. doi:10.1051/0004-6361/201118197, 1111.5806

72 Pre-supernova Evolution and Nucleosynthesis in Massive Stars and. . .

1929

von Zeipel H (1924) The radiative equilibrium of a rotating system of gaseous masses. Mon Not R Astron Soc 84:665 Walder R, Folini D, Meynet G (2011) Magnetic fields in massive stars, their winds, and their nebulae. Space Sci Rev 125. doi:10.1007/s11214-011-9771-2, 1103.3777 Wiescher M, Käppeler F, Langanke K (2012) Critical reactions in contemporary nuclear astrophysics. Annu Rev Astron Astrophys 50:165–210. doi:10.1146/annurev-astro-081811-125543 Woosley SE, Heger A (2006) The progenitor stars of gamma-ray bursts. Astrophys J 637:914–921. doi:10.1086/498500 Woosley SE, Heger A (2015) The remarkable deaths of 9-11 solar mass stars. Astrophys J 810:34. doi:10.1088/0004-637X/810/1/34, 1505.06712 Yoon SC, Langer N (2005) Evolution of rapidly rotating metal-poor massive stars towards gammaray bursts. Astron Astrophys 443:643–648. doi:10.1051/0004-6361:20054030 Yoon SC, Langer N, Norman C (2006) Single star progenitors of long gamma-ray bursts. I. Model grids and redshift dependent GRB rate. Astron Astrophys 460:199–208. doi:10.1051/0004-6361:20065912, arXiv:astro-ph/0606637 Yusof N, Hirschi R, Meynet G, Crowther PA, Ekström S, Frischknecht U, Georgy C, Abu Kassim H, Schnurr O (2013) Evolution and fate of very massive stars. Mon Not R Astron Soc 433:1114– 1132. doi:10.1093/mnras/stt794, 1305.2099 Zahn J, Brun AS, Mathis S (2007) On magnetic instabilities and dynamo action in stellar radiation zones. Astron Astrophys 474:145–154. doi:10.1051/0004-6361:20077653, 0707.3287 Zahn JP (1992) Circulation and turbulence in rotating stars. Astron Astrophys 265:115–132

Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

73

Ken’ichi Nomoto

Abstract

We present nucleosynthesis in very energetic hypernovae, whose kinetic energy (KE) is more than 10 times the KE of normal core-collapse supernovae (SNe). The light curve and spectra fitting of individual SN are used to estimate the mass of the progenitor, explosion energy, and produced 56 Ni mass. Comparison with the abundance patterns of extremely metal-poor (EMP) stars has made it possible to determine the model parameters of core-collapse SNe. Nucleosynthesis in hypernovae is characterized by larger abundance ratios (Zn, Co, V, Ti)/Fe and smaller (Mn, Cr)/Fe than normal SNe, which can explain the observed trends of these ratios in EMP stars. Hypernovae are also jet-induced explosions, so that their nucleosynthesis yields can well reproduce the large C/Fe ratio observed in carbon-enhanced metal-poor (CEMP) stars if a small fraction of Fe-peak elements is mixed into the C-rich ejecta in the form of a jet while the bulk of Fe undergoes fallback from equatorial direction (faint supernovae/hypernovae).

Contents 1 2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supernova-Gamma-Ray Burst Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 GRB-Supernova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Non-GRB Hypernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 XRF–Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Non-SN Gamma-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Progenitors of Supernovae and Hypernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nucleosynthesis in Hypernovae and Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Iron-Peak Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Abundance Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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K. Nomoto () Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_86

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4

Abundance Patterns of Extremely Metal-Poor (EMP) Stars and Hypernovae . . . . . . . . 4.1 Very Metal-Poor (VMP) Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Extremely Metal-Poor (EMP) Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Carbon-Enhanced Metal-Poor (CEMP) Stars and Mixing Fallback . . . . . . . . . . 5 Nucleosynthesis in Jet-Induced Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Faint Supernovae and Non-SN GRBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 CEMP Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Cross-Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1945 1945 1946 1948 1949 1950 1951 1951 1952 1952

Introduction

Massive stars in the range of 8 to  130Mˇ undergo core-collapse at the end of their evolution and become Type II and Ib/c supernovae (SNe) unless the entire star collapses into a black hole with no mass ejection (Arnett 1996). The explosion energies of core-collapse supernovae are fundamentally important quantities, and an estimate of E  1  1051 ergs has often been used in calculating nucleosynthesis and the impact on the interstellar medium. (In the present chapter, we use the explosion energy E for the final kinetic energy (KE) of explosion, and E51 D E=1051 erg.) A good example is SN 1987A in the Large Magellanic Cloud, whose energy is estimated to be E51 D 1:0–1:5 from its early light curve (Arnett 1996; Nomoto et al. 1994b). An interesting development regarding the diversity among Type Ib/c supernovae (SNe Ibc) is the discovery of the SN Ic-gamma-ray burst (GRB) connection, for example, SN 1998bw-GRB 980425 (Galama et al. 1998). Moreover, these GRBSNe Ic are very energetic. The KE of SN 1998bw is estimated to exceed 1052 erg, about 10 times the KE of normal core-collapse SNe (Iwamoto et al. 1998). In the present chapter, we use the term “hypernova (HN)” to describe such a hyperenergetic supernova with E & 1052 ergs. Following SN 1998bw, other “hypernovae” of Type Ic have been discovered (Nomoto et al. 2004). Even more extreme SNe Ic, superluminous supernovae (SLSNe) of Type I have been discovered (Gal-Yam 2012; Quimby 2012), which are more than five times brighter than SNe Ia. Although the power of superluminosity is not clear, they belong to “stripped-envelope” SNe. The opposite extreme SNe Ibc are the faint SNe and fast-decline transients, which could belong to the core-collapse SNe (Kawabata et al. 2010). Nucleosynthesis features in such hyperenergetic (and hyperaspherical) supernovae must show some important differences from normal supernova explosions. This might be related to the unpredicted abundance patterns observed in the extremely metal-poor (EMP) halo stars (Beers and Christlieb 2005; Hill et al. 2005). This approach leads to identifying the first stars in the universe, that is, metal-free, Population III (Pop III) stars born in a primordial hydrogen-helium gas cloud. This is one of the important challenges of current astronomy. We summarize here the nucleosynthesis yields for various stellar masses, explosion energies, and metallicities (Nomoto et al. 2006, 2013). From the light

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

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curve and spectra fitting of individual supernova, the relations between the mass of the progenitor, explosion energy, and produced 56 Ni mass have been estimated. We should note that the current approach is just the first step to the full understanding of these complex events and that the model parameters obtained here are still very preliminary, especially because of our still poor understanding of the exact mechanisms of core-collapse supernovae and gamma-ray bursts. Further deeper work is certainly necessary as partially seen in the Cross-References section at the end of the chapter.

2

Supernova-Gamma-Ray Burst Connection

GRBs at sufficiently close distances (z < 0:2) have been found to be accompanied by luminous core-collapse SNe Ic (GRB 980425/SN 1998bw (Galama et al. 1998); GRB 030329/ SN 2003dh (Hjorth et al. 2003; Stanek 2003); GRB 031203/SN 2003lw (Malesani et al. 2006)). Such a GRB-SN connection now reveals quite a large diversity as follows. (1) GRB-SNe: The three SNe Ic associated with the above GRBs have similar properties; showing broader lines than normal SNe Ic (Fig. 1: so-called broadlined SNe). These three GRB-SNe have all been found to be hypernovae (HNe) (Iwamoto et al. 1998; Nomoto et al. 2004). (2) Non-GRB HNe/SNe: These SNe show broad line features but are not associated with GRBs (SN 1997ef (Iwamoto et al. 2000); SN 2002ap (Mazzali et al. 2002); SN 2003jd (Mazzali et al. 2005)). These are either less energetic than GRB-SNe or observed off-axis. (3) XRF-SNe: X-Ray Flash (XRF) 060218 has been found to be connected to SN Ic 2006aj (Campana et al. 2006; Pian et al. 2006; Soderberg et al. 2006). The progenitor’s mass is estimated to be small enough to form a “neutron starmaking SN” (Mazzali et al. 2006). (4) Non-SN GRBs: In GRB 060605 and 060614, no SN feature was observed in the late light curve despite their distances being close enough to detect an SN 1998bw-like HN (Della Valle et al. 2006; Fynbo et al. 2006; Gal-Yam et al. 2006; Gehrels et al. 2006).

2.1

GRB-Supernova

Figure 1 compares the spectra of GRB-HNe (SN 1998bw), non-GRB SN, XRFSNe, and normal SN Ic. The spectrum of SN 1998bw has very broad lines. The strongest absorptions are Ti II-Fe II (short of 4000 Å, Fe II-Fe III (near 4500 Å), Si II (near 5700 Å), and O I-Ca II (between 7000 and 8000 Å). The spectroscopic modelings are combined with light curve (LC) modeling to give estimates of the mass of the ejecta Mej and E. The peak width of the LC, peak ,

1934

K. Nomoto 8.0

7.0

Relative flux + const

6.0

5.0

SN 2006aj t=14 days

SN 1998bw t∼16 days

4.0

3.0 SN 2002ap t∼13 days

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1.0 SN 1994I t∼13 days

0 4000

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6000 7000 8000 Rest Wavelength

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SN 2006aj SN 1998bw SN 2003dh SN 2003lw SN 2002ap SN 1994I

-18 Bolometric Magnitude

9000

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-16

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-14 0

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Days since GRB/XRF explosion

Fig. 1 (Top): The spectra of three hypernovae and one normal SN a few days before maximum. SN 1998bw/GRB 980425 represents the GRB-SNe. SN 2002ap is a non-GRB hypernova. SN 2006aj is associated with XRF 060218, being similar to SN 2002ap. SN 1994I represents normal SNe. (Bottom): The bolometric light curves of GRB-SN (SNe 1998bw, 2003dh), non-GRBSN (2002ap), XRF-SN (2006aj), and normal SNe Ic (1994I) are compared

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reflects the timescales of dynamical expansion dyn and for optical photons to diffuse diff , thus related to Mej and E as follows. peak 

 p 3=4 diff  dyn  . /1=2 Mej E 1=4 ; c

(1)

where  is the opacity. For larger Mej and smaller E, the LC peaks later and the LC width becomes broader because it is more difficult for photons to escape. In addition, the large E=Mej is required to reproduce the broad spectral features. From these synthetic spectra and light curves, SN 1998bw was interpreted as the explosion of a massive star, with E51  30 and Mej  10 Mˇ (Iwamoto et al. 1998). SN 1998bw is also as luminous at peak as a SN Ia. Such a high luminosity of SN 1998bw indicates that a large amount of 56 Ni (0:5 Mˇ ) was synthesized in the explosion, which is 7 times larger than typical SNe Ic (M .56 Ni/  0:07 Mˇ (Nomoto et al. 1994a)). The other two GRB-SNe, 2003dh and 2003lw, are also characterized by very broad line features and very high luminosity. Mej and E are estimated from synthetic spectra and light curves and summarized in Fig. 2 (top). It is clearly seen that GRBSNe are explosions of massive progenitor stars (with the main sequence mass of Mms  35–50 Mˇ ), have large explosion kinetic energies (E51  30–50), and synthesized large amounts of 56 Ni ( 0:3–0:5 Mˇ ). These GRB-associated HNe (GRB-HNe) are suggested to be the outcome of a very energetic black hole (BH) forming explosions of massive stars (Iwamoto et al. 1998).

2.2

Non-GRB Hypernovae

These HNe show spectral features similar to those of GRB-SNe but are not known to have been accompanied by a GRB. The estimated Mej and E, obtained from synthetic light curves and spectra, show that there is a tendency for non-GRB HNe to have smaller Mej and E, and lower luminosities as summarized in Fig. 2. SN 1997ef is found to be in the HN class of energetic explosions, although E=Mej is a factor of 3 smaller than GRB-SNe. It is not clear whether SN 1997ef was not associated with a GRB because of this smaller E=Mej or whether it was actually associated with the candidate GRB 971115. SN 2002ap was not associated with a GRB and no radio has been observed. It has similar spectral features, but narrower and redder (Fig. 1), and was modeled as a smaller energy explosion, with E51  4 and Mej  3 Mˇ (Mazzali et al. 2002). The early time spectrum of SN 2003jd is similar to SN 2002ap. Interestingly, its nebular spectrum shows a double peak in O-emission lines (Mazzali et al. 2005).

1936

K. Nomoto

Kinetic Energy (1051 ergs)

100 98bw

03dh

03Iw 97ef

10 02ap 06aj 05bf

93J

1

87A

94I

99br 97D

0.1 10

15

25

30

35

40

45

50

Main Sequence Mass (M . )

1 06aj

Ejected 56Ni mass (M . )

20

05bf

03dh 98bw

0.1 93J

03Iw

97ef 94I 87A

02ap

0.01 97D

99br

0.001 10

15

20 25 30 35 40 Main Sequence Mass (M . )

45

50

Fig. 2 The kinetic explosion energy E (top) and the ejected 56 Ni mass (bottom) as a function of the main-sequence mass of the progenitors for several supernovae/hypernovae (Nomoto et al. 1993, 2003, 2006). SNe that are observed to show broad-line features are indicated. Hypernovae are the SNe with E51 > 10

This has exactly confirmed the theoretical prediction by the asymmetric explosion model (Maeda et al. 2002). In this case, the orientation effect might cause the nondetection of a GRB.

2.3

XRF–Supernovae

The discovery of XRF 060218/SN 2006aj and their properties extends the GRBHN connection to XRFs and to the HN progenitor mass as low as 20 Mˇ . The XRF 060218 may be driven by a neutron star rather than a black hole. GRB 060218 is the second closest event ever (140 Mpc). The GRB was weak (Campana et al. 2006) and classified as X-Ray Flash (XRF) because of its soft spectrum. The presence of SN 2006aj was soon confirmed (Modjaz 2006). Here we summarize the properties of SN 2006aj by comparison with other SNe Ic.

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

1937

SN 2006aj has several features that make it unique. It is less bright than the other GRB/SNe (Fig. 1). Its rapid photometric evolution is very similar to that of a dimmer, nonGRB SN 2002ap (Mazzali et al. 2002), but it is somewhat faster. Although its spectrum is characterized by broader absorption lines as in SN 1998bw and other GRB/SN, they are not as broad as those of SN 1998bw, and it is much more similar to that of SN 2002ap (Fig. 1). The most interesting property of SN 2006aj is surprisingly weak oxygen lines, much weaker than in Type Ic SNe. Modeling the spectra and the light curve of SN 2006aj leads to Mej  2 Mˇ and E51  2. Lack of oxygen in the spectra indicates 1:3 Mˇ of O, and oxygen is still the dominant element. The theoretical light curve is in good agreement with observations for a total 56 Ni mass of 0:21 Mˇ in which 0:02 Mˇ is located above 20,000 km s1 (Fig. 1). The properties of SN 2006aj (smaller E and smaller Mej ) suggest that SN 2006aj is not the same type of event as the other GRB-SNe. One possibility is that the initial mass of the progenitor star is much smaller than the other GRB-SNe, so that the collapse/explosion generated less energy. If Mms is  20–25 Mˇ , the star would be at the boundary between collapse to a black hole or to a neutron star. In this mass range, there are indications of a spread in both E and the mass of 56 Ni synthesized (Hamuy 2003). The fact that a relatively large amount of 56 Ni is required in SN 2006aj possibly suggests that the star collapsed only to a neutron star because more core material would be available to synthesize 56 Ni in this case. Although the kinetic energy of E51  2 is larger than the canonical value (11051 erg) in the mass range of Mms  20–25 Mˇ , such an energy might be obtained from magnetar-type activity. XRFs may be associated with less massive progenitor stars than those of canonical GRBs, and the two groups may be differentiated by the formation of a neutron star (Nakamura 1998) or a BH. In order for the progenitor star to have been thoroughly stripped of its H and He envelopes, the progenitor may be in a binary system.

2.4

Non-SN Gamma-Ray Bursts

For recently discovered nearby long-duration GRB 060505 (z D 0:089 (Fynbo et al. 2006)) and GRB 060614 (z D 0:125 (Della Valle et al. 2006; Fynbo et al. 2006; Gal-Yam et al. 2006; Gehrels et al. 2006)), no SN has been detected. Upper limits to brightness of the possible SNe are about 100 times fainter than SN 1998bw. These correspond to upper limits to the ejected 56 Ni mass of M .56 Ni/  103 Mˇ . Such a “dark HN” (D “non-SN GRB” D long GRB with no SN) can occur if the jet-induced explosion is associated with fallback of the ejecta that contain most of 56 Ni. Such fallback associated with an energetic explosion has been predicted to exist to explain some of the peculiar abundance patterns (such as the large Zn/Fe and Co/Fe ratios) in carbon-enhanced extremely metal-poor stars (Nomoto et al. 2007).

1938

2.5

K. Nomoto

Progenitors of Supernovae and Hypernovae

Figure 2 summarizes the properties of core-collapse SNe as a function of the mainsequence mass Mms of the progenitor star (Nomoto et al. 1993, 2003, 2013). The broad-line SNe include both GRB-SNe and Non-GRB SNe. (1) GRB versus Non-GRB: Three GRB-SNe are all similar hypernovae (i.e., E51 & 10). Thus E could be closely related to the formation of GRBs. SN 1997ef seems to be a marginal case. E=Mej could be more important because SN 1997ef has significantly smaller E=Mej than GRB-SNe. (2) Broad-Line Features: The mass contained at v > 30,000 km s1 (or even higher boundary velocity) might be critical in forming the broad-line features, although further modeling is required to clarify this point (Nomoto et al. 2006).

2.5.1 Neutron Star or Black Hole Remnants The final fate of 20–25 Mˇ stars shows an interesting variety. Even the normal SN Ib 2005bf is very different from previously known SNe/HNe (Tominaga et al. 2005). This mass range corresponds to the transition from the NS formation to the BH formation. The NSs from this mass range could be much more active than those from the lower mass range because of possibly much larger NS masses (near the maximum mass) or possibly a large magnetic field (magnetar). XRFs and GRBs from the mass range of 20–25 Mˇ might form a different population. 2.5.2 Hypernovae of Type II and Type Ib Suppose that smaller losses of mass and angular momentum from low metallicity massive stars lead to the formation of more rapidly rotating NSs or BHs and thus more energetic explosions. Then the existence of Type Ib and Type II HNe has been predicted (Nomoto et al. 2007). Thus far all observed HNe are of Type Ic except for SN IIb. However, most SNe Ic are suggested to have some He. If even the small amount of radioactive 56 Ni is mixed in the He layer, the He feature should be seen. For HNe, the upper mass limit of He has been estimated to be 2 Mˇ (Mazzali et al. 2002) for the case of no He mixing. If He features were seen in future HN observations, it would provide an important constraint on the models, especially the fully mixed WR models (Meynet and Maeder 2007; Woosley and Heger 2006; Yoon and Langer 2006).

3

Nucleosynthesis in Hypernovae and Supernovae

3.1

Iron-Peak Elements

In core-collapse supernovae and hypernovae, stellar material undergoes shock heating as seen in the temperature evolution for a Pop III 30 Mˇ supernova (E51 D 1) and a hypernova (E51 D 10) in Fig. 3, where the higher peak temperature,

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

1939

Fig. 3 Time evolution of the density and temperature for E51 = 1 and E51 = 10. Here T9 D T =109 (K), and  in g cm3 (Umeda and Nomoto 2002)

Tpeak , is reached for the higher energy explosion (Umeda and Nomoto 2002). Then the shock-heated materials undergo explosive nucleosynthesis. Iron-peak elements are produced in two distinct regions, which are characterized by Tpeak of the shocked material. For Tpeak > 5109 K, material undergoes complete Si burning whose products include Co, Zn, V, and some Cr after radioactive decays. For 4  109 K < Tpeak < 5  109 K, incomplete Si burning takes place and its after-decay products include Cr and Mn (e.g., Nakamura et al. 2001). The radius of the sphere in which 56 Ni is dominantly produced is estimated as RNi  3700 .E  =1051 ergs/1=3 

3 4 =3RNi aTs4 

km;

(2) 9

which is derived from E D with Ts D 5  10 K (e.g., Thielemann et al. 1996). Here the deposited energy E is approximately equal to the sum of the explosion energy E and the binding energy (Ebin > 0/ of the progenitor, that is, E  ' E C Ebin . Note that Equation (1) indicates that smaller Mej correspond to smaller E for a given peak , whereas Equation (2) relates a smaller E to smaller RNi . Thus, combining these two equations, we find that RNi is smaller for smaller Mej . In other words, a small mass progenitor may not produce a significantly large amount of 56 Ni. Figure 4 shows the mass Mr enclosed within a radius r of the precollapse stars  for stellar masses of M D 25–100 Mˇ for E51 D 1; 10; 50, and 100 (Umeda and Nomoto 2008). The filled circles on the Mr  r curves indicate the outer edge of the core, that is, the masses of Fe-cores. Figure 4 suggests that the 56 Ni synthesis is larger for larger E  and for models with steeper Mr  r curves, that is, more massive stars. The mass between the outer edge of the Fe-core and r D RNi gives the crude upper limit to M .56 Ni) in the ejecta. If the mass-cut is larger, the ejected mass will be smaller.

1940

K. Nomoto

Fig. 4 The enclosed mass (Mr ) – radius relations for M D 25–100 Mˇ pre-SN progenitors (Umeda and Nomoto 2008). For each model the location of the top of the Fe-core is shown by the filled circle. RNi is the upper radius for the region where 56 Ni is dominantly produced as a function of the deposited energy E  given by Equation 2

An interesting question is how much 56 Ni production is theoretically possible for core collapse SNe. There may be an upper limit to M .56 Ni), because the reasonable range of the explosion energy has an upper limit, and also a larger explosion energy leads to stronger ˛rich freezeout, thus yielding a larger 4 He to 56 Ni ratio in the complete Si-burning region. Figure 5 shows this upper-limit M .56 Ni/up for various M and E with Z D 4 10 D Zˇ =200 (Umeda and Nomoto 2008). It is seen that M .56 Ni/up increases with E and M . The effect of M is more important than E because more massive stars tend to have steeper Mr  r curves in the density structure of the progenitors, so that M .56 Ni) increases steeply with M for the same E. Larger E leads to a larger 56 Ni-producing region according to Equation 2; however, this also leads to a smaller Ni/He ratio in that region. As a result, a large E does not result in a very large M .56 Ni). For E51 D 30, M .56 Ni/ D 2:2, 2.3, 5.0, and 6.6 Mˇ can be produced for M D 30, 50, 80, and 100 Mˇ , respectively, or for C+O core masses of MCO D 11.4, 19.3, 34.0, and 42.6 Mˇ , respectively. For SN 1998bw, 0.4–0.7 Mˇ 56 Ni is ejected. Because the mass of a collapsed star (neutron star or black hole) is at least as large as the mass of the precollapse Fe core (1.2–1.9 Mˇ as indicated in Fig. 4), the mass contained within RNi should exceed 1.6–2.3 Mˇ . For example, consider an explosion of a 6Mˇ C+O star, corresponding to a main-sequence mass 25Mˇ . If such a C+O star explodes, the

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

1941

Fig. 5 The upper limit to the 56 Ni mass produced by core-collapse SNe with various masses and explosion energies (Umeda and Nomoto 2008). M .56 Ni)up shown here are the ejected 56 Ni mass when the mass-cut is located at the top of the Fe-core. If the mass-cut is larger, the ejected mass will be smaller

ejecta mass becomes Mej . 4.4 Mˇ , which, along with the light curve width (Eq. 1), yields E . 2  1051 ergs. Substituting E . 21051 ergs for Equation (2), we obtain RNi . 4700 km. Within this RNi , only 1.8Mˇ is enclosed (Fig. 4), therefore only 0.2Mˇ56 Ni can be ejected. From this, we exclude those models less massive than 25Mˇ on their main sequence because they cannot eject enough 56 Ni. The preceding argument is further evidence that the progenitor of SN 1998bw is a massive star.

3.2

Abundance Ratios

The characteristics of nucleosynthesis with very large explosion energies (Nakamura et al. 2001; Nomoto et al. 2001; Umeda and Nomoto 2005) are seen in Fig. 6, where the lower panel shows the composition in the ejecta of a 25 Mˇ hypernova model (E51 D 10). The nucleosynthesis in a normal 25 Mˇ SN model (E51 D 1) is also shown for comparison in the upper panel of Fig. 6 (Umeda and Nomoto 2002). We note: (1) Both complete and incomplete Si-burning regions shift outward in mass compared with normal supernovae, thus the mass ratio between the complete and incomplete Si-burning regions becomes larger. As a result, higher energy explosions tend to produce larger [(Zn, Co, V)/Fe] and smaller [(Mn, Cr)/Fe],

1942

K. Nomoto

Fig. 6 Abundance distribution against the enclosed mass Mr after supernova explosions of Pop III 25Mˇ stars with E51 D 1 (upper panel) and E51 D 10 (lower panel) (Umeda and Nomoto 2002)

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

1943

Fig. 7 The maximum [Zn/Fe] ratios as a function of M and E51 . The arrow (obs.) indicates the range of observed high [Zn/Fe] values at [Fe/H]< 2:6 (Umeda and Nomoto 2002)

which can explain the trend observed in very metal-poor stars (Umeda and Nomoto 2005). The dependence of [Zn/Fe] on M and E is as follows. In Fig. 7, [Zn/Fe] is shown as a function of M and E, where the plotted ratios correspond to the maximum values for given E. We have found that models with E51 D 1 do not produce sufficiently large [Zn/Fe]. To be compatible with the observations of [Zn/Fe]  0:5, the explosion energy must be much larger, that is, E51 & 2 for M  13Mˇ and E51 & 20 for M & 20Mˇ as discussed in the next subsection. (2) In the complete Si-burning region of hypernovae, elements produced by ˛-rich freezeout are enhanced because nucleosynthesis proceeds at lower densities than in normal supernovae (Fig. 8). Hence, elements synthesized through capturing of ˛-particles, such as 44 Ti, 48 Cr, and 64 Ge (decaying into 44 Ca, 48 Ti, and 64 Zn, resp.) are more abundant. (3) Oxygen and carbon burning take place in more extended regions for the larger KE. Then more O, C, and Al are burned to produce a larger amount of burning products such as Si, S, and Ar. Therefore, hypernova nucleosynthesis is characterized by large abundance ratios of [Si,S/O], which can explain the abundance feature of M82 (Umeda and Nomoto 2002). Figure 9 shows the ratios between the intermediate mass elements and oxygen relative to the solar values for M D 25Mˇ as a function of E (Nakamura et al. 2001). It is seen that [C/O] and [Mg/O] are not sensitive to E because C, O, and Mg are mostly synthesized in hydrostatic burning. On the other hand, [Si/O], [S/O], [Ti/O], and [Ca/O] are larger for larger E, because Si, S, Ti, and Ca are produced in explosive burning, thus are sensitive to E.

1944

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Fig. 8 The  - T conditions of individual mass zones at their temperature maximum in hypernovae (E D 30  1051 ergs: filled circles) and normal supernovae (E D 1  1051 erg: open circles) (Nakamura et al. 2001). The lines that separate the Si-burning regimes and contour lines for constant 4 He mass fractions are taken from Thielemann et al. (1998)

Fig. 9 The abundance ratios between the intermediate mass elements and oxygen relative to the solar values for M D 25Mˇ as a function of E (Nakamura et al. 2001)

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

4

1945

Abundance Patterns of Extremely Metal-Poor (EMP) Stars and Hypernovae

Hypernova nucleosynthesis may have made an important contribution to galactic chemical evolution. In the early universe, enrichment by a single SN can dominate the pre-existing metal contents. Therefore, the comparison between the SN model and the abundance patterns of EMP stars can provide a new way to discover individual SN nucleosynthesis.

4.1

Very Metal-Poor (VMP) Stars

VMP stars defined as [Fe/H] . 2:5 (Beers and Christlieb 2005) are likely to have the abundance pattern of well-mixed ejecta of many SNe. Thus the abundance patterns of VMP stars are compared with the yields of SN models (E51 D 1 for M D 10  20Mˇ ) and HN models (E51 D 10 for M > 20Mˇ ) integrated over the progenitors of 10–50 Mˇ with the Salpeter IMF (Fig. 10). It is seen that many elements are in reasonable agreement (Tominaga et al. 2007b). (Here the Pop III yields are used for comparison, because the abundance patterns of supernova models with [Fe/H] . 2:5 are quite similar to those of Pop III star models.)

-2.7 < [Fe/H] < -2.0 (Cayrel et al. 2004)

Fig. 10 Comparison between the abundance patterns of VMP stars (Cayrel et al. 2004) (filled circles with error bars) and the IMF integrated yield of Pop III SNe (10–20 Mˇ ) and HNe (20–50 Mˇ ) (Tominaga et al. 2007b)

1946

4.2

K. Nomoto

Extremely Metal-Poor (EMP) Stars

In the early galactic epoch when the galaxy was not yet chemically well-mixed, each EMP star ([Fe/H] . 2:5) might have been formed mainly from the ejecta of a single Pop III SN (although some of them might have been second or later generation SNe) (Argast et al. 2000; Audouse and Silk 1995; Tumlinson 2006). In the observed abundances of halo stars, there are significant differences between the abundance patterns in the iron-peak elements below and above ŒFe=H  2:5 to 3. (1) For [Fe/H]. 2:5, the mean values of [Cr/Fe] and [Mn/Fe] decrease toward smaller metallicity, whereas [Co/Fe] increases (McWilliam et al. 1995; Ryan et al. 1996). (2) [Zn/Fe] 0 for [Fe/H] ' 3 to 0, and at [Fe/H] < 3:3, [Zn/Fe] increases toward smaller metallicity (Cayrel et al. 2004). The larger [(Zn, Co)/Fe] and smaller [(Mn, Cr)/Fe] in the supernova ejecta can be realized if the mass ratio between the complete and incomplete Si-burning regions is larger, or equivalently if deep material from the complete Si-burning region is ejected by mixing or aspherical effects. This can be realized if (a) the mass-cut between the ejecta and the compact remnant is located at smaller Mr (Nakamura et al. 1999); (b) E is larger, moving the outer edge of the complete Si-burning region to larger Mr (Nakamura et al. 2001); or (c) the asphericity in the explosion is larger. Among these possibilities, a large explosion energy E enhances ˛-rich freezeout, which results in an increase of the local mass fractions of Zn and Co, whereas Cr and Mn are not enhanced (Umeda and Nomoto 2002). Models with E51 D 1 do not produce sufficiently large [Zn/Fe]. To be compatible with the observations of [Zn/Fe]  0:5, the explosion energy must be much larger, that is, E51 & 20 for M & 20Mˇ ; that is, hypernova-like explosions of massive stars (M & 25Mˇ ) with E51 > 10 are responsible for the production of Zn. As examples, the theoretical yields are compared with the averaged abundance pattern of four EMP stars, CS 22189-009, CD-38:245, CS 22172-002, and CS 22885-096, which have low metallicity (4:2 < ŒFe=H < 3:5) and normal [C/Fe]  0 (Cayrel et al. 2004). Figure 11 shows that the averaged abundances of EMP stars can be fitted well with the hypernova model of 20 Mˇ and E51 D 10 (Fig. 11) but not with the normal SN model of 15 Mˇ and E51 D 1 (Nomoto et al. 2006). In the normal SN model (upper panel), the mass-cut is determined to eject Fe of mass 0.14 Mˇ ). Then the yields are in reasonable agreement with the observations for [(Na, Mg, Si)/Fe], but give too small [(Mn, Co, Ni, Zn)/Fe] and too large [(Ca, Cr)/Fe]. In the HN model (lower panel), these ratios are in much better agreement with observations. The ratios of Co/Fe and Zn/Fe are larger in higher energy explosions because both Co and Zn are synthesized in complete Si-burning at the

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

1947

-4.2 < [Fe/H] < -3.5 (Cayrel et al. 2004)

Fig. 11 Averaged elemental abundances of stars with ŒFe=H D 3:7 (Cayrel et al. 2004) compared with the normal SN yield (upper panel: 15 Mˇ , E51 D 1) and the hypernova yield (lower panel: 20 Mˇ , E51 D 10) (Nomoto et al. 2006)

high-temperature region (see the next subsection). To account for the observations, materials synthesized by complete Si-burning in high-temperature regions should be ejected, but the amount of Fe should be small. This is realized in the mixing-fallback models (Umeda and Nomoto 2002, 2005). Therefore, if hypernovae made significant contributions to the early galactic chemical evolution, it could explain the large Zn and Co abundances and the small Mn and Cr abundances observed in very metal-poor stars (Tominaga et al. 2005). The trends of [(Zn, Co, Mn, Cr)/Fe] toward smaller [Fe/H] mentioned in (1) and(2) above can be explained as follows. The formation of EMP stars was driven by a supernova shock, therefore [Fe/H] was determined by the ejected Fe mass and the amount of circumstellar hydrogen

K. Nomoto

Abundance raTios [C/Fe]

Ejected 56Ni masses [M . ]

1948

100 10–1

GRB 060505 Sub-luminous or faint SN GRB 060614

GRB-HN

Explosive

10–2 10–3 10–4

Jet

10–5 10–6 4

HMP

3 2

CEMP

1 0

EMP 10 100 1000 1 Energy deposition rates [1051 erg s–1]

Fig. 12 Top: the ejected 56 Ni mass (red: explosive nucleosynthesis products, blue: the jet contribution) as a function of the energy deposition rate. The background color shows the corresponding SNe (red: GRB-HNe, yellow: subluminous SNe, blue: faint SNe, green: GRBs 060505 and 060614). Vertical lines divide the resulting SNe according to their brightness. Bottom: dependence of the abundance ratio [C/Fe] on the energy deposition rate. The background color shows the corresponding metal-poor stars (yellow: EMP, red: CEMP, blue: HMP stars)

swept up by the shock wave (Ryan et al. 1996). Then, hypernovae with larger E were likely to induce the formation of stars with smaller [Fe/H], because the mass of interstellar hydrogen swept up by a hypernova is roughly proportional to E (Thornton et al. 1998) and the ratio of the ejected iron mass to E is smaller for hypernovae than for normal supernovae.

4.3

Carbon-Enhanced Metal-Poor (CEMP) Stars and Mixing Fallback

The abundance patterns of EMP stars are good indicators of SN nucleosynthesis because the galaxy was effectively unmixed at [Fe/H] < 3 (e.g., Tumlinson 2006). They are classified into three groups according to [C/Fe]: (1) [C/Fe]  0, normal EMP stars (4 < [Fe/H] < 3, e.g., (Cayrel et al. 2004)) (2) [C/Fe] & C1, carbon-enhanced EMP (CEMP) stars (4 < [Fe/H] < 3, e.g., CS 22949–37 (Depagne et al. 2002)) (3) [C/Fe]  C4, hyper metal-poor (HMP) stars ([Fe/H] < 5, e.g., HE 0107–5240 (Christlieb et al. 2002); HE 1327–2326 (Frebel et al. 2005))

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

1949

3 C

O

Ne Mg

Si

S

Ar

Ca

Ti

Cr

Fe

Ni

Zn

EMP stars CS22949-37

2 1 0

[X/Fe]

-1 B 5

N C

F O

Na

Al

Ne Mg

P Si

Cl S

K Ar

4

Sc Ca

V Ti

Mn Co Cu Ga Cr

Fe

Ni

Zn

HE1327-2326 HE0107-5240

3 2 1 0 -1

B 5

N

F

Na 10

Al

P

Cl

K

Sc 20

15

V

Mn Co Cu Ga 25

30

Z Fig. 13 A comparison of the abundance patterns of metal-poor stars and of the jet-induced explosion models. Top: typical EMP (red dots (Cayrel et al. 2004)) and CEMP (blue triangles, CS 22949–37 (Depagne et al. 2002)) stars and models with EP dep;51 D 120 (solid line) and D 3:0 (dashed line). Bottom: HMP stars: HE 1327–2326 (red dots (Frebel et al. 2005)), and HE 0107– 5240 (blue triangles (Christlieb et al. 2002)), and models with EP dep;51 D 1:5 (solid line) and D 0:5 (dashed line)

As discussed below, Fig. 13 shows that the general abundance patterns of the normal EMP stars, CEMP stars, and HMP stars are well reproduced by the mixingfallback models and thus the jet-induced explosion models.

5

Nucleosynthesis in Jet-Induced Explosions

The abundance patterns of extremely metal-poor (EMP) stars, such as the excess of C, Co, and Zn relative to Fe, can be modeled in a unified manner with the jet-induced explosion model. Tominaga et al. (2007a) calculated the jet-induced explosions of the 40 Mˇ stars by injecting the jets at a radius R  900 km, corresponding to an enclosed mass of M  1:4 Mˇ . They investigated the dependence of nucleosynthesis outcome on the “rate” of energy deposition EP dep for a range of EP dep;51  EP dep =1051 ergs s1 D 0:3  1500.

1950

K. Nomoto

They have shown that (1) the explosions with large energy deposition rate, EP dep , are observed as GRB-HNe and their yields can explain the abundances of normal EMP stars; and (2) the explosions with small EP dep are observed as GRBs without bright SNe and can be responsible for the formation of the CEMP and the HMP stars. They thus propose that GRB-HNe and GRBs without bright SNe belong to a continuous series of BH-forming massive stellar deaths with the relativistic jets of different EP dep . The diversity of EP dep is consistent with the wide range of the observed isotropic equivalent  -ray energies and timescales of GRBs. Variations of activities of the central engines, possibly corresponding to different rotational velocities or magnetic fields, may well produce the variation of EP dep . The top panel of Fig. 12 shows the dependence of the ejected M .56 Ni/ on the energy deposition rate EP dep . For lower EP dep , smaller M .56 Ni/ is synthesized in explosive nucleosynthesis because of lower postshock densities and temperatures. If EP dep;51 & 3, the jet injection is initiated near the bottom of the C+O layer, leading to the synthesis of M .56 Ni/ & 103 Mˇ . If EP dep;51 < 3, on the other hand, the jet injection is delayed and initiated near the surface of the C+O core; then the ejected 56 Ni is as small as M .56 Ni/ < 103 Mˇ . 56 Ni contained in the relativistic jets is only M .56 Ni/  106 104 Mˇ because the total mass of the jets is Mjet  104 Mˇ in this model with the Lorentz factor

jet D 100 and Edep D 1:51052 ergs. Thus the 56 Ni production in the jet dominates over explosive nucleosynthesis in the stellar mantle only for EP dep;51 < 1:5. For high-energy deposition rates (EP dep;51 & 60), the explosions synthesize large start M .56 Ni/ (&0:1 Mˇ ) as consistent with GRB-HNe. The remnant mass was Mrem  1:5 Mˇ when the jet injection started, but it grows as material is accreted from the equatorial plane. The final BH masses range from MBH D 10:8 Mˇ for EP dep;51 D 60 to MBH D 5:5 Mˇ for EP dep;51 D 1500, which are consistent with the observed masses of stellar-mass BHs. The model with EP dep;51 D 300 synthesizes M .56 Ni/  0:4 Mˇ and the final mass of BH left after the explosion is MBH D 6:4 Mˇ .

5.1

Faint Supernovae and Non-SN GRBs

Tominaga et al. (2007a) have pointed out that nucleosynthesis in HNe can explain some of the peculiar abundance patterns (such as the large Zn/Fe and Co/Fe ratios) in EMP stars. In particular, Nomoto et al. (2007) have predicted that the dark HN (D “non-SN GRB” D long GRB with no SN) should exist and be responsible for the formation of the carbon-enhanced extremely metal-poor stars as follows. For low-energy deposition rates (EP dep;51 < 3), the ejected 56 Ni masses (M .56 Ni/ < 103 Mˇ ) are smaller than the upper limits for GRBs 060505 and 060614. The final BH mass is larger for smaller EP dep . Although the material ejected along the jet-direction involves those from the C+O core, the material along the equatorial plane falls back.

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

1951

If the explosion is viewed from the jet direction, we would observe GRB without SN rebrightening. In particular, for EP dep;51 < 1:5, 56 Ni cannot be synthesized explosively and the jet component of the Fe-peak elements dominates the total yields (Fig. 13). The models eject very little M .56 Ni/ (106 Mˇ ). The predicted “nonSN GRBs” (Nomoto et al. 2007) have actually been discovered (GRB 060605 and 060614). For intermediate energy deposition rates (3 . EP dep;51 < 60), the explosions eject 103 Mˇ . M .56 Ni/ < 0:1 Mˇ and the final BH masses are 10:8 Mˇ . MBH < 15:1 Mˇ . The resulting SN is faint (M .56 Ni/ < 0:01 Mˇ ) or subluminous (0:01 Mˇ . M .56 Ni/ < 0:1 Mˇ ). Nearby GRBs with faint or subluminous SNe have not been observed. This may be because they do not occur intrinsically in our neighborhood or because the number of observed cases is still too small. In the latter case, further observations may detect GRBs with a faint or subluminous SN.

5.2

CEMP Stars

The bottom panel of Fig. 12 shows the dependence of the abundance ratio [C/Fe] on EP dep . Lower EP dep yields larger MBH and thus larger [C/Fe], because the infall decreases the amount of inner core material (Fe) relative to that of outer material (C). As in the case of M .56 Ni/, [C/Fe] changes dramatically at EP dep;51  3. Figure 13 shows that the general abundance patterns of the normal EMP stars, the CEMP star CS 22949–37, and the HMP stars HE 0107–5240 and HE 1327– 2326 are reproduced with EP dep;51 D 120, 3.0, 1.5, and 0.5, respectively. The model for the normal EMP stars ejects M .56 Ni/  0:2 Mˇ , that is, a factor of 2 less than SN 1998bw. On the other hand, the models for the CEMP and HMP stars eject M .56 Ni/  8  104 Mˇ and 4  106 Mˇ , respectively, which are always smaller than the upper limits for GRBs 060505 and 060614. The N/C ratio in the models for CS 22949–37 and HE 1327–2326 is enhanced by partial mixing between the He and H layers during presupernova evolution (Iwamoto et al. 2005).

6

Conclusions

We have shown that nucleosynthesis yields in jet-induced faint HNe is in better agreement with the abundance patterns of EMP and CEMP stars than normal SN yields. Thus the observed GRB-SN connection suggests the existence of the GRBFirst Star connection. The large Zn, Co, and C abundances and the small Mn and Cr abundances with respect to Fe as observed in EMP and CEMP stars can be better explained by introducing HNe. This would imply that HNe have made significant contributions to the early galactic chemical evolution. In theoretical models, some element ratios, such as (K, Sc, Ti, V)/Fe, are too small, whereas some ratios such as Cr/Fe are too large compared with the observed abundance ratios (Cayrel et al. 2004). Underproduction of Sc and K may require a

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significantly higher entropy environment for nucleosynthesis, for example, the “low density” progenitor models for K, Sc, and Ti (Umeda and Nomoto 2005). GRBs would have possible nucleosynthesis sites, such as accretion disks around the black hole. Neutrino processes in the deepest layers of SN ejecta and a possible accretion disk around a black hole would open a new window for SN nucleosynthesis (Fröhlich et al. 2006).

7

Cross-Reference

 Influence of Non-spherical Initial Stellar Structure on the Core-Collapse Super-

nova Mechanism  Making the Heaviest Elements in a Rare Class of Supernovae  Neutrinos and Their Impact on Core-Collapse Supernova Nucleosynthesis  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Nucleosynthesis in Thermonuclear Supernovae  Pre-supernova Evolution and Nucleosynthesis in Massive Stars and Their Stellar

Wind Contribution  The Multidimensional Character of Nucleosynthesis in Core-Collapse Super-

novae Acknowledgements This work has been supported in part by Grants-in-Aid for Scientific Research (JP26400222, JP16H02168, JP17K05382) from the Japan Society for the Promotion of Science and by the WPI Initiative, MEXT, Japan.

References Argast D, Samland M, Gerhard OE et al (2000) Metal-poor halo stars as tracers of ISM mixing processes during halo formation. A&A 356:873 Arnett WD (1996) Supernovae and nucleosynthesis. Princeton University Press, Princeton Audouse J, Silk J (1995) The first generation of stars: first steps toward chemical evolution of galaxies. ApJ 451:L49 Beers T, Christlieb N (2005) The discovery and analysis of very metal-poor stars in the galaxy. ARAA 43:531 Campana S et al (2006) The association of GRB 060218 with a supernova and the evolution of the shock wave. Nature 442:1008 Cayrel R et al (2004) First stars V – abundance patterns from C to Zn and supernova yields in the early galaxy. A&A 416:1117 Christlieb N et al (2002) A stellar relic from the early milky way. Nature 419:904 Della Valle M et al (2006) An enigmatic long-lasting gamma ray burst not accompanied by a bright supernova. Nature 444:1050 Depagne E et al (2002) First stars. II. Elemental abundances in the extremely metal-poor star CS 22949–037. A diagnostic of early massive supernovae. A&A 390:187 Frebel A et al (2005) Nucleosynthetic signatures of the first stars. Nature 434:871 Fröhlich C, Hauser P, Liebendörfer M et al (2006) Composition of the innermost core-collapse supernova ejecta. ApJ 637:415

73 Nucleosynthesis in Hypernovae Associated with Gamma-Ray Bursts

1953

Fynbo JPU et al (2006) No supernovae associated with two long-duration gamma-ray bursts. Nature 444:1047 Galama T et al (1998) An unusual supernova in the error box of the gamma-ray burst of 25 April 1998. Nature 395:670 Gal-Yam A et al (2006) A novel explosive process is required for the gamma-ray burst GRB 060614. Nature 444:1053 Gal-Yam A (2012) Luminous supernovae. Science 337:927 Gehrels N et al (2006) A new gamma-ray burst classification scheme from GRB060614. Nature 444:1044 Hamuy M (2003) Observed and physical properties of core-collapse supernovae. ApJ 582:905 Hill V, François P, Primas F (eds) (2005) IAU symposium 228, from lithium to uranium: elemental tracers of early cosmic evolution. Cambridge University Press, Cambridge Hjorth J et al (2003) A very energetic supernova associated with the gamma-ray burst of 29 March 2003. Nature 423:847 Iwamoto K, Mazzali PA, Nomoto K et al (1998) A hypernova model for the supernova associated with the gamma-ray burst of 25 April 1998. Nature 395:672 Iwamoto K, Nakamura T, Nomoto K et al (2000) The peculiar Type Ic supernova 1997EF: another hypernova. ApJ 534:660 Iwamoto N, Umeda H, Tominaga N, Nomoto K, Maeda K (2005) The first chemical enrichment in the universe and the formation of hyper metal-poor stars. Science 309:451 Kawabata K et al (2010) A massive star origin for an unusual helium-rich supernova in an elliptical galaxy. Nature 465:326 Maeda K, Nakamura T, Nomoto K et al (2002) Explosive nucleosynthesis in aspherical hypernova explosions and late-time spectra of SN 1998bw. ApJ 565:405 Malesani J et al (2006) SN 2003lw and GRB 031203: a bright supernova for a faint gamma-ray burst. ApJ 609:L5 Mazzali PA, Deng J, Maeda K, Nomoto K et al (2002) The Type Ic hypernova SN 2002ap. ApJ 572:L61 Mazzali PA, Kawabata KS, Maeda K, Nomoto K et al (2005) An asymmetric energetic Type Ic supernova viewed off-axis, and a link to gamma ray bursts. Science 308:1284 Mazzali PA, Deng J, Nomoto K et al (2006) A neutron-star-driven X-ray flash associated with supernova SN 2006aj. Nature 442:1018 McWilliam A, Preston GW, Sneden C, Searle L (1995) Spectroscopic analysis of 33 of the most metal poor stars. II. AJ 109:2757 Meynet G, Maeder A, (2007) Wind anisotropies and GRB progenitors. A&A 464:L11 Modjaz M et al (2006) Early-time photometry and spectroscopy of the fast evolving SN 2006aj associated with GRB 060218. ApJ 645:L21 Nakamura TK (1998) A model for non high energy gamma ray bursts and sources of ultra high energy cosmic rays – super strongly magnetized milli-second pulsar formed from a (C + O) star and a neutron star (black hole) close binary system. Prog Theor Phys 100:921 Nakamura T, Umeda K, Nomoto K, Thielemann F-K, Burrows A (1999) Nucleosynthesis in Type II supernovae and the abundances in metal-poor stars. ApJ 517:193 Nakamura T, Umeda K, Iwamoto K, Nomoto K, Hashimoto M, Hix WR, Thielemann F-K (2001) Explosive nucleosynthesis in hypernovae. ApJ 555:880 Nomoto K, Suzuki T, Shigeyama T, Kumagai S, Yamaoka H, Saio H (1993) A Type IIb model for supernova 1993J. Nature 364:507 Nomoto K et al (1994a) A carbon-oxygen star as progenitor of the Type Ic supernova 1994I. Nature 371:227 Nomoto K, Shigeyama T, Kumagai S et al (1994b) Supernova 1987A: from progenitor to remnant. In: Bludmann S et al (ed) Supernovae. NATO ASI series C, proceedings of session LIV held in Les Houche. North-Holland, p 489 Nomoto K, Mazzali PA, Nakamura T et al (2001) The properties of hypernovae: SNe Ic 1998bw, 1997ef, and SN IIn 1997cy. In: Livio M et al (eds) Supernovae and gamma ray bursts. Cambridge University Press, p 144. astro-ph/0003077

1954

K. Nomoto

Nomoto K et al (2003) Hypernovae and their nucleosynthesis. In: Hucht V et al (eds) IAU symposium 212, a massive star odyssey, from main sequence to supernova. ASP, p 395. astroph/0209064 Nomoto K et al (2004) Hypernovae and other black-hole-forming supernovae. In: Fryer CL (ed) Stellar collapse. Astrophysics and Space Science, Kluwer, p 277. astro-ph/0308136 Nomoto K, Tominaga N, Umeda H, Kobayashi C, Maeda K (2006) Nucleosynthesis yields of corecollapse supernovae and hypernovae, and galactic chemical evolution. Nucl Phys A 777:424. astro-ph/0605725 Nomoto K et al (2007) Diversity of the supernova – gamma-ray burst connection. Nuovo Cinento B121:1207. astro-ph/0702472 Nomoto K, Kobayashi C, Tominaga N (2013) Nucleosynthesis in stars and the chemical enrichment of galaxies. ARAA 51:457 Pian E et al (2006) An optical supernova associated with the X-ray flash XRF 060218. Nature 442:1011 Quimby RM (2012) Superluminous supernovae. In: Roming P et al (ed) IAU symposium 279, death of massive stars: supernovae and gamma-ray bursts, p 22 Ryan SG, Norris JE, Beers TC (1996) Extremely metal-poor stars. II. Elemental abundances and the early chemical enrichment of the galaxy. ApJ 471:254 Soderberg AM et al (2006) Relativistic ejecta from X-ray flash XRF 060218 and the rate of cosmic explosions. Nature 442:1014 Stanek KZ et al (2003) Spectroscopic discovery of the supernova 2003dh associated with GRB 030329. ApJ 591:L17 Thielemann F-K, Nomoto K, Hashimoto M (1996) Core-collapse supernovae and their ejecta. ApJ 460:408 Thielemann F-K, Rauscher T, Freiburghaus C, Nomoto K et al (1998) Nucleosynthesis basics and applications to supernovae. In: Hirsch J, Page D (eds) Nuclear and particle astrophysics. Cambridge University Press, Cambridge, p 27 Thornton K, Gaudlitz M, Janka H-Th et al (1998) Energy input and mass redistribution by supernovae in the interstellar medium. ApJ 500:95 Tominaga N, Tanaka M, Nomoto K et al (2005) The unique Type Ib supernova 2005bf: a WN star explosion model for peculiar light curves and spectra. ApJ 633:L97 Tominaga N, Maeda K, Umeda H, Nomoto K, Tanaka M et al (2007a) The connection between gamma-ray bursts and extremely metal-poor stars: black hole-forming supernovae with relativistic jets. ApJ 657:L77 Tominaga N, Umeda H, Nomoto K (2007b) Supernova nucleosynthesis in population III 13-50 Mˇ stars and abundance patterns of extremely metal-poor stars. ApJ 660:516 Tumlinson J (2006) Chemical evolution in hierarchical models of cosmic structure. I. Constraints on the early stellar initial mass function. ApJ 641:1 Umeda H, Nomoto K (2002) Nucleosynthesis of zinc and iron peak elements in population III Type II supernovae: comparison with abundances of very metal poor halo stars. ApJ 565:385 Umeda H, Nomoto K (2005) Variations in the abundance pattern of extremely metal-poor stars and nucleosynthesis in population III supernovae. ApJ 619:427 Umeda H, Nomoto K (2008) How much 56 Ni can be produced in core-collapse supernovae? Evolution and explosions of 30–100 Mˇ stars. ApJ 673:1014 Woosley SE, Heger A (2006) The progenitor stars of gamma-ray bursts. ApJ 637:914 Yoon S-C, Langer N (2006) Evolution of rapidly rotating metal-poor massive stars towards gammaray bursts. A&A 443:643

Nucleosynthesis in Thermonuclear Supernovae

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Ivo Rolf Seitenzahl and Dean M. Townsley

Abstract

The explosion energy of thermonuclear (type Ia) supernovae is derived from the difference in nuclear binding energy liberated in the explosive fusion of light “fuel” nuclei, predominantly carbon and oxygen, into more tightly bound nuclear “ash” dominated by iron and silicon group elements. The very same explosive thermonuclear fusion event is also one of the major processes contributing to the nucleosynthesis of the heavy elements, in particular the iron-group elements. For example, most of the iron and manganese in the sun and its planetary system were produced in thermonuclear supernovae. Here, we review the physics of explosive thermonuclear burning in carbon-oxygen white dwarf material and the methodologies utilized in calculating predicted nucleosynthesis from hydrodynamic explosion models. While the dominant explosion scenario remains unclear, many aspects of the nuclear combustion and nucleosynthesis are common to all models and must occur in some form in order to produce the observed yields. We summarize the predicted nucleosynthetic yields for existing explosion models, placing particular emphasis on characteristic differences in the nucleosynthetic signatures of the different suggested scenarios leading to type Ia supernovae. Following this, we discuss how these signatures compare with observations of several individual supernovae, remnants, and the composition of material in our galaxy and galaxy clusters.

I.R. Seitenzahl () School of Physical, Environmental, and Mathematical Sciences, University of New South Wales (UNSW) Canberra, Australian Defense Force Academy, Canberra, ACT, Australia e-mail: [email protected] D.M. Townsley Department of Physics and Astronomy, The University of Alabama, Tuscaloosa, AL, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_87

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Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physics Background and Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Explosive Thermonuclear Burning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Explosive Nucleosynthesis Predictions of Thermonuclear Supernova Models . . . . . . . 3.1 Thermonuclear SNe from Near-MC h Primary WDs . . . . . . . . . . . . . . . . . . . . . . 3.2 Thermonuclear SNe from Detonating Sub-MC h WDs . . . . . . . . . . . . . . . . . . . . . 3.3 WD+WD Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 p-Nuclei Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Direct and Indirect Observable Signatures of Nucleosynthesis . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

“Thermonuclear supernovae” is the collective name given to the family of supernova explosions that derive the energy that drives their expansion against gravity from the exothermic transmutation of less tightly bound nuclear “fuel” (such as e.g., 4 He, 12 C, or 16 O) into more tightly bound nuclear “ashes” (such as e.g., 28 Si or 56 Ni). This is in contrast to “core-collapse supernovae,” which, in spite of a contribution to the explosion energy by nuclear burning behind the outgoing shock wave, are largely powered by the gravitational binding energy that is released during the stellar core collapse. A key difference between the thermonuclear burning in thermonuclear supernovae and core-collapse supernovae is that the nucleosynthesis in the former generally proceeds at higher fuel density and therefore at lower entropy. For a (text) book on supernovae and nucleosynthesis, see Arnett (1996). Although details of the progenitor system and explosion mechanism are still unknown, there is a general consensus that thermonuclear supernovae are the physical mechanism behind what are observationally classified as “type Ia supernovae” (SNe Ia); the two terms are therefore often used interchangeably. Note that while it is likely that all SNe Ia are of thermonuclear origin, the converse need not be true. A key aspect all subclasses of thermonuclear supernova models have in common is that they all feature explosive (meaning dynamical) thermonuclear burning in white dwarfs (WD), stars that are supported against gravitation collapse by electron degeneracy pressure. We begin by summarizing the physical processes of explosive fusion involved in thermonuclear supernovae and how the interplay of these with the structure and dynamics of the exploding WD leads to the major yields of the explosion. A short discussion of the techniques used to compute yields in modern simulations follows. Our discussion of the expectations for the yields of thermonuclear supernovae then proceeds by treating several of the major proposed scenarios for the explosion. The nucleosynthesis of p-nuclei is discussed separately, and we end the chapter with a discussion of the observational signatures of various aspects of nucleosynthesis in thermonuclear supernovae.

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Physics Background and Methodology

2.1

Explosive Thermonuclear Burning

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The key fundamental aspect of nucleosynthesis in a type Ia supernova comes from the realization, established by Nomoto et al. (1984), that if a near-Chandrasekhar mass carbon-oxygen (CO) WD star is incinerated on a similar timescale to its dynamical time, the resulting ejecta gives rise to a transient that is spectroscopically characteristic of a type Ia. That is, it is poor in H and He and shows strong Si features at maximum light, with a power source interior to the maximum light photosphere provided by the radioactive decay of 56 Ni. Exactly how such an incineration of a WD comes about, and even where the massive CO WD required by some scenarios might come from are still mysterious, the basic model remains clear. Some time spent on why incineration of a WD leads to the observed synthesized ejecta is worthwhile. The density structure of a hydrostatic WD, along with the density dependence of the nucleosynthetic outcome of explosive CO fusion, leads naturally to an ejecta structure in which iron-group elements (IGE), including 56 Ni, make up the inner regions, surrounded by Si-rich outer layers. Figure 1 shows roughly how the products of burning depend on the local fuel density, with high densities leading to more complete processing to IGE in nuclear statistical equilibrium (NSE) and lower densities truncating the nuclear processing with the production of Si-group intermediate mass elements (IME). In NSE, material is hot and dense enough that all nuclear reactions that preserve the number of protons and neutrons can be approximated as occurring quickly. As a result, the composition is determined by the relative binding energies of various species and statistical mechanical considerations and does not depend on individual reaction rates or, in a computation, their uncertainty. Also shown in Fig. 1 is the density structure of a near-Chandrasekhar mass (MCh ) WD (1.38 Mˇ ), as well as a 1.05 Mˇ WD. It is immediately clear that the hydrostatic state of the WD at the time the burning takes place has a direct role in the nucleosynthetic yield produced. A MC h WD burned by a detonation, for example, with no opportunity to expand, will produce nearly all IGE. Comparatively, a 1.05 Mˇ star subjected to a detonation will produce only about 0.6 Mˇ of IGE, with the balance being mostly IME, all simply due to the lower overall density. A similar balance of yields favoring more IME can be obtained if the beginning of the incineration occurs slightly more slowly than the dynamical time of the star (around 1 s). Then the star can expand as shown in the middle curve in Fig. 1, so that the lowered densities lead to the production of IME in the outer region. We will only discuss the physics of the relevant modes of combustion briefly. The deflagration, or flame, mode is more slowly propagating and therefore able to allow the star to globally respond and expand. Its propagation is driven by heat conduction in the degenerate electron medium. The faster mode, detonation, is propagated by a shock that is self-sustained by the energy release and propagates across the star in less than the dynamical time.

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1010 stable IGE (56 Ni consumed) 109 Density (g cm−3 )

Mn produced 108

56

Ni (radioactive IGE)

107 Si group (IME) 106

105 0.0

Si + O (C consumed)

0.2

0.4 0.6 0.8 1.0 Enclosed Mass (M )

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Fig. 1 Nucleosynthetic products are determined principally by the density of the fuel when the reaction front passes. High densities lead to more complete burning. Profiles of WDs of several masses are shown, demonstrating that a WD close to the Chandrasekhar mass (solid green), if burned without any expansion, produces almost solely IGE, while a 1.05 Mˇ WD (dashed orange) will not produce Mn or stable IGE due to electron capture. In the delayed-detonation family of scenarios, early burning expands the MCh WD to a state in which significant amounts of IME are produced upon full incineration (dot-dashed blue)

The observed nucleosynthesis of SNe Ia shows evidence of a large fraction of stable IGE in the innermost regions of the ejecta (e.g., Mazzali et al. 2007, 2015). As seen in Fig. 1, synthesis of stable IGE requires densities above a few 108 g cm3 . These densities are only present in CO WDs above about 1.2 Mˇ , which can only be formed by accretion. Conversion of protons to neutrons by capture of electrons proceeds at high densities because the Fermi energy of the degenerate electrons, which hold the star up against gravity, is high enough for this conversion to be favorable. At densities above a few 108 g cm3 , the conversion rate is fast enough that, in less than the dynamical time of the expanding star, the 56 Ni-dominated NSE is changed first into one in which 54 Fe and 58 Ni, both of which are stable, are the dominant species. Longer exposure can lead to even more neutron-rich products. Comparison of the balance of neutron-enriched and non-enriched isotopes produced by the explosion to those found in the solar distribution constrains the central density during the initial part of the explosion (Brachwitz et al. 2000). These observational constraints are important due to uncertainty in the ignition physics (e.g., Gasques et al. 2005, 2007). In addition to its importance for the isotopic abundances, neutron enrichment also decreases the amount of radioactive 56 Ni available to power the observed bright transient. The overall neutron richness of the material is determined by both the

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amount of electron capture during the supernova, as just described, and the initial metallicity and electron capture during the pre-explosion core convection phase. The initial metallicity controls the initial neutron excess mostly via the abundance of 22 Ne in the progenitor WD (Timmes et al. 2003). Almost all the initial C, N, and O elements in the progenitor star are first converted to 14 N in the H-burning CNO cycle. Then during the He burning phase that forms the CO WD, ˛ captures and beta decay convert this 14 N into 22 Ne. Core ignition of a thermonuclear SN is preceded by a phase of convective core carbon burning. During this phase, electron capture near the center increases neutron enrichment (Chamulak et al. 2008; MartínezRodríguez et al. 2016; Piro and Bildsten 2008), with significant uncertainty due to the convective Urca process (Stein and Wheeler 2006). For sub-MCh scenarios, the settling of the 22 Ne within the WD (Bildsten and Hall 2001) may be important for the distribution of stable IGE in the ejecta. Metallicity can also change the explosion in other ways (Calder et al. 2013) including modification of the DDT density (Jackson et al. 2010). Another product only obtained in large quantities from high-density burning is manganese (Seitenzahl et al. 2013a). This is produced as 55 Co in the explosion and then decays. Figure 1 shows the dividing line, at about 2  108 g cm3 , between alpha-rich freeze-out of NSE at lower densities and normal NSE freeze-out at higher densities. At high densities, and therefore comparatively lower entropies for similar energy deposited, as the temperature falls, freeze-out occurs as the reactions that maintain the NSE become starved of ˛ and other light particles. By comparison, somewhat lower densities produce entropies at which ˛ and other light particles are still present during freeze-out and destroy some species present in the NSE, including 55 Co. The solar ratio of Mn to Fe is higher than that produced by core-collapse SNe, thus requiring production in thermonuclear SNe. This therefore implies a significant fraction of events with material burned above this threshold density (Seitenzahl et al. 2013a), another indication of near-MCh progenitors.

2.2

Methodology

Two aspects of the combustion length scales in SNe Ia make it challenging to compute accurate yields in explosion simulations. Both of these are related to the relatively small length and time scales on which the reactions involved occur (For a summary see the introduction of Townsley et al. 2016). While the WD is of order several 108 cm across, the length scales of the combustion front can be microns for the highest densities to cm for moderate densities 107 g cm3 . In addition to this, the contrast in reaction length and time scales within the reaction front can be similarly vast. At 107 g cm3 , the length scale for full conversion to IGE in a planar detonation is 108 cm, while the peak Si abundance only occurs some 103 cm behind the shock, and the carbon consumption scale is of order centimeter (Seitenzahl et al. 2009a; Townsley et al. 2016). These two contrasts in length scale make it computationally infeasible to compute the reaction front structure explicitly in simulations of the explosion of the star.

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Another challenge comes from the number of species involved in the nuclear reactions. Accurate computation of carbon combustion with a nuclear reaction network (Hix and Meyer 2006) requires of order 200–300 species in order to accurately capture combustion, silicon burning, and finally the electron capture at high densities (Calder et al. 2007; Seitenzahl et al. 2009c). Larger reaction networks can give a few percent improvement in accuracy, but around 200–300 appears to be sufficient. For most of the history of SNe Ia simulations, it was not possible to perform star-scale fluid dynamics simulations with such a large number of species. This is currently improving with current very large machines having a high degree of parallelism in each node, but there will continue to be a trade-off between fidelity of nuclear processes with more species and resolution of hydrodynamic processes such as turbulence with more spatial cells. These two challenges, of unresolved reaction length scales and the preference for good spatial resolution in multidimensional simulations, preferably 3D, instead of many species, have led to the current strategy in which the reactions in the explosion simulation are modeled in some way and then the yields are determined via postprocessing of Lagrangian tracers (Seitenzahl et al. 2010; Townsley et al. 2016; Travaglio et al. 2004). The post-processing proceeds by using Lagrangian fluid histories, often called “tracks,” “trajectories,” or “tracers,” recorded at many places in the hydrodynamic simulation of the explosion. Two examples of the density and temperature history tracks recorded in this manner from a two-dimensional simulation (assuming azimuthal symmetry) of the deflagration-detonation transition (DDT) scenario (Townsley et al. 2016) are shown in Fig. 2. The top two panels show tracks for fluid elements that were processed in the detonation (solid) and deflagration (dashed) modes. Another advantage of separating the hydrodynamics and nucleosynthesis is that the influence of some changes, such as minor rates or initial abundances, can be evaluated based on a smaller number of hydrodynamic simulations (e.g., Bravo and Martínez-Pinedo 2012; Miles et al. 2016; Parikh et al. 2013). This strategy of computing the explosion using large eddy simulation (LES) is neither unique to astrophysics nor to SNe Ia. In other contexts it may be used in circumstances where the physical turbulence dissipation scale is unresolved, but the behavior of turbulence in small scales is relatively well understood from the Kolmogorov model of turbulence and its successors. As a result, it is possible to do a valid simulation by only explicitly simulating the largest scales in an LES. Supernovae present the additional complication of reactions, which are also subgrid scale like the turbulent dissipation. The necessity of having a combustion model that accurately captures unresolved phenomena then introduces the topic of calibration and verification of that model. The development of improved combustion models for LES and their verification is therefore a central topic in simulation of SNe Ia and continues as increasingly detailed comparisons to observations are performed (Ciaraldi-Schoolmann et al. 2013; Jackson et al. 2014; Schmidt et al. 2006; Seitenzahl et al. 2010; Townsley et al. 2016). In addition to uncertainty due to the modelling of unresolved processes in the hydrodynamics, there are also reaction rate uncertainties (Bravo and Martínez-Pinedo 2012; Parikh et al. 2013).

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ηn

Density (g cm−3 )

Temperature (K)

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Mass Fraction

Fig. 2 Nucleosynthesis is computed by processing the temperature-density history of a fluid element, shown in the top two panels, computed in a hydrodynamic simulation of the explosion. The lower two panels show the resulting abundance neutron excess and abundance history. The solid lines show a track processed by the detonation which only partially processes IME to IGE. Only a few major abundances are shown: 12 C (red), 28 Si (green), and 56 Ni (black). The dashed lines show a track processed by the deflagration which has the 56 Ni yield reduced by electron capture, enhancing the neutron excess n . The short blue sections in the upper panels are the portion of the time history that is reconstructed (Townsley et al. 2016)

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109 108 109 108 107 106 105 0.03 0.02 0.01 0.00 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.5

1.0

1.5 2.0 2.5 Time (s)

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Examples of two tracks processed under different conditions in the same explosion, taken from Townsley et al. (2016), are shown in Fig. 2. The solid lines show the track for a fluid parcel that undergoes combustion via a detonation late in the simulation, about 1.7 s. As can be seen, most of the nuclear processing of this parcel occurs near the reaction front or within about 0.2 s after the detonation passage. The density when the detonation shock arrives is around 107 g cm3 , leading to incomplete burning of Si, as seen in the final abundances for this track, which have a mixture of IME andPIGE. No significant Pelectron capture takes P place so that the neutron excess n D i .Ni  Zi /Yi D i .Ni C Zi /Yi  2 i Zi Yi D 1  2Ye is unchanged. Here Ye is the number of electrons per baryon, Yi is the number of nuclei of species i per baryon, Ni and Zi are the number of neutrons and protons in the nucleus of species i , and charge balance is assumed. The dashed lines show the track for a fluid parcel processed by the deflagration earlier in the simulation, about 0.6 s. The deflagration track’s final abundances are markedly different from the detonation, mostly because the chosen track shows a significant degree of conversion of protons to neutrons by electron capture, as shown by the difference in n . Immediately after passage of the deflagration front, all the fuels

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and the synthesized Si have been destroyed, and the 56 Ni fraction is low due the high-temperature, high-density NSE state; much of the material is in the form of ˛ particles. As the material cools and expands, the 56 Ni abundance rises, but only to a fraction of about 0.3 by mass, because most of the IGE are in the form of more neutron-rich species like 54 Fe and 58 Ni. While both detonation and deflagration fronts are unresolved in this 4 km resolution simulation, in Fig. 2 it is much more obvious for the deflagration case because the reaction front moves more slowly. At the deflagration propagation speed, which is km s1 , thousands of times less than the sound speed, it takes several tenths of a second for a fluid parcel to pass through the thickened reaction front that is a few times the grid resolution in thickness. In order to improve yield accuracy in the context of this artificial broadening, Townsley et al. (2016) developed a technique in which part of the thermal history recorded during the simulation is replaced in post-processing by a separate computation of the fully resolved structure of a steady-state deflagration (blue curve in upper panels). The temperature rise in such a reconstruction is much faster, giving a more physically realistic temperature peak and therefore total integrated amount of electron captures.

3

Explosive Nucleosynthesis Predictions of Thermonuclear Supernova Models

We give here only a broad overview that focuses on the qualitative differences of existing models in their respective nucleosynthetic yields. There are many different ways of categorizing thermonuclear SNe. From a nucleosynthesis point of view, it makes most sense to group the explosion models into (i) near-Mch models (involving deflagrations ignited at high density and the associated neutronization) and (ii) pure detonation models of less massive WDs and (iii) models including detonations of thick He shells and special nucleosynthesis products thereof.

3.1

Thermonuclear SNe from Near-MCh Primary WDs

These models have in common the near central ignition of a deflagration via pycnonuclear fusion reactions as the accreting primary WD grows in mass and the central density increases. From a nucleosynthesis standpoint, these are generally the only models where in situ electron captures significantly lower the electron fraction and drives the yields toward more neutron-rich isotopes. Further, these are the only models where low entropy “normal” freeze-out from NSE occurs, with its typical nucleosynthetic signature, such as enhanced production of Mn (see discussion in Sect. 5). For these two reasons, deflagrations in high central density ( & 5  109 g cm3 ) WDs have been suggested as the only plausible production site of certain neutron-rich intermediate mass and iron-group isotopes, such as 48 Ca, 50 Ti, or 54 Cr (see discussion in Sect. 5). Since in situ electron captures

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significantly increase the neutron excess after ignition, the ignition density of the WD can have a greater effect on the final yields (e.g., Seitenzahl et al. 2011) than the metallicity of the progenitor star (e.g., Miles et al. 2016).

3.1.1 Pure (Turbulent) Deflagrations A detonation in a hydrostatic near-Mch CO WD (Arnett 1969) would burn most of the star at high density to 56 Ni and other IGE, producing insufficient IMEs such as Si and S to explain observed spectra of SNe Ia. This has led to deflagrations as the longtime favored model, since a subsonic flame allows the WD to respond to the nuclear energy release with expansion to lower densities where the flame can produce IMEs. The widely referenced W7 model of a deflagration in a 1.38 Mˇ CO WD (Nomoto et al. 1984) has been very successful in reproducing key elements of the inferred structure of normal SNe Ia, such as the mass of 56 Ni and the layered profile of the IMEs. However, W7 overproduced neutron-rich nuclear species such as, e.g., 54 Cr, 54 F e, or 58 Ni (Iwamoto et al. 1999; Thielemann et al. 1986), a shortcoming that was ameliorated (Brachwitz et al. 2000) when the electron capture rates of Fuller et al. (1982) were replaced with new electron capture rates for pf-shell nuclei from Langanke and Martínez-Pinedo (2001). The initially slow evolution of the flame and the suppression of buoyancy still lead to enhanced electron captures in the W7 model even for the updated electron capture rates and hence too much 58 Ni (Maeda et al. 2010). The one-dimensional W7 model implements a subsonically moving flame that moves outward in the mass coordinate, which means buoyancy and turbulent mixing are suppressed. As an unphysical consequence, the flame overruns the whole star and the burning ashes do not mix, retaining their original positions in the mass coordinate. Three-dimensional pure deflagration models, which take buoyancy, fluid instabilities, and mixing into account, are too faint and chemically mixed to explain normal SNe Ia (e.g., Röpke et al. 2007), and their colors and spectra do not agree (Fink et al. 2014). Weakly ignited pure deflagration models that only partially unbind the star and leave a bound remnant behind do, however, provide excellent models for subluminous SNe Iax (Kromer et al. 2013, 2015). While the ejecta of deflagration models that fail to completely unbind the whole WD (Fink et al. 2014) are rich in IGE and contain little unburned 12 C and 16 O, more strongly ignited deflagrations that unbind the whole WD, such as, e.g., the N1600 model from Fink et al. (2014), eject > 0:3 Mˇ of both 12 C and 16 O, in addition to large amounts (0:1 Mˇ of 54 Fe and 0:07 Mˇ of 58 Ni) of neutron-rich stable iron-group isotopes, as well as ŒMn=Fe > 0. Here we use the widespread “bracket” notation: the logarithm of the ratio of element A to element B relative to the corresponding ratio in the sun, ŒA=B D log10 .A=B/  log10 .A=B/ˇ . 3.1.2 Deflagration to Detonation Transition (DDT) Models To overcome the nucleosynthetic shortcomings of pure detonation and pure deflagration models, Khokhlov (1991) introduced a delayed-detonation model, where an initial subsonic deflagration can transition to a supersonic detonation under suitable conditions. The expansion of the star prior to the detonation results in the

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desired nuclear burning at densities .107 g cm3 where IMEs such as Si and S are synthesized. The significant contribution of the deflagration to IGE nucleosynthesis however still leaves an imprint on the overall yields, with overall ŒMn=Fe > 0 and (slightly) super-solar 54 Fe=56 Fe and 58 Ni=56 Fe (Seitenzahl et al. 2013b). The white dwarf’s carbon fraction (or C/O ratio) is only a secondary parameter; it does not influence the nucleosythesis in Mch models a lot since a lot of material burns into NSE (Ohlmann et al. 2014). DDT models tend to produce low light ˛-element to Fe ratios, with typical O yields around 0:1 Mˇ , and Ne and Mg yield around 0:01 Mˇ or lower.

3.1.3 GCD and PRD Models The so-called gravitationally confined detonation (GCD) model (Plewa et al. 2004) is based on a deflagration that ignites off-center in a single bubble and a detonation that is triggered just under the WD surface on the opposite side of the ignition point, when the deflagration ash compresses unburned fuel there after rising toward the surface and expanding laterally around the star. For this type of explosion model, detailed nucleosynthesis calculations that go beyond a basic 13 isotope ˛-network have been presented for 2D simulations by Meakin et al. (2009) and for 3D simulations by Seitenzahl et al. (2016). A key signature of GCD models is that although it is technically a near-Mch explosion model, very little mass is burned in the deflagration. As such, their isotopic nucleosynthesis signature resembles more that of pure detonations in massive sub-Chandrasekhar mass WDs, such as presented in Marquardt et al. (2015). Mn/Fe is sub-solar, and products of neutronization, in particular the stable iron-group isotopes 54 Fe and 58 Ni, are not overly abundant. Burning is quite complete, only 0:1 Mˇ 16 O and a few 102 Mˇ of 12 C survive the explosion. The pulsating reverse detonation (PRD) model (Bravo and García-Senz 2009) evolves initially analogous to the GCD model from a weak deflagration, although here the detonation is though to be triggered when an accretion shock forms during the contraction phase of the WD after the first radial pulsation brought about by the energy released in the deflagration. Since again not very much mass, 0.14–0.26 Mˇ in the Bravo et al. (2009) models, is burned in the deflagration, the nucleosynthesis products do not carry the typical signature of near-Mch models, for example, Mn/Fe is sub-solar (Bravo et al. 2009).

3.2

Thermonuclear SNe from Detonating Sub-MCh WDs

Next, we group and discuss explosion models that are fundamentally based on detonations in sub-Mch WDs. Compared to near-Mch models, the smaller mass of the detonating primaries means that explosive nuclear burning at densities above 108 g cm3 does generally not contribute to the yields. Consequently, the typical nucleosynthetic signatures of deflagrations, such as ŒMn=Fe > 0 or copious production of electron capture nuclei 58 Ni or 54 Fe, are collectively absent in this

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group of models. In the following, we briefly discuss the main proposed scenarios of detonating sub-Mch WDs, once again with a focus on their nucleosynthetic signatures.

3.2.1 Violent WD+WD Merger For a mass ratio close to unity, the violent merger of two WDs is thought to provide a means to detonate at least one of the two WDs to produce a thermonuclear SN. The mass of the primary (heavier) WD is hereby the most important factor in determining whether the SN is subluminous (Pakmor et al. 2010), of “normal” SN Ia luminosity (Pakmor et al. 2012), or over-luminous (Moll et al. 2014), since in the violent merger models, the primary WD detonates close to hydrostatic equilibrium (cf. Ruiter et al. 2013; Sim et al. 2010). A small layer of helium present on the primary is thought to be essential in achieving robust detonations (Pakmor et al. 2013). Generally, the densities achieved in violent mergers are too low for low entropy freeze-out from NSE or enhanced production of neutron-rich electron capture nuclei (e.g., 54 Fe or 58 Ni) to occur. The isotopic composition of the IGEs therefore directly reflects the neutron excess and hence the progenitor system metallicity mainly through the abundance of 22 Ne (see Sect. 2). Whether or not the secondary WD detonates or gets disrupted is particularly important for setting the overall production ratios, especially affecting the nucleosynthesis of the intermediate mass ˛-elements, with a detonation in the lower mass secondary mostly (depending on the exact mass) ejecting 12 C, 16 O, 28 Si, and other IMEs (Pakmor et al. 2012). 3.2.2 Double-Detonation Models with He shells WDs accreting H at a low accretion rate . few  108 Mˇ yr1 process the H to He and accumulate thick He shells that may ignite explosively (e.g., Taam 1980). Similarly, such thick He shells can be accumulated by directly accreting He, either from a degenerate He WD (Tutukov and Yungelson 1996) or a nondegenerate He star (Iben et al. 1987). Multidimensional simulations have shown that detonations in the He layer compress the core and likely (at least for high-mass CO cores) initiate a second CO detonation there (e.g., Livne 1990; Shen and Bildsten 2014; Woosley and Weaver 1994), providing a possible explosion scenario for SNe Ia. Detonations in thick helium shells of &0:1 Mˇ process enough material in the He detonation to have a global impact on the yields; in particular ˛-isotopes such as 36 Ar, 40 Ca, 44 Ti (decaying to stable 44 Ca), 48 Cr (decaying to stable 48 Ti), or 52 Fe (decaying to stable 52 Cr) are significantly enhanced compared to the products of explosive CO burning (e.g., Livne and Arnett 1995; Woosley and Weaver 1994). The mass fraction of metals (e.g, C, N, O, Ne, . . . ) in the He layer has a significant influence on the final nucleosynthesis products (e.g., Kromer et al. 2010; Moore et al. 2013; Shen and Moore 2014; Waldman et al. 2011) and complicates model predictions. Double-detonation explosion models with relatively large primary WD masses &0:9 Mˇ and relatively small He shell masses 1 (e.g., Kobayashi and Nomoto 2009; Timmes et al. 1995). In addition to Fe, SNe Ia are also the dominant production sites of Cr and Mn, as well as contributing significantly, perhaps even the majority, to other iron-group elements (such as Ti, Ni) and the heavier ˛-elements, such as Si, S, Ar, and Ca (e.g., de Plaa 2013).

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Of all these, the monoisotopic Mn is of particular interest. Mn/Fe indicates that SNe Ia from near-Mch WD primaries cannot be uncommon, since they are the only viable proposed nucleosynthesis site that predicts Mn=Fe > 0. The reason for this is that high density is required for the entropy to be low enough such that 55 Co, which decays to 55 Mn via 55 Fe, largely survives the freeze-out from NSE. This provides strong evidence that explosive nuclear burning at high density,  & 2  108 g cm3 , must have contributed significantly to the synthesis of Fe in the galaxy (Seitenzahl et al. 2013a). It is worth noting here that this strongly density-/entropy-dependent 55 Co yield can be used as a model discriminant for individual, nearby SNe via the 5:9 keV X-ray emission from the decay of 55 Fe (Seitenzahl et al. 2015) or via the effect of radioactive heating by X-rays and Auger electrons from decaying 55 Fe (Röpke et al. 2012). Of interest in the context of GCE are further the chemical peculiarities of Local Group dwarf galaxies (Kobayashi et al. 2015), which could be explained by the nucleosynthetic contribution of SNe Iax, in particular pure deflagration models that fail to completely unbind the WD and leave remnants behind (e.g., Kromer et al. 2013, 2015). X-ray spectroscopy of hot intra-cluster medium (ICM) has emerged as one of the most promising ways to measure chemical abundances to constrain SN explosion models (e.g., de Plaa et al. 2007; Dupke and White 2000). The hot ICM is generally optically thin to X-rays and close to collisional ionization equilibrium (see e.g., Dopita and Sutherland 2003), making abundance measurements relatively straightforward (for a review see e.g., Böhringer and Werner 2010). The gravitational potential of large galaxy clusters is deep enough to retain the SN ejecta, and the metal abundance of the ICM therefore directly reflects the integrated yields of all SNe (core collapse and thermonuclear) up to the present. Fits to the observed ICM abundances (Mernier et al. 2016a) indicate that to explain the large abundances of Ar and Ca (and perhaps Cr) (de Plaa 2013; Mernier et al. 2016b), a further component has to be invoked, in addition to the contributions from normal SNe Ia and CCSNe. Since no such contribution is required to explain the abundances in the sun (Mernier et al. 2016b), this points at very old stellar populations (long delay time) giving rise to these explosions. A promising match to these requirements could be 1991bg-like SNe, a scenario that could simultaneously explain the origin and morphology of the galactic 511 keV antimatter annihilation line (Crocker et al. 2016). Moreover, once again based on the Mn abundance, it is disfavored that most SNe Ia originate from detonating sub-Mch WDs (Mernier et al. 2016b). X-ray observations of supernova remnants can provide further independent information about the chemical elements synthesized by SNe Ia and constrain explosion scenarios for individual SNRs. For example, the high Mn/Fe and Ni/Fe ratios determined for SNR 3C 397 from Suzaku observations are indicative of neutronized material that could only be explained by an exploding massive nearMch WD (Yamaguchi et al. 2015). Last but not the least, the nucleosynthesis origin of a few neutron-rich intermediate mass and iron-group isotopes is very likely also linked to thermonuclear SNe, in particular for 48 Ca but also 50 Ti, 54 Cr, and others (e.g., Woosley 1997). Meyer et al. (1996) showed that nucleosynthesis of 48 Ca cannot primarily occur in

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CCSNe since the formation and subsequent survival of the 48 Ca quasi-equilibrium cluster (Bodansky et al. 1968; Woosley et al. 1973) not only requires high neutron excess but also low entropy, such as is only obtained in explosive thermonuclear burning at the highest densities obtained in near-Mch SN Ia explosions, for example, from explosive thermonuclear burning in ONeMg WDs. Recent three-dimensional simulations by Jones et al. (2016) cast serious doubt on the canonical wisdom that near-Mch accreting ONeMg WDs collapse to neutron stars after central Ne and O-burning is ignited, opening the exciting possibility that such events may indeed be the primary nucleosynthesis site of 48 Ca and a few other neutron-rich isotopes.

6

Cross-References

 Combustion in Thermonuclear Supernova Explosions  Dynamical Mergers  Explosion Physics of Thermonuclear Supernovae and Their Signatures  Thermonuclear Explosions of Chandrasekhar Mass White Dwarfs  Violent Mergers Acknowledgements IRS was supported during this work by Australian Research Council Laureate Grant FL09921.

References Anders E, Grevesse N (1989) Abundances of the elements – meteoritic and solar. Geochimica et Cosmochimica Acta 53:197–214. doi:10.1016/0016-7037(89)90286-X Arnett D (1996) Supernovae and nucleosynthesis: an investigation of the history of matter from the big bang to the present. Princeton University Press, Princeton Arnett WD (1969) A possible model of supernovae: detonation of 12 C. Astrophys Space Sci 5:180– 212. doi:10.1007/BF00650291 Arnett WD (1982) Type I supernovae. I – analytic solutions for the early part of the light curve. Astrophys J 253:785–797. doi:10.1086/159681 Arnould M (1976) Possibility of synthesis of proton-rich nuclei in highly evolved stars. II. Astron Astrophys 46:117–125 Audouze J, Truran JW (1975) P-process nucleosynthesis in postshock supernova envelope environments. Astrophys J 202:204–213. doi:10.1086/153965 Benetti S, Cappellaro E, Mazzali PA, Turatto M, Altavilla G, Bufano F, Elias-Rosa N, Kotak R, Pignata G, Salvo M, Stanishev V (2005) The diversity of Type Ia supernovae: evidence for systematics? Astrophys J 623:1011–1016. doi:10.1086/428608, astro-ph/0411059 Bildsten L, Hall DM (2001) Gravitational settling of 22 Ne in liquid white dwarf interiors. Astrophys J Lett 549:L219–L223. doi:10.1086/319169, astro-ph/0101365 Bodansky D, Clayton DD, Fowler WA (1968) Nuclear quasi-equilibrium during silicon burning. Astrophys J Suppl 16:299. doi:10.1086/190176 Böhringer H, Werner N (2010) X-Ray spectroscopy of galaxy clusters: studying astrophysical processes in the largest celestial laboratories. Astron Astrophys Rev 18:127–196. doi:10.1007/s00159-009-0023-3 Borkowski KJ, Reynolds SP, Green DA, Hwang U, Petre R, Krishnamurthy K, Willett R (2010) Radioactive scandium in the youngest galactic supernova remnant G1.9+0.3. Astrophys J Lett 724:L161–L165. doi:10.1088/2041-8205/724/2/L161, 1006.3552

1972

I.R. Seitenzahl and D.M. Townsley

Brachwitz F, Dean DJ, Hix WR, Iwamoto K, Langanke K, Martínez-Pinedo G, Nomoto K, Strayer MR, Thielemann FK, Umeda H (2000) The role of electron captures in Chandrasekharmass models for Type Ia supernovae. Astrophys J 536:934–947. doi:10.1086/308968, astroph/0001464 Bravo E, García-Senz D (2009) Pulsating reverse detonation models of Type Ia supernovae. I. Detonation ignition. Astrophys J 695:1244–1256. doi:10.1088/0004-637X/695/2/1244, 0901.3008 Bravo E, Martínez-Pinedo G (2012) Sensitivity study of explosive nucleosynthesis in Type Ia supernovae: modification of individual thermonuclear reaction rates. Phys Rev C 85(5):055805. doi:10.1103/PhysRevC.85.055805, 1204.1981 Bravo E, García-Senz D, Cabezón RM, Domínguez I (2009) Pulsating reverse detonation models of Type Ia supernovae. II. Explosion. Astrophys J 695:1257–1272. doi:10.1088/0004-637X/695/2/1257, 0901.3013 Burbidge EM, Burbidge GR, Fowler WA, Hoyle F (1957) Synthesis of the elements in stars. Rev Mod Phys 29:547–650. doi:10.1103/RevModPhys.29.547 Calder AC, Townsley DM, Seitenzahl IR, Peng F, Messer OEB, Vladimirova N, Brown EF, Truran JW, Lamb DQ (2007) Capturing the fire: flame energetics and neutronization for Type Ia supernova simulations. Astrophys J 656:313–332. doi:10.1086/510709, astro-ph/0611009 Calder AC, Krueger BK, Jackson AP, Townsley DM (2013) The influence of chemical composition on models of Type Ia supernovae. Front Phys 8:168–188. doi:10.1007/s11467-013-0301-4, 1303.2207 Cameron AGW (1957) Nuclear reactions in stars and nucleogenesis. Publ Astron Soc Pac 69:201. doi:10.1086/127051 Carlton AK, Borkowski KJ, Reynolds SP, Hwang U, Petre R, Green DA, Krishnamurthy K, Willett R (2011) Expansion of the youngest galactic supernova remnant G1.9+0.3. Astrophys J Lett 737:L22. doi:10.1088/2041-8205/737/1/L22, 1106.4498 Chamulak DA, Brown EF, Timmes FX, Dupczak K (2008) The reduction of the electron abundance during the pre-explosion simmering in white dwarf supernovae. Astrophys J 677:160–168. doi:10.1086/528944, 0801.1643 Churazov E, Sunyaev R, Isern J, Knödlseder J, Jean P, Lebrun F, Chugai N, Grebenev S, Bravo E, Sazonov S, Renaud M (2014) Cobalt-56 -ray emission lines from the Type Ia supernova 2014J. Nature 512:406–408. doi:10.1038/nature13672, 1405.3332 Churazov E, Sunyaev R, Isern J, Bikmaev I, Bravo E, Chugai N, Grebenev S, Jean P, Knödlseder J, Lebrun F, Kuulkers E (2015) Gamma-rays from Type Ia supernova SN 2014J. Astrophys J 812:62. doi:10.1088/0004-637X/812/1/62, 1502.00255 Ciaraldi-Schoolmann F, Seitenzahl IR, Röpke FK (2013) A subgrid-scale model for deflagrationto-detonation transitions in Type Ia supernova explosion simulations. Numerical implementation. Astron Astrophys 559:A117. doi:10.1051/0004-6361/201321480, 1307.8146 Crocker RM, Ruiter AJ, Seitenzahl IR, Panther FH, Baumgardt H, Moller A, Nataf DM, Ferrario L, Eldridge JJ, White M, Sim S, Tucker BE, Aharonian F (2016) Sub-luminous ‘1991bg-Like’ thermonuclear supernovae account for most diffuse antimatter in the milky way. ArXiv e-prints 1607.03495 de Plaa J (2013) The origin of the chemical elements in cluster cores. Astronomische Nachrichten 334:416. doi:10.1002/asna.201211870, 1210.1093 de Plaa J, Werner N, Bleeker JAM, Vink J, Kaastra JS, Méndez M (2007) Constraining supernova models using the hot gas in clusters of galaxies. Astron Astrophys 465:345–355. doi:10.1051/0004-6361:20066382, astro-ph/0701553 Dhawan S, Leibundgut B, Spyromilio J, Blondin S (2016) A reddening-free method to estimate the 56 Ni mass of Type Ia supernovae. Astron Astrophys 588:A84. doi:10.1051/0004-6361/201527201, 1601.04874 Diehl R, Siegert T, Hillebrandt W, Grebenev SA, Greiner J, Krause M, Kromer M, Maeda K, Röpke F, Taubenberger S (2014) Early 56 Ni decay gamma rays from SN 2014J suggest an unusual explosion. Science 345:1162–1165. doi:10.1126/science.1254738, 1407.3061

74 Nucleosynthesis in Thermonuclear Supernovae

1973

Dopita MA, Sutherland RS (2003) Astrophysics of the diffuse universe. Springer, Berlin/Heidelberg Dupke RA, White RE III (2000) Constraints on Type Ia supernova models from X-Ray spectra of galaxy clusters. Astrophys J 528:139–144. doi:10.1086/308181, astro-ph/9907343 Dwek E (2016) Iron: a key element for understanding the origin and evolution of interstellar dust. ArXiv e-prints 1605.01957 Fink M, Röpke FK, Hillebrandt W, Seitenzahl IR, Sim SA, Kromer M (2010) Double-detonation sub-Chandrasekhar supernovae: can minimum helium shell masses detonate the core? Astron Astrophys 514:A53. doi:10.1051/0004-6361/200913892, 1002.2173 Fink M, Kromer M, Seitenzahl IR, Ciaraldi-Schoolmann F, Röpke FK, Sim SA, Pakmor R, Ruiter AJ, Hillebrandt W (2014) Three-dimensional pure deflagration models with nucleosynthesis and synthetic observables for Type Ia supernovae. Mon Not R Astron Soc 438:1762–1783. doi:10.1093/mnras/stt2315, 1308.3257 Foley RJ, Chornock R, Filippenko AV, Ganeshalingam M, Kirshner RP, Li W, Cenko SB, Challis PJ, Friedman AS, Modjaz M, Silverman JM, Wood-Vasey WM (2009) SN 2008ha: an extremely low luminosity and exceptionally low energy supernova. Astron J 138:376–391. doi:10.1088/0004-6256/138/2/376, 0902.2794 Fransson C, Jerkstrand A (2015) Reconciling the infrared catastrophe and observations of SN 2011fe. Astrophys J Lett 814:L2. doi:10.1088/2041-8205/814/1/L2, 1511.00245 Fuller GM, Fowler WA, Newman MJ (1982) Stellar weak interaction rates for intermediate-mass nuclei. II - A = 21 to A = 60. Astrophys J 252:715–740. doi:10.1086/159597 Gasques LR, Afanasjev AV, Aguilera EF, Beard M, Chamon LC, Ring P, Wiescher M, Yakovlev DG (2005) Nuclear fusion in dense matter: reaction rate and carbon burning. Phys Rev C 72(2):025806. doi:10.1103/PhysRevC.72.025806, astro-ph/0506386 Gasques LR, Brown EF, Chieffi A, Jiang CL, Limongi M, Rolfs C, Wiescher M, Yakovlev DG (2007) Implications of low-energy fusion hindrance on stellar burning and nucleosynthesis. Phys Rev C 76(3):035802. doi:10.1103/PhysRevC.76.035802 Graur O, Zurek D, Shara MM, Riess AG, Seitenzahl IR, Rest A (2016) Late-time photometry of Type Ia supernova SN 2012cg reveals the radioactive decay of 57 Co. Astrophys J 819:31. doi:10.3847/0004-637X/819/1/31, 1505.00777 Hix WR, Meyer BS (2006) Thermonuclear kinetics in astrophysics. Nucl Phys A 777:188–207. doi:10.1016/j.nuclphysa.2004.10.009, astro-ph/0509698 Howard WM, Meyer BS, Woosley SE (1991) A new site for the astrophysical gamma-process. Astrophys J Lett 373:L5–L8. doi:10.1086/186038 Iben I Jr (1981) On intermediate-mass single stars and accreting white dwarfs as sources of neutron-rich isotopes. Astrophys J 243:987–993. doi:10.1086/158663 Iben I Jr, Nomoto K, Tornambe A, Tutukov AV (1987) On interacting helium star-white dwarf pairs as supernova precursors. Astrophys J 317:717–723. doi:10.1086/165318 Iwamoto K, Brachwitz F, Nomoto K, Kishimoto N, Umeda H, Hix WR, Thielemann FK (1999) Nucleosynthesis in Chandrasekhar mass models for Type IA supernovae and constraints on progenitor systems and burning-front propagation. Astrophys J Suppl 125:439–462. doi:10.1086/313278, astro-ph/0002337 Jackson AP, Calder AC, Townsley DM, Chamulak DA, Brown EF, Timmes FX (2010) Evaluating systematic dependencies of Type Ia supernovae: the influence of deflagration to detonation density. Astrophys J 720:99–113. doi:10.1088/0004-637X/720/1/99, 1007.1138 Jackson AP, Townsley DM, Calder AC (2014) Power-law wrinkling turbulence-flame interaction model for astrophysical flames. Astrophys J 784:174. doi:10.1088/0004-637X/784/2/174, 1402.4527 Jones S, Roepke FK, Pakmor R, Seitenzahl IR, Ohlmann ST, Edelmann PVF (2016) Do electroncapture supernovae make neutron stars? First multidimensional hydrodynamic simulations of the oxygen deflagration. ArXiv e-prints 1602.05771 Kasliwal MM, Kulkarni SR, Gal-Yam A, Nugent PE, Sullivan M, Bildsten L, Yaron O, Perets HB, Arcavi I, Ben-Ami S, Bhalerao VB, Bloom JS, Cenko SB, Filippenko AV, Frail DA, Gane-

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shalingam M, Horesh A, Howell DA, Law NM, Leonard DC, Li W, Ofek EO, Polishook D, Poznanski D, Quimby RM, Silverman JM, Sternberg A, Xu D (2012) Calcium-rich gap transients in the remote outskirts of galaxies. Astrophys J 755:161. doi:10.1088/0004-637X/755/2/161, 1111.6109 Kerzendorf WE, Taubenberger S, Seitenzahl IR, Ruiter AJ (2014) Very late photometry of SN 2011fe. Astrophys J Lett 796:L26. doi:10.1088/2041-8205/796/2/L26, 1406.6050 Khokhlov AM (1991) Delayed detonation model for Type Ia supernovae. Astron Astrophys 245:114–128 Kobayashi C, Nomoto K (2009) The role of Type Ia Supernovae in chemical evolution. I. Lifetime of Type Ia supernovae and metallicity effect. Astrophys J 707:1466–1484. doi:10.1088/0004-637X/707/2/1466, 0801.0215 Kobayashi C, Nomoto K, Hachisu I (2015) Subclasses of Type Ia supernovae as the origin of [˛/Fe] ratios in dwarf spheroidal galaxies. Astrophys J Lett 804:L24. doi:10.1088/2041-8205/804/1/L24, 1503.06739 Kromer M, Sim SA, Fink M, Röpke FK, Seitenzahl IR, Hillebrandt W (2010) Double-detonation sub-Chandrasekhar supernovae: synthetic observables for minimum helium shell mass models. Astrophys J 719:1067–1082. doi:10.1088/0004-637X/719/2/1067, 1006.4489 Kromer M, Fink M, Stanishev V, Taubenberger S, Ciaraldi-Schoolman F, Pakmor R, Röpke FK, Ruiter AJ, Seitenzahl IR, Sim SA, Blanc G, Elias-Rosa N, Hillebrandt W (2013) 3D deflagration simulations leaving bound remnants: a model for 2002cx-like Type Ia supernovae. Mon Not R Astron Soc 429:2287–2297. doi:10.1093/mnras/sts498, 1210.5243 Kromer M, Ohlmann ST, Pakmor R, Ruiter AJ, Hillebrandt W, Marquardt KS, Röpke FK, Seitenzahl IR, Sim SA, Taubenberger S (2015) Deflagrations in hybrid CONe white dwarfs: a route to explain the faint Type Iax supernova 2008ha. Mon Not R Astron Soc 450:3045–3053. doi:10.1093/mnras/stv886, 1503.04292 Lambert DL (1992) The p-nuclei – abundances and origins. Astron Astrophys Rev 3:201–256. doi:10.1007/BF00872527 Langanke K, Martínez-Pinedo G (2001) Rate tables for the weak processes of pf-SHELL nuclei in stellar environments. At Data Nucl Data Tables 79:1–46. doi:10.1006/adnd.2001.0865 Livne E (1990) Successive detonations in accreting white dwarfs as an alternative mechanism for Type I supernovae. Astrophys J Lett 354:L53–L55. doi:10.1086/185721 Livne E, Arnett D (1995) Explosions of Sub–Chandrasekhar mass white dwarfs in two dimensions. Astrophys J 452:62. doi:10.1086/176279 Lopez LA, Grefenstette BW, Reynolds SP, An H, Boggs SE, Christensen FE, Craig WW, Eriksen KA, Fryer CL, Hailey CJ, Harrison FA, Madsen KK, Stern DK, Zhang WW, Zoglauer A (2015) A spatially resolved study of the synchrotron emission and titanium in Tycho’s supernova remnant using NuSTAR. Astrophys J 814:132. doi:10.1088/0004-637X/814/2/132, 1504.07238 Maeda K, Röpke FK, Fink M, Hillebrandt W, Travaglio C, Thielemann FK (2010) Nucleosynthesis in two-dimensional delayed detonation models of Type Ia supernova explosions. Astrophys J 712:624–638. doi:10.1088/0004-637X/712/1/624, 1002.2153 Marquardt KS, Sim SA, Ruiter AJ, Seitenzahl IR, Ohlmann ST, Kromer M, Pakmor R, Röpke FK (2015) Type Ia supernovae from exploding oxygen-neon white dwarfs. Astron Astrophys 580:A118. doi:10.1051/0004-6361/201525761, 1506.05809 Martínez-Rodríguez H, Piro AL, Schwab J, Badenes C (2016) Neutronization during carbon simmering in Type Ia supernova progenitors. ArXiv e-prints 1602.00673 Mazzali PA, Röpke FK, Benetti S, Hillebrandt W (2007) A common explosion mechanism for Type Ia supernovae. Science 315:825. doi:10.1126/science.1136259, astro-ph/0702351 Mazzali PA, Sullivan M, Filippenko AV, Garnavich PM, Clubb KI, Maguire K, Pan YC, Shappee B, Silverman JM, Benetti S, Hachinger S, Nomoto K, Pian E (2015) Nebular spectra and abundance tomography of the Type Ia supernova SN 2011fe: a normal SN Ia with a stable Fe core. Mon Not R Astron Soc 450:2631–2643. doi:10.1093/mnras/stv761, 1504.04857 McWilliam A (1997) Abundance ratios and galactic chemical evolution. Annu Rev Astron Astrophys 35:503–556. doi:10.1146/annurev.astro.35.1.503

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Meakin CA, Seitenzahl I, Townsley D, Jordan GC IV, Truran J, Lamb D (2009) Study of the detonation phase in the gravitationally confined detonation model of Type Ia supernovae. Astrophys J 693:1188–1208. doi:10.1088/0004-637X/693/2/1188, 0806.4972 Mernier F, de Plaa J, Pinto C, Kaastra JS, Kosec P, Zhang YY, Mao J, Werner N (2016a) On the origin of central abundances in the hot intra-cluster medium – I. Individual and average abundance ratios from XMM-Newton EPIC. Astron Astrophys 592:1–18, id.A157. doi:10.1051/0004-6361/201527824 Mernier F, de Plaa J, Pinto C, Kaastra JS, Kosec P, Zhang YY, Mao J, Werner N, Pols OR, Vink J (2016b Origin of central abundances in the hot intra-cluster medium – II. Chemical enrichment and supernova yield models. Astron Astrophys 595:1–19, id.A126. doi:10.1051/0004-66361/201628765 Meyer BS, Krishnan TD, Clayton DD (1996) 48 Ca production in matter expanding from high temperature and density. Astrophys J 462:825. doi:10.1086/177197 Miles BJ, van Rossum DR, Townsley DM, Timmes FX, Jackson AP, Calder AC, Brown EF (2016) On measuring the metallicity of a Type Ia supernova progenitor. Astrophys J 824:59. doi:10.3847/0004-637X/824/1/59, 1508.05961 Moll R, Raskin C, Kasen D, Woosley SE (2014) Type Ia supernovae from merging white dwarfs. I. Prompt detonations. Astrophys J 785:105. doi:10.1088/0004-637X/785/2/105, 1311.5008 Moore K, Townsley DM, Bildsten L (2013) The effects of curvature and expansion on helium detonations on white dwarf surfaces. Astrophys J 776:97. doi:10.1088/0004-637X/776/2/97, 1308.4193 Nomoto K, Thielemann FK, Yokoi K (1984) Accreting white dwarf models of Type I supernovae. III – carbon deflagration supernovae. Astrophys J 286:644–658. doi:10.1086/162639 Ohlmann ST, Kromer M, Fink M, Pakmor R, Seitenzahl IR, Sim SA, Röpke FK (2014) The white dwarf’s carbon fraction as a secondary parameter of Type Ia supernovae. Astron Astrophys 572:A57. doi:10.1051/0004-6361/201423924, 1409.2866 Pakmor R, Kromer M, Röpke FK, Sim SA, Ruiter AJ, Hillebrandt W (2010) Sub-luminous Type Ia supernovae from the mergers of equal-mass white dwarfs with mass 0.9Msolar . Nature 463:61–64. doi:10.1038/nature08642, 0911.0926 Pakmor R, Kromer M, Taubenberger S, Sim SA, Röpke FK, Hillebrandt W (2012) Normal Type Ia supernovae from violent mergers of white dwarf binaries. Astrophys J Lett 747:L10. doi:10.1088/2041-8205/747/1/L10, 1201.5123 Pakmor R, Kromer M, Taubenberger S, Springel V (2013) Helium-ignited violent mergers as a unified model for normal and rapidly declining Type Ia supernovae. Astrophys J Lett 770:L8. doi:10.1088/2041-8205/770/1/L8, 1302.2913 Papish O, Perets HB (2016) Supernovae from direct collisions of white dwarfs and the role of helium shell ignition. Astrophys J 822:19. doi:10.3847/0004-637X/822/1/19, 1502.03453 Parikh A, José J, Seitenzahl IR, Röpke FK (2013) The effects of variations in nuclear interactions on nucleosynthesis in thermonuclear supernovae. Astron Astrophys 557:A3. doi:10.1051/0004-6361/201321518, 1306.6007 Pignatari M, Göbel K, Reifarth R, Travaglio C (2016) The production of proton-rich isotopes beyond iron: the -process in stars. Int J Mod Phys E 25:1630003-232. doi:10.1142/S0218301316300034, 1605.03690 Pinto PA, Eastman RG (2000) The physics of Type Ia supernova light curves. I. Analytic results and time dependence. Astrophys J 530:744–756. doi:10.1086/308376 Piro AL, Bildsten L (2008) Neutronization during Type Ia supernova simmering. Astrophys J 673:1009–1013. doi:10.1086/524189, 0710.1600 Plewa T, Calder AC, Lamb DQ (2004) Type Ia supernova explosion: gravitationally confined detonation. Astrophys J Lett 612:L37–L40. doi:10.1086/424036, astro-ph/0405163 Rauscher T, Dauphas N, Dillmann I, Fröhlich C, Fülöp Z, Gyürky G (2013) Constraining the astrophysical origin of the p-nuclei through nuclear physics and meteoritic data. Rep Prog Phys 76(6):066201. doi:10.1088/0034-4885/76/6/066201, 1303.2666 Röpke FK, Hillebrandt W, Schmidt W, Niemeyer JC, Blinnikov SI, Mazzali PA (2007) A threedimensional deflagration model for Type Ia supernovae compared with observations. Astrophys J 668:1132–1139. doi:10.1086/521347, 0707.1024

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Röpke FK, Kromer M, Seitenzahl IR, Pakmor R, Sim SA, Taubenberger S, Ciaraldi-Schoolmann F, Hillebrandt W, Aldering G, Antilogus P, Baltay C, Benitez-Herrera S, Bongard S, Buton C, Canto A, Cellier-Holzem F, Childress M, Chotard N, Copin Y, Fakhouri HK, Fink M, Fouchez D, Gangler E, Guy J, Hachinger S, Hsiao EY, Chen J, Kerschhaggl M, Kowalski M, Nugent P, Paech K, Pain R, Pecontal E, Pereira R, Perlmutter S, Rabinowitz D, Rigault M, Runge K, Saunders C, Smadja G, Suzuki N, Tao C, Thomas RC, Tilquin A, Wu C (2012) Constraining Type Ia supernova models: SN 2011fe as a test case. Astrophys J Lett 750:L19. doi:10.1088/2041-8205/750/1/L19, 1203.4839 Ruiter AJ, Sim SA, Pakmor R, Kromer M, Seitenzahl IR, Belczynski K, Fink M, Herzog M, Hillebrandt W, Röpke FK, Taubenberger S (2013) On the brightness distribution of Type Ia supernovae from violent white dwarf mergers. Mon Not R Astron Soc 429:1425–1436. doi:10.1093/mnras/sts423, 1209.0645 Scalzo RA, Aldering G, Antilogus P, Aragon C, Bailey S, Baltay C, Bongard S, Buton C, Childress M, Chotard N, Copin Y, Fakhouri HK, Gal-Yam A, Gangler E, Hoyer S, Kasliwal M, Loken S, Nugent P, Pain R, Pécontal E, Pereira R, Perlmutter S, Rabinowitz D, Rau A, Rigaudier G, Runge K, Smadja G, Tao C, Thomas RC, Weaver B, Wu C (2010) Nearby supernova factory observations of SN 2007if: first total mass measurement of a super-Chandrasekhar-mass progenitor. Astrophys J 713:1073–1094. doi:10.1088/0004-637X/713/2/1073, 1003.2217 Scalzo RA, Ruiter AJ, Sim SA (2014) The ejected mass distribution of Type Ia supernovae: a significant rate of non-Chandrasekhar-mass progenitors. Mon Not R Astron Soc 445:2535– 2544. doi:10.1093/mnras/stu1808, 1408.6601 Schmidt W, Niemeyer JC, Hillebrandt W, Röpke FK (2006) A localised subgrid scale model for fluid dynamical simulations in astrophysics. II. Application to Type Ia supernovae. Astron Astrophys 450:283–294. doi:10.1051/0004-6361:20053618, astro-ph/0601500 Seitenzahl IR, Meakin CA, Townsley DM, Lamb DQ, Truran JW (2009a) Spontaneous initiation of detonations in white dwarf environments: determination of critical sizes. Astrophys J 696:515– 527. doi:10.1088/0004-637X/696/1/515, 0901.3677 Seitenzahl IR, Taubenberger S, Sim SA (2009b) Late-time supernova light curves: the effect of internal conversion and auger electrons. Mon Not R Astron Soc 400:531–535. doi:10.1111/j.1365-2966.2009.15478.x, 0908.0247 Seitenzahl IR, Townsley DM, Peng F, Truran JW (2009c) Nuclear statistical equilibrium for Type Ia supernova simulations. At Data Nucl Data Tables 95:96–114. doi:10.1016/j.adt.2008.08.001 Seitenzahl IR, Röpke FK, Fink M, Pakmor R (2010) Nucleosynthesis in thermonuclear supernovae with tracers: convergence and variable mass particles. Mon Not R Astron Soc 407:2297–2304. doi:10.1111/j.1365-2966.2010.17106.x, 1005.5071 Seitenzahl IR, Ciaraldi-Schoolmann F, Röpke FK (2011) Type Ia supernova diversity: white dwarf central density as a secondary parameter in three-dimensional delayed detonation models. Mon Not R Astron Soc 414:2709–2715. doi:10.1111/j.1365-2966.2011.18588.x, 1012.4929 Seitenzahl IR, Cescutti G, Röpke FK, Ruiter AJ, Pakmor R (2013a) Solar abundance of manganese: a case for near Chandrasekhar-mass Type Ia supernova progenitors. Astron Astrophys 559:L5. doi:10.1051/0004-6361/201322599, 1309.2397 Seitenzahl IR, Ciaraldi-Schoolmann F, Röpke FK, Fink M, Hillebrandt W, Kromer M, Pakmor R, Ruiter AJ, Sim SA, Taubenberger S (2013b) Three-dimensional delayed-detonation models with nucleosynthesis for Type Ia supernovae. Mon Not R Astron Soc 429:1156–1172. doi:10.1093/mnras/sts402, 1211.3015 Seitenzahl IR, Summa A, Krauß F, Sim SA, Diehl R, Elsässer D, Fink M, Hillebrandt W, Kromer M, Maeda K, Mannheim K, Pakmor R, Röpke FK, Ruiter AJ, Wilms J (2015) 5.9-keV Mn Kshell X-ray luminosity from the decay of 55 Fe in Type Ia supernova models. Mon Not R Astron Soc 447:1484–1490. doi:10.1093/mnras/stu2537, 1412.0835 Seitenzahl IR, Kromer M, Ohlmann ST, Ciaraldi-Schoolmann F, Marquardt K, Fink M, Hillebrandt W, Pakmor R, Roepke FK, Ruiter AJ, Sim SA, Taubenberger S (2016) Three-dimensional simulations of gravitationally confined detonations compared to observations of SN 1991T. ArXiv e-prints 1606.00089

74 Nucleosynthesis in Thermonuclear Supernovae

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Shen KJ, Bildsten L (2014) The ignition of carbon detonations via converging shock waves in white dwarfs. Astrophys J 785:61. doi:10.1088/0004-637X/785/1/61, 1305.6925 Shen KJ, Moore K (2014) The initiation and propagation of helium detonations in white dwarf envelopes. Astrophys J 797:46. doi:10.1088/0004-637X/797/1/46, 1409.3568 Sim SA, Röpke FK, Hillebrandt W, Kromer M, Pakmor R, Fink M, Ruiter AJ, Seitenzahl IR (2010) Detonations in sub-Chandrasekhar-mass C+O white dwarfs. Astrophys J Lett 714:L52–L57. doi:10.1088/2041-8205/714/1/L52, 1003.2917 Stein J, Wheeler JC (2006) The convective Urca process with implicit two-dimensional hydrodynamics. Astrophys J 643:1190–1197. doi:10.1086/503246, astro-ph/0512580 Stritzinger M, Mazzali PA, Sollerman J, Benetti S (2006) Consistent estimates of 56 Ni yields for Type Ia supernovae. Astron Astrophys 460:793–798. doi:10.1051/0004-6361:20065514, astroph/0609232 Taam RE (1980) The long-term evolution of accreting carbon white dwarfs. Astrophys J 242:749– 755. doi:10.1086/158509 Taubenberger S, Elias-Rosa N, Kerzendorf WE, Hachinger S, Spyromilio J, Fransson C, Kromer M, Ruiter AJ, Seitenzahl IR, Benetti S, Cappellaro E, Pastorello A, Turatto M, Marchetti A (2015) Spectroscopy of the Type Ia supernova 2011fe past 1000 d. Mon Not R Astron Soc 448:L48–L52. doi:10.1093/mnrasl/slu201, 1411.7599 Thielemann FK, Nomoto K, Yokoi K (1986) Explosive nucleosynthesis in carbon deflagration models of Type I supernovae. Astron Astrophys 158:17–33 Timmes FX, Woosley SE, Weaver TA (1995) Galactic chemical evolution: hydrogen through zinc. Astrophys J Suppl 98:617–658. doi:10.1086/192172, astro-ph/9411003 Timmes FX, Brown EF, Truran JW (2003) On variations in the peak luminosity of Type Ia supernovae. Astrophys J Lett 590:L83–L86. doi:10.1086/376721, astro-ph/0305114 Townsley DM, Miles BJ, Timmes FX, Calder AC, Brown EF (2016) A tracer method for computing Type Ia supernova yields: burning model calibration, reconstruction of thickened flames, and verification for planar detonations. Astrophys J Supp 225:3. doi:10.3847/0067-0049/225/1/3. ArXiv e-prints 1605.04878 Travaglio C, Hillebrandt W, Reinecke M, Thielemann FK (2004) Nucleosynthesis in multi-dimensional SN Ia explosions. Astron Astrophys 425:1029–1040. doi:10.1051/0004-6361:20041108, astro-ph/0406281 Travaglio C, Röpke FK, Gallino R, Hillebrandt W (2011) Type Ia supernovae as sites of the p-process: two-dimensional models coupled to nucleosynthesis. Astrophys J 739:93. doi:10.1088/0004-637X/739/2/93, 1106.0582 Travaglio C, Gallino R, Rauscher T, Röpke FK, Hillebrandt W (2015) Testing the role of SNe Ia for galactic chemical evolution of p-nuclei with two-dimensional models and with s-process seeds at different metallicities. Astrophys J 799:54. doi:10.1088/0004-637X/799/1/54, 1411.2399 Troja E, Segreto A, La Parola V, Hartmann D, Baumgartner W, Markwardt C, Barthelmy S, Cusumano G, Gehrels N (2014) Swift/BAT detection of hard X-Rays from tycho’s supernova remnant: evidence for titanium-44. Astrophys J Lett 797:L6. doi:10.1088/2041-8205/797/1/L6, 1411.0991 Tutukov A, Yungelson L (1996) Double-degenerate semidetached binaries with helium secondaries: cataclysmic variables, supersoft X-Ray sources, supernovae and accretion-induced collapses. Mon Not R Astron Soc 280:1035–1045. doi:10.1093/mnras/280.4.1035 Waldman R, Sauer D, Livne E, Perets H, Glasner A, Mazzali P, Truran JW, Gal-Yam A (2011) Helium shell detonations on low-mass white dwarfs as a possible explanation for SN 2005E. Astrophys J 738:21. doi:10.1088/0004-637X/738/1/21, 1009.3829 Woosley SE (1997) Neutron-rich nucleosynthesis in carbon deflagration supernovae. Astrophys J 476:801–810 Woosley SE, Howard WM (1978) The p-process in supernovae. Astrophys J Suppl 36:285–304. doi:10.1086/190501 Woosley SE, Kasen D (2011) Sub-Chandrasekhar mass models for supernovae. Astrophys J 734:38. doi:10.1088/0004-637X/734/1/38, 1010.5292

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Woosley SE, Weaver TA (1994) Sub-Chandrasekhar mass models for Type Ia supernovae. Astrophys J 423:371–379. doi:10.1086/173813 Woosley SE, Arnett WD, Clayton DD (1973) The explosive burning of oxygen and silicon. Astrophys J Suppl 26:231. doi:10.1086/190282 Yamaguchi H, Badenes C, Foster AR, Bravo E, Williams BJ, Maeda K, Nobukawa M, Eriksen KA, Brickhouse NS, Petre R, Koyama K (2015) A Chandrasekhar mass progenitor for the Type Ia supernova remnant 3C 397 from the enhanced abundances of nickel and manganese. Astrophys J Lett 801:L31. doi:10.1088/2041-8205/801/2/L31, 1502.04255

Part X Evolution of Supernovae and the Interstellar Medium

Dynamical Evolution and Radiative Processes of Supernova Remnants

75

Stephen P. Reynolds

Abstract

I outline the dynamical evolution of the shell remnants of supernovae (SNRs), from initial interaction of supernova ejecta with circumstellar material (CSM) through to the final dissolution of the remnant into the interstellar medium (ISM). Supernova ejecta drive a blast wave through any CSM from the progenitor system; as material is swept up, a reverse shock forms in the ejecta, reheating them. This ejecta-driven phase lasts until ten or more times the ejected mass is swept up, and the remnant approaches the Sedov or self-similar evolutionary phase. The evolution to this time is approximately adiabatic. Eventually, as the blast wave slows, the remnant age approaches the cooling time for immediate post-shock gas, and the shock becomes radiative and highly compressive. Eventually the shock speed drops below the local ISM sound speed, and the remnant dissipates. I then review the various processes by which remnants radiate. At early times, during the adiabatic phases, thermal X-rays and nonthermal radio, X-ray, and gamma ray emission dominate, while optical emission is faint and confined to a few strong lines of hydrogen and perhaps helium. Once the shock is radiative, prominent optical and infrared emission is produced. Young remnants are profoundly affected by interaction with often anisotropic CSM, while even mature remnants can still show evidence of ejecta.

Contents 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Evolutionary Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Radiation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1982 1982 1985

S.P. Reynolds () Department of Physics, North Carolina State University, Raleigh, NC, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_89

1981

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S.P. Reynolds

2

Dynamical Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Ejecta-Driven Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Sedov Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Radiative Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Radiative Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1988 1988 1992 1992 1994 2001 2001 2002

Introduction

In this review, I shall first give a brief overview of the dynamical evolution and radiative properties of SNRs. I then provide a more detailed discussion of each. I shall assume a basic familiarity with fluid dynamics, shock waves, and radiative processes, at the level of Shu (1991) and Rybicki and Lightman (1979). General physics of the interstellar medium is covered in Spitzer (1978) and Draine (2011). Subsequent chapters in this section cover in more detail most of the issues raised in this review.

1.1

Evolutionary Overview

As described in previous chapters, stellar ejecta are accelerated by the emerging shock wave to speeds ranging as high as 30;000 km s1 but with average values of order 5;000 km s1 for core-collapse (CC) explosions and 10;000 km s1 for Type Ia events. This material may be quite anisotropic, and it initially encounters material which may have been substantially modified by the progenitor system. This circumstellar material (CSM) is likely also to be quite anisotropic, most likely resulting from a stellar wind which may have an azimuthal density dependence or from interaction of the progenitor star with a binary companion. For Type Ia events, it is also possible that the immediate SN environment is almost devoid of material or containing only typical ISM. In either case, the SN blast wave or forward shock begins to decelerate almost immediately as it moves into this surrounding CSM or ISM, heating it to X-ray emitting temperatures, with a “contact discontinuity,” across which the pressure is roughly constant, separating shocked CSM/ISM from ejecta. The rapid expansion at early stages cools the ejecta adiabatically to very low temperatures, so that even a small amount of deceleration of the blast wave results in a velocity difference that is greater than the sound speed in the cold ejecta, and a “reverse shock” is born, facing inward and reheating the ejecta. In even the youngest known SNRs, this reverse shock is inferred to be present (Fig. 1). The evolutionary stage in which both forward and reverse shocks are present can last for hundreds to thousands of years. It is sometimes called the “ejecta-driven” stage. During this stage, the remnant evolution depends on the density structure in the ejecta as well as in the surrounding material. Observational signatures of this phase typically center on the identifiable presence of enhanced elemental

75 Dynamical Evolution and Radiative Processes of Supernova Remnants

1983

Ambient ISM or CSM Shocked ISM or CSM

Shocked ejecta

Unshocked ejecta

Reverse shock Contact discontinuity Forward shock (blast wave)

Fig. 1 Schematic of the two-shock structure of an SNR in the ejecta-driven stage. Rapidly moving, cold unshocked ejecta are heated and decelerated at the reverse shock. Hot ejecta are separated from shocked ambient material at a contact discontinuity. The forward shock or blast wave heats and accelerates ambient ISM or CSM

abundances in X-ray spectra. Relative contributions from the forward and reverse shocks depend on density structure as well. However, the energy radiated is a small fraction of the kinetic energy released in the explosion, so this evolution is approximately adiabatic. The progressive deceleration of the blast wave can be conveniently described with an “expansion parameter” m defined by Rs / t m , with Rs the (forward) shock radius. Undecelerated expansion with m D 1 almost immediately gives way to m < 1, and various analytic solutions exist describing subsequent evolution. However, numerical simulations demonstrate the gradual decrease in m as swept-up material comes to dominate the expansion: The five youngest Galactic shell SNRs are shown in (Figs. 2–5). For constant-density ambient material, after about ten times the ejected mass has been swept up, the value of m approaches 0.4, its value for the idealized Sedov selfsimilar solution for a point explosion in a uniform medium. (There is also a Sedov solution for expansion into a power-law density gradient  / r s ; for s D 2, appropriate for a steady spherically symmetric stellar wind, m approaches 2/3. However, this situation may not often be realized in practice.) Thus both the ejecta-driven and Sedov phases can be termed adiabatic. (The ejecta-driven phase is still occasionally referred to as the “free-expansion” phase, but this is not really accurate.)

1984

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Fig. 2 Remnants of the two most recent known supernovae in the Milky Way. Left: G1.9+0.3 (about 1900 CE) (X-rays) (K. Borkowski). Center: Cassiopeia A (5 GHz, VLA; DeLaney et al. 2014). Right: Cassiopeia A (about 1680 CE). Green: Si band. Red: Fe K˛ band. (both with Chandra ; U. Hwang). Blue: 44 Ti emission (68 keV) with NuSTAR (Grefenstette et al. 2014)

Fig. 3 The remnant of Kepler’s supernova of 1604 CE. Left: radio (VLA at 5 GHz; T. DeLaney). Center: Spitzer MIPS at 24 m (deconvolved; K. Borkowski). Right: Chandra between 0.3 and 7 keV (Reynolds et al. 2007)

Fig. 4 The remnant of Tycho’s supernova of 1572 CE. Left: radio (VLA at 5 GHz; Reynoso et al. 1997). Center: Spitzer MIPS at 24 m (Williams et al. 2013). Right: Chandra image (NASA/CXC)

For CC remnants, a neutron star is likely to be present. If it functions as a pulsar, it can inflate a bubble of relativistic particles and magnetic field, a pulsar-wind nebula (PWN), in the remnant interior. For a young, luminous pulsar, the PWN can expand and overtake inner ejecta, driving a shock into them with possible observational

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1985

Fig. 5 Left: Remnant of SN 1006 CE (X-ray, Chandra ; Winkler et al. 2014). Right: G11.2–0.3, roughly 2000 y old (X-ray, Chandra ; Borkowski et al. 2016)

consequences. However, for all but exceptional cases, the pulsar energy input is not sufficient to alter the gross evolution of the shell SNR. PWNs are the subject of a later chapter. As the blast wave decelerates, eventually the timescale for radiative cooling of the shocked material becomes comparable to the remnant age. (Cooling is typically by UV, optical, and near-IR fine-structure transitions of astrophysically common elements such as C, O, and Fe.) This is normally for shock speeds vs  200 km s1 , only weakly dependent on density, with corresponding ages of order 10,000 or more years. Once cooling is important, deceleration is more rapid, though the continuing presence of hot gas in the SNR interior, where cooling times are longer, continues to operate in what is called a “pressure-driven snowplow,” with m  0:3: If that pressure is negligible, material essentially coasts, conserving (local) momentum, with m ! 0:25: However, by these late stages, most remnants have been interacting with inhomogeneous ISM for some time and are quite irregular, with properties varying substantially with position in the remnant. Densities in cooling shocks can be quite high, as the compression may be limited only by magnetic pressure, so radiative-phase remnants can be quite bright in optical emission. Eventually, shock speeds become comparable to local sound speeds, and the SNR dissipates into the ISM.

1.2

Radiation Overview

At different stages, SNR radiation is dominated by different processes. After the initial SN light has declined, the rapid expansion of the ejecta cools them to very low temperatures. However, the very strong, highly supersonic blast wave heats surrounding material to X-ray-emitting temperatures. Since all the relevant astrophysical shock waves in SNRs are collisionless (gas is heated not by binary collisions among particles but by interaction with a magnetic field), the particle distribution downstream is not perfectly Maxwellian. Instead, diffusive shock

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acceleration (DSA) of a small fraction of electrons crossing the shock produces a (nearly) power-law nonthermal tail attached to the thermal peak of the electron energy distribution. The tail normally extends to relativistic energies, where electrons can radiate synchrotron radiation at radio wavelengths. For appropriate conditions, the synchrotron component can extend all the way to the X-ray band. Optical emission at early stages is faint. These fast shocks are called “nonradiative”; cooling times of the shocked gas are initially much longer than the shock age, so relatively little radiation is produced, and the compression ratio r has the value appropriate for a strong (highly supersonic) adiabatic shock into monatomic gas, r D 4. However, some radiation can be detected from such shocks; if the remnant expands into neutral material, hydrogen can be excited before being ionized and radiate Lyman and Balmer-series photons. Infrared radiation at early stages is predominantly thermal radiation from dust grains heated by collisions with hot gas; the temperature of that infrared emission is a good diagnostic of plasma density. As the blast wave decelerates, the initially weak and radiative reverse shock strengthens and becomes nonradiative. The reverse shock reheats the ejecta that overtake it, rendering them observable in X-ray emission. SNRs in this stage primarily radiate radio synchrotron emission and thermal X-ray emission from roughly solar-abundance gas behind the blast wave and from enhanced abundances of heavy elements behind the reverse shock. Disentangling these two contributions is a significant challenge in studying ejecta-driven SNRs. The process of collisional ionization of heavier elements in either the shocked CSM/ISM or the shocked ejecta is not instantaneous. In fact, plasmas in young SNRs are typically underionized, that is, at a lower stage of ionization, than would be the case for a gas in equilibrium at the observed temperature. This nonequilibrium ionization (NEI), as it is called, means that X-ray spectra depend on R a parameter  ne dt , the “ionization timescale,” which controls the degree of ionization of the plasma. In a shock wave, gas with all values of from zero up to the shock age can emit radiation. When exceeds a few times 1012 cm3 s, plasma is close to collisional ionization equilibrium (CIE). For typical ambient densities of order 1 cm3 , this occurs in 30,000 year. The ionization state of the plasma at this stage does not affect the overall dynamics, however. Infrared emission can be produced by radiation from collisionally heated grains in either the shocked CSM/ISM or, if dust is formed in the cool ejecta, in the post-reverse-shock region. Line emission can be detected from unshocked ejecta in regions of particularly high density. Finally, a few of the youngest remnants produce detectable emission that is not related to shocks at all but results from the decay of radioactive 44 Ti into 44 Sc and then 44 Ca, with the emission of hard X-ray and gamma ray nuclear de-excitation lines and a line at 4.1 keV from filling the vacancy resulting from the electron capture decay of 44 Ti to 44 Sc. Once the reverse shock has disappeared and the remnant is fully in the Sedov stage, spectral signatures of enhanced-abundance ejecta may still be present in Xrays in the interior. However, the shocked CSM/ISM mass dominates the shocked ejecta and the integrated spectrum. IR continuum from heated grains can still be produced.

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Fig. 6 Three older SNRs. Left: Three-color image of W28. Red: infrared; cyan: H˛; blue: radio (VLA) (NRAO/AUI/NSF; Brogan et al.) Center: Cygnus Loop (X-ray; ROSAT) (NASA/GSFC). Right: Puppis A (X-ray; ROSAT) (NASA/GSFC)

The onset of radiative cooling dramatically alters the spectral energy distribution (SED) of an SNR. Now, UV, optical and IR-permitted, forbidden, and fine-structure transitions produce optically bright spectra dominated in optical by low ionization stages of elements like sulfur and oxygen. In fact, for SNRs in external galaxies, a powerful method of identifying radiative-stage remnants is the ratio of [S II]  6717, 6731 to H˛ flux, which is very much different for a radiative shock than for photoionized H II regions. Since adiabatic-phase SNRs do not produce bright optical emission, this method does not identify them. However, most of the observable life of an SNR is spent in the later phases, so a relatively small fraction of remnants in other galaxies is overlooked. For shock velocities below 200 km/s or so, X-ray emission is now quite weak. Nonthermal radio synchrotron emission from electrons with GeV energies can persist and remains the most easily observed observational signature of SNRs. The high compression ratios characteristic of radiative shock waves will also enhance the synchrotron brightness. Figure 6 shows three older SNRs with mainly radiative shocks. Nonthermal emission at X-ray wavelengths and above can be observed in a few remnants. Sufficiently energetic relativistic electrons (and positrons, if present) can produce not only synchrotron emission up to X-rays but inverse-Compton emission from upscattering any photon fields (cosmic microwave background and possibly any locally strong IR or optical radiation) and bremsstrahlung from interaction with thermal ions. These leptonic contributions can extend to GeV and even TeV photon energies. In addition, the shock acceleration process is expected to accelerate ions as well. While they do not directly radiate, they can inelastically scatter from thermal ions, producing charged and neutral pions (and secondary positrons and electrons). The charged pions decay eventually to electrons and positrons, but the neutral pions decay to pairs of gamma rays once the cosmicray proton energies are sufficient to produce 0 particles (around 70 MeV). This “hadronic” process is the only direct evidence for cosmic-ray ions in SNRs. See Reynolds (2008) for a review of supernova remnants with emphasis on high-energy radiative processes.

1988

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Dynamical Evolution

I shall now consider in more detail the dynamical evolution, dividing the discussion into the phases outlined above: ejecta driven, Sedov, and radiative.

2.1

Ejecta-Driven Evolution

We can consider the “initial conditions” for supernova-remnant evolution to be the distribution of ejected material once pressure forces from the original explosion are negligible (“ballistic expansion”). This is certainly true for all but very exceptional cases after a few weeks. The density profile of expanding material is determined by the density structure of the progenitor star and its interaction with the shock wave that disrupts the star. Early 1D hydrodynamic simulations showed that both CC (nondegenerate) and Type Ia (degenerate) progenitors produced expanding profiles roughly describable as a central region of roughly constant density and an outer region of steeply declining density following an approximately power-law density dependence,  / r n with n  7 for white dwarf progenitors and n  10–12 for CC progenitors. More extensive hydrodynamic simulations and analytic calculations have refined these numbers somewhat. Dwarkadas and Chevalier (1998) find that exponential density profiles provide better fits to simulations for Type Ia SNRs. Matzner and McKee (1999) used realistic 1D stellar progenitor models for CC events and calculated the resulting ejecta distribution after the passage of the original supernova shock wave. The steep outer power laws are reproduced, but there is a clear density jump (corresponding to the original interface between the progenitor’s hydrogen envelope and interior) of about a factor of 3–10, within which the density is very roughly constant. Of course, real supernovae are not likely to be perfectly spherical. Rotation of the progenitor is an obvious cause of asymmetry, but in addition, the fundamental explosion mechanism may be asymmetric. If the standing accretion shock instability (SASI, Blondin et al. 2003) or another convective instability is important for CC events, material may be primarily ejected in one direction, with a high-velocity neutron star moving off in the opposite direction. In addition to large-scale asymmetries such as these, there may be smaller-scale clumping or other irregularities. Ejecta clumps are seen ahead of the average blast-wave radius in most young, and a few older, SNRs, and high-density knots of fast-moving material with enhanced abundances are seen in Cas A (roughly 330 year old). (See, e.g., Winkler et al. 2014 for SN 1006 and Hammell & Fesen 2008 for Cas A.) Radiative knots in the interior of Kepler’s SNR (CE 1604) may be CSM, but some knots ahead of the blast wave are ejecta (Reynolds et al. 2007). As the 56 Ni synthesized in a CC explosion decays, its decay products will heat local material which will then expand into cooler ejecta (the “nickel bubble” effect; Li et al. 1993). The effect is enhanced if the 56 Ni is not uniformly distributed but in clumps instead. This effect may well produce inhomogeneities in SN ejecta that are detectable in young SNRs (Fig. 6).

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The immediate surroundings of the SN are almost certainly not uniform. A steady-state constant-velocity wind in spherical symmetry produces a 1=r 2 density profile. For spherical power-law supernova ejecta with e / r n encountering a surrounding medium with  / r s , similarity solutions exist for the shock radii and for the density and pressure profiles everywhere. Outer shock waves in such cases have values of the expansion index m intermediate between 1 and the Sedov uniform-density value of 0.4: in fact, m D .n  3/=.n  s/, as long as n > 5 and s < 3 (Chevalier 1982; Nadezhin 1985). As required by the self-similarity, the ratio between forward and reverse-shock radii is constant; both move out, but the reverse shock is overtaken by faster-moving ejecta. The character of the solutions is quite different depending on the outer index. For the steady wind value of s D 2, the density peaks at the contact discontinuity; since the pressure is roughly uniform, the temperature decreases there. For uniform ISM (s D 0), the density drops to zero at the contact discontinuity, and the temperature rises. The same qualitative behavior occurs for decreasing, but non-power-law, ejecta density profiles, such as the exponential profile. Figures 7 and 8 show 1D hydrodynamic simulations of a blast wave with power-law density profile moving into a uniform medium and a steady wind. The shock radii are scaled by t 0:4 (the Sedov value). Quantities are plotted as a function of the swept-up mass in units of the ejected mass. While the forward and reverse shocks in the ejecta-driven phase are hydrodynamically stable, the region between them is not, in general. The Rayleigh-Taylor instability of a heavy fluid supported by a light one (or, in general, if the effective gravity g opposes the density gradient r, g  r < 0) operates as the deceleration provides an effective inward gravity, and outer less dense material decelerates denser inner material. The growth rate of this instability is maximum at the contact discontinuity. It may produce turbulence that could accelerate particles; this may explain the bright ring of radio emission seen inside the outer blast wave of Cas A. However, the surroundings may not even be spherically symmetric. It is becoming increasingly apparent that a large fraction of supernovae occur in binary systems. All SNe Ia, of course, result from binaries, but several categories of CC event, such as SNe Ib/c and IIb, seem to result from stripped cores which probably require a binary companion (Smith et al. 2011). The companion star may be near enough to decelerate ejecta, possibly producing effects detectable in remnants for hundreds of years. Even if not, mass lost from either the companion or the SN progenitor star itself is likely to be asymmetric in the immediate neighborhood, probably focused into the orbital plane in a disk wind. (See Smith (2014) for a review of mass loss in massive stars.) An SN blast wave encountering an equatorially enhanced CSM, with the whole system moving at high velocity, seems to be the picture required to explain various features of Kepler’s SNR (Burkey et al. 2013). Winds of supernova progenitor systems go through various phases. A massive OB star will have a fast wind while on the main sequence, but as a red giant is likely to produce a slow, dense wind with a much higher mass-loss rate. Thus, the CSM into which the SNR expands may be highly structured. The cumulative effect of the various wind phases is generally to produce a low-density cavity or bubble (Castor et al. 1975), eventually of roughly constant density except near the star if

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Fig. 7 Top: Shock locations and forward-shock expansion index m for the case n D 6, s D 0. Shock positions are scaled by t 0:4 (the Sedov value). Bottom: Profiles of density, temperature, and pressure during the self-similar phase for this calculation (J. Blondin, private communication)

mass loss continues. There is evidence that such cavities can be produced by both CC and Type Ia progenitor systems; the SN Ia remnant RCW 86 is an excellent example of the latter (Williams et al. 2011). An SN blast wave can race through the low-density cavity, remaining strong but not terribly luminous, until encountering the cavity wall, where a much slower transmitted shock moves into the wall while reflected shocks reheat the bubble interior. Pre-SN wind phases, or, for massive stars, episodic mass loss shortly before the SN, can result in a shell of CSM at a range of possible distances. The SNR blast wave will slow on encountering the shell but can

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1991

Fig. 8 Top: Shock locations and forward-shock expansion index m for the case n D 6, s D 2. Shock positions are scaled by t 0:4 (the Sedov value). Bottom: Profiles of density, temperature, and pressure during the self-similar phase for this calculation (J. Blondin, private communication)

accelerate again after traversing it. This can result in overionized shocked plasma, with observational consequences (Yamaguchi et al. 2009). Any structure in the ambient ISM will also affect SNR evolution. SNe Ia may be encountering such material after only a few hundred years; there is evidence that Tycho’s SNR (CE 1572) is interacting with such material (Williams et al. 2013). However, the ISM near Tycho appears to have a substantial gradient in density, with densities a factor of 6 or more higher on one side than the other, in addition to smaller-scale variations. Hydrodynamic simulations of remnants expanding into a

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smooth density gradient show that they can remain remarkably round for hundreds or thousands of years but that their geometric centers can depart from the true explosion location by tens of percent of the mean remnant radius, complicating any search for remaining binary companions (Dohm-Palmer and Jones 1996). In general, while the simple spherically symmetric analytic pictures are adequate for rough categorization of SNRs, detailed descriptions of individual objects require hydrodynamical simulations, generally in two and three dimensions.

2.2

Sedov Evolution

As long as the ejecta moving through the reverse shock are part of the envelope material with a steep density profile, the ram pressure upstream (inside) the reverse shock can keep it moving outward as higher-density material arrives. However, when the roughly constant-density central ejecta reach the reverse shock, this is no longer the case, and the reverse shock will move back toward the remnant center. In 1D analytic or numerical calculations, it reflects strongly, but in 2D and 3D (and, presumably, in reality), the reverse shock does not return exactly to the remnant center but reverberates in a complex way for a substantial transition period. However, once all the ejecta have been shocked by the reverse shock, we may assert that the remnant is fully in the Sedov stage. Analytic solutions (Sedov 1959) describe the run of density, pressure, and temperature behind the shock. The shock radius is given by a simple analytic expression: Rs D 1:15.E=/1=5 t 2=5 , where E is the explosion energy and  the ambient (uniform) density (We presume a ratio of specific heats of 5/3.) (Fig. 9). Analytic solutions have been produced by Truelove and McKee (1999) that describe the evolution in spherical symmetry from the early ejecta-driven stage through the transition into Sedov evolution. While there are self-similar solutions for a point explosion in a medium with an arbitrary power-law density profile (Sedov 1959), in almost all cases, uniform ambient density will be the best approximation. That produces a solution in which the post-shock velocity is almost linear from zero at the center to 3/4 of the blast wave speed just behind the shock, the density drops steeply with most of the mass within the outermost 10% of the radius, and the pressure drops slightly behind the shock, leveling out in most of the interior at about 0.3 times its post-shock value. This means the temperature rises to unphysical values at small radii; in general, the interior of a Sedov blast wave consists of very hot, low-density material.

2.3

Radiative Phase

A perfectly spherical remnant in a perfectly uniform medium would experience a sudden transition when its age reached a characteristic cooling time for the gas (which depends on its composition; initial cooling is from Fe, and, as the shock slows, from elements such as C and O). At that point, gas behind the shock would

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Fig. 9 Top: Sedov self-similar profiles of velocity, pressure, and density for a blast wave into uniform-density surroundings. Bottom: Sedov profiles for a blast wave into an r 2 density profile. Density and velocity profiles are identical in this case; both are linear with radius. (J. Blondin, private communication)

radiate away significant amounts of energy and become much more compressible. The overall shock compression ratio would rise until some other mechanism, perhaps magnetic fields, limited further compression. Hydrodynamic simulations in one and two dimensions show that the onset of cooling is sudden, with the rapid formation of a cool dense shell subject (in 2D and 3D) to instabilities which rapidly disrupt it (Blondin et al. 1998). By this time, a typical remnant is so large that the ISM it encounters is unlikely to be uniform. Remnants may encounter strong ISM inhomogeneities, such as dense molecular clouds, or may produce “blowouts” into

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much less dense regions (e.g., 3C 391; Reynolds and Moffett 1993). Dense material near an SNR can serve as a target for escaping cosmic-ray ions, which can produce gamma rays from the decay of 0 ’s produced in inelastic collisions with thermal gas (e.g., W28: Aharonian et al. 2008). Since the remnant interior has a much lower density than the outer regions, it has a much longer cooling time and that gas can remain adiabatic long after the immediate post-shock gas has cooled. It can provide significant pressure to keep the expansion parameter significantly above the value of 0.25 that characterizes purely momentum-conserving evolution (Blondin et al. 1998). Remnants in this stage are large, complex objects with typically large variations in conditions at different locations. See Fig. 6 for images of later-stage SNRs.

3

Radiative Processes

As a remnant evolves through the stages outlined above, the characteristic radiation it emits changes as well. “Prompt” X-ray and radio emission from the original supernova event, generally attributed to interaction with a CSM of decreasing density, may take years to decay away. At some point, thermal X-ray emission from the increasing volume of shock-heated gas and synchrotron emission from a nonthermal electron distribution whose maximum energy rises with time produce true remnant X-ray and radio emission. Only one Galactic object has been caught in this rising phase: the remnant of the most recent known Galactic supernova, G1.9+0.3, brightening at both radio and X-ray wavelengths (Carlton et al. 2011). SNR 1987A in the LMC is also brightening in both regimes (see the review “ Chap. 83, “The Physics of Supernova 1987A” in this volume). Ejecta emission. The unshocked ejecta rapidly cool over the months after the explosion to temperatures of order 100 K. However, the ejecta are illuminated by UV and soft X-ray emission from the interaction region between the blast wave and newly formed reverse shock. This radiation can ionize elements with low ionization potentials to produce near and mid-IR fine-structure lines from species such as singly-ionized iron, argon, and neon. In Cas A, where this emission can be studied in detail, temperatures of a few thousand K and densities . 100 cm3 are deduced in the unshocked ejecta, although only in the denser regions; a considerable amount of lower-density material could still be present. (See Isensee et al. 2010 for a thorough study.) Shocked ejecta will typically be heated to X-ray-emitting temperatures, kT & 1 keV. However, evidence from comparing X-ray and optical data indicates that the electron and ion temperatures are not equal in fast shocks (Itoh 1978). A shock initially randomizes electron and ion speeds, so that the pre-shock bulk velocity is (mostly) converted to post-shock random velocity. But if ion and electron speeds are equal, proton and electron temperatures would differ by the ratio of masses. The timescale for electrons to equilibrate in temperature with one another, tee , is extremely rapid, as is the equivalent for protons, ti i . These are the timescales on

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which Maxwellian distributions are produced (e.g., Spitzer 1978). But electron-ion temperature equilibration takes place on a much longer timescale, so electrons and ions can have different temperatures for times not short compared to the ages of young supernova remnants. (Once full temperature equilibration has been attained, the gas will have the temperature given by the Rankine-Hugoniot shock jump conditions, kTs D .3=16/mp vs2 , where mp is the mean mass per particle behind the shock.) Observationally, electron temperatures determine the ionization state of the gas, and strengths of lines, while ion temperatures can only be inferred from line widths, if Doppler broadening due to bulk motions can be removed. Typical electron temperatures deduced in young SNRs are several keV, though kTs can be 20 keV or higher (e.g., Rakowski 2005). The emission produced by such ejecta is a combination of bremsstrahlung continuum and line emission characteristic of the ionization state of the gas. As with electron-ion temperature equilibration, ionization is not instantaneous, and SNR plasmas are very frequently ionizing (i.e., their ionization state lags behind that of an equilibrium plasma at the same temperature; Itoh 1977). Ionization is typically quite rapid up to helium-like states of common elements, though lithiumlike states of iron can be present as well. So a typical SNR X-ray spectrum at CCD energy resolution (E=E  20) is dominated by blends of helium-like triplets (K˛ lines) of O, Ne, Mg, Si, S, Ar, and Ca. (See the  Chap. 78, “X-Ray Emission Properties of Supernova Remnants” in this volume.) In SNe Ia, L-shell transitions of Fe tend to produce a broad peak around 1 keV. Grating or microcalorimeter energy resolution (E=E & 100) is required to resolve these triplets. Since ejecta contain much higher proportions of heavier elements, those line complexes are normally substantially stronger than the continuum, as compared with solarabundance plasma. Temperatures in the keV range are reached for ejecta densities of order 1 cm3 . If clumps are present, such as the “FMKs” (fast-moving knots) seen in Cas A, the densities can be very much higher – high enough that the shocks driven into clumps may have speeds down to a few km s1 . Such a shock will be radiative, and the resulting clump emission can be primarily observed in forbidden lines of ions such as OC and OC2 . Post-shock densities in such clumps can be 103 cm3 or greater (Peimbert and van den Bergh 1970). If dust is formed in the cold unshocked ejecta, it can be radiatively heated by the local UV photon field or, more likely, collisionally heated once it passes through the reverse shock (e.g., Dwek and Arendt 1992). Dust in unshocked ejecta has been detected in a few cases; since the temperatures are only a few tens of K, this radiation is in the far IR. The Herschel mission has found evidence for cold dust in a few SNRs (e.g., SNR 1987A: Matsuura et al. 2011). However, in most cases, the infrared continuum one expects for ejecta dust heated in the reverse shock is not present, and limits can be set on the mass of dust produced in the SN and surviving the passage of the reverse shock (e.g., Gomez et al. 2012). Blast wave emission. The forward shock also heats surrounding CSM or ISM to comparable temperatures, normally somewhat higher than in the reverse shock. Here

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too, the issues of incomplete temperature or ionization equilibrium are important. A typical pre-Sedov SNR will show a thermal X-ray spectrum which is a complex mix of blast wave and reverse-shock emission, with varying temperatures. Decomposing that complex spectrum into the constituent parts is a demanding task. For a CC remnant, the blast wave normally encounters ionized material. For a red supergiant (RSG) progenitor, the pre-explosion spectrum includes relatively little ionizing radiation, but the shock breakout of the RSG envelope will produce a UV flash that can ionize all the surrounding material (normally the RSG wind) out to a distance that can be many pc. A compact progenitor that has lost most of its envelope would not produce such a UV flash but would have had a much stronger pre-explosion ionizing flux (Reynolds et al. 2007). In contrast, all Type Ia SNRs less than a few thousand years old show emission from nonradiative or Balmer-dominated shocks, resulting from partially neutral upstream gas (Heng 2010). Neutral H atoms do not feel the magnetically mediated collisionless shock and remain at rest as the shock sweeps over them. On being suddenly immersed in 107 K plasma, most are immediately collisionally ionized, but a few are first excited and can emit Balmer-series photons before being ionized. Those photons show a Doppler broadening reflective of the (cold) preshock distribution, resulting in a narrow line. Some H atoms are ionized by charge exchange, resulting in a fast neutral atom which can also emit Balmer photons, but with a velocity distribution characteristic of the downstream proton distribution, resulting in a broad line. The relative strengths, widths, and centroids of broad and narrow components of lines from nonradiative shocks contain a great deal of information about the upstream neutral fraction, the shock geometry, and the upand downstream temperatures. See Heng (2010) for a review. For young remnants, the presence of nonradiative, Balmer-dominated shocks is strong evidence in favor of a Type Ia origin. (See the Chaps.  84, “The Supernova – Supernova Remnant Connection” and  85, “Supernova Remnants as Clues to Their Progenitors” for more information on typing SNe from their remnants.) SNR blast waves are virtually always easily detectable by their synchrotron radio emission. For the typical magnetic fields of tens to hundreds of microgauss, this requires electron energies of order 1–10 GeV; electrons radiating their peak synchrotron energy at frequency have energies E D 14:7. GHz =BG /1=2 GeV. For most remnants, ongoing electron acceleration is required; the interstellar cosmicray electron energy spectrum is considerably flatter than what is seen in SNRs, and for young remnants with adiabatic shock waves in particular, the limited shock compression means that compressing ambient magnetic field and electrons cannot produce the observed radio surface brightnesses typical of young remnants (Reynolds 2008). The radio spectra are well described by power laws, S / ˛ with ˛ 0.4–0.7 for most objects. Young SNRs tend to have steeper radio spectra; Cas A has ˛ D 0:77. See Green (2014) for an extensive compilation of observations of 294 Galactic SNRs. The theory of diffusive shock acceleration (DSA) is generally thought to be responsible for the relativistic particle populations we infer in SNRs. The review by Blandford and Eichler (1987) is still an excellent introduction. If nonthermal

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fluid velocity

dynamical precursor

u1

Larger compression ratio "thermal subshock"

u2 x=0

upstream

shock

downstream

Fig. 10 Schematic of a cosmic-ray modified shock. Dotted line: velocity profile of test-particle shock. Solid line: same for a modified shock. In the shock frame, material enters from the left and is gradually decelerated by cosmic rays diffusing upstream in a “dynamical precursor” until a sharp drop in speed at the thermal subshock. The overall shock compression ratio can be considerably larger than in an unmodified shock

particles make up a small fraction of the post-shock energy density (the “test-particle limit”), DSA predicts a particle spectrum N .E/ / E s with s D 2 in a strong shock (Mach number M  1) with compression ratio r D 4. The synchrotron spectrum from such a population of electrons is a power-law with ˛ D .s  1/=2 D 0:5. However, if SNRs are the source of Galactic cosmic rays, the total Galactic content of cosmic-ray energy requires that of order 10% of SNR energy be put into fast particles – too large for the test-particle limit. In this case, the fast particles can modify the shock structure as they diffuse ahead of the shock, producing a gradual rather than sudden change in flow velocity, until a “viscous subshock” with a compression ratio of 2–3 and thickness of a few ion mean free paths heats the gas (Fig. 10). Then if (as is likely) particle mean free paths increase with energy, more energetic particles diffuse further ahead of the shock before being scattered back, sampling a larger compression ratio and forming a locally harder spectrum. That is, the energy distribution of accelerated particles becomes concave up, steeper than the test-particle limit at low energies and flatter at high energies. This effect could produce the steeper radio spectra of young SNRs. However, the large numbers of older SNRs with ˛ < 0:5 are still difficult to explain. Contamination of the spectrum with optically thin thermal bremsstrahlung (˛ D 0:1) at higher energies could be responsible in some cases. The maximum energy to which particles can be accelerated depends on the shock age, magnetic field, and other properties (Reynolds 1998). The time tacc .E/ to reach an extremely relativistic energy E, for both electrons and protons, depends on the diffusion coefficient .E/ and shock speed vs , where  D mfp c=3. The mean free path mfp is often assumed proportional to the particle gyroradius rg , mfp D rg (“Bohm-like” diffusion, with  D 1 giving the “Bohm limit.”) In this case, tacc  .E/=vs2 , so fast shocks can produce much higher energies. Since rg D E=eB for relativistic particles (cgs units; e is the electronic charge), high magnetic fields also produce more rapid acceleration. For ions, radiative losses are insignificant; the limitation is basically the shock age, t D tacc . For electrons, radiative losses

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due to synchrotron radiation or inverse-Compton upscattering of any local photon fields can limit the maximum energy much more severely. For synchrotron losses, Emax / B 1=2 . However, since an electron of energy E radiates its peak synchrotron power at a frequency / E 2 B, the peak frequency max radiated by a distribution of shock-accelerated electrons limited by losses is independent of the magnetic-field strength B. For young remnants with shock velocities of order 1000 km s1 or greater, h max can easily exceed 1 keV, so synchrotron radiation is produced all the way from radio to X-ray energies, with electron energies reaching 10 TeV or more (Reynolds and Chevalier 1981). Thermal emission at optical and infrared wavelengths normally swamps this contribution, although near-IR observations of Cas A have identified a synchrotron contribution. However, in X-rays, a handful of Galactic remnants are dominated by synchrotron emission (including most notably the youngest Galactic SNR, G1.9+0.3), while all historical shell SNRs show local regions dominated by synchrotron – usually, but not always in “thin rims” at the location of the blast wave. If the rims are thin because electrons rapidly lose energy as they advect downstream, magnetic-field values of 100 G or higher are inferred (Parizot et al. 2006). These particle energies can result in significant photon emission above the X-ray region, at GeV and TeV energies. See Reynolds (2008) for a review. Depending on the energy density of the local radiation field, inverse-Compton scattering by the same relativistic electrons can make substantial contributions, with a minimum set by upscattering of cosmic microwave background photons (“ICCMB”). In addition, mildly relativistic electrons (the same that produce radio synchrotron) can produce a nonthermal bremsstrahlung contribution. Protons and other ions ought to reach energies at least as high as electrons in DSA. Relativistic ions do not radiate significantly but can produce pions through inelastic collisions with thermal gas, once they reach the energy threshold of about 70 MeV. The neutral pions decay to gamma rays which can be detected. There are currently a dozen or more SNRs with detected gamma ray emission in the Fermi LAT band (GeV) or by ground-based ˇ air-Cerenkov detectors (TeV). The question of whether the gamma ray emission from these objects is due to leptons or hadrons is actively discussed. Hadronic domination requires substantial thermal target densities. Escaping particles ahead of the SNR blast wave may impinge on dense clouds to produce emission in some cases. The evolution of the synchrotron radio emission from an SNR is straightforward to estimate, for various possible assumptions about the efficiency of shock acceleration and magnetic-field amplification. The synchrotron volume emissivity due to a power-law energy distribution of electrons N .E/ D KE s cm3 erg1 can be conveniently written j D cj .˛/KB 1C˛ ˛ (e.g., Pacholczyk 1970). Then the flux density from a spherical remnant at distance d is given by  S D .4 j /

Rs3  3d 2

 (1)

75 Dynamical Evolution and Radiative Processes of Supernova Remnants

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where  is the volume filling factor of emitting material (  0:25 for a Sedov remnant with shock compression ratio 4). If the shock puts constant fractions B and e of the post-shock pressure vs2 into magnetic-field energy and electron energy, respectively, and if the upper and lower bounds on the electron distribution Eh and El do not change, we have .1C˛/=2

S / B

e Rs3 .3C˛/=2 vs3C˛ / t m.6C˛/.3C˛/

(2)

since if Rs / t m , then vs / t m1 . This assumes constant ambient density. For a remnant with a typical value of ˛ D 0:5, S / t 6:5m3:5 D t 0:9 for a Sedov remnant (m D 0:4), and rises with time for an ejecta-driven remnant with m > 0:54 (although the simple assumptions made here may not hold for such early times). For a remnant encountering a steady wind with  / r 2 , we have S / t 3m3:5 (still with ˛ D 0:5) which never increases. Other assumptions are possible. If the magnetic field is not amplified but is simply compressed from a uniform value upstream, and the ambient density is uniform, then S / t 5m2 which is constant in the Sedov phase. The shock may accelerate all electrons with energies above some threshold which varies with shock velocity. Or efficiencies may change with time. It is not known at present which of these assumptions is correct. At this time, only the Galaxy’s youngest SNR, G1.9+0.3, is brightening with time at radio frequencies (Murphy et al. 2008), while the next three youngest, Cas A, Tycho, and Kepler, are all fading, at rates between 0.2 and 0.7% yr1 (Stankevich et al. 2003; Vinyaikin 2014). (An exception is the SN(R) 1987A in the LMC, which is brightening at both radio and X-ray wavelengths (Helder et al. 2013; Zanardo et al. 2010)). For reasons still not completely clear, reverse shocks are not obvious particle accelerators. The theory of DSA has been very successful in interpreting forwardshock nonthermal emission, but there may be circumstances in which other processes, such as stochastic or turbulent acceleration, play a role. The nonthermal X-ray emission in Cas A above 20 keV (Grefenstette et al. 2015) does not appear to be associated with either the forward or reverse shocks and is still not fully understood. Infrared continuum emission can be produced by any dust present either in the ejecta or the ISM/CSM. Many remnants show emission in mid-IR bands such as Spitzer ’s 24 m band which is morphologically well correlated with radio emission and is consistent with being produced by collisional heating of surrounding dust by the forward-shocked plasma (Borkowski et al. 2006; Williams et al. 2006). This heating process depends strongly on the plasma density and much less strongly on the plasma temperature, so IR spectra, or even two-point color temperatures, can provide powerful diagnostics of SNR densities. The results can be surprising; the symmetric circular outline of Tycho’s SNR masks density variations of a factor of 6 or greater (Williams et al. 2013). Later stages. Once the reverse shock has disappeared and all ejecta have been reheated, a spherical remnant can be well described by Sedov profiles of density

2000

S.P. Reynolds

and temperature. Typically by this stage, gas in the outermost 10% or so of the radius (most of the material) is dense enough that electron and ion temperatures have come into equilibration, andRionization equilibrium has been reached as well (i.e., the ionization timescale  ne dt & 312 cm3 s). While this considerably simplifies X-ray spectral analysis, the plasma temperature still varies widely, rising from its immediate post-shock value toward the interior. For the fast shocks of young remnants, single-temperature plane shocks may provide adequate descriptions in restricted band-passes. Structure in the surrounding medium, either modified CSM or pre-existing inhomogeneities, can result in non-monotonic evolution of the blast wave speed. If the shock breaks out of a denser region into a less dense one, rapid adiabatic cooling can leave the shocked plasma in an overionized state. Spectral diagnostics of this state, including radiative recombination continuum and line ratios inconsistent with temperatures derived from X-ray continua, have been seen in a few SNRs, of which one of the first was the middle-aged remnant W49B (Ozawa et al. 2009). The primary change in emission properties of an SNR at late stages is the appearance of bright optical emission as the shocks become radiative and roughly isothermal. That is, an initial jump in density of a factor of 4 at the shock is followed downstream by a much larger density increase in the “cooling layer,” where much of the shock energy is radiated. This layer can be identified by bright emission from such species as OC2 . Compressions can reach factors of 100 or more, so regions with densities of 103 cm3 and higher now dominate the remnant spectrum. Shock speeds are now in the range of 100 km s1 or lower; optical diagnostics of various line ratios are available to characterize the temperature and density of such regions. Radiative shocks are complex and heterogeneous, typically involving a superposition of shock speeds, but models do a fairly good job of accounting for ratios of line strengths of many species that can be observed (Cox and Raymond 1985; Innes et al. 1987). The high compressions mean that radio emission can be quite bright as well, as even without additional electron acceleration, energy densities of ambient cosmicray electrons and magnetic field can be increased by large factors (van der Laan 1962). Gas densities from optical diagnostics heavily favor very dense regions that occupy relatively little volume and so are probably not typical of most of the radioemitting volume. With shock velocities of 100 km s1 or lower, ongoing particle acceleration is probably weak at best. Some tendency of the very oldest SNRs to have the flattest radio spectra may simply reflect the greater importance of thermal radio contamination (Oni´c 2013). Most extragalactic SNRs are found with methods that favor large optically bright radiative remnants. (See “ Chap. 76, “Galactic and Extragalactic Samples of Supernova Remnants: How They Are Identified and What They Tell Us” in this volume.) These objects tell us as much about the homogeneity and character of surrounding ISM as about the nature of the supernova or its progenitor system. However, since most remnants spend most of their detectable lifetimes in these stages, statistics of SNRs do not suffer terribly. Most important in the analysis of such statistics is the range of ambient densities into which a population of SNRs

75 Dynamical Evolution and Radiative Processes of Supernova Remnants

2001

may be evolving. Most of the scatter in distributions of SNRs in plots such as the surface brightness – diameter (“˙  D”) relation is probably caused by variations in upstream density, making these relations unreliable at best for inferring basic information about SNR evolution. Subsequent chapters will examine in more detail these various issues.

4

Conclusions

The traditional outline of SNR evolution from free expansion to Sedov evolution to radiative snowplow provides only a crude description of a continuous development in which ejecta immediately begin interacting with CSM, with the rapid formation of a reverse shock. Deceleration of the outer blast wave begins in a few years, so there is no real free expansion (the expansion parameter m is less than 1 almost from the beginning and smoothly evolves toward its Sedov value of 0.4). The details of this evolution depend on the ejecta density structure. The reverse shock eventually moves to the remnant center and reheats all ejecta, though this may not occur until many times the ejected mass has been swept up. The blast wave is a strong source of thermal X-rays and nonthermal radio emission and, for young remnants, also nonthermal X-ray and gamma ray emission. The reverse shock produces strong thermal X-ray emission as well. Until ionization equilibrium is reached, X-ray emissivities from both shocks can be much higher than for equilibrium plasmas. Since cooling times are a strong function of density, for an older remnant encountering inhomogeneous ISM, some regions (“clumps” or “clouds”) will become radiative sooner than others, and optical emission will be dominated by small regions of very high, atypical, densities. Thus the optical luminosity of an older SNR is not a good indicator of its global evolutionary state. Thermal X-ray emission from heated ISM and ejecta can remain detectable even after much of the shock is radiative. Improving our understanding of SNRs, of the supernovae that produce them, and of the CSM and ISM with which they interact requires more realistic descriptions of both evolution and radiation.

5

Cross-References

 Galactic and Extragalactic Samples of Supernova Remnants: How They Are

Identified and What They Tell Us  Infrared Emission from Supernova Remnants: Formation and Destruction of Dust  Pulsar Wind Nebulae  Radio Emission from Supernova Remnants  Supernova Remnants as Clues to Their Progenitors  The Physics of Supernova 1987A  The Supernova – Supernova Remnant Connection  Ultraviolet and Optical Insights into Supernova Remnant Shocks  X-Ray Emission Properties of Supernova Remnants

2002

S.P. Reynolds

Acknowledgements I am grateful for discussions with many colleagues over many years, among whom Roger Chevalier, Kazimierz Borkowski, John Blondin, and Roger Blandford are particularly prominent. I am pleased to acknowledge support from the National Science Foundation and National Aeronautics and Space Administration for research support over the last 30 years.

References Aharonian F, Akhperjanian AG, Bazer-Bachi AR, Behera B, Beilicke M, Benbow W, Berge D, Bernlöhr K, Boisson C, Bolz O, Borrel V, Braun I, Brion E, Brown AM, Bühler R, Bulik T, Büsching I, Boutelier T, Carrigan S, Chadwick PM, Chounet L-M, Clapson AC, Coignet G, Cornils R, Costamante L, Degrange B, Dickinson HJ, Djannati-Ataï A, Domainko W, Drury LO-C, Dubus G, Dyks J, Egberts K, Emmanoulopoulos D, Espigat P, Farnier C, Feinstein F, Fiasson A, Förster A, Fontaine G, Fukui Y, Funk S, Füßling M, Gallant YA, Giebels B, Glicenstein JF, Glück B, Goret P, Hadjichristidis C, Hauser D, Hauser M, Heinzelmann G, Henri G, Hermann G, Hinton JA, Hoffmann A, Hofmann W, Holleran M, Hoppe S, Horns D, Jacholkowska A, de Jager OC, Kendziorra E, Kerschhaggl M, Khélifi B, Komin Nu, Kosack K, Lamanna G, Latham IJ, Le Gallou R, Lemière A, Lemoine-Goumard M, Lenain J-P, Lohse T, Martin JM, Martineau-Huynh O, Marcowith A, Masterson C, Maurin G, McComb TJL, Moderski R, Moriguchi Y, Moulin E, de Naurois M, Nedbal D, Nolan SJ, Olive J-P, Orford KJ, Osborne JL, Ostrowski M, Panter M, Pedaletti G, Pelletier G, Petrucci P-O, Pita S, Pühlhofer G, Punch M, Ranchon S, Raubenheimer BC, Raue M, Rayner SM, Reimer O, Renaud M, Ripken J, Rob L, Rolland L, Rosier-Lees S, Rowell G, Rudak B, Ruppel J, Sahakian V, Santangelo A, Saugé L, Schlenker S, Schlickeiser R, Schröder R, Schwanke U, Schwarzburg S, Schwemmer S, Shalchi A, Sol H, Spangler D, Stawarz Ł, Steenkamp R, Stegmann C, Superina G, Takeuchi T, Tam PH, Tavernet J-P, Terrier R, van Eldik C, Vasileiadis G, Venter C, Vialle JP, Vincent P, Vivier M, Völk HJ, Volpe F, Wagner SJ, Ward M (2008) Discovery of very high energy gamma ray emission coincident with molecular clouds in the W 28 (G6.4-0.1) field. A&A 481:401–410 Blandford RD, Eichler D (1987) Particle acceleration at astrophysical shocks: a theory of cosmic ray origin. Phys Rep 154:1–75 Blondin JM, Wright EB, Borkowski KJ, Reynolds SP (1998) Transition to the radiative phase in supernova remnants. ApJ 500:342–354 Blondin JM, Mezzacappa A, DeMarino C (2003) Stability of standing accretion shocks, with an eye toward core-collapse supernovae. ApJ 584:971–980 Borkowski KJ, Reynolds SP, Roberts MSE (2016) G11.2-0.3: the young remnant of a strippedenvelope supernova. ApJ 819:160 (17 pp) Borkowski KJ, Williams BJ, Reynolds SP, Blair WP, Ghavamian P, Sankrit R, Hendrick SP, Long KS, Raymond JC, Smith RC, Points S, Winkler PF (2006) Dust destruction in Type Ia supernova remnants in the large magellanic cloud. ApJ 642:L141–L144 Burkey M, Reynolds SP, Borkowski KJ, Blondin JM (2013) X-ray emission from strongly asymmetric circumstellar material in the remnant of Kepler’s supernova. ApJ 764:63 Carlton AK, Borkowski KJ, Reynolds SP, Hwang U, Petre R, Green DA, Krishnamurthy K, Willett R (2011) Expansion of the youngest Galactic supernova remnant G1.9+0.3. ApJ 737:22 Castor J, McCray R, Weaver R (1975) Interstellar bubbles. ApJ 200:107–110 Chevalier RA (1982) Self-similar solutions for the interaction of stellar ejecta with an external medium. ApJ 258:790–797 Cox DP, Raymond JC (1985) Preionization-dependent families of radiative shock waves. ApJ 298:651–659 DeLaney T, Kassim NE, Rudnick L, Perley RA (2014) The density and mass of unshocked ejecta in Cassiopeia A through low frequency radio absorption. ApJ 785:7 (16pp) Dohm-Palmer RC, Jones TW (1996) Young supernova remnants in nonuniform media. ApJ 471:279:291 Draine B (2011) Physics of the interstellar and intergalactic medium. Princeton University Press, Princeton

75 Dynamical Evolution and Radiative Processes of Supernova Remnants

2003

Dwarkadas VV, Chevalier RA (1998) Interaction of Type Ia supernovae with their surroundings. ApJ 497:807–823 Dwek E, Arendt RG (1992) Dust-gas interactions and the infrared emission from hot astrophysical plasmas. ARA&A 30:11–50 Gomez HL, Clark CJR, Nozawa T, Krause O, Gomez EL, Matsuura M, Barlow MJ, Besel M-A, Dunne L, Gear WK, Hargrave P, Henning T, Ivison RJ, Sibthorpe B, Swinyard BM, Wesson R (2012) Dust in historical galactic Type Ia supernova remnants with Herschel. MNRAS 420:3557–3573 Grefenstette BW, Harrison FA, Boggs SE, Reynolds SP, Fryer CL, Madsen KK, Wik DR, Zoglauer A, Ellinger CI, Alexander DM, An H, Barret D, Christensen FE, Craig WW, Forster K, Giommi P, Hailey CJ, Hornstrup A, Kaspi VM, Kitaguchi T, Koglin JE, Mao PH, Miyasaka H, Mori K, Perri M, Pivovaroff MJ, Puccetti S, Rana V, Stern D, Westergaard NJ, Zhang WW (2014) Asymmetries in core-collapse supernovae from maps of radioactive 44Ti in Cassiopeia A. Nature 506:339–342 Grefenstette BW, Reynolds SP, Harrison FA, Humensky TB, Boggs SE, Fryer CL, DeLaney T, Madsen KK, Miyasaka H, Wik DR, Zoglauer A, Forster K, Kitaguchi T, Lopez L, Nynka M, Christensen FE, Craig WW, Hailey CJ, Stern D, Zhang WW (2015) Locating the most energetic electrons in Cassiopeia A. ApJ 802:15 (11pp) Green DA (2014) A catalogue of galactic supernova remnants (2014 May version). Cavendish Laboratory, Cambridge. Available at http://www.mrao.cam.ac.uk/surveys/snrs/ Hammell MC, Fesen RA (2008) A catalog of outer ejecta knots in the Cassiopeia A supernova remnant. ApJS 179:196–208 Helder EA, Broos PS, Dewey D, Dwek E, McCray R, Park S, Racusin JL, Zhekov SA, Burrows DN (2013) Chandra observations of SN 1987A: the soft x-ray light curve revisited. ApJ 764:11 (7pp) Heng K (2010) Balmer-dominated shocks: a concise review. PASA 27:23–44 Innes DE, Giddings JR, Falle SAEG (1987) Dynamical models of radiative shocks. III – spectra. MNRAS 227:1021–1053 Isensee K, Rudnick L, DeLaney T, Smith JD, Rho J, Reach WT, Kozasa T, Gomez H (2010) The three-dimensional structure of interior ejecta in Cassiopeia A at high spectral resolution. ApJ 700:2059–2070 Itoh H (1977) Theoretical spectra of the thermal x-rays from young supernova remnants. PASJ 29:813–830 Itoh H (1978) Two-fluid blast-wave model for supernova remnants. PASJ 30:489–498 Li H, McCray R, Sunyaev RA (1993) Iron, Cobalt, and Nickel in SN 1987A. ApJ 419:824–836 Matzner CD, McKee CF (1999) The expulsion of stellar envelopes in core-collapse supernovae. ApJ 510:379–403 Matsuura M, Dwek E, Meixner M, Otsuka M, Babler B, Barlow MJ, Roman-Duval J, Engelbracht C, Sandstrom K, Laki´cevi´c M, van Loon JT, Sonneborn G, Clayton GC, Long KS, Lundqvist P, Nozawa T, Gordon KD, Hony S, Panuzzo P, Okumura K, Misselt KA, Montiel E, Sauvage M (2011) Herschel detects a massive dust reservoir in supernova 1987A. Science 333:1258–1261 Murphy T, Gaensler BM, Chatterjee S (2008) A 20-yr radio light curve for the young supernova remnant G1.9+0.3. MNRAS 389:L23–L27 Nadezhin, DK (1985) On the initial phase of interaction between expanding stellar envelopes and surrounding medium. Ap&Sp Sci 112:225–249 Oni´c D (2013) On the supernova remnants with flat radio spectra. Ap&Sp Sci 346:3–13 Ozawa M, Koyama K, Yamaguchi H, Masai K, Tamagawa T (2009) Suzaku Discovery of the strong radiative recombination continuum of Iron from the supernova remnant W49B. ApJ 706:L71–L75 Pacholczyk AG (1970) Radio astrophysics. Freeman, San Francisco Parizot E, Marcowith A, Ballet J, Gallant YA (2006) Observational constraints on energetic particle diffusion in young supernovae remnants: amplified magnetic field and maximum energy. A&A 453:387–395 Peimbert M, van den Bergh S (1970) Optical studies of Cassiopeia A.IV. Physical conditions in the gaseous remnant. ApJ 167:223–234

2004

S.P. Reynolds

Rakowski C (2005) Electron ion temperature equilibration at collisionless shocks in supernova remnants. Ad&Sp Res 35:1017–1026 Reynolds SP (1998) Models of synchrotron X-rays from shell supernova remnants. ApJ 493:375–396 Reynolds SP (2008) Supernova remnants at high energy. ARA&A 46:89–126 Reynolds SP, Chevalier RA (1981) Nonthermal radiation from supernova remnants in the adiabatic phase of evolution. ApJ 245:912–919 Reynolds SP, Moffett DA (1993) High-resolution radio observations of the supernova remnant 3C 391 – possible breakout morphology. AJ 105:2226–2230 Reynolds SP, Borkowski KJ, Hwang U, Hughes JP, Badenes C, Laming JM, Blondin JM (2007) A deep Chandra observation of Kepler’s supernova remnant: a Type Ia event with circumstellar interaction. ApJ 668:L135–L138 Reynoso EM, Moffett DA, Goss WM, Dubner GM, Dickel JR, Reynolds SP, Giacani EB (1997) A VLA study of the expansion of Tycho’s supernova remnant. ApJ 491:816–828 Rybicki GB, Lightman AP (1979) Radiative processes in astrophysics. Wiley, New York Sedov LI (1959) Similarity and dimensional methods in mechanics. Academic, New York Shu FH (1991) The physics of astrophysics. University Science Books, Mill Valley Smith N (2014) Mass loss: its effect on the evolution and fate of high-mass stars. ARA&A 52:487–528 Smith N, Li W, Filippenko AV, Chornock R (2011) Observed fractions of core-collapse supernova types and initial masses of their single and binary progenitor stars. MNRAS 412:1522–1538 Spitzer L (1978) Physical processes in the interstellar medium. Wiley-Interscience, New York Stankevich KS, Aslanyan AM, Ivanov VP, Martirosyan RM, Terzian Ye (2003) Evolution of the radio luminosities of the Tycho and Kepler supernovae remnants. Astrophysics 46:429–433 Truelove JK, McKee CF (1999) Evolution of nonradiative supernova remnants. ApJS 120:299–326 van der Laan H (1962) Expanding supernova remnants and galactic radio sources. MNRAS 124:125–145 Vinyaikin EN (2014) Frequency dependence of the evolution of the radio emission of the supernova remnant Cas A. Astrophys Rep 58:626–639 Williams BJ, Borkowski KJ, Reynolds SP, Blair WP, Ghavamian P, Hendrick SP, Long KS, Points S, Raymond JC, Sankrit R, Smith RC, Winkler PF (2006) Dust destruction in fast shocks of core-collapse supernova remnants in the large magellanic cloud. ApJ 652:L33–L36 Williams BJ, Blair WP, Blondin JM, Borkowski KJ, Ghavamian P, Long KS, Raymond JC, Reynolds SP, Rho J, Winkler PF (2011) RCW 86: a Type Ia supernova in a wind-blown bubble. ApJ 741:96 (15pp) Williams BJ, Borkowski KJ, Ghavamian P, Hewitt JW, Mao SA, Petre R, Reynolds SP, Blondin JM (2013) Azimuthal density variations around the rim of Tycho’s supernova remnant. ApJ 770:129–139 Winkler PF, Williams BJ, Reynolds SP, Petre R, Long KS, Katsuda S, Hwang, U (2014) A highresolution X-ray and optical study of SN 1006: asymmetric expansion and small-scale structure in a Type Ia supernova remnant. ApJ 781:65 Yamaguchi H, Ozawa M, Koyama K, Masai K, Hiraga JS, Ozaki M, Yonetoku D (2009) Discovery of strong radiative recombination continua from the supernova remnant IC 443 with Suzaku. ApJ 705:L6–L9 Zanardo G, Staveley-Smith L, Ball L, Gaensler BM, Kesteven MJ, Manchester RN, Ng C-Y, Tzioumis AK, Potter TM (2010) Multifrequency radio measurements of supernova 1987A over 22 years. ApJ 710:1515–1529

Galactic and Extragalactic Samples of Supernova Remnants: How They Are Identified and What They Tell Us

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Knox S. Long

Abstract

Supernova remnants (SNRs) arise from the interaction between the ejecta of a supernova (SN) explosion and the surrounding circumstellar and interstellar medium. Some SNRs, mostly nearby SNRs, can be studied in great detail. However, to understand SNRs as a whole, large samples of SNRs must be assembled and studied. Here, we describe the radio, optical, and X-ray techniques which have been used to identify and characterize almost 300 Galactic SNRs and more than 1200 extragalactic SNRs. We then discuss which types of SNRs are being found and which are not. We examine the degree to which the luminosity functions, surface brightness distributions, and multiwavelength comparisons of the samples can be interpreted to determine the class properties of SNRs and describe efforts to establish the type of SN explosion associated with an SNR. We conclude that in order to better understand the class properties of SNRs, it is more important to study (and obtain additional data on) the SNRs in galaxies with extant samples at multiple wavelength bands than it is to obtain samples of SNRs in other galaxies.

Contents 1 2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Techniques for Finding SNRs and SNR Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Optical Identification of SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Radio Identification of SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 X-ray Identification of SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 IR Identification of SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Samples Today . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2006 2008 2009 2012 2013 2016 2016

K.S. Long () Space Telescope Science Institute, Baltimore, MD, USA Eureka Scientific, Inc., Oakland, CA, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_90

2005

2006

K.S. Long

3.1 The Galaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Magellanic Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 M33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 M31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Supernova Remnants Beyond the Local Group . . . . . . . . . . . . . . . . . . . . . . . . . . 4 What the Samples Tell Us About SNRs as a Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Luminosity Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Diameter Distribution of SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Radio Surface Brightness – Diameter Relationship ˙ -D . . . . . . . . . . . . . . . . . . 4.4 X-Ray: Optical Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 The Progenitors of SNRs and the Type of the SN Explosion . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Supernova remnants (SNRs) are the visible manifestation of the interaction between material ejected in a supernova explosion (SN) and the surrounding circumstellar and interstellar medium. SNRs radiate across the entire magnetic spectrum from radio wavelengths to  -rays. They provide the working surface where the elements produced in stars and supernovae (SNe) and the kinetic energy of SN explosions mix with and stir the interstellar medium (ISM). Shocks in SNR are responsible for the cosmic rays. SNRs are heterogenous. The observational appearance of an SNR depends in a complex manner upon local factors such the nature of the SN explosion, the presence or absence of an active pulsar, the time since the explosion, the mass loss history of the progenitor, the presence or absence of earlier SN, and the density and complexity of the surrounding medium. Their appearance also depends on external factors such as the amount of absorption along the line of sight and the distance to the object. Samples of SNRs provide an instantaneous picture of where stars are exploding in galaxies. It is only a partial picture though, because many SNe explode in young massive star clusters, where other SNe have gone off recently. Superbubbles, the emission nebulae created by the collective interaction of stellar winds and multiple SN from young star clusters on the ISM (Chu and Mac Low 1990), are excluded from this discussion and usually, though not always, have different observational characteristics. For the purpose of this review, we define an SNR as the remnant of a single SN explosion. Although two SNRs – the Crab Nebula and Kepler’s SNR – were identified earlier (Minkowski 1964), the study to SNRs really began with the advent of radio astronomy, as it became clear that a significant number of bright sources in the plane of the Galaxy were indeed SNRs. Today, there are about 300 identified Galactic SNRs, most within 90ı of the Galactic Center, and thus they are affected by interstellar absorption (Green 2014a). Most were first identified through their radio properties. The first extragalactic SNRs were identified in the Magellanic Clouds in the 1960s and 1970s (Mathewson and Clarke 1973; Mathewson and Healey 1963)

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Table 1 SNRs and SNR candidates in nearby galaxies Galaxy LMC SMC M31 M33 NGC300 NGC4214 NGC2403 M82 M81 NGC3077 NGC7793 NGC4449 M83 NGC4395 NGC5204 NGC5585 NGC6946 M101 M74 NGC2903

Distance (Mpc) 0.05 0.06 0.79 0.84 2.00 2.92 3.22 3.53 3.63 3.82 3.91 4.21 4.61 4.61 4.65 5.70 5.90 6.70 6.30 8.90

SNRs 53 25 156 217 22 92 150 50 41 24 27 71 296 47 36 5 26 93 9 5

References Maggi et al. (2016) Haberl et al. (2012) Lee and Lee (2014a) Long et al. (2010) and Lee and Lee (2014b) Millar et al. (2011) Leonidaki et al. (2013) Matonick and Fesen (1997) and Leonidaki et al. (2013) Huang et al. (1994) Matonick and Fesen (1997) Leonidaki et al. (2013) Blair and Long (1997) Leonidaki et al. (2013) Blair et al. (2012) and Blair et al. (2014) Leonidaki et al. (2013) Leonidaki et al. (2013) Matonick and Fesen (1997) Matonick and Fesen (1997) Matonick and Fesen (1997) and Franchetti et al. (2012) Sonba¸s et al. (2010) Sonba¸s et al. (2010) and Sonbas et al. (2009)

through a combination of radio and optical techniques. Since then it has become possible to assemble large samples of SNRs in galaxies out to a distance of about 10 Mpc. Today there are about 59 SNRs and SNR candidates identified in the Large Magellanic Cloud (LMC) at distance 50 kpc (Maggi et al. 2016), 217 in M33 at 812 kpc (Lee and Lee 2014b; Long et al. 2010), nearly 300 in M83 at 4.6 Mpc (Blair et al. 2012, 2015), and 93 in M101 at 6.7 Mpc (Matonick and Fesen 1997). The total number of SNRs and credible SNR candidates in nearby galaxies exceeds 1200, four times the Galactic sample (see, e.g., the compilation of Vuˇceti´c et al. (2015) and Table 1). With the exception of SNRs in the Magellanic Clouds, nearly all of the extragalactic SNRs have first been identified optically. The goals of research on SNRs are to understand what factors cause SNRs, individually and collectively, to appear as they do and to separate the environmental factors from the astrophysics, such as the nature of the SN explosion and the effects of the explosion on the ISM as a whole. Both the Galactic and the extragalactic samples are important in this regard. Because the SNRs in the Galactic and Magellanic Cloud samples are nearby and bright, they provide the most direct confrontations of observations and theory. For example, in Cas A, where spectra of the light echoes from the explosion show the SN to have been of Type IIb (Krause et al. 2008), Doppler imaging

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has allowed 3D reconstruction of the ejecta at IR, optical, and X-ray wavelengths (DeLaney et al. 2010; Fesen et al. 2006), and the spatial distribution of radioactive Ti from the explosion has been mapped (Grefenstette et al. 2014). And in SN1006, where spatially resolved X-ray images were used to show that emission from the bright radio rims was synchrotron dominated and hence that SN shocks are capable of accelerating electrons to TeV energies (Koyama et al. 1995), high spatial resolution X-ray images obtained with Chandra are being used to limit the magnetic field amplification in the shock precursor (Winkler et al. 2014). And, with a few exceptions, only in Galactic SNR is it possible to identify pulsars and pulsar wind nebulae within an SNR (Gaensler and Slane 2006), as seen, for example, in G292 + 1.8 (Park et al. 2007). Extragalactic samples are also important: First, all of the SNRs observed in an external galaxy are effectively at the same distance, and thus it is straightforward to translate observed fluxes and angular sizes to the physically more relevant quantities. Second, the effects of line of sight absorption on the appearance of an SNR are generally less severe and less variable than in the Galaxy, because one can choose to study external galaxies that are relatively face-on. Third, it is easier, at least in principle, to account for observational selection effects in extragalactic samples because one can often conduct studies of SNRs in external galaxies with a single instrument at one time. The SNRs in the Magellanic Clouds merit special mention in terms of their utility; they are all at about the same distance along lines of sight with relatively little interstellar absorption so that it is fairly straightforward to examine them as a class and close enough so that detailed multiwavelength studies can be carried out of individual objects. The purpose of this article is to describe how the SNRs in the Galaxy and external galaxies were and are continuing to be found and to discuss the degree to which these samples are actually helping to address the goals of research on SNRs. We will conclude that we have accumulated much useful information about SNRs as a class of objects, but that simple interpretations of the data, especially those that use diameter as a proxy for effective age, are naive. Multifrequency studies, involving X-ray, optical, IR, and radio observations, of galaxies where SNR samples already exist are the best hope for gaining a more complete picture of SNRs as a class of objects.

2

Techniques for Finding SNRs and SNR Candidates

Most of the SNRs in the Galaxy were initially identified as extended radio sources with nonthermal radio spectra. However, most extragalactic SNRs, and SNR candidates, an example of which is shown in Fig. 1, have been identified optically using narrow band imaging. Progress has been rapid, due to the development of CCD detectors, which coupled with the angular resolution of optical telescopes allowed one to isolate SNR candidates from H II regions. X-ray and radio discovery of SNRs in external galaxies has largely, though not exclusively, been limited to

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Fig. 1 An example of an SNR in M33 as described by Long et al. (2010). From left to right, the panels show the field of the SNR as observed in X-rays with Chandra, and in H˛, [S II] and the V-band continuum as observed in ground-based images from the Local Group Galaxy Survey of Massey et al. (2006). Stars have been subtracted from the emission line images. Notice that the H˛ region seen in the lower left corner of the H˛ fades compared the SNR in the [S II] image. Had this object not been known as an SNR as a result of the optical observations, it would have been discovered as an X-ray SNR due to its soft spectrum and spatial extent in the X-ray image

the Magellanic Clouds, where limitations associated with angular resolution and sensitivity are less severe. Some progress in detecting SNRs in X-rays has been made with the launch of Chandra and XMM-Newton and in the radio with the increasing sensitivity of the Jansky Very Large Array (JVLA) and the Multi Element Radio Linked Interferometer Network (MERLIN). The most useful studies of SNRs, especially in galaxies beyond the Magellanic Clouds, will be those that involve observations in at least these three wavebands, so it is important to pursue each of them vigorously.

2.1

Optical Identification of SNRs

Optically, SNRs are extended sources, which must be distinguished from the other type of emission nebulae – H II regions – that exist in galaxies. In SNRs, optical emission normally arises from shocks, most commonly from radiative shocks driven into relatively dense clouds in the ISM by the primary shock wave. These secondary shocks, with typical velocities v of 200 km s1 , heat the post-shock gas to a temperature of order 500,000 .v=200 km s1 /2 K, ionizing it to a degree which depends on the shock velocity. However, at these temperatures, the plasma radiates very efficiently. As a result, gas cools behind the shock, increasing further in density, recombining to the neutral state on a timescale that is short compared to the cloud crossing time. As a consequence, models predict (Allen et al. 2008; Dopita 1977; Raymond 1979) and observations show optical spectra containing forbidden lines from a wide range of ionization states , including in the optical, [O III] 4959,5007, [O I] 6300,6363, [N II] 6549,6583, and [S II] 6717,6731. Unlike SNRs, the optical emission in H II regions arises from gas photoionized by UV photons from hot stars. In H II regions, most of the optical emission is produced by recombination and emerges in the Balmer lines. Most of the material in H II regions is too highly ionized to produce forbidden lines of O I, S II, and N II.

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Fig. 2 The spectra of a typical SNR candidate and a bright H II region in M83 as observed by Blair et al. (2004). The SNR shows much more [S II] 6717,6731 compared to H˛ than the H II region, as well as emission from [O I] 6300,6363 and [N II] 6549,6583. The quality of the spectra is also fairly typical of those observers who try to obtain and to confirm line ratios from imaging observations

Furthermore, at least in bright H II regions, there is a sharp boundary between fully ionized gas inside the so-called Strömgren sphere and unionized gas in the region outside the sphere, so there is relatively little gas at intermediate ionization states. As a result, as shown in Fig. 2, the spectra of SNRs and H II regions differ. First suggested as a technique by Mathewson and Clarke (1973), essentially all SNRs that have been identified optically in external galaxies have been identified as emission nebulae with elevated [S II]:H˛ ratios compared to H II regions. In bright H II regions, the [S II]:H˛ is typically about 0.1, whereas in SNRs the ratio is typically 0.4 or greater. Searches are conducted using interference filter imaging, with filters centered on H˛ (often also including a contribution from [NII]), [S II], and a continuum band. One inspects these images for emission nebulae that show elevated [S II] compared to H˛, designating as candidates extended objects with [S II]:H˛ > 0:4. (Occasionally, slightly lower or higher values have been used.) An example of an SNR discovered in this way is shown in Fig. 1. The SNR is recognized

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by the fact that it is relatively much brighter in the [S II] image than the H II region in the lower left hand corner. Often, follow-up spectroscopy is carried out, which not only confirms the [S II]:H˛ ratios but also allows searches for additional SNR indicators, usually [O I] emission, and in rare cases velocity broadening of the lines. The technique works best for isolated SNRs, where one can measure the ratio of [SII]:H˛ emission without the diluting effect of an adjacent/underlying H II region, and for high surface brightness nebulae. Lower surface brightness H II regions tend to have higher [S II]:H˛ ratios. In particularly, Blair and Long (1997) found that in NGC7793, the [S II]:H˛ ratio often exceeds 0.5 in nebulae with surface brightnesses of less than 1015 erg cm2 s1 arcsec2 . The Strömgren sphere is simply not as well defined in low-density H II regions, and the ionization levels drop more slowly with distance from the ionizing stars than with higher density, so that there is an extended region where ions, such as S II, are prevalent. Partly to address these problems, many observers eliminate from consideration nebulae with high [S II]:H˛ ratios with obvious evidence of a concentration of blue stars. The advantage of this strategy is that it makes it more likely that an object identified as an SNR actually is an SNR. The disadvantage is that SN does explode in regions with blue stars, and one’s candidate list is less complete. Observers also have to decide whether to include or exclude nebulae which satisfy the [S II]:H˛ test but which are larger than expected from a single SN with a typical explosion energy. Many of these objects are, as argued recently by Franchetti et al. (2012), superbubbles or collections of SNRs. Consequently, some observers have excluded objects larger than (typically) 100 pc from SNR candidate lists (Lee and Lee 2014a, b). Others have retained them (Long et al. 2010; Matonick and Fesen 1997), feeling any particular diameter arbitrary and arguing that over time the reality or not of any particular candidate will be determined by future observations. Although the optical emission from most SNRs arises from radiative shocks in gas with near interstellar abundances, several other types of optical emission are observed less commonly in SNRs: (a) A small number of SNRs exist, notably SN1006 and Tycho’s SNR, which radiate only in the Balmer lines (Chevalier and Raymond 1978; Raymond et al. 2010; Winkler et al. 2014). In these SNRs, the optical emission arises from a so-called non-radiative shock, in which a fast shock, typically >1000 km s1 , encounters a partially neutral ISM. In these situations, the cooling time behind the shock is long compared to the age of the SNR, and the only optical radiation arises as the plasma is ionizing. The surface brightness of the optical emission from these Balmer-dominated SNRs is low compared to those that emit via radiative shocks, and the spectra are not easy to distinguish from H II regions. Consequently, the only extragalactic SNRs to have been identified of this type have been in the LMC (Tuohy et al. 1982), objects which were first detected as X-ray sources (Long et al. 1981). A few remnants of this type continue to be discovered in the Galaxy, including recently G70.0–21.5 (Fesen et al. 2015b). In principle, such objects could be discovered in other galaxies if observed with sufficient spectral resolution to detect large velocity broadening; in practice, it

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is more likely that a Balmer-dominated SNR will be identified first in another wavelength range. (b) SNRs also exist in which line emission arises from interactions with the ejecta from core-collapse SNe, such as is the case for the Galactic SNRs, Cas A (Kirshner and Chevalier 1977), and G292 + 1.5 (Goss et al. 1979). Optical emission from the ejecta of such SNe is characterized by very strong emission from forbidden lines of O II and O III, which are very efficient coolants for a plasma with abundances expected in the ejecta of core-collapse objects (Dopita et al. 1984). A number of searches for SNRs of this type have been carried out. A few objects have been found, e.g., E0102-72.9 in the SMC (Finkelstein et al. 2006) and the remnants of some very young SNe, such as SN 1957D in M83 (Long et al. 1989) and the very bright SNR in NGC4449 (Kirshner and Blair 1980). The numbers are, however, very small, and all of these objects were first discovered by other means. Optical searches for these SNRs are difficult because they are expected to be small-diameter objects and easy to confuse with planetary nebulae and certain stars with strong emission lines. (c) Finally, there are some SNRs, often referred to a pulsar wind nebulae, where optical line emission arises from circumstellar material/ejecta photoionized by synchrotron radiation due ultimately to the active pulsar. Unlike the photoionization produced by thermal emission from hot stars, the hard power law synchrotron spectrum is capable of leaving the plasma in a large variety of ionization states, which results in emission line spectra that look significantly different from a normal H II region. In principle, such SNRs could be discovered through measurements of the [S II]:H˛ ratio or could be buried in existing catalogs of extragalactic planetary nebulae. To date, none has been recognized beyond the Magellanic Clouds, with the possible exception of SN 1957D in M83 (Long et al. 2012).

2.2

Radio Identification of SNRs

At radio wavelengths, SNRs in the Galaxy are extended, nonthermal radio sources. Shell-like SNRs in particular typically have radio spectral indices ˛ of about 0.5 though with considerable dispersion (see, e.g., Fig. 6 of Dubner and Giacani 2015). H II regions, which are also extended sources at radio wavelengths, are the main source of confusion. These are thermal radio sources, radiating primarily by freefree emission, which has a spectral index of 0.1. This means that shell-like SNRs can in principle be separated from H II regions if the spectral index can be measured. The pulsar-dominated SNRs, like the Crab Nebulae, have flatter spectral indices from 0.0 to 0.3 (Kargaltsev et al. 2015) and are harder to identify on this basis, but these constitute a relatively small portion of the total sample of the Galactic sample and would presumably be a similarly small portion of any complete extragalactic sample as well. Not surprisingly the first extragalactic radio SNRs to be identified/detected are located in the Magellanic Clouds (Mathewson and Clarke 1973; Mathewson and

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Healey 1963). Indeed, with the availability of the Australia Telescope Compact Array (ATCA), all known SNRs in the Large and Small Magellanic Clouds have been detected at radio wavelengths (Filipovi´c et al. 2005; Maggi et al. 2016). Identification at radio wavelengths of SNRs in more distant galaxies has been hampered by a number of factors. First, until very recently radio observations did not generally have the combination of sensitivity and angular resolution necessary to detect and measure the spectral indices of potential SNR candidates in more distant galaxies. Secondly, SNRs are often found in regions with other diffuse emission and this can dilute the spectral index of putative SNRs, especially in the absence of multifrequency maps with the same spatial resolution. Finally, as surveys have grown, more sensitive contamination from background sources has become an issue, particularly in Local Group galaxies, which have substantial angular diameters. Consequently, most of the radio-detected SNR candidates are sources which were identified as SNR candidates optically and then detected as radio sources (see, e.g., Gordon et al. (1999) for the case of M33). There have been some searches particularly in galaxies outside the Local Group where observers have identified as SNRs nonthermal radio sources with associated H˛ emission (see, e.g., Chomiuk and Wilcots 2009a; Lacey and Duric 2001). This mitigates the background source problem and is positive in the sense that it does not depend on optical SNR identification, but it also introduces spatial biases into the sample that are difficult to quantify. Objects such as RXJ1713-39 (Pfeffermann and Aschenbach 1996) and RX J0852.0-4622 (also known as Vela Junior) (Aschenbach 1998), which have no associated H˛ emission, and the historical SNRs, SN1006, and Tycho, which are very faint in H˛ would almost certainly be missed. Lacey and Duric (2001) used this approach to identify 35 radio point sources in NGC6946 as SNRs, almost none of which were in Matonick and Fesen (1997) list of 27 optical SNR candidates. The radio sample in NGC6946 has radio fluxes corresponding to 0.1–2 times that of Cas A and is systematically brighter than the radio-detected optical sample in M33. The radio candidates are more closely associated with bright H II regions and with the spiral arms than the optically identified SNRs, which Lacey & Duric suggest is at least partially due to observational biases associated with identification of optical SNR candidates. They suspect SNRs in the radio sample in NGC6946 are evolving in denser interstellar environments than SNRs in the optical sample.

2.3

X-ray Identification of SNRs

SNRs, as indicated in the leftmost panel of Fig. 1, are also extended sources at X-ray wavelengths. Most have soft, line-dominated X-ray spectra, arising from hot 1  106 –5  107 K gas produced by the reverse shock interaction with SN ejecta or the primary shock interaction with the ISM. Even if the shocks speeds are high enough to produce a plasma hotter than this, the spectra looks as if it has a temperature in this range due to ionization equilibration effects. Chandra spectra obtained by Long et al. (2010) of the two brightest SNRs in M33 are shown in Fig. 3. A small number

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Fig. 3 X-ray spectra of the two brightest X-ray SNRs in M33 as observed with Chandra by Long et al. (2010). The spectra show clear evidence of the line emission expected from a shocked thermal plasma

Fig. 4 Predicted Chandra count rates in 3 bands (0.35–1.1 keV, 1.1–2.6 keV, and 2.6–8 keV) for SNRs at a distance of 1 Mpc assuming they are in the Sedov phase and assuming a line of sight absorption of 51020 cm2 . All of the curves terminate at a kT of about 0.09 keV (because XSPEC models do not exist at lower kT); this however, is well before the beginning of the radiative phase

of SNRs, those powered by pulsars, such as the Crab and 3C58 in the Galaxy, and a few young synchrotron-dominated SNRs, such as RXJ1713-39 and Vela Junior have power law spectra. To give an indication of what one expects to see from an X-ray SNR in a nearby galaxy, we show, in Fig. 4, estimated Chandra count rates for SNRs in the Sedov phase at a distance of 1 Mpc as function of age and size, as calculated with the program XSPEC, a routine used widely in the astrophysics community to fit X-ray spectra (Arnaud 1996). The three sets of curves are for SNRs expanding into ISM with densities of 10, 1, and 0.1 cm3 . These rates are indicative of a number of

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important “facts” about the expected detectability of SNRs in X-rays. SNRs brighten through much of their Sedov phase and are easiest to detect at ages of 10,000–20,000 years. In the early Sedov phase, SNRs are relatively faint because they have not swept up enough material; in the late Sedov phase, they fade because the post-shock plasma temperature has dropped. SNRs expanding into a dense ISM are brighter but evolve more rapidly. The spectra are soft, at least at ages greater than 1000 years. H II regions also contain thermal plasma, but they typically are much less luminous (< 1034 ergs s1 ) than SNRs. Giant H II regions do have X-ray luminosities of up to 1037 ergs s1 but are easy to isolate based on their H˛ luminosities and stellar content. Wind-blown bubbles are occasionally not distinguishable from SNRs, especially if one allows large objects (>100 pc diameter) in the sample. Although most Galactic SNRs were first identified as radio sources, a number were first detected or suggested as SNRs as a result of their detection as extended Xray sources from the ROSAT All-Sky Survey (Schaudel et al. 2002). These include the aforementioned RXJ1713-39 and Vela Junior, as well as more typical thermal plasma-dominated objects, such as G38.7 + 1.4 (Huang et al. 2014), G296.7-0.9 (Robbins et al. 2012), G299.2-2.9 (Busser et al. 1996), and G308-1.4 (Hui et al. 2012). It is quite likely that additional Galactic SNRs will be identified as part of the eROSITA all-sky survey (Predehl et al. 2014), which will be about 30 times more sensitive than ROSAT. In other galaxies, especially those beyond the Local Group, SNRs are relatively faint and difficult or impossible to distinguish from point sources on the basis of spatial extent. Fortunately, most other Galactic X-ray sources (neutron star and black hole binaries) and most background sources (AGN and galaxy clusters) have relatively featureless hard spectra that with spectral resolution, and counting statistics are easy to distinguish from the thermal plasma-dominated spectra of most SNRs, simply on the basis of hardness ratios. However, this still leaves a group of compact sources, the so-called supersoft sources thought to be white dwarf binaries that have luminosities as high as 1038 ergs s1 . These objects have very soft hardness ratios (corresponding to effective temperatures of 105 –106 K) (Kahabka and van den Heuvel 1997), which makes them hard to separate from SNRs (given limited source counts). Stiele et al. (2011) identify 30 sources in their survey of M31 with XMM as supersoft sources, which is comparable to the number of objects they suggest are SNRs. Many of these supersoft sources are variable, but the fact that this source population exists means that it is dangerous to assume that all soft X-ray sources in a galaxy are SNRs. Consequently, most observers require something other than a hardness ratio to declare an X-ray source as an SNR candidate, usually association with an optical or radio source that has the properties of an SNR. There have been a few X-ray only searches for SNRs, where observers have tried to establish a set of X-ray candidates without complementary information at other wavelengths. Leonidaki et al. (2010) identified 37 objects in archival Chandra data as SNR candidates in six nearby galaxies (NGC2403, NGC3077, NGC4214, NGC4449, NGC4395, and NGC5204) based on their X-ray hardness ratios or colors. Of these, only 7 had been previously suggested as SNR candidates. This is a useful exercise since one is not biased by the characteristics expected for SNRs at

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other wavelengths, though it remains to be seen how many of these objects actually turn out so be SNRs as more sensitive observations are carried out.

2.4

IR Identification of SNRs

Historically, very few SNRs have been identified via observations in the IR. However, the [Fe II] 1.27,1.64 m is, like [S II], a tracer of radiative shocks and can be used in conjunction with, for example, Paˇ, to separate H II regions from SNRs (see, e.g., Mouri et al. (2000) for a discussion of the shock models and Oliva et al. (1989, 1990) for early IR spectroscopy of Galactic SNRs ). Greenhouse et al. (1997) used Fabry–Perot imaging of the [Fe II] 1.64 m line to identify 6 sources in M83 which they argued were an older population of SNRs than those identified in the radio. Subsequently, Morel et al. (2002) imaged 42 [S II]identified SNRs in M33, detecting about 10, with [Fe II] 1.64 m luminosities of 0:2271035 ergs s1 . The advantage of NIR imaging is that line of sight absorption is less of a problem in the IR; the disadvantages are that the night sky is much more of a problem in the IR and, until recently, advances in detector technology were delayed compared to CCDs. However, the picture is changing with improvements in IR detectors. Blair et al. (2015), as part of Hubble Space Telescope (HST) imaging study of M83, has found a number of emission nebulae in M83 coincident with X-ray sources that are apparent in [Fe II] 1.64 m, but not in [S II], that are likely to be SNRs. An example is shown in Fig. 5. Some impetus for such studies should arise both from the more systematic studies of [Fe II] emission in Galactic SNRs that are currently underway (Lee et al. 2014a) and from assertions that the [Fe II] imaging of galaxies can be used an estimator of the SN rates (Rosenberg et al. 2012).

3

The Samples Today

3.1

The Galaxy

According to Green (2014a), there are now 294 identified SNRs in the Galaxy. Nearly all have been detected at radio wavelengths, while 40 % have been detected in X-rays and 30 % have been detected in the optical (the low fraction being a result of the effects of absorption in the plane of the Galaxy). Of the SNRs, 79 % are shell-like (though in many cases the actual shell structure is quite complex), and 5 % are center-filled (dominated by emission from the “wind” of a central pulsar like the Crab). The remaining SNRs have a composite morphology, with evidence for emission from both the central pulsar and a shell. Usually, SNRs with radio shells detected at X-ray wavelengths also show X-ray shells, but there is a group comprising some 20 % of the total that have center-filled X-ray morphologies. Mid-IR emission, which arises both from shock-heated dust grains and from IR lines in hot gas, from SNRs was first detected in the all-sky survey conducted

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Fig. 5 A 16" by 20" portion of M83 as observed with HST and Chandra (Blair et al. 2015). The upper left panel shows the [Fe II] image; the upper right panel shows a composite H˛, [SII], and [O III] image; the lower left panel shows a composite of U, B, and V images; and the lower right panel shows the Chandra image. Objects identified as SNRs from [S II] imaging by Blair et al. (2012) are shown in green; X-ray sources from the catalog of Long et al. (2014) are shown red, one of which the X-ray counterpart to an optical SNR. All of the SNRs have [Fe II] counterparts. The field also contains one other object, identified in yellow, that is bright in [Fe II] and is most likely an SNR behind a dust lane

with the Infrared Astronomical Satellite (IRAS) at 12, 25, 60, and 160 . Arendt (1989) and later Saken et al. (1992) claimed detections of about 30 % of the SNRs known at the time. They found that the morphologies of SNRs in the mid-IR were similar to that observed at X-ray and radio wavelengths and established that the IR luminosities of SNRs were in some cases comparable to their X-ray luminosities. With the Spitzer Space Telescope, new surveys of SNRs were undertaken with considerably higher precision. In particular, Pinheiro Gonçalves (2011) found 39 counterparts to the 121 SNRs contained in the region surveyed with Multiband Imaging Photometer for Spitzer (MIPS) as part of the MIPSGAL Survey (at 24, 60, and 160 ); they argued that the detection rate was primarily limited by confusion in the plane of the Galaxy, that X-ray bright SNRs were found preferentially, and that the IR luminosities of the detected SNRs were comparable to X-ray luminosities. At shorter Infrared Array Camera (IRAC) wavelengths (3.6, 4.5, 5.8, and 8.0 ),

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where emission from SNRs can arise from shock-heated dust, atomic fine-structure lines, molecular lines, and occasionally synchrotron emission, (Reach et al. 2006) reported 18 detections in the GLIMPSE survey region containing 95 SNRs. Many of the other SNRs in the survey region could have significant infrared emission but are located along lines of sight with large amount of emission due to H II regions and atomic and molecular clouds. At least 30 of the Galactic SNRs have been detected in  -rays (1–100 GeV) with Fermi LAT (see Acero et al. (2015) for a good summary of the current list of detections, and an overall interpretation). The detected SNRs, which have typical L luminosities of 1035 ergs s1 , fall into two subclasses, “young SNRs” in the free expansion or Sedov phases and SNRs interacting with molecular clouds.  -rays can be produced from relativistic electrons either through inverse Compton emission or by bremsstrahlung radiation or alternatively from relativistic protons (and other hadrons) which created pions which then decay to  rays. Both processes are thought to play a role. To date, a correlation between the radio and  -ray fluxes has not been demonstrated (Acero et al. 2015). The sample of SNRs in the Galaxy is not really complete, at least in the sense that all SNRs of certain intrinsic properties in the Galaxy have been discovered. Green (2014b) estimates that the radio sample is approximately complete to a surface brightness limit of 1020 Watts m2 Hz1 sr1 . There are 68 SNRs brighter than this limit, but Green notes that a selection bias still exists. Specifically, it is hard to recognize small-diameter, distant SNRs which will be in the Galactic plane along a line of sight near the Galactic Center where source confusion is likely. The situation is clearly worse at optical and X-ray wavelengths, where absorption is more of a problem. The number of Galactic SNRs should continue to grow with better all-sky surveys at X-ray wavelengths, such as eROSITA (Predehl et al. 2014), and emission line surveys, including the Isaac Newton Telescope Photometric H˛ Survey IPHAS (Drew et al. 2005; Sabin et al. 2013), its southern hemisphere VLT counterpart VPHAS (Drew et al. 2014), and the UKIRT wide field imaging survey of Fe+ (UWIFE) (Lee et al. 2014a). The follow-up from detections of  -ray sources is also likely to continue to pay dividends in this regard.

3.2

Magellanic Clouds

Because the Large and Small Magellanic Clouds are nearby (50 and 60 kpc, respectively) and because they lie along lines of sight with very low Galactic and internal absorption, more is known about the SNRs in the Magellanic Cloud as a group than in any other galaxy. Not only is it fairly straightforward to study the SNRs, it is also possible to study the environments around them as result of the large amount of ancillary data that has been accumulated on the Magellanic Clouds for a variety of other purposes.

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The first SNRs in the LMC were detected as nonthermal radio sources by Mathewson and Healey (1964) and subsequently confirmed as SNRs on the basis of strong [SII]:H˛ ratios by Westerlund and Mathewson (1966). The numbers grew during the 1970s, primarily as a result of work by Mathewson and Clarke (1973), as radio and optical instrumentation became more sensitive and as systematic searches for SNRs were carried out. Long et al. (1981) used Einstein to carry out the first X-ray imaging survey of the LMC; of the 97 X-ray sources detected, they found 26 SNRs, including a number which had not been known previously. According to Maggi et al. (2016), there are currently 59 confirmed SNRs in the LMC. Nearly all have been detected at X-ray, optical, and radio wavelengths. Most of the SNRs have optical spectra. Russell and Dopita (1990) (see, also Payne et al. 2008) have used the spectra to measure ISM abundances in the LMC. Echelle spectra exist for a significant fraction of the SNRs, allowing one to study the expansion velocity of the optical filaments (Chu 1997). One of these SNRs B0540-69.3 (Brantseg et al. 2014; Mathewson et al. 1980) contains an 80 ms pulsar (Seward et al. 1984) which produces  -ray pulses 20x brighter than the Crab pulsar (Fermi LAT Collaboration 2015). One young SNR, N49, is coincident with a soft  -ray repeater (Cline et al. 1980; Güver et al. 2012; Kulkarni et al. 2003). Light echoes from the SN explosion have been seen from three (Rest et al. 2005). At least one X-ray bright SNR, N132D, has portions of its optical spectrum dominated by emission from the shocked ejecta optical spectrum dominated by emission from the shocked ejecta (Danziger and Dennefeld 1976; Vogt and Dopita 2011) About 60 % of the SNRs known in the LMC have been detected with Spitzer (Seok et al. 2013) in the NIR where emission can arise from molecular shocks, synchrotron radiation, ionic lines, or PAH emission and/or in the MIR (mainly) from shock-heated dust. Seok et al. (2013) use these data to argue that LMC SNRs are fainter on average than Galactic SNRs in the IR, presumably due to lower dust to gas ratios in the LMC than the Galaxy, and that the SNRs of Type Ia SNe are significantly fainter than those arising from core-collapse SNe. This situation is similar for the Small Magellanic Cloud (SMC) although the total number of SNRs (25) is smaller, as one would expect since the SMC is less massive than the LMC. The first optical/radio SNR in the SMC was discovered by Mathewson and Clarke 1972), the first X-ray SNR; the second brightest X-ray source in the SMC was found by Seward and Mitchell (1981), as part of the first Xray imaging survey carried out with the Einstein Observatory. Nearly all of the SMC SNRs have been detected in X-rays (Haberl et al. 2012) with XMM, and most have radio fluxes (Filipovi´c et al. 2005; Payne et al. 2007) and optical spectra (Payne et al. 2007; Russell and Dopita 1990). Many of the SNRs have been studied in detail. The remnant E0102-72.3, discovered with Einstein, is one of the very small number of SNRs showing emission from ejecta at optical wavelengths (Blair et al. 2000). One SNR, HFPC 334, appears to be a composite SNR, comprised of an active pulsar inside a shell-like radio source (Crawford et al. 2014).

2020

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K.S. Long

M33

The first three SNRs in M33 were identified by Dodorico et al. (1978) using interference filters and image tube photography, and the numbers grew significantly with the advent of CCDs (Gordon et al. 1998; Long et al. 1990). A detailed study of SNRs in M33 using a combination of deep Chandra exposures and optical data from the Local Group Galaxy Survey (LGGS) (Massey et al. 2006) survey was carried out by Long et al. (2010). They found 137 optical SNR candidates (with [S II]:H˛ >0.4) in M33, with diameters ranging from 8 to 179 pc. Of these, 82 were detected in X-rays with 0.35–2 keV luminosities in excess of 2  1035 ergs s1 , and of these seven were bright enough for detailed spectral analysis. Based on a spectral analysis of all of the sources detected in M33, Long et al. estimated that they had identified all of the thermal plasma-dominated X-ray SNRs brighter than 4  1035 ergs s1 , at least in the region covered by the Chandra survey. Subsequently, Lee and Lee (2014b) reexamined the LGGS data and produced a larger sample of 199 optical SNR candidates. Their sample is larger in part because they surveyed a larger region of M33 and pushed to fainter surface brightnesses and somewhat different because they excluded objects with diameters greater than 100 pc. They argued that objects with these characteristics were unlikely to be SNRs and should be excluded. Long et al. discussed some of these concerns but felt that excluding such objects as candidates was premature. However, the differences also reflect the subjective aspects of identifying optical SNR candidates, the majority of which are very faint and near the sky background limit in the LGGS and other ground-based data. If the two lists are combined, there are 217 optically identified SNRs and SNR candidates in M33. Of these, 86 of these, all from the list of Long et al., have optical spectra. Most recently, Williams et al. (2015) have described the results of their analysis of a new deep set of XMM observations covering a larger region of M33 than was observed with Chandra; in addition to recovering most of the SNRs reported as Xray sources by Long et al., they detected 8 new X-ray SNRs, three of which are in the outskirts of the galaxy. D’Odorico et al. (1982) carried out the first successful radio search for SNRs in M33 using the Westerbork Synthesis Radio Telescope (WSRT) at 21 cm. They reported five certain and three probable detections of sources at the positions of the 12 optically identified SNRs known at the time. Subsequently, Gordon et al. (1999) used the a combination of Very Large Array (VLA), and WSRT observations obtained at 6 and 20 cm with an angular resolution of 700 , or 30 pc, to construct a catalog of 186 sources in M33. Of these sources, they identified 53 sources as spatially coincident with one of the 98 optically identified SNRs known at this later date. The mean radio spectral index of the radio sources identified as SNRs was 0.5, and the summed radio luminosity of SNRs in M33 comprised 2 %–3 % of the total synchrotron emission in M33. There were a number of other nonthermal sources detected above their surface brightness limit of 0.2 mJy along the line of sight to M33, but they noted that most of these were likely background sources.

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None of SNRs identified in M33 is very young. There are no objects, like N132D or E0102-72.3, in the Magellanic Clouds, whose optical emission is dominated by emission from shocked ejecta, or even any SNRs with broad optical emission lines. There is an X-ray source with a power law spectrum coincident with a smalldiameter radio source that Long et al. suggest may be a pulsar wind nebula.

3.4

M31

The first few SNRs in M31 were identified by Kumar (1976), and subsequent image tube photography by Dodorico et al. (1980) and Blair et al. (1981), respectively, expanded the number of spectroscopically confirmed SNRs to 14. Because of its very large size, M31 was actually less surveyed than several other nearby galaxies for many years. Braun and Walterbos (1993) found 52 SNR candidates in the first CCD-based search for SNRs in M31 but surveyed only a portion of the galaxy. Magnier et al. (1995) identified 179 candidates in 17 fields totaling a square degree of the galaxy, but their selection of candidates was based on morphology in H˛. They did not use the [SII]:H˛ ratio as a criterion, and as a result, there was no direct evidence that the majority of the nebulae selected by Magnier et al. actually contained shocks. The situation has changed recently, however, as Lee and Lee (2014a) have searched the LGGS survey images of M31 for SNRs, just as they had done for M33. They identified 156 emission nebulae with diameters less than 100 pc as SNRs or SNR candidates on the basis of [S II]:H˛ >0.4 and circular morphology. Most of the candidates are associated with the spiral arms of M31. Although the first X-ray detection of an SNR in M31 was most likely made by Blair et al. (1981) using Einstein, the first reliable characterization of the X-ray properties of SNRs in M31 has required the greater sensitivity of Chandra and especially XMM (Pietsch et al. 2005; Stiele et al. 2011). According to Sasaki et al. (2012), there are now 26 confirmed X-ray SNRs in M31, 21 of which had been thought to be SNRs based on earlier observations and 6 of which were discovered as a result of the XMM studies. These SNRs are confirmed in the sense that they have both the X-ray and optical characteristics of SNRs. The X-ray luminosities of the SNRs range from 2  1035 ergs s1 to 8  1036 ergs s1 in the 0.3–2 keV band. There are also 20 candidate SNR, objects that either have soft X-ray spectra, but ambiguous evidence from other wavelength bands as to whether the object is an SNR, or hard X-ray spectra but evidence for a radio source or a nebula with high [S II]:H˛ ratios at that position. The first radio search for SNRs in M31 was carried out by Dickel et al. (1982) who used the VLA at 20 cm and reported the radio detection of 7 SNRs identified earlier by Dodorico et al. (1980). Although some other efforts to characterize small numbers of SNRs in M31 have taken place since then (Braun and Walterbos 1993; Sjouwerman and Dickel 2001), the SNR population of M31 is still not well characterized at radio wavelengths. Galvin and Filipovic (2014) have published a catalog of 916 point sources in 20 cm radio images of M31 constructed from archival VLA data and compared the positions of these point sources to SNR candidates

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suggested by others. With a flux limit of about 2 mJy, they find 13 objects whose position matches those contained in the list of optical candidates produced by Lee and Lee (2014a). Of the 47 SNRs and SNR candidates reported by Sasaki et al. (2012) in X-rays with XMM, they find 11 overlaps. As is true of M33, no very young SNRs have been identified as yet, with the exception of the remnant of SN 1885, which (Fesen et al. 2015a) have imaged in absorption with HST against the stars in bulge of M31.

3.5

Supernova Remnants Beyond the Local Group

The first 17 SNR candidates in six galaxies beyond the Local Group were identified by Dodorico et al. (1980) using photogaphic plates. The first large CCD-based searches were carried out by Blair and Long (1997) who identified 56 SNR candidates in the Sculptor Group Galaxies, NGC300 and NGC7793 and by Matonick and Fesen (1997) who identified a total of about 400 SNR candidates in NGC5204, NGC5585, NGC6946, M81, and M101. As shown in Table 1, optical samples of varying depths now exist for more than 20 galaxies within 10 Mpc (Vuˇceti´c et al. 2015). These include NGC2403 with 150 candidates (Leonidaki et al. 2013), M83 with nearly 300 candidates (Blair et al. 2014, 2012), and M101 with 93 candidates (Matonick and Fesen 1997). A necessary next step for improving the reliability of these samples is to obtain the spectra of as many of these candidates as possible. This is underway for many of these galaxies, including M81, where (Lee et al. 2015) have obtained spectra of 28 of 41 optically identified SNR candidates; they find that 26 of their 28 objects should be retained as candidates. As noted earlier, there have been relatively few dedicated radio searches for SNRs outside of the Local Group. In the Sculptor group spiral NGC300, (Payne et al. 2004) used data from the VLA and from ATCA to identify 18 nonthermal radio sources associated with H˛ emission or an X-ray point source in XMM data as SNRs; five of these were in Blair & Long’s list of optical SNRs, but 13 were new. Of the 18 sources, six were also detected with XMM. In another Sculptor group spiral NGC7793, (Pannuti et al. 2002) identified five radio SNR candidates. Lacey and Duric (2001), as discussed earlier, identified 35 objects in the starburst galaxy NGC6946 as radio SNRs, six of which (Pannuti et al. 2007) found to be X-ray sources in Chandra images. M82 is an exception in terms of the importance of radio observations. At 3.2 Mpc, M82 is the closest example of a prototypical starburst galaxy, that is, a galaxy undergoing a huge burst of star formation (due in the case of M82 to a near collision with M81). Such galaxies contain a large amount of dust, and this dust, heated by early type stars, radiates strongly in the FIR. The current star formation rate (SFR) in M82 is about 10 Mˇ yr1 , much greater than the Galaxy. With this SFR, M82 produces a large number of SNe, 1 every 10–20 years, and hence a large number of very young SNRs. The SNRs are mostly buried behind large amounts of dust and hence primarily accessible at radio wavelengths. The first radio studies of M82

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were carried out by Kronberg et al. (1985), and the galaxy has been monitored since that time with the VLA and MERLIN. Huang et al. (1994) observed the highly reddened galaxy with the VLA at a resolution of 0.200 and identified 50 sources near the center of the galaxy with diameters all less than that of Cas A and with higher radio surface brightness as well. They argued the vast majority of these were SNRs expanding into the high-pressure ISM of the central region of M82. They found these sources obey a ˙-D relationship that extrapolates to that of the ˙-D of Galactic and Magellanic Cloud SNRs. Repeated observations with Merlin and the VLA and with very long baseline interferometry have allowed one to measure the time evolution of the radio fluxes and, in many cases, the expansion velocities of the SNRs. For example, Fenech et al. (2008) used MERLIN to detect about 35 SNR in M82 ranging in diameter from 0.3 to 6.7 pc, with a mean of 2.9 pc. Most of the sources show shell-like morphologies. They measured expansion velocities ranging from 2200 km s1 to 10,500 km s1 in 10 SNRs. These velocities are significantly larger than predicted by Chevalier and Fransson (2001) who suggested that the radio SNRs in M82 were expanding into a dense 103 cm3 ISM and mostly in their radiative phase. The distribution of diameters in this SNRs measured by Fenech et al. suggests that most of the SNRs are in the free expansion phase and that the SNRs are expanding into the region carved out by the winds of a progenitor red giant star. X-ray identifications of SNR candidates in galaxies beyond the Local Group have mostly proceeded from attempts to identify X-ray sources with nebulae satisfying the optical criteria for SNRs or as radio SNRs. Deep observations with Chandra are required to see all but the most luminous SNRs in Galaxies beyond the Local Group. Matonick and Fesen (1997) had identified 93 emission nebulae as optical SNR candidates in M101. Franchetti et al. (2012) reexamined the 55 objects in the sample that were contained in archival H˛ images obtained with HST, ranging in size from 20 to 330 pc, including 16 with diameters greater than 100 pc. They found that 21 of the 55 candidates had X-ray counterparts in very deep (1 Ms) Chandra observations (Kuntz and Snowden 2010). And Long et al. (2014) analyzed a series of Chandra observations of M83 totaling 729 ks. They found 378 point sources within the D25 contour of the galaxy, including 87 sources which appeared to be SNRs based on a combination of their X-ray properties and coincidence with either an optical SNR candidate or a radio source within the galaxy. Smaller numbers of X-ray detected SNRs exist in other galaxies outside the Local Group. Not surprisingly, most of the SNRs that have been discovered in galaxies beyond the Local Group appear, with the limited information available, to be older, largerdiameter SNRs, since one typically looks for objects with some indication of spatial extent, and small-diameter SNRs radiating primarily in the oxygen lines are hard to separate from planetary nebulae. There have been nine SNe in NGC6946, and six in M83 in the last 100 years, which implies there are about 90 and 60 SNRs in these galaxies of age less than 1000 years. But this also means there are many more SNRs with ages of up to 20,000 years, so young SNRs are going to be rare. A few may have been found depending on one’s decision about when to declare an object an SNR, as opposed to late time emission from an SN since some SNe have

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been observed essentially continuously from the time they exploded (Milisavljevic et al. 2012). The bright optical, radio, and X-ray SNR in NGC4449 was probably due to an SN that was missed in the last 50–100 years (Milisavljevic and Fesen 2008). One pathway forward to identifying younger SNRs is through higher angular resolution observations at optical or radio wavelengths. There are now some searches that are being carried out with the WFC3 on HST, which has the requisite filters, that might address this problem. For example, in M83, (Blair et al. 2014) found 26 new small-diameter SNRs (by carefully inspecting HST images near Xray point sources) and measured small ( 0.5 arcsec or 10 pc) diameters for 37 others. However, so far only one of these objects is known to have very broad optical emission lines (Blair et al. 2015); this particular object, which was also detected as an X-ray source and a radio source, was most likely another example of an SN in the last 100 years that was missed. The rest of the small-diameter objects look to be SNRs that are evolving in a denser ISM than the typical SNR in other galaxies.

4

What the Samples Tell Us About SNRs as a Class

The past 50 years have seen a lot of progress in terms of identifying samples of SNRs both in the Galaxy and nearby galaxies. However, we now need to ask what we can learn from these samples.

4.1

Luminosity Function

The luminosity function of SNRs, expressed as the number of SNRs with a luminosity less than a specific value, at radio, optical (H˛), and X-ray wavelengths for several galaxies is shown in Fig. 6. In all cases, the shapes of the luminosity functions are affected by sample completeness at low luminosity. To the extent that conditions are similar in these galaxies, one might expect that the normalization of the luminosity functions would reflect the number of SNe in each galaxy, and, since most SNe arise from relatively young stellar populations, the overall SFR. Leonidaki et al. (2010), for example, assert that the number of X-ray SNRs brighter than 1036 ergs s1 in a galaxy is proportional to the SFR. They also suggest that SNRs in irregular galaxies tend to be more luminous than in spiral galaxies, possibly due to the fact that the lower metal abundances observed in irregular galaxies results in more massive SN progenitors. Maggi et al. (2016) find the X-ray luminosity functions of both M31 and M33 can be fitted as a power law with a slope about 0.8, but that the SMC is significantly flatter (0.5). They find that the luminosity function of the LMC is complex, with 13 SNRs brighter than 1036 ergs s1 . Like Leonidaki et al., they attribute this due to low metallicity but suggest that the winds of more massive stars in the LMC create low-density cavities, which result in luminous SNRs when the SN shock reaches the cavity walls at ages of a few thousand years (Dwarkadas 2005).

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Fig. 6 The radio, H˛, and X-ray luminosity functions of SNRs in several nearby galaxies. The various luminosity functions M31, M33, and the Large and Small Magellanic Clouds are shown in blue, black, green, and red, respectively. Data for M33 was taken from Gordon et al. (1999) and Long et al. (2010), for M31 from Lee and Lee (2014a), and for the Large and Small Magellanic Clouds from Badenes et al. (2010) and Maggi et al. (2016). The radio luminosity shown is the specific luminosity at 20 cm

Similarly, Chomiuk and Wilcots (2009b), using a sample of radio SNR candidates in 18 galaxies, ranging from the Magellanic Clouds to galaxies like M51 and M82, argue SNRs generally have a power distribution of luminosities with a scaling that is proportional to the SFR. Specifically, they find overall dN D 92 SFR L2:02 dL

(1)

where L is the specific luminosity at 1.4 GHz (20 cm) in mJy and SFR is in units Mˇ yr1 . Unlike Thompson et al. (2009), they find no indication that the peak (or average) luminosity is related to the gas density of the galaxy. At optical and X-ray wavelengths, luminosity functions are difficult to interpret in terms of physical models because the amount of emission is very dependent on the local ISM density. However, this may not be the case at radio wavelengths. Following early theoretical work by Reynolds and Chevalier (1981) and Berezhko and Völk (2004), Chomiuk and Wilson argue that the slope of the radio luminosity function can be understood in terms of a model in which (a) most of the SNRs are in the Sedov phase, (b) the cosmic ray energy is a fixed fraction of the SN explosion energy throughout the Sedov phase, and (c) the magnetic field energy density behind the shock is amplified to  0:01 o vs2 . Whether this particular interpretation of the radio luminosity function is actually physically correct is difficult to determine; as the specific luminosities of SNRs with the same diameter vary substantially (see below), so a complete interpretation

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of the radio emission from SNRs has to account for these differences. Nevertheless, luminosity functions at all wavelengths are clearly useful for estimating completeness of samples, and the total amount of radiation arising from SNRs at the various wavelengths.

4.2

The Diameter Distribution of SNRs

A natural question arising in any attempt to explain the properties of any SNR sample is how to explain the distribution of diameters in the sample. If most SNRs are in the Sedov phase, then one would naively expect the number of SNRs in a sample with diameters less than D (N< D) to increase as D5=2 . However, early versions of the N 10Lˇ , and none showed evidence for being a former donor star, including no red giant, AGB, or post-AGB surviving companions in the inner 4000 of the remnant. Similar searches for companions in the LMC remnants SNR 0519-67.5

J Fig. 4 Left: Kepler’s SNR viewed in X-rays with Chandra ACIS-S3. The RGB image shows 0:4– 0:75 keV emission in red, 0:75–1:2 keV emission in green, and 1:2–7:0 keV emission in blue. In the image, north is up and east is to the left. The outlined region corresponds to the blastwave–ejecta interaction discussed in Patnaude et al. (2012). Right: In the upper panel, we plot the measured versus computed line centroids for Si K˛, S K˛, and Fe K˛, for the DDTa (black solid) and DDTg (red dashed) models. The hatched region in each panel corresponds to the measured centroid including the 90% confidence interval The DDTg models and a subset of the DDTa models (MP < 4106 Mˇ yr1 ) do not produce any Fe K emission. In the lower panel, we plot the line centroids for the DDTa cavity models for vwind = 10 (green solid) and 20 (blue dashed) km s1 , for a range of mass loss rates. The line centroids and errors are indicated by the vertical hatched regions in each panel. The allowed mass loss rates as dictated by the comparison between the measured and modeled line centroids are marked by the horizontal cross hatched region (Figures reproduced with the permission of the authors; Patnaude et al. 2012)

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and 0509-67.5 also turn up no evidence for a surviving companion (Edwards et al. 2012; Schaefer and Pagnotta 2012). While this isn’t firm proof for the viability of the DD scenario, it does suggest that, at least in these cases, the double degenerate progenitor model could be required in order to produce these SNRs. To conclude, observations of Type Ia SNRs provide clear evidence for a MCh SN Ia progenitor in SNR 3C 397 (Yamaguchi et al. 2015), and the presence of a fast, sustained outflow in SNR RCW 86 (Badenes et al. 2007; Williams et al. 2011). Taken at face value, this seems to support the SD scenario for at least some local Type Ia SNe. However, the bulk properties of most Type Ia SNRs are at odds with the CSM configurations expected in SD progenitors (see Fig. 3 and Badenes et al. 2007,for a detailed discussion). More contrived CSM profiles are certainly possible in some cases, as shown by Patnaude et al. (2012) for Kepler, but a more likely explanation is that DD progenitors also make a significant contribution to the local SN Ia rate (see Badenes and Maoz 2012). A mixture of progenitor channels has interesting implications for cosmology (Ponder et al. 2016).

2.2

Core Collapse SNRs: Progenitor Connections

A good review concerning the connections between young supernova remnants and their progenitors can be found in Chevalier (2005). They note that different supernova types arise from different zero-age main sequence masses, with SNe IIP occuring in the 8–15 Mˇ range, SNe Ib/c occuring in stars with ZAMS mass & 35Mˇ , and IIb/IIL SNe resulting from stars in the middle, with observational results providing information on the progenitor to supernova type relationship Smartt (e.g., 2015). If firm connections between progenitor and supernova type can be established, then connecting a remnant to it’s parent supernova provides an indirect path back to the progenitor type. Chevalier (2005) attempted this for several objects, including the Crab, 3C 58, and G292.0+1.8. In the Crab, measured abundances suggest that the progenitor lacked an O-rich mantle, placing the progenitor star at the low end of the supernova progenitor mass range, 8–10 Mˇ , suggesting that the Crab supernova was of the Type IIP variety. On the other hand, the SNR G292.0+1.8 probably arises from a more massive progenitor, as the blastwave has swept up 15–40 Mˇ of RSG wind (Lee et al. 2010). Estimates of a high swept up mass points to a massive progenitor, with an initial mass of 20–35 Mˇ . In general, the range of progenitor models which lead to core collapse supernova remnants is much larger than one sees in the case of Type Ia SNRs. This is reflected in the morphological and compositional diversity of CC SNR we observe in the Galaxy. Ranges in mass loss rates and wind speeds, combined with the initial mass of the star (which will influence the final abundances), as well as evolutionary changes that the progenitor may go through (such as a Wolf-Rayet phase), not to mention the effects that a binary companion can have on the progenitor’s evolution, leads to larger parameter space to explore when comparing CC SNR to their progenitors. As seen in Lee et al. (2010) and others, examples exist where broad

85 Supernova Remnants as Clues to Their Progenitors

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Fig. 5 Left: Cas A in X-rays. The three color image shows 0.5–1.5 keV in red, 1.5–3.0 keV in green, and 4.2–6.0 keV in green. The neutron star is clearly visible near the center. Right: Density of the supernova remnant at a time of 330 years after explosion. The left panel shows the remnant that results from the evolution of ejecta in a CSM modified by a pure RSG wind, with the middle and righthand panels showing the case where the Wolf-Rayet phase lasted for 2265 and 3480 years, respectively. The forward shock of the remnant in all three cases is located at a distance of 2:4 pc, while the reverse shock is located increasingly farther inward for longer WR phases. Details of the models may be found in Schure et al. (2008) (Righthand figure reproduced with the permission of the authors; Schure et al. 2008,Figure 4, pp 403)

statements about the progenitor can be made, but few objects allow for the same types of detailed analyses that we find in Ia studies. The exceptions are the Galactic SNR Cassiopeia A (Cas A), and the youngest known remnant, SN 1987A, in the Large Magellanic Cloud. Cas A, shown in Fig. 5 (left), may represent the most well studied of the Galactic SNR. At an age of 330 yr (Thorstensen et al. 2001), it has a morphology which is consistent with that of a SNR interacting with a RSG wind (Chevalier and Oishi 2003). Hwang and Laming (2012); Lee et al. (2014) undertook detailed studies of the mass loss history of the Cas A progenitor, and estimate that the progenitor star shed &6Mˇ of material prior to core–collapse. Combined with the estimated mass of the neutron star and ejecta, the progenitor zero-age main sequence mass is  12 Mˇ . The light echo spectra of the Cas A SN obtained by Krause et al. (2008) and Rest et al. (2011) suggest a Type IIb origin, similar to SN 1993J, implying a red supergiant origin. The analysis by Lee et al. (2014) suggest that the Cas A progenitor lost much of its mass through the RSG wind, compatible with the IIb SN type, though this is at odds with the mass loss rates adopted for single RSG stars (Woosley et al. 2002). Solutions to the high amount of mass lost from Cas A include episodic mass loss through pulsational instabilities in the RSG phase Yoon and Cantiello (2010), or enhanced mass loss through the interaction of a binary companion (Young et al. 2006).

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Another possibility is that the Cas A progenitor went through a short Wolf-Rayet phase prior to core collapse. The fast wind from a Wolf-Rayet progenitor would clear out a small cavity, much like is required in Kepler’s SNR, and would imprint itself on the dynamics and X-ray emission of the remnant. Hwang and Laming (2012) required such a cavity in order to match the observed X-ray emission. Schure et al. (2008) modeled the evolution of the Cas A jet in a cavity, and found that if a Wolf-Rayet phase existed, it would be rather short ( a few thousand years; Fig. 5, right). Besides Cas A, perhaps the most well-studied supernova remnant is that of SN 1987A, a recent review of which can be found in McCray and Fransson (2016). SN 1987A is the closest example of a remnant where the progenitor is known through pre-explosion imaging. However, supernovae are now regularly identified with their progenitors through the use of pre-explosion images. Smartt (2015) notes 18 detections of supernova progenitors, with 27 additional upper limits – a large number of the sample of detected supernova progenitors result in SN IIP, IIL, or IIb. This is consistent with Chevalier (2005), who associated many Galactic SNR with Type II SNe, resulting from RSG progenitors of various masses. Only one or possibly two Galactic SNR have been firmly associated with SNe Type Ib/c (and hence with a Wolf-Rayet progenitor) – W49B as a possible gamma-ray burst remnant (Lopez et al. 2013), and RX J1713–3946 (Katsuda et al. 2015b).

3

SNR Bulk Properties

As discussed in the previous sections, typing individual supernova remnants remains challenging. Recently, Yamaguchi et al. (2014) presented a method of typing SNRs based on the Fe-K˛ line centroid and luminosity. Since Fe is produced in the center of the progenitor during the explosion, heating of Fe can be delayed, resulting in ionization states lower than He-like (Fe24C ) in young and middle-aged SNRs. The ionization state affects the Fe-K line centroid, which can be measured with high precision with satellites such as Chandra, XMM–Newton, or Suzaku. In brief, they found a correlation between supernova type, and the Fe-K line centroid: the line centroid for Type Ia SNRs are generally lower ( 0. Therefore, in order to relase the secondary component from the system, mo1  2"mo1  m2 > 0;

(25)

or the reduction factor " (recall that this is the ratio of post-supernova to presupernova mass of the exploding star) must fulfill the following inequality:

"
105:5 K) gas is for galactic SN rates about 20 %, both for the HD (de Avillez and Breitschwerdt 2004) and MHD (de Avillez and Breitschwerdt 2005) cases due to disk outflow, as compared to 70 %–80 % in the standard model (McKee and Ostriker 1977).

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0 290.00 Myr –1

log dN/N

–2

–3

–4

–5

–6 –5

–4

–3

–2

–1 0 log n [cm–3]

1

2

3

Fig. 4 Volume-weighted density pdf for the ISM simulations shown in Figs. 1 and 2 at t D 290 Myr. Here the logarithmic occupation fraction is plotted against the logarithmic density of the ISM gas. The finest AMR level is 0.25 pc

Apart from the magnetic field, whose energy density is comparable to the thermal and kinetic energies of the plasma, a similar amount goes into CRs, which can transfer some of their momentum and energy to the gas by scattering off magnetic irregularities (in general MHD waves), which are frozen into the plasma.

2.4

Cosmic Rays

CRs are the high-energy component of the Universe and below 1018 eV of the ISM. The term is a misnomer, as the primary component consists of high-energy charged particles, with photons being only a by-product of their interaction with matter. CRs are predominantly protons, electrons (about 1 %), and heavier nuclei, close to ISM abundances, with notable differences in some elements, which are mainly the spallation products of heavier nuclei (e.g., iron) due to collisions with ISM gas. Observationally, CRs exhibit a power-law differential energy spectrum dN .E/ / E  dE in energy from about 109 –1021 eV with two spectral breaks at 1015 (“knee”,   2:7) and 1018 (“ankle”,   3:0) eV. Particles with higher energies are of extragalactic origin, because their gyroradius, and hence any accelerator, exceeds the size of the Galaxy. This criterion, put forward by Hillas (1984), arises from the fact that the maximum energy a particle can attain can be derived from integrating RL over the Lorentz force, Emax ' 0 .q=c/ v B d l, where q, c, L, B, and v are the electric charge, the speed of light, the size of the acceleration region, the magnetic field strength there, and the effective particle speed, respectively. Of course, it is not

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the magnetic fields which accelerate the particles, but the electric fields associated with it due to induction. CRs interact resonantly with MHD waves, arising from magnetic field perturbations, due to a gyro-resonance condition for wave numbers of the order of the gyroradius rL D p=.qB/, where p is the (relativistic) particle momentum. Loosely speaking, the particles pick out the waves from the Fourier spectrum, which fulfill the resonance condition, thus getting strongly scattered in pitch angle, essentially performing a random walk, i.e., diffusion, in the plasma.pTherefore their effective drift velocity is of the order of the Alfvén speed, vA D B=.4 /, in the ISM typically less than 0.1 % of the speed of light. This also explains the near isotropy of CRs in arrival directions observed with satellite and terrestrial detectors. In the Galaxy, the most likely accelerators are shock waves in the ISM, in particular those of SNRs. The process is called diffusive shock acceleration (DSA) or first-order Fermi acceleration, in which up- and downstream of the shock, MHD waves act as magnetic mirrors, reflecting the particles across the shock front like a ping-pong ball across the net. In the shock frame, the particles see the waves, which are frozen into the converging plasma, approaching the shock front on either side, thus converting plasma kinetic energy into particle energy. In the analogy, this would correspond to the ping-pong ball gaining energy by the rackets moving toward each other. Hence every collision is a head-on collision in contrast to the second-order Fermi process, in which the stochastic motions of the magnetic mirrors induce headon and following collisions, so that the energy gain is of second order, as for a moving particle the number of head-on collisions dominates. The process is not very efficient per se, as the energy gain of a particle is only a small fraction of order Vs =c, where Vs is the shock speed with respect to a fixed Eulerian frame. However, it is a probabilistic process, in which the probability that a particle gets reflected back and forth many times decreases with increasing energy (i.e., number of crossings). Let E D ˇE0 be the energy after one collision, and let P be the probability of a particle remaining in the acceleration process, so that after one collision the number of particles is N D PN0 . Hence after k collisions, N D N0 P k , and E D E0 ˇ k . Since then k D log.E=E0 /= log ˇ, we have N =N0 D .E=E0 /log P = log ˇ , and the differential energy spectrum is a power law, dN / .E=E0 /.log P = log ˇ/1 , as observed. Let U be the downstream fluid velocity in the laboratory frame, which for a strong shock is given by U D 3=4 Vs . The energy gain per roundtrip is E=E D 4=3 U =c D Vs =c (averaging over pitch angles) and hence ˇ D 1 C E=E D 1 C Vs =c, while the escape probability of the particles is related to the downstream and shock velocity, Pesc  Vs =c, due to advection away from the shock. The probability to stay in the acceleration process is P D 1  Pesc D 1  Vs =c, so that log P  Vs =c, log ˇ  Vs =c, and log P = log ˇ  1 (see Bell 1978). Therefore the power-law index in the energy spectrum is   log P = log ˇ  1  2, close to the observational value of   2:7. The difference can be attributed to the energy-dependent diffusive transport of CRs, with a diffusion coefficient  / E 0:7 , because scattering becomes less efficient for particles with higher energies particles, as there exist fewer and fewer waves to scatter off.

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The maximum energy reachable in DSA is Emax  .q=c/ Vs B L, which is about 3  1014 eV for protons in a SNR with a microgauss field and L  10 pc, making use of the fact that the highest energies are obtained in young SNRs, when the shock is still strong, and Vs  104 km=s. This agrees remarkably well with the location of the knee in the spectrum. As the CRs propagate by diffusion and advection from their sites of origin to the heliosphere, they suffer several energy losses. While protons and nuclei lose energy by spallation processes and 0 -production via collisions with ISM protons, synchrotron and inverse Compton losses (mainly with cosmic microwave background photons) affect mostly the electrons because of their lower mass. Ionization and bremsstrahlung losses are usually negligible in comparison for particles with energies above 100 MeV.

3

Heliosphere

While the previous considerations describe the general, large-scale structure of the interstellar medium in which stars predominantly serve as a means to uphold a constant input of energy, planets reside inside quite different environments. In the case of the Earth, this well-shielded location is known as the heliosphere which, energetically, is relatively unimportant for the global behavior of the ISM. However, interaction regions always host interesting physics, which in this case modifies the information transmitted by particle populations. In addition, so far all manmade observatories are confined to the neighborhood of Earth, which all the more emphasizes that the heliosphere merits special attention. In this section, therefore, the transition from interstellar to interplanetary space will be described in more detail. The heliosphere arises from the interaction of the solar wind and the solar magnetic field with the surrounding local interstellar medium. More precisely, the term heliosphere refers to the region surrounding the Sun where the particles of solar origin – the supersonic solar wind – dominate the interstellar plasma. As the solar wind streams radially outward, its density decreases until it matches that of the interstellar medium (Frisch et al. 2011), and the sound speed increases until the flow speed eventually becomes subsonic. The structure of the transition region is quite complicated and is characterized by a variety of phenomena that will be described in more detail in the following subsection. These include one or more shocks and a tangential discontinuity, all of which are turbulent and variable in time, thus impeding a simplified stationary description. In addition, high intensities of non-thermal particles have been found inside and outside of the heliospheric termination shock. Together with the collisional mean free path of a few astronomical units (au), such indicates that a (magneto)hydrodynamic description cannot be applied especially near the shocks. Moreover, even diffusion as a means to describe the interaction of charged particles and electromagnetic waves may sometimes be insufficient, as there are observational indications of superdiffusion (Perri and Zimbardo 2009).

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The understanding of these “foreground” processes is a prerequisite for any attempt at inferring the conditions in the pristine interstellar medium based on particle measurements in the heliosphere. On a more positive note, the heliosphere provides an excellent laboratory to study dilute plasma phenomena both remotely and in situ. This is even more important as the structure of the heliosphere is believed to be typical for stars with masses comparable to that of the Sun. While these are more difficult to observe – for instance, Ly ’ lines can be used to probe stellar winds – they nevertheless can provide additional information concerning the long-term evolution of these so-called astrospheres (Wood 2004).

3.1

Heliospheric Boundaries

There are several phenomena that define the boundaries of the heliosphere, all of which are illustrated in Fig. 5 together with typical particle populations and the magnetic field structure (Opher 2016; Zank 2015). Toward the direction of the incoming interstellar medium, which has a density of 0:2 cm3 , the heliosphere is flattened. In the opposite direction – at the so-called heliotail – the structure is considerably more complex. So far, however, in situ measurements exist only from the nose direction, while the heliotail is uncharted territory. In general, the extent of an astrosphere depends on the respective pressures of the stellar wind and that of the surrounding interstellar medium. Notably, the latter contains contributions from the ionized and neutral gas components, the (non-thermal) galactic cosmic ray (GCR) population, and the magnetic field. Since all these components are in approximate equipartition, neither may be neglected (Biermann and Davis 1960; Schlickeiser 2012). The medium that streams toward the heliosphere is partially ionized and contains GCRs, i.e., a non-thermal particle population. Embedded into it is a weak magnetic field with a strength of 2–4 G. The outermost heliospheric boundary is formed by the deceleration of the local interstellar medium, through which the heliosphere moves with approximately 26 km/s. That speed is close to the local sound speed, so that it is currently unknown precisely if the flow is super- or subsonic (McComas et al. 2012; Scherer and Fichtner 2014). Accordingly, either a bow shock or a bow wave is possible. The compressed and heated interstellar particles then act as partners for charge-exchange processes with inflowing neutral atoms, thereby forming the so-called hydrogen wall. Using Ly ’ absorption, this wall has indeed been detected. Unfortunately, however, the presence of the hydrogen wall does not prove the existence of a bow shock because it is also compatible with a bow wave. For the time being, therefore, that question remains unanswered, and more precise determinations of the sound speed will be required. In the region containing this so-called very local interstellar medium with a maximum distance of 0.01 pc from the Sun, the influence of heliospheric particles such as pickup ions is still palpable. The separation of the local interstellar medium from the solar wind plasma has been predicted to be a tangential discontinuity. Its location depends on the orientation relative to the local interstellar flow but, in upwind direction, has a

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Fig. 5 General structure of the transition region between the solar system and the interstellar medium. Shown are the heliospheric shocks and boundaries, the particle populations, and the magnetic field orientations (Source: Opher (2016) and Jet Propulsion Laboratory (1999), courtesy of Steven T. Suess. With permission from Springer Science+Business Media)

distance from the Sun of at least 130 au. In 2012, observations of low-energy particles led to the impression that Voyager 1 had crossed the heliopause and entered the (very) local interstellar medium. There was, however, some debate as to whether Voyager 1 has indeed encountered the heliopause, mainly because the magnetic field direction has remained unchanged, in contrast to expectations. Therefore, the term “heliocliff” was coined to indicate a transition layer before the actual heliopause. Despite additional measurements, however, it is still not unanimously accepted that Voyager 1 is in the outer heliosheath. While a variety of promising theoretical models – including magnetic reconnection, turbulence, and magnetic bubbles – have

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been proposed, it will require additional observational evidence to resolve this issue. As of 2016, it is expected that Voyager 2 will soon reach the heliopause. The highly turbulent region inside the heliopause that contains basically subsonic plasma flows is called the (inner) heliosheath. Here, the solar wind ions are diverted to stream toward the heliotail, thus remaining inside the heliopause. Note that, analogously, the region outside the heliopause is sometimes called the outer heliosheath, even though, strictly speaking, this term would require the presence of a bow shock, so there is no general consensus. Voyager 1 has revealed a variety of surprises, the most prominent of which is the heliosheath being surprisingly thin. Almost all models had overestimated the thickness by nearly a factor of two. As of yet, no all-encompassing solution to this mystery has been found, even though it is believed that magnetic reconnection may play an important role (Opher 2016). Reconnecting magnetic fields and turbulence may extract energy from the heliosheath, thereby reducing the pressure and leading to a region that is smaller than predicted by traditional models. Further difficulties arise from the observations of possibly compressible, magnetized turbulence that has been observed both by Voyagers 1 and 2. The understanding of particle observations is thus made significantly more complicated. This is even more so as the turbulence is partly supersonic, which results in a series of shocks propagating from the termination shock into the heliosheath. In December 2004, Voyager 1 found the termination shock to be located at a radial distance from the Sun of 94 au (Richardson 2013). The distance at which Voyager 2 encountered the termination shock in August 2007, however, was only 84 au. This asymmetry can be explained either by the oblique angle of the interstellar magnetic field (see below) or by oscillations induced by the solar wind. However, these are responsible only for variations of up to 2–3 au. In each case, the shock crossing was indicated by a sudden decrease of the flux of low-energy particles while, at the same time, the flux of high-energy particles increased. Since the magnetic field direction did not change, the shock, which is collisionless in nature and surprisingly thin, appears to be almost perpendicular (Balogh and Treumann 2013). It was believed for a long time that the termination shock marks the transition of the solar wind from the supersonic to the subsonic regime. However, there are in fact observations indicating that, instead, pickup ions (see below) are heated, while the solar wind ions continue to stream at a supersonic speed (Zank 2015). Despite the fact that the termination shock is the most prominent boundary of the solar system, it is relatively weak in terms of the shock compression ratio, which is between 1.4 for the particle density and 1.7 for the magnetic field (Burlaga et al. 2013).

3.2

Interaction with the ISM

There is a variety of processes by which the interstellar medium affects the heliosphere, including forming its very shape. Likewise, the heliosphere also has

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– albeit to a lesser degree – a certain influence on the very local interstellar medium, mainly through the magnetic field. The termination shock cannot be directly observed with Earth-based instruments or from (near-Earth) space. Indirectly, the anomalous component of the cosmic ray particles (ACRs) – originally named after their peculiar feature in the energy spectrum – as well as energetic neutrals may represent an exception. In contrast to ionized particles, neutral interstellar atoms stream unhindered into the heliosphere, owing to the collisionless nature of the limiting shocks. These particles are therefore particularly suited to characterize the conditions in the outer the heliosphere and the local interstellar medium. Some fraction of these neutrals – mostly hydrogen – undergo multiple collisions with energetic protons of the solar wind, thereby exchanging one or more electrons (Balogh and Treumann 2013). Initially, these pickup ions are cold but are typically heated up to form a supra-thermal population with energies of 10–100 MeV per nucleon. The particle spectrum therefore is a power law with an index between 1.5 and 3.2, depending on the location close to the termination shock or deep inside the heliosheath. Originally, ACRs (see, e.g., Fichtner 2001) were thought to be accelerated at the termination shock. So far, however, evidence for this scenario has been found only for particles with moderately low energies, which have thus been named termination shock particles (TSP). In contrast, Voyager 1 found that the intensity of ACRs kept rising without an intensity peak at the termination shock. This fact represents a challenge for the widely accepted picture of diffusive shock acceleration and hints at a source inside the heliosheath. While the heliopause generally hinders the interstellar plasma from streaming into the heliosphere, neutral particles cross the heliopause to become pickup ions. In these charge-exchange processes, energetic neutral atoms (ENA) are created which, in turn, may move inward and thus can be detected at Earth. Based on the theoretical understanding of their origin, ENAs can therefore be used to probe the plasma conditions at the outer heliosphere where they had been created. In particular, a bright narrow band of energetic neutral atoms with energies around 0.7–1.7 keV has been discovered by the Interstellar Boundary Explorer (IBEX), which was therefore called the “IBEX Ribbon” (McComas et al. 2014). There are indications that it is aligned with the interstellar magnetic field as well as with solar latitude, thus pointing at a direct connection with the solar wind. Based on these findings, a number of theoretical models have been brought forward, some of which are based on multiple charge-exchange processes. In particular, aside from the so-called primary or classic pickup ions, a second population of higher-energy ions (dubbed “ACR pickup ions”) is required that are transported back to the termination shock (e.g., McComas et al. 2014; Siewert et al. 2012). However, the precise mechanism by which the Ribbon is produced is currently still under active debate. Even though Voyager 1 seems to have crossed the heliopause, the magnetic field still appears to be that of the heliosphere. Therefore, direct observations are mainly important to measure the strength and the fluctuations of the local magnetic field. But the direction of the local interstellar magnetic field can be inferred indirectly to account for the asymmetries observed in situ by the Voyagers. However, to

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reconstruct the large-scale structure of the surrounding interstellar magnetic field, mainly remote observations are being used. For instance, anisotropies in TeV cosmic rays from the ISM can be taken to infer the orientation of the local interstellar magnetic field (Schwadron et al. 2014), which is in agreement with results based on the polarization of starlight. In addition, the IBEX Ribbon appears to be oriented in the direction perpendicular to the ambient interstellar magnetic field. There is no reason why the interstellar magnetic field should be aligned with the flow direction of the ISM, and indeed it is not. Accordingly, the shape of the heliosphere is not symmetric which, in turn, accounts for some of the differences in the observations of Voyagers 1 and 2. It is these findings that connect observations of GCRs to the structure of the heliosphere (Desiati and Lazarian 2013), thereby emphasizing the importance of high-energy particles not only to probe the conditions of supernova remnants but also as a diagnostic tool for the heliosphere. While it may sound like a trivial statement, the Sun is the origin of the heliosphere for mainly two reasons (Zurbuchen 2007). First, a tenuous plasma – dubbed the solar wind – streams radially outward with a supersonic speed of 250–2200 km/s. It consists of two distinct components, the slow and the fast solar wind, with typical speeds of 400 and 750 km/s, respectively. The mass loss rate of 3  1014 Mˇ per year is low compared to that of massive OB stars, which can be nine orders of magnitude higher and thus amount up to 105 Mˇ per year. Still, the solar wind is the basis for all phenomena discussed above, and more. For instance, shocks in the solar wind – so-called co-rotating interaction regions – are known to affect the spectrum of GCRs measured on Earth (Kóta and Jokipii 1995). Second, the solar magnetic field extends outward in the form of an Archimedean spiral – also known as the famous Parker (1958) spiral. The polarity reversals, which follow the 11-year solar cycle, affect the particle spectra in a variety of ways (Potgieter 2013). For instance, the cosmic ray energy spectrum becomes softer for a positive solar polarity, even though it has to be noted that particles of opposite charge will react differently. In addition, also the dynamics of the warped heliospheric current sheet, which separates the two hemispheres of opposite polarity, has an influence on the particle populations. All of these effects are summarized under the term solar modulation. In conclusion, particle measurements in the heliosphere – and in particular near Earth – require a thorough understanding of the solar wind. Charge-exchange processes creating pickup ions, acceleration processes creating ACRs, and the solar modulation need to be taken into account. The interpretation of what is recorded inside the heliosphere does not directly reflect what will be found in the interstellar medium. However, our understanding of the interaction regions grows so that neutral particles as well as cosmic rays are increasingly recognized as being messengers of interstellar conditions. Nevertheless, given the history of the Voyager observations, it is most likely that further surprises will follow as the Voyagers go where no space probe has gone before.

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Conclusions

The ISM is not a quiescent place in the Galaxy, as strong shocks from stellar winds and SNe from massive stars permanently sweep across it and stir it up by turbulence. In addition, each point in the ISM is constantly exposed to CRs, which are a serious threat to the biosphere of planets. We may therefore speculate that life primarily exists, where it is shielded from high-energy particles by astrospheres in general and in the case of the solar system by the heliosphere. It is essentially the supersonic solar wind and its non-negligible magnetic field, interacting with the local ISM, which are responsible for the origin of the heliosphere. Nevertheless, neutral and galactic CRs are able to penetrate deep into the heliosphere, allowing us to study their propagation and origin. It is finally the Earth’s magneto- and atmosphere which protect us from the influx of high-energy particles. Eventually, air showers are generated, which enable us to measure the primary CR energy and direction, e.g., by Cherenkov telescopes and fluorescence detectors like H.E.S.S. and Auger. One might expect that SNR shock waves hitting the heliosphere may pose another potential hazard, but the solar wind carries a considerable amount of ram pressure (due to its relative high density and velocity), which is comparable to or larger than that of a SN shock, if the explosion is about 100 pc or further away. Finally, messengers of SNe, apart from neutrinos, i.e., radionuclides like 60 Fe, which are generated in AGB stars by s-process and by explosive nucleosynthesis in SNe, can be measured on Earth in the deep-sea ferromanganese crust and ocean sediments and are direct witnesses of the SN history in the local ISM. The data show a flux enhancement about 2.2 Myr ago (Knie et al 2004; Wallner et al. 2016), which can be explained by detailed numerical modeling, thus unraveling the site and time of nearby explosive events in the recent past. It has been found Breitschwerdt et al. (2016) that the SNe, which formed the Local Bubble, are also responsible for the deposition of 60 Fe on the ocean floor and even on the moon, as inferred from the analysis of lunar samples (Fimiani et al. 2016). Moreover, recently an enhancement of cosmic rays, presumably due to nearby SN explosions, has been found in PAMELA data (Kachelrieß et al. 2015), as well as 60 Fe in cosmic ray primaries by ACE-CRIS observations (Binns et al. 2016). Detailed analysis of the trajectory of nearby stars in the past, and hence their massive siblings that have already exploded, reveals that the two closest SNe probably occurred at distances of 91 and 96 pc at 2.3 and 1.5 Myr ago, respectively (Breitschwerdt et al. 2016).

5

Cross-References

 Dynamical Evolution and Radiative Processes of Supernova Remnants  Effect of Supernovae on the Local Interstellar Material

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 Electron Capture Supernovae from Super Asymptotic Giant Branch Stars  Galactic Winds and the Role Played by Massive Stars  High-Energy Cosmic Rays from Supernovae  Isotope Variations in the Solar System: Supernova Fingerprints  Mass Extinctions and Supernova Explosions  Possible and Suggested Historical Supernovae in the Galaxy  Stardust from Supernovae and Its Isotopes  Structures in the Interstellar Medium Caused by Supernovae: The Local Bubble  Supernovae and Supernova Remnants: The Big Picture in Low Resolution  Supernovae and the Chemical Evolution of Galaxies  Supernovae, Our Solar System, and Life on Earth  The Supernova – Supernova Remnant Connection Acknowledgements D.B., M.A.de A. and R.C.T. acknowledge funding by the DFG priority program 1573 ‘Physics of the Interstellar Medium’. M.A. de A. is supported by the project “Hybrid computing using accelerators & coprocessors – modelling nature with a novel approach” funded by the InAlentejo program, CCDRA, Portugal.

References Balogh A, Treumann RA (2013) The heliospheric termination shock. In: Physics of collisionless shocks. ISSI scientific report series, vol 12. Springer, New York Bell AR (1978) The acceleration of cosmic rays in shock fronts. I. Mon Not R Astron Soc 182: 147–156 Biermann PL, Davis L Jr (1960) Considerations bearing on the structure of the galaxy. Zs f Astrophys 51:19–31 Binns WR et al (2016) Observation of the 60 Fe nucleosynthesis-clock isotope in galactic cosmic rays. Science 352:677–680. doi:10.1126/science.aad600417424 Blaauw A (1964) The O associations in the solar neighborhood. Astron Astrophys Rev 2:213 Breitschwerdt D, de Avillez MA (2006) The history and future of the Local and Loop I bubbles. Astron Astrophys 452:L1–L5. doi:10.1051/0004-6361:20064989. arXiv:astro-ph/0604162 Breitschwerdt D, Schmutzler T (1994) Delayed recombination as a major source of the soft X-ray background. Nature 371:774–777 Breitschwerdt D, de Avillez MA, Feige J, Dettbarn C (2012) Interstellar medium simulations. Astron Nachr 333:486 Breitschwerdt D, Feige J, Schulreich MM, de Avillez MA, Dettbarn C, Fuchs B (2016) The locations of recent supernovae near the Sun from modelling 60 Fe transport. Nature 532:73–76. doi:10.1038/nature17424 Burlaga LF, Ness NF, Stone EC (2013) Magnetic field observations as Voyager 1 entered the heliosheath depletion region. Science 341:147–150 Cappellaro E, Evans R, Turatto M (1999) A new determination of supernova rates and a comparison with indicators for galactic star formation. Astron Astrophys 351:459–466 de Avillez MA, Breitschwerdt D (2004) Volume filling factors of the ISM phases in star forming galaxies. I. The role of the disk-halo interaction. Astron Astrophys 425:899–911 de Avillez MA, Breitschwerdt D (2005) Global dynamical evolution of the ISM in star forming galaxies. I. High resolution 3D simulations: effect of the magnetic field. Astron Astrophys 436:585–600 de Avillez MA, Breitschwerdt D (2007) The generation and dissipation of interstellar turbulence: results from large-scale high-resolution simulations. Astrophys J Lett 665:L35–L38

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de Avillez MA, Breitschwerdt D (2012a) Non-equilibrium ionization modeling of the Local Bubble. I. Tracing Civ, Nv, and Ovi ions. Astron Astrophys 539:L1 de Avillez MA, Breitschwerdt D (2012b) Time-dependent cooling in astrophysical plasmas: the non-equilibrium ionization structure of the interstellar medium and X-ray emission at low temperatures. Astrophys J Lett 756:L3 de Avillez MA, Spitoni E, Breitschwerdt D (2012) E(A+M)PEC – an OpenCL atomic & molecular plasma emission code for interstellar medium simulations. In: Capuzzo-Dolcetta R, Limongi M, Tornambè A (eds) Advances in computational astrophysics: methods, tools, and outcome. Astronomical society of the Pacific conference series, vol 453. Astronomical Society of the Pacific, San Francisco, p 341 Desiati P, Lazarian A (2013) Anisotropy of TeV cosmic rays and outer heliospheric boundaries. Astrophys J 762:44 Dobbs CL, Burkert A, Pringle JE (2011) The properties of the interstellar medium in disc galaxies with stellar feedback. Mon Not R Astron Soc 417:1318–1334 Elmegreen BG, Scalo J (2004) Interstellar turbulence I: observations and processes. Astron Astrophys Rev 42:211–273 Ferrière KM (2001) The interstellar environment of our galaxy. Rev Mod Phys 73: 1031–1066 Fichtner H (2001) Anomalous cosmic rays: messengers from the outer heliosphere. Space Sci Rev 95:639–754 Fimiani L et al (2016) Interstellar 60 Fe on the surface of the Moon. Phys Rev Lett 116(15):151104. doi:10.1103/PhysRevLett.116.151104 Fleck RC Jr (1996) Scaling relations for the turbulent, non–self-gravitating, neutral component of the interstellar medium. Astrophys J 458:739 Freeman KC (1987) The galactic spheroid and old disk. Astron Astrophys Rev 25: 603–632 Frisch PC, Redfield S, Slavin JD (2011) The interstellar medium surrounding the Sun. Annu Rev Astron Astrophys 49:237–279 Fuchs B, Breitschwerdt D, de Avillez MA, Dettbarn C, Flynn C (2006) The search for the origin of the Local Bubble redivivus. Mon Not R Astron Soc 373:993–1003 Galametz M et al (2016) The dust properties and physical conditions of the interstellar medium in the LMC massive star-forming complex N11. Mon Not R Astron Soc 456: 1767–1790 Galeazzi M et al (2014) The origin of the local 1/4-keV X-ray flux in both charge exchange and a hot bubble. Nature 512:171–173 Girichidis P et al (2016) The SILCC (SImulating the LifeCycle of molecular Clouds) project – II. Dynamical evolution of the supernova-driven ISM and the launching of outflows. Mon Not R Astron Soc 456:3432–3455 Heiles C, Troland TH (2003) The millennium Arecibo 21 centimeter absorption-line survey. II. Properties of the warm and cold neutral media. Astrophys J 586:1067–1093 Hillas AM (1984) The origin of ultra-high-energy cosmic rays. Astron Astrophys Rev 22: 425–444 Kachelrieß M, Neronov A, Semikoz DV (2015) Signatures of a two million year old supernova in the spectra of cosmic ray protons, antiprotons, and positrons. Phys Rev Lett 115(18):181103. doi:10.1103/PhysRevLett.115.181103. arXiv:1504.06472 Kafatos M (1973) Time-dependent radiative cooling of a hot low-density cosmic gas. Astrophys J 182:433–448 Kennicutt RC Jr (1998) The global Schmidt law in star-forming galaxies. Astrophys J 498:541–552 Knie K, Korschinek G, Faestermann T, Dorfi EA, Rugel G, Wallner A (2004) 60 Fe anomaly in a deep-sea manganese crust and implications for a nearby supernova source. Phys Rev Lett 93(17):171103 Kolmogorov AN (1941) Dissipation of energy in locally isotropic turbulence. Doklady Akad Nauk SSSR 32(16); German translation in Sammelband zur Statistischen Theorie der Turbulenz. Akademie Verlag, Berlin (1958), p 77

2380

D. Breitschwerdt et al.

Korpi MJ, Brandenburg A, Shukurov A, Tuominen I, Nordlund Å (1999) A supernova-regulated interstellar medium: simulations of the turbulent multiphase medium. Astrophys J Lett 514:L99–L102 Kóta J, Jokipii JR (1995) Corotating variations of cosmic rays near the South heliospheric pole. Science 268:1024–1025 Kritsuk AG, Norman ML, Padoan P, Wagner R (2007) The statistics of supersonic isothermal turbulence. Astrophys J 665:416–431 Mac Low MM, Klessen RS (2004) Control of star formation by supersonic turbulence. Rev Mod Phys 76:125–194 Mac Low MM, Klessen RS, Burkert A, Smith MD (1998) Kinetic energy decay rates of supersonic and super-alfvénic turbulence in star-forming clouds. Phys Rev Lett 80:2754–2757 McComas DJ, Alexashov D, Bzowski M, Fahr H, Heerikhuisen J, Izmodenov V et al (2012) The heliosphere’s interstellar interaction: no bow shock. Science 336:1291–1293 McComas DJ, Lewis WS, Schwadron NA (2014) IBEX’s enigmatic ribbon in the sky and its many possible sources. Rev Geophys 52:118–155 McKee CF, Ostriker JP (1977) A theory of the interstellar medium – three components regulated by supernova explosions in an inhomogeneous substrate. Astrophys J 218:148–169 Opher M (2016) The Heliosphere: what did we learn in recent years and the current challenges. In: Multi-scale structure formation and dynamics in cosmic plasmas. Space sciences series of ISSI, vol 51. Springer, Berlin, pp 211–230 Parker EN (1958) Dynamics of the interplanetary gas and magnetic fields. Astrophys J 128: 664–676 Perri S, Zimbardo G (2009) Ion superdiffusion at the solar wind termination shock. Astrophys J 693:L118–L121 Piontek RA, Ostriker EC (2005) Saturated-state turbulence and structure from thermal and magnetorotational instability in the ISM: three-dimensional numerical simulations. Astrophys J 629:849–864 Potgieter MS (2013) Solar modulation of cosmic rays. Living Rev Solar Phys 10:3 Richardson JD (2013) Voyager observations of the interaction of the heliosphere with the interstellar medium. J Adv Res 4:229–233 Robitaille TP, Whitney BA (2010) The present-day star formation rate of the Milky Way determined from spitzer-detected young stellar objects. Astrophys J Lett 710:L11–L15 Rosen A, Bregman JN (1995) Global models of the interstellar medium in disk galaxies. Astrophys J 440:634 Salpeter EE (1955) The luminosity function and stellar evolution. Astrophys J 121:161 Scherer K, Fichtner H (2014) The return of the bow shock. Astrophys J 782:25 Schlickeiser R (2012) Cosmic magnetization: from spontaneously emitted aperiodic turbulent to ordered equipartition fields. Phys Rev Lett 109:261,101 Schwadron FC et al (2014) Global anisotropies in TeV cosmic rays related to the Sun’s local galactic environment from IBEX. Science 343:988–990 Shapiro PR, Moore RT (1976) Time-dependent radiative cooling of a hot, diffuse cosmic gas, and the emergent X-ray spectrum. Astrophys J 207:460–483 She ZS, Leveque E (1994) Universal scaling laws in fully developed turbulence. Phys Rev Lett 72:336–339 Siewert M, Fahr HJ, McComas DJ, Schwadron NA (2012) The inner heliosheath source for keV-ENAs observed with IBEX. Shock-processed downstream pick-up ions. Astron Astrophys 539:A75 Stone JM, Ostriker EC, Gammie CF (1998) Dissipation in compressible magnetohydrodynamic turbulence. Astrophys J Lett 508:L99–L102 von Weizsäcker CF (1951) The evolution of galaxies and stars. Astrophys J 114:165 Wada K, Norman CA (2001) Numerical models of the multiphase interstellar matter with stellar energy feedback on a galactic scale. Astrophys J 547:172–186 Wallner A et al (2016) Recent near-Earth supernovae probed by global deposition of interstellar radioactive 60 Fe. Nature 532:69–72. doi:10.1038/nature17196

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Weibel ES (1959) Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys Rev Lett 2:83–84 Wolfire MG, Hollenbach D, McKee CF, Tielens AGGM, Bakes ELO (1995) The neutral atomic phases of the interstellar medium. Astrophys J 443:152–168 Wood BE (2004) Astrospheres and solar-like stellar winds. Living Rev Solar Phys 1:2 Zank GP (2015) Faltering steps into the galaxy: the boundary regions of the heliosphere. Annu Rev Astron Astrophys 53:449–500 Zurbuchen TH (2007) A new view of the coupling of the Sun and the heliosphere. Annu Rev Astron Astrophys 45:297–338

Determining Amino Acid Chirality in the Supernova Neutrino Processing Model

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Michael A. Famiano and Richard N. Boyd

Abstract

Recent work has suggested that the chirality of the amino acids could be established in the magnetic field of a nascent neutron star from a core-collapse supernova via processing by the neutrinos that would be emitted. A model is described that can be used to estimate the bulk polarization of large rotating meteoroids in the magnetic field of a neutron star. This model assumes that the neutrinos emitted from the nascent neutron star would interact with the amino acids, which had been oriented by the neutron star’s magnetic field. The results of this model are applicable to the Supernova Neutrino Amino Acid Processing model, which describes one possible way in which the amino acids, known in many cases to exhibit supramolecular chirality, could have become enantiomeric. We have studied the capability of this model for selective destruction of one molecular chirality. Although some aspects of the model are speculative, tests may be possible to at least check the capability of this most basic aspect of the model.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Models of Amino Acid Chirality Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Weak Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Circularly Polarized Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The SNAAP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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M.A. Famiano () Department of Physics, Western Michigan University, Kalamazoo, MI, USA e-mail: [email protected] R.N. Boyd Department of Physics, Department of Astronomy, Ohio State University (Emeritus), Columbus, OH, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_20

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3 The SNAAP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Dynamical Model of Chiral State Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Results of the Dynamical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Analyses of inclusions in meteoritic carbonaceous chondrites (Bada et al. 1983; Cronin and Pizzarello 1997; Cronin et al. 1988; Glavin and Dworkin 2009; Glavin et al. 2010; Hurd et al. 2011; Kvenvolden et al. 1970) have shown that the molecules of life, especially the amino acids, are made in outer space. Furthermore, some of the amino acids so synthesized tend to have the left-handed chirality that is observed almost entirely in earthly amino acids. It is generally accepted that if some mechanism can introduce an imbalance in the populations of the left- and right-handed forms of any amino acid (Glavin and Dworkin 2009), successive synthesis or evolution of the molecules involving autocatalytic reactions can amplify this enantiomerism ultimately to produce a single form. What is not well understood, though, is the mechanism by which the initial imbalance is produced and the means by which it always produces the lefthanded chirality observed in the amino acids. This enigma has been discussed in numerous reviews in past years (see, e.g., Barron 2008; Bonner 1991; Boyd 2012; Frank 1953; Gol’danskii and Kuz’min 1989; Kondepudi and Nelson 1985; Mason 1984). The amount by which one chirality exceeds the other is represented by the enantiomeric excess, ee, defined as ee 

N R  NS N R C NS

(1)

where NS and NR represent the number of left- and right-handed amino acids, respectively, of a specific type in an ensemble. Thus, Earth’s amino acids (with the exception of the non-chiral glycine) have enantiomeric excesses of 1.0 or 100 %.

2

Models of Amino Acid Chirality Formation

The energy states of the left- and right-handed forms have been shown, by detailed computations, to differ at most by infinitesimal amounts due to parity violation (Quack 2002; Tranter and MacDermott 1986), so it would be difficult for thermal equilibrium to produce the imbalance. However, some evidence exists that electroweak parity-violating energy shifts could produce an enantiomeric excess if the molecules are in a gas phase (MacDermott et al. 2009).

92 Determining Amino Acid Chirality in the Supernova Neutrino Processing Model

2.1

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The Weak Interaction

Recent work (Boyd et al. 2010, 2011) has suggested that the chirality of the amino acids could be established in the magnetic field of a nascent neutron star from a core-collapse supernova via processing by the neutrinos that would be emitted. This model, the Supernova Neutrino Amino Acid Processing model, or SNAAP model, not only appears to produce a small chiral imbalance but always produces the same sign of the chirality. Another possibility (Mann and Primakoff 1981) invoked selective processing by some manifestation of the weak interaction, which does violate parity conservation, so might perform a chiral selection. This idea was based on earlier work (Ulbricht and Vester 1962; Vester et al. 1959). Mann et al. (Mann and Primakoff 1981) focused on the ˇ-decay of 14 C to produce the selective processing. However, it was not possible in that study to show how simple ˇ-decay could produce chiral-selective molecular destruction. A modern update on this possibility (Gusev et al. 2008) does appear to produce some enantiomerism. Another suggestion (Cline 2005) assumed that neutrinos emitted by a core-collapse supernova would selectively process the carbon or the hydrogen in the amino acids to produce enantiomerism. However, this also did not explain how a predisposition toward one or the other molecular chirality could evolve from the neutrino interactions. A similar suggestion (Bargueno and Perez de Tudela 2007) involves the effects of neutrinos from supernovae on molecular electrons. It was also suggested that the differences between ortho- and para-hydrogen pairs (Shinitzky and Elitzur 2006) in the amino acids could produce a chiral selection. The possibility that dark matter or cosmological neutrinos could select enantiomers has also been studied (Bargueno et al. 2008).

2.2

Circularly Polarized Light

Another mechanism lies with processing of a population of amino acids in interstellar space by circularly polarized light (Bailey et al. 1988; de Marcellus et al. 2011; Meierhenrich et al. 2002; Meinert et al. 2010; Takahashi et al. 2009; Takano et al. 2007); this could select one chirality over the other. This solution does have the benefit of being experimentally verifiable, at least in some of its aspects, a result of the large cross section for interaction of photons with matter. It therefore has been demonstrated to produce an enantiomeric excess in amino acids in laboratory experiments (Takano et al. 2007). A number of different regions of space have been identified as possibilities with light having large enough circular polarization, at least over some bandwidth, to perform the necessary amino acid processing (Bailey 2001). This model, however, is not without its difficulties. It does not easily explain why the physical conditions that would select one chirality in one place would not select the other in a different location. Nonetheless, a region as small as a planetary system

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could be processed by the output from a single star (de Marcellus et al. 2011) so that all the light in that region could be of a single circular polarization. This could explain the observed meteoritic and Earth’s results. Another problem, though, is that circularly polarized light must destroy most of the material it is processing in order to produce a significant enantiomeric excess (Bailey 2001; de Marcellus et al. 2011). Finally, assumed circularly polarized x-rays could only process to a small depth of the surface of a larger object. Given that much of the material in the interstellar medium is in the form of dust grains, this would not present a problem for processing a lot of such material. However, dust grains would not be likely to reach the surface of a planet, since the grains would have to pass through at least some sort of atmosphere. This could be overcome if the grains could agglomerate into larger entities, but that just adds another complexity or uncertainty to consider when determining the enantiomeric excess this model would produce. If the agglomeration occurred before the amino acids had been processed, only the molecules on the surface of the larger objects would be processed, and these would very likely be ablated away as the resulting meteoroids passed through the planetary atmosphere.

2.3

The SNAAP Model

The capability of the SNAAP model for selective destruction of one molecular chirality has been studied in prior work (Famiano et al. 2014). This summarizes previous work (Boyd et al. 2011) to date but does add some comments on the potential applicability of this model, as well as on some others. The SNAAP model has many similarities to nuclear magnetic resonance, even though it is essentially classical. The study does show that the amino acids contained in a large meteoroid could undergo orientation from the magnetic field of the neutron star, subsequent chiral substate selection from the combination of that field and the rotation of the meteoroids, and finally chiral selection by the neutrinos emitted as the neutron star produced by a core-collapse supernova cools over its characteristic few second cooling time. Section 3 reviews the SNAAP model. Section 4 presents the model used to determine the chiral state selection and determines the resulting population imbalance. Section 5 estimates the magnitude of the enantiomeric excess that might be expected from this model, while Sect. 6 presents some conclusions and discusses questions that must be addressed in determining the veracity of any model.

3

The SNAAP Model

This model assumes that the neutrinos emitted from the nascent neutron star would interact with the amino acids that had been oriented by the neutron star’s magnetic field. These molecules would have to be contained in large meteoroids that happened to be passing by the star as it became a supernova, so some fraction of them

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could survive the high-temperature environment existing near the star. The crucial interaction that destroys 14 N is 14

N C N e !14 C C e C

(2)

where N e is an electron antineutrino and eC is a positron. It was also assumed that some imbalance in the total angular momentum of the molecules would be achieved, perhaps by the Buckingham effect (Buckingham 2004; Buckingham and Fischer 2006), which would produce a redistribution in the molecular magnetic substate population that would depend on the spin of the molecules. Then, the conversion from 14 N to 14 C would, because of a spin selection effect on the strength of the interaction, preferentially destroy one orientation compared to the other. The geometry surrounding this neutron star is indicated in Fig. 1. The strong magnetic field of a neutron star will produce a favored chirality as the molecular electronic orbital configuration couples to the molecular configuration. The strength of the neutrino interactions that destroy the 14 N depends on the orientation of the neutrino’s spin with that of the 14 N, as well as conservation of angular momentum. This is indicated by Eqs. 3 and 4. 14 N has a spin of 1, in units of Planck’s constant divided by 2 , whereas the N e and the eC each have spins of 12 . 14 C has a spin of zero. Antialigned case: Aligned case:

Fig. 1 Magnetic field around a neutron star, indicated by B; directions of the antineutrino spins, indicated by S ; and the alignment direction of the 14 N, indicated by SN (Boyd et al. 2010, 2011) (Courtesy of the International Journal of Molecular Sciences and Springer Publishing)

N C N e !14 C C e C

(3)

N C N e !14 C C e C C‹

(4)

14 14

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In Eq. 3, the antialigned case, the two spin vectors on the left-hand side of the equation can add up to 12 , so it can equal the sum of the spin vectors on the righthand side. In Eq. 4, the aligned case, the two spin vectors on the left-hand side of the equation add up to 32 , so it cannot equal the spin vector sum on the right-hand side without an additional unit of angular momentum, indicated by the question mark. This must come from the wave function of the e or the eC , and it is known (Boyd 2008) to inhibit the destruction of 14 N in the aligned case with respect to the antialigned case by about an order of magnitude. One expects that the alignment of the nuclear spin in the neutron star’s magnetic field will result in a slight enantiomeric excess. The hyperfine interaction will couple the nuclear and electronic spins and has been well studied in stellar environments (Berdyugina and Solanski 2002; Berdyugina et al. 2005). Then, while the relationship is much more complicated for complex molecules, the molecular chirality can be shown to be related to the electron angular momentum (PerezGarcia et al. 1992). Thus, this would select one chirality on each side of the neutron star. Although the effects on the two sides of the star would come close to canceling out if the neutrino fluxes were the same on both sides, that has been shown not to be the case in the strong magnetic field of the star (Arras and Lai 1999; Horowitz and Li 1998; Lai and Qian 1998; Maruyama et al. 2011), so that one of the chiral states would then be selected. Although the cross section for the neutrino-14 N interaction is tiny, roughly 40 10 cm2 , this will produce an the enantiomeric excess of about a part in 106 in this model (Boyd et al. 2011). This is comparable to or greater than that achieved in other models, although direct comparison is difficult. With any model of chirality selection, amplification, presumably by autocatalysis (Frank 1953; Gol’danskii and Kuz’min 1989; Kondepudi and Nelson 1985; Mason 1984), is required to produce the order-of-a-few percent magnitudes of the enantiomeric excess observed in the meteorites. Autocatalysis has been demonstrated to occur in several situations in laboratory experiments (Breslow and Levine 2006; Mathew et al. 2004; Soai and Sato 2002; Soai et al. 1995). However, the initial enantiomeric excesses were never as small as one part in 106 ; they were generally of order of 1 %. Additional details of the SNAAP model are discussed in Boyd et al. (2011).

4

Dynamical Model of Chiral State Selection

The vectors that are relevant to this model are shown in Fig. 2. These include the magnetic field vector, B; the molecular total angular momentum vector, I; and the vector that characterizes the rotation of the meteoroid, !, in which the molecules are contained. Clearly the orientation of the rotation vector of the meteoroid, !, is random with respect to the direction of the magnetic field, B, and the orientation of the molecules within the meteoroid is random with respect to the direction of !. Thus, any dynamical description of the effects associated with molecular substate reorientation needs to average over the directions of two of the vectors with respect

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Fig. 2 The vectors relevant to the dynamical model of chiral state selection in the SNAAP model. B is the magnetic field vector, I is the total spin of the molecule, and ! is the vector that characterizes the rotation of the meteoroid in which the molecules are contained

to that of the magnetic field. A Monte Carlo code was written and the averages performed, not only over the directions but over the magnitude of the magnetic field B as well. The quantity calculated by the Monte Carlo code is the bulk polarization of the meteoroid, M, which results from the interaction between the magnetic field of the nascent neutron star and the rotation of the meteoroid. This is similar to that from nuclear magnetic resonance, in which the slight imbalance in magnetic substate distribution in thermal equilibrium is shifted by a radio-frequency signal as the magnetic field passes through the value at which the energy difference between the substates is resonant. In the present model, the shift is not due to a resonant condition but rather to an adiabatic transition between the chiral states that results from the interaction between the magnetic field of the neutron star and the rotating total angular momentum of each molecule. The bulk polarization of the molecules trapped in a meteoroid will depend on the strength of the star’s field at the meteoroid’s location, the gyromagnetic ratio of the molecule  , the meteoroid’s angular speed, and the orientation of the angular velocity vector with respect to the magnetic field. In the reference frame of the meteoroid, the magnetic field has a component parallel to the angular velocity vector and a component perpendicular to this vector with the perpendicular component rotating at the angular frequency of the meteoroid. The polarization is well established in this condition (Bloch 1946). For a population of polarized states

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with a rotating component of a magnetic field, the magnetization vector is given by the Bloch equation (Bloch 1946): dM 1 M.t / C  M.t /  B.t / D n  dt TR

(5)

where the bulk magnetization M is initiated in the external magnetic field for a material with number density n and magnetic moment . The relaxation time, TR , corresponds to the damping time constant during which a magnetized medium returns to a state of random orientation. The last term in Eq. 5 corresponds to the torque on the magnetic moment from the medium’s motion in the external magnetic field. For a material of nonzero magnetic moment in an external magnetic field Bı , the angular momentum vector will precess about the magnetic field axis with the precession frequency !ı = Bı . The rotation of the meteoroid in the magnetic field induces a NMR-like situation – in the reference frame of the meteoroid – in which the external field B (see Fig. 2) can be resolved into a field parallel of the rotation axis, which is Bı , and a field perpendicular to the rotation axis, B1 . The perpendicular component rotates about Bı with a frequency !; the precession frequency about this field vector is defined as !1 D  B1 . Equation 5 can then be solved by assuming a rotating reference frame in which B1 is stationary. This analysis begins with a simplified model in which the medium is assumed to be rotating at constant angular speed in the magnetic field from a central neutron star. For this situation, the time spent in the magnetic field is assumed to be much longer than the relaxation time. For this reason, one can take the stationary solution of the bulk magnetization: dM D0 (6) dt from which the average magnetization of a population of molecules can be written in component form: hM ix D

!1 ! nTR .!/2 C! 2 C.1=T

hM iy D

1

2 R/

n .!/2 C!!21C.1=T /2 R 1

h hM iz D nTR 1 

!12 .!/2 C!12 C.1=TR /2

(7) i

where ! D ! !ı . In Eqs. 7, the maximum polarization in the z-direction, defined to be parallel to the field Bı , will occur for a large ! corresponding to a large difference in the perpendicular field rotation rate and the precession frequency about the parallel field. This corresponds to a minimum in the x and y components of the bulk magnetization. The overall polarization angle  with respect to Bı is given by:

tan  D

1=2  hM i2x C hM i2y hM iz

(8)

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The parallel and perpendicular components of the magnetic field are determined by the angle between the meteoroid’s angular velocity vector and the magnetic field produced by the neutron star: B? D Bns sin  Bk D Bns cos 

(9)

where  is the angle between the angular velocity vector of the meteoroid and the local field vector of the neutron star Bns at the location of the meteoroid. The rotation rate of B? about Bk is equal to the angular speed of the meteoroid in the stellar field. Equation 7 shows that there is an interdependence of ! and !1 . In order to examine this interdependence, several Monte Carlo simulations of meteoroids in the vicinity of a neutron star’s (dipole) magnetic field to simulate a spatial distribution of meteoroids with varying angular speeds and orientations relative to the external dipole field were performed. Ideally, meteoroids in polar orbits will be most significantly affected as the neutrino spin vectors are aligned with the magnetic field in the neutron star’s polar region. In this way, the average bulk polarization angle is determined using Eq. 8. For each simulation, meteoroids were assumed to be distributed evenly in a volume of space about the neutron star with random angular orientations and velocities. Several cases were studied. In each case, meteoroids were assumed to be evenly distributed in a volume of space about the neutron star. For each sample in the Monte Carlo calculation, the components of the magnetization were calculated along with the polarization angle. These calculations have ignored the effects of thermalization. If such effects were important, they would produce a competition between the thermalization lifetime and the time associated with producing the substate imbalance, which is the order of the inverse of the meteoroid rotation time. The lifetimes of the chiral states of the amino acids at the temperatures of outer space have been found to be hundreds of years or even much longer (Ehrenfreund 2001), even at the relatively high temperatures assumed in that study. Thus, the thermalization times were assumed to be infinite.

5

Results of the Dynamical Model

An example of the bulk polarizations from the SNAAP model is shown in Fig. 3 for three example models studied. The angular orientations of the meteoroids’ rotation axes were evenly distributed between 0 and 90ı . In this figure, the surface field of the star is varied, while a distribution of angular speeds and radii is simulated. While a higher field will exert a stronger initial torque on the molecules, the steadystate condition of the system for strong fields becomes more significantly affected by the randomly distributed perpendicular components of the field in the reference frame of the meteoroid. Then, the resonant precession frequency of the external

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Bsurf = 1014 G Bsurf = 5⫻1014 G

N (/0.05°)

10-3

Bsurf = 1015 G

10-4

10-5 0

10

20

30

40

50

60

70

80

90

o

φ( )

Fig. 3 Polarization distribution for three example models. This figure compares the polarization distribution for various neutron star surface magnetic fields

field differs significantly from the angular speed of the meteoroid. The polarization distribution is then more strongly affected by the perpendicular components of the field. Models for the SNAAP calculation have examined the influence of the neutron star’s magnetic field, the meteoroid rotation rate, and the distance from the neutron star surface. The angular speed of the meteoroid in each event varies uniformly between 0 and 10 rad/s. The distribution of polarization with respect to the stellar magnetic field vector is shown for these models in the figure. The bulk polarization was found to increase dramatically with radius. For the random orientation of the meteoroid rotational velocity vectors, the value of the precession frequency !1 about the perpendicular component of the magnetic field in the meteoroid’s reference frame decreases as well, resulting in a smaller perpendicular component of magnetization and a larger parallel component (Eq. 7). While one may conclude that larger radii are more important for this scenario, the neutrino fluence decreases as the inverse square of the radius, resulting in a reduced selective production effect. Likewise, as the field weakens, the overall polarization may be more susceptible to stochastic effects since the net torque of the external field is much weaker. The angular speed also has an effect on the bulk polarization. Equation 7 shows that a quasi-resonant condition occurs in the magnetic field in the case where ! D 0. For a time that is long compared to the relaxation time of the molecule, the difference in rotational frequency and the magnetic field resonance frequency increases, resulting in a larger polarization component parallel to the magnetic field vector and smaller perpendicular components of polarization. Thus, a larger rotation speed will move the meteoroid farther away from the resonant region. The smallest amount of polarization in the z-direction will result for values of ! D 0 or for

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meteoroid rotation speeds equal to that of the molecular precession frequency of the local magnetic field. For a gyromagnetic ratio of 2  107 rad s1 T1 and a surface magnetic field of 1014 G, this would correspond to an angular speed 5 rad s1 at 0.025 AU. Thus, the effect of meteoroid rotation can be significant in reducing the overall polarization for small rotation rates. While the rotational rate distribution is assumed flat in this model, very likely the rotation rates are heavily weighted toward zero. The effects of increasing the molecular gyromagnetic ratios are similar to the effects of increasing the external magnetic fields. While a stronger gyromagnetic ratio will result in a larger external torque on the molecule’s magnetic moment, the torque from the effective field, with a significant contribution from a perpendicular component, will contribute to the overall molecular orientation. It has been found that in the steady state, a smaller gyromagnetic ratio results in a smaller contribution from the random orientations of the angular speed vectors of the meteoroids, and the overall polarization is more randomly distributed. However, even for a fairly large gyromagnetic ratio of 5  107 rad s1 T1 , there is a net polarization parallel to the local magnetic field. The meteoroids were assumed to be constrained within a radius of 0.01–0.05 AU about a population of stars with a distribution of magnetic fields. As discussed previously, a stronger magnetic field will result in a loss of net polarization, so that a model with a distribution of larger magnetic fields has a polarization distribution that is not as pronounced about zero degrees. These particular models are interesting as they enable a more accurate estimate of the enantiomerism that could be produced in the SNAAP model than was done previously. In Boyd et al. (2011), an estimated cross section for antineutrino conversion from 14 N to 14 C was made from the results of Fuller et al. (1999), and it was assumed that the minimum distance from the nascent neutron star to the meteoroid that would permit survival of the meteoroid would be 0.01 AU. At that distance, the estimated enantiomeric excess was 1  104 %. However, implicit in that assumption was the estimate that the molecular polarization was 100 %. The fraction of the molecules that occur within 10ı of the direction of the magnetic field of the neutron star, as determined from these calculations, is not 100 %, though it can be above 90 % given the right conditions. The very smallest values occur at the smallest radii, at which the magnetic field becomes so strong that the model probably breaks down anyway. At a radius of 2 AU, the estimate of the bulk polarization is about 50 %, and the neutrino flux will have fallen off from the value used in the estimate of Boyd et al. (2011) by a factor of 4. The result is that the estimated enantiomeric excess becomes 1  105 %, one part in 107 . Details of this calculation, along with additional calculations, are described in Famiano et al. (2014). Does so low a value permit the SNAAP model to drive the ultimate homochirality of the Earth or even the few percent enantiomeric excesses found in the meteoritic samples? The favored mechanism by which amplification could occur, autocatalysis, was originally suggested by Frank (1953) but has been elaborated since by others (Gol’danskii and Kuz’min 1989; Kondepudi and Nelson 1985; Mason 1984). More

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significantly, it has been demonstrated experimentally (Breslow and Levine 2006; Mathew et al. 2004; Soai and Sato 2002; Soai et al. 1995), thus showing that autocatalysis does work. However, the minimum levels of enantiomeric excess in those experiments were fractions of a percent, several orders of magnitude larger than the value estimated for the SNAAP model. Existing experiments have not yet determined the lower limit for autocatalysis to prevail. A qualitative evaluation of the optimal radius about the neutron star at which the polarization can occur can be made by examining the product of the neutrino flux and the average normalized polarization. This is described as the bulk polarization normalized to unity by subtracting this from =4, which is the bulk polarization for a completely unpolarized medium:

=4  hM i

=4

(10)

The calculated polarization with respect to the magnetic field vector increases with radius, while the neutrino flux decreases as r2 . Thus, the product of the normalized polarization and 1/r2 will provide a rough idea of an optimal radius for which chiral selection occurs. This product is shown as a function of radius in Fig. 4 for a surface field of 1014 G and  D 2  107 . It is noted, however, that this calculation does not account for thermalization, the effects of which are difficult to estimate, since molecules buried in pockets of the meteoroid may be more immune

Bulk Polarization Map, B surf = 1014 G, γ = 2×107 1

(45° - )/45°

0.8

0.6

0.4

0.2

0 0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

x (AU)

Fig. 4 Product of the normalized polarization and 1/r2 for a surface field strength of 1014 G and  D 2  107 . The black line is the normalized polarization. The green line is the 1/r2 relationship, and the red line is the product of the two. Large fluctuations near 0 AU are because fewer events are averaged over in the Monte Carlo calculation in the region closest to the star

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to thermalization effects than those on the surface. However, these effects may be small as amino acids buried deep within a meteoroid may be quite cold.

6

Conclusions

In order for an effective production of an enantiomeric excess of polar atoms or molecules via the SNAAP model, three things are required. These are (1) a strong external magnetic field, (2) a species with a nonzero magnetic moment (gyromagnetic ratio), and (3) an external polarized weak interaction mechanism. All three of these are satisfied by introducing a meteoroid containing a molecular species which is not initially polarized with respect to the magnetic field in the vicinity of a nascent neutron star from a core-collapse supernova. The meteoroid acts as the substrate carrying the molecular or atomic species, and the neutron star provides both the external magnetic field and the polarized weak interaction in the form of selective destruction of the molecule via neutrinos, which are naturally polar, since they have a definite helicity. The differential in interaction cross sections between the neutrino-nucleus collisions in which the reactants are aligned parallel or antiparallel, together with the asymmetric emission of the neutrinos, provides a difference in the destruction of the polar molecule, and an enantiomeric excess is created. Of course, it is difficult to test the SNAAP model because of the tiny cross sections with which neutrinos interact. However, one could envision bombarding amino acids contained in a strong magnetic field with neutrinos from, for example, the Spallation Neutron Source; such experiments were discussed in Boyd (2012). This would not provide a complete test of the model, but it would test the most basic features. In the SNAAP model, the meteoroids provide a mode of transport by which molecules are moved close enough to the neutron star surface to benefit from the intense neutrino flux from the cooling star but sufficiently distant and/or large to avoid complete destruction from supernova photons. Molecular polarization is accomplished via the intense magnetic field. Molecules within the meteoroid are polarized, and the bulk polarization of the material has been calculated for several situations. Magnetic resonance conditions were examined as natural precession frequencies of the molecular medium interact with the angular speed of the meteoroid. The final simulation in this study not only considered the effects of a population of meteoroids about a single star but also the effects of various neutron star magnetic fields in a “galaxy-wide” sampling to gain a perspective of the overall simulation. It is found that a significant net molecular polarization can be produced. Confirmation of cosmic production of amino acid enantiomerism is crucial to the veracity of this or any other model that purports to explain how it is produced. Although the meteorites in which it has been observed are strongly suggestive, it was hoped that the data from the Rosetta mission and its lander Philae (Thiemann and Meierhenrich 2011) would confirm these observations. Unfortunately, it appears

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that this will not be the case, although future missions may provide the essential tests. However, other considerations are important to models of enantiomerism production. For example, Glavin et al. (2010) found that the meteoritic enantiomerism depended critically on the amount of aqueous alteration the material had undergone before it arrived on Earth. Perhaps water is essential for the formation of the enantiomeric supramolecular assembly. Or it may provide a mobility necessary for molecular alignment in the magnetic field. It has also been suggested (Glavin et al. 2010; Pizzarello and Weber 2004) that some molecules that are especially resistant to racemization, for example, alpha-dialkyl amino acids such as isovaline, could be formed by whatever process is responsible for producing its enantiomerism, and it could then transfer its asymmetry to other amino acids. As noted above, the size of the meteoroid also appears to be important to its ability to deliver its amino acids to the surface of a planet. Small meteoroids would almost certainly be destroyed by their passage through the atmosphere of the early planet. And larger meteoroids would certainly have some portion of their surface ablated away by the atmosphere or have it heated sufficiently to destroy any enantiomerism of near-surface molecules that might have been produced even if the molecules survived planetary entry. In this context, the SNAAP model, or any model that involves neutrinos, has an advantage over models that involve processing by photons, since the neutrinos process the entire object, even one as large as a planet. Thus, if some of the meteoroid was ablated away, or achieved a high surface temperature, molecules and their enantiomeric excesses, within a larger object, would still have a good chance of survival. This fact makes it difficult to make direct comparisons between models. The enantiomeric excess created by the SNAAP model can be estimated, as was done above. However, the survivable enantiomeric excess that could be delivered by circularly polarized light becomes much more difficult to estimate. It appears to be comparable to that achieved by the SNAAP model as it is produced but may be decreased by several orders of magnitude when its survivability, together with the depth to which circularly polarized light could penetrate, is considered. Indeed, it may become vanishingly small when passage through the planetary atmosphere is considered.

7

Cross-References

 Discovery, Confirmation, and Designation of Supernovae  Effect of Supernovae on the Local Interstellar Material  Electron Capture Supernovae from Super Asymptotic Giant Branch Stars  Evolution of the Magnetic Field of Neutron Stars  Hydrogen-Rich Core-Collapse Supernovae  Mass Extinctions and Supernova Explosions  Neutrino Emission from Supernovae  Stardust from Supernovae and Its Isotopes

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 Supernovae and Supernova Remnants: The Big Picture in Low Resolution  Supernovae and the Formation of Planetary Systems  Supernovae from Massive Stars  Supernovae, our Solar System, and Life on Earth Acknowledgements MF’s work is supported by NSF grant #PHY-1204486 and #PHY-0855013. Both MF and RNB’s work was supported by the NAOJ Visiting Professor program.

References Arras P, Lai D (1999) Neutrino-nucleon interactions in magnetized neutron-star matter: the effects of parity violation. Phys Rev D60:043001-1–043001-28 Bada JL, Cronin JR, Ho M-S, Kvenvolden KA, Lawless JG, Miller SL, Oro J, Steinberg S (1983) On the reported optical activity of amino acids in the Murchison meteorite. Nature 1301: 494–496 Bailey J (2001) Astronomical sources of circularly polarized light and the origin of homochirality. Orig Life Evol Biosph 31:167–183 Bailey J, Chrysostomou A, Hough JH, Gledhill TM, McCall A, Clark S, Menard F, Tamura M (1988) Circular polarization in star-formation regions: implications for biomolecular homochirality. Science 281:672–674 Bargueno P, Perez de Tudela R (2007) The role of supernova neutrinos on molecular homochirality. Orig Life Evol Biosph 37:253–257 Bargueno P, Dobado A, Gonzalo I (2008) Could dark matter or neutrinos discriminate between the enantiomers of a chiral molecule? Europhys Lett 82:13002–13005 Barron LD (2008) Chirality and life. Space Sci Rev 135:187–201 Berdyugina SV, Solanki SK (2002) The molecular Zeeman effect and diagnostics of solar and stellar magnetic fields I. Theoretical spectral patterns in the Zeeman regime. Astron Astrophys 385:701–715 Berdyugina SV, Braun PA, Fluri DM, Solanki SK (2005) The molecular Zeeman effect and diagnostics of solar and stellar magnetic fields III. Theoretical spectral patterns in the PaschenBack regime. Astron Astrophys 444:947–960 Bloch F (1946) Nuclear induction. Phys Rev 70:460–474 Bonner W (1991) The origin and amplification of biomolecular chirality. Orig Life Evol Biosph 21:59–111 Boyd RN (2008) An introduction to nuclear astrophysics. The University of Chicago Press, Chicago, pp 126–132 Boyd RN (2012) Stardust, supernovae and the molecules of life. Springer, New York Boyd RN, Kajino T, Onaka T (2010) Supernovae and the chirality of the amino acids. Astrobiology 10:561–568 Boyd RN, Kajino T, Onaka T (2011) Supernovae, neutrinos, and the chirality of the amino acids. Int J Mol Sci 12:3432–3444 Breslow R, Levine MS (2006) Amplification of enantiomeric concentrations under credible prebiotic conditions. Proc Natl Acad Sci 103:12979–12980 Buckingham AD (2004) Chirality in NMR spectroscopy. Chem Phys Lett 398:1–5 Buckingham AD, Fischer P (2006) Direct chiral discrimination in NMR spectroscopy. Chem Phys 324:111–116 Cline D (2005) Supernova antineutrino interactions cause chiral symmetry breaking and possibly homochiral biomaterials for life. Chirality 17:S234–S239 Cronin JR, Pizzarello S (1997) Enantiomeric excesses of meteoritic amino acids. Science 275: 951–955

2398

M.A. Famiano and R.N. Boyd

Cronin JR, Pizzarello S, Cruikshank DP (1988) Organic matter in carbonaceous chondrites, planetary satellites, asteroids and comets. In: Kerridge JF, Matthews MS (eds) Meteorites and the early solar system. University of Arizona Press, Tucson, pp 819–857 de Marcellus P, Meinert C, Nuevo M, Filippi J-J, Danger G, Deboffle D, Nahon L, d’Hendecourt LLS, Meierhenrich UJ (2011) Non-racemic amino acid production by ultraviolet irradiation of achiral interstellar ice analogs with circularly polarized light. Astrophys J 727:L1–L6 Ehrenfreund P, Bernstein MP, Dworkin JP, Sandford SA, Allamandola LJ (2001) The photostability of amino acids in space. Astrophys J 550:L95–L99 Famiano, MA, Boyd, R, Kajino, T,Onaka, T, Koehler, K, Hulbert, S (2014) Determining amino acid chirality in the supernova neutrino processing model. Symmetry 6:909–925 Frank F (1953) On spontaneous asymmetric synthesis. Biochim Biophys Acta 11:459–463 Fuller GM, Haxton WC, McLaughlin GC (1999) Prospects for detecting neutrino flavor oscillations. Phys Rev D59:085005-1–085005-15 Glavin DP, Dworkin JP (2009) Enrichment of the amino acid l-isAvaline by aqueous alteration on CI and CM meteorite parent bodies. Proc Natl Acad Sci USA 106:5487–5492 Glavin DP, Callahan MP, Dworkin JP, Elsila JE (2010) The effects of parent body processes on amino acids in carbonaceous chondrites. Met Plan Sci 45:1948–1972 Gol’danskii VI, Kuz’min VV (1989) Spontaneous breaking of mirror symmetry in nature and the origin of life. Sov Phys Usp 32:1–29 Gusev GA, Kobayashi K, Moiseenko EV, Poluhina NG, Saito T, Ye T, Tsarev VA, Xu J, Huang Y, Zhang G (2008) Results of the second stage of the investigation of the radiation mechanism of chiral influence (RAMBAS-2 experiment). Orig Life Evol Biosph 38:509–515 Horowitz CJ, Li G (1998) Cumulative parity violation in supernovae. Phys Rev Lett 80:3694–3697 Hurd CDK, Blinova A, Simkus DN, Huang Y, Tarozo R, Alexander CM O’D, Gyngard F, Nittler LR, Cody GD, Fogel ML, Kebukawa Y, Kilcoyne ALD, Hilts RW, Slater GF, Glavin DP, Dworkin JP, Callahan MP, Elsila JE, De Gregorio BT, Stoud RM (2011) Origin and evolution of prebiotic organic matter as inferred from the Tagish Lake meteorite. Science 332:1304–1307 Kondepudi DK, Nelson GW (1985) Weak neutral currents and the origin of biomolecular chirality. Nature 314:438–441 Kvenvolden K, Lawless J, Pering K, Peterson E, Flores J, Ponnamperuma C, Kaplan IR, Moore C (1970) Evidence for extraterrestrial amino-acids and hydrocarbons in the Murchison meteorite. Nature 228:923–926 Lai D, Qian Y-Z (1998) Neutrino transport in strongly magnetized proto-neutron stars and the origin of pulsar kicks: the effect of asymmetric magnetic field topology. Astrophys J 505:844– 853 MacDermott AJ, Fu T, Nakastuka R, Coleman AP, Hyde GO (2009) Parity-violating energy shifts of Murchison L-amino acids are consistent with an electroweak origin of meteoric L-enantiomeric excesses. Orig Life Evol Biosph 39:459–478 Mann AK, Primakoff H (1981) Chirality of electrons from beta-decay and the left-handed asymmetry of proteins. Orig Life 11:255–265 Maruyama T, Kajino T, Yasutake N, Cheoun M-K, Ryu C-Y (2011) Asymmetric neutrino emission from magnetized proton-neutron star matter including hyperons in relativistic mean field theory. Phys Rev D83:081303-1–081303-5 Mason SF (1984) Origins of biomolecular handedness. Nature 311(5981):19–23 Mathew SP, Iwamura H, Blackmond DG (2004) Amplification of enantiomeric excess in a prolinemediated reaction. Angew Chem Int Ed 43:3317–3321 Meierhenrich UJ, Filippi J-J, Meinert C, Bredehoft JH, Takahashi J-I, Nahon L, Jones NC, Hoffman SV (2002) Circular dichroism of amino acids in the vacuum-ultraviolet region. Angew Chem Int Ed 49:7799–7802 Meinert C, Filippi J-J, Nahon L, Hoffman SV, d’Hendecourt L, de Marcellus P, Bredehoft JH, Thiemann WH-P, Meierhenrich UJ (2010) Photochirogenesis: photochemical models on the origin of biomolecular homochirality. Symmetry 2:1055–1080 Perez-Garcia VM, Gonzalo I, Perez-Diaz JL (1992) Theory of the stability of the quantum chiral state. Phys Lett A 167:377–382

92 Determining Amino Acid Chirality in the Supernova Neutrino Processing Model

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Pizzarello S, Weber AL (2004) Prebiotic amino acids as asymmetric catalysts. Science 303:1151– 1152 Quack M (2002) How important is parity violation for molecular and biomolecular chirality? Angew Chem Int Ed 41:4618–4630 Shinitzky M, Elitzur AC (2006) Ortho-para spin isomers of the protons in the methylene group – possible implications for protein structure. Chirality 18:754–756 Soai K, Sato I (2002) Asymmetric autocatalysis and its application to chiral discrimination. Chirality 14:548–554 Soai K, Shibata T, Morioka H, Choji K (1995) Asymmetric autocatalysis and amplification of enantiomeric excess of a chiral molecule. Nature 378:767–768 Takahashi J-I, Shinojima H, Seyama M, Ueno Y, Kaneko T, Kobayashi K, Mita H, Adachi M, Hosaka M, Katoh M (2009) Chirality emergence in thin solid films of amino acids by polarized light from synchrotron radiation and free electron laser. Int J Mol Sci 10:3044–3064 Takano Y, Takahashi J, Kaneko T, Marumo K, Kobayashi K (2007) Asymmetric synthesis of amino acid precursors in interstellar complex organics by circularly polarized light. Earth Planet Sci Lett 254:106–114 Thiemann WH-P, Meierhenrich U (2011) ESA mission ROSETTA will probe for chirality of cometary amino acids. Orig Life Evol Biosph 31:199–200. For updated information see http:// sci.esa.int/rosetta/ Tranter GE, MacDermott AJ (1986) Parity-violating energy differences between chiral conformations of tetrahydrofuran, a model system for sugars. Chem Phys Lett 130:120–122 Ulbricht TLV, Vester F (1962) Attempts to induce optical activity with polarized-radiation. Tetrahedron 18:629–637 Vester F, Ulbricht TLV, Krauch H (1959) Optical activity and parity violation in beta-decay. Naturwissenschaften 46:68–69

Supernovae and the Formation of Planetary Systems

93

Alan P. Boss

Abstract

Immediately after the discovery in 1976 of strong evidence for live “Aluminum26 (26 Al)” during the formation of certain portions of the Allende meteorite, the suggestion was made that this short-lived radioisotope may have been synthesized in a core-collapse (type II) supernova, transported across the interstellar medium by a supernova remnant, and injected into a dense molecular cloud core, which then collapsed as a result of the impact of the supernova remnant shock wave and subsequently formed our solar system. This theoretical hypothesis has been investigated in the intervening years with increasingly detailed hydrodynamical models of the interaction of supernova shock waves with target cloud cores, and it remains as a viable explanation for the source of the 26 Al and various other short-lived radioisotopes discovered since 1976 in samples of the most primitive, unprocessed meteorites. While the formation processes of exoplanetary systems are much harder to decipher, based on our extremely limited information about their constituent planets and small bodies, much less their isotopic compositions, the supernova triggering and injection scenario is an attractive means for explaining the initiation of the formation of our own planetary system, and hence might be expected to be a formation mechanism for some currently uncertain fraction of the exoplanetary systems that we now know are common in our galaxy.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short-Lived Radioisotopes in Chondritic Meteorites . . . . . . . . . . . . . . . . . . . . . . . . . . .

2402 2403

A.P. Boss () Department of Terrestrial Magnetism (DTM), Carnegie Institution for Science, Washington, DC, USA e-mail: [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_21

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2.1 26 Al . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 60 Fe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 41 Ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Astrophysical Sources of SLRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 AGB Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 WR Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Type II Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Nuclear Spallation Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Supernovae Remnants and Triggered Star Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Theoretical Injection Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Disk Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Molecular Cloud Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Molecular Cloud Core Injection by AGB Star . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Molecular Cloud Core Injection by WR Star Wind . . . . . . . . . . . . . . . . . . . . . . . 5.5 Molecular Cloud Core Injection by SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

The advent in 1995 of the discovery of planetary systems orbiting sunlike stars has led to an explosion in the number of exoplanets known to exist in our galaxy. Ground-based radial velocity, microlensing, transit photometry, and direct imaging searches, coupled with ground- and space-based transit photometry and direct imaging surveys, have detected literally thousands of exoplanets with a bewildering range of masses and orbital properties. Understanding the formation mechanisms of these exoplanetary systems is a major theoretical challenge, one that is made all the more challenging by the skimpy amount known about their physical and chemical constituents. One might expect that given the incredibly more detailed knowledge about our own solar system, the formation of our planetary system must be well understood. While there is general agreement that the collisional accumulation of increasingly larger solid bodies played the major role in forming our solar system, at least in the inner solar system, this agreement is largely restricted to the final phases of the planet formation process, long after the sun has formed and the solar nebula that gave birth to the planets has largely disappeared. This chapter will focus instead on the initial phases of the formation of our solar system, namely, the processes involved in the collapse of a dense molecular cloud core, leading to the formation of a central protostar surrounded by a rotating disk of gas and dust, the configuration usually assumed as a starting point for theoretical studies of the later phases of planet formation, here and elsewhere. We will see that, at least in the case of our own solar system, there is good reason to believe that a supernova may have played a primary role in inducing the birth of our sun and planets, as presented by Boss and Keiser (2013, 2014, 2015).

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Short-Lived Radioisotopes in Chondritic Meteorites

The supernova trigger story begins with the fall of the Allende meteorite in northern Mexico in 1969. This chondritic meteorite contains mm-sized spherical chondrules and cm-sized irregular refractory inclusions, the latter composed primarily of calcium and aluminum oxides. These Ca-Al-rich inclusions (CAIs) have the oldest measured ages of anything found so far in the solar system, having formed some 4.568 Gyr ago (e.g., Bouvier and Wadhwa 2010, using lead isotope measurements). Such primitive, relatively unprocessed chondritic meteorites form much of the basis for our understanding of the physical and chemical processes that occurred during the earliest phases of the formation of our planetary system.

2.1

26

Al

The Allende CAIs show evidence for the presence of the live, undecayed shortlived radioisotope (SLRI) 26 Al, with a half-life of 0.72 Myr (Lee et al. 1976), evidence that was revealed by the distinctive distribution in different phases of the Allende CAIs of the 26 Al daughter product, 26 Mg. Because of the short half-life for 26 Al, the implication was that 26 Al must have been synthesized by some process, injected deep into the solar nebula, and then incorporated into cm-sized refractory inclusions, all within a time period of about a million years. This remarkable discovery prompted Cameron and Truran (1977) to advance the supernova trigger hypothesis, whereby the 26 Al was produced by nucleosynthesis in a type II (corecollapse) supernova, which ejected the freshly synthesized 26 Al during its explosion. The resulting expanding shell of supernova ejecta would then propagate across the interstellar medium, finally reaching a molecular cloud core, which it then triggered into collapse while simultaneously injecting the 26 Al as well as other SLRIs produced by the supernova. Cosmochemical evidence for 26 Al has been exhaustively pursued in the intervening decades, and evidence for live 26 Al has been found not only in CAIs, but also in chondrules, though typically at lower levels. Initial 26 Al=27 Al ratios observed in refractory inclusions are scattered around the so-called canonical value of 5  105 (MacPherson et al. 1995), although claims for supra-canonical values (7  105 / have also been advanced (Young et al. 2005). The clustering of inferred initial 26 Al=27 Al ratios for the oldest chondritic inclusions has led to the widespread use of the Mg-Al system for dating the earliest events in the solar nebula, from the formation of the first solids to the accretion of the first asteroidsize planetesimals. Lower initial ratios of 26 Al=27 Al are believed to result from radioactive decay, i.e., crystallization of the various mineral phases several million years after the CAIs formed, though this interpretation assumes that the 26 Al was initially homogeneously distributed in the solar nebula (see Boss 2011).

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A.P. Boss 60

Fe

A supernova explosion results in the nucleosynthesis of many SLRIs besides 26 Al, such as 60 Fe, with a half-life of 2.6 Myr. Tachibana et al. (2006) found evidence for live 60 Fe in high Fe/Ni ferromagnesian chondrules from the ordinary chondrites (OCs) Semarkona and Bishunpur. Tachibana et al. (2006) inferred an initial ratio of 60 Fe=56 Fe in the range of 5  107 to 106 , a level high enough to suggest a nearby supernova origin. However, ongoing cosmochemical work has cast considerable doubt on the initial 60 Fe=56 Fe ratios in the solar nebula. Whole-rock analyses on a range of meteorites have suggested lowering this initial ratio to an apparently solarsystem-wide, uniform ratio of 1:15  108 (Tang and Dauphas 2012). As noted by Boss and Keiser (2013), given that the interstellar medium (ISM) has a 60 Fe=56 Fe ratio of 2:8  107 , Tang and Dauphas (2012) suggested that the meteoritical 60 Fe may have originated from the ISM rather than a nearby supernova, though this would require the presolar cloud core to have formed from a molecular cloud that had not been injected with any fresh 60 Fe for about 15 Myr, allowing the 60 Fe to decay for about 5 half-lives, thereby reducing the ISM 60 Fe=56 Fe ratio by a factor of about 30 to the meteoritical value they inferred. Tang and Dauphas (2012) then suggested that the solar nebula’s 26 Al may have arisen from the 26 Al-rich, 60 Fe-poor wind of a pre-supernova massive (>30 Mˇ / star, i.e., a Wolf-Rayet (WR) star (e.g., Gaidos et al. 2009). Tang and Dauphas (2012) predicted that if their suggestion is correct, CAIs, which have some variability in their initial 26 Al=27 Al ratios (e.g., Krot et al. 2012), should have uniform initial 60 Fe=56 Fe ratios, which remains to be seen. As also pointed out by Boss and Keiser (2013), Gounelle and Meynet (2012) proposed that these two SLRIs came from a mixture of supernovae (for the 60 Fe) and massive star winds (for the 26 Al) from several generations of stars in a giant molecular cloud (GMC). Their scenario proposes that a first generation of massive stars became supernovae and ejected 60 Fe and 26 Al into the GMC. After about 10 Myr, a second generation of massive O stars formed, with the wind from one of them sweeping up GMC gas into an expanding shell of gas, rich with 26 Al from its own prior outflows. Because of the shorter half-life of 26 Al compared to 60 Fe, after 10 Myr the 60 Fe from the first generation of massive stars decays much less than the original 26 Al, which has essentially disappeared. Gounelle and Meynet (2012) then proposed that the sun formed from the expanding shell surrounding the massive star’s ionized HII region, before the massive star itself became a supernova. Whether a single GMC, with a typical mass of about 106 Mˇ , could have two distinct episodes of massive star formation, separated by 10 Myr, with no other massive star formation occurring during this interval, also remains to be seen. Tang and Dauphas (2012) pointed out yet another possible explanation for low 60 Fe=56 Fe ratios and high 26 Al=27 Al ratios: 26 Al is synthesized in the outer layers of massive stars, whereas 60 Fe is formed in the inner layers. If only the outer layers of the progenitor star are ejected during the supernova explosion, or if only the outer layers of the supernova shock are injected into the presolar cloud, then the proper mixture of SLRIs might result from a nearby supernova (e.g., Gritschneder et al. 2012). Boss

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and Foster (1998), however, found that the tail-end gas in a shock front is injected into a cloud core just as efficiently as the leading-edge gas, casting some doubt on this explanation. In spite of all of this controversy, new evidence on the initial 60 Fe=56 Fe ratio continues to appear. A combined study of 60 Fe and 26 Al in chondrules from an unequilibrated OC (UOC) implied an initial 60 Fe=56 Fe ratio of about 7  107 (Mishra and Goswami 2014) and supported a supernova as the source of the SLRIs. Analyses of other chondrules from the UOCs Semarkona and Efremovka yielded initial 60 Fe=56 Fe ratios in the range of about 2  107 to 8  107 (Mishra and Chaussidon 2014). Thus while there is as yet no explanation for these discrepancies between bulk samples and chondrule fragments, evidently a supernova remains as a plausible source for the SLRIs.

2.3

41

Ca

The half-life of 41 Ca is 0.1 Myr, even shorter than that of 26 Al and 60 Fe. Measurements of 41 Ca=40 Ca ratios in CAIs (Liu et al. 2012) lowered a previously determined meteoritical ratio of .1:41 C =  0:14/  108 to a value of about 4:2  109 , about 10 times less than expected ISM ratios, which lie in the range of about 1:6  108 to 6:4  108 based on steady-state galactic nucleosynthesis models. This finding implies that the solar system’s 41 Ca may have decayed in, e.g., a GMC, for about 0.2 to 0.4 Myr prior to CAI formation (Liu et al. 2012), much shorter than the inferred free decay interval for 60 Fe hypothesized by Gounelle and Meynet (2012). Alternatively, the 41 Ca may have been injected into the presolar cloud, or solar nebula, shortly before CAI formation (Liu et al. 2012).

3

Astrophysical Sources of SLRI

The origin of the short-lived radioisotopes that were present during the formation of the earliest solids in the solar nebula remains as a largely unsolved mystery (Boss and Keiser 2013). The origins of 60 Fe and 26 Al have been ascribed to nucleosynthesis in asymptotic giant branch (AGB) stars, WR star phases and outflows, type II (core-collapse) supernovae, or, for 26 Al, in addition to these stellar nucleosynthetic sources, to irradiation of the inner edge of the solar nebula by the protosun’s high-energy particles. We consider here each of these four possible sources in turn.

3.1

AGB Stars

Intermediate-mass (roughly 5 Mˇ / AGB stars are possible sources for several of these SLRIs (Huss et al. 2009). Super-AGB stars, with masses in the range of 7 to

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11 Mˇ , are also possible sites for synthesizing the SLRIs 60 Fe and 26 Al, as well as 41 Ca. Due to their advanced ages, AGB stars are not likely to be found in regions of ongoing star formation. However, over a giant molecular cloud lifetime, the chances of an AGB star interaction could be as high as about 70 %, which is significant. AGB stars eject their nucleosynthetic products in their outflows, known as planetary nebulae, which traverse the ISM with speeds of order 10 km/s and thicknesses of about 0.1 pc (Boss and Keiser 2013), the combination of which unfortunately makes them apparently unable to simultaneously trigger collapse and inject appreciable levels of SLRIs.

3.2

WR Stars

WR stars have been suggested as likely sources for the live 26 Al found in chondrites (e.g., Tang and Dauphas 2012). Tatischeff et al. (2010) proposed that a runway WR star delivered a large dose of 26 Al to a molecular cloud prior to exploding as a supernova. However, as pointed out by Boss and Keiser (2013), there are severe problems with having a WR star wind be the direct agent of injecting SLRIs into the presolar cloud core. Boss and Keiser (2013) noted that WR star winds start out as fast winds with speeds of 2000 km/s, slowing down to about 100 km/s only after sweeping up the wind previously ejected during the red supergiant phase. At this point, the WR wind has a shock front that is quite wide and low density, so low in density in fact that Foster and Boss (1996) showed that such a wind would not carry enough momentum to trigger the collapse of a dense cloud core. In addition, WR winds are hot and fully ionized, being driven by thermal pressure rather than momentum, a situation that is likely to result in the shredding to pieces of any dense cloud core it encounters, based on the models of Foster and Boss (1996).

3.3

Type II Supernovae

Having a nearby supernova as a source of SLRIs requires that the sun formed in a massive cluster with about 1000 stars or more, so that at least one of the stars is likely to have a mass greater than 25 Mˇ . Most stars are born in such clusters, making such a birth site a likely possibility for the sun. Limongi and Chieffi (2006) presented detailed nucleosynthesis models of the evolution of solar metallicity stars with masses between 11 and 120 Mˇ , finding that both 60 Fe and 26 Al were produced in abundances high enough to be consistent with observations of their decay products (gamma rays) in the ISM. Tur et al. (2010) have also modeled the production of 60 Fe and 26 Al in massive core-collapse supernova, as well as of 44 Ti, and found that high levels of all three of these SLRIs can be synthesized in the same layers deep within a 25 Mˇ supernova. In addition, Tatischeff et al. (2014) found that cosmic rays associated with a supernova remnant could produce sufficient levels of the SLRI

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10

Be, with a half-life of 1.4 Myr, to explain the evidence for live 10 Be in certain CAIs, giving strong support to the supernova triggering and injection hypothesis.

3.4

Nuclear Spallation Reactions

Shu et al. (1997) proposed that energetic particles from the protosun could strike suitable target nuclei orbiting at the inner edge of the solar nebula, leading to the production of fresh 26 Al by nuclear spallation reactions. Numerous objections have been raised to the basic assumptions involved in this scenario (e.g., Desch et al. 2010), such as producing the inferred levels, and apparent nebula-wide homogeneity, of the 26 Al=27 Al ratio, but the most persuasive argument appears to be the evidence for live 60 Fe in chondrules, as this SLRI cannot be produced in significant amounts by the hypothesized spallation reactions. If the controversial evidence for live 60 Fe disappears, however, the role of nuclear spallation reaction for SLRIs such as 26 Al will need to be revisited.

4

Supernovae Remnants and Triggered Star Formation

Supernova remnants (SNRs) are copious contributors of SLRIs and other newly synthesized elements and isotopes to the ISM. For example, the Cassiopeia A SNR is the result of a type II supernova explosion (Fig. 1), and space X-ray telescopes (Chandra and NuSTAR) have mapped the distributions of various elements and isotopes across its diameter, including the extremely short-lived nuclide 44 Ti, with a half-life of only 60 yr. 44 Ti is synthesized in the same regions of supernova explosion models as 26 Al and 60 Fe (Tur et al. 2010), so the distribution of 44 Ti seen in Fig. 1 provides reassurance that the SLRIs produced deep with supernova do indeed get ejected outward into the escaping SNR, though clearly their spatial distributions are not necessarily uniform, with important implications for our ability to estimate the SLRI dosage received from any given SNR. Herbst and Assousa (1977) presented evidence that star formation in the young association CMa R1 was initiated by a type II supernova explosion that occurred about 0.5 Myr earlier. Since that pioneering work, abundant observational support for the triggering of star formation by expanding supernova shells has appeared. For example, Balazs et al. (2004) showed on the basis of star counts that the star-forming cloud L1251 has a shape that appears to have been created by the interaction of a shock wave from a nearby supernova explosion. This interpretation was supported by the detection of excess soft X-ray emission near the edge of the cloud, as well as the discovery of a runaway star that appears to be the remnant of the supernova explosion. Radio and submillimeter observations of the type II SNR W44 (with a size of about 5 pc) and its interaction with the W44 giant molecular cloud complex imply the presence of dense clumps of molecular gas that have been struck and compressed to sizes much less than 0.3 pc by the SNR shock front, with shock

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Fig. 1 Cassiopeia A SNR, with a diameter of 3.1 pc. Red, yellow, and green data were collected by NASA’s Chandra space X-ray telescope at energies ranging from 1 to 7 kiloelectron volts (keV). The red color shows heated iron, and green represents heated silicon and magnesium. The yellow is continuum X-ray emission. Titanium-44 (44 Ti), with a half-life of 60 year, shown in blue, was detected by NASA’s NuSTAR space telescope, at energies ranging between 68 and 78 keV (Credit: NASA/JPL-Caltech/CXC/SAO Publically available source of image: http://www.nustar.caltech. edu/image/nustar140219a/)

Fig. 2 Image of a small portion of the Cygnus Loop SNR taken by the Hubble Space Telescope WFPC2 instrument. The Cygnus Loop has an overall size of about 10 pc and is about 0.01 Myr old. The image is an optical R band centered at 656 nm (Credit: ESA & Digitized Sky Survey (Caltech) Publically available source of image: https://www.spacetelescope.org/images/heic0006b/)

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speeds of 20 to 30 km/s (Reach et al. 2005; Sashida et al. 2013). These observations are clear evidence that SNR shock fronts can trigger cloud collapse, after having been slowed down by snowplowing ISM gas and dust to speeds amenable to cloud core compression (i.e., tens of km/s); newly formed SNRs, with speeds of thousands of km/s, on the other hand, will shred and disperse any dense cloud cores they encounter. Hubble Space Telescope images of the Cygnus Loop type II SNR (Fig. 2) reveal shock front thicknesses of order 2  104 pc (Blair et al. 1999) even though the entire SNR has expanded over the last 0.01 Myr to a diameter of about 10 pc. A core-collapse supernova is thought to be the progenitor for the Cygnus Loop SNR.

5

Theoretical Injection Models

We now turn to a summary of the progress made in developing detailed hydrodynamical models of the various ways in which a shock front carrying freshly synthesized SLRIs might have resulted in their incorporation in cm-sized refractory inclusions in the solar nebula that formed our solar system. Models have been calculated of shock-wave interactions with large-scale molecular clouds, with smallscale protoplanetary disks, and with intermediate-scale dense molecular cloud cores, with a wide variety of shock front parameters intended to sample the possible types of shock waves. We concentrate here though on models involving shock fronts appropriate for SNRs.

5.1

Disk Injection

Ouellette et al. (2007, 2010) studied the two-dimensional injection of SLRIs from a massive (greater than 20 Mˇ / supernova into a nearby protoplanetary disk, 0.3 pc away, showing that injection of shock wave gas could not occur, but that refractory grains with sizes of about 1 micron or larger could be injected, as the large grains could penetrate right through the shock-nebula interface before encountering enough gas to slow them down. In this case, SLRI injection could occur for large grains, assuming that the grains contain the bulk of the SLRIs, though obviously this scenario does not envision simultaneous triggering and collapse, as it assumes a preexisting protostar and protoplanetary disk. Supernovae are known to produce large amounts of dust grains, but nearly all of these grains are smaller than 0.1 micron and are sputtered to even smaller sizes in the shock front, presenting a problem for this scenario. In addition, statistical analysis of the SLRI enrichments expected for disks and cloud cores in clusters containing massive stars showed that cloud cores receive a larger dose on average than disks (Adams et al. 2014), favoring the presolar cloud scenario (Boss 1995; Cameron and Truran 1977) over injection into a previously formed solar nebula.

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A.P. Boss

Molecular Cloud Injection

Gounelle and Meynet (2012) proposed injection into a GMC, as discussed in Sect. 2.2. As noted by Boss and Keiser (2013), Pan et al. (2012) studied the threedimensional interaction of a supernova remnant with the gaseous edge of the HII region created by a supernova’s progenitor star, finding that the supernova ejecta could contaminate enough of the large-scale giant molecular cloud gas to explain the observed levels of some solar system SLRIs. However, the fact that the FUN (fractionation unknown nuclear) refractory inclusions in CAIs show no evidence for live 26 Al, coupled with the significant 26 Al depletions found in some other CAIs and refractory grains, implies that these refractory objects may have formed prior to the injection, mixing, and transport of 26 Al into the refractories-forming region of the solar nebula (Mishra and Chaussidon 2014; Sahijpal and Goswami 1998). The 26 Al data alone, therefore, seems to require the late arrival of SLRIs derived from a supernova into the inner region of the solar nebula, as opposed to injection into a giant molecular cloud complex, followed by thorough mixing and SLRI homogenization prior to the collapse of the presolar cloud core.

5.3

Molecular Cloud Core Injection by AGB Star

As noted by Boss and Keiser (2013), planetary nebula shock waves emanating from AGB stars have thicknesses of about 0.1 pc. They performed a survey of twodimensional models of molecular cloud cores struck by shock waves with large variations in their basic parameters, namely, the shock speeds, shock thicknesses, and shock densities, finding that planetary nebula shocks were too thick to simultaneously trigger collapse and result in significant injection of SLRIs. While not completely ruled out, AGB star winds do not seem to be as favorable for the triggering and injection process as a SNR.

5.4

Molecular Cloud Core Injection by WR Star Wind

Similar to the case for AGB star outflows, Boss and Keiser (2013) found that WR star winds are not as attractive for simultaneous triggering and injection as SNR, but unlike the case for AGB star winds, they found that WR star winds could be effectively ruled out as being much more likely to shred a target cloud than to induce collapse, as a result of the low density, high temperature gas in the shock front.

5.5

Molecular Cloud Core Injection by SNR

Most work has been performed on the original suggestion of the interaction of a SNR with a target molecular cloud core. Boss (1995) showed that shock fronts

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from a relatively distant supernova could trigger the isothermal collapse of a threedimensional dense cloud core and inject shock front material into the collapsing cloud. Foster and Boss (1996, 1997) studied this process in greater detail for axisymmetric, two-dimensional clouds and pointed out the crucial role of the assumed isothermal shock front for achieving both goals of triggered collapse and injection. A supernova shock passes through three distinct phases: (1) ejectadominated, (2) Sedov blast wave, and (3) radiative. The latter phase occurs at distances of about 10 pc, by which time the shock front has swept up from the ISM a cool shell of gas and dust as it propagates. Shock-triggered star formation is likely to occur only when the supernova shock front has evolved into a radiative shock, i.e., the shock front is able to cool so rapidly by radiation that the thin shock front gas is essentially at the same temperature as the ambient gas, which is similar to the situation in the isothermal shocks considered by Boss (1995) and Foster and Boss (1996, 1997). Rayleigh-Taylor (R-T) fingers were identified as the physical mechanism for achieving injection of dust grains and gas into the collapsing presolar cloud (Foster and Boss 1997; Vanhala and Boss 2000, 2002). Because the R-T fingers strike the outermost layers of the presolar cloud, inducing collapse, the R-T fingers do not reach the central regions until shortly after the central protosun and the early solar nebula have formed, possibly explaining the lack of 26 Al in certain (FUN) refractory inclusions (Sahijpal and Goswami 1998) that may have formed before the R-T fingers arrived. While isothermal shock fronts were evidently capable of simultaneous triggering and injection, it was unclear what happens when detailed heating and cooling processes in the shock front are considered. Vanhala and Cameron (1998) found that when they allowed nonisothermal shocks in their models, they could not find a combination of target cloud and shock-wave parameters that permitted both triggered collapse and injection to occur: they could trigger cloud collapse or they could inject particles, but not both in the same simulation. Such an outcome would be fatal to the triggering and injection hypothesis if definitive. However, Vanhala and Cameron’s (1998) thermodynamical routines led to post-shock thermal profiles that were quite hot: with a 25 km/s shock in their models, the post-shock temperature rose to 3000 K and showed no signs of decreasing over a distance on the order of 0.5 pc. Later work showed that when an improved formulation of the dust grain cooling law was employed, the post-shock temperature maximum dropped, and the gas quickly cooled back down to 10 K, for shock speeds less than 40 km/s. Boss et al. (2008) used an adaptive mesh refinement hydrodynamics code to show that including molecular line cooling in the shock-cloud interaction region is crucial for obtaining simultaneous triggered cloud collapse and SLRI injection. Molecular species such as H2 O, CO, and H2 can provide the needed cooling in shocked regions; in the absence of such cooling, adiabatic heating of the shock-compressed regions leads to only a minor degree of target cloud compression that is insufficient to trigger the dynamic self-gravitational collapse needed to form a protostar. Boss and Keiser (2010) continued to study the two-dimensional interactions of shock waves with a variety of speeds with a 2 Mˇ cloud core, finding that shock speeds in

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the range of 5 to 70 km=s were able to simultaneously trigger cloud collapse and inject significant amounts of shock wave gas and dust. Shocks slower than 5 km=s did not lead to appreciable injection, whereas shocks faster than 70 km=s could not trigger sustained collapse. Gritschneder et al. (2012) modeled the twodimensional interaction of higher-speed (97.5 or 276 km/s) supernova shock waves with a 10 Mˇ cloud core, finding that simultaneous triggered collapse and SLRI enrichment was still possible in that case. Boss and Keiser (2010) showed that the injection efficiency depended sensitively on the assumed shock width and density and suggested that thin supernova shocks were therefore preferable to the thick planetary nebula winds outflowing from AGB stars. Boss and Keiser (2013) found that two-dimensional model injection efficiencies could be increased when the cloud was rotating about an axis aligned with the direction of the shock wave, by as much as a factor of 10. In addition, the amount of gas and dust accreted from the postshock wind can exceed that injected from the shock wave, with implications for the isotopic abundances expected for a supernova source. Boss and Keiser (2012) extended their (2010, 2013) models to three dimensions, revealing the three-dimensional structure of the R-T fingers that form during the shock-cloud collision and which constitute the injection mechanism (Fig. 3). Boss and Keiser (2014, 2015) then studied rotating cloud cores, again in three dimensions, and showed how R-T fingers could inject SLRIs into the protostellar disk that eventually became the solar nebula (Fig. 4). Li et al. (2014) also studied injection into rotating, three-dimensional clouds, but apparently were unable to resolve the R-T fingers, in spite of also using an adaptive mesh refinement code, perhaps because they only considered a 3 km/s shock speed, found to be too slow to result in R-T finger injection by Boss et al. (2010). Remarkably, Boss and Keiser (2015) found that R-T fingers could be responsible for providing most of the spin angular momentum of the collapsing presolar cloud, in addition to enhanced SLRI injection. In addition, estimates of the injection efficiency and dilution factors expected for SNR-derived SLRIs (Boss and Keiser 2012, 2014, 2015) fall within the range expected from analyses based on the somewhat uncertain inferred initial ratios of 60 Fe=56 Fe and 26 Al=27 Al.

J Fig. 3 Three-dimensional model of 40 km/s shock-wave-triggered collapse and injection through fingerlike Rayleigh-Taylor (R-T) instability (Boss and Keiser 2012). Left column: central cross section through a target cloud showing the R-T fingers and gas density at two times, above, shortly after the downward-moving shock wave has struck the cloud (0.020 Myr) and below, after the cloud has been triggered into dynamic collapse (0.063 Myr). Right column: at the same two times, the density of shock-wave-derived SLRIs is shown in a plane perpendicular to that shown in the left column, illustrating the structure of the R-T fingers. The target cloud is not rotating in this model, and as a result a protostellar disk does not form (Adapted from Figures 1, 2, 3, and 4 of Boss and Keiser 2012)

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Fig. 4 Three-dimensional model of 40 km/s shock-wave-triggered collapse and injection for an initially rotating target cloud core (Boss and Keiser 2014) at the four times noted. The gas density is shown in a central plane perpendicular to the direction (downward) of the shock wave (thin line at 0.0 Myr) and perpendicular to the spin axis of the target cloud. R-T fingers are formed (0.028 Myr), as well as a protostellar disk (0.083 Myr) that will be mostly accreted by the central protostar, leaving behind a protoplanetary disk suitable for planet formation (Adapted from Figure 1 of Boss and Keiser 2014)

6

Conclusions

Detailed two-dimensional axisymmetric (Boss and Keiser 2010, 2013; Boss et al. 2008, 2010; Gritschneder et al. 2012) and fully three-dimensional (Boss and Keiser 2012, 2014, 2015; Li et al. 2014) hydrodynamical models of shock waves with the speeds and thicknesses of observed SNR have demonstrated the viability of the triggered collapse of dense molecular cloud cores along with simultaneous injection

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of shock front material into the resulting collapsing protostar and protoplanetary disk. Given the problems with shocks waves associated with AGB and WR star winds (Boss and Keiser 2013), a SNR shock appears to be the leading contender for achieving simultaneous triggering and injection of core-collapse supernovaderived short-lived radioisotopes (e.g., 60 Fe and 26 Al) into the presolar cloud and the resulting solar nebula (Boss 1995; Cameron and Truran 1977). Given the observational evidence for star formation triggered by SNRs, we can expect that our planetary system is by no means the only one in our galaxy that started its life with a dose of these and other SLRIs.

7

Cross-References

 Dynamical Evolution and Radiative Processes of Supernova Remnants  Isotope Variations in the Solar System: Supernova Fingerprints  Pre-supernova Evolution and Nucleosynthesis in Massive Stars and Their Stellar

Wind Contribution  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Stardust from Supernovae and Its Isotopes  The Multidimensional Character of Nucleosynthesis in Core-Collapse Super-

novae  Ultraviolet and Optical Insights into Supernova Remnant Shocks

References Adams FC, Fatuzzo M, Holden L (2014) Distributions of short-lived radioactive nuclei produced by young embedded star clusters. Astrophys J 789:86–104 Balazs LG, Abraham P, Kun M, Keleman J, Toth LV (2004) Star count analysis of the interstellar matter in the region of L1251. Astron Astrophys 425:133–141 Blair WP, Sankrit R, Raymond JC, Long KS (1999) Distance to the cygnus loop from Hubble Space Telescope imaging of the primary shock front. Astrophys J 118:942–947 Boss AP (1995) Collapse and fragmentation of molecular cloud cores. II. Collapse induced by stellar shock waves. Astrophy J 439: 224–236 Boss AP (2011) Mixing and transport of isotopic heterogeneity in the early solar system. Ann Rev Earth Planet Sci 40:23–43 Boss AP, Foster PN (1998) Injection of short-lived isotopes into the presolar cloud. Astrophys J Lett 494:L103–L106 Boss AP, Keiser SA (2010) Who pulled the trigger: a Supernova or an asymptotic giant branch star? Astrophys J 717:L1–L5 Boss AP, Keiser SA (2012) Supernova-triggered molecular cloud core collapse and the RayleighTaylor fingers that polluted the solar nebula. Astrophys J Lett 756:L9-L15 Boss AP, Keiser SA (2013) Triggering collapse of the presolar dense cloud core and injecting short-lived radioisotopes with a shock wave. II. Varied shock wave and cloud core parameters. Astrophys J 770:51–62 Boss AP, Keiser SA (2014) Triggering collapse of the presolar dense cloud core and injecting shortlived radioisotopes with a shock wave. III. Rotating three dimensional cloud cores. Astrophys J 788:20–29

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Boss AP, Keiser SA (2015) Triggering collapse of the presolar dense cloud core and injecting short-lived radioisotopes with a shock wave. IV. Effects of rotational axis orientation. Astrophys J 809:103–114 Boss AP, Ipatov SI, Keiser SA, Myhill EA, Vanhala HAT (2008) Simultaneous triggered collapse of the presolar dense cloud core and injection of short-lived radioisotopes by a supernova shock wave. Astrophys J 686:L119–L122 Boss AP, Keiser SA, Ipatov SI, Myhill EA, Vanhala HAT (2010) Triggering collapse of the presolar dense cloud core and injecting short-lived radioisotopes with a shock wave. I. Varied shock speeds. Astrophys J 708:1268–1280 Bouvier A, Wadhwa M (2010) The age of the Solar System redefined by the oldest Pb-Pb age of a meteoritic inclusion. Nat Geo Sci 3:637–641 Cameron AGW, Truran JW (1977) The supernova trigger for the formation of the solar system. Icarus 30:447–461 Desch SJ, Morris MA, Connolly HC, Boss AP (2010) A critical examiniation of the X-wind model for chondrule and Calcium-Rich, Aluminum-Rich inclusion formation and radionuclide production. Astrophys J 725:692–711 Foster PN, Boss AP (1996) Triggering star formation with stellar ejecta. Astrophys J 468: 784–796 Foster PN, Boss AP (1997) Injection of radioactive nuclides from the stellar source that triggered the collapse of the presolar nebula. Astrophys J 489:346–357 Gaidos E, Krot AN, Williams JP, Raymond SN (2009) 26 Al and the formation of the Solar System from a molecular cloud contaminated by Wolf-Rayet winds. Astrophys J 696:1854–1863 Gounelle M, Meynet G (2012) Solar system genealogy revealed by extinct short-lived radionuclides in meteorites. Astron Astrophys 545:A4–A13 Gritschneder M, Lin DNC, Murray SD, Yin Q-Z, Gong M-N (2012) The supernova triggered formation and enrichment of our solar system. Astrophys J 745:22–34 Herbst W, Assousa GE (1977) Observational evidence for supernova-induced star formation: Canis Major R1. Astrophys J 217:473–487 Huss GR, Meyer BS, Srinivasan G, Goswami JN, Sahijpal S (2009) Stellar sources of the shortlived radionuclides in the early solar system. Geochim Cosmochim Acta 73:4922–4945 Krot AN, Makide K, Nagashima K, Huss GR, Ogliore, RC, Ciesla FJ, Yang L, Hellebrand E, Gaidos E (2012) Heterogeneous distribution of 26 Al at the birth of the solar system: evidence from refractory grains and inclusions. Meteoritics Planet Sci 47:1948–1979 Lee T, Papanastassiou DA, Wasserburg GJ (1976) Demonstration of 26 Mg excess in Allende and evidence for 26 Al. Geophys Res Lett 3:109–112 Li S, Frank A, Blackman EG (2014) Triggered star formation and its consequences. Mon Not Roy Astron Soc 444:2884–2892 Limongi M, Chieffi A (2006) The nucleosynthesis of 26 Al and 60 Fe in solar metallicity stars extending in mass from 11 to 120 Mˇ : the hydrostatic and explosive contributions. Astrophys J 647:483–500 Liu M-C, Chaussidon M, Srinivasan G, McKeegan KD (2012) A lower initial abundance of shortlived 41 Ca in the early Solar System and its implications for solar system formation. Astrophys J 761:137–144 MacPherson GJ, Davis AM, Zinner EK (1995) The distribution of aluminum-26 in the early Solar System – a reappraisal. Meteoritics 30:365–386 Mishra RK, Chaussidon M (2014) Fossil records of high level of 60 Fe in chondrules from unequilibrated chondrites. Earth Planet Sci Lett 398:90–100 Mishra RK, Goswami JN (2014) Fe-Ni and Al-Mg isotope records for UOC chondrules: plausible stellar source of 60 Fe and other short-lived nuclides in the early solar system. Geochim Cosmochim Acta 132:440–457 Ouellette N, Desch SJ, Hester JJ (2007) Interaction of supernova ejecta with nearby proto-planetary disks. Astrophys J 662:1268–1281 Ouellette N, Desch SJ, Hester JJ (2010) Injection of supernova dust in nearby protoplanetary disks. Astrophys J 711:597–612

93 Supernovae and the Formation of Planetary Systems

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Pan L, Desch SJ, Scannapieco E, Timmes FX (2012) Mixing of clumpy supernova ejecta into molecular clouds. Astrophys J 756:102–123 Reach WT, Rho J, Jarrett TH (2005) Shocked molecular gas in the supernova remnants W28 and W44: near-infrared and millimeter-wave observations. Astrophys J 618:297–320 Sahijpal S, Goswami JN (1998) Refractory phases in primitive meteorites devoid of 26 Al and 41 Ca: representative samples of first solar system solids? Astrophys J 509:L137–L140 Sashida T, Oka T, Tanaka K, Aono K, Matsumura S, Nagai M, Seta M (2013) Kinematics of shocked molecular gas adjacent to the supernova remnant W-44. Astrophys J 774:10–17 Shu FH, Shang H, Glassgold AE, Lee T (1997) X-rays and fluctuating X-winds from proto-stars. Science 277:1475–1479 Tachibana S, Huss GR, Kita NT, Shimoda G, Morishita Y. (2006) 60 Fe in chondrites: debris from a nearby supernova in the early solar system? Astrophys J 639:L87–L90 Tang H, Dauphas N (2012) Abundance, distribution, and origin of 60 Fe in the solar protoplanetary disk. Earth Planet Sci Lett 359–360:248–263 Tatischeff V, Duprat J, De Sereville N (2010) A runaway Wolf-Rayet star as the origin of 26 Al in the early solar system. Astrophy J 714:L26–L30 Tatischeff V, Duprat J, De Sereville N (2014) Light-element nucleosynthesis in a molecular cloud interacting with a supernova remnant and the origin of Beryllium-10 in the protosolar nebula. Astrophy J 796:124–144 Tur C, Heger A, Austin SM (2010) Production of 26 Al, 44 Ti, and 60 Fe in core-collapse supernovae: sensitivity to the rates of the triple alpha and 12 C.˛; /16 O reactions. Astrophys J 718:357–367 Vanhala HAT, Boss AP (2000) Injection of radioactivities into the presolar cloud: convergence testing. Astrophys J 538:911–921 Vanhala HAT, Boss AP (2002) Injection of radioactivities into the forming Solar System. Astrophys J 575:1144–1150 Vanhala HAT, Cameron AGW (1998) Numerical simulations of triggered star formation. I. collapse of dense molecular cloud cores. Astrophys J 508:291–307 Young ED, Simon JI, Galy A, Russell SS, Tonui E, Lovera O (2005) Supra-canonical 26 Al=27 Al and the residence time of CAIs in the solar protoplanetary disk. Science 308:223–227

Mass Extinctions and Supernova Explosions

94

Gunther Korschinek

Abstract

A nearby supernova (SN) explosion could have negatively influenced life on Earth, maybe even been responsible for mass extinctions. Mass extinction poses a significant extinction of numerous species on Earth, as recorded in the paleontologic, paleoclimatic, and geological record of our planet. Depending on the distance between the Sun and the SN, different types of threats have to be considered, such as ozone depletion on Earth, causing increased exposure to the Sun’s ultraviolet radiation or the direct exposure of lethal X-rays. Another indirect effect is cloud formation, induced by cosmic rays in the atmosphere which result in a drop in the Earth’s temperature, causing major glaciations of the Earth. The discovery of highly intensive gamma-ray bursts (GRBs), which could be connected to SNe, initiated further discussions on possible life-threatening events in the Earth’s history. The probability that GRBs hit the Earth is very low. Nevertheless, a past interaction of Earth with GRBs and/or SNe cannot be excluded and might even have been responsible for past extinction events.

Contents 1 2

3

4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Different Effects of Nearby SNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Case A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Case B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biological Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Direct Biological Effects (Case B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Indirect Effects on the Biosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frequency of Close SNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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G. Korschinek () Physik-Department, Technische Universität München, Garching, Germany e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_22

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5 Gamma-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Candidates of Nearby SNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

In 1912, Hess discovered cosmic rays. Utilizing a so-called Wulfscher Strahlungsapparat (2015) during several balloon rides for the measurements, he found that background radioactivity increases with rising altitude. In 1936 he received the Nobel prize for his discovery. It took 22 years until work by Baade and Zwicky (1934) indicated that fluctuations in cosmic ray intensity can be caused by supernovae (SNe), a word also coined by them. SNe are among the most energetic events in the universe, occurring either after the core collapse of massive stars running out of nuclear fuel (type II SNe) or in binary systems, where mass flows from a main sequence star onto a white dwarf, exceeding the Chandrasekhar limit and causing a thermonuclear explosion (type IaSNe). Cosmic rays are a particle radiation, composed mostly of protons and a small fraction of heavier atomic nuclei and electrons. The sources of these particles include our Sun and SN explosions. In addition there are photons, penetrating into the solar system, including X-rays and gamma rays. An interesting question arose, whether a nearby SN explosion could have negative influence on life on Earth, maybe even be responsible for mass extinctions. The term mass extinction refers to a significant extinction of numerous species on Earth, as recorded in the paleontologic, paleoclimatic, and geological record of our planet. Twenty years after the discovery of cosmic rays, one of the earliest speculations about the connection between mass extinctions on Earth and SN explosions was presented by O.H. Schindewolf (1954). He assumed that highly energetic radiation from an SN might cause the extinction of marine organisms, either by the radiation directly or indirectly by forming hazardous radioisotopes. Since then, different authors Terry and Tucker (1968), Rudermann (1975), Ellis and Schramm (1995), and later Gehrels et al. (2003) studied further aspects of correlations between SNe and mass extinctions. Figure 1 depicts the fraction of genera that are present in each interval of time but do not exist in the following interval. The yellow line is a cubic polynomial to show the long-term trend. Note that these data do not represent all genera that have ever lived, but rather only a selection of marine genera whose qualities are such that they are easily preserved as fossils. The “Big Five” mass extinctions (Raup and Sepkoski 1982) are labeled in large font, and a variety of other features are labeled in smaller font. The two extinction events occurring in the Cambrian (i.e., Dresbachian and Botomian) are very large in percentage magnitude, but are not well known because of the relative scarcity of fossil producing life at that time (i.e., they are small in absolute numbers of known taxa). The Middle Permian extinction is now argued by many to constitute

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Fig. 1 This figure shows the fraction of genera that are present in each interval of time but do not exist in the following interval. The data itself is taken from Rohde and Muller (2005, Supplementary Material), and are based on the Sepkoski’s Compendium of Marine Fossil Animal Genera (Sepkoski 2002). The yellow line is indicating the long-term trend. Note that these data do not represent all genera that have ever lived, but rather only a selection of marine genera whose qualities are such that they are easily preserved as fossils. The figure, part of the accompanying wording, and the caption (shortened) are taken from GNU Free Documentation License. This version is released under the GFDL

a distinct extinction horizon, though the actual extinction amounts are sometimes lumped together with the end-Permian extinctions in literature. As indicated, the “Late Devonian” extinction is actually resolvable into at least three distinct events spread out over a period of 40 million years. As these data are derived at the genus level, one can anticipate that the number of actual species extinctions is even larger than shown here. Such mass extinction events can have paleoclimatic, paleoecologic, and paleoenvironmental explanations (Twitchett 2006). For example, the KT (CretaceousTertiary) extinction (66 Ma B.P., indicated in the graph by End K) yielding the famous dinosaur-killing mass extinction (Alvarez et al. 1980) is thought to have been caused by a massive meteorite impact. However there are still inconsistencies which might contradict a large meteorite impact only. A different scenario is discussed in a recent publication by Large et al. (2015); it is argued that a lack of trace nutrient elements in the Phanerozoic ocean might have caused mass extinctions. An additional scenario for mass extinctions that can be considered is nearby SN explosions.

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Different Effects of Nearby SNe

We can roughly distinguish two different scenarios for the effect of nearby SN on the Earth. On the one hand, (case A) Earth can be exposed to an irradiation by cosmic rays, which have traveled through the interstellar medium (ISM). This effect is expected to dominate for SN distances of above 15 pc or 20 pc, depending on the density of the ISM. The other scenario (B) involves a direct interaction of the SN ejecta in the form of plasma overcoming the solar wind pressure and penetrating deep into the solar system, reaching the Earth.

2.1

Case A

In case of the first situation (A), the cosmic ray intensity at different distances and times has been analyzed by Knie et al. (2004). It has been supposed that a first-order Fermi mechanism operating in shock waves is the most promising mechanism for the source of galactic CR. For the numerical simulations (Dorfi 1990) of a supernova remnant (SNR) evolution in spherical symmetry, a typical value of 1051 erg has been assumed for the total ejection energy (not counting neutrino losses). The time-dependent acceleration of CR is included through a hydrodynamical formalism characterizing the cosmic rays where a mean diffusion coefficient KCR D 1027 cm2 s1 , as well as the adiabatic coefficient CR D 4/3, had to be specified in accordance with the observed properties of CR. The intensity and the duration of the CR exposure depend on the gas density of the surrounding ISM where Dorfi (1990) has chosen values between 0:1 atoms cm3 and 1 atom cm3 . During the SNR evolution, the total energy of the ejecta is shared between kinetic energy of the ejecta (including CR), thermal energy, and photons. In particular, the SNR evolution at later stages is characterized by radiative losses of the thermal plasma. The onset of this radiative phase depends on the particle density and occurs for the adopted values of the ISM for radii larger than about 20 pc (Kahn 1976). Hence, the amount of cosmic rays accelerated by the remnants shock wave can only be calculated if the radiative cooling effects are taken into account. A typical result for 0:5 atoms cm3 is depicted in Fig. 2 where the grid surface shows the temporal variation of the CR energy density relative to the initial value for distances from 30 to 50 pc from the explosion center. After the shock wave has passed, the CR intensity decreases due to the adiabatic expansion of the remnant, and the further evolution is then characterized by a diffusive transport of the accelerated particles from the shock wave toward the interior. For a remnant of radius R, the diffusion timescale can be estimated according to t  R2 =KCR yielding values between 270 and 750 kyr for 30 pc R 50 pc, respectively. In order to compute the CR intensity, the SNR simulations have to be carried throughout the radiative cooling phase, and it has been found that an SN at a distance of 40 pc increases the CR intensity only by about 15 %, however, for a period of some 100 kyr. In case of a distance of 30 pc, it will be already around 25 %. Figure 2

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Fig. 2 Temporal variation of the cosmic ray energy intensity Ec relative to the initial value Ec,0 (100 %) for distances from 30–50 pc from the explosion center. The calculations have been performed for an ISM density of 0:5 atoms cm3 (Dorfi 1990)

shows the temporal variation of the cosmic ray energy density Ec relative to the initial value Ec,0 (100 %) for distances from 30 to 50 pc from the explosion center. The calculations have been performed for an ISM density of 0.5 atoms cm. Less ISM density yields a lower CR intensity and vice versa.

2.2

Case B

The situation is however different for a closer SN (case B). In this case the pressure of the remnant Pej might overcome the solar wind ram pressure PSW ; this yields solar wind penetration: Pej  .Mtot  v/=.D2  t/ PSW I PSW  mH  vSW x¥SW I vSW  400km=sI ¥SW  3  108 HC =.cm2  s/ Dcrit  20pc Mtot total mass of remnant plus collected ISM .&ISM  1 cm3 / V  100km=s velocity of remnantI t  durationI ¥SW solar wind flux The transition from case A to case B is expected to occur roughly between 10 and 30 pc (transition from the Taylor-Sedov phase to the Snow-plow phase), but it depends also on the density  of the interstellar medium. Early studies on the impact to the Earth of such a close SN have been performed by Terry and Tucker (1968), Rudermann (1975), and rather elaborated studies have been performed later by Ellis and Schramm (1995) and Ellis et al. (1996). J. Ellis et al. considered an SN at a distance of 10pc. They estimated the fluence of neutral ionizing radiation at Earth’s surface to be ¥n D 6:6  105 .10=Dpc /2 erg=cm2 lasting for about a year. The charged CR fluence is estimated to be ¥cr D 7:4  106 .10=Dpc /4 erg=cm2 over a duration of 3D2pc yr. Dpc is the distance of the SN

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measured in pc. We note that the normal cosmic ray flux (in absence of SN events) at the top of the atmosphere is 9  104 erg=.cm2 yr/ (Terry and Tucker 1968). Thus in case of a distance of  10pc for an SN, the cosmic ray flux is estimated to be two orders of magnitude above the normal cosmic ray flux.

3

Biological Effects

3.1

Direct Biological Effects (Case B)

Terry and Tucker (1968). discussed the biological consequence for terrestrial life in case of an increased cosmic ray flux of more than one order of magnitude lasting, at most, a few days. Considering the arguments presented above, only an SN closer than 20pc could generate such a flux (scenario B). Because the observed mass extinctions of the fauna show, at the same time, little effect on the flora, the authors conclude that the explosion of an SN should be considered as one possible mechanism. From recent studies by Batlle (2012) and taking 0:3  103 Gy=year as normal cosmic ray intensity on Earth, the authors argue that an increase of about two orders of magnitude would be required for producing a harmful dosage: “For small mammals, dose rates 2  102 Gy=day are not fatal to the population; for larger mammals, chronic exposure at this level is predicted to be harmful.” The effects are quite diverse because of the variations in radiation resistance of different specious. For example, as female mice are sterilized at a certain dose, it needs an about two orders of magnitude, higher dose to kill insects and single-cell organisms (Terry and Tucker 1968). In a similar way, plants are as well less affected than animals at high doses (Terry and Tucker 1968). Hence the argument is that little effect on the flora but mass extinctions at the fauna could be an indication for a threat by an SN.

3.2

Indirect Effects on the Biosphere

3.2.1 Ozone Depletion (Case B) In a different approach from the previous discussion, Ellis and Schramm (1995) followed the discussion of Rudermann (1975) who studied the depletion of the ozone layer. Because of the enhancement of the cosmic ray intensity of more than one magnitude (scenario B), they estimate in the same way an increase of stratospheric production of NO. This is by a catalytic destruction of ozone due to two reactions (Crutzen 1970) NO C O3 ! NO2 C O2

(1)

O C NO2 ! NO C O2

(2)

and

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Ellis and Schramm concluded in their analyses an ozone hole depletion of roughly 95 %, induced by an SN at a distance of 10 pc, would last for 300yr. They focus on a disruption of the food chain, induced by the depletion of photosynthesizing organism. They describe consequences of a long-term exposure of the ultraviolet radiation: mass extinctions of marine life and also buildup of CO2 , yielding greenhouse episodes. However in a later publication, (Crutzen and Brühl 1996) estimated a substantial smaller ozone depletion. Instead of 95 % (Ellis and Schramm 1995), they estimated by using a detailed atmospheric model calculation a much smaller ozone depletion of at most 60 % at high latitudes and below 20 % at the equator. They conclude that a significant stress might have affected the biosphere at high latitudes only but much less on the tropical and subtropical biosphere, not strong enough to cause mass extinctions. Never the less we know that marine organisms and also the terrestrial ecosystems are affected by damages and also mutations by an increased exposure of UV radiation (Smith 1972). Marine organism in shallow water suffers damage by increased UV radiation. Plants, animals, and microorganisms are as well affected by increased UV radiation. More recently, a very detailed study on ozone depletion has been performed by Gehrels et al. (2003). They used a quite elaborated, two- dimensional, photochemical transport model from NASA Goddard Space Flight Center. They concluded that a significant effect of ozone depletion due to the combined effect of gamma and cosmic rays from an SN might occurs by an SN closer than 8 pc. However to get a clear picture is rather difficult. The reason is the enormous complexity of the biosphere and the uncertainties of the different parameters involved. Also Gehrels et al. (2003) point out that only since between around 600–500 Ma before present, the Earth has had developed enough oxygen in the atmosphere to form an ozone shield. Hence all the discussions above are only valid after this time. At any time before, different scenarios between cosmic rays from a close SN and the atmosphere might have determined the climate at that time. Martin et al. (2009) discuss only short-term effects of gamma-ray bursts on Earth covering mostly Archean and Proterozoic eons. It will be discussed below in the context of gamma-ray bursts.

3.2.2 Cloud Formation (Cases A and B) It was Ney (1959) who first pointed out the existence of a large tropospheric and stratospheric effects produced by the solar-cycle modulation of cosmic rays confirmed by weather observations. He also suggested climatological effects due to cosmic rays. Later Svensmark (1998); Svensmark and Friis-Christensen (1995) propagated also the idea that cloud formation follows the variations in GCR. It has also shown experimentally that ions play an important role for nucleation process in the atmosphere and, as they state, at the end for cloud formation (Svensmark et al. 2007). The connection between cloud formation and the climate on Earth is well known. In their book, Svensmark and Calder (2007) postulate that ice ages might be caused by temporary increases in the intensity of CR. This is actually a proposition introduced by Shaviv (2002). Shaviv suggested that through the periodical crossing

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of the spiral arms in our galaxy, the solar system is exposed also to a periodical increase of SNe and hence CR, since SNe tend to occur in the active star-forming regions in the spiral arms (Dragicevich et al. 1999). Shaviv constructed a galactic cosmic ray diffusion model and deduced a periodically increase in the CR flux associated with the travel of the solar system through the spiral arms of the Milky Way. In addition he compared his results with the exposure ages of iron meteorites and found correlations: iron meteorites are usually exposed to CR for several 100 My within of the solar system. By nuclear reactions on the elements in the meteoroid, radionuclides and stable isotopes are formed, from which the exposure time can be deduced. A considerable correlation, postulated by Shaviv (2002), is seen between the cosmic ray fluctuation and ice-age epochs. Never the less there are still discussions on the unambiguously disentangling of Shaviv’s arguments from the climate forcing induced by the, normally invoked, Croll-Milankovitch effect for glaciation cycles (Beech 2011; Williams et al. 2003). Also a detailed analysis of the exposure time of iron meteorites, considering also minor elements like S and P for the production of stable 21Ne (neglected by Shaviv), indicates that the variations mentioned by Shaviv might be less pronounced as thought before (Ammon et al. 2008). Although our understanding of the connection between cosmic rays and cloud formation is incomplete, this field of research is experimentally accessible at accelerator facilities able to simulate CR. The Cosmics Leaving Outdoor Droplets (CLOUD) (2015) experiment at CERN studies the possible link between galactic cosmic rays and cloud formation (Cloud 2015). Based at the Proton Synchrotron (PS) at CERN, simulating cosmic rays, CLOUD aims to further understand aerosols and clouds and unravel possible connections between cosmic rays and clouds and their effect on climate. This might help to quantify any possible correlations between SN and climate and perhaps also mass extinctions.

4

Frequency of Close SNe

Gehrels et al. (2003) estimated the frequency of close SN within the past several hundred million years. They considered an SN with total gamma-ray energy of 1:8  1047 erg. For a critical distance, to disrupt Earth’s ozone layer, of Dcrit  8pc (case B), the time-averaged galactic rate of close core-collapse SNe was calculated to be 1:5 Ga1 . A more frequent rate has been calculated by Beech (2011). Beech estimates, assuming random locations for SNe within the galactic disk, a time interval of the order of 112 Ma. He considered SNe occurring within a critical distance of 10 pc. He discusses also that most of the SNe occur mostly interior to the Sun’s orbit about the galactic center which should change the time interval. Other effects, like the encounter with the spiral arm structure of the galaxy, are also discussed. His final conclusion is that the time interval should likely be between 75Ma and 150Ma. However we should keep in mind that the rate would go up significantly for more than one order of magnitude if distances like 40 pc would be included (case A). This average rate might, however, not represent a good

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estimate for near past/future, since this depends on the local composition of the solar neighborhood, such as possible encounters of the solar system with highly active star associations (Breitschwerdt et al. 2012).

5

Gamma-Ray Bursts

A different scenario of an SN threat to life on Earth could be posed gamma-ray bursts (GRBs). In the electromagnetic spectrum, GRBs are the most energetic events in the universe, lasting only milliseconds to hours. This short time scale leads to the association of GRBs with explosion-like events such as SNe and neutron star mergers. At first gamma-ray bursts have been observed by the US spacecraft Vela, initially installed in Earth’s orbit for surveillance of nuclear bomb tests. It is believed that the flash is released in two narrow cones, opposite to each other, a precondition which drastically reduce the probability of an interaction. Longlasting gamma-ray bursts (>2 s) are discussed in conjunction with core collapse of very massive stars which yield a neutron stare or a black hole. Hypothetical hypernovae yielding a black hole are as well considered. Among others, one scenario being discussed is the astrophysical site of shortlasting flashes ( Tesc locally. How prevalent that gas is, and whether it participates in driving out the cold gas is a separate question. The second is that the merely hot gas (T  1067 K) and warm diffuse ionized gas (T  104 K) are ubiquitous along the minor axes of wind-driving galaxies, and in M 82 and other well-studied systems, there is a tight spatial correspondence between the two phases (Sect. 3). The third and most constraining fact is that the ionized gas and neutral atomic gas reaches high velocities in many systems. These velocities, which are relatively easy to measure in absorption on lines of sight toward the galaxies, are constraining since they range from 100 to 1000 km/s. The key physical problem for theorists is how to get gas, either by direct acceleration or by transformation from some other phase to many hundreds of km/s without shock heating it to temperatures where it would cease to produce the emission and absorption seen.

2.1

Hot Winds

The picture of supernova-heated hot winds is well developed. We imagine a region of size R – either an individual star cluster or an entire galaxy – where kinetic energy is injected in the form of core-collapse supernovae and stellar winds and that this kinetic energy thermalizes. It then drives a super-heated outflow that escapes the region. The energy and mass injection rates within the volume (r R) are EP and MP , respectively. Neglecting radiative cooling, gravity, and other effects, energy P MP /1=2 and that conservation implies that the asymptotic velocity is V1 D .2E= 2 the characteristic temperature is T / V1 . Assuming the flow is steady state, mass continuity gives the density of the hot gas within the energy injection region. For r > R, one expects adiabatic expansion with T / r 4=3 (for  D 5=3), n / r 2 , and V  V1 . These expressions are the essence of the Chevalier and Clegg (1985) (CC85) model, which gives a self-similar solution for a hot flow valid for r R that smoothly connects to the adiabatic expansion r > R region through a sonic point. In general, the sonic point for such a flow (without gravity) is located at

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the “edge” (r D R) of the energy/mass injection region (Wang 1995), and for parameters typical of supernova heating from star formation (see below), gravity can be neglected at R. The critical point topology changes if the flow is slow enough – either because of inefficient heating or heavy mass loading – that gravity should be included, as shown by Johnson and Axford (1971). Radiative cooling in the context of early-type galaxies and heating was explored by Mathews and Baker (1971). Scaling the energy injection rate to EP D ˛ EP SN , where ˛ is the thermalization efficiency and EP SN is the energy injection rate expected from core-collapse supernovae (1051 ergs per 100 Mˇ of star formation), and the mass injection rate to the star-formation rate MP D ˇ SFR, where SFR is the star-formation rate, one finds that P MP /1=2 ' 103 km=s .˛=ˇ/1=2 : Vhot; 1 ' .2E=

(1)

Equating the Bernoulli integral, B D constant D V 2 =2 C .5=2/P =; at the sonic point (r D R) with its value at infinity, we have that 2 7 Thot ' .mp =kB /.3=20/Vhot; 1 ' 2  10 K .˛=ˇ/:

(2)

Using mass continuity, the density at the sonic point is 3=2

nhot ' 1  102 cm3

ˇ 3=2 SFR1 ; 2 ˛ 1=2 Rkpc

(3)

where Rkpc D R=kpc and SFR1 D SFR=Mˇ yr 1 . The asymptotic kinetic power 2 of the wind is EP D .1=2/MP V1 , and its momentum injection rate is PPhot D MP V1 ' .2EP MP /1=2 ' 5.˛ˇ/1=2 L=c

(4)

where for the last approximate equality, we have used the fact that the bolometric luminosity of steady-state star formation is related both to the supernova rate and to P such that L ' 1010 Lˇ SFR1 . The momentum injection rate of supernova-heated E, winds is thus comparable to the expectation from radiation pressure in the singlescattering limit (L=c) discussed below. Limits on the parameters ˛ and ˇ can be derived for individual systems or for collections of star-forming galaxies from X-ray observations (e.g., Strickland and Heckman 2009; Zhang et al. 2014). Hot winds in the spirit of CC85 and their interaction with the ISM have been investigated numerically by a number of groups, both in idealized setups of blowout from a smooth galactic disk (e.g., Strickland and Stevens 2000) and in the more realistic fully 3d case (e.g., Cooper et al. 2008, 2009) and in planar geometry, where the turbulence of the galaxy and the outflow are directly coupled (e.g., Creasey et al. 2013).

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The CC85 theory has also been applied on much smaller scale in the context of individual superstar clusters (e.g., Silich et al. 2003, 2004). The picture of individual star-forming regions punching out of the local disk and injecting outflow into a large-scale galactic wind may be more realistic than the picture of an entire starburst functioning as envisioned by the CC85 model. Numerical galaxy formation models attempt to capture this dynamics (e.g., Hopkins et al. 2012).

2.2

Warm, Cool, and Cold Winds

An important puzzle in the theory of galactic winds is how to accelerate the cool atomic and warm ionized gas we see in emission and absorption to hundreds or even a thousand km/s. Several mechanisms have been proposed. One idea is that the outflowing hot supernova-heated phase cools radiatively. Other ideas include the direct acceleration of ISM material from the host galaxy, either with the ram pressure of a hot CC85-like outflow, the radiation pressure of starlight on dusty gas, and/or the pressure gradient from cosmic rays.

2.2.1 High Velocity Cool Gas from Radiative Cooling of the Hot Wind One way to produce fast outflowing cool/warm gas is to precipitate it directly from the hot phase. If the hot wind is sufficiently mass loaded – high ˇ in Eqs. (1), (2), and (3) – the radiative cooling time for the outflow can become shorter than the dynamical timescale, and we expect any hot wind launched from a galaxy or starforming region to cool on larger scales (r > R) (Wang 1995). The wind may start at R with Thot given by Eq. (2), but as it cools adiabatically, the temperature drops to 107 K, below which metal line cooling dominates over bremsstrahlung. Here, the cooling rate increases as the temperature decreases, and the medium can become radiatively unstable. For solar metallicity gas, the cooling radius can be approximated as (see Thompson et al. 2016 for details) rcool ' 4 kpc

2:13 1:79 ˛ R0:3kpc 2:92

ˇ



˝4

SFR10

0:789 ;

(5)

where the opening angle of the wind is ˝4 D ˝=4 and we have scaled the starburst for parameters typical of M 82 or a high-redshift star-forming clump. The strong parameter dependencies for the cooling radius follow from the strong density and temperature dependence of the cooling function in the region where metal cooling dominates at T . 107 K. The temperature of the cooling gas should drop precipitously at the cooling radius to 103:5 –104 K. The velocity of the cooling material is expected to be of order 700–1200 km/s. The minimum ˇ above which the flow must cool on large scales is actually not very large – ˇmin ' 0:6˛ 0:636 .R0:3 ˝4 =SFR10 /0:364 – suggesting that radiative cooling of hot winds may be a ubiquitous source of the high-velocity cool/warm gas seen in starbursting systems (Thompson and Krumholz 2016).

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2.2.2 Accelerating Cool Gas with the Ram Pressure of the Hot Wind Given its large momentum flux (Eq. 4), it is natural to consider the ram pressure acceleration of cool clouds by the hot outflow. Many papers treat the numerical problem of the interaction between a hot high-velocity flow as it interacts with a single cool cloud, compressing, accelerating, and shredding it. An important problem with this mechanism is the short timescale for cloud destruction via hydrodynamical instabilities, which set in on a multiple of the cloud-crushing timescale tcc ' .rc =Vhot /.c =hot /1=2 , where rc is the initial radius of the (assumed) spherical cloud and c is its density (e.g., Banda-Barragán et al. 2016; Brüggen and Scannapieco 2016; Cooper et al. 2009; Scannapieco and Brüggen 2015). For typical parameters, tcc is short enough that the cloud is not accelerated to high velocities before complete destruction (Scannapieco and Brüggen 2015; Zhang et al. 2015). However, Cooper et al. (2009) find that some of their cloud contrails reach velocities of hundreds of km/s. In addition, magnetic fields may significantly prolong the life of clouds so that they can be accelerated (McCourt et al. 2015). Banda-Barragán et al. (2016) find that clouds may be accelerated to 10 % of the hot wind speed. Additionally, conduction has recently been shown to increase cloud lifetime, but without increasing the acceleration to the point where ram pressure can work to explain the high-velocity cool/warm outflows seen (Brüggen and Scannapieco 2016). An important additional constraint on this mechanism, and all mechanisms that rely on momentum injection, is an Eddington-like limit (e.g., Murray et al. 2005; Zhang et al. 2015). If Vhot is large compared to the velocity of the cool cloud, balancing the ram pressure of a spherical wind and the gravitational forces for a cloud of surface density ˙c D Mc = rc2 (which changes in time as the cloud is compressed and shredded), one obtains the critical condition PPEdd D 4 GMtot ˙c ;

(6)

which one can view as either a critical momentum injection rate required to accelerate a cloud of some ˙c , or, for a given value of PP (e.g., Eq. 4), the critical value of ˙c below which the cloud is super-Eddington and should be accelerated. For example, taking Mtot D 2 2 r=G, as appropriate for an isothermal sphere with velocity dispersion  and using Eq. (4), one finds a critical cloud surface density of ˙c; crit  PP =.8  2 r), which corresponds to a cloud column density of 2 N  4  1021 cm2 .˛ˇ/1=2 SFR10 =200 R0:3 , where  is scaled to 200 km/s. For the elongated cometary cloud morphology found in simulations (e.g., Cooper et al. 2009), the cloud column density should naively increase, and for a given wind PP , the cloud may not be accelerated in the extended gravitational field of galaxies. However, the cool cloud gas mass rapidly decreases on the cloud-crushing timescale, and thus the increase in ˙c may be mitigated. Overall, the simulations done so far imply that clouds cannot be accelerated by a hot CC85-like flow to the asymptotic velocities seen in galactic winds, unless magnetic fields dramatically increase the cloud lifetime (Banda-Barragán et al. 2016; McCourt et al. 2015).

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2.2.3

Accelerating Cool Gas with Radiation Pressure on Dusty Gas and Supernova Explosions Galactic winds are dusty. As a result, the same massive stars that produce supernovae may also drive the cool gas out of galaxies via the absorption and scattering of starlight by dust grains (Murray et al. 2005, 2010; Murray, Menard, and Thompson; Zhang and Thompson 2012; Hopkins et al. 2012; Krumholz and Thompson 2013; Davis et al. 2014; Thompson et al. 2015). This mechanism is particularly attractive for young massive star clusters that disrupt their natal gas clouds before the first supernovae have gone off, but radiation pressure may also act on galaxy scales in systems that are both IR and UV bright. Observations suggest the direct singlescattering radiation pressure force may have dominated the dynamics of 30 Dor (Lopez et al. 2011; Pellegrini et al. 2011). Assuming that the dust and gas are dynamically coupled so that dust grains share their momentum with the surrounding gas and assuming that the starlight is dominated by UV, as appropriate for a very young stellar population, there are three limits for the wind medium: (1) optically thin to the UV ( UV . 1), (2) optically thick to the UV but optically thin to the reradiated FIR (the so-called single-scattering limit; UV > 1 and IR < 1), and (3) optically thick to both the incident UV and the reradiated IR photons (Andrews and Thompson 2011). For a typical gas-to-dust mass ratio for the ISM, a UV opacity of UV  103 cm2 /g of gas, and an IR opacity of order IR  1 cm2 =g of gas, the two breakpoints between these three limits correspond to gas surface densities of order 5 Mˇ =pc2 and 5  103 Mˇ =pc2 for a Milky Way-like gas-to-dust ratio. Combining each of these regimes into a single Eddington limit for the dusty gas Mg in the galaxy, one finds that (e.g., Thompson et al. 2015)

LEdd '

GM .< r/Mg c Œ1 C IR  exp. UV /1 r2

(7)

where M is the total mass, IR ' IR Mg =4 r 2 , IR is the Rosseland-mean opacity, which is a function of temperature, UV ' UV Mg =4 r 2 , and UV is the flux-mean opacity over the radiation field from the stellar population. Note that Eq. (7) assumes a spherical distribution of gas Mg at R around a point source of radiation and that it is simply generalized to a thin plane parallel disk geometry. Taking the limit UV  1 or IR  1, Eq. (7) reduces to the more familiar limits LEdd ' 4 GM c=UV and ' 4 GM c=IR , respectively. In the single-scattering limit, applicable over a wide range of column densities from 5 to 5000 Mˇ /pc2 , LEdd ' 4 GM ˙g c ' 2  1011 Lˇ M10 N21

(8)

where ˙g D Mg =4 r 2 , N21 D N =1021 cm2 is the particle column density, and M10 D M =1010 Mˇ . This expression for the Eddington luminosity should be compared with Eq. (4).

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For continuous optically thin radiation pressure-driven flow in a point-mass gravitational potential, from the momentum equation, one finds that the asymptotic velocity of the gas is V1 D Vesc .R0 / .  1/1=2

(9)

2 where Vesc .R0 / D 2GM .R0 /=R0 , R0 is the launch radius, and D L=LEdd is the Eddington ratio. For an Eddington ratio of order  few, the expectation is that the bulk of the material should be accelerated to of order the local escape velocity. For an isothermal sphere of velocity dispersion  , V1  2 . For a geometrically thin initially optically thick dusty shell, the flow can achieve higher velocity because while it is in the single-scattering limit, it gathers all of the momentum. In this case (Thompson et al. 2015)

 V1 '

2RUV L Mg c

1=2

1=2 1=4

1=4

' 600 km=s L12 UV; 3 Mg; 9 ;

(10)

where RUV D .UV Mg =4 /1=2 is the radial scale where the shell becomes optically thin to the incident UV radiation, L12 D L=1012 Lˇ (SFR ' 100 Mˇ /yr), UV; 3 D 1=4 UV =103 cm2 /g, and Mg; 9 D Mg =109 Mˇ . Many questions about the importance of radiation pressure feedback in galaxies remain. The first is that although radiation pressure may dominate the dispersal of gas in GMCs before the first supernovae explode, on average, supernova explosions inject more total momentum into the ISM than photons under standard assumptions and may thus dominate the driving of turbulence within galaxies and potentially wind driving. The total momentum of a given supernova remnant is enhanced relative to the initial value of the explosion as it sweeps up ISM material during its energy-conserving phase. This boost to the asymptotic momentum means that the momentum injection from supernova remnants can be as large as PPSN; remnants  10 L=c for steady-state star formation. How the momentum injection and turbulence driven by supernovae couples to a galaxy-scale wind is a topic of active research. A second issue for radiation pressure feedback is that in dense star clusters and starburst galaxies, the IR optical depth may significantly exceed unity, leading to the question of whether or not there is a significant boost to the total momentum deposited or whether the trapped photons escape via low-column-density sightlines. In principle, the momentum input could be as large as IR L=c. Finally, the full dynamical radiation transport problem has not yet been solved self-consistently in multidimensional simulations of galaxies, star formation, and winds.

2.3

Cosmic Ray Driven Winds

Although massive stars deposit energy and momentum directly into the ISM via their supernova explosions, there is another way they may drive the emergence

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of large-scale galactic winds in star-forming galaxies: cosmic rays. Approximately 10 % of the 1051 ergs in kinetic energy of supernova explosions is thought to go into primary cosmic ray protons (and other nuclei), with a power-law spectrum of particle energies from GeV to PeV produced by Fermi shock acceleration. The total energy injection rate in cosmic rays is then of order LCR ' 3  1040 ergs s1 SFR1 ' 8  104 L:

(11)

Once injected by supernovae, cosmic rays scatter off of magnetic inhomogeneities in the ISM with pc-scale mean free path  as they diffuse out of the host galaxy. The scattering process transfers cosmic ray momentum to the gas, and the large implied scattering optical depth ( CR  R=  kpc=pc  103 ) implies a large steady-state cosmic ray pressure and energy density (Breitschwerdt et al. 1991; Everett et al. 2008; Ipavich 1975; Jubelgas et al. 2008; Socrates et al. 2008). In the Milky Way, the local cosmic ray energy density is roughly comparable to the energy density in magnetic fields, photons, and turbulence. Each has an associated pressure roughly comparable to that required to support the gas of the galaxy in vertical hydrostatic equilibrium (Boulares and Cox 1990). The same may be true of starburst galaxies like M 82, and if so, cosmic rays may be important in wind driving. Indeed, analytic arguments akin to the Eddington limit for photons discussed above have been made by Socrates et al. (2008) that show cosmic rays may be important in regulating star formation and driving outflows. The large scattering optical depth implies that the total effective momentum injection rate would be PPCR  CR LCR =c  .L=c/. CR =103 /, of order the momentum input in light from massive stars, but with very different transport properties. Multidimensional simulations of galaxies are beginning to simulate CR-driven winds in detail (e.g., Girichidis et al. 2016). Several questions still need to be addressed. The first is the importance of pion production via inelastic scattering of cosmic rays off of ISM gas. These collisions produce charged and neutral pions that decay to secondary electron/positron pairs, neutrinos, and gamma rays. Because nearby starbursts like M 82 are observed to be gamma ray bright, the implication is that many cosmic rays interact to produce pion emission before escaping the host galaxy. This may limit the effective total scattering optical depth, the steady-state pressure, and the total cosmic ray momentum available to drive outflows. A related issue is how the cosmic rays couple to the gas and whether or not they sample the average-density gas or a lower-density medium. Since the timescale for pion production is inversely proportional to the gas density sampled, this is a key issue for determining how much momentum is transferred from the cosmic rays to the gas before pion production. Nevertheless, extended radio emission is observed along the minor axis of M 82 (Seaquist and Odegard 1991), which indicates the presence of relativistic electrons/positrons and magnetic fields, and cosmic ray-driven models remain a topic of active research.

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3

Observational Properties of Outflows

3.1

A Guided Tour of the Multi-phase Outflow in M 82

The conditions needed to drive galactic outflows are rare in the local universe but common at redshifts above about one (we will quantify these statements in Sect. 3.4 below). In fact, in the local universe, galactic outflows are only observed in galaxies undergoing unusually intense episodes of star formation (“starburst galaxies”). We therefore begin our discussion of observations of galactic outflows with a summary of the prototypical example associated with the starburst galaxy M 82. Located at a distance of only 3.6 Mpc, this is the brightest and best-studied example of a starburst-driven outflow. While the data are therefore the best and most complete, observations of other starburst-driven outflows are qualitatively consistent with those of M 82. The M 82 starburst has a star-formation rate of about 7–10 Mˇ per year (assuming a standard Chabrier/Kroupa) initial mass function. The starburst has a radius of 400 pc, yielding a star-formation rate per unit area (SFR/A) of about 15– 20 Mˇ year1 kpc2 . For context, this is over two orders of magnitude larger than the characteristic value in the disk of the Milky Way but is typical of present-day starbursts and star-forming galaxies at high redshift. These high values for SFR/A may allow for the efficient conversion of the kinetic energy supplied by core-collapse supernovae and winds from massive stars into the thermal energy of a very hot fluid since most supernovae will explode in the hot rarified gas created by prior supernovae. Subsequently, there can be efficient conversion of this thermal energy into the bulk kinetic energy of a volume-filling “wind fluid” (as discussed above in Sect. 2). The direct observational evidence for the existence for this hot fluid of thermalized stellar ejecta in the M 82 starburst is provided by hard X-ray observations which reveal that dominant ionic stage of Fe in the diffuse hot gas inside the starburst is helium-like. The implied temperature of the gas is between 30 and 80 106 K. Analysis of the properties of this gas shows that it is consistent with the simple Chevalier and Clegg (1985) model described above, with a thermalization efficiency of ˛  0:3  1 and a mass-loading factor of ˇ  0:2  0:6. The implied terminal velocity for an outflow fed by this very hot gas is Vhot; 1 ' 1400 – 2200 km s1 (Strickland and Heckman 2009; Eq. 1). Direct observational evidence for an outflow in M 82 dates back decades (Lynds and Sandage 1963) to the discovery of an extensive system of filamentary optical emission-line gas extending to radii of several kpc from the central starburst out along the minor axis of the edge-on galaxy (Fig. 1). This gas can also be observed through nebular line and continuum emission in the vacuum ultraviolet and through mid- and far-IR fine-structure line emission (Hoopes et al. 2005; Beirão et al. 2015; Contursi et al. 2013). Detailed spectroscopy has shown that this T  104 K gas has emission-line ratios consistent with a mixture of gas that is photoionized by radiation leaking out of the starburst and shock heated by the outflowing wind fluid generated within the starburst (Heckman et al. 1990). We will henceforth refer to this as the warm ionized phase. The kinematics of this gas implies that we are

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Fig. 1 A triptych showing the outflow in the proto-typical starburst galaxy M 82. From left to right the colors map the surface brightness of the outflow as observed in the far-ultraviolet continuum (primarily light scattered by dust in the outflow), in soft X-rays (tracing gas at 3 to 10 million K), and in H˛ plus [NII]6548,6584 optical emission-lines (tracing gas at 104 K). Note the strong morphological correspondences among the three images. The imaged region is 14.8 by 20 arcmin, corresponding to 15.4 by 20.9 kpc at the distance of M 82. North is at the top and East is to the left. The starburst itself coincides with the region of highest surface-brightness at the center of the outflow. The starburst extends over a diameter of 0.8 kpc with a major axis that is aligned with that of the galaxy disk in an ENE to WSW orientation (as seen in the FUV image). The main body of the outflow as seen in emission extends perpendicular to the starburst/galaxy disk out to projected distances of about 6 kpc above and below the disk. The “cap” is located about 12 kpc NNW of the starburst, and is likely to represent the site of a collision between the wind fluid and a cloud in the halo of M 82, implying that the wind fluid propagates well beyond the bright region traced by the far-UV, X-ray, and optical emission

seeing material located largely along the surfaces of a biconical or bicylindrical structure that originates at the starburst. The interior of this structure is presumably filled by the outflowing wind fluid (Shopbell and Bland-Hawthorn 1998). Correcting the measured outflow speed of the warm ionized gas for line-of-sight effects yields intrinsic outflow speeds of about 600 km s1 . Note that this significantly slower than the inferred outflow velocity for the hot wind fluid itself (1400–2200 km s1 ). The velocity field shows rapid acceleration of the gas from the starburst itself out to a radius of about 600 pc, beyond which the flow speed is roughly constant. The morphological structure of this warm ionized phase is strongly correlated with the structure of the co-spatial soft ( 1. Because SiC is predicted to form only from a gas that has C/O > 1, matter from the intermediate oxygen-rich zones must be strongly limited. The 29 Si and 30 Si excesses of C grains, however, require significant contributions from the intermediate oxygen-rich zones which will result in C/O < 1. Although many isotopic signatures of SiC supernova grains can be qualitatively matched by the Rauscher et al. (2002) models, there are still a number of problems, e.g., to account for the 29 Si/30 Si ratios and highest abundances of 15 N and 26 Al (Lin et al. 2010). Astronomical observations indicate extensive mixing in supernova ejecta. Mixing matter from interior zones with matter from outer zones might be possible due to the formation of Rayleigh-Taylor instabilities, which are predicted from hydrodynamical models of supernova explosions (Cherchneff 2013). More recently, attempts were made to find SiC formation scenarios that avoid the selective, largescale mixing. In the model of Pignatari et al. (2013a), a carbon- and silicon-rich and oxygen-poor zone (C/Si) forms at the bottom of the helium-burning zone (Fig. 7), an attractive site for SiC formation. The inner part of this zone is rich in 28 Si and

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Fig. 7 Profiles of 12 C, 16 O, and 28 Si mass fractions and of solar-normalized 12 C/13 C, 18 O/16 O, and 29 Si/28 Si ratios in the interior of a 15 Mˇ Type II supernova according to the model of Pignatari et al. (2013a). The layer labeled “C/Si” is rich in carbon and silicon and poor in oxygen and provides a favorable site for SiC formation

contains 44 Ti, the signature of X grains. In the context of this model, C grains could have formed from matter from the outer part of this zone which exhibits excesses in 29 Si and 30 Si. The Pignatari et al. (2013a) model predicts very high 12 C/13 C and very low N/C ratios in the C/Si zone, contrary to the X and C grain data; ingestion of hydrogen into the helium-burning shell before the explosion might be a way out to overcome these problems, as this could be a source of 13 C and high nitrogen abundances (Pignatari et al. 2015). Type Ia supernovae (SNe Ia), triggered by mass transfer from a companion star onto a white dwarf, cannot be completely ruled out as sources of X grains. Selective, large-scale mixing is not required, and mixing is limited to material from helium burning and to matter that experienced hydrogen burning in an earlier stage. Explosive helium burning produces 12 C, 15 N, 26 Al, 28 Si, and 44 Ti (Clayton et al. 1997), all of which are prominent in X grains. However, mixtures that best match the isotope data of X grains have C/O < 1 and whether SNe Ia can provide an environment for the neutron burst required to account for the molybdenum isotope data of X grains remains questionable.

2.2

Silicon Nitride

Presolar Si3 N4 grains are related to X grains in that they exhibit similar C, N, and Si isotopic signatures (Figs. 4 and 5) as well as high abundances of 26 Al (Lin et al. 2010; Nittler et al. 1995). Essentially all presolar Si3 N4 grains have a supernova origin, although their abundance is much lower (1 to 2 orders of magnitude) than that of SiC supernova grains (Fig. 3 and Table 1).

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2.3

P. Hoppe

Graphite

Graphite stardust is not graphite in the strict mineralogical sense but is carbon with different degrees of graphitization. It is less abundant than SiC and is found with concentrations of up to 10 ppm in the most primitive meteorites (Fig. 3). Presolar graphite grains are mostly round and larger than 1 m (Fig. 2). They have a range of densities and have been divided into low-density (LD; 2.0 g/cm3 / graphite grains. LD graphite grains comprise about 25 % of all presolar graphite grains. Both populations host small (20–500 nm) internal subgrains, mostly titanium carbide (TiC). Besides TiC, LD graphite grains, most of which have likely a supernova origin (see below), contain kamacite (ironnickel), iron, cohenite (Fe3 C), and rutile (TiO2 / subgrains (Bernatowicz et al. 1991; Croat et al. 2003). The range of carbon isotopic ratios of presolar graphite (12 C/13 C D 2–7200) is similar to that observed for presolar SiC. The distribution of 12 C/13 C ratios, however, is different. Most HD graphite grains exhibit enrichments in 12 C with a peak in the 12 C/13 C distribution at a value of around 500. In contrast, most LD graphite grains have lower than solar 12 C/13 C ratios (Fig. 8). Although the distribution of 12 13 C/ C ratios of LD graphite grains is distinct from supernova SiC X and C grains (Fig. 8), most LD (and some HD) graphite grains are likely from supernovae. This is based on high abundances of 26 Al, enrichments in 15 N and 18 O relative to solar isotopic abundances, and large Si isotopic anomalies, mostly enrichments in 28 Si, as in SiC X grains, and sometimes in 29 Si and 30 Si, as in SiC C grains (Amari et al. 2014; Jadhav et al. 2013; Travaglio et al. 1999). The lower 15 N enrichments in LD grains compared to SiC supernova grains (Fig. 4) have been explained by

Fig. 8 Histograms of 12 13 C/ C ratios of supernova SiC X (bottom) and LD graphite grains (top). The solar ratio is indicated by the dashed line

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isotopic equilibration with nitrogen of solar system origin. The 18 O enrichments can be explained by matter from the He/C zone in SNeII (Fig. 6). Furthermore, LD graphite grains show clear evidence for the incorporation of 44 Ti at the time of grain formation (Nittler et al. 1996). Large excesses in 41 K point toward decay of radioactive 41 Ca (half-life 105000 years) (Amari et al. 1996). Inferred 41 Ca/40 Ca ratios are higher than predicted for AGB stars but compatible with predictions for C- and O-rich zones in supernovae. Travaglio et al. (1999) and Jadhav et al. (2013) performed mixing calculations for matter from different supernova layers and showed that many isotopic signatures of LD graphite grains can be qualitatively matched. Finally, bulk samples of LD graphite carry the so-called Ne-E(L), neon with large enrichments in 22 Ne which most likely originates from decay of radioactive 22 Na (half-life 2.6 years). Sodium-22 is predicted to be produced in large quantities in SNeII if hydrogen ingestion into the helium shell is considered (Pignatari et al. 2015).

3

Oxygen-Rich Supernova Dust

3.1

Oxides

Presolar oxides are found with concentrations of up to 50 ppm in the most primitive meteorites. Although oxides can be chemically separated from meteorites, isotope studies are not as straightforward as for presolar SiC because most oxide grains have a solar system origin. Based on the isotopic composition of the major element oxygen, presolar oxides are divided into four distinct groups (Nittler et al. 2008, 1997) (Fig. 9). Most abundant are Group 1 grains which show moderate to large excesses in 17 O and about solar or slightly lower than solar 18 O/16 O ratios. From a comparison with stellar models, Group 1 grains appear to come from 1.2 to 2.2 Mˇ red giant and AGB stars of about solar metallicities. A small group of grains has very high 17 O/16 O ratios, higher than predicted for red giant and AGB stars, and these grains might have formed in the ejecta of nova explosions. Group 2 grains exhibit strong depletions in 18 O and moderate excesses in 17 O. These grains are believed to originate from low-mass AGB stars that experienced “cool-bottom processing.” Group 3 grains show slight enrichments in 16 O. Among the proposed stellar sources are low-mass, low-metallicity AGB stars and supernovae. Group 4 grains show large excesses in 18 O and predominantly 17 O excesses. Supernovae are the most likely sources of these grains. The same holds for two grains with large 16 O excesses. Overall, supernova grains account for 10 % of all oxide grains. Other important characteristics of supernova oxide grains are predominantly lower than solar 25 Mg/24 Mg ratios and 26 Mg excesses. The latter points to decay of radioactive 26 Al, although at lower levels (26 Al/27 Al up to a few times 102 / than inferred for carbonaceous supernova grains. One of the 16 O-rich grains shows clear evidence for the incorporation of 44 Ti at the time of grain formation which was taken

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Fig. 9 Oxygen isotopic compositions of oxide and silicate stardust grains. The four O isotope groups and a few unusual grains are indicated by different symbols. Group 4, a few Group 3, and the unusual grains in the lower left represent stardust from supernovae. The solar system isotopic ratios are indicated by dashed lines (Data are taken from the Washington University Presolar Grain Database. Figure adapted from Hoppe 2011)

as proof for the supernova origin of 16 O-rich grains (Gyngard et al. 2010). Clear evidence for the initial presence of 41 Ca was reported for another grain (Nittler et al. 2008). The enrichments in 18 O of Group 4 oxide grains were taken as evidence for an origin in SNeII (Choi et al. 1998). In the context of the 15 Mˇ supernova model of Rauscher et al. (2002), O isotopic ratios of Group 4 grains can be explained by mixing matter from the H and He/N zones with minor contributions from zones below; admixture of matter from the He/C zone leads to the characteristic enrichments in 18 O of Group 4 grains (Fig. 6). The 18 O-rich zone is also evident in the SN model of Pignatari et al. (2013a). Additional strong support for the proposed supernova origin of Group 4 oxide grains comes from an excellent agreement between multi-element (O, Mg, Ca) isotope data and predictions from supernova mixing models (Nittler et al. 2008). The fact that the majority of supernova grains is 18 O- and not 16 O-rich is surprising because the intermediate O-rich zones of SNeII are strongly enriched in 16 O (Fig. 6). Apparently, dust formation is more favorable in matter from outer SN zones.

3.2

Silicates

Although they represent the most abundant group of stardust minerals in primitive solar system materials, with concentrations of up to 200 ppm in meteorites, 375 ppm on average in isotopically primitive IDPs, and up to the percent level in individual IDPs, comparatively little isotope information exists for presolar silicates, mostly for oxygen and silicon. The reason for this is that presolar silicates can be identified only

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Fig. 10 18 O/16 O ratio image recorded by ion imaging with the NanoSIMS of a 5  5m2 -sized region in the fine-grained matrix of the Acfer 094 meteorite. A supernova silicate (encircled), about 160 nm in size, stands out by its high enrichment in 18 O (Picture credit: MPI for Chemistry)

in situ in thin sections of meteorites and IDPs by ion imaging techniques (Fig. 10), a time-consuming task. Furthermore, sizes of typical presolar silicates are only 200– 300 nm, and measured isotope compositions suffer from dilution with surrounding material of solar system origin. In general, presolar silicates exhibit the same O isotopic systematics (Floss and Stadermann 2009; Nguyen et al. 2010; Vollmer et al. 2009) as presolar oxides (Fig. 9). Supernova grains make up about 10 % of presolar silicates with sizes >150 nm; if smaller grains are considered then their contribution may be as high as 20 %. The most 18 O-rich grain among the O-rich supernova grains is an olivine with enrichment in 18 O of a factor of 14 and depletion in 17 O of a factor of 4 relative to solar isotope abundances (Messenger et al. 2005). Silicon isotopic compositions of supernova silicates are on average more 28 Si rich than grains from red giant and AGB stars, but, overall, their signatures are not very conclusive. Supernova silicates have similar Mg isotopic compositions as supernova oxides, i.e., predominantly depletions in 25 Mg and enrichments in 26 Mg. The latter points to 26 Al decay. Because Al/Mg ratios are generally low in presolar silicates, it is difficult to infer proper 26 Al/27 Al ratios from 26 Mg excesses.

4

Cross-References

 Effect of Supernovae on the Local Interstellar Material  Isotope Variations in the Solar System: Supernova Fingerprints  Nucleosynthesis in Spherical Explosion Models of Core-Collapse Supernovae  Nucleosynthesis in Thermonuclear Supernovae  Pre-supernova Evolution and Nucleosynthesis in Massive Stars and Their Stellar

Wind Contribution  Supernovae from Massive Stars  The Multidimensional Character of Nucleosynthesis in Core-Collapse Super-

novae

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References Amari S, Anders E, Virag A, Zinner E (1990) Interstellar graphite in meteorites. Nature 345:238–240 Amari S, Hoppe P, Zinner E, Lewis RS (1992) Interstellar SiC with unusual isotopic compositions: grains from a supernova? Astrophys J 394:L43–L46 Amari S, Zinner E, Lewis RS (1996) 41 Ca in presolar graphite of supernova origin. Astrophys J 470:L101–L104 Amari S, Zinner E, Lewis RS (1999) A singular presolar SiC grain with extreme 29;30 Si excesses. Astrophys J 517:L59–L62 Amari S, Zinner E, Gallino R (2014) Presolar graphite from the Murchison meteorite: an isotopic study. Geochim Cosmochim Acta 133:479–522 Bernatowicz T, Amari S, Zinner E, Lewis RS (1991) Interstellar grains within interstellar grains. Astrophys J 373:L73–L76 Bernatowicz T, Fraundorf G, Ming T, Anders E, Wopenka B, Zinner E, Fraundorf P (1987) Evidence for interstellar SiC in the Murray carbonaceous meteorite. Nature 330: 728–730 Black DC, Pepin RO (1969) Trapped neon in meteorites. II. Earth Planet Sci Lett 6:395–405 Cherchneff I (2013) Dust production in supernovae. In: The life cycle of dust in the Universe, Taipei. PoS(LCDU 2013), p 18 Choi B-G, Huss GR, Wasserburg GJ, Gallino R (1998) Presolar corundum and spinel in ordinary chondrites: origins from AGB stars and a supernova. Science 282:1284–1289 Choi B-G, Wasserburg GJ, Huss GR (1999) Circumstellar hibonite and corundum and nucleosynthesis in asymptotic giant branch stars. Astrophys J 522:L133–L136 Clayton DD, Arnett WD, Kane J, Meyer BS (1997) Type X silicon carbide presolar grains: Type Ia supernova condensates? Astrophys J 486:824–834 Croat TK, Bernatowicz TJ, Amari S, Messenger S, Stadermann FJ (2003) Structural, chemical, and isotopic microanalytical investigations of graphite from supernovae. Geochim Cosmochim Acta 67:4705–4725 Floss C, Stadermann F (2009) Auger nanoprobe analysis of presolar ferromagnesian silicate grains from primitive CR chondrites QUE 99177 and MET 00426. Geochim Cosmochim Acta 73:2415–2440 Groopman E, Zinner E, Amari S, Gyngard F, Hoppe P, Jadhav M, Lin Y, Xu YC, Marhas KK, Nittler LR (2015) Inferred initial 26Al/27Al ratios in presolar stardust grains from supernovae are higher than previously estimated. Astrophys J 809:31(16pp) Gyngard F, Zinner E, Nittler LR, Morgand A, Stadermann FJ, Hynes KM (2010) Automated NanoSIMS measurements of spinel stardust from the Murray meteorite. Astrophys J 717:107–120 Hoppe P (2011) Measurements of presolar grains. In: Proceedings of the 11th symposium on nuclei in the cosmos (NIC XI), Heidelberg, 19 July–23 July 2010. Available online at http://pos.sissa. it/cgi-bin/reader/conf.cgi?confid=100#session-121 Hoppe P (2015) NanoSIMS and more: New tools in nuclear astrophysics. J Phys Conf Ser 665:012075 Hoppe P, Besmehn A (2002) Evidence for extinct Vanadium-49 in presolar silicon carbide grains from supernovae. Astrophys J 576:L69–L72 Hoppe P, Fujiya W, Zinner E (2012) Sulfur molecule chemistry in supernova ejecta recorded by silicon carbide stardust. Astrophys J 745:L26 Hoppe P, Leitner J, Gröner E, Marhas KK, Meyer BS, Amari S (2010) NanoSIMS studies of small presolar SiC grains: new insights into supernova nucleosynthesis, chemistry, and dust formation. Astrophys J 719:1370–1384 Hoppe P, Strebel R, Eberhardt P, Amari S, Lewis RS (2000) Isotopic properties of silicon carbide X grains from the Murchison meteorite in the size range 0.5–1.5 um. Meteorit Planet Sci 35:1157–1176

97 Stardust from Supernovae and Its Isotopes

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Hutcheon ID, Huss GR, Fahey AJ, Wasserburg GJ (1994) Extreme 26 Mg and 17 O enrichments in an Orgueil corundum: identification of a presolar oxide grain. Astrophys J 425:L97–L100 Hynes KM, Gyngard F (2009) The presolar grain data base. http://presolar.wustl.edu/~pgd. LunarPlanetSci40:abstract#1398 Jadhav M, Zinner E, Amari S, Maruoka T, Marhas KK, Gallino R (2013) Multi-element isotopic analyses of presolar graphite grains from Orgueil. Geochim Cosmochim Acta 113:193–224 Lewis RS, Tang M, Wacker JF, Anders E, Steel E (1987) Interstellar diamonds in meteorites. Nature 326:160–162 Lin Y, Gyngard F, Zinner E (2010) Isotopic analysis of supernova SiC and Si3 N4 grains from the Qingzhen (EH3) chondrite. Astrophys J 709:1157–1173 Messenger S, Keller LP, Lauretta DS (2005) Supernova olivine from cometary dust. Science 309:737–741 Messenger S, Keller LP, Stadermann F, Walker RM, Zinner E (2003) Samples of stars beyond the solar system: silicate grains in interplanetary dust. Science 300:105–108 Meyer BS, Clayton DD, The L-S (2000) Molybdenum and zirconium isotopes from a supernova neutron burst. Astrophys J 540:L49–L52 Nguyen A, Nittler LR, Stadermann F, Stroud R, Alexander CMOD (2010) Coordinated analyses of presolar grains in the Allan Hills 77307 and Queen Elizabeth Range 99177 meteorites. Astrophys J 719:166–189 Nguyen AN, Zinner E (2004) Discovery of ancient silicate stardust in a meteorite. Science 303:1496–1499 Nittler LR, Alexander CMOD, Gallino R, Hoppe P, Nguyen AN, Stadermann FJ, Zinner EK (2008) Aluminum-, calcium- and titanium-rich oxide stardust in ordinary chondrite meteorites. Astrophys J 682:1450–1478 Nittler LR, Alexander CMOD, Gao X, Walker RM, Zinner E (1997) Stellar sapphires: the properties and origins of presolar Al2 O3 in meteorites. Astrophys J 483:475–495 Nittler LR, Alexander CMOD, Gao X, Walker RM, Zinner EK (1994) Interstellar oxide grains from the Tieschitz ordinary chondrite. Nature 370:443–446 Nittler LR, Amari S, Zinner E, Woosley SE, Lewis RS (1996) Extinct 44 Ti in presolar graphite and SiC: proof of a supernova origin. Astrophys J 462:L31–L34 Nittler LR, Hoppe P, Alexander CMOD, Amari S, Eberhardt P, Gao X, Lewis RS, Strebel R, Walker RM, Zinner E (1995) Silicon nitride from supernovae. Astrophys J 453:L25–L28 Pignatari M, Wiescher M, Timmes FX, Boer RJd, Thielemann FK, Fryer C, Heger A, Herwig F, Hirschi R (2013a) Production of carbon-rich presolar grains from massive stars. Astrophys J 767:L22 (6pp) Pignatari M, Zinner E, Bertolli MG, Trappitsch R, Hoppe P, Rauscher T, Fryer C, Herwig F, Hirschi R, Timmes FX, Thielemann F-K (2013b) Silicon carbide grains of type C provide evidence for the production of the unstable isotope 32Si in supernovae. Astrophys J 771:L7(5pp) Pignatari M, Zinner E, Hoppe P, Jordan CJ, Gibson BK, Trappitsch R, Herwig F, Fryer C, Hirschi R, Timmes FX (2015) Carbon-rich presolar grains from massive stars: subsolar 12C/13C and 14N/15N ratios and the mystery of 15N. Astrophys J 808:L43(6pp) Rauscher T, Heger A, Hoffman RD, Woosley SE (2002) Nucleosynthesis in massive stars with improved nuclear and stellar physics. Astrophys J 576:323–348 Reynolds JH, Turner G (1964) Rare gases in the chondrite Renazzo. J Geophys Res 69:3263–3281 Richter S, Ott U, Begemann F (1998) Tellurium in pre-solar diamonds as an indicator for rapid separation of supernova ejecta. Nature 391:261–263 Travaglio C, Gallino R, Amari S, Zinner E, Woosley S, Lewis RS (1999) Low-density graphite grains and mixing in type II supernovae. Astrophys J 510:325–354 Vollmer C, Hoppe P, Stadermann FJ, Floss C, Brenker F (2009) NanoSIMS analysis and Auger electron spectroscopy of silicate and oxide stardust from the carbonaceous chondrite Acfer 094. Geochim Cosmochim Acta 73:7127–7149 Zinner E (2014) Presolar grains. In: Davis AM (ed) Meteorites and cosmochemical processes. Treatise on geochemistry update 2, vol 1. Elsevier, Amsterdam, pp 181–213

Supernovae, Our Solar System, and Life on Earth

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Arnold Hanslmeier

Abstract

Supernovae in the solar neighborhood can have influence on the dynamics of small solar system bodies as well as on the atmospheres of planets. During a supernova outburst enhanced particle emissions as well as enhanced short wavelength radiation occur. We give an overview of the interaction of nearby supernovae to the outer parts of the solar system, the Oort cloud, and then on the heliosphere which deflects charged particles and provides a shielding. Finally, the influence of supernova radiation and short wavelength radiation on the Earth’s atmosphere is discussed. Enhanced cosmic ray particles from supernovae may also act as condensation nuclei and therefore trigger cloud formation in the Earth’s atmosphere.

Contents 1 2

3

4

5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Solar System-A Quick Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Influence of a Nearby Supernova Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supernovae and the Dynamics of the Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Oort Cloud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Heliosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Supernova-Heliosphere Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supernovae and Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Star Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Supernovae and Solar System Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supernovae and Earth’s Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 The Earth’s Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A. Hanslmeier () Institute of Physics, University of Graz, Graz, Austria e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_114

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5.2 Evolution of the Earth’s Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Supernova Explosions and Earth Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Cosmic Rays and Cloud Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Nearby Supernova Explosions in the Past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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Introduction

Supernova research today is mainly done by a systematic scanning of a large sample of galaxies inasmuch as the chance to observe a supernova in an individual galaxy is about one per several decades. This is accomplished by robotic telescopes and the detection of most supernovae in distant galaxies is done by comparing images of a certain galaxy and searching for an enhancement of its brightness because a supernova in a galaxy usually reaches the same brightness as the whole galaxy. However, galactic supernovae can be observed even without telescopes. Examples of bright supernovae that were clearly seen as extremely bright stellar objects in the sky in historic times since 1000 AD are supernovae. • SN 1006, constellation Lupus, distance 7000 Ly, max. magnitude 7.5, brightest stellar object ever observed in history. • SN 1054, constellation Taurus, distance 6500 Ly, max. magnitude: 6.0, also known as the Crab Nebula. • SN 1572, constellation Cassiopeia, distance 8000 Ly, max. magnitude 4.0, also known as Tycho’s Nova. • SN 1604, constellation Ophiuchus, distance 14,000 Ly, max. magnitude 3.0, also known as Kepler’s Nova. These supernovae occurred in the galaxy. The first extragalactic supernova observed was SN 1885A in the Andromeda galaxy (distance 2.5 million l.y.), the max. magnitude was +7.0. Because it is well known that supernovae mark the transition of a star more massive than the Sun to a neutron star or even a black hole at the end of stellar evolution in some cases, and that during the collapse to a neutron star or even a black hole and the expulsion of the outer stellar layers, a huge amount of energetic particles and short wavelength radiation is to be expected, the question arose whether a nearby supernova explosion can influence the planetary system or might even lead to one of the mass extinctions that occurred at least five times over the last 500 million years on Earth. In this review we first start with a short description of the solar system, then the heating effects on objects in the Oort cloud are discussed. Such a heating may affect the dynamics and trigger cometary showers that penetrate to the inner planetary system and the risk of collision of comets with planets increases considerably. Then the influence of supernovae on the heliosphere is discussed. For the formation of the

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solar system from an interstellar cloud, a nearby supernova explosion might have started the process of cloud contraction. Finally, the influence of a nearby supernova explosion on the Earth’s atmosphere is discussed.

2

The Solar System

In this section we start with a brief description of the solar system and then we investigate how energetic particles and radiation from supernovae interact with the boundaries of the solar system and propagate into the inner planetary system.

2.1

The Solar System-A Quick Overview

The Sun contains 99.8 % of the total mass of the solar system and therefore its gravity dominates all other influences. The planetary system contains eight planets and several asteroid belts such as the main belt between the orbit of Mars and Jupiter or the Kuiper belt that is located just outside the orbit of Neptune. This is the flattened part of the solar system because all of its objects are strongly concentrated to the ecliptic. The solar system is surrounded by a cloud of small-sized cometarylike bodies that are not concentrated on the ecliptic but are spherically distributed. This cloud of objects is called the Oort cloud and its existence was first suggested by the distribution of long period comets (see also Weissman 2000) that seem to enter the inner solar system from all directions. Therefore, radiation and particles from supernova explosions first encounter the objects in the Oort cloud before penetrating through the inner solar system. The Oort cloud contains approximately 1012 comets and the radius is about R2 D 105 AU. The typical mass of a comet ranges from 1016 to 1017 g. Therefore, this huge amount of comets may represent about 1030 g which is about 1/1000 times the mass of the Sun.

2.2

Influence of a Nearby Supernova Explosion

Before giving a quantitative estimate of the influence of a nearby supernova explosion on solar system bodies we give a qualitative estimate: a nearby supernova explosion leads to a propagation of radiation, charged particles that can have an influence on: • Oort cloud: This is the outmost part of the solar system; objects in the Oort cloud can be mainly affected by heating and therefore volatile components evaporate affecting the dynamics of these bodies. The typical extension of the Oort cloud is up to 50,000 AU. • Heliosphere: The heliosphere marks the boundary where the solar wind (and magnetic) pressure equals the interstellar pressure. The heliosphere provides a

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magnetic shielding against charged supernova particles. The typical extension of the heliosphere is up to 100 AU. • Inner planetary system: Here we concentrate on the influence on the Earth’s atmosphere. On the surface of the Earth, life is protected by the magnetosphere (against charged particles) and the atmosphere (against short wavelength radiation). The realm of terrestrial planets goes up to about 2 AU.

3

Supernovae and the Dynamics of the Solar System

3.1

The Oort Cloud

The Oort cloud contains several 1012 cometary-like objects that consist of rock and volatile elements. Several hundred comets in the Oort cloud may penetrate by some triggering mechanism to the inner solar (planetary) system. During such showers of cometary-like objects the risk of collisions with terrestrial planets becomes considerably enhanced. Impacting objects larger than several km may have led to mass extinction on Earth (Hanslmeier 2009) as has been reported. One of the triggering mechanisms of cometary showers might be a nearby supernova explosion. The main idea is that heating of 30 K will considerably change objects in the Oort cloud and also affect their dynamics. Here we follow the paper of Stern and Shull (1988). To study the interaction between supernova explosions and objects in the Oort cloud, a radius of influence Ri .Te / can be estimated from 

L cos  Ri .Te / D 4  Te4

1j2

L cos  2 T30 D 0:84.pc/ 106 Lˇ 

(1)

L denotes the luminosity of the star, Lˇ denotes the solar luminosity,  the angle of incidence, Te the effective temperature to which a comet should be heated,  D 5:67  108 W m2 K4 the Stefan-Boltzmann constant, T30 D .Te =30 K/, and Lˇ D 3:89  1033 erg s1 . For the global average comet temperature, Ri is a factor of 2 smaller (maximum is at  D 0). 1 pc D 3:086  1018 cm D 3:262 l:y: From this we can estimate at what distance a star with 1 Lˇ should pass in order to heat a comet by 30 K. The value is 173 AU. This distance is about a factor of 2 of the extension of the heliosphere. Therefore, stars of about the same luminosity as the Sun are not likely to heat any objects in the Oort cloud because they must pass very close, which might be an extremely rare event over the evolution of the solar system. The more luminous the star, the farther away from an object in the Oort cloud such heating will occur. An O3 III star, for example, has L D 106 Lˇ . This will cause heating by passing at a distance of 0.84 pc. Such a distance corresponds to typical distances between stars in the solar neighborhood. Therefore, nearby bright luminous stars can considerably heat objects in the Oort cloud.

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However, what about a nearby supernova explosion during which a much higher amount of luminosity is achieved? For a few months, a typical supernova reaches a luminosity of about 109 Lˇ . The energy release occurs in three parts: • 1049 erg in light, • 1051 erg in mechanical energy (blastwave), • 1053 erg in neutrinos. If we concentrate on the electromagnetic heating of comets then we find the following radii of influence for the two types of supernovae: 1 Ri .Type I/ D 17:3 pc  T2 30 h

(2)

1 T2 30 h

(3)

Ri .Type II/ D 12:7 pc 

In these equations h is the scaling parameter that is related to the Hubble constant H0 D .100 km s1 Mpc1 /h

(4)

and currently h D 0:70. The difference between heating the Oort cloud by nearby passing stars and a supernova explosion is: • A nearby passing star heats only a small fraction of the cloud. • A nearby supernova explosion heats comets from quite large distances, and almost the entire Oort cloud is heated uniformly. In order to estimate how often a nearby supernova explosion has to be expected we need estimated Supernova rates SN in our galaxy: • Estimated supernova rate for Type I: one per 36 yrs. • Estimated supernova rate for Type II: one per 44 yrs. So, on the average one SN per 20 yr is to be expected. From that number one can estimate: 3 Ne .Type I/ D 5:3T6 30 h

(5)

3 Ne .Type II/ D 5:4T6 30 h

(6)

If h D 0:70 then we can expect all comets have been heated about 30 times to Te  30 K. This number refers to the age of the solar system, D 4:5  109 yr.

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Table 1 Some critical temperatures for comets.

Temperature (K) 5 17–26 22 24 25

Event H2 sublimation Trapped H realesed from H2 O clathrates N2 sublimation O2 sublimation CO sublimation

What are the effects of such a heating? In addition to causing orbital instabilities, we also have to take into account that the composition of a comet might be altered. The comet gets heated (in our estimates above by about 30 K) and several compounds on its surface have low sublimation temperatures and evaporate. Just a few examples of critical temperatures of gases found on cometary surfaces are given in Table 1. A clathrate is a chemical substance consisting of a lattice that traps molecules. Supernova: comet heating These few examples demonstrate how comets in the Oort cloud could have been influenced by nearby supernova explosions. During the solar system evolution, cometary showers to the inner solar system could have happened about 30 times, triggered by nearby supernova explosions.

3.2

The Heliosphere

The heliosphere is dominated by particles and magnetic fields originating from the Sun. Its outer boundary provides a shielding against cosmic ray particles. In the hot solar corona, solar wind, consisting of charged particles, streams outwards with typical velocities in the range from 300 to 800 km s1 . This is a supersonic shockwave propagating through the whole planetary system. At the termination shock the supersonic velocities become subsonic. The deceleration of the solar wind particles continues until a balance between interstellar medium and solar wind particles is achieved at the so-called heliopause. The existence of the termination shock was proven by observations when it was transversed by two spacecraft: Voyager 1 in 2004 and Voyager 2 in 2007. The termination shock is located at solar distances between 75 and 90 AU. The interaction with the interstellar medium causes a compression, heating, and also a change in the magnetic field that was measured by the spacecraft. At the heliopause that was determined by both spacecraft at a distance of 121 AU a strong increase of cosmic rays occurs, because there is no further shielding of the particles (Fig. 1). A recent review about the heliosphere was given by Opher et al. (2015). In this article several estimations of the impact of a supernova blast on the heliosphere and outward propagation solar wind are given.

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Fig. 1 The heliosheath and the termination shock region in the heliosphere (Credit: NASA)

3.3

Supernova-Heliosphere Interaction

What is the interaction between a supernova blast and the heliosphere? The solar wind properties at 1 AU vary with time, on shorter timescales and on the solar cycle timescale. Data from SOHO (Ipavich et al. 1998) give the following values (for 1 AU): np;SW D 8:1 ˙ 4:3 cm3 (7) vSW D 412 ˙ 76 km s1

(8)

np denotes the proton number density; the suffix SW stands for solar wind. There is a correlation np;SW D 7:6 cm3 .vSW =400 km s1 /

(9)

The solar wind ram pressure is 2 Pram;SW D mp np;SW vSW  2:0  108 dyne cm2

(10)

There is a weak correlation Pram;SW / .vSW =400 km s1 /0:08

(11)

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Table 2 Interstellar medium (ISM) parameters Model Local interstellar cloud Local Bubble Average ISM

Density nH .cm3 ) 0.1 0.005 1.0

Temperature (K) 8000 1:28  106 8000

Pressure (P dyne cm2 ) 2:2  1013 1:8  1012 2:2  1012

The solar Ulysses probe (launched in 1990) found that the solar wind ram pressure was stronger toward the solar poles and at 1 AU a 50 % enhancement was found (Phillips et al. 1995). Therefore, the maximum penetration distance of a supernova blast depends on the inclination of the ecliptic relative to the incoming supernova blast. The local interstellar medium values are given in Table 2. The local interstellar medium is a 100 pc region surrounding the heliosphere. It consists of a hot, low-density gas. It is known as the local bubble (see Frisch 1995). The local interstellar cloud is the immediate environment of the Sun (local fluff). The Sun entered this region in the past 10,000 yr. For a simple treatment of the interaction of a supernova blastwave with the heliosphere we need the following expressions: • Supernova shock front position, RSN RSN D ˇ.ESN =mp nISM /1=4 t 2=5

(12)

ESN is the explosion energy D 1051 erg. nISM is the ambient interstellar (hydrogen) density, and ˇ  1 depends on the adiabatic index  . For  D 5=3 this value is ˇ D 1:1517. • Shock front arrival at position RSN is: t D ˇ 5=2

r

1=2  n mp nISM 5=2 ISM RSN D 4:8 kyr 3 ESN 1 cm



RSN 10 pc

5=2 (13)

• The shockfront speed is vshock

2 2 RSN D ˇ 5=2 D 5 t 5

s

ESN 3=2 R mp nISM SN

(14)

• The speed behind the shock is

vSNR

2 4 ˇ 5=2 vshock D D  C1 5 C1 D 610 km s1



1 cm3 nISM

s

ESN 3=2 R mp nISM SN

1=2 

10 pc RSN

3=2 (15)

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• All these quantities are measured in the ISM frame. The sound speed behind the shock is 2 cS2 D 2.  1/vshock =. C 1/2

(16)

The postshock flow is mildly supersonic. • The density behind the shock is enhanced over the ambient density by the usual compression SNR D

 C1 ISM D 4ISM  1

(17)

• The postshock ram pressure in the ISM frame is 2 PSNR;ram D SNR vSNR

(18)

2 PSNR;therm D 2ISM vshock =. C 1/

(19)

• The thermal pressure is

• The total pressure then becomes: 8

PSNR;tot D 3:3  10

dyne cm

2



10pc RSN

3 (20)

By self-similarity, a supernova pressure scales as E=R3 and it is independent of the density of the medium. The solar wind pressure can be estimated from the mass flux at radius r: jSW .RSW / D SW vSW

  MP 1 AU 2 D D jSW .1 AU/ 2 RSW 4 RSW

(21)

For distances 1 AU we can neglect the acceleration of the solar wind and 2 assume a constant velocity. The density then falls off as RSW as does the ram 2  pressure. The thermal pressure drops more sharply: P /  / RSW , and can be fully neglected. Therefore we arrive at:

Ptot;SW

vSW  vSW;1 AU  450 km=s   1 AU 2 SW  SW;1 AU RSW   1AU 2 D 2  108 dyne cm2 RSW

(22) (23) (24)

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When the two flows become equal, balancing each other, we have the pressure balance or stagnation distance: s Rstag D

2 PSW C SW vSW AU 2 PSNR C SNR vSNR

(25)

Therefore we see that: • At the heliopause: nISM D 0; 1 cm3 and vˇ D 26 km s1 , Pram;ISM D 1012 dyne cm2 . From that we can calculate Rstag D 100 AU which is in good agreement with observations. • The solar wind at 1 AU has a pressure of about 2  108 dyne cm2 which is comparable to a SNR at 10 pc. This has important consequences. We see that supernova penetration to the Earth’s orbit is feasible for nearby supernovae (10 pc). Also other instabilities including Kelvin-Helmholtz instability or Rayleigh-Taylor instability occur. Other authors (Gehrels et al. 2003) speak of a killing radius of a supernova explosion 8 pc implying biologically damaging events accompanied by radioactive deposition. A nearby supernova can strongly influence the heliopause and can compress it to within 1 AU. A supernova explosion might also have had an impact on sublimation of volatile elements of small-scale solar system bodies in the asteroid belts.

4

Supernovae and Isotopes

Nearby exploding supernovae lead to an enhanced production of certain isotopes in the Earth’s atmosphere and surface. These isotopes can serve as a proxy to confirm nearby supernova explosions in the past.

4.1

Star Formation

From stellar evolution theory it is well known that stars form out of interstellar clouds as soon as these clouds become gravitationally unstable; that means when the gravitational force becomes larger than the internal pressure force of the gas cloud. The condition for a huge cloud to collapse to a smaller denser cloud is known as the Jeans criterion. For stability, the cloud must be in hydrostatic equilibrium: dp G.r/Menc .r/ D dr r2

(26)

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where Menc is the enclosed mass, p is the pressure, and .r/ is the density of the gas at radius r. A gas cloud is assumed to be spherical. For a stable cloud the virial theorem 2U C  D 0

(27)

  > 2U

(28)

holds. For a collapsing cloud

The  for a homogeneous cloud with mass M and radius R is:

D

3 GM 2 5 R

(29)

For an isothermal cloud with uniform density, N particles: U D

3 N kT 2

(30)

 is the mean molecular weight of the particle, N D M =mH , and H is the molecular weight of hydrogen. The condition for a collapse becomes: 3M kT 3 GM 2 > 5 R mH

(31)

and from

RD

M 4

 3

!1=3 (32)

the Jeans’ mass becomes:  M >

5kT mH G

3=2 

3 4 

1=2 D MJ

(33)

A 10 K molecule cloud of 1000 solar masses and a density of 1000 H2 cm3 becomes Jeans’ unstable and star formation sets in.

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Supernovae and Solar System Formation

However, this scenario works only with external triggering forces. Possible triggers for star formation could be • Cloud merging • Supernova explosions • Turbulence, magnetic fields,. . . The question is, what mechanism triggered the formation of the solar system? If it was triggered by a nearby supernova explosion, how then can we trace back such an explosion? Supernova explosions produce remnants such as radioactive isotopes. For example, 60 Fe was found in relatively high amounts in certain sedimentary layers on the Earth’s surface; this will give evidence for a supernova that occurred during the phase of deposition of that sedimentary layer. 60 Fe has a half-lifetime of 2:6106 yr. In order to test whether a supernova explosion was the trigger for the formation of the solar system, the 60 Fe abundance in objects that have not changed since the solar system formation can be examined. Also the isotope 58 Fe can be used as a proxy. This is a stable isotope, however, its production can only be explained by supernova explosion. From different samples of meteorites it was found that these isotopes were relatively uniformly distributed and the abundance found was very low. Therefore, from the measurements of Fe isotope abundance one could conclude that no supernova explosion has triggered the formation of the solar system. This seems to be in contradiction with 26 Al (half-life 7:17  105 yr) measurements. This isotope can also be used as an indicator for a nearby supernova explosion. Therefore it seems that • Fe measurements suggest that the solar system formation was not triggered by nearby supernovae explosion. • Al isotope measurements, however, suggest a triggering of gravitational collapse by a nearby supernova explosion. This contraction could be resolved by assuming that the triggering has occurred by a close nearby massive star that enriched the solar nebula by 26 Al through stellar wind-nebula interaction, however, the Fe remained in its core. Other authors (including Gritschneder et al. 2012) stress the triggering by a supernova explosion. From 26 Al measurements it was concluded that a supernova shock could trigger a cold 10 solar mass cloud at a distance of 5 pc within a range of 18 kyrs to collapse. Using 54 Cr=52 Cr (both are stable isotopes) measurements in meteorites, a heterogeneous distribution of these meteorites suggests a late supernova injection event. This also seems to be confirmed by O-isotopic distribution in planetary materials and other presolar oxide and silicate grains from supernovae (Qin et al. 2011).

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Supernovae and Earth’s Atmosphere

In this section we describe the influence of nearby supernova explosions on the Earth’s atmosphere and also mass extinction events that happened during the Earth’s history.

5.1

The Earth’s Atmosphere

The Earth is protected by its atmosphere against short wavelength radiation mainly arriving from the Sun. The atmosphere absorbs radiation at different wavelengths at different heights. From the surface, we can only observe in the visible and near IR-wavelengths as well as in the radio window (several cm to about 20 m). The total mass of the Earth’s atmosphere is about 5:151018 kg. Three quarters of that mass is found within the first 11 km. Air pressure and density decrease with height whereas the temperature might well decrease as well as increase depending on the absorption of short wavelength radiation. The principal layers are:Earth’s atmosphere • • • • •

Troposphere (0–12 km) Stratosphere (12–50 km) Mesosphere (50–80 km) Thermosphere (80–700 km) Exosphere (700–10,000 km)

The main constituents are listed in Table 3. In this table water vapor is not included in a dry atmosphere. In the lower atmosphere the content of water vapor is between 10 and 50,000 ppmv (0.001 %– 5 %). Compared with the full atmosphere, the mass of water vapor is about 0.25 %. The ozone layer is part of the stratosphere. Here, the ozone concentrations are 2–8 ppmv; the main concentration occurs at heights ranging from 15 to 35 km. About 90 % of the ozone in Earth’s atmosphere is contained in the stratosphere. The ionosphere is a region that is ionized mainly by solar radiation. Here, aurorae also occur. The ionization strongly depends on a day/night rhythm. During daytime it stretches from 50 to 1000 km and includes the mesosphere, thermosphere, and parts of the exosphere. During nighttime, ionization in the mesosphere no longer occurs.

Table 3 Main constituents of the Earth’s atmosphere. ppmv denotes parts per million per volume

Name Nitrogen Oxygen Argon Carbon dioxide

Formula N2 O2 Ar CO2

ppmv 780;840 209;460 9;340 397

% 78:084 20:946 0:9340 0:0397

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Fig. 2 Earth’s atmosphere. Penetration of various shortwavelength radiation (Credit: NASA)

In the homosphere the gases are well mixed; in the heterosphere they become separated in the sense that heavier gases are found at deeper layers. The homosphere ends at about 100 km. The penetration of various components of short wavelength radiation from the Sun is shown in Fig. 2.

5.2

Evolution of the Earth’s Atmosphere

At the time of the formation of the planets the first atmosphere of Earth and other planets would have consisted mainly of gases in the solar nebula. These gases were mainly hydrogen, water vapor, methane, and ammonia. Then the solar nebula dissipated; the gases would have escaped, driven also by the solar wind. However, this escape strongly depended on the gravity of the planet. Then on Earth a second atmosphere was formed. This formation was mainly due to volcanism and due to gases produced by the late heavy bombardment. This atmosphere mainly consisted of nitrogen, carbon dioxide, and inert gases. Also the influence of life has to be taken into account. Early lifeforms on Earth date back as early as 3.5 billion years ago. Free oxygen did not exist in the atmosphere until about 2.4 billion years ago. This can be measured by the end of banded iron formations. Before this time,

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any oxygen produced by photosynthesis was consumed by oxidation of reduced materials, mostly by iron. The evolution of the atmosphere of the terrestrial planets is reviewed by Baines et al. (2013).

5.3

Supernova Explosions and Earth Atmosphere

Supernovae that explode near Earth produce • Intense cosmic ray shower • Gamma rays Both effects can substantially deplete the Earth’s ozone shield. This was first studied by Ruderman (1974). Incident ionizing radiation produces large quantities of nitrogen oxide, NOx , in the stratosphere. This NOx catalytically converts the ozone to molecular oxygen: NO C O3 ! NO2 C O2

(34)

NO2 C O ! NO C O2

(35)

In Whitten et al. (1976) the influence of a supernova shock on the Earth’s stratospheric ozone content was estimated. The energy content of a gamma ray pulse was assumed to be 1047 –1048 erg; the energy deposited at an altitude between 25 and 35 km was calculated as a dynamic response to a pulse in the form of a square wave duration equal to the optical event of a supernova explosion (100 days). If the supernova occurs at 10 pc distance the peak ozone-column reduction could be 35 %–65 %. The stratospheric residence time of NOx is about 3 yr; the time for the atmosphere to recover to 95 % of normal would be about 10 yr. It can also be estimated how long it would take for a supernova outburst to occur within a volume V0 D .4 =3/r03

(36)

of the galaxy. VGal is the galactic average time between supernovae in a total volume VGal . Then the waiting time TW becomes: TW D TGal VGal =V0

(37)

Within 8 kpc of the galactic center the supernova remnants are found in a disk of thickness 120 pc; from 8 to 14 kpc the thickness becomes approximately twice as large and the total volume density is about 1/4 as great as in the inner regions. It was estimated that TGal  50 yr.

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Thus far we have treated only the supernova explosion event and not considered what the influence from the supernova remnants would be Superonva remnants. An extended ozone depletion can be estimated from the lifetime of supernova remnants; the time is about 104 yr. • At the location of the solar system: Waiting times for extended ozone depletions of 20 %–50 % are between 2  109 yr and 2  1010 yr and therefore in Whitten et al. (1976) the authors conclude that the probability that such an event occurred closer than 10 pc is 1 to 5/5. • The waiting time decreases by a factor of 10 for a planet closer to the galactic center. The conclusion is that such an ozone-depleting effect is significant and long lasting and may strongly affect biology on planets, however, at the distance of the solar system from the galactic center, such an event is not very likely to happen. In the paper of Gehrels et al. (2003) a similar result was obtained. They assume that an increase of the UV flux by a factor of 2 would be a threshold for significant biological effects. Such an increase of the UV flux would correspond to an ozone depletion of 47 %. Input spectrum data from the SN 1987A were used. They concluded that the critical distance of a supernova must be approximately 8 pc to produce a combined ozone depletion from both gamma rays and cosmic rays of 47 % which would double the globally averaged biologically active UV reaching the Earth’s surface. The rate of core-collapse supernovae occurring within 8 pc is 1.5 per Gyr. The timescale for multicellular life on Earth is about 0.5 Gyr, therefore the extinction mechanism by supernovae appears to be less important.

5.4

Cosmic Rays and Cloud Formation

The flux of cosmic rays arriving at the Earth’s upper atmosphere is modulated by solar activity (strength of the heliosphere, emission of energetic solar particles) and by the strength of the geomagnetic field. The solar wind modulates the cosmic ray flux and therefore also ionization in the Earth’s upper troposphere. The complex and interdisciplinary approach to that topic is summarized in Scherer et al. (2006). Whether there exists any relation between cosmic rays and Earth’s climate constitutes the crucial question. In the first of their papers Svensmark and Friis-Christensen (1997) claimed a correlation between cosmic ray intensity and global cloud coverage by combining a neutron monitor and satellite data. They found a variation of the total cloud cover of about 3 %–4 % during a solar cycle. The variation was higher at higher latitudes which they explained as a consequence of the stronger geomagnetic field there. Other authors favor a stronger influence of solar irradiance variations on the Earth’s climate than by cosmic ray forcing. Whereas the relation between a direct variation of the Earth’s climate with solar activity is not really firmly established, variations on a longer timescale seem to be important. For example, temperature variations of

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the Earth over the last 500 million years show a quasi-period of 135 million years and could be related to spiral arm crossings of the solar system that modulated the cosmic ray particle flux (Shaviv 2002).

5.5

Nearby Supernova Explosions in the Past

In the work of Benítez et al. (2002) it is shown that the Scorpius-Centaurus OB association, a group of young stars currently located at 130 pc from the Sun, has generated 20 SN explosions during the last 11 Myr, some of them probably as close as 40 pc to Earth. The deposition on Earth of 60 Fe isotopes produced by these explosions can explain the recent measurements of an excess of this isotope in deep ocean crust samples. The marine ecosystem could have been affected by a nearby supernova that exploded about 2 Myr ago. An increase in the UV-B flux could provoke a significant reduction in the phytoplankton abundance and biomass. Such a decline of ocean surface phytoplankton productivity without evidence of other causes such as volcanism, impacts, or strong climate variations might be a strong hint of the biological impact of a nearby supernova explosion. About two million years ago there was the so-called Pleistocene-Pliocene extinction.

6

Conclusions

It was shown that nearby supernova explosions that certainly happened during the evolution of the solar system lead to several effects in the solar system: • The outer parts of the solar system (objects in the Oort cloud) become dynamically unstable because of heating effects; cometary showers may then penetrate to the inner solar system and the risk of collision of such comets with planets strongly increases. • Supernova explosions might trigger the collapse of an interstellar gas cloud and therefore enable the formation of the solar system. • Supernova explosions within less than 10 pc strongly influence the ozone concentration in the Earth’s atmosphere and it takes several decades before the initial concentration becomes re-established. Also taking into account the radiative influence of supernova remnants (with a timescale of several 103 yr) this influence becomes even more dramatic. • Nearby supernova explosions might also influence the Earth’s climate because cloud formation might be influenced by enhanced cosmic ray particle flux. • During the last 500 million years at least five big mass extinctions have occurred on Earth and at least some of them could be attributed to a nearby supernova explosion. Supernova explosions have to be considered for the detected exoplanetary systems and the search for life in such systems. Inasmuch as the star density

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increases toward the galactic center, the probability of supernova explosions also increases and therefore the galactic habitable zone is always at a certain distance from the galactic center.

References Baines KH, Atreya SK, Bullock MA, Grinspoon DH, Mahaffy P, Russell CT, Schubert G, Zahnle K (2013) The atmospheres of the terrestrial planets: clues to the origins and early evolution of Venus, Earth, and Mars, pp 137–160 Benítez N, Maíz-Apellániz J, Canelles M (2002) Evidence for nearby supernova explosions. Phys Rev Lett 88(8):081101 Frisch PC (1995) Characteristics of nearby interstellar matter. Space Sci Rev 72:499–592 Gehrels N, Laird CM, Jackman CH, Cannizzo JK, Mattson BJ, Chen W (2003) Ozone depletion from nearby supernovae. Astrophys J 585:1169–1176 Gritschneder M, Lin DNC, Murray SD, Yin Q-Z, Gong M-N (2012) The supernova triggered formation and enrichment of our solar system. Astrophys J 745:22 Hanslmeier A (2009) Habitability and cosmic catastrophes Ipavich FM, Galvin AB, Lasley SE, Paquette JA, Hefti S, Reiche K-U, Coplan MA, Gloeckler G, Bochsler P, Hovestadt D, Grünwaldt H, Hilchenbach M, Gliem F, Axford WI, Balsiger H, Bürgi A, Geiss J, Hsieh KC, Kallenbach R, Klecker B, Lee MA, Managadze GG, Marsch E, Möbius E, Neugebauer M, Scholer M, Verigin MI, Wilken B, Wurz P (1998) Solar wind measurements with SOHO: the CELIAS/MTOF proton monitor. J Geophys Res 103: 17205–17214 Opher M, Drake JF, Zieger B, Gombosi TI (2015) Magnetized jets driven by the sun: the structure of the heliosphere revisited. Astrophys J 800:L28. doi:10.1088/2041-8205/800/2/L28 Phillips JL, Bame SJ, Barnes A, Barraclough BL, Feldman WC, Goldstein BE, Gosling JT, Hoogeveen GW, McComas DJ, Neugebauer M, Suess ST (1995) Ulysses solar wind plasma observations from pole to pole. Geophys Res Lett 22:3301–3304 Qin L, Nittler LR, Alexander CMO’, Wang J, Stadermann FJ, Carlson RW (2011) Extreme 54 Crrich nano-oxides in the CI chondrite Orgueil – implication for a late supernova injection into the solar system. Geochimica et Cosmochimica Acta 75:629–644 Ruderman MA (1974) Possible consequences of nearby supernova explosions for atmospheric ozone and terrestrial life. Science 184:1079–1081 Scherer K, Fichtner H, Borrmann T, Beer J, Desorgher L, Flükiger E, Fahr H-J, Ferreira SES, Langner UW, Potgieter MS, Heber B, Masarik J, Shaviv N, Veizer J (2006) Interstellarterrestrial relations: variable cosmic environments, the dynamic heliosphere, and their imprints on terrestrial archives and climate. Space Sci Rev 127:327–465 Shaviv NJ (2002) Cosmic ray diffusion from the galactic spiral arms, iron meteorites, and a possible climatic connection. Phys Rev Lett 89(5):051102 Stern SA, Shull JM (1988) The influence of supernovae and passing stars on comets in the Oort cloud. Nature 332:407–411 Svensmark H, Friis-Christensen E (1997) Variation of cosmic ray flux and global cloud coverage-a missing link in solar-climate relationships. J Atmos Solar-Terr Phys 59:1225–1232 Weissman P (2000) Oort Cloud, p 2183. Nov 2000 Whitten RC, Borucki WJ, Wolfe JH, Cuzzi J (1976) Effect of nearby supernova explosions on atmospheric ozone. Nature 263:398–400

The Moon as a Recorder of Nearby Supernovae

99

Ian A. Crawford

Abstract

The lunar geological record is expected to contain a rich record of the Solar System’s galactic environment, including records of nearby (i.e., a few tens of parsecs) supernova explosions. This record will be composed of two principal components: (i) cosmogenic nuclei produced within, as well as radiation damage to, surface materials caused by increases in the galactic cosmic ray flux resulting from nearby supernovae and (ii) the direct collection of supernova ejecta, likely enriched in a range of unusual and diagnostic isotopes, on the lunar surface. Both aspects of this potentially very valuable astrophysical archive will be best preserved in currently buried, but nevertheless near-surface, layers that were directly exposed to the space environment at known times in the past and for known durations. Suitable geological formations certainly exist on the Moon, but accessing them will require a greatly expanded program of lunar exploration.

Contents 1 2 3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Galactic Environment of the Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Possible Supernova Records on the Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Detecting an Enhanced GCR Flux from Nearby Supernovae . . . . . . . . . . . . . . . 3.2 Supernova Ejecta on the Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Accessing the Lunar Record . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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I.A. Crawford () Department of Earth and Planetary Sciences, Birkbeck College, University of London, London, UK e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_115

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Introduction

In contrast to the geologically active surface of the Earth, which has been protected by a dense atmosphere and strong magnetic field throughout Solar System history, the surface of the Moon has been exposed directly to the space environment since the Earth-Moon system formed approximately 4.5 billion years ago. During this time the Solar System has orbited the Galaxy approximately 20 times and will have experienced a wide range of galactic environments, including passages through spiral arms and star-forming regions where the rate of supernova (SN) explosions will have been enhanced. This raises the possibility that such events have been recorded in the lunar geological record and especially in the surface regolith which is, or has been, exposed directly to space. Such a record could take several forms, including radiation damage to near-surface materials exposed to an enhanced flux of relativistic subatomic particles (i.e., cosmic rays), the production of cosmogenic nuclei when such particles interact with target nuclei in near-surface materials, and, for nearby events, the possibility of direct collection of SN ejecta, likely bearing unique isotopic signatures, on the lunar surface. As argued below, the geological evolution of the Moon, having been relatively inactive for billions of years, but just active enough to occasionally cover, and thereby protect, surficial deposits bearing evidence of the outer space environment, makes the lunar geological record an ideal recorder of such events throughout Solar System history.

2

The Galactic Environment of the Solar System

The Solar System has orbited the center of the Milky Way Galaxy approximately 20 times since the Sun formed 4.6 billion years ago (e.g., Gies and Helsel 2005; Overholt et al. 2009). During this time the Solar System will therefore have been exposed to a wide range of galactic environments, including passing through spiral arms where an enhanced probability of passing close to SN explosions, and associated supernova remnants, would be expected. In searching for a record of such events in the Solar System, it is actually the Sun’s motion with respect to the Galaxy’s spiral arm structure that is important. There is considerable uncertainty regarding the angular velocity of the Sun with respect to the more slowly rotating pattern of spiral arms, with values between 0 and 13:5 km s1 kpc1 appearing in the literature; see Shaviv (2003) for a summary of the earlier literature and Overholt et al. (2009) for a more recent discussion. The current consensus appears to be that the value lies probably somewhere between 6 and 13:5 km s1 kpc1 (Overholt et al. 2009), which correspond to orbital periods relative to the spiral pattern of approximately 1 Gyr and 450 Myr, respectively. These values imply that the Solar System will have traversed the entire spiral pattern of the Galaxy, which appears to consist of four main spiral arms and a number of inter-arm “spurs” (Fig. 1; Churchwell et al. 2009), between five and ten times in the course of its history. Whenever the Sun passes through a spiral arm, several observable consequences may be expected. Of most relevance to this chapter is an enhanced flux of galactic

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Fig. 1 A recent reconstruction of the structure of the Milky Way Galaxy (Churchwell et al. 2009). Galactic longitudes, major spiral features, and the present location of the Sun are indicated. Since the Solar System formed, it will have passed through the entire spiral pattern between five and ten times (depending on the assumed angular velocities of the Sun and the Galaxy’s spiral pattern; see text) and will therefore have experienced a wide range of different galactic environments. Evidence for this cosmic odyssey may be preserved in the lunar geological record (Image credit: NASA/JPLCaltech/R. Hurt/Wikipedia Commons)

cosmic rays (GCRs) resulting from the fact that massive stars, which comprise the progenitors of type II supernovae, are largely confined to the spiral arms and that supernova remnants are major sources of cosmic rays (e.g., Ackermann et al. 2013). Shaviv (2003) has attempted to model this effect and finds that the GCR flux during spiral arm passages may be enhanced by factors of between two and five compared to inter-arm regions. In addition to records of nearby supernovae, spiral arm passages may also be expected to result in compression of the heliosphere owing to a denser interstellar medium (which would also result in an increased GCR flux), increased accretion of interstellar dust particles onto planetary surfaces, and perhaps an enhanced cometary impact rate on the terrestrial planets (e.g., Shaviv 2006; see also discussion by Crawford et al. 2010 and references cited therein). There have been multiple attempts (e.g., Filipovic et al. 2013; Shaviv 2003; see also the summary by Overholt et al. 2009) to use the Earth’s geological record, and especially the alleged periodicity of mass extinction events and/or ice ages, to constrain models of galactic structure. Overholt et al. (2009) have shown that to date

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no such correlations with galactic structure have been convincingly demonstrated and, given all the uncertainties in interpreting the Earth’s complex geological and biological history, this is hardly surprising. However it is important to realize that much better records of spiral arm passages probably exist elsewhere in the Solar System. Indeed, all the effects of spiral arm passages noted above have the potential to leave records in the near-surface environments of geologically inactive and airless bodies such as asteroids and the Moon. Uncovering them is a major potential astrophysical benefit of continued Solar System exploration (e.g., Crawford and Joy 2014; Spudis 1996). Although using Solar System records to infer how the Sun’s galactic environment has changed over one or more revolutions of the Galaxy will be a challenging project for future research, we do at least have reliable information on the present galactic environment of the Sun. It has been known for several decades that the Sun is currently passing through a hot (T  106 K), mostly ionized, low-density (nH  0:005 cm3 / region of the interstellar medium of the order of 150 pc in size that has become known as the Local Bubble (e.g., Frisch et al. 2011; Galeazzi et al. 2014). The origin of the Local Bubble has been a subject of debate ever since its discovery, but there is now a consensus that multiple (>10) supernova events arising within the nearby Sco-Cen OB Association during the last 10–15 Myr were largely responsible (Breitschwerdt et al. 2009, 2016; Maíz-Apellániz 2001). The Sun’s velocity of  20 kms1 .20 pc Myr1 / relative to the local standard of rest implies that the Solar System will have resided within the Local Bubble for several (probably 3) million years and may therefore have experienced an enhanced GCR flux during this time.

3

Possible Supernova Records on the Moon

Studies of Apollo samples have revealed that the lunar regolith (Fig. 2) is efficient at collecting and retaining materials that impinge upon it from space. Specifically, in addition to meteoritic debris, which is primarily of interest to planetary scientists studying the evolution of the Solar System (e.g. Joy et al. 2012), the regolith also contains a physical record of a range of important astrophysical processes. These include the flux and composition of the solar wind, as well as cosmogenic nuclides and tracks of radiation damage produced by high-energy GCRs (e.g., Crozaz et al. 1977; Lucey et al. 2006; McKay et al. 1991). The GCR records are of particular relevance for SN studies because, as discussed above, nearby supernovae will result in a temporal enhancement in the cosmic ray flux which may therefore be recorded in the lunar geological record. In addition, if a SN explosion were to occur within a few tens of parsecs of the Solar System (e.g., those thought to be responsible for creating the Local Bubble), there is the additional possibility that supernova ejecta might be directly implanted onto the lunar surface (e.g., Benítez et al. 2002; Fry et al. 2015). These two broad classes of possible SN records on the Moon are discussed below.

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Fig. 2 Close-up of the lunar regolith with astronaut’s boot for scale. The uppermost meter or so of the regolith is an efficient recorder of materials and influences impinging on it from space, including meteoritic debris, solar wind particles, cosmogenic nuclides produced by GCRs, and possibly ejecta from nearby supernova explosions. See text for discussion (NASA image AS1140-5880)

3.1

Detecting an Enhanced GCR Flux from Nearby Supernovae

When GCRs interact with atoms in geological materials, a variety of cosmogenic nuclei are produced as a result of spallation and neutron capture reactions (e.g., Eugster et al. 2006; Wieler et al. 2013). Typical cosmogenic nuclei include the stable isotopes, 3 He, 21 Ne, 38 Ar, 83 Kr, and 126 Xe, and the unstable isotopes, 10 Be;36 Cl, and 39 Ar, and it is by measuring the concentrations of these and other cosmogenic isotopes, under the assumption of a constant (or at least known) background GCR flux, that cosmic ray exposure (CRE) ages are commonly derived for lunar and planetary materials (Eugster 2003; Wieler et al. 2013). In reality, however, for the reasons discussed in Sect. 2, the GCR flux must vary with the changing galactic environment of the Solar System. In this context, it is interesting to note that studies of iron meteorites (Lavielle et al. 1999; Marti et al. 2004) have indicated possible variations in the GCR flux based on discrepancies between CRE ages obtained from the concentrations of stable cosmogenic nuclei and radioactive nuclides having different half-lives (e.g., 36 Cl=36 Ar, 39 Ar=38 Ar, 10 Be=21 Ne). For example, Marti et al. (2004) inferred that the primary GCR flux over the last 10 Myr may have been almost 40 % higher than the average of the period 150–700 Myr ago. The GCR flux over the latter period will have been

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averaged over a significant fraction of the galactic disk, and an enhancement within the last 10 Myr could be consistent with the Sun’s encounter with the local Orion Spur (Fig. 1) and, more particularly, the Local Bubble. More recently, however, Wieler et al. (2013) have reanalyzed the meteoritic data and have not been able to confirm the evidence for an enhanced GCR flux within this time period. As stressed by Wieler et al. (2013), the usefulness of meteorites in attempting to identify variations in the flux of GCRs is constrained, as it is for all extraterrestrial samples studied to date, by the fact that they can only record an integrated GCR flux since they became exposed to the space environment. For this reason, Wieler et al. combined their meteoritic analyses with those of terrestrial sedimentary samples for which independent exposure histories are available. As they explained: “because of the limited sensitivity of the time-integrated GCR signals provided by meteorites, it is wise to consider . . . also the differential GCR flux signals provided by terrestrial sediment samples” (Wieler et al. 2013). This is potentially a much more powerful approach, but it relies on a terrestrial sedimentary record of cosmogenic isotopes within only the last few million years (for which ice and/or ocean sediment cores preserve an independent control of the age and depositional environment). Owing to the complexity of Earth’s geological and erosional history, and the fact that Earth’s atmosphere and magnetic field act to attenuate the primary GCR flux, it seems unlikely that reliance on terrestrial records alone, or a combination of terrestrial and meteoritic records, will be sufficient to measure variations in the GCR flux over the hundreds of millions of years required to reconstruct the past galactic environment of the Solar System. It is in this context that the lunar geological record has the potential to help, mainly by providing GCR records from independently dated materials with known exposure histories spanning most of Solar System history. It is true that the lunar samples currently available for study (principally obtained by the Apollo and Luna missions of forty years ago, supplemented more recently by lunar meteorites) suffer from essentially the same problems as the meteoritic samples owing to their poorly constrained exposure histories. Indeed, the fact that the present surficial regolith (Fig. 2), from which the samples were collected, has been subject to comminution and overturning (“gardening”) by meteorite impacts for the last 3–4 Gyr, with the result that any given sample has a poorly constrained history of burial and exhumation (and thus an unknown time-variable shielding from GCRs), greatly complicates retrieval and interpretation of the GCR record (e.g., Levine et al. 2007; Lorenzetti et al. 2005). However, the Moon’s near-surface environment hosts geological formations that are far better suited to the preservation of GCRs, and indeed other evidence for the Solar System’s galactic environment, than the surficial regolith sampled by previous space missions. From the point of view of obtaining ancient records of the Solar System’s cosmic environment, what is required is access to materials that have been exposed to the space environment at known times and for known durations throughout Solar System history. Unlike the geologically inert asteroids, from which meteorites are mostly derived, the Moon has hosted a range of geological processes which can provide just such a temporally calibrated record by covering over, and

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thereby preserving, previously exposed surfaces. A key concept in this respect is that of a paleoregolith – a term coined, by analogy with paleosols in terrestrial geology, for a once surficial regolith layer that has been buried by later processes (e.g., lava flows, pyroclastic deposits, or impact crater ejecta; see, e.g., Crawford et al. 2007, 2010; McKay 2009; Spudis 1996). Such paleoregoliths will preserve a record of everything that impinged upon them, including GCRs and other aspects of the space environment, dating from their time on the surface. If the strata underlying and overlying the paleoregolith layer can be independently dated, then the record retained in the paleoregolith can be assigned a precise age and duration. In essence, this extends the argument made by Wieler (2013) for the use of the terrestrial sedimentary record in interpreting variations in GCR flux to a lunar “sedimentary” record of greatly improved fidelity and vastly longer duration. Figure 3 illustrates the basic concept in terms of paleoregolith layers trapped between lava flows. For reasons discussed by Crawford et al. (2007, 2010), such

Fig. 3 Schematic representation of the formation of a paleoregolith layer (Crawford and Joy 2014; Crawford et al. 2007): (1) a new lava flow is emplaced, and meteorite impacts begin to develop a surficial regolith; (2) solar wind particles, galactic cosmic ray particles, and “exotic” material (possibly including supernova ejecta) are implanted; (3) the regolith layer, with its embedded historical record, is buried by a more recent lava flow, forming a paleoregolith; (4) the process begins again on the upper surface (Image credit: Royal Astronomical Society/K.H. Joy)

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situations will have been common on the Moon throughout the entire duration of active lunar volcanism, believed on the basis of sample studies and crater counting to have occupied at least the period 4.3 to  1:2 Gyr ago (e.g., Hiesinger et al. 2011; Joy and Arai 2013). Moreover, recent high-resolution images of the lunar surface have provided evidence for very young ( 0:1) need the combination of large field of view and deep exposures,

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which required the use of mosaic cameras at 4 m telescopes. Examples of searches at intermediate redshifts (0:03 < z < 0:3) are the Sloan Digital Sky Survey SN search (Frieman et al. 2008) and the deep part of the CSP (Freedman et al. 2009). Distant searches (z > 0:3) were pioneered by a Danish team using a 1.5 m telescope (Hansen et al. 1987; Nørgaard-Nielsen et al. 1989) and the Berkeley SN Cosmology Project (Perlmutter et al. 1995, 1997). Other searches include the High-Z SN Search Team (Schmidt et al. 1998), the Supernova Legacy Survey (SNLS, Astier et al. 2006), and ESSENCE (Miknaitis et al. 2007; Wood-Vasey et al. 2007). The highest redshift searches used HST (Dawson et al. 2009; Riess et al. 2004, 2007). A detailed discussion of these distant searches can be found in the  Chap. 105, “Discovery of Cosmic Acceleration”. It is remarkable how the sample of SNe has grown through the observational revolution. The early searches collectively would provide about a dozen objects per year. Today’s robotic searches find several hundred supernovae each year. The searches are generally set up to find any transients and then separate them into different classes for the follow-up. This also means that there has been a proliferation of new supernova classes. The future will see thousands of transient objects discovered every night, and the selection for follow-up observations will become a critical component of future SN studies.

4

Type Ia Supernovae

The observed photometric and spectroscopic uniformity of type Ia supernovae raised hopes that they represent a singular explosion process and hence provide a “standard candle” for distance measurements. The early studies were from before the class of SN Ib/c was separated. The most direct demonstration that SNe Ia reach a uniform maximum luminosity is the Hubble diagram (observed peak magnitude vs. recession velocity or redshift). Early versions can be found in Zwicky (1965), Kowal (1968), Barbon et al. (1975), Branch and Bettis (1978), Tammann (1978), Sandage and Tammann (1982), Branch (1982), and Tammann and Leibundgut (1990). This requires light curves covering the maximum phase and a spectrum or sufficient temporal coverage of the light curve to classify the supernova. A small scatter in the Hubble diagram around the line of linear expansion in the local universe implies that the objects reach the same maximum luminosity, but does not provide a value of the luminosity itself. A free fit to the slope of the line, which is given through the definition of magnitudes and the distance modulus, i.e., m D 5 log.v/ C 25 C M  5 log.H0 / with recession velocity v in km s1 and the Hubble constant H0 in km s1 Mpc1 , gives an indication whether the distance indicator has a uniform luminosity or demonstrates deviation from a linear expansion field. Corrections for absorption (in the Milky Way and the host galaxy) need to be applied. During the early times, no distinction between SNe Ia and Ib/c was made and some contamination by core-collapse supernovae (SNe Ib/c) was present. The first papers noted different slopes for samples of SNe I in elliptical

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galaxies from the one in spirals, which was attributed to selection effects due to internal absorption in spiral host galaxies. In particular, the SNe in spiral galaxies seemed to indicate a deviation from the linear expansion rate, i.e., a slope different from 5, as given in the equation above. The scatter around the Hubble line was about 0.5 magnitudes, which was considered excellent given that distances based on galaxy properties typically showed much larger scatter. The mood at that time was optimistic enough that predictions for the potential measurement of the deceleration parameter were ventured (Tammann 1979). An important additional argument that SNe Ia might reach the same peak luminosity was provided by their observed uniformity in light curves and spectral evolutions. The uniform light curves displayed by type I supernovae were first pointed out by Barbon et al. (1973, 1974) and Doggett and Branch (1985) and extensively investigated by the group of Gustav Andreas Tammann in Basel (Tammann 1978; Cadonau et al. 1985; Cadonau and Leibundgut 1990; Leibundgut et al. 1991). A comprehensive review of the supernova research done in Basel can be found in Sandage (1998). The optical light curves of SNe Ia are not completely uniform and subdivision into different light curve shapes was attempted. The separation into “fast” and “slow” light curves (Barbon et al. 1975, 1973) became obsolete, when it was realized that several of the “slow” supernovae were actually SNe Ib/c. Early claims to a continuous shape distribution of optical light curves were based on inadequate data (Pskovskii 1967, 1984) and could not be substantiated for some time. Another camp continued to advocate a unique light curve shape and tried to establish a template light curve (Leibundgut 1989). It was only the extreme objects SN 1986G (Frogel et al. 1987; Phillips et al. 1987), SN 1991T (Filippenko et al. 1992a; Phillips et al. 1992), and SN 1991bg (Filippenko et al. 1992b; Leibundgut et al. 1993) that led Mark Phillips to establish a correlation between optical light curve shape and the peak luminosity (Phillips 1993). Several methods for the normalization of SN Ia light curves have been developed over the past 20 years (m15 : Hamuy et al. 1996b; Phillips et al. 1999; MLCS: Jha et al. 2007; Riess et al. 1996; SALT: Guy et al. 2005, 2007). They result in a critical improvement of the distance determinations by SNe Ia and a reduction of the scatter in the Hubble diagrams to less than about 0.2 magnitudes. This ultimately enabled the discovery of the accelerated expansion of the universe. Near-infrared light curves of SNe Ia display a remarkable uniformity around maximum light. The earliest studies (Elias et al. 1981, 1985) demonstrated that the JHK light curves of type I supernovae were nearly identical with the exception of a few objects, which were suggested to be part of a different subclass and then later identified as SNe Ib/c (Elias et al. 1985). Meikle (2000), Krisciunas et al. (2000), Contreras et al. (2010), Stritzinger et al. (2011), and Dhawan et al. (2015) have described the uniformity of infrared light curves in detail. The construction of infrared Hubble diagrams has become possible through the development of infrared detector arrays (Meikle 2000; Krisciunas et al. 2004; Nobili et al. 2005; Freedman et al. 2009). There is very little data available outside the optical/near-infrared wavelengths for SNe Ia (e.g. Leibundgut 2000).

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The spectral evolution of SNe Ia is also very homogeneous. Early spectroscopy (Minkowski 1964) indicated uniform explosions, which was confirmed with more objects (Oke and Searle 1974). Hoyle and Fowler (1960) were the first to propose a degenerate star, i.e., white dwarf, as the SN Ia progenitor and Colgate and McKee (1969) identified the radioactive 56 Ni decay chain as the energy source for the optical display. The Chandrasekhar mass white dwarf explosion appeared ideal for the “standard bomb” that was indicated by the observations in terms of luminosity and the lack of hydrogen lines in the spectrum. The neatness of the “natural” mass limit provided by the Chandrasekhar mass was later used as an argument, why SN Ia should be good standard candles resulting in a circular argument. This has changed again and a dispersion of ejecta masses is advocated (Stritzinger et al. 2006; Scalzo et al. 2014). An independent calibration of the absolute peak luminosity is required to determine the Hubble constant from SNe Ia. This can be established through a distance ladder approach, where distances to nearby SNe Ia are measured by other means, mostly Cepheid stars (e.g. Freedman et al. 2001; Sandage et al. 2006; Riess et al. 2011), or through models (Branch 1982; Arnett et al. 1985; Leibundgut and Pinto 1992; Stritzinger and Leibundgut 2005). Type Ia supernovae are the “cosmological” step of the distance ladder and have replaced all other distance indicators beyond the Virgo Cluster. The direct determination of the luminosity from models is based on the assumption that the optical (or bolometric) light curve can be matched to the energy generation by the radioactive decays. There are several parameters which play an important role in this assumption, and the diversity of SNe Ia has so far precluded an accurate measurement of the Hubble constant through this route. The determination of the local expansion rate is essential to compare to the cosmological expansion rate as derived from other methods, e.g., SunyaevZeldovich effect and cosmic microwave background. The measurement of other cosmological parameters, in particular the accelerated expansion, does not depend on absolute distances, but is determined through relative distances.

5

Type II Supernovae

The luminosity evolution of type II supernovae is not uniform. Several different light curve shapes are observed and they are related to the different radiation hydrodynamics in the explosion. While it was clear from the beginning that type II supernovae display some diversity, several attempts to use them as luminosity distance indicators were made (e.g. Barbon et al. 1979).

5.1

Expanding Photosphere Method (EPM)

It appears that Leonard Searle was the initiator of a method, originally proposed by Walter Baade (1926) and modified by Adriaan Wesselink (1946) for pulsating stars, to determine the distances of supernovae based on their expansion history.

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This was attempted for type I supernovae by Branch and Patchett (1973) and type II supernovae by Kirshner and Kwan (1974). The physical size of an object in free expansion is approximated by the radial velocity. At the same time, the angular size of the photosphere can be determined by the color temperature of the black body radiation and the observed brightness of the object. This implies spherical symmetry of the explosion and that the absorption lines providing the radial velocity are formed at, or at least near, the photosphere. By observing an expanding object at several epochs, the explosion date and the distance can be inferred. A relatively sharp photosphere is required, which means that the atmosphere has to be close to thermal equilibrium and can be represented by a black body. Since the underlying assumption of thermal emission from an optically thick, expanding photosphere does not hold for thermonuclear explosions, the “modified BaadeWesselink” method cannot be applied reliably. The explosions do not form a sharp photosphere because the opacity in SNe Ia is dominated by atomic transitions and the association of the expansion velocity, as measured from the blueshift of spectral lines, and the size of the explosion is highly uncertain (e.g. Pinto and Eastman 2000). Explosions within a massive envelope are more suitable and detailed modeling of the spectra has shown that fairly accurate distances can be achieved. Deriving distances to type II supernovae was regarded as very promising to determine the Hubble constant H0 and even the deceleration parameter q0 during the early years (Wagoner 1977, 1979). Line opacities influence the radiation and lead to deviations from a pure black body radiation (Wagoner 1981). Dilution factors must be applied to use the expanding photosphere method (Eastman et al. 1996). SN 1987A provided a unique test case where ample data of a supernova at a known distance could be used to refine the spectral models (Branch 1987; Chilukuri and Wagoner 1988; Höflich 1988; Eastman and Kirshner 1989; Jeffery and Branch 1990; Schmutz et al. 1990; see the review by McCray 1993). Two students of Bob Kirshner started work on the expanding photosphere method in the early 1990s: Brian Schmidt collected the observational data and Ron Eastman improved the photospheric models, i.e., worked on the dilution factor. They determined EPM distances to several type II supernovae and produced a Hubble diagram (Schmidt et al. 1992, 1994a, b; Eastman et al. 1996). Another important PhD project was by Mario Hamuy who finished work on EPM in 2001 exploring the limitations as exemplified by the distance to the well-observed SN 1999em (Hamuy et al. 2001). SN 1999em became a critical test case for EPM (Hamuy et al. 2001; Leonard et al. 2002; Elmhamdi et al. 2003). An independently determined Cepheid distance (Leonard et al. 2003) provides a check of the distance accuracy, and it became apparent that previous EPM implementations underestimated the distance by about 30 %. Improved spectroscopic models yielded new black body dilution factors to determine a distance in accordance with the Cepheids (Dessart and Hillier 2005, 2006). A variant of EPM is the spectral-fitting expanding atmosphere model (SEAM; Baron et al. 2004; Dessart and Hillier 2006). In SEAM the simple dilution factor is replaced by a detailed spectral fit. While this implies a higher computational effort and also requires sufficient signal in the observed spectra,

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it delivers an independent check on how well the observed spectrum can be reproduced by the model. Jones et al. (2009) provide a discussion on the distance to SN 1999em and present the effects of choice of filters and the influence by the host galaxy absorption on the determination of the Hubble constant. A typical uncertainty of about 15 % remains in the distance measurements through EPM and SEAM. The expanding photosphere method has now been applied to a fair sample of nearby supernovae (Takáts and Vinkó 2012; Bose and Kumar 2014). Due to the required detailed spectroscopy, it is difficult to measure faint and distant objects.

5.2

Normalized Plateau Luminosity (“Standardized Candle Method”)

Mario Hamuy and Philip Pinto (2002) established an independent method, which they called “standardized candle method” (SCM), where the relation between expansion velocity and observed brightness 50 days after explosion is used to derive a normalized luminosity during the plateau phase. SCM distances are comparable, or even more accurate, than the ones determined through EPM. The relative simplicity has provided distances toward many SNe II (e.g. Poznanski et al. 2009; Olivares et al. 2010). Maguire et al. (2010) extended SCM to infrared wavelengths thereby reducing the dependency on absorption. This method was used to calibrate the distance of NGC 4258 (Polshaw et al. 2015), which has an independent geometric distance from megamasers (Humphreys et al. 2013). Nugent et al. (2006) included a reddening correction based on the observed color and velocity measurements from H’ and H“, which form typically above the photosphere, to derive cosmological distances. The difficulties are the exact determination of the epoch after explosion; the velocity determination, which is based on faint lines similar to EPM; and the uncertain reddening law in the host galaxies. SCM is not without exceptions and there is a report of at least one object deviating significantly from the expansion velocity vs. luminosity relation (SN LSQ13fn; Polshaw et al. 2016). A direct comparison of EPM and SCM has been presented for nearby supernovae (Olivares et al. 2010) demonstrating that both methods provide similar distances within the respective uncertainties. At cosmological distances, such a comparison will be a direct test of general relativity as a metric theory of gravitation (Wagoner 1977; Gall et al. 2016). Gall et al. (2016) demonstrated an extension to higher redshifts, albeit not yet at the cosmologically interesting level, for both methods for a single supernova (SN 2013eq at z D 0:04). A further extension of this method is the reduction to photometric observations only as proposed by de Jaeger et al. (2015). The method is based on a correction using the V filter slope of the plateau phase decline and a color. The latter is mostly accounting for the reddening toward the supernova. The coefficients for these parameters are optimized by reducing the scatter of a sample of SNe II in the Hubble flow in the Hubble diagram. The achieved accuracy of this method is rather more limited than EPM and SCM, but it has the advantage that it can be applied to large

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samples of photometrically well-observed supernovae, e.g., coming from LSST. It will have to be seen at what level this purely empirical method will be limited by systematic effects.

6

Other Methods

A geometric distance to SN 1987A has been derived by observing the fluorescence of its circumstellar ring. The ionization of the dense, stationary, equatorial ring material by the extreme UV flash from the SN shock breakout leads to a fluorescent display of a source whose geometry can be directly measured. The extent of the ring can be determined from the successive illumination of the ring and the light travel time. The angular size compared to the physical size yields a distance (Panagia et al. 1991; Sonneborn et al. 1997). Nearby supernovae which can be spatially resolved by very long baseline radio observations can provide a distance through the “expanding shock front method” (ESM; Bartel and Bietenholz 2003; Bartel et al. 1985, 2007). The angular size of the radio shell is compared to the radial velocity as measured from optical spectra. The deceleration of the forward shock has to be considered and can be derived from the change of the angular size as a function of time. ESM has been successfully applied to SN 1993J by mapping the expansion of the radio shell for over 9 years (Bartel et al. 2007), and the derived distance compares well to the Cepheid distance to this galaxy. Whenever new supernova types are found, new ways to apply them for distance measurements are explored. This was the case for gamma-ray bursts and more recently for super-luminous supernovae. SLSN Ic show a light curve shape vs. maximum luminosity relation similar to the one observed in SNe Ia (Inserra and Smartt 2014). Distances of about 10 %–15 % accuracy can be derived, when such a correction is applied. If such a relation holds for larger samples, then distances to redshift z > 1 could be determined and the cosmic acceleration as derived from the SNe Ia could be checked independently.

7

Conclusions

The history of supernovae as distance indicators spans a little more than five decades. During this time, the applications have evolved toward ever-increasing accuracy. The limiting uncertainties have shifted from inadequate detectors (photographic plates) to the exact definitions and implementations of the filter systems and an improved absolute calibration. The largest current systematic uncertainties stem from the unknown absorption law in other galaxies. Supernovae have assisted in several cosmological paradigm changes and have been instrumental in the discovery of the accelerated cosmic expansion. The

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application of supernovae to distance measurements has also been a driving force for a better physical understanding of the explosions and the radiation hydrodynamics.

8

Cross-References

 Characterizing Dark Energy Through Supernovae  Confirming Cosmic Acceleration in the Decade That Followed from SNe Ia at

z>1  Cosmology with Type IIP Supernovae  Discovery of Cosmic Acceleration  Historical Records of Supernovae  Historical Supernovae in the Galaxy from AD 1006  Light Curves of Type I Supernovae  Light Curves of Type II Supernovae  Low-z Type Ia Supernova Calibration  Observational and Physical Classification of Supernovae  Spectra of Supernovae During the Photospheric Phase  Superluminous Supernovae  Supernova 1604, Kepler’s Supernova, and its Remnant  Supernova of 1572, Tycho’s Supernova  The Physics of Supernova 1987A  The Hubble Constant from Supernovae  The Infrared Hubble Diagram of Type Ia Supernovae  The Peak Luminosity-Decline Rate Relationship for Type Ia Supernovae  Type Ia Supernovae Acknowledgements This research was supported by the DFG Cluster of Excellence “Origin and Structure of the Universe.” I would also like to acknowledge the support of the Deutsche Forschungsgesellschaft through the TransRegio project TRR33 “The Dark Universe.”

References Aldering G, Adam G, Antilogus P, Astier P, Bacon R, Bongard S et al (2002) Overview of the nearby supernova factory. In: Tyson JA, Wolff S (eds) Survey and other telescope technologies and discoveries. SPIE conference series, vol 4836. Society of Photo-optical Instrumentation Engineers, Bellingham, pp 61–72 Arnett WD, Branch D, Wheeler JC (1985) Hubble’s constant and exploding carbon-oxygen white dwarf models for Type I supernovae. Nature 314:337–338 Astier P, Guy J, Regnault N, Pain R, Aubourg E, Balam D et al (2006) The supernova legacy survey: measurement of M , ƒ and w from the first year data set. A&A 447:31–48 Baade W (1926) Über eine Möglichkeit, die Pulsationstheorie der • Cephei-Veränderlichen zu prüfen. Astron Nachr 228:359–362 Baade W, Zwicky F (1934) On super-novae. Publ Natl Acad Sci 20:254–259 Baltay C, Rabinowitz D, Hadjiyska E, Walker ES, Nugent P, Coppi P et al (2013) The La SillaQUEST low redshift supernova survey. PASP 125:683–694

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Barbon R, Cappaccioli M, Ciatti F (1975) Studies of supernovae. A&A 44:267–271 Barbon R, Ciatti F, Rosino L (1973) Light curves and characteristics of recent supernovae. A&A 29:57–67 Barbon R, Ciatti F, Rosino L (1974) On the light curve of type I supernovae. In: Cosmovici CB (ed) Supernovae and supernova remnants. Astrophys Sp Sci Libr 45:99–102 Barbon R, Ciatti F, Rosino L (1979) Photometric properties of type II supernovae. A&A 72: 287–292 Baron E, Nugent P, Branch D, Hauschildt P (2004) Type IIP supernovae as cosmological probes: a spectral-fitting expanding atmosphere model distance to SN 1999em. ApJ 616: L91–L94 Bartel N (1985) Supernovae as distance indicators. Lecture notes in physics, vol 224. Springer, Berlin Bartel N, Bietenholz MF (2003) SN 1979C VLBI: 22 years of almost free expansion. ApJ 591:301– 315 Bartel N, Rogers AEE, Shapiro II, Gorenstein MV, Gwinn CR, Marcaide JM, Weiler KW (1985) Hubble’s constant determined using very-long baseline interferometry of a supernova. Nature 318:25–30 Bartel N, Bietenholz MF, Rupen MP, Dwarkadas VV (2007) SN 1993J VLBI. IV. A geometric distance to m81 with the expanding shock front method. ApJ 668:924–940 Blondin S, Matheson R, Kirshner RP, Mandel KS, Berlind P, Calkins M et al (2012) The spectroscopic diversity of type Ia supernovae. AJ 143:126(33pp) Bose S, Kumar B (2014) Distance determination to eight galaxies using expanding photosphere method. ApJ 782:98(12pp) Brahe T (1573) De Nova Et Nullius Aevi Memoria A Mundi Exordio Prius Conspecta Stella. E.g. in Dreyer JLE (ed), Tychonis Brahe Dani Opera Omnia (Copenhagen: Libraria Gyldendaliana (1913–1929)) Branch D (1982) The Hubble diagram for type I supernovae. ApJ 258:35–40 Branch D (1987) Blackbody emissivity of supernova 1987A and the extragalactic distance scale. ApJ 320:L23–L25 Branch D (1998) Type Ia supernovae and the Hubble constant. ARAA 36:17–56 Branch D, Bettis C (1978) The Hubble diagram for supernovae. AJ 83:224–227 Branch D, Patchett B (1973) Type I supernovae. MNRAS 161:71–83 Branch D, Tammann GA (1992) Type Ia supernovae as standard candles. ARAA 30:359–389 Cadonau R, Tammann GA, Sandage A (1985) Type I supernovae as standard candles. In: Bartel N (ed) Supernovae as distance indicators. Lecture notes in physics, vol 224. Springer, Berlin/New York, pp 151–165 Cadonau R, Leibundgut B (1990) Supernova studies. I – a catalogue of magnitude observations of supernovae I. A&AS 82:145–178 Cappellaro E (2005) Seventy years of supernova searches. In: Turatto M, Benetti S, Zampieri L, Shea W (eds) 1604–2004: supernovae as cosmological lighthouses. ASPC, vol 342. Astronomical Society of the Pacific, San Francisco, pp 71–77 Chilukuri M, Wagoner RV (1988) Type-II supernova photospheres and the distance to supernova 1987A. In: Nomoto K (ed) Atmospheric diagnostics of stellar evolution. Lecture notes in physics, vol 305. Springer, Berlin/New York, pp 295–304 Colgate SA, McKee C (1969) Early supernova luminosity. ApJ 157:623–643 Contreras C, Hamuy M, Phillips MM, Folatelli G, Suntzeff NB, Persson SE et al (2010) The carnegie supernova project: first photometry data release of low-redshift type Ia supernovae. AJ 139:519–539 Cosmovici CB (1974) Supernovae and supernova remnants. Astrophysics and space science library, vol 45. Reidel, Dordrecht Curtis HD (1921) The scale of the universe. Bull Natl Res Counc 2:194–217 Dawson KS, Aldering G, Amanullah R, Barbary K, Barrientos LF, Brodwin M et al (2009) An intensive Hubble space telescope survey for z>1 type Ia supernovae by targeting galaxy clusters. AJ 138:1271–1283

100 History of Supernovae as Distance Indicators

2537

de Jaeger T, González-Gaitán S, Anderson J et al (2015) A Hubble diagram from type II supernovae based solely on photometry: the photometry color method. ApJ 815:121(13pp) Dessart L, Hillier DJ (2005) Quantitative spectroscopy of photospheric-phase type II supernovae. A&A 437:667–685 Dessart L, Hillier DJ (2006) Quantitative spectroscopic analysis of and distance to SN 1999em. A&A 447:691–707 Dhawan S, Leibundgut B, Spyromilio J, Maguire K (2015) Near-infrared light curves of Type Ia supernovae: studying properties of the second maximum. MNRAS 448:1345–1359 Doggett JB, Branch D (1985) A comparative study of supernova light curves. AJ 90:2303–2311 Eastman RG, Kirshner RP (1989) Model atmospheres for SN 1987A and the distance to the large magellanic cloud. ApJ 347:771–793 Eastman RG, Schmidt BP, Kirshner RP (1996) The atmospheres of type II supernovae and the expanding photosphere method. ApJ 466:911–937 Elias JH, Frogel JA, Hackwell JA, Persson SE (1981) Infrared light curves of Type I Supernovae. ApJ 251:L13–L16 Elias JH, Matthews K, Neugebauer G, Persson SE (1985) Type I supernovae in the infrared and their use as distance indicators. ApJ 296:379–389 Elmhamdi A, Danziger IJ, Chugai N, Pastorello A, Turatto M, Cappellaro E et al (2003) Photometry and spectroscopy of the type IIP SN 1999em from outburst to dust formation. MNRAS 338:939–956 Evans R (1994) Searching for supernovae–visually and otherwise. Proc Aust Soc Astron 11:7–11 Filippenko AV, Richmond MW, Matheson T, Shields JC, Burbidge EM, Cohen RD et al (1992a) The peculiar type IA SN 1991T – detonation of a white dwarf? ApJ 384:L15–L18 Filippenko AV, Richmond MW, Branch D, Gaskell M, Herbst W, Ford CH et al (1992b) The subluminous, spectroscopically peculiar type Ia supernova 1991bg in the elliptical galaxy NGC 4374. AJ 104:1543–1556 Freedman WL, Madore BF (2010) The Hubble constant. ARAA 48:673–710 Freedman WL, Madore BF, Gibson BK, Ferrarese L, Kelson DD, Sakai S et al (2001) Final results from the Hubble space telescope key project to measure the Hubble constant. ApJ 553: 47–72 Freedman WL, Burns CR, Phillips MM, Wyatt P, Persson SE, Madore BF et al (2009) The Carnegie Supernova Project: First Near-Infrared Hubble Diagram to z.7. ApJ 704:1036–1058 Frieman JA, Bassett B, Becker A, Choi C, Cinabro D, DeJongh F et al (2008) The sloan digital sky survey-II supernova survey: technical summary. AJ 135:338–347 Frogel JA, Brooke G, Kawara K, Laney D, Phillips MM, Terndrup D et al (1987) Infrared photometry and spectroscopy of supernova 1986g in NGC 5128-centaurus A. ApJ 315:L129– L134 Gall EEE, Kotak R, Leibundgut B, Taubenberger S, Hillebrandt W, Kromer M (2016) Applying the expanding photosphere and standardized candle methods to type II-plateau supernovae at cosmologically significant redshifts: the distance to SN 2013eq. A&A 592:A129(12pp) Goobar A, Leibundgut B (2011) Supernova cosmology: legacy and future. ARNPS 61:251–279 Guy J, Astier P, Nobili S, Regnault N, Pain R (2005) SALT: a spectral adaptive light curve template for type Ia supernovae. A&A 443:781–791 Guy J, Astier P, Baumont S, Hardin D, Pain R, Regnault N et al (2007) SALT2: using distant supernovae to improve the use of type Ia supernovae as distance indicators. A&A 466:11–21 Hamuy M, Pinto P (2002) Type II supernovae as standardized candles. ApJ 566:L63–L65 Hamuy M, Maza J, Phillips MM, Suntzeff NB, Wischnjewsky M, Smith RC et al (1993) The 1990 Calán/Tololo supernova search. AJ 106:2392–2407 Hamuy M, Phillips MM, Suntzeff NB, Schommer RA, Maza J, Antezana AR et al (1996a) BVRI light curves for 29 type Ia supernovae. AJ 112:2408–2437 Hamuy M, Phillips MM, Suntzeff NB, Schommer RA, Maza J, Smith RC et al (1996b) The morphology of type Ia supernovae light curves. AJ 112:2438–2447

2538

B. Leibundgut

Hamuy M, Phillips MM, Suntzeff NB, Schommer RA, Maza J, Avilés R (1996c) The Hubble diagram of the Calán/Tololo type Ia supernovae and the value of H. AJ 112:2398–2407 Hamuy M, Pinto PA, Maza J, Suntzeff NB, Phillips MM, Eastman RG et al (2001) The distance to SN 1999em from the expanding photosphere method. ApJ 558:615–642 Hamuy M, Folatelli G, Morrell NI, Phillips MM, Suntzeff NB, Persson SE et al (2006) The Carnegie supernova project: the Low-Redshift survey. PASP 118:2–20 Hansen L, Nørgaard-Nielsen HU, Jørgensen HE (1987) Search for supernovae in distant clusters of galaxies. ESO Messenger 47:46–49 Hicken M, Challis P, Jha S, Kirshner RP, Matheson T, Modjaz M et al (2009) CfA3: 185 type Ia supernova light curves from the CfA. ApJ 700:331–357 Hicken M, Challis P, Kirshner RP, Rest A, Cramer CE, Wood-Vasey WM et al (2012) CfA4: light curves for 94 type Ia supernovae. ApJS 200:12(15pp) Hoffleit D (1939) Observations of supernovae. Publ Am Phil Soc 81:265–276 Höflich P (1988) Spectral analysis of SN 1987A: the First 7 Months. Proc ASA 7:434–442 Hoyle F, Fowler WA (1960) Nucleosynthesis in supernovae. ApJ 132:565–590 Humphreys EML, Reid MJ, Moran JM, Greenhill LJ, Argon AL (2013) Toward a new geometric distance to the active galaxy NGC 4258. III. Final results and the Hubble constant. ApJ 775:13(10pp) Inserra C, Smartt SJ (2014) Superluminous supernovae as standardizable candles and high-redshift distance probes. ApJ 796:87(18pp); erratum ApJ 807:112(6pp) Jeffery DJ, Branch D (1990) Analysis of supernova spectra. In: Wheeler JW, Piran T, Weinberg S (eds) Supernovae. World Scientific Publisher, Singapore, pp 149–247 Jha S, Kirshner, RP, Challis P, Garnavich PM, Matheson T, Soderberg AM (2006) UBVRI light curves of 44 type Ia supernovae. AJ 131:527–554 Jha S, Riess AG, Kirshner RP (2007) Improved distances to type Ia supernovae with multicolor light-curve shapes: MLCS2k2. ApJ 659:122–148 Jones MI, Hamuy M, Lira P, Maza J, Clocchiatti A, Phillips MM et al (2009) Distance determination to 12 type II supernovae using the expanding photosphere method. ApJ 696:1176–1194 Kirshner RP, Kwan J (1974) Distances to extragalactic supernovae. ApJ 193:27–36 Kowal CT (1968) Absolute magnitudes of supernovae. AJ 73:1021–1024 Koenig T (2005) Fritz Zwicky: novae become supernovae. In: Turatto M, Benetti S, Zampieri L, Shea W (eds) 1604-2004: supernovae as cosmological lighthouses. ASPC, vol 342. Astronomical Society of the Pacific, San Francisco, pp 53–60 Krisciunas K, Hastings NC, Loomis K, McMillan R, Rest A, Riess AG, Stubbs C (2000) Uniformity of (V-near-infrared) color evolution of type Ia supernovae and implications for host galaxy extinction determination. ApJ 539:658–674 Krisciunas K, Phillips MM, Suntzeff NB (2004) Hubble diagrams of type Ia supernovae in the near-infrared. ApJ 602:L81–L84 Labhardt L, Binggeli B, Buser R (1998) Supernovae and cosmology. Astronomical Institute of the University of Basel, Basel Law NM, Kulkarni SR, Dekany RG, Ofek EO, Quimby RM, Nugent PE et al (2009) The Palomar Transient Factory: system overview, performance, and first results. PASP 121:1395–1408 Leaman J, Li W, Chornock R, Filippenko AV (2011) Nearby supernova rates from the Lick Observatory Supernova Search – I. The methods and data base. MNRAS 412:1419–1440 Leibundgut B (1989) Light curves of supernovae type I. PhD thesis, University of Basel, Basel Leibundgut B (2000) Type Ia supernovae. A&AR 10:179–209 Leibundgut B (2001) Cosmological implications from observations of type Ia supernovae. ARA&A 39:67–98 Leibundgut B (2008) Supernovae and cosmology. Gen Relativ Gravit 40:221–248 Leibundgut B, Pinto PA (1992) A distance-independent calibration of the luminosity of type Ia supernovae and the Hubble constant. ApJ 401:49–59 Leibundgut B, Tammann GA, Cadonau R, Cerrito D (1991) Supernova studies. VII – an atlas of light curves of supernovae type I. A&AS 89:537–579

100 History of Supernovae as Distance Indicators

2539

Leibundgut B, Kirshner RP, Phillips MM, Wells LA, Suntzeff NB, Hamuy M et al (1993) SN 1991bg – a type Ia supernova with a difference. AJ 105:301–313 Leonard DC, Filippenko AV, Gates EL, Li W, Eastman RG, Barth AJ et al (2002) The distance to SN 1999em in NGC 1637 from the expanding photosphere method. PASP 114:35–64; erratum PASP 114:1291–1291 Leonard DC, Kanbur SM, Ngeow CC, Tanvir NR (2003) The cepheid distance to NGC 1637: a direct test of the expanding photosphere method distance to SN 1999em. ApJ 594: 247–278 Li W, Leaman J, Chornock R, Filippenko AV, Poznanski D, Ganeshalingam M et al (2011) Nearby supernova rates from the Lick Observatory Supernova Search – II. The observed luminosity functions and fractions of supernovae in a complete sample. MNRAS 412:1441–1472 Li W, Chornock R, Leaman J, Filippenko AV, Poznanski D, Wang X et al (2011b) Nearby supernova rates from the Lick Observatory Supernova Search – III. The rate-size relation, and the rates as a function of galaxy Hubble type and colour. MNRAS 412:1473–1507 Lundmark KE (1925) Nebulae, the motions and the distances of spiral. MNRAS 85:865–894 Lundmark KE (1932) The pre-tychonic novae. Lund Obs. Circ. 8:216–218 Maguire K, Kotak R, Smartt SJ, Pastorello A, Hamuy M, Bufano F (2010) Type II-P supernovae as standardized candles: improvements using near-infrared data. MNRAS 403:L11–L15 McCray R (1993) Supernova 1987A revisited. ARA&A 31:175–216 Meikle WPS (2000) The absolute infrared magnitudes of type Ia supernovae. MNRAS 314: 782–792 Miknaitis G, Pignata G, Rest A, Wood-Vasey WM, Blondin S, Challis P et al (2007) The ESSENCE supernova survey: survey optimization, observations, and supernova photometry. ApJ 666: 674–693 Minkowski R (1964) Supernovae and supernova remnants. ARA&A 2:247–266 Nobili S, Amanullah R, Garavini G, Goobar A, Lidman C, Stanishev V et al (2005) Restframe I-band Hubble diagram for type Ia supernovae up to redshift z.5. A&A 437:789–804 Nørgaard-Nielsen HU, Hansen L, Jørgensen HE, Aragon-Salamanca A, Ellis RS (1989) The discovery of a type Ia supernova at a redshift of 0.31. Nature 339:523–525 Nugent P, Sullivan M, Ellis R, Gal-Yam A, Leonard DC, Howell DA et al (2006) Toward a cosmological Hubble diagram for type II-P supernovae. ApJ 645:841–850 Oke JB, Searle L (1974) The spectra of supernovae. ARA&A 12:315–329 Olivares F, Hamuy M, Pignata G, Maza J, Bersten M, Phillips MM et al (2010) The standardized candle method for type II plateau supernovae. ApJ 715:833–853 Panagia N, Gilmozzi R, Macchetto F, Adorf H-M, Kirshner RP (1991) Properties of the SN 1987A circumstellar ring and the distance to the Large Magellanic Cloud. ApJ 380:L23–L26; erratum ApJ 386:L31–L32 Perlmutter S (2003) Supernovae, dark energy, and the accelerating universe. Phys Today 56:53–62 Perlmutter S, Schmidt BP (2003) Measuring cosmology with supernovae. In: Weiler K (ed) Supernovae and Gamma-Ray Bursters. Lecture notes in physics, vol 598. Springer, Berlin/New York, pp 195–217 Perlmutter S, Pennypacker CR, Goldhaber G, Goobar A, Muller RA, Newberg HJM et al (1995) A supernova at z = 0.458 and implications for measuring the cosmological deceleration. ApJ 440:L41–L44 Perlmutter S, Gabi S, Goldhaber G, Goobar A, Groom DE, Hook IM et al (1997) Measurements of the cosmological parameters  and ƒ from the first seven supernovae at z >D 0:35. ApJ 483:565–581 Phillips MM (1993) The absolute magnitudes of type Ia supernovae. ApJ 413:L105–L108 Phillips MM (2003) Supernovae as cosmological standard candles. In: Alloin D, Gieren W (eds) Stellar candles for the extragalactic distance scale. Lecture notes in physics, vol 635. Springer, Berlin/New York, pp 175–185 Phillips MM, Phillips AC, Heathcote SR, Blanco VM, Geisler D, Hamilton D et al (1987) The type Ia supernova 1986G in NGC 5128 – optical photometry and spectra. PASP 99:592–605

2540

B. Leibundgut

Phillips MM, Wells LA, Suntzeff NB, Hamuy M, Leibundgut B, Kirshner RP, Foltz CB (1992) SN 1991T – further evidence of the heterogeneous nature of type IA supernovae. AJ 103:1632–1637 Phillips MM, Lira P, Suntzeff NB, Schommer RA, Hamuy M, Maza J (1999) The reddening-free decline rate versus luminosity relationship for type Ia supernovae. AJ 118:1766–1776 Pignata G, Maza J, Antezana R, Cartier R, Folatelli G, Forster F et al (2009) The CHilean Automatic Supernova sEarch (CHASE). In: Giobbi G et al (eds) Probing stellar populations out to the distant universe. AIPC 1111:551–554 Pinto PA, Eastman RG (2000) The physics of type Ia supernova light curves. II. Opacity and diffusion. ApJ 530:757–776 Polshaw J, Kotak R, Chambers KC, Smartt SJ, Taubenberger S, Kromer M et al (2015) A supernova distance to the anchor galaxy NGC 4258. A&A 580:15(6pp) Polshaw J, Kotak R, Dessart L, Fraser M, Gal-Yam A, Inserra C et al (2016) LSQ13fn: a type IIPlateau supernova with a possibly low metallicity progenitor that breaks the standardised candle relation. A&A 588:1(17pp) Poznanski D, Butler N, Filippenko AV, Ganeshalingam M, Li W, Bloom JS et al (2009) Improved standardization of type II-P supernovae: application to an expanded sample. ApJ 694:1067– 1079 Pskovskii Yu P (1967) The photometric properties of supernovae. Sov Astron 11:63 Pskovskii Yu P (1984) Photometric classification and basic parameters of type I supernovae. Sov Astron 28:658 Rau A, Kulkarni SR, Law NM, Bloom JS, Ciardi D, Djorgivsku GS et al (2009) Exploring the optical transient sky with the Palomar Transient Factory. PASP 121:1334–1351 Rees MJ, Stoneham RJ (eds) Supernovae: a survey of current research. Reidel, Dordrecht Richmond M, Treffers RR, Filippenko AV (1993) The Berkeley automatic imaging telescope. PASP 105:1164–1174 Riess AG (2000) The case for an accelerating universe from supernovae. PASP 112:1284–1299 Riess AG, Press WH, Kirshner RP (1996) A precise distance indicator: type Ia supernova multicolor light-curve shapes. ApJ 473:88–109 Riess AG, Kirshner RP, Schmidt BP, Jha S, Challis P, Garnavich PM et al (1999) BVRI light curves for 22 type Ia supernovae. AJ 117:707–724 Riess AG, Strolger L-G, Tonry J, Casertano S, Ferguson HC, Mobasher B et al (2004) Type Ia supernova discoveries at z > 1 from the Hubble Space Telescope: evidence for past deceleration and constraints on dark energy evolution. ApJ 607:665–687 Riess AG, Strolger L-G, Casertano S, Ferguson HC, Mobasher B, Gold B et al (2007) New Hubble Space Telescope discoveries of type Ia supernovae at z >D 1: narrowing constraints on the early behavior of dark energy. ApJ 659:98–121 Riess AG, Macri L, Casertano S, Lampeitl H, Ferguson HC, Filippenko AV et al (2011) A 3 % solution: determination of the Hubble constant with the Hubble Space Telescope and wide field camera 3. ApJ 730:119(18pp); erratum ApJ 732:129(1p) Rosino L, di Tullio G (1974) The Asiago supernova search. In: Cosmovici CB (ed) Supernovae and supernova remnants. Astrophys Space Sci Libr 45:19–27 Ruiz-Lapuente P, Canal R, Isern J (1997) Thermonuclear supernovae. Kluwer, Dordrecht Sandage A (1998) SN 1932 GAT: a supernova of unique class. In: Labhardt L, Binggeli B, Buser R (eds) Supernovae and cosmology. Astronomisches Institut der Universität, Basel, pp 201–220 Sandage A, Tammann GA (1982) Steps toward the Hubble constant. VIII – the global value. ApJ 256:339–345 Sandage A, Tammann GA, Saha A, Reindl B, Macchetto FD, Panagia N (2006) The Hubble constant: a summary of the Hubble Space Telescope program for the luminosity calibration of type Ia supernovae by means of Cepheids. ApJ 522:802–860 Sargent WLW, Searle L, Kowal CT (1974) The Palomar supernova search. In: Cosmovici CB (ed) Supernovae and supernova remnants. Astrophys Space Sci Libr 45:33–49 Scalzo RA, Aldering G, Antilogus P, Aragon C, Bailey S, Baltay C et al (2014) Type Ia supernova bolometric light curves and ejected mass estimates from the nearby supernova factory. MNRAS 440:1498–1518

100 History of Supernovae as Distance Indicators

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Schmidt BP, Kirshner RP, Eastman RG (1992) Expanding photospheres of type II supernovae and the extragalactic distance scale. ApJ 395:366–386 Schmidt BP, Kirshner RP, Eastman RG, Hamuy M, Phillips MM, Suntzeff NB et al (1994a) The expanding photosphere method applied to SN 1992am at cz D 14600 km/s. AJ 107: 1444–1452 Schmidt BP, Kirshner RP, Eastman RG, Phillips MM, Suntzeff NB, Hamuy M et al (1994b) The distances to five Type II supernovae using the expanding photosphere method, and the value of H. ApJ 432:42–48 Schmidt BP, Suntzeff NB, Phillips MM, Schommer RA, Clocchiatti A, Kirshner RP et al (1998) The high-z supernova search: measuring cosmic deceleration and global curvature of the universe using type Ia supernovae. ApJ 507:46–63 Schmutz W, Abbott DC, Russell RS, Hammann W-R, Wessolowski U (1990) Non-LTE model calculations for SN 1987A and the extragalactic distance scale. ApJ 355:255–270 Schramm DN (1977) Supernovae. Astrophysics and space science library, vol 66. Reidel, Dordrecht Shapley H (1921) The scale of the universe. Bull Natl Res Counc 2:171–193 Smartt SJ, Valenti S, Fraser M, Inserra C, Young DR, Sullivan M et al (2015) PESSTO: survey description and products from the first data release by the public ESO spectroscopic survey of transient objects. A&A 579:40(25pp) Sonneborn G, Fransson C, Lundqvist P, Cassatella A, Gilmozzi R, Kirshner RP et al (1997) The evolution of ultraviolet emission lines from circumstellar material surrounding SN 1987A. ApJ 477:848–864 Stritzinger M, Leibundgut B (2005) Lower limits on the Hubble constant from models of type Ia supernovae. A&A 431:423–431 Stritzinger M, Leibundgut B, Walch S, Contardo G (2006) Constraints on the progenitor systems of type Ia supernovae. A&A 450:241–251 Stritzinger M, Phillips MM, Boldt LN, Burns C, Campillay A, Contreras C et al (2011) The Carnegie supernova project: second photometry data release of low-redshift type Ia supernovae. AJ 142:156(14pp) Takáts K, Vinkó J (2012) Measuring expansion velocities in Type II-P supernovae. MNRAS 419:2783–2796 Tammann GA (1978) Some statistical properties of supernovae. Mem Soc Astron It 49:315–329 Tammann GA (1979) Cosmology with the space telescope. In: Macchetto FD, Pacini F, Tarenghi M (eds) Astronomical uses of the space telescope. ESO proceedings, Garching, pp 329–341 Tammann GA, Leibundgut B (1990) Supernova studies. IV – the global value of H from supernovae Ia and the peculiar motion of field galaxies. A&A 236:9–14 Tonry JL, Stubbs CW, Kilic M, Flewelling HA, Deacon NR, Chornock R et al (2012) First results from Pan-STARRS1: faint, high proper motion white dwarfs in the medium-deep fields. ApJ 745:42(13pp) Trimble V (1982) Supernovae. Part I: the events. Rev Mod Phys 54:1183–1224 Trimble V (1995) The 1920 Shapley-Curtis discussion: background, issues, and aftermath. PASP 107:1133–1144 Turatto M, Benetti S, Zampieri S, Shea W (2005) 1604–2004: supernovae as cosmological lighthouses. ASPC, vol 342. Astronomical Society of the Pacific, San Francisco Wagoner RV (1977) Determining q from supernovae. ApJ 214:L5–L7 Wagoner RV (1979) Determining H and q from supernova atmospheres. Comments Astrophys 8:121–131 Wagoner RV (1981) Effects of scattering on continuous radiation from supernovae and determination of their distances. ApJ 250:L65–L69 Weiler K (2003) Supernovae and gamma-ray bursts. Lecture notes in physics, vol 598. Springer, Berlin/New York Wesselink AJ (1946) The observations of brightness, colour and radial velocity of • Cephei and the pulsation hypothesis. Bull Astron Inst Neth 10:91–98 Wheeler JC (1980) Texas workshop on type I supernovae. University of Texas Press, Austin

2542

B. Leibundgut

Wild P (1974) The supernovae search at Zimmerwald. In: Cosmovici CB (ed) Supernovae and supernova remnants. Astrophys Space Sci Libr 45:29–32 Wood-Vasey WM, Aldering G, Lee BC, Loken S, Nugent P, Perlmutter S et al (2004) The nearby supernova factory. New Astron Rev 48:637–640 Wood-Vasey WM, Miknaitis G, Stubbs CW, Jha S, Riess AG, Garnavich PM et al (2007) Observational constraints on the nature of dark energy: first cosmological results from the ESSENCE supernova survey. ApJ 666:694–715 Zwicky F (1965) Supernovae. In: Stellar structure, stars and stellar systems, vol VIII. The Chicago University Press, Chicago, pp 367–424

The Peak Luminosity–Decline Rate Relationship for Type Ia Supernovae

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Mark M. Phillips and Christopher R. Burns

Abstract

The peak luminosity–decline rate relationship for Type Ia supernovae is one of the most important underpinnings of modern cosmology. Reproducing it is also a fundamental test for any viable progenitor/explosion scenario. In this chapter, a short history of the discovery of the peak luminosity–decline rate relationship is presented, along with descriptions and comparisons of different methods used to characterize light curve shape. The importance of disentangling host galaxy dust reddening from intrinsic luminosity and color variations is also emphasized. It has been known for some time that certain spectral features correlate with decline rate and that these correspond to the amount of 56 N i produced in the explosion. Nevertheless, details regarding the progenitor and explosion mechanism(s) that create the tight relation observed between luminosity and decline rate are still lacking.

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Measuring the Decline Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Disentangling Host Galaxy Dust Reddening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The Peak Luminosity–Decline Rate Relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Toward a Theoretical Understanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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M.M. Phillips () Carnegie Observatories, Las Campanas Observatory, La Serena, Chile e-mail: [email protected] C.R. Burns Carnegie Observatories, Pasadena, CA, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_100

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M.M. Phillips and C.R. Burns

Introduction

Two of the greatest triumphs of modern observational cosmology – the discovery of the accelerating expansion of the Universe (Perlmutter et al. 1999; Riess et al. 1998) and the measurement of the Hubble constant to a precision of 10 % or better (Freedman et al. 2001; Riess et al. 2016) – relied on the use of Type Ia supernovae (SNe Ia) as standard candles, a technique that was anticipated approximately 60 years earlier in a remarkable paper by Olin Wilson (1939). Wilson’s colleagues on the staff of the Mount Wilson Observatory, Walter Baade and Rudolph Minkowski, and Fritz Zwicky of Caltech had shown that certain supernovae displayed remarkably similar light curves and spectra. Baade (1938) had also found that the absolute peak magnitudes of this class of supernova, which 2 years later Minkowski (1941) designated as “Type I” on the basis of their spectra, displayed a dispersion of 1 mag or less. Wilson proposed two cosmological uses for the Type I supernovae: (1) testing whether the redshift was due to the Doppler effect by looking for time dilation effects in distant events – realized years later by Leibundgut et al. (1996), Goldhaber et al. (2001) – and (2) extending the Hubble diagram to large distances. Concrete progress on realizing the promise of Type I supernovae as standard candles did not begin in earnest until the 1960s, when Charles Kowal of Caltech searched for supernovae using the Palomar Observatory 48 in Schmidt telescope in a survey led by Zwicky. Kowal discovered 81 supernovae during this period and published a Hubble diagram with an observed dispersion of 0.6 mag (30 % in distance) for 16 Type I events with photographic photometry (Kowal 1968). Kowal commented that the true dispersion should be even smaller, and, indeed, at a median redshift of z  0:004 for the sample, peculiar velocities alone would produce an observed dispersion of 0.5 mag. Moreover, Kowal’s sample is now known to have been contaminated by a few stripped-envelope core-collapse events whose photographic light curves mimic those of the thermonuclear Type Ia supernovae (SNe Ia). For much of the 1980s, the working hypothesis of many investigators was that SNe Ia were characterized by the same intrinsic luminosities and light curve shapes (e.g., see Cadonau et al. 1985). Under this assumption, Tammann and Leibundgut (1990) concluded that the luminosity scatter for a sample of 35 SNe was 0:25 mag after correcting for host galaxy peculiar velocities. Nevertheless, in the 1970s, Barbon et al. (1973) had suggested there were two subclasses of SNe I that they called “fast” and “slow.” Pskovskii (1977, 1984) and Branch (1981) concluded a few years later that SNe I displayed a continuous range of decline rates after maximum and that the decline rate was correlated with peak luminosity. However, Boisseau and Wheeler (1991) questioned these findings, arguing that contamination of the supernova photometry by light from the host galaxy would naturally produce such a correlation. The idea that SNe Ia formed a uniform class was conclusively laid to rest in the late 1980s and early 1990s with the introduction of linear, high quantum efficiency CCD detectors that allowed SNe Ia light curves to be measured with significantly greater precision than that afforded by photographic plates or photoelectric

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photometers. The first SN Ia whose optical light curves were measured using a CCD, SN 1986G, showed a much faster initial decline rate than the prototypical SN Ia 1981B and also displayed peculiar light curves in the near infrared (Frogel et al. 1987; Phillips et al. 1987). Observations of the luminous, slow-declining, spectroscopically peculiar SN 1991T (Filippenko et al. 1992b; Phillips et al. 1992) and the very fast-declining, subluminous SN 1991bg (Filippenko et al. 1992a; Leibundgut et al. 1993) led Phillips (1993) to reexamine the possibility of a correlation between peak luminosity and initial decline rate. Phillips employed a sample of nine well-observed SNe Ia covering a range of decline rates and with distances estimated via surface brightness fluctuations (Tonry and Schneider 1988) or the Tully–Fisher relation (Tully and Fisher 1977). He found that the absolute magnitudes were tightly correlated with the initial rate of decline of the B light curve, with the slope of the correlation being steepest in B and becoming progressively flatter in the V and I bands. Confirmation of the peak luminosity– decline rate relationship soon came from observations of the Calán-Tololo (CT) Survey (Hamuy et al. 1995, 1996a; Maza et al. 1994). At a median redshift of z  0:04, the CT sample allowed the most precise determination yet of the intrinsic dispersion of SNe Ia peak luminosities, yielding values of 0.17, 0.14, and 0.13 mag in the B, V , and I bands, respectively, after accounting for the dependence on decline rate. Confirmation of these results was provided by an independent analysis of the CT sample (Riess et al. 1996a), and within 2 years, observations of distant SNe Ia, analyzed using the same basic techniques, led to the discovery of dark energy. In this chapter, we review the progress that has been made over the past 20 years in describing and understanding the peak luminosity–decline rate relation (also known as the “luminosity–width” relation). Not only has it become one of the principal tools of observational cosmology, but it also is a fundamental physical property of SNe Ia that must be explained by successful progenitor and explosion models.

2

Measuring the Decline Rate

Pskovskii (1977, 1984) was the first to attempt to measure SNe Ia decline rates. He employed a slope parameter, ˇ, defined as the mean rate of decline of the B band light curve between maximum and the transition to a slower decline rate that occurs typically 25–30 days later. The units of ˇ were expressed in magnitudes per 100 days. In practice, the ˇ parameter is subject to rather large uncertainties depending on sampling of the light curve and has not seen much use since Pskovskii’s papers. Phillips (1993) introduced a simpler, more robust parameter, m15 .B/, defined as the amount in magnitudes that the B light curve declines during the first 15 days following maximum. The interval of 15 days was found to provide the greatest discrimination between the slowest and fastest declining light curves. A problem with the m15 .B/ parameter is that it requires that the SN observations begin at

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or before maximum light and extend to at least 15 days past maximum. To remedy this, Hamuy et al. (1995) defined a set of template light curves in B and V derived from five well-observed SNe with decline rates in the range 0:9 m15 .B/ 1:9. For an SN with observations beginning after maximum or with poor coverage at 15 days past maximum, the light curve observations were fitted to the templates via a 2 -minimization technique to infer the time of maximum, tBmax ; the maximumlight magnitudes, Bmax and Vmax ; and the decline rate m15 .B/. This approach, which is sometimes referred to as the “m15 .B/ method,” was modified to include the I band by Hamuy et al. (1996b) and was improved further by Prieto et al. (2006) who developed a technique to construct B, V , R, and I templates over a continuous range of m15 .B/ through linear combination of a discrete set of 14 templates derived from well-observed SNe Ia. An example of how the m15 .B/ parameter is measured for three SNe spanning the range of observed decline rates is illustrated in Fig. 1. In the upper panel, the B-band light curves normalized to a peak magnitude of 0.0 are plotted as a function of time since the epoch of B maximum. The intersection of the light curves with the dashed vertical line at 15 days past B maximum corresponds to the m15 .B/ measurement for each SN. Perlmutter et al. (1997) proposed a simple alternative to using multiple light curve templates that became known as the “stretch” method. The idea was to linearly stretch or contract the time axis of an average light curve template by a factor, s. The method was described in detail for the B band by Goldhaber et al. (2001). Jha et al. (2006) demonstrated that the stretch method can also be used in the U and V filters but does not work in the I band (or the near-infrared YJHK bands) due to variations in the strength of the secondary maximum that are a function of the decline rate (Hamuy et al. 1996b). The stretch method is illustrated in the top panel of Fig. 1 where the “parab18” B-band stretch template for s D 1:0 given by Goldhaber et al. (2001) is plotted as a solid red line. Reasonable fits to the observations of SNe 2006bh and 2006et (shown as dashed red lines) are obtained by contracting the time axis by a factor of 0.8 and stretching it by a factor 1.2, respectively. Note, however, that the method breaks down for the very fast-declining SN 2006mr since the stretch template cannot be made to fit the observations because the transition to a final decline phase occurs very early for this extreme event. Riess et al. (1996a) developed a method for fitting B, V , R, and I photometry known as “MLCS” (multicolor light curve shapes) that models the light curve as a sum of vectors, with the coefficients of the vectors corresponding to the distance modulus, V , the dust extinction, AV , and a luminosity correction, . To account for the correlation between luminosity and light curve shape, correction templates in each filter were introduced that, when added in the right amount, correct a mean template to match the observed SN light curves. The authors used photometry of nine nearby, well-observed SNe Ia with independently determined distances as a training set for deriving the mean and correction templates. The MLCS method was updated by Riess et al. (1998) to include a second order term in , and the training set was replaced by a set of 27 SNe Ia in the Hubble flow (cz 2500 km s1 ).

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Fig. 1 Illustration of how the m15 .B/, stretch (s), and color-stretch (sBV ) parameters are measured for three SNe Ia covering the full range of observed decline rates. The data for the SNe are from the Carnegie Supernova Project (Hamuy et al. 2006). See text for further details

The version of this method commonly in use today, “MLCS2k2” (Jha et al. 2007), incorporates improved K-corrections and dust extinction corrections and was expanded to include the U band. It should be noted that in the MLCS method, the  parameter is defined as the difference between the absolute V magnitude at maximum of an SN and a fiducial value and thus is not strictly a measurement of the decline rate. Two more recent light curve fitters are SALT2 (Guy et al. 2007) and SiFTO (Conley et al. 2008). Like its predecessor, SALT (“Spectral Adaptive Light curve Template”), SALT2 parameterizes light curves using a light curve stretch parameter, “x1 ,” in the B band. However, it differs from SALT in using a large sample of rest frame U to I band light curves and spectra of both nearby and distant SNe Ia to produce an empirical model of the average spectrophotometric evolution

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with time as well as its variations as a function of light curve shape and color. SiFTO also outputs a B band stretch, but the model is generalized so that different observed filters stretch by different amounts as a function of wavelength and the B band stretch. The stretch model is then used to adjust a standard spectral energy distribution (SED) model to match the observed colors so that the final result is a single SED which can be used to compute rest-frame magnitudes in some standard set of filters. A significant advantage of both SALT2 and SiFTO is that the effects of redshifting the spectrum are handled as part of the light curve model, rather than computing a K-correction. In 2004, the Carnegie Supernova Project (CSP) began a program to establish a fundamental data set of optical and near-infrared (NIR) light curves in a welldefined and understood photometric system (Hamuy et al. 2006). Optical imaging was obtained of over 100 SNe Ia in the Sloan Digital Sky Survey (SDSS) ugri filters and Johnson BV filters, while NIR imaging was carried out mostly in the YJH bandpasses. Since no light curve fitters existed to handle the SDSS ugri or NIR photometry, a new set of tools in a package called “SNooPy” (SuperNova in objectoriented Python) was developed by Burns et al. (2011). SNooPy can be thought of as an extension of the Prieto et al. (2006) template generating technique to the NIR bandpasses. A training set of photometric data for a sample of well-observed SNe Ia is used to define a three-dimensional surface of normalized flux versus t  tBmax versus decline rate. Generating a light-curve template can therefore be thought of as interpolation on this surface. Note that Burns et al. (2011) use m15 .B/ as the decline rate parameter for the training set, but when using SNooPy to fit a set of light curves, the template-derived value of the decline rate parameter, denoted as m15 , can deviate somewhat from the directly measured value since it is constrained by all the filters simultaneously. At the fastest decline rates (m15 .B/ 1:7), the change in intrinsic shape of the B light-curve becomes more complicated than a simple stretch relationship, and the m15 .B/ parameter becomes a poor discriminate of the light curve width (Burns et al. 2014; Phillips 2012). Noting that the timing of the reddest .B  V / color attained by SNe Ia after maximum light is a function of the decline rate, Burns et al. (2014) defined a dimensionless stretch-like parameter sBV D t.BV /max =30 days, which they called a “color stretch”. These authors found that when using sBV rather than m15 .B/, the fastest-evolving SNe Ia appear less as a distinct population of objects and more as the tail end of normal SNe Ia. The sBV parameter has been incorporated into SNooPy as an user-selectable alternative to m15 . Like the MLCS2k2  parameter, sBV does not directly measure the decline rate or width of the light curve but rather is an independent parameter that correlates with decline rate. In the lower panel of Fig. 1, measurement of the color-stretch parameter, sBV , is illustrated for SNe 2006mr, 2006bh, and 2006et. The evolution of the .B  V / colors as a function of time since B maximum for each SN has been normalized to a maximum color of 0.0. The epoch of the maximum of the .B  V / color, t.BV /max , for the three SNe is denoted by the three red dashed vertical lines, with the fiducial value of 30 days corresponding to the solid red vertical line. The color-stretch parameters, sBV , are then found by dividing the values of t.BV /max by 30 days.

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Fig. 2 Comparison of different parameters used to parameterize the decline rate or width of SN Ia light curves. (Left) The SALT2 stretch parameter x1 is plotted versus the SNooPy color-stretch parameter sBV . Black points are from Hicken et al. (2009) and red points are from Burns et al. (2014). (Middle) The MLCS2k2  parameter is plotted versus sBV . Black points are from Hicken et al. (2009), and red points are from Jha et al. (2007). (Right) The m15 .B/ parameter is plotted versus sBV for the CSP-I DR3 sample (Krisciunas et al. (in preparation))

Figure 2 shows a comparison of the SALT2 x1 , MLCS2k2 , and the classical m15 .B/ light curve parameters with the SNooPy sBV color-stretch parameter. Over the range of decline rates of “normal” SNe Ia (0:7 sBV 1:1), the correlations of the x1 and m15 .B/ parameters with sBV are essentially linear. This is not true for the  parameter since  is an indicator of the B band luminosity which, as shown in Sect. 4, varies nonlinearly with decline rate. Note the flattening of the correlations of sBV with x1 and m15 .B/ at the fastest decline rates (sBV < 0:7) and the considerable scatter observed in the x1 and  parameters in this same range. Interestingly, a similar flattening in the correlation of m15 .B/ and sBV appears to occur at the slowest decline rates (sBV > 1:1). The usage of SNe Ia as standard candles at these extremes of decline rate should be considered unreliable, at least for the SALT2, MLCS2k2, and m15 .B/ methods.

3

Disentangling Host Galaxy Dust Reddening

A precise determination of the peak luminosity–decline rate relation for SNe Ia is complicated by dust absorption, particularly at optical wavelengths. Absorption due to dust in the Milky Way (MW) is universely corrected for using the reddening maps of Schlegel et al. (1998) generated from COBE/DIRBE and IRAS/ISSA infrared emission data. More recently, these maps have been recalibrated using measurements of the colors of stars from the SDSS (Schlafly and Finkbeiner 2011). The latter paper assumes a reddening law with RV D 3:1. Although RV is known to vary over the sky, recent work indicates that the dispersion is relatively small ( D 0:18) (Schlafly et al. 2016) except toward the Galactic Bulge (see Nataf 2016 and references therein). Correcting for dust absorption produced in the host galaxy or immediate environment of the SN is a more complex issue since it requires assumptions about

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the intrinsic colors of the SNe and the absorbing properties of the dust. The earliest papers to study the luminosity–decline rate relation either ignored reddening or made color cuts to exclude the reddest SNe. van den Bergh (1995) called attention to an apparent coincidence between the MV versus .B  V / relation for theoretical models of SNe Ia and the slope of the standard MW reddening vector in the same diagram. Perhaps inspired by this paper, Tripp (1998) discovered, using the CT data, that it was possible to reduce the B-band Hubble diagram dispersion significantly by applying linear corrections as a function of both m15 .B/ and .B  V /, but the color correction implied an unusually low value of RB  2 (cf. RB  4 for standard MW dust). The Tripp method is commonly adopted by light curve fitters used for cosmology (e.g., SALT2 and SifTO), but more recent results with large samples of SNe Ia give values of RB  3:1  3:7, depending on whether the intrinsic distance scatter is modeled as luminosity or color variations (Rest et al. 2014; Scolnic et al. 2014). While the Tripp method is computationally attractive, it lumps together intrinsic luminosity–color effects with dust reddening. Early attempts by Riess et al. (1996b) and Phillips et al. (1999) to separate these dependencies yielded values of RV  2:6 (RB  3:6). In principle, the correct way to study the peak luminosity–decline rate relation is to measure the extinction due to the interstellar medium of the host galaxy and/or the circumstellar environment for each individual SN. Krisciunas et al. (2000) were the first to emphasize the advantage of combining optical and NIR photometry to estimate the visual extinction, AV , to an SN Ia. Since the extinction in the H band is 5-times less than in V , the color excess E.V  H / D AV  AH  AV . As shown by Folatelli et al. (2010), Phillips (2012), and Burns et al. (2014), the measurement of color excesses as a function of wavelength also provides invaluable information on the shape of the reddening curve (i.e., the value of RV ). In Fig. 3, we update the latter work by plotting observed pseudocolors at maximum light versus the light curve decline rate as parameterized by the color-stretch parameter, sBV , for the full set of SNe Ia observed by the CSP-I (Krisciunas et al., in preparation). Note that a “pseudocolor” is defined as the difference between the magnitudes at maximum light in two different filters. Since maximum light occurs at slightly different times at different wavelengths, a pseudocolor is not an actual measurement of the color of the SN at a specific time. Figure 3 shows that a sharp blue edge to the distribution of pseudocolors is clearly visible in each of the panels. Assuming that the distribution of pseudocolors seen in Fig. 3 is due to dust extinction, the vertical offset of each SN from the blue edge (approximated by a dashed line) provides a measurement of its color excess. Figure 4 shows the resulting color excesses, E.V  i /, E.V  Y /, E.V  J /, and E.V  H /, plotted versus E.B  V /. The diagonal lines in each graph indicate the expected correlations of the color excesses for two different values of RV assuming a standard Galactic reddening law. As is seen, most SNe Ia suffer only a small amount of reddening consistent with RV  3, while the reddening of the more highly extinguished objects often appears to be produced by dust characterized by an unusually low value of RV . Indeed, using all of the color excess information afforded by the CSP-I photometry and fitting for the values of E.B  V / and RV

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Fig. 3 Observed maximum-light rest-frame pseudocolors, corrected for foreground MW extinction, are plotted versus the color-stretch parameter sBV . A best-fit model for the intrinsic color loci is plotted as a dashed blue line in each panel

Fig. 4 Montage of color excess versus color excess plots. Two representative reddening laws are plotted in each panel: RV D 3:1 is plotted as a dashed line, while RV D 1:7 is plotted as a solid line

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for each individual SN, Burns et al. (2014) found evidence for a correlation between RV and E.B  V /, such that larger E.B  V / tends to favor lower RV . This finding confirms a similar conclusion reached by Mandel et al. (2011) using a different data set and analysis technique.

4

The Peak Luminosity–Decline Rate Relation

Phillips et al. (1999) used B, V , and I photometry of a sample of well-observed SNe Ia and the Lira (1995) relation, which has the advantage of being independent of the decline rate, to estimate individual dust reddenings for 41 SNe with z 0:01. Utilizing only those SNe with color excesses E.B  V / < 0:05 mag and determining relative luminosities using the redshift as the distance indicator, these authors confirmed the result of Phillips (1993) that the peak luminosity–decline rate relation is steepest in the B band and progressively less steep in the V and I filters. They also found clear evidence that the relations are nonlinear in the B and V bands and perhaps also in I . In the NIR J , H , and K bands, Elias et al. (1985) found from a sample of 10 SNe Ia that the light curves appeared to have a dispersion in color and absolute magnitude of 0:2 mag with no correction for decline rate. This was confirmed by Meikle (2000) who also found no significant evidence for a correlation between absolute magnitude and m15 .B/ over the range 0:87 < m15 .B/ < 1:31 for a sample of seven nearby SNe Ia. From a larger sample of 16 SNe Ia, Krisciunas et al. (2004) confirmed these results, finding dispersions in absolute magnitude of 0.12– 0.18 mag in the J , H , and K bands, with no evidence for a significant decline rate dependence. More recently as the observations in the NIR have increased both in quality and quantity, some evidence for absolute magnitude differences have been found. From a study of 30 SNe Ia, including nine fast decliners (m15 .B/ > 1:6), Krisciunas et al. (2009) concluded that the fast-declining SNe whose NIR light curves peaked after the epoch of B maximum were subluminous in JHK, whereas those that peaked in the NIR before B maximum had absolute magnitudes indistinguishable from those of normal slower-declining SNe Ia. Kattner et al. (2012) used a sample of 27 SNe Ia from the CSP-I to study the luminosity– decline rate relationship in the NIR. These authors confirmed the apparent bimodal distribution of absolute magnitudes for fast-declining SNe Ia found by Krisciunas et al. (2009). Moreover, the data revealed a weak dependence of luminosity on decline rate for normal SNe Ia at the 2–3  level in the J and H bands. Figure 5 shows the peak luminosity–decline rate relations in the B, V , i , Y , J , and H bands. The data correspond to events in the CSP-I DR3 photometry release (Krisciunas et al., in preparation) with E.B  V / < 0:10 mag. Included for comparison in the B, V , and i plots are the 18 SNe Ia comprising the lowreddening sample of Phillips et al. (1999). In the left-hand side of the figure, the absolute magnitudes are plotted versus the color-stretch parameter, sBV , while on the right hand side m15 .B/ is employed as the decline rate parameter. Some things to be noted in this figure are:

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Fig. 5 Absolute magnitudes at maximum light plotted as a function of the color-stretch parameter sBV (left) and m15 .B/ (right) for two samples of SN Ia with negligible reddening. The filled circles are SNe drawn from the CSP-I DR3 sample (Krisciunas et al., in preparation), while the open circles correspond to the low-reddening sample of Phillips et al. (1999). The I -band magnitudes from the latter publication have been converted to the SDSS i -band. Distances were calculated using the host redshifts and Ho D 75 km s1

• The effect of the peak luminosity–decline relation is strongest in the blue and only weakly present in the NIR. This fact, combined with the much smaller effect of dust extinction at NIR wavelengths, means that most SNe Ia are excellent standard candles in the NIR with no correction for either decline rate or host dust extinction. • When m15 .B/ is used as the decline rate parameter instead of sBV , the dispersion increases for those objects with m15 .B/ > 1:7 as found by Krisciunas et al. (2009) and Kattner et al. (2012).

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• There is a hint that the fastest-declining events may be a smooth extension of normal SNe Ia when the absolute magnitudes are plotted versus sBV , although this must be confirmed with more data. If this is the case, it suggests that one progenitor and explosion mechanism could explain all SNe Ia. As mentioned in Sect. 3, in most modern cosmology studies the residuals in distance modulus, , are minimized by fitting the observed SN magnitudes, decline rates, and colors using the Tripp (1998) relation which assumes linear corrections as a function of both decline rate and color. The model employed in SALT2 is

 D mB  .MB  ˛  X1 C ˇ  C / where the observed quantities for each SN are the apparent B-band rest-frame peak magnitude, mB , and the decline rate and color measurements, X1 and C . The nuisance parameters of the fit to the model are ˛, ˇ, and MB . Both MB and ˇ have been found to depend on host galaxy properties (e.g., see Sullivan et al. 2011), but there is no evidence to date that the slope of the luminosity–stretch relation, ˛, shows such a dependency or varies with look-back time (e.g., see Betoule et al. 2014).

5

Toward a Theoretical Understanding

Soon after the confirmation of the existence of a luminosity–decline rate relation for SNe Ia, Nugent et al. (1995) showed that certain spectroscopic features also correlate with decline rate. By varying the luminosity, and thus the “effective” temperature of the same theoretical model, these authors were able to reproduce this spectral sequence from the coolest (SN 1991bg) to the hottest (SN 1991T) events. Since SNe Ia are powered by radioactive decay, Nugent et al. concluded that both the photometric and spectroscopic sequences were likely to be due to variations in the total amount of 56 N i produced in the explosion. This has since been confirmed by a number of studies (Childress et al. 2015; Mazzali et al. 2007; Scalzo et al. 2014; Stritzinger et al. 2006b) that have demonstrated that the light curve decline rate is well correlated with the 56 N i mass, with the amounts ranging from 0:1– 1:0 Mˇ for normal SNe Ia. Interestingly, the fastest-declining SNe Ia are found preferentially in early-type galaxies, and slow-declining events in spiral galaxies (Hamuy et al. 1996a, 2000), suggesting that the age of the progenitor is a factor in determining the amount of 56 N i produced in the explosion. There is also evidence that the most luminous SNe Ia are produced in metal-poor neighborhoods (Hamuy et al. 2000), and so metallicity likely also plays a role. The question, then, is what physical processes are responsible for producing SNe Ia with this range of 56 N i masses? More than 50 years ago, Hoyle and Fowler (1960) recognized that SNe Ia were the observational signature of the thermonuclear disruption of a white dwarf, but our knowledge of the progenitors and explosion scenario(s) remains frustratingly uncertain. There is widespread agreement that

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the white dwarf must be in a binary system, with either another white dwarf (“double degenerate”) or a main sequence, giant, or helium star companion (“single degenerate”). Currently the weight of evidence seems to favor double-degenerate systems (see Maoz et al. 2014,and references therein), although at least one normal event may have had a nondegenerate companion (Marion et al. 2014). Within either the double-degenerate or single-degenerate scenarios, it has been shown in a number of papers (Blondin et al. 2013; Höflich et al. 1996, 2002, 2010) that spherically symmetric (1-D) delayed-detonation transition (DDT) models (Khokhlov 1991) are capable of reproducing the observed photometric and spectroscopic characteristics of SNe Ia. In the DDT scenario, the explosion of a Chandrasekhar-mass (MC h ) C/O white dwarf transitions from a subsonic deflagration to a supersonic detonation wave at some transition density, t r . For the most part, the amount of 56 N i produced during the detonation phase is determined by t r . The greater the 56 N i , the more luminous the SN and the higher the temperature in the outer envelope. Higher temperatures mean a larger fraction of the radiation is produced at shorter wavelengths where opacities are greater, resulting in longer photon diffusion time scales – and, thus, broader light curves. However, Kasen and Woosley (2007) argue that an even more important factor is that more luminous SNe Ia undergo a slower ionization evolution from Fe III to Fe II in the ejecta than less luminous events, resulting in a less rapid color evolution to the red and thus a slower decline of the B light curve. The fact that the color-stretch parameter does the best job of sorting the fastest-declining SNe Ia would seem to support this interpretation. The success of one-dimensional DDT models in reproducing the general characteristics of the observed light curves as well as the spectra at early and late phases suggests that this explosion scenario may explain most SNe Ia. Nevertheless, 3-D DDT models predict Rayleigh-Taylor mixing of stable iron-group elements into the outer layers and mixing of C and O inward (Seitenzahl et al. 2013). The resulting spatial distribution of elements in the ejecta is quite different than the “onion skin” produced by the spherically symmetric models. And while synthetic light curves and spectra calculated from these 3-D models match some of the observed properties of SNe Ia, the luminosity–decline rate relation is not reproduced (Sim et al. 2013). It is possible that physical properties not included in the 3-D models – e.g., high magnetic fields (Penney and Hoeflich 2014) – may influence burning instabilities, but it may also be that an alternative explosion scenario is required. Evidence has been put forward that at least some SNe Ia are produced in sub-MC h explosions. Stritzinger et al. (2006a) applied an analytic treatment of the radioactive decay energy deposition function to the UV/Optical/IR (UVOIR) bolometric light curves of 16 nearby SNe Ia at phases between 50–100 days past maximum to place constraints on the total ejected mass, Mej . They found that Mej ranged approximately between 0:5 Mej 1:4 Mˇ and concluded that the fastestdeclining events likely arise from sub-MC h white dwarfs. In a similar analysis, Scalzo et al. (2014) derived ejected masses for a sample of 19 spectroscopically normal SNe Ia using Monte Carlo Markov chain techniques to model the late-time bolometric light curve. A tight correlation was found between the inferred values of

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Mej and decline rate, with most SNe with m15 .B/ > 1:3 having sub-MC h ejecta masses. The implication of these results is that the decline rate–luminosity relation not only reflects a sequence of 56 N i mass but also progenitor mass. Although alternative scenarios to the DDT such as double detonations (Woosley and Weaver 1994), violent white dwarf mergers (Pakmor et al. 2010), and collisions of two white dwarfs in a triple system (Katz and Dong 2012) have the potential for producing subMC h explosions, it is not yet clear if any one of these could by itself produce the continuous range of luminosities and decline rates observed in Fig. 5. Moreover, from a spectral analysis of many of the same SNe studied by Stritzinger et al. (2006a) and Mazzali et al. (2007) concluded that the progenitors of all SNe Ia have masses near MC h .

6

Conclusions

The existence of a peak luminosity–decline relation for SNe Ia was hinted at by the pioneering work of Barbon et al. (1973), Pskovskii (1977, 1984), and Branch (1981) in the 1970s and 1980s. However, it was the revolution in detector technology brought about by the introduction of CCDs in the 1980s and 1990s that provided indisputable evidence that such a relation existed. We now know that SNe Ia display a range of decline rates, or light curve widths, and that there are subtle spectroscopic differences that accompany this photometric sequence. It is also clear that the underlying cause of the peak luminosity–decline relation is the amount of 56 N i synthesized in the explosion. The discovery of the peak luminosity–decline relation was the key breakthrough that permitted SNe Ia to be used to determine distances with errors less than 10 %. Today, in cosmology studies employing hundreds (and, soon, thousands) of SNe Ia, the width–luminosity relation is nothing more than a nuisance parameter that must be taken account of in the quest to determine the nature of dark energy. Nevertheless, the embarrassing fact is that we still do not fully understand why SN Ia explosions produce such a sequence of 56 N i masses. The continuity and tightness of the peak luminosity–decline rate relation is impressive, and it is tempting to infer that a single progenitor/explosion scenario is required to produce it. From theory, we know that many possible supernova models are not consistent with the peak luminosity– decline rate relation (e.g., see Woosley et al. 2007). Thus, the existence of such a relation provides perhaps the most important piece of evidence that will ultimately allow us to decipher the mystery of the nature of the progenitors and explosion mechanism(s) of SNe Ia.

7

Cross-References

 Discovery of Cosmic Acceleration  History of Supernovae as Distance Indicators

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 Light Curves of Type I Supernovae  Low-z Type Ia Supernova Calibration  The Hubble Constant from Supernovae  The Infrared Hubble Diagram of Type Ia Supernovae  Type Ia Supernovae Acknowledgements We gratefully acknowledge support for the CSP by the National Science Foundation under grants AST–0306969, AST–0607438, and AST–1008343.

References Baade W (1938) The absolute photographic magnitude of supernovae. Astrophys J 88:285–304 Barbon R, Ciatti F, Rosino L (1973) On the light curve and properties of Type I supernovae. Astron Astrophys 25:241–248 Betoule M, Kessler R, Guy J, Mosher J, Hardin D, Biswas R et al (2014) Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples. Astron Astrophys 568:A22 Blondin S, Dessart L, Hillier DJ, Khokhlov AM (2013) One-dimensional delayed-detonation models of Type Ia supernovae: confrontation to observations at bolometric maximum. Mon Not R Astron Soc 429:2127–2142 Boisseau JR, Wheeler JC (1991) The effect of background galaxy contamination on the absolute magnitude and light curve speed class of Type IA supernovae. Astron J 101:1281–1285 Branch D (1981) Some statistical properties of Type I supernovae. Astrophys J 248:1076–1080 Burns CR, Stritzinger M, Phillips MM, Kattner S, Persson SE, Madore BF et al (2011) The Carnegie Supernova Project: light-curve fitting with SNooPy. Astron J 141:19–38 Burns CR, Stritzinger M, Phillips MM, Hsiao EY, Contreras C, Persson SE et al (2014) The Carnegie Supernova Project: intrinsic colors of Type Ia supernovae. Astrophys J 789:32–51 Cadonau R, Tammann GA, Sandage A (1985) Type I supernovae as standard candles. In: Bartel N (ed) Supernovae as distance indicators. Lecture notes in physics, vol 224. Springer, Berlin, pp 151–165 Childress MJ, Hillier DJ, Seitenzahl I, Sullivan M, Maguire K, Taubenberger S et al (2015) Measuring nickel masses in Type Ia supernovae using cobalt emission in nebular phase spectra. Mon Not R Astron Soc 454:3816–3842 Conley A, Sullivan M, Hsiao EY, Guy J, Astier P, Balam D et al (2008) SiFTO: an empirical method for fitting SN Ia light curves. Astrophys J 681:482–498 Elias JH, Matthews K, Neugebauer G, Persson SE (1985) Type I supernovae in the infrared and their use as distance indicators. Astrophys J 296:379–389 Filippenko AV, Richmond MW, Branch D, Gaskell M, Herbst W, Ford CH et al (1992a) The subluminous, spectroscopically peculiar Type Ia supernova 1991bg in the elliptical galaxy NGC 4374. Astron J 104:1543–1556 Filippenko AV, Richmond MW, Matheson T, Shields JC, Burbidge EM, Cohen RD et al (1992b) The peculiar Type Ia SN 1991T – detonation of a white dwarf? Astrophys J Lett 384:L15–L18 Folatelli G, Phillips MM, Burns CR, Contreras C, Hamuy M, Freedman WL et al (2010) The Carnegie Supernova Project: analysis of the first sample of low-redshift Type-Ia supernovae. Astron J 139:120–144 Freedman WL, Madore BF, Gibson BK, Ferrarese L, Kelson DD, Sakai S et al (2001) Final results from the Hubble space telescope key project to measure the Hubble constant. Astrophys J 553:47–72 Frogel JA, Gregory B, Kawara K, Laney D, Phillips MM, Terndrup D et al (1987) Infrared photometry and spectroscopy of supernova 1986g in NGC 5128-Centaurus A. Astrophys J Lett 315:L129–L134

2558

M.M. Phillips and C.R. Burns

Goldhaber G, Groom DE, Kim A, Aldering G, Astier P, Conley A et al (2001) Timescale stretch parameterization of Type Ia supernova B-band light curves. Astrophys J 558:359–368 Guy J, Astier P, Baumont S, Hardin D, Pain R, Regnault N et al (2007) SALT2: using distant supernovae to improve the use of Type Ia supernovae as distance indicators. Astron Astrophys 466:11–21 Hamuy M, Phillips MM, Maza J, Suntzeff NB, Schommer RA, Aviles R (1995) A Hubble diagram of distant Type IA supernovae. Astron J 109:1–13 Hamuy M, Phillips MM, Suntzeff NB, Schommer RA, Maza J, Aviles R (1996a) The absolute luminosities of the Calan/Tololo Type Ia supernovae. Astron J 112:2391–2397 Hamuy M, Phillips MM, Suntzeff NB, Schommer RA, Maza J, Smith RC et al (1996b) The morphology of Type Ia supernovae light curves. Astron J 112:2438–2447 Hamuy M, Trager SC, Pinto PA, Phillips MM, Schommer RA, Ivanov V, Suntzeff NB (2000) A search for environmental effects on Type Ia supernovae. Astron J 120:1479–1486 Hamuy M, Folatelli G, Morrell NI, Phillips MM, Suntzeff NB, Persson SE et al (2006) The Carnegie Supernova Project: the low-redshift survey. Publ Astron Soc Pac 118:2–20 Hicken M, Wood-Vasey WM, Blondin S, Challis P, Jha S, Kelly PL et al (2009) Improved dark energy constraints from 100 new CfA supernova Type Ia light curves. Astrophys J 700: 1097–1140 Höflich P, Khokhlov A, Wheeler JC, Phillips MM, Suntzeff NB, Hamuy M (1996) Maximum brightness and postmaximum decline of light curves of Type Ia supernovae: a comparison of theory and observations. Astrophys J Lett 472:L81–L84 Höflich P, Gerardy CL, Fesen RA, Sakai S (2002) Infrared spectra of the subluminous Type Ia supernova SN 1999by. Astrophys J 568:791–806 Höflich P, Krisciunas K, Khokhlov AM, Baron E, Folatelli G, Hamuy M et al (2010) Secondary parameters of Type Ia supernova light curves. Astrophys J 710:444–455 Hoyle F, Fowler WA (1960) Nucleosynthesis in supernovae. Astrophys J 132:565–590 Jha S, Kirshner RP, Challis P, Garnavich PM, Matheson T, Soderberg AM et al (2006) UBVRI light curves of 44 Type Ia supernovae. Astron J 131:527–554 Jha S, Riess AG, Kirshner RP (2007) Improved distances to Type Ia supernovae with multicolor light-curve shapes: MLCS2k2. Astrophys J 659:122–148 Kasen D, Woosley SE (2007) On the origin of the Type Ia supernova width-luminosity relation. Astrophys J 656:661–665 Kattner S, Leonard DC, Burns CR, Phillips MM, Folatelli G, Morrell N et al (2012) The standardizability of Type Ia supernovae in the near-infrared: evidence for a peak-luminosity versus decline-rate relation in the near-infrared. Publ Astron Soc Pac 124:114–127 Katz B, Dong S (2012) The rate of WD-WD head-on collisions may be as high as the SNe Ia rate. ArXiv e-prints 1211.4584 Khokhlov AM (1991) Delayed detonation model for Type Ia supernovae. Astron Astrophys 245:114–128 Kowal CT (1968) Absolute magnitudes of supernovae. Astron J 73:1021–1024 Krisciunas K, Contreras C, Burns CR, Phillips MM et al (in preparation) The Carnegie supernova project I: third photometry data release of low-redshift type Ia supernovae and other white dwarf explosions Krisciunas K, Hastings NC, Loomis K, McMillan R, Rest A, Riess AG, Stubbs C (2000) Uniformity of (V-near-infrared) color evolution of Type Ia supernovae and implications for host galaxy extinction determination. Astrophys J 539:658–674 Krisciunas K, Phillips MM, Suntzeff NB (2004) Hubble diagrams of Type Ia supernovae in the near-infrared. Astrophys J Lett 602:L81–L84 Krisciunas K, Marion GH, Suntzeff NB, Blanc G, Bufano F, Candia P et al (2009) The fast declining Type Ia supernova 2003gs, and evidence for a significant dispersion in near-infrared absolute magnitudes of fast decliners at maximum light. Astron J 138: 1584–1596

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Leibundgut B, Kirshner RP, Phillips MM, Wells LA, Suntzeff NB, Hamuy M et al (1993) SN 1991bg – a Type Ia supernova with a difference. Astron J 105:301–313 Leibundgut B, Schommer R, Phillips M, Riess A, Schmidt B, Spyromilio J et al (1996) Time dilation in the light curve of the distant Type Ia supernova SN 1995K. Astrophys J Lett 466: L21–L24 Lira P (1995) Curvas de luz de las supernovas 1990n and 1991t. Master’s thesis, Universidad de Chile Mandel KS, Narayan G, Kirshner RP (2011) Type Ia supernova light curve inference: hierarchical models in the optical and near-infrared. Astrophys J 731:120–145 Maoz D, Mannucci F, Nelemans G (2014) Observational clues to the progenitors of Type Ia supernovae. Annu Rev Astron Astr 52:107–170 Marion GH, Brown PJ, Vinkó J, Silverman JM, Sand DJ, Challis P et al (2014) SN 2012cg: evidence for interaction between a normal Type Ia supernova and a non-degenerate binary companion. Astrophys J 820:92–107 Maza J, Hamuy M, Phillips MM, Suntzeff NB, Aviles R (1994) SN 1992bc and SN 1992bo: evidence for intrinsic differences in Type Ia supernova luminosities. Astrophys J Lett 424: L107–L110 Mazzali PA, Röpke FK, Benetti S, Hillebrandt W (2007) A common explosion mechanism for Type Ia supernovae. Science 315:825–828 Meikle WPS (2000) The absolute infrared magnitudes of Type Ia supernovae. Mon Not R Astron Soc 314:782–792 Minkowski R (1941) Spectra of supernovae. Publ Astron Soc Pac 53:224–225 Nataf DM (2016) The interstellar extinction towards the Milky Way bulge with planetary nebulae, red clump, and RR Lyrae stars. Publ Astron Soc Aust 33:eo24–33 Nugent P, Phillips M, Baron E, Branch D, Hauschildt P (1995) Evidence for a spectroscopic sequence among Type Ia supernovae. Astrophys J Lett 455:L147–L150 Pakmor R, Kromer M, Röpke FK, Sim SA, Ruiter AJ, Hillebrandt W (2010) Sub-luminous Type Ia supernovae from the mergers of equal-mass white dwarfs with mass 0.9Msolar . Nature 463:61–64 Penney R, Hoeflich P (2014) Thermonuclear supernovae: probing magnetic fields by positrons and late-time IR line profiles. Astrophys J 795:84–96 Perlmutter SA, Deustua S, Gabi S, Goldhaber G et al (1997) Scheduled discoveries of 7+ highredshift SNe: first cosmology results and bounds on q0. In: Ruiz-Lapuente P, Canal R, Isern J (eds) Thermonuclear supernovae. NATO Advanced Science Institutes (ASI) series C, vol 486. Kluwer Academic, Dordrecht, pp 749–763 Perlmutter SA, Aldering G, Goldhaber G, Knop RA, Nugent P, Castro PG et al (1999) Measurements of ˝ and  from 42 high-redshift supernovae. Astrophys J 517:565–586 Phillips MM (1993) The absolute magnitudes of Type Ia supernovae. Astrophys J Lett 413: L105–L108 Phillips MM (2012) Near-infrared properties of Type Ia supernovae. Publ Astron Soc Aust 29: 434–446 Phillips MM, Phillips AC, Heathcote SR, Blanco VM, Geisler D, Hamilton D et al (1987) The Type Ia supernova 1986G in NGC 5128 – optical photometry and spectra. Publ Astron Soc Pac 99:592–605 Phillips MM, Wells LA, Suntzeff NB, Hamuy M, Leibundgut B, Kirshner RP, Foltz CB (1992) SN 1991T – further evidence of the heterogeneous nature of Type Ia supernovae. Astron J 103:1632–1637 Phillips MM, Lira P, Suntzeff NB, Schommer RA, Hamuy M, Maza J (1999) The reddeningfree decline rate versus luminosity relationship for Type Ia supernovae. Astron J 118: 1766–1776 Prieto JL, Rest A, Suntzeff NB (2006) A new method to calibrate the magnitudes of Type Ia supernovae at maximum light. Astrophys J 647:501–512

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Pskovskii YP (1977) Light curves, color curves, and expansion velocities of Type I supernovae as functions of the rate of brightness decline. Astron Zh+ 54:1188–1201 Pskovskij YP (1984) Photometric classification and basic parameters of Type I supernovae. Astron Zh+ 61:1125–1136 Rest A, Scolnic D, Foley RJ, Huber ME, Chornock R, Narayan G et al (2014) Cosmological constraints from measurements of Type Ia supernovae discovered during the first 1.5 yr of the Pan-STARRS1 survey. Astrophys J 795:44–77 Riess AG, Press WH, Kirshner RP (1996a) A precise distance indicator: Type Ia supernova multicolor light-curve shapes. Astrophys J 473:88–108 Riess AG, Press WH, Kirshner RP (1996b) Is the dust obscuring supernovae in distant galaxies the same as dust in the Milky Way? Astrophys J 473:588–594 Riess AG, Filippenko AV, Challis P, Clocchiatti A, Diercks A, Garnavich PM et al (1998) Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron J 116:1009–1038 Riess AG, Macri LM, Hoffmann SL, Scolnic D, Casertano S, Filippenko AV et al (2016) A 2.4 % determination of the local value of the Hubble constant. Astrophys J 826:56–86 Scalzo R, Aldering G, Antilogus P, Aragon C, Bailey S, Baltay C et al (2014) Type Ia supernova bolometric light curves and ejected mass estimates from the nearby supernova factory. Mon Not R Astron Soc 440:1498–1518 Schlafly EF, Finkbeiner DP (2011) Measuring reddening with Sloan Digital Sky Survey stellar spectra and recalibrating SFD. Astrophys J 737:103–125 Schlafly EF, Meisner AM, Stutz AM, Kainulainen J, Peek JEG, Tchernyshyov K et al (2016) The optical-infrared extinction curve and its variation in the Milky Way. Astrophys J 821: 78–102 Schlegel DJ, Finkbeiner DP, Davis M (1998) Maps of dust infrared emission for use in estimation of reddening and cosmic microwave background radiation foregrounds. Astrophys J 500: 525–553 Scolnic DM, Riess AG, Foley RJ, Rest A, Rodney SA, Brout DJ, Jones DO (2014) Color dispersion and Milky-Way-like reddening among Type Ia supernovae. Astrophys J 780:37–46 Seitenzahl IR, Ciaraldi-Schoolmann F, Röpke FK, Fink M, Hillebrandt W, Kromer M et al (2013) Three-dimensional delayed-detonation models with nucleosynthesis for Type Ia supernovae. Mon Not R Astron Soc 429:1156–1172 Sim SA, Seitenzahl IR, Kromer M, Ciaraldi-Schoolmann F, Röpke FK, Fink M et al (2013) Synthetic light curves and spectra for three-dimensional delayed-detonation models of Type Ia supernovae. Mon Not R Astron Soc 436:333–347 Stritzinger M, Leibundgut B, Walch S, Contardo G (2006a) Constraints on the progenitor systems of Type Ia supernovae. Astron Astrophys 450:241–251 Stritzinger M, Mazzali PA, Sollerman J, Benetti S (2006b) Consistent estimates of 56 Ni yields for Type Ia supernovae. Astron Astrophys 460:793–798 Sullivan M, Guy J, Conley A, Regnault N, Astier P, Balland C et al (2011) SNLS3: constraints on dark energy combining the Supernova Legacy Survey three-year data with other probes. Astrophys J 737:102–120 Tammann GA, Leibundgut B (1990) Supernova studies. IV – the global value of H0 from supernovae Ia and the peculiar motion of field galaxies. Astron Astrophys 236:9–14 Tonry J, Schneider DP (1988) A new technique for measuring extragalactic distances. Astron J 96:807–815 Tripp R (1998) A two-parameter luminosity correction for Type Ia supernovae. Astron Astrophys 331:815–820 Tully RB, Fisher JR (1977) A new method of determining distances to galaxies. Astron Astrophys 54:661–673 van den Bergh S (1995) A new method for the determination of the Hubble parameter. Astrophys J Lett 453:L55–L56 Wilson OC (1939) Possible applications of supernovae to the study of the nebular red shifts. Astrophys J 90:634–636

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Woosley SE, Weaver TA (1994) Sub-Chandrasekhar mass models for Type Ia supernovae. Astrophys J 423:371–379 Woosley SE, Kasen D, Blinnikov S, Sorokina E (2007) Type Ia supernova light curves. Astrophys J 662:487–503

Low-z Type Ia Supernova Calibration

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Mario Hamuy

Abstract

The discovery of acceleration and dark energy in 1998 arguably constitutes one of the most revolutionary discoveries in astrophysics in recent years. This paradigm shift was possible thanks to one of the most traditional cosmological tests: the redshift-distance relation between galaxies. This discovery was based on a differential measurement of the expansion rate of the universe: the current one provided by nearby (low-z) type Ia supernovae and the one in the past measured from distant (high-z) supernovae. This paper focuses on the first part of this journey: the calibration of the type Ia supernova luminosities and the local expansion rate of the universe, which was made possible thanks to the introduction of digital CCD (charge-coupled device) digital photometry. The new technology permitted us in the early 1990s to convert supernovae as precise tools to measure extragalactic distances through two key surveys: (1) the “Tololo Supernova Program” which made possible the critical discovery of the “peak luminosity-decline rate” relation for type Ia supernovae, the key underlying idea today behind precise cosmology from supernovae, and (2) the Calán/Tololo project which provided the lowz type Ia supernova sample for the discovery of acceleration.

Contents 1 2 3

4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Brief History on the Role of Type Ia Supernovae in Cosmology . . . . . . . . . . . . . . . . The Modern Era of Type Ia Supernova Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Tololo Supernova Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Calán/Tololo Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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M. Hamuy () Astronomy Department, University of Chile, Santiago, Chile Millennium Institute of Astrophysics, Santiago, Chile e-mail: [email protected]; [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_101

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5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

We live in an accelerating universe due to a mysterious dark energy that comprises 70 % of the universe. While this paradigm is quite familiar to us today, it was virtually unimaginable until a few years. How did we get to this intriguing situation? Through one of the most traditional cosmological tests: the redshift-distance relationship between galaxies, a.k.a. Hubble diagram, in recognition to E. Hubble who discovered this law in 1929 and, incidentally, the global expansion of the universe (Hubble 1929). This discovery was based on two fundamental ingredients: the slow and painstaking process by Vesto Slipher of measuring redshifts for a few dozen “nebulae” at the beginning of the twentieth century (Slipher 1917) and the careful measurement by Hubble of extragalactic distances using Cepheid variables (Hubble 1929). Hubble’s law established a proportionality between redshift and distance, where the slope of this relationship (a.k.a Hubble constant, H0 ) is a universal constant that corresponds to the current expansion rate of the universe. The “0” suffix is meant to represent the expansion rate at the present time, and its most accepted value today lies between 68 and 72 km s1 Mpc1 . Given the finite nature of the speed of light, as one observes more distant galaxies, we are also entering into the past of the universe, so much so that one should be able to observe the change in the expansion rate of the universe along its evolution. According to Einstein’s theory of general relativity, one would expect the universe to slow down owing to its own mass. Ever since the discovery of cosmic expansion, the study of the Hubble diagram over a wide range of redshifts offered the promise to “weigh” the universe, measure its deceleration, and determine its fate and geometry, thus becoming one of the most favored cosmological tests during the twentieth century. Since the effects of deceleration were predicted to become noticeable only at high redshifts (>0.3) and at the level of a few % in distance, the observational challenge focused in identifying and calibrating the luminosity of luminous astrophysical sources. Various techniques were attempted in order to measure precise distances using the galaxy luminosities themselves, such as the Tully-Fisher and surface brightness fluctuations methods, among others, but none of them proved to be sufficiently precise to allow a successful measurement of deceleration. In parallel, and ever since the pioneering work of Baade and Zwicky who recognized in 1938 that supernova (SNe) constituted a new class of very luminous astrophysical objects (Baade 1938; Zwicky 1938), the astronomical community began to value the potential of SNe as extragalactic distance indicators. The attention was primarily focused on type Ia SNe, those arising from the thermonuclear explosion of white dwarfs, which proved to be the most luminous and homogeneous subclass of SNe. It took, however, nearly 60 years to obtain a precise calibration of the SN Ia luminosities to allow

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the extension of the Hubble diagram to sufficiently high redshifts and obtain a significant measurement of the change of the expansion rate of the universe. The answer in 1998–1999 came as a big surprise: contrary to the theoretical expectations, the expansion rate has been increasing over the past five billion years; in other words, the universe is currently accelerating, thus challenging what became the standard prediction of cosmology, originally derived by Georges Lemaître from the first versions of general relativity. The revolutionary discovery of acceleration must be understood as a differential measurement of the expansion rate: the current one provided by nearby (low-z) and the one in the past measured from distant (high-z) SNe. In this paper, I focus on the first part of this amazing journey: the key calibration of the SNe Ia luminosities and the local expansion rate of the universe. In Sect. 2 I give a brief history on the role of SNe Ia in cosmology in the era of the photographic technology. Sect 3 refers to the revolutionary changes brought about by the introduction of CCD digital photometry in the usage of supernovae as precise tools to measure extragalactic distances, focusing on two key programs: (1) the “Tololo Supernova Program” which made possible the critical discovery of the “peak luminosity-decline rate” relation for SNe Ia (the key underlying idea today behind precise cosmology from SNe Ia) and (2) the Calán/Tololo project which provided the lowz SNe Ia sample for the discovery of acceleration. Finally, Sect. 4 summarizes the contents of this paper.

2

A Brief History on the Role of Type Ia Supernovae in Cosmology

For a thorough history of the role of SNe Ia in cosmology, the reader is referred to the accompanying paper by Leibundgut ( Chap. 100, “History of Supernovae as Distance Indicators”). Here I present only a brief summary to provide historical context for this paper. The discovery of acceleration through SNe Ia is the pinnacle of a series of scientific efforts that goes back to the pioneering work of Baade and Zwicky who recognized in 1938 that SNe constituted a new class of very luminous astrophysical objects (Baade 1938; Zwicky 1938). The first Hubble diagram from SNe Ia was presented by Kowal (1968) based on 16 objects with photographic photometry (before the recognition of the Ia subclass by Elias et al. (1985), yielding a dispersion of  = 0.61 mag, significantly less than the previous studies, and an average Mpg D 18:6 C 5log.H0 =100//. In the early 1970s, Pskovski (1971) detected that, despite their overall similarity, SNe I have differences in the post-maximum rate of decline. Based on an increased dataset of SN I light curves obtained in the course of the Asiago Supernova Program, Barbon et al. (1973) also noted that it was difficult to fit all SN I photometry with a unique template light curve and admitted the possibility of the existence of two subclasses: “fast” and “slow.” Pskovski (1977) went a step further, showing a range of a factor of two in the decline rate of SNe I and a possible dependence of the type I peak magnitudes with decline rate, noting that “the absolute magnitudes

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of Type I supernovae of junior classes such as I.6 are 0.9 mag brighter, on the average, than those of class I.14 supernovae.” In modern language, Pskovski (1977) was reporting that slowly declining SNe were brighter than rapidly declining objects. Contrary to the evidence previously reported, Cadonau et al. (1985) analyzed a sample of 22 SNe I to construct a mean light curve of SNe Ia, noting that, “individual SNe I show generally no systematic deviations from the template light curves” and that ”the peak luminosity of absorption-free SNe I is also uniform with an intrinsic rms scatter of = 0.35. ApJ 483:565 Perlmutter S, Aldering G, Goldhaber G, Knop RA, Nugent P, Castro PG et al (1999) Measurements of ˝ and  from 42 high-redshift supernovae. ApJ 517:565 Phillips MM (1993) The absolute magnitudes of Type Ia supernovae. ApJ 413:L105 Phillips MM, Phillips AC, Heathcote SR, Blanco VM, Geisler D, Hamilton D et al (1987) The type Ia supernova 1986G in NGC 5128 – optical photometry and spectra. PASP 99:592

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Phillips MM, Wells LA, Suntzeff NB, Hamuy M, Leibundgut B, Kirshner RP et al (1992) SN 1991T – further evidence of the heterogeneous nature of type Ia supernovae. AJ 103:1632 Pskovski YP (1971) Photometric aspects of Type I supernovae. Sov Astron 14:798 Pskovski YP (1977) Light curves, color curves, and expansion velocity of type I supernovae as functions of the rate of brightness decline. Sov Astron 21:675 Riess AG, Press WH, Kirshner RP (1995) Using Type Ia supernova light curve shapes to measure the Hubble constant. ApJ 438:L17 Riess AG, Filippenko AV, Challis P, Clocchiatti A, Diercks A, Garnavich PM et al (1998) Observational evidence from supernovae for an accelerating universe and a cosmological constant. ApJ 116:1009 Riess AG, Kirshner RP, Schmidt BP, Jha S, Challis P, Garnavich PM et al (1999) BVRI light curves for 22 type Ia supernovae. ApJ 117:707 Slipher VM (1917) Radial velocity observations of spiral nebulae. The observatory, vol 40, p 304–306 Stritzinger MD, Phillips MM, Boldt LN, Burns C, Campillay A, Contreras C et al (2011) The Carnegie Supernova project: second photometry data release of low-Redshift type Ia supernovae. AJ 142:156 Tammann G, Leibundgut B (1990) Supernova studies. IV – the global value of H0 from supernovae Ia and the peculiar motion of field galaxies. A&A 236:9 Zwicky F (1938) On the search for supernovae. PASP 50:215

The Hubble Constant from Supernovae

103

Abhijit Saha and Lucas M. Macri

Abstract

The decades-long quest to obtain a precise and accurate measurement of the local expansion rate of the universe (the Hubble Constant or H0 ) has greatly benefited from the use of supernovae (SNe). Starting from humble beginnings (dispersions of 0:5 mag in the Hubble flow in the late 1960s/early 1970s), the increasingly more sophisticated understanding, classification, and analysis of these events turned type Ia SNe into the premiere choice for a secondary distance indicator by the early 1990s. While some systematic uncertainties specific to SNe and to Cepheid-based distances to the calibrating host galaxies still contribute to the H0 error budget, the major emphasis over the past two decades has been on reducing the statistical uncertainty by obtaining ever-larger samples of distances to SN hosts. Building on early efforts with the first-generation instruments on the Hubble Space Telescope, recent observations with the latest instruments on this facility have reduced the estimated total uncertainty on H0 to 2.4 % and shown a path to reach a 1 % measurement by the end of the decade, aided by Gaia and the James Webb Space Telescope.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Distance Scale Problem Before HST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A. Saha () Kitt Peak National Observatory, National Optical Astronomy Observatory (NOAO), Tucson, AZ, USA e-mail: [email protected] L.M. Macri Department of Physics and Astronomy, Texas A&M University, College Station, TX, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_102

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3

Early Efforts with HST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Imaging with WF/PC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Improvements in Classification of SNe Ia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The WFPC2 Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Unsolved Issues Awaiting Further Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Recent Efforts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

In this article we take a somewhat chronological view through the process of establishing type Ia supernovae (hereafter, SNe Ia) as standard candles, and the developments, sometimes quite dialectic, which shaped our present-day understanding of the precision and accuracy with which they serve as indicators of luminosity distance. Progress has been dramatic and rapid over the last three decades, driven first by the race to resolve the dichotomy between the “long” and “short” distance scales and the consequent discord over the Hubble Constant (H0 ) that divided investigators into at least two distinct “camps.” In Sect. 2 we sketch the state of the subject before the advent of the Hubble Space Telescope (HST) and trace the growing promise of SNe Ia as standard candles, and how finer characterization of their light curves and spectra produced improved determinations of their peak luminosity. HST has been essential for applying SNe Ia as standard candles to measure H0 . The history and evolution of our understanding has been related in this article in “early” and “recent” sects. (3 and 4 respectively): the two authors of this article, AS and LM, have been respectively associated with these two periods. There have been, and continue to be, points of difference in the interpretation of these experiments. The object of this article is to lay these out in the spirit of dialectics and allow the reader and future investigations to resolve the remaining questions.

2

The Distance Scale Problem Before HST

Before the advent of HST, which produced a tenfold increase in spatial resolution compared to ground-based imaging (corresponding also to a hundredfold increase in contrast against the background for a point source), there were two distinct classes of distance indicators to galaxies. Those close enough to be anchored by distance measurements within the galaxy were referred to as “primary,” while those that required calibration using measurements in external galaxies but could probe to larger distances were called “secondary.” Examples of the former are the Cepheid period-luminosity relation (hereafter, PLR; Leavitt and Pickering 1912), RR Lyraes, and detached eclipsing binaries (DEBs), while the latter include the Faber-Jackson, Tully-Fisher, and Dn   relations and the tip of the red giant branch (TRGB) and

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the surface brightness fluctuation (SBF) methods. The goal then (as it is now) was to measure distances that were far enough to probe the “smooth” Hubble flow, i.e., where the peculiar velocity perturbations over the expansion velocity of the cosmic manifold become negligible. The problem was enunciated succinctly in Sandage and Tammann (1974), where they embarked upon the task of refining the calibration of various secondary distance indicators, using Cepheid-based distances available at the time, to galaxies out to the M81 group. From the ground, the goal of reaching to distances where the Hubble flow is undisturbed was not realizable. In his seminal paper, Kowal (1968) showed that type I supernovae (hereafter, SNe I) in the Hubble flow had a dispersion of 0:6 mag and expressed “[: : :] considerable hope that the magnitudes of type I supernovae, at least, can be used as distance indicators [: : :] visible at great distances.” His work had to necessarily assume a value of H0 estimated by other means since no absolute calibration of SNe existed at the time. In closing, the author stated that “[: : :] distances of the parent galaxies of the nearer supernovae may soon become available through studies of Cepheid variables, HII regions, or red supergiant stars.” The possibility of SNe as secondary distance indicators was very attractive because of their large luminosities and the promise that at least one class could have homogeneous light curves (Pskovskii 1967). Oke and Searle (1974) summarized spectroscopic work on this field, drawing attention to the great similarity in the spectra of most SNe I even as they evolve in phase. This provided further interest and rationale in using them as standard candles. Perhaps the earliest attempts to estimate H0 directly from SNe were those by Branch and Patchett (1973) and Kirshner and Kwan (1974), who applied the BaadeWesselink method to types I and II, respectively. Both studies were suggested by L. Searle, who discussed the method in Searle (1974). However, SNe were not among the viable secondary distance indicators at the time due to the lack of fundamental distances to their hosts (Tammann 1974). It is well known that when observing a magnitude-limited sample of any standard candle (which is typically the case), the intrinsic scatter in its luminosity causes only the brighter ones to be included in the sample as one approaches the observed magnitude limit. The resulting bias, called the Malmquist bias, is an important consideration for interpretation of the Hubble diagram. There is a similar bias due to observational scatter in the measured brightness, which in principle can be mitigated by better observations. However, the Malmquist effect is due to the intrinsic scatter in the luminosity, and is a property of the standard candle itself, and standards that show low or negligible scatter in their intrinsic properties are therefore preferred. Sandage and Tammann (1982) argued that the Hubble diagram from a subsample of SNe I, chosen in elliptical galaxy hosts at high galactic latitude to minimize extinction from either galactic or host-galaxy dust, showed a very small dispersion consistent with the prevalent measuring errors of the time. Urged on, therefore, by the promise of having a distance indicator virtually free of Malmquist bias, they proceeded to establish a calibration for absolute peak brightness for SNe I using the brightest blue and red stars in two host galaxies: IC 4182 (SN 1937C) and NGC 4214 (SN 1954A).

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Beginning with Elias et al. (1985), a further distinction was made within the SNe I class based on their infrared light curves. The more common of these were now labeled type Ia, while others which have slower declining light curves were labeled type Ib. This work demonstrated that SNe Ia were potentially (pending a larger sample of unambiguous members) very good standard candles in the infrared, with scatter below 0:2 mag. Recognition of the spectroscopic differences within SNe I at optical wavelengths and spectroscopic criteria for identifying SNe Ia were developing at approximately the same time (e.g., Uomoto and Kirshner 1985; Wheeler and Levreault 1985) and were reviewed in Harkness and Wheeler (1990). The Asiago Supernova Catalog (Barbon et al. 1989) was very influential in the compilation of light curves, and in the creation of photometric templates for SNe Ia. Aided by theoretical understanding of SNe Ia in addition to the observed nearhomogeneity of their light curves (a standard B band template light curve was available from Cadonau 1987) and spectra, as well as the low observed scatter in the B and V band Hubble diagrams (Branch and Tammann 1992; Leibundgut and Tammann 1990), it was argued that the peak brightness of SNe Ia should serve as standard candles with intrinsic scatter of only 0:25 mag. This claim would be severely tested, challenged, and refined in the years to come, but it was a driving force at the time and already hinted at a standard candle with potentially less scatter than all other secondary indicators. By virtue of their extreme luminosities, SNe could reach farther than the other distance indicators and directly into the smooth Hubble flow. Yet, there were still no known bona fide SNe I with adequately recorded light curves in galaxies within reach of Cepheids from the ground. There were two additional attempts of note to determine the absolute peak brightness of SNe I, now restricted to SNe Ia, before Cepheids in their host galaxies could be identified with HST. Leibundgut and Tammann (1990) related the light curves of nine SNe Ia in galaxies in the Virgo cluster to an adopted distance for the cluster to obtain MB .max/ D 19:79 ˙ 0:12. The distance to Virgo was then (and to some extent even today continues to be) a matter of debate. Branch (1992) calculated the peak brightness from nickel production and radioactive decay where a SN Ia explosion “is thought to be the complete thermonuclear disruption of a carbon-oxygen white dwarf that accretes matter from a companion star until it approaches the Chandrasekhar mass.” The state of understanding of SNe Ia and their light curves just before the launch of HST is summarized in Branch and Tammann (1992). There were other efforts in progress, whose results would emerge after the first Cepheid-based calibration of SNe Ia peak luminosity was obtained. The increasing availability of digital detectors throughout the late 1980s and early 1990s enabled the collection of larger, bettersampled, and more homogeneous sets of light curves in multiple filters; chief among these were the Calán-Tololo survey (Hamuy et al. 1993, 1995, 1996b) and the CfA survey (Riess et al. 1999). These would lead to refinements in light curve analysis, whose discussion is deferred to a later section. Of parallel interest is the use of core-collapse SNe as distance indicators; this continued to develop with a thorough study of SN 1979C in M100 by Branch et al. (1981), who obtained a 15 % estimate of the distance to this galaxy. Unfortunately,

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any determination of H0 from this object was subject to even greater uncertainty given that the infall into the Virgo cluster was poorly constrained at that time. SN 1987A was the subject of intense scrutiny, and in the following years, the “expanding photosphere method” was further refined Baron et al. (1995); Eastman et al. (1996); Schmidt et al. (1992), including a determination of H0 with roughly equal 10 % statistical and systematic uncertainties (Schmidt et al. 1994).

3

Early Efforts with HST

The development of HST led two teams to propose large programs to determine H0 . The “HST Key Project on the Extragalactic Distance Scale,” initially led by Aaronson and Mould, undertook a comprehensive calibration of multiple secondary distance indicators (for a critical review of these methods, see Jacoby et al. 1992). The other team was led by Sandage and Tammann who, motivated by the promise of SNe Ia, focused on their Cepheid-based calibration believing that they would outperform the competing secondary indicators. Their arguments are best stated in Sandage et al. (1992). Sandage and Tammann (1993) presented Hubble diagrams using historical data on nearby SNe Ia in three different passbands (pg, B, and V ), showing how the scatter diminished going toward redder passbands. They surmised that the effects of uncertain host-galaxy reddening diminish with increased wavelength and help to reduce the scatter, dropping from  D 0:65 mag in mpg to only  D 0:36 in V . They argued that by extension the intrinsic scatter is even smaller than the value for V , which effectively makes them free from Malmquist bias. Their Hubble diagrams did not include objects with peculiar spectra or signs of having significant reddening, an approach that they would refine later. There was at the time a great rift among investigators relating to the determination of H0 . The exposition of Sandage and Tammann through their classic series of papers in the 1970s sought to establish H0  55 km s1 Mpc1 , but were contradicted by others (well summarized in de Vaucouleurs 1993; van den Bergh 1992). One of the most contentious issues between the so-called long- and short distance scales was about the importance and role of the Malmquist bias, and the other about the role of reddening. That SNe Ia could remove the Malmquist bias from the equation was one of its key attractions, the other being that it could probe distances much further out and determine the deceleration in the cosmic expansion. The plans of both teams were hindered by the spherical aberration in the HST primary mirror: point sources were imaged with a sharp core, but with a large fraction of light going into an extended skirt around the core, with structure that lacked azimuthal symmetry. It would be a few years before the flaw could be mitigated with a repair mission.

3.1

Imaging with WF/PC

Despite the significant problems introduced by spherical aberration, the Sandageled collaboration proceeded to discover and measure Cepheids in the two nearest

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then-known SNe Ia host galaxies: IC 4182 (SN 1937C) and NGC 5253 (SN 1972E and SN 1895B). The first to be done was IC 4182 (Saha et al. 1994; Sandage et al. 1992), where the Cepheid V and I PLRs were used to derive a dereddened distance modulus of 28:36 ˙ 0:09 mag (4.7 Mpc) and a consequent value of MV .max/ D 19:72 ˙ 0:13 mag for SN 1937C, using previously published photometry of its light curve in the pg and vis systems. The Cepheids and their colors are consistent with those observed in the Large Magellanic Cloud (LMC), lending confidence in their measurement. The inferred distance was found by Saha et al. (1994) to be consistent with an estimate based on the TRGB. The preliminary resulting value for H0 was 52 ˙ 9 in the usual units. Soon after this, the source material for the light curve of SN 1937C was critiqued, and concerned conflicting takes on the color response of the vis photometry (Pierce and Jacoby 1995; Schaefer 1996). Pierce and Jacoby (1995) measured a light curve from previously unused V emulsion imaging of SN 1937C by Baade and Zwicky, whose results were also debated between Schaefer (1996) and Jacoby and Pierce (1996), who gave a revised value of H0 D 66 ˙ 5. The Cepheid-based distance of Saha et al. (1994) to IC 4182 has never been challenged: Gibson et al. (2000) obtained an identical value and it is in agreement with later determinations of distance to other members of the Canes Venatici group of galaxies to which IC 4182 belongs (Karachentsev 2005). Both the Cepheid distance and the supernova light curve are consistent with zero extinction, as gleaned from their colors. While in IC 4182 the reddening effects are small and essentially negligible, the complications with the treatment of reddening began to show themselves with the next target. Ideally, one would like to have an unreddened/unextinguished or true distance modulus to the host galaxy, which involves correcting for both the foreground extinction within the Milky Way and extinction in the host galaxy. A similar correction is then also needed for the supernova, which may in general suffer different host-galaxy extinction (further complicated because we now know that the total-to-selective extinction toward SNe Ia can be quite different from the galactic reddening law). Each set of corrections bring their own uncertainties, which in special circumstances, one might be able to finesse. Different investigators may not agree on the assumptions needed for such mitigation and fall back on the formally correct way for consistency, bringing along the attendant uncertainties in their full form. The Cepheid distance to NGC 5253 (Saha et al. 1995) was beset by a higher degree of crowding and confusion, and by the absence of longer period (and hence brighter) Cepheids. They reported an apparent distance modulus of .m  M /V D 28:08 ˙ 0:10 mag and argued that SN 1972E would have suffered the same extinction. From the (photoelectric) supernova photometry by Ardeberg and de Groot (1973), it was surmised that MV .max/ D 19:50 ˙ 0:21 mag. Saha et al. (1995) argued that the TRGB distance from I -band photometry from the HST WF/PC images was consistent with the apparent modulus, and within the measurement errors, with near-zero reddening from the host galaxy (and E.V I /  0:08 mag of foreground galactic reddening). It was argued that SN 1972E, which is far from the center of NGC 5253, would suffer no more reddening from within the host galaxy than the Cepheids. Gibson et al. (2000), in re-deriving the distance from

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the same data (with additional observations from WFPC2) obtained a true distance modulus of .m  M /0 D 27:61 ˙ 0:11 mag. Further comparison of the derived peak luminosity of the supernova is complicated by different source light curves and treatment of reddening and is beyond the scope of this review, but can be had by a detailed reading of Gibson et al. (2000) and references therein. It is also worth noting that the photometry of the same data yielded results within expected possible differences (of a few hundredths of a magnitude), and the difference in distance moduli was driven by differences in the Cepheid samples used. The Cepheids in common to both studies yield the same results, but each study used a nonoverlapping set of Cepheids compared with the other, and it is the differences in these samples that drives the different final distance moduli, as noted by Gibson et al. (2000). These issues would reappear later, sometimes in more striking ways, as host galaxies increasingly farther away were investigated with a repaired HST.

3.2

Improvements in Classification of SNe Ia

By the time HST was serviced, with WFPC2 replacing WF/PC and curing the imaging pathology due to the misshapen primary mirror, there were several other refinements taking place regarding our state of knowledge of SNe light curves and spectra. The first of these was by Phillips (1993), comparing the decline rate of SNe Ia light curves characterized by the quantity m15 .B/ (the decline in brightness in the B band in the first 15 days after B maximum) to their absolute peak magnitudes estimated from distances to their host galaxies via the TullyFisher relation or the SBF method. He surmised that faster-declining SNe Ia are intrinsically fainter than the ones that decline slowly. This echoed earlier work on SNe light curve properties by Pskovskii (1977). If the light curves of the Cepheidcalibrated SNe Ia differ from those that define the Hubble diagram, the Phillips relation necessitates a systematic correction. A meme emerged that SNe Ia were not standard candles, but “standardizable” candles (even though the meme is never applied to Cepheids, which have an analogous period dependence). At about the same time, the results of the Calán-Tololo survey (Hamuy et al. 1993), monitoring light curves and spectra of 0:01 . z . 0:1, lead to unprecedentedly clean Hubble diagrams (Hamuy et al. 1995). The detailed light curves permitted the study of differences within the type Ia subclass in a larger sample, and with more precise scrutiny. In a seminal paper, Hamuy et al. (1996a) re-derived the peak luminosity vs. m15 .B/ relation using light curves from the Calán-Tololo survey in the smooth Hubble flow: relative distances to them were assigned according to recession velocity. A definitive dependence was derived, but with a slope very much more muted than the original Phillips relation; the reason for the difference in slopes likely lies in the fact that the distances assigned by the recession velocities have far less scatter than those from secondary distance indicators. Using their relation, the scatter in the Hubble diagram from SNe Ia was reduced to 0:15 mag rms (see Table 3 of Hamuy et al. 1996a,for details) for objects that did not show excessive

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reddening. Riess et al. (1995) and Riess et al. (1996) presented a novel technique to simultaneously fit photometry in multiple passbands based on a linear model of corrective templates, derived from the light curves published by Hamuy et al. (1995) and Riess et al. (1999). This so-called multicolor light curve shape method (MLCS) was the first to simultaneously determine the luminosity correction and measure the reddening to a given SN Ia, yielding Hubble diagrams with reduced scatter. There were also other correlations that came to light: SNe Ia were on average brightness in late-type galaxies (e.g., Hamuy et al. 1995; Riess et al. 1999); their luminosities correlate with color at maximum light (e.g., Tripp 1998); and the more luminous SNe Ia also show higher ejection velocities as measured by the Doppler shift of the blue edge of calcium absorption (e.g., Fisher et al. 1995). While these diagnostics correlated among themselves for the most part, it was also clear that subtyping within the SNe Ia class was not a one-parameter affair. In particular, the decline rate relation still fails to account for all the objects with very steep decline rates (m15 .B/ > 1:7): e.g., Hamuy et al. (1995) pointed out that SN 1992bo and SN 1991bg, which have very similar (but large) values of m15 .B/, differ in absolute peak brightness by nearly 2 mag. The spectra of these two SNe however show significant differences. Branch et al. (1993) classified SNe Ia spectra into three subcategories: (i) those with time-evolving spectra that resemble those of SNe 1981B, 1989B, 1992A, and 1972E; (ii) those like SN 1991T, which at early phases show “unusually weak lines of SiII, SII, and CaII but prominent features of FeIII”; and (iii) those like SN 1986G and SN 1991bg, which show absorption features of TiII. Of the 84 spectra classified by them, 83 % were in the first, “normal” category (later literature refers to this spectroscopic subclass as “Branch normal”). They also recognized subtle variations in spectra within the subclasses and that all of the spectra could be arranged in a sequence, with SN 1991T at one extreme, followed by the “normal” SNe, and finally by the third category. At the time, SN 1991T was in a class by itself, with all the rest of the “peculiar” SNe being like SN 1986G and SN 1991bg. Branch et al. (1993) also noted that the spectral sequence parallels the light curve decline rates, with SN 1991T as the slowest, and SN 1991bg and SN 1986G among the slowest. Interestingly though, SN 1992bo has “normal” spectra, and quite distinct from the spectra of SN 1991bg, whose light curve declines only slightly faster than SN 1992bo, defying any claim that the distinctions among the SNe Ia can be characterized as a single-parameter family. The decline rate vs. luminosity relation for only the “Branch-normal” SNe Ia from the Calán-Tololo survey is only half again of that derived by Hamuy et al. (1996a), since it samples a restricted range of m15 .B/, where the dependence is shallow.

3.3

The WFPC2 Era

Cepheid distances to farther host galaxies, using the repaired HST with WFPC2, were obtained as soon as the camera became available: NGC 4536 (SN 1981B;

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Saha et al. 1996a), NGC 4496F (SN 1960F; Saha et al. 1996b), and NGC 4639 (SN 1990N; Saha et al. 1997), where the SNe were all “Branch normal,” and relatively slow decliners. In Saha et al. (1997), the authors constructed a Hubble diagram with SNe Ia recession velocity satisfying 3 < log v < 4:5. They applied a color cut for peak brightness color (after correcting for foreground reddening within the galaxy) 0:25 < .B  V /max < 0:25, meant to bracket the intrinsic color range within which the Branch-normal SNe Ia layer, and also at the same time reject SNe Ia that were highly reddened due to host-galaxy extinction. The SNe Ia with Cepheid distances thus far also satisfied this criterion. The decline rate relation for a subsample chosen this way was derived independently and used to de-trend both calibrated SNe Ia and those that probed the Hubble flow. Parsing the data in multiple ways, including using a restricted sample to spiral galaxies only, they obtained H0 values close to 60, in the usual units. A prescient statement appears in their paper: “A most unexpected result is that distant SNe Ia in spirals ( 3:8 < log v < 4:5) are fainter than the nearer ones (3:0 < log v < 3:8) by 0:27 ˙ 0:13 mag in B and 0:16 ˙ 0:12 mag in V . Even if SNe Ia are good standard candles, this is contrary to all selection effects that bias the most distant SNe Ia to be overluminous.” With the paucity of available SNe Ia hosts that could be reached with WFPC2, the next results were from two interesting cases. SN 1989B in NGC 3627 (Saha et al. 1999) was a Branch-normal SNe Ia, but one with high yet known hostgalaxy reddening. It could be added to the calibrators after explicitly accounting for the host-galaxy reddening. SN 1991T in NGC 4527 (Saha et al. 2001b) exhibited a very slow decline rate and was studied to examine how its peak luminosity differed relative to other objects in the decline-rate vs. luminosity relation. Both these galaxies, viewed nearly edge on, exhibit extreme stellar crowding and differential internal reddening, which likely affected the photometry of the discovered Cepheids. For SN 1991T, no large difference in luminosity with respect to the other Cepheid-calibrated SNe Ia was seen, but crowding effects could have resulted in underestimation of the supernova luminosity. For SN 1989B, the reanalysis of the same data by Gibson et al. (2000) would produce very discrepant results: as in the case of NGC 5253, the cause revolves around differences in the Cepheid samples and in the way reddening is treated, even though the photometry of individual Cepheids in common hardly differ between the two studies. A new SNe Ia, SN 1998aq in NGC 3982, and within range of WFPC2 photometry, became available, and a Cepheid distance was obtained (Saha et al. 2001a). In addition to the increasingly finer categorization of SNe Ia described above, there were also emerging questions about the accuracy and universality of the Cepheid PLR. Kennicutt et al. (1998) measured a metallicity dependence for the zero point of the PLR, by measuring Cepheids in both inner and outer regions of M101, which have very different attendant metallicity as measured from the gas-phase emission lines. Even though the size and even the sign of the metallicity dependence continue to be debated, consideration of the metallicity of the Cepheid progenitor population has become necessary. Combining all the elements of systematics discussed above, Sandage et al. (2006) summarized the results of their

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team’s investigations, with a best estimate for H0 of 62:3 ˙ 1:3 .stat:/ ˙ 5 .sys:/. This contrasted somewhat with the results from the overall Key Project result from Freedman et al. (2001) of 72 ˙ 8 km s1 Mpc1 , which was by now heavily weighted by the Gibson et al. (2000) reanalysis of the Sandage et al SNe Ia sample. The key differences arose not from the photometry, but from sample selection for Cepheids (see Sect. 3.1) and treatment of reddening (see Sect. 3.4).

3.4

Unsolved Issues Awaiting Further Studies

With the progressive improvement in our understanding of the relative luminosity of SNe Ia as gleaned from the residuals in the Hubble diagram, with scatter less than 0.15 mag, the focus of systematic uncertainties turned toward uncertainties in the Cepheid distance scale. Both the Sandage team and the “Key Project” team based their final results assuming/asserting a distance modulus to the LMC of 18.50, with further corrections for metallicity dependence from the empirical study by Kennicutt et al. (1998). Alternate results were available (e.g., Romaniello et al. 2006), which contest the magnitude and even the sign of the metallicity dependence. Implicit in all of these is tacit assumption that the helium-to-metal ratio (Y =Z) has no cosmic variance, since such a variation can drive very significant changes in the luminosities of Cepheids (Fiorentino et al. 2002). The mechanics of performing the photometry and discovering and measuring Cepheids in the WFPC2 images brought several issues to surface that even today do not have definite solutions. The combination of stellar crowding and undersampling of the stellar PSF by these detectors may well have resulted in systematic measurement bias that affected the work of both the Sandage and the “Key Project” teams. Artificial star tests (Ferrarese et al. 2000; Saha et al. 2000) indicated that the effects were not severe. However, for Cepheids in NGC 4536 (Saha et al. 1996a), there is clear evidence that individual Cepheids with higher-quality light curves result in larger dereddened distances than from those with poorer light curves (see Fig. 7 in Saha et al. 1996a). A key issue is that of correcting for reddening to the Cepheids. Madore (1982) constructed the so called Wesenheit relation, which combines the P-L relations in two (or three) distinct passbands into one relation that effectively marginalizes the reddening. Freedman et al. (2001) used a Wesenheit relation uniformly for all their distance determinations. Sandage et al. (2006) argued that application of the Wesenheit relation has the net effect of interpreting all color excesses/anomalies in the Cepheid photometry as reddening, and chose instead to treat each galaxy by what they considered optimal. They argued that application of the Wesenheit relation to correct for reddening can amplify both intrinsic color variations and any systematic measurement biases (see Fig. 11 in Saha et al. 1996a). A more detailed critique can be found in Saha (2003). These effects become progressively stronger as distance to the galaxy under study increases, implying that such hidden systematics affects more distant galaxies with increasing severity. They are neither fully systematic, nor random, rather they come from the effect of measurement biases that are amplified

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through the application of other systematic corrections. Szabados and Klagyivik (2012) review several sources of uncertainty in the Cepheid PLR, several of which may be lensed unfavorably through the Wesenheit relation. There has been a trend in later literature to disregard SNe Ia with light curves from the pre-CCD era; however there have not been suitable SNe Ia nearer than the Virgo cluster since the advent of CCDs (with the exception of SN 2011fe in M101). Is there a trade-off between more accurate distances to nearer SNe Ia with less certain photometry on the one hand, and accurate photometry but poorer distances to SNe Ia that are farther away? The case of SN 2011fe illustrates the problem. This object erupted after a multitude of distance estimates of M101 from Cepheids and TRGB measures using HST data were already in the literature. Matheson et al. (2012) showed that the derived distances from these various studies span a range of 0.5 mag in distance modulus. Even if the reddening to the supernova were understood perfectly, the derived value of H0 could be held hostage to the disagreements over the distance modulus to M101. This highlights the danger of relying on a small number of calibrators and the importance of ensuring consistent absolute calibrations of different primary distance indicators and critical comparisons of their relative distances over overlapping ranges.

4

Recent Efforts

The discovery that type II “plateau” supernovae could also be turned into “standardizable candles” (Hamuy and Pinto 2002) led to significant reductions in the scatter of the Hubble diagrams for core-collapse SNe (Olivares et al. 2010). A promising recent extension of this technique (Rodríguez et al. 2014) found 8–9 % uncertainties in relative distances, but its application to H0 is still limited due to the very small number of calibrating objects (four in that publication). A precise geometric distance to the nearby spiral galaxy NGC 4258 (Herrnstein et al. 1999) and the installation of the Advanced Camera for Surveys (ACS) onboard HST motivated an independent calibration of the Cepheid PLR by Macri et al. (2006). This work also highlighted the impact of an increasingly more precise and accurate value of H0 for constraining the properties of dark energy. At the same time, ACS was also used by Riess et al. (2005) to improve the absolute calibration of SNe Ia by obtaining a Cepheid distance to NGC 3370 (host of SN 1994ae). That paper also presented the first photometry for SN 1998aq and a determination of H0 based on a reanalysis of all “ideal” SNe Ia to date, a rather small sample of four objects with low reddening, well-observed light curves starting before peak light, decline rate within a well-defined “normal” range, and photoelectric or CCD-based photometry. In mid-2006, Riess and Macri established the “Supernovae and H0 for Equation of State of dark energy” (SH0ES) project with the goal of significantly reducing the uncertainty in H0 . A modest reduction in the statistical uncertainty was obtained by increasing the sample of host galaxies to six “ideal” SNe Ia (Riess et al. 2009b). More importantly, a significant improvement was obtained in the systematic

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uncertainty by constructing a sturdier distance ladder that minimized or eliminated many of the sources of uncertainty that plagued the WFPC2-based studies. SH0ES based its Cepheid distances on near-infrared (H -band) observations of these variables, which are preferred to optical measurements for several reasons. The intrinsic scatter of the PLR decreases significantly, thanks to the reduced effect of the finite temperature range of the instability strip, the impact of reddening is diminished by factors of 6 and 3 relative to V and I ; variations in Cepheid luminosity as a function of chemical abundance are predicted by all models to reach a minimum in this passband. The absolute calibration of the Cepheid PLR was based on the maser distance to NGC 4258. Since all the photometry was on the same system, thanks to the use of a single telescope (HST) and well-calibrated modern cameras, this “differential ladder” reduced  .H0 / to 5 % (Riess et al. 2009a). Furthermore, this work emphasized proper accounting and full propagation of all sources of statistical and systematic uncertainty via a matrix approach. The installation of the Wide-Field Camera 3 as part of the last servicing mission to HST greatly improved the observatory’s near-infrared capability. Soon after becoming available, the SH0ES team used this instrument to obtain Cepheid distances to two additional SN Ia hosts and to greatly increase the number of Cepheids with homogeneous near-infrared photometry in the anchor galaxy and the previously studied SN hosts. Further improvements on the absolute calibration of Cepheid luminosities were possible, thanks to the availability of DEB distances to the LMC and HST-based parallaxes to Milky Way Cepheids, leading to H0 D 73:8 ˙ 2:4 km s1 Mpc1 and  .H0 / D 3:3 % (Riess et al. 2011). Since then, the SH0ES team has been carrying out a large observational effort to more than double the number of Cepheid distances to “ideal” SN Ia hosts (now 19) and to obtain parallaxes to additional Milky Way Cepheids using new HST-based techniques (Riess et al. 2014). Helped by independent advances on a refined distance to NGC 4258 (Humphreys et al. 2013), an improved DEB distance to the LMC (Pietrzy´nski et al. 2013), an 8 larger sample of LMC Cepheids with nearinfrared photometry (Macri et al. 2015), a large sample of M31 Cepheids with HST photometry (Kodric et al. 2015), and 300 SNe Ia in the Hubble flow (0:023 < z < 0:15), the uncertainty in H0 has been reduced to 2.4 % (Riess et al. 2016).

5

Conclusions

The full potential of type Ia supernovae as distance indicators is finally within reach, thanks to the efforts of many individuals and teams during the past five decades. As a result, SNe Ia have played a key role in ever more precise and accurate determinations of H0 . We are now able to perform a critical test ofPthe assumed “standard” cosmological model (CDM, w D 1, Neff ' 3:046, m D 0:06 eV) by comparing the directly measured local expansion rate (based on Cepheids and SNe Ia) with the predicted value based on observations of the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO). Presently, there is “tension” between the

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direct and inferred values of H0 at the 1  3 level depending on the set of CMB observations that is adopted. If confirmed at higher significance, this difference could hint at Physics beyond the standard model such as an additional source of dark radiation in the early universe. While we await results from Stage IV CMB and BAO experiments, the Cepheid-based calibration of SNe Ia luminosities marches toward a goal of 1 % total uncertainty by 2020 based on Gaia discovery and parallaxes of thousands of Cepheids to dramatically improve the galactic PLR, another doubling of the number of SNe Ia hosts with HST-based Cepheid distances, and JWST NIR observations of Cepheids in all hosts to reduce photometric errors due to crowding.

6

Cross-References

 Cosmology with Type IIP Supernovae  History of Supernovae as Distance Indicators  Low-z Type Ia Supernova Calibration  The Peak Luminosity-Decline Rate Relationship for Type Ia Supernovae  Type Ia Supernovae Acknowledgements The introduction benefited from John Huchra’s historical compilation of H0 measurements; we thank our departed colleague and mentor who is still sorely missed. AS acknowledges the privilege of working with both “camps” on their respective projects to determine H0 with HST and expresses his gratitude for the intellectual trust from Allan Sandage and Gustav Tammann.

References Ardeberg A, de Groot M (1973) The 1972 supernova in NGC 5253. Photometric results from the first observing season. A&A 28:295 Barbon R, Cappellaro E, Turatto M (1989) The Asiago supernova catalogue. A&AS 81:421 Baron E et al (1995) Non-LTE spectral analysis and model constraints on SN 1993J. ApJ 441:170 Branch D (1992) The Hubble constant from nickel radioactivity in type Ia supernovae. ApJ 392:35 Branch D, Patchett B (1973) Type I supernovae. MNRAS 161:71 Branch D, Tammann GA (1992) Type Ia supernovae as standard candles. ARA&A 30:359 Branch D et al (1981) The type II supernova 1979c in M100 and the distance to the Virgo cluster. ApJ 244:780 Branch D, Fisher A, Nugent P (1993) On the relative frequencies of spectroscopically normal and peculiar type Ia supernovae. AJ 106:2383 Cadonau R (1987) Standard light curves and other properties of type I supernovae. PhD thesis, University of Basel. http://baselbern.swissbib.ch/Record/296631906/ de Vaucouleurs G (1993) The extragalactic distance scale. VIII - A comparison of distance scales. ApJ 415:10 Eastman RG, Schmidt BP, Kirshner R (1996) The atmospheres of Type II supernovae and the expanding photosphere method. ApJ 466:911 Elias JH, Matthews K, Neugebauer G, Persson SE (1985) Type I supernovae in the infrared and their use as distance indicators. ApJ 296:379 Ferrarese L et al (2000) Photometric recovery of crowded stellar fields observed with HST/WFPC2 and the effects of confusion noise on the extragalactic distance scale. PASP 112:177

2590

A. Saha and L.M. Macri

Fiorentino G, Caputo F, Marconi M, Musella I (2002) Theoretical models for classical Cepheids. VIII. Effects of helium and heavy-element abundance on the Cepheid distance scale. ApJ 576:402 Fisher A, Branch D, Hoflich P, Khokhlov A (1995) The minimum ejection velocity of calcium in type Ia supernovae and the value of the Hubble constant. ApJ 447:L73 Freedman WL et al (2001) Final results from the Hubble space telescope key project to measure the Hubble constant. ApJ 553:47 Gibson BK et al (2000) The Hubble space telescope key project on the extragalactic distance scale. XXV. A recalibration of Cepheid distances to type Ia supernovae and the value of the Hubble constant. ApJ 529:723 Hamuy M, Pinto PA (2002) Type II supernovae as standardized candles. ApJ 566:L63 Hamuy M et al (1993) The 1990 Calan/Tololo supernova search. AJ 106:2392 Hamuy M et al (1995) A Hubble diagram of distant type Ia supernovae AJ 109:1 Hamuy M et al (1996a) The absolute luminosities of the Calan/Tololo type Ia supernovae. AJ 112:2391 Hamuy M et al (1996b) The Hubble diagram of the Calan/Tololo type Ia supernovae and the value of H0 . AJ 112:2398 Harkness RP, Wheeler JC (1990) Classification of supernovae. In: Petschek AG (ed) Supernovae. Springer, New York, pp 1–29. doi:10.1007/978-1-4612-3286-5_1 Herrnstein JR et al (1999) A geometric distance to the galaxy NGC4258 from orbital motions in a nuclear gas disk. Nature 400:539 Humphreys EML, Reid MJ, Moran JM, Greenhill LJ, Argon AL (2013) Toward a new geometric distance to the active galaxy NGC 4258. III. Final results and the Hubble constant. ApJ 775:13 Jacoby GH, Pierce MJ (1996) Response to Schaefer’s comments on Pierce & Jacoby (1995) regarding the type Ia supernova 1937C. AJ 112:723 Jacoby GH et al (1992) A critical review of selected techniques for measuring extragalactic distances. PASP 104:599 Karachentsev ID (2005) The Local Group and other neighboring galaxy groups. AJ 129:178 Kennicutt RC Jr et al (1998) The Hubble space telescope key project on the extragalactic distance scale. XIII. The metallicity dependence of the Cepheid distance scale. ApJ 498:181 Kirshner RP, Kwan J (1974) Distances to extragalactic supernovae. ApJ 193:27 Kodric M et al (2015) The M31 near-infrared period-luminosity relation and its non-linearity for ı Cep variables with 0:5 log.P / 1:7. ApJ 799:144 Kowal CT (1968) Absolute magnitudes of supernovae. AJ 73:1021 Leavitt HS, Pickering EC (1912) Periods of 25 variable stars in the small magellanic cloud. Harvard College Observatory Circular 173:1 Leibundgut B, Tammann GA (1990) Supernova studies. III - The calibration of the absolute magnitude of supernovae of type Ia. A&A 230:81 Macri LM, Ngeow C-C, Kanbur SM, Mahzooni S, Smitka MT (2015) Large Magellanic Cloud near-infrared synoptic survey. I. Cepheid variables and the calibration of the Leavitt law. AJ 149:117 Macri LM, Stanek KZ, Bersier D, Greenhill LJ, Reid MJ (2006) A new Cepheid distance to the maser-host galaxy NGC 4258 and its implications for the Hubble constant. ApJ 652:1133 Madore BF (1982) The period-luminosity relation. IV - Intrinsic relations and reddenings for the Large Magellanic Cloud Cepheids. ApJ 253:575 Matheson T et al (2012) The infrared light curve of SN 2011fe in M101 and the distance to M101. ApJ 754:19 Oke JB, Searle L (1974) The spectra of supernovae. ARA&A 12:315 Olivares EF et al (2010) The standardized candle method for Type II plateau supernovae. ApJ 715:833 Phillips MM (1993) The absolute magnitudes of Type Ia supernovae. ApJ 413:L105 Pierce MJ, Jacoby GH (1995) ”New” B and V photometry of the “Old” type Ia supernova SN 1937C: implications for HO. AJ 110:2885

103 The Hubble Constant from Supernovae

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Pietrzy´nski G et al (2013) An eclipsing-binary distance to the Large Magellanic Cloud accurate to two per cent. Nature 495:76 Pskovskii YP (1967) The photometric properties of supernovae. Soviet Ast 11:63 Pskovskii YP (1977) Light curves, color curves, and expansion velocity of type I supernovae as functions of the rate of brightness decline. Soviet Ast 21:675 Riess AG, Press WH, Kirshner RP (1995) Using type Ia supernova light curve shapes to measure the Hubble constant. ApJ 438:L17 Riess AG, Press WH, Kirshner RP (1996) A precise distance indicator: type Ia supernova multicolor light-curve shapes. ApJ 47388 Riess AG et al (1999) BVRI light curves for 22 type Ia supernovae. AJ 117:707 Riess AG et al (2005) Cepheid calibrations from the Hubble space telescope of the luminosity of two recent type Ia supernovae and a redetermination of the Hubble constant. ApJ 627:579 Riess AG et al (2009a) A redetermination of the Hubble constant with the Hubble space telescope from a differential distance ladder. ApJ 699:539 Riess AG et al (2009b) Cepheid calibrations of modern type Ia Supernovae: implications for the Hubble constant. ApJS 183:109 Riess AG et al (2011) A 3 % Solution: determination of the Hubble constant with the Hubble space telescope and Wide Field Camera 3. ApJ 730:119 Riess AG et al (2014) Parallax beyond a kiloparsec from spatially scanning the Wide Field Camera 3 on the Hubble space telescope. ApJ 785:161 Riess AG et al (2016) A 2.4% determination of the local value of the Hubble constant. ArXiv e-prints Rodríguez Ó, Clocchiatti A, Hamuy M (2014) Photospheric magnitude diagrams for type II supernovae: a promising tool to compute distances. AJ 148:107 Romaniello M et al (2006) The metallicity dependence of the Cepheid period-luminosity relation. Mem Soc Astron Italiana 77:172 Saha A (2003) In: Alloin D, Gieren W (ed) Stellar candles for the extragalactic distance scale. Lecture notes in physics, vol 635. Springer, Berlin, pp 71–83 Saha A et al (1994) Discovery of Cepheids in IC 4182: absolute peak brightness of SN Ia 1937C and the value of H0 . ApJ 425:14 Saha A et al (1995) Discovery of Cepheids in NGC 5253: absolute peak brightness of SN Ia 1895B and SN Ia 1972E and the value of H0 . ApJ 438:8 Saha A et al (1996a) Cepheid calibration of the peak brightness of SNe Ia. V. SN 1981B in NGC 4536. ApJ 466:55 Saha A et al (1996b) Cepheid calibration of the peak brightness of type Ia supernovae. VI. SN 1960F in NGC 4496A. ApJS 107:693 Saha A et al (1997) Cepheid calibration of the peak brightness of type Ia supernovae. VIII. SN 1990N in NGC 4639. ApJ 486:1 Saha A et al (1999) Cepheid calibration of the peak brightness of type Ia supernovae. IX. SN 1989B in NGC 3627. ApJ 522:802 Saha A, Labhardt L, Prosser C (2000) On deriving distances from Cepheids using the Hubble space telescope. PASP 112:163 Saha A et al (2001a) Cepheid calibration of the peak brightness of type Ia supernovae. XI. SN 1998aq in NGC 3982. ApJ 562:314 Saha A et al (2001b) Cepheid calibration of the peak brightness of type Ia supernovae. X. SN 1991T in NGC 4527. ApJ 551:973 Sandage A, Tammann GA (1974) Steps toward the Hubble constant. calibration of the linear sizes of extra-galactic H II regions. ApJ 190:525 Sandage A, Tammann GA (1982) Steps toward the Hubble constant. VIII – The global value. ApJ 256:339 Sandage A et al (1992) The Cepheid distance to IC 4182 – calibration of MV(max) for SN Ia 1937C and the value of H0. ApJ 401:L7 Sandage A, Tammann GA (1993) The Hubble diagram in V for supernovae of type Ia and the value of H(0) therefrom. ApJ 415:1

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A. Saha and L.M. Macri

Sandage A et al (2006) The Hubble constant: a summary of the Hubble space telescope program for the luminosity calibration of type Ia supernovae by means of Cepheids. ApJ 653:843 Schaefer BE (1996) The peak brightness of SN 1937C in IC 4182 and the Hubble constant: comments on Pierce & Jacoby [AJ, 110, 2885 (1995)]. AJ 111:1668 Schmidt BP, Kirshner RP, Eastman RG (1992) Expanding photospheres of type II supernovae and the extragalactic distance scale. ApJ 395:366 Schmidt BP et al (1994) The distances to five Type II supernovae using the expanding photosphere method, and the value of H0 . ApJ 432:42 Searle L (1974) Supernovae and Supernova Remnants. In: Cosmovici CB (ed) Astrophysics and space science library, vol 45. Springer, Dordrecht/NewYork, p 125 Szabados L, Klagyivik P (2012) Problems and possibilities in fine-tuning of the Cepheid P-L relationship. Ap&SS 341:99 Tammann GA (1974) Confrontation of Cosmological Theories with Observational Data. In: Longair MS (ed) IAU Symposium, Vol 63. Boston, Dordrecht, pp 47–59 Tripp R (1998) A two-parameter luminosity correction for Type Ia supernovae. A&A 331:815 Uomoto A, Kirshner RP (1985) Peculiar Type I supernovas. A&A 149:L7 van den Bergh S (1992) The Hubble parameter. PASP 104:861 Wheeler JC, Levreault R (1985) The peculiar Type I supernova in NGC 991. ApJ 294:L17

The Infrared Hubble Diagram of Type Ia Supernovae

104

Kevin Krisciunas

Abstract

Photometry of Type Ia supernovae reveals that these objects are standardizable candles in optical passbands – the peak luminosities are related to the rate of decline after maximum light. In the near-infrared bands, there is essentially a characteristic brightness at maximum light for each photometric band. Thus, in the near-infrared they are better than standardizable candles; they are essentially standard candles. Their absolute magnitudes are known to ˙0.15 magnitude or better. The infrared observations have the extra advantage that interstellar extinction by dust along the line of sight is a factor of 3–10 smaller than in the optical B- and V -bands. The size of any systematic errors in the infrared extinction corrections typically become smaller than the photometric errors of the observations. Thus, we can obtain distances to the hosts of Type Ia supernovae to ˙8 % or better. This is particularly useful for extragalactic astronomy and precise measurements of the dark energy component of the universe.

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Challenge of Infrared Observing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Standard Candle Nature of Type Ia Supernovae in the Near-Infrared . . . . . . . . . . 4 Pushing the Hubble Diagram to Higher and Higher Redshifts . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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K. Krisciunas () Department of Physics and Astronomy, George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_103

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Introduction

It is believed that Type Ia supernovae are the result of the thermonuclear destruction of a single carbon-oxygen white dwarf (owing to mass transfer from a nearby dwarf or subgiant star) or owing to the merger of two white dwarfs. That being stated, we should not assume that all Type Ia supernovae explode at the Chandrasekhar limit. Type Ia supernovae are generally not associated with star-forming regions and in fact also occur in elliptical galaxies, which have minimal or negligible interstellar gas and dust. Thus, we can build up a list of Type Ia supernovae that are essentially unreddened, and we can exploit the uniformity of their photometric color curves to determine how dust extinction affects those that are dimmed and reddened by dust (Krisciunas et al. 2000). This makes Type Ia supernovae particularly useful for the determination of extragalactic distances. In order to understand the phenomenon of supernovae, we need to know the energy budget. Using the sum of observed flux in all passbands, corrected for interstellar extinction, and distances to nearby host galaxies obtained via Cepheid variable stars or galaxy surface brightness fluctuations, we can obtain the bolometric absolute magnitudes of nearby supernovae. This helps the supernova modelers. Observers assume (with some justification) that nearby and distant Type Ia supernovae have the same intrinsic brightness. They use Type Ia supernovae to derive distances to galaxies. This allows us to do observational cosmology at a level of accuracy unachievable a generation ago.

2

The Challenge of Infrared Observing

Infrared photometry of supernovae was pioneered by Elias et al. (1981, 1985) using single-channel infrared photometers. Previously, Kirshner et al. (1973) presented graphs of the near-infrared light curves of SN 1972E. Their individual data points are given by Elias et al. (1985). While single-channel photometry can be reliable for supernovae in the outskirts of galaxies, if a supernova’s location overlaps a bright part of its host galaxy, in order to properly isolate the signal due to the supernova alone, one needs to obtain template observations of the host galaxy after the supernova has faded. Infrared observations of galaxy with supernova and galaxy without supernova are best done with an infrared array detector. In the year 2000 only a few observatories had 256 by 256-pixel infrared cameras. These gave a field of view of about 2 arc minutes on a side. Larger and larger arrays have been built since then. This allows one to observe bigger areas of the sky. With more field stars available as secondary standards, one can derive accurate photometry of a supernova even under non-photometric sky conditions, providing that the field is calibrated on several clear nights. Observations of SN 1998bu were made with a combination of single-channel instruments and small infrared arrays on a number of telescopes (Hernandez et al. 2000; Jha et al. 1999). These observations represent the beginning of the modern era of infrared measurements of supernovae using infrared arrays.

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One square arc second of sky at a pristine site on a moonless night, averaged over the course of the Sun’s 11-year sunspot cycle, is the equivalent of a star of magnitude B  22:6, V  21:6 (Krisciunas et al. 2007). For the optical B- and V -bands, a typical Type Ia supernova at redshift 0.01 (distance D 42 Mpc) has an apparent magnitude of about +13.8 at maximum light, assuming no dimming by interstellar dust. This is considerably brighter than the background sky, even on a night with moonlight. Such a supernova ten times more distant (at redshift 0.1) would be five magnitudes fainter, or B  V  19 at maximum light. With a modern optical CCD camera on a 1-m class telescope, one can obtain accurate photometry of Type Ia supernovae out to redshift 0.1. With a 4-m class telescope, one can detect supernovae at redshift 0.3 to 0.8 at a sufficiently high signal-to-noise ratio in optical bands to show evidence for the acceleration of the expansion of the universe (Perlmutter et al. 1999; Riess et al. 1998). Throughout this chapter we adopt a Hubble constant of 72 km s1 Mpc1 (Freedman et al. 2001). If we consider a model of the universe with ˝M D 0:3 and ˝ D 0:0 (the “open” model) and a geometrically flat one with ˝M D 0:3 and ˝ D 0:7, then the acceleration of the expansion of the universe will cause the supernovae at redshift 0.1 to be 0.067 mag fainter in the flat model compared to the open model. At redshift 0.2 this difference is 0.120 mag. From redshift 0.5 to 1.0 the difference slowly increases from 0.216 to 0.256 mag. The photometric signal that the supernovae are “too faint” at redshift 0.1 is buried in the errors of the measurements. It is marginally detectable at redshift 0.2 and easier to substantiate beyond redshift 0.3. For ground-based observing, the near-infrared sky is much brighter than in the optical bands. In the near-infrared one square arc second of sky has the equivalent brightness of a star of magnitude J D 16:5, H D 14:4, Ks D 13:0 (Cuby et al. 2000) . A typical Type Ia supernova at maximum light has a near-infrared brightness of magnitude 14.5–15.0 at redshift 0.01 and 19.5–20.0 at redshift 0.10. The sky brightness is up to 100 times brighter than the object we wish to measure! We require a 1-m class telescope to do infrared photometry of relatively nearby Type Ia supernovae (to redshift 0.02), but we require a 6.5–8-m class telescope to get a useful infrared photometry of more distant objects. Because of the brightness of the infrared sky, it requires several hours of integration on a supernovae of redshift 0.35 with an 8-m class telescope to measure its H -band (1.65 micron) brightness to ˙10 %. Such observations are not a good use of large ground-based telescopes. One would like to obtain the data using satellites outside the Earth’s atmosphere.

3

The Standard Candle Nature of Type Ia Supernovae in the Near-Infrared

Phillips reviews the decline-rate relations for Type Ia supernovae in his  Chap. 101, “The Peak Luminosity-Decline Rate Relationship for Type Ia Supernovae”. By convention the “decline rate” is the number of magnitudes in the

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B-band ( = 0.44 microns) that a Type Ia supernova fades in the first 15 days after maximum light. We call this m15 .B/. It ranges from about 0.7 to 2.0 magnitudes per 15 days. Phillips (1993) first convincingly showed a correlation between the absolute magnitudes of Type Ia supernovae at maximum light and m15 .B/. Type Ia supernovae range in absolute magnitude at maximum light by about 2.5 magnitudes in the B-band. In the V -band (0.55 microns), the range is about 2.0 magnitudes. In the I -band (0.75 microns), the decline-rate relation is slightly shallower (Hamuy et al. 1996). Soon there was evidence that Type Ia supernovae at 10–14 days after maximum light might have one characteristic absolute magnitude for each nearinfrared band (Krisciunas et al. 2003; Meikle 2000; Phillips 2012); they might be bona fide standard candles in the near infrared. Starting in 1999 astronomers at Cerro Tololo Inter-American Observatory and Las Campanas Observatory began systematic collection of optical and infrared photometry of Type Ia supernovae. This was due to the more widespread use of infrared array cameras and the greater discovery rate of supernovae of all types. The growing number of well-sampled light curves has allowed us to construct light-curve templates. This is particularly useful for deriving light- curve maxima for those objects that for one reason or another are not actually observed at the time of maximum light. An example of multiband light-curve fits is shown in Fig. 1. The data were first presented by Contreras et al. (2010). Most of the Type Ia supernovae measured in the infrared have m15 .B/ in the range 0.8–1.4. For the fast decliners (m15 .B/ > 1:6), it is found that there is a bifurcation in the near-infrared decline-rate relations. Those that peak in the nearinfrared after the time of B-band maximum are subluminous in all bands (both optical and infrared), but those that peak in the near-infrared prior to the time of B-band maximum are only slightly fainter (0.2 mag) in the infrared compared to the objects with much slower decline rates (see Folatelli et al. 2010; Krisciunas et al. 2009, and Kattner et al. 2012). One such dataset is shown in Fig. 2. We note that in high-redshift surveys for Type Ia supernovae, very few (if any) fast decliners are discovered. This is because high-redshift surveys are flux limited, not volume limited. Since fast decliners are subluminous in all optical bands and the high-redshift surveys have been optical surveys, we sample a considerably smaller volume for the fast decliners. As we push the infrared observations to higher and higher redshift, we may regard Type Ia supernovae with m15 .B/ < 1:4 essentially as standard candles. The only exceptions would be the so-called super-Chandrasekhar objects resulting from the merger of two white dwarfs whose combined mass exceeds the Chandrasekhar mass. These are overluminous. In Fig. 2 we should consider that the X-axis values and the Y-axis values have non-negligible errors. From a Monte Carlo simulation that takes into consideration those errors, one finds that the slope of the J -band decline-rate relation is 0:174 ˙ 0:144. For the H -band it is 0:080 ˙ 0:150, and for the K-band it is 0:168 ˙ 0:192. Thus, in the J - and K-bands, the slope is nonzero at the 1- significance level. In the H -band Type Ia supernovae at maximum light are almost perfect standard candles.

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Fig. 1 BV YJH light curves of SN 2006ax, fitted with a Python-based program developed by Burns et al. (2011). The dashed lines represent the deviations from supernova to supernova in the training sample. The separation of the upper and lower dashed lines for a given filter represents 1- uncertainties from the observations

As part of the Carnegie Supernova Project, in the near future, we can expect robust analysis of a more homogeneous dataset four times larger than that shown in Fig. 2. One new infrared band that holds great promise for observations of Type Ia supernovae is the Y -band (1.03 microns), especially since future wide-scale sky surveys such as the Large Synoptic Survey Telescope will cover this band. Krisciunas et al. (2004b) presented the first Y -band light curves of Type Ia supernovae, for supernovae 1999ee and 2000bh. Since then it has been found that the slope of the Y -band decline-rate relation is nonzero at the 1- significance level and with the same arithmetic sign as for other near-infrared bands (Kattner et al. 2012). Observations made using red and near-infrared filters have demonstrated prominent secondary humps in the light curves of Type Ia supernovae. The actual Y -band maximum typically occurs at the time of the second maximum, not the first one, as can be seen in Fig. 1. Kasen (2006) showed that the secondary hump is due to the change in opacity in the expanding fireball when doubly ionized ions combine with electrons to form singly ionized ions.

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Fig. 2 Near-infrared peak absolute magnitude decline-rate relations (Krisciunas 2012). On the Y-axis are the absolute magnitudes at maximum light. The J -, H -, and K-bands are centered at 1.25, 1.65, and 2.25 microns, respectively. On the X-axis is the decline-rate parameter m15 .B/. SN 2009dc is a possible super-Chandrasekhar mass object, which might explain its excess brightness. Diamond-shaped points at the right-hand sides represent objects that peaked in the near-infrared after the time of B-band maximum. They and SN 2009dc have been excluded from the fits (Reproduced with permission from the American Association of Variable Star Observers. Copyright 2012. All rights reserved)

4

Pushing the Hubble Diagram to Higher and Higher Redshifts

Consider the standard relation between the absolute magnitude, apparent magnitude, and distance: MX D mX C 5  5 log Dpc ; where the apparent magnitudes mX have been corrected for any dimming effects of dust along the line of sight and D is the distance in parsecs. (The subscripts on the magnitudes indicate that we are considering one particular photometric band

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at a time.) If there is a characteristic absolute magnitude for some type of object, then a plot of the extinction-corrected apparent magnitudes vs. the logarithm of the distance will provide a linear relationship out to at least redshift 0.1, and the slope of that relationship will be identically equal to 5. The distances we use for such a plot are based on Hubble’s Law: recession velocity cz D H0 DMpc , where z is the redshift and H0 is the current cosmic expansion rate, a universal constant known as the Hubble constant, and here D is the distance in megaparsecs. Redshift 0.01 indicates a recession velocity of 3000 km s1 owing to the expansion of the universe. Every galaxy’s motion is affected by the gravity of the galaxies near it. One expects peculiar velocities on the order of ˙300 km s1 with respect to the smooth Hubble flow. For our purposes here the start of the smooth Hubble flow corresponds to a recession velocity of about 3000 km s1 , where the expected peculiar velocities are a 10 % effect. This corresponds to a distance of about 42 Mpc given a Hubble constant of 72 km s1 Mpc1 . Some astronomers take a more conservative approach and adopt redshift 0.03 as the start of the smooth Hubble flow (Barone-Nugent et al. 2012). A Hubble diagram is a plot of m  M (called the distance modulus) or m vs. D, recession velocity, or redshift (or their logarithms), as the latter parameters are all related to each other thanks to Hubble’s Law. At redshifts beyond 0.2, the Hubble diagram deviates from a straight line as one begins to probe the expansion rate in the past. Thus, it is necessary to adopt an appropriate cosmological model by specifying the total matter density (which causes cosmic deceleration) and the dark energy density of the universe (which causes cosmic acceleration if ˝ is positive). We end up with families of curves in the Hubble diagram. In fact this is how supernovae were first used to demonstrate the acceleration of the expansion of the universe and provide evidence for a nonzero cosmological constant (Perlmutter et al. 1999; Riess et al. 1998). Actual supernovae were “too faint” compared to what was considered prior to that time, a decelerating model with no cosmological constant. If a plot of the distance moduli or apparent magnitudes of a particular type of astrophysical object vs. log D (or log z) gives a tight fit, it means that: (1) these objects are excellent standard candles; and (2) the universe beyond some adopted minimum redshift is uniformly expanding. Elias et al. (1985) plotted the H -band magnitudes of a small sample of supernovae at 20 days after maximum light vs. the logarithm of the distance. Since the data were consistent with a straight line relation, this constituted the first infrared Hubble diagram for supernovae. Krisciunas et al. (2004a) presented the first Hubble diagrams of Type Ia supernovae based on infrared maxima (see Fig. 3). Ten of their 16 supernovae were observed by them at Apache Point Observatory (New Mexico), Cerro Tololo, and Las Campanas observatories. The residuals in the Hubble diagram were ˙0.14, 0.18, and 0.12 mag, respectively, in the J -, H -, K-bands. After this time the goal was to expand the number of objects at redshift 0.01 and beyond. Along those lines, since 2005 Harvard astronomers have used a dedicated 1.3-m telescope and infrared camera at Mt. Hopkins, Arizona, to observe nearly 100 Type Ia supernovae

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Redshift in CMB frame (km/sec) Fig. 3 The first infrared Hubble diagrams of Type Ia supernovae that relied on the infrared maxima (Krisciunas et al. 2004a). The points with recession velocity less than 2000 km s1 represent objects whose distances were determined directly using Cepheids or the method of surface brightness fluctuations of the host galaxies. These distances and a Hubble constant of H0 = 72 km s1 Mpc1 give for the abscissa the equivalent velocities in the frame of the cosmic microwave background (CMB). The points with recession velocity greater than 2000 km s1 represent objects with velocities obtained directly from spectra of the host galaxies or the supernovae themselves, corrected to the CMB frame. That the fits are so tight is clear evidence of the uniformity of intrinsic brightness of Type Ia supernovae at maximum light in the near infrared. Reproduced with permission from the American Astronomical Society. Copyright 2004. All rights reserved.

(Friedman et al. 2015; Wood-Vasey et al. 2008). European astronomers have used facilities at Tenerife and La Palma and at La Silla and Paranal observatories in Chile to obtain infrared photometry and spectroscopy of Type Ia supernovae. Barone-Nugent et al. (2012) observed 12 Type Ia supernovae in the redshift range 0.03–0.09 with the European Southern Observatory’s 8.1-m Very Large Telescope (VLT) and the 8.2-m Gemini North telescope. They provided evidence that the scatter of the absolute magnitudes at maximum light of Type Ia supernovae might be as small as ˙0.10 mag in the rest-frame near-infrared J - and H -bands. Stanishev et al. (2015) present multi-epoch UBVRI optical photometry and single-epoch J - and H -band photometry of 16 Type Ia supernovae in the redshift

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Fig. 4 H -band Hubble diagram of Type Ia supernovae at maximum light, including all corrections for extinction and the shallow decline-rate relations. Based on Figure 12 of reference Stanishev et al. (2015). The fitted function is linear with respect to the fit parameters, but the best-fit line is nonlinear because the error term in the 2 statistics depends on some of the fit parameters in a nonlinear fashion. The bottom graph (B) gives the residuals of the data points from the best fit (Reproduced with permission from The European Southern Observatory. Copyright 2015. All rights reserved)

range 0.037–0.183. The data were taken with the 1.4-m Japanese InfraRed Survey Facility at the South African Astronomical Observatory, the 2.5-m Nordic Optical Telescope at La Palma, and the 8.1-m VLT. These authors analyze infrared light curves of 102 normal Type Ia supernovae (see Fig. 4). This is the most complete treatment of the subject to date.

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Depending on your definition of “infrared,” we already have an infrared Hubble diagram of Type Ia supernovae out to redshift 0.7 (Freedman et al. 2009). The 6.5-m Magellan Baade Telescope was used to observe 35 such objects in the observer frame Y - and J -bands (1.03 and 1.25 microns). Given the redshifts of the objects, the photometry corresponds to rest-frame photometry at 0.75 microns. With the elimination of one outlier, the dispersion is ˙0.13 mag. The goal today is to observe Type Ia supernova in the rest-frame near-infrared bands and to push to the highest possible redshift. Since the observed wavelengths of light from distant objects are stretched by a factor of (1 + z), rest-frame J -band (1.25 micron) photometry of an object at redshift 0.35 must actually be data taken in the H -band at 1.65 microns. Rest-frame H -band photometry of the object must be data taken in the K-band at 2.25 microns. These and longer wavelength bands used outside the Earth’s atmosphere will allow us to test the evidence for the acceleration of the universe with minimal worries about the dimming effect of interstellar dust on the measurements. If a supernova were dimmed by 0.5 mag in the rest-frame V -band (0.55 microns), the rest-frame J -, H -, and K-band extinction would be roughly 0.15, 0.09, and 0.06 mag, respectively (Cardelli et al. 1989; Krisciunas et al. 2006). The uncertainties of these near-infrared extinction corrections would be considerably smaller than the random errors of the photometry. The use of restframe infrared photometry of Type Ia supernovae has the potential to provide the very best possible distances to the host galaxies of these objects. This is true even if these objects are dimmed by dust that is considerably different than “normal” dust in the Milky Way galaxy.

5

Conclusions

For a Type Ia supernova, roughly a Chandrasekhar mass (1.4 Mˇ ) of carbon and oxygen explodes, so we obtain a standard bomb. The absolute magnitudes at maximum light in the optical bands are related to the B-band decline-rate parameter m15 .B/. These are the decline-rate relations. However, in the near infrared, the slopes of these relationships are very nearly zero. This means that in the nearinfrared Type Ia supernovae are very nearly standard candles. Another advantage of observing these objects in the near-infrared is that the extinction by interstellar dust is significantly smaller than in the rest-frame optical bands. Rest-frame infrared data may provide the most accurate distances to Type Ia supernovae and their host galaxies. The biggest challenge inherent in infrared observations at ground-based observatories is the brightness of the night sky. It is like optical ground-based observing during full Moon on any night of the year. As a result, while we have observed Type Ia supernovae to redshift  0.8 in optical bands from the ground, we have only reached redshift 0.18 in the near infrared. With fewer worries about systematic errors due to dust extinction corrections, observations made with the Hubble Space Telescope, the James Webb Space Telescope, and other planned facilities will

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extend the near-infrared Hubble diagram far enough to study the effect of cosmic acceleration on the brightness of supernovae observed in the near infrared.

6

Cross-References

 Characterizing Dark Energy Through Supernovae  Discovery of Cosmic Acceleration  The Peak Luminosity-Decline Rate Relationship for Type Ia Supernovae  Type Ia Supernovae Acknowledgements We thank Chris Burns for Fig. 1, and we thank Vallery Stanishev for a version of his H -band Hubble diagram, reproduced here as Fig. 4. Jose Prieto provided a program to calculate the luminosity distance of an object for the case of a geometrically flat universe with nonzero cosmological constant.

References Barone-Nugent RL, Lidman C, Wyithe JSB, Mould J, Howell DA, Hook IM et al (2012) Nearinfrared observations of type Ia supernovae: the best known standard candle for cosmology. Mon Not R Astron Soc 425:1007–1012 Burns CR, Stritzinger M, Phillips MM, Kattner S, Persson SE, Madore BF et al (2011) The Carnegie supernova project: light-curve fitting with SNooPy. Astron J 141(article 19):20 Cardelli JA, Clayton GC, Mathis JS (1989) The relationship between infrared, optical, and ultraviolet extinction. Astrophys J 345:245–256 Contreras C, Hamuy M, Phillips MM, Folatelli G, Suntzeff NB, Persson SE et al (2010) The Carnegie supernova project: first photometry data release of low-redshift type Ia supernovae. Astron J 139:519–539 Cuby JG, Lidman C, Moutou C (2000) ISAAC: 18 months of Paranal science operations. The Messenger 101:2–8 Elias JH, Frogel JA, Hackwell JA, Persson SE (1981) Infrared light curves of type I supernovae. Astrophys J 251:L13–L16 Elias JH, Matthews K, Neugebauer G, Persson SE (1985) Type I supernovae in the infrared and their use as distance indicators. Astrophys J 296:379–389 Folatelli G, Phillips MM, Burns CR, Contreras C, Hamuy M, Freedman WL et al (2010) The Carnegie supernova project: analysis of the first sample of low-redshift type Ia supernovae. Astron J 139:120–144 Freedman WL, Madore BF, Gibson BK, Ferrarese L, Kelson DD, Sakai S et al (2001) Final results from the hubble space telescope key project to measure the hubble constant. Astrophys J 553:47–72 Freedman WL, Burns CR, Phillips MM, Wyatt P, Persson SE, Madore BF et al (2009) The carnegie supernova project: first near-infrared hubble diagram to z  0.7. Astrophys J 704:1036–1058 Friedman AS, Wood-Vasey WM, Marion GH, Challis P, Mandel KS, Bloom JS et al (2015) CfAIR2: near-infrared light curves of 94 type Ia supernovae. Astrophys J Suppl 220(article 9):35 Hamuy M, Phillips MM, Schommer RA, Suntzeff NB, Maza J, Avilés R (1996) The absolute luminosities of the Calan/Tololo supernovae. Astron J 112:2391–2397

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Hernandez M, Meikle WPS, Aparicio A, Benn CR, Burleigh MR, Chrysostomou AC, Fernandes AJL et al (2000) An early-time infrared and optical study of the type Ia supernova 1998bu in M96. Mon Not R Astron Soc 319:223–234 Jha S, Garnavich PM, Kirshner RP, Challis P, Soderberg AM, Macri LM et al (1999) The type Ia supernova 1998bu in M96 and the hubble constant. Astrophy J Suppl 125:73–97 Kasen D (2006) Secondary maximum in the near-infrared light curves of type Ia supernovae. Astrophy J 649:939–953 Kattner S, Leonard DC, Burns CR, Phillips MM, Folatelli G, Morrell N et al (2012) The standardizability of type Ia supernovae in the near-infrared: evidence for a peak-luminosity versus decline-rate relation in the near-infrared. Publ Astron Soc Pac 124:114–127 Kirshner RP, Willner SP, Becklin EE, Neugebauer G, Oke JB (1973) Spectrophotometry of the supernova in NGC 5253 from 0.33 to 2.2 microns. Astrophys J 180:L97–L100 Krisciunas K (2012) The usefulness of type Ia supernovae for cosmology – a personal review. J Am Assoc Var Star Obs 40:334–347 Krisciunas K, Hastings NC, Loomis K, McMillan R, Rest A, Riess AG, Stubbs C (2000) Uniformity of (Vnear-infrared) color evolution of type Ia supernovae and implications for host galaxy extinction determination. Astrophys J 539:658–674 Krisciunas K, Suntzeff NB, Candia P, Arenas J, Espinoza J, Gonzalez D et al (2003) Optical and infrared photometry of the nearby type Ia supernova 2001el. Astron J 125:166–180 Krisciunas K, Phillips MM, Suntzeff NB (2004a) Hubble diagrams of type Ia supernovae in the near-infrared. Astrophys J 602:L81–L84 Krisciunas K, Phillips MM, Suntzeff NB, Persson SE, Hamuy H, Antezana R et al (2004b) Optical and infrared photometry of the nearby type Ia supernovae 1999ee, 2000bh, 2000ca, and 2001ba. Astron J 127:1664–1681 Krisciunas K, Prieto JL, Garnavich PM, Riley J-LG, Rest A, Stubbs C, McMillan R (2006) Photometry of the Type Ia Supernovae 1999cc, 1999cl, and 2000cf. Astron J 131:1639–1647 Krisciunas K, Semler DR, Richards J, Schwarz HE, Suntzeff NB, Vera S, Sanhueza P (2007) Optical sky brightness at Cerro Tololo Inter-American Observatory from 1992 to 2006. Publ Astron Soc Pac 119:687–696 Krisciunas K, Marion GH, Suntzeff NB, Blanc G, Bufano F, Candia P et al (2009) The fastdeclining type Ia supernova 2003gs, and evidence for a significant dispersion in near-infrared absolute magnitudes of fast decliners at maximum light. Astron J 138:1584–1596 Meikle WPS (2000) The absolute infrared magnitudes of type Ia supernovae. Mon Not R Astron Soc 314:782–792 Perlmutter S, Aldering G, Goldhaber G, Knop RA, Nugent A, Castro PG et al (1999) Measurements of ˝ and  from 42 high-redshift supernovae. Astrophys J 517:565–586 Phillips MM (1993) The absolute magnitudes of type Ia supernovae. Astrophys J 413:L105–L108 Phillips MM (2012) Near-infrared properties of type Ia supernovae. Publ Astron Soc Aust 29: 434–446 Riess AG, Filippenko AV, Challis P, Clocchiatti A, Diercks A, Garnavich PM et al (1998) Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron J 116:1009–1038 Stanishev V, Goobar A, Amanullah R, Bassett B, Fantaye YT, Garnavich P et al (2015) Type Ia supernova cosmology in the near-infrared. Astron Astrophys. arXiv:1505.07707 Wood-Vasey WM, Friedman AS, Bloom JS, Hicken M, Modjaz M, Kirshner RP et al (2008) Type Ia supernovae are good standard candles in the near infrared: evidence from PAIRITEL. Astrophys J 689:377–390

Discovery of Cosmic Acceleration

105

Peter Garnavich

Abstract

Recognizing that the expansion of the universe is accelerating due to dark energy was one of the most fundamental and exciting discoveries of the twentieth century. Two teams of scientists took advantage of advances in detector technology and improved understanding of supernovae to map the expansion history of the universe half way back to the Big Bang. Their original goal was to estimate the mass density of the universe, but as their measurements became more precise, they were eventually faced with the need to radically change the standard model of cosmology.

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Standardizable Candles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Early Days of Distant Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Two Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Initial Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 The Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

The idea of dark energy is the invention of A. Einstein and his cosmological constant. The cosmological constant may be interpreted as an energy distributed uniformly throughout space and unchanging as the universe expands. While the Peter Garnavich () Physics Department, University of Notre Dame, Notre Dame, IN, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_104

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gravity due to matter slows the expansion of the universe, an energy similar to a cosmological constant will lead to a surprising acceleration of the expansion. Einstein had hoped to make a static universe by balancing contributions of matter and energy. Today, the cosmological constant is the most basic form of a wide range of models generically referred to as dark energy. After Hubble’s discovery of dynamic, expanding universe, the need to balance the gravitational pull of matter with a dark energy disappeared. In the following decades, research focused on estimating the universe’s matter density while dark energy was considered an unlikely and ugly complication. In a fundamental paper, Sandage (1961) laid out methods to estimate the deceleration parameter, q0 , as a measure of the matter density and geometry of the universe, but he paid little attention to the possibility of an accelerating expansion. By the early 1990s, constraints on the matter density appeared to contradict inflation theory leading to a revival of interest in dark energy (Ostriker and Steinhardt 1995). The development of type Ia supernovae as precise distance indicators also began in the early 1990s (Phillips 1993) and led two groups, the High-Z Team (HZT) and the Supernova Cosmology Project (SCP), to successfully apply supernovae to the problem of accurate measurement of the matter density of the universe.

2

Standardizable Candles

Sandage (1961) sketched out a plan to use the brightest galaxies in clusters as standard candles to measure deviations from the linear magnitude-redshift relation or Hubble relation. In astronomy, a standard candle is a class of objects that emits the same amount of energy so that their apparent brightness depends only upon their distance. The deceleration of the universe, and therefore the matter density, could be deduced from the brightness of standard candles at high redshifts. The trick is that light travels relatively slowly and that measurements made at great distances means looking back into a past when the expansion rate was different than it is today. Unfortunately, cluster galaxies proved to be poor standard candles, and other possible candidates were either too faint to reach the required distances or were, like cluster galaxies, not sufficiently precise. Kowal (1968) looked at a sample of type I supernovae and found them promising distance indicators with peak luminosities similar to the total light of all the stars in a medium-sized galaxy. But Kowal found a peak luminosity dispersion of nearly a factor of two, meaning type I supernovae were also insufficiently precise to estimate the deceleration parameter. Eventually, the class of type I supernovae would be divided into three spectrographic subclasses with only type Ia coming from the detonation of a white dwarf star. The other two subclasses were explosions of massive stars, and their inclusion had contributed to the scatter in Kowal’s luminosity estimates. Disentangling type Ia events from the diverse collection of core-collapse supernovae was a huge leap toward their use as precise standardizable candles. By the late 1980s, it was becoming clear that the light curves and peak luminosities of normal type Ia supernovae were very uniform (Leibundgut and

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Tammann 1990) and their use as distance indicators had already begun. But in 1991, two well-observed supernovae were found to have peak luminosities that differed by a factor of 10 at blue wavelengths. While classified as peculiar, these two supernovae had the overall characteristics of type Ia events and cast doubts on the reliability of type Ia events as standard candles. Fortunately Phillips (1993), working on ideas from Pskovskii (1984), found that the rate of fading after maximum light was correlated with the peak luminosity in type Ia supernovae. Simply observing the light curve decline rate of a type Ia supernova allowed an estimate of how much its luminosity deviated from a typical event. While not all type Ia events have the same peak luminosity, observation of their light curve shape allows them to be standardizable candles with a scatter of about 30% in brightness or 15% in distance. In a few years, refinements in the light curve fitting technique (Hamuy et al. 1996) and improvements in CCD photometry reduced the distance uncertainty to individual type Ia supernovae to 8%. The final hurdle was to solve the problem of dust. Micron-sized particles in galaxies scatter light traveling from a supernova and make it appear fainter than it would be without dust in the way. Dust is an insidious source of distance error because it only works to dim supernovae producing a systematic offset instead of increasing scatter. Generally, dust scatters blue light more efficiently than red, so a supernova is both dimmed and reddened by dust. In principle, if one knows the intrinsic color of a source and measures how much more red it appears, then the amount of dimming by dust can be deduced. Riess et al. (1996) found that type Ia supernova colors are correlated with their light curve shapes and developed a way to correct for dust extinction. In thirty years, supernovae had gone from a rough distance indicator with some promise to the most precise distance tool available for extragalactic astronomy.

3

Early Days of Distant Supernovae

A group led by C. Pennypacker began searching for distant type Ia supernovae in the late 1980s, before their precision as standardizable candles was fully established. This group would become the SCP led by S. Perlmutter in the 1990s. But finding supernovae at cosmologically interesting distances proved difficult, mainly due to detector and software limitations. An early successful search for distant supernovae was conducted by Norgaard-Nielsen et al. (1989). After two years of searching with a small telescope, they discovered a single type Ia supernova at a redshift of 0.3. While the supernova was not useful for constraining deceleration, their work demonstrated that it was possible to find these events at distances useful for cosmological measurement. The development of large format CCD detectors was critical for discovering significant numbers of high-redshift supernovae. A major step was the construction of mosaic imagers for the Cerro-Tololo (CTIO) 4-m telescope and the CanadaFrance-Hawaii Telescope (CFHT). Until 1997 the patch of sky that could be searched for new supernovae in a single exposure was limited by the physical size

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of CCD detectors to about 0.06 square degrees. Tiling the focal plane with several detectors immediately quadrupled the search area making the searches faster and more productive. Measuring the cosmic deceleration rate required building a reliable sample of nearby type Ia supernovae. The experiment outlined by Sandage directly compares the peak brightness of local and distant standard candles, thus eliminating the need to know an accurate value of the Hubble constant or the true luminosity of the candles. The SCP and HZT were not in the nearby supernova business and had to rely on existing supernova light curves that often were poorly calibrated. Fortunately, the Calán-Tololo Supernova Survey (Hamuy et al. 1993) had begun in the late 1980s to discover supernovae that were then followed and calibrated with CCD detectors. The Calán-Tololo supernovae were critical to the calibration of the type Ia luminosity/decline-rate relation, and they formed the foundation for the extension of the Hubble relation to high redshifts.

4

Two Teams

The SCP discovered its first high-redshift supernova in 1992, but really got the hang of it in 1994 with the discovery of six distant supernovae. In the early 1990s, each discovery was hard fought with the follow-up photometry and spectroscopy difficult. In those earliest days, the discovery of a candidate would mean coldcalling astronomers on telescopes around the world to try to get a spectrum before the supernova faded. Eventually, expanding the collaboration (A. Filippenko joined the SCP in 1993) and coordinating search and follow-up proposals for telescopes worldwide ended those annoying phone calls in the middle of the night. Just as the SCP was beginning to find significant numbers of supernovae, the High-Z team was getting organized. B. Schmidt and N. Suntzeff led a proposal in 1994 to search for type Ia supernovae with the CTIO 4-m. The new HZT discovered three distant supernovae in 1995 (Schmidt et al. 1998), and with that, the game was afoot. A friendly competition between the two teams ensued, and this competition likely shortened the time to the discovery of dark energy. The formation of a second team with essentially the same science goals as the first was the result of personality and philosophical differences. The members of the SCP mainly came from a physics culture, while the majority of the HZT members were astronomers by trade. At the time, astronomers tended to work in small groups and avoid hierarchical structures. For example, B. Schmidt was democratically elected by the members to be HZT leader. Further, the HZT designed the project so that junior members would be lead authors on key papers; in contrast, the first author of the SCP publications would always be S. Perlmutter, the leader. This clash of cultures is one reason astronomer A. Filippenko moved from the SCP to the HZT in 1995. Many of the astronomers on the HZT had been leaders in developing type Ia supernovae standardizable candles. M. Phillips, N. Suntzeff, and M. Hamuy at CTIO and A. Riess and R. Kirshner at the Center for Astrophysics (CfA) were applying

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type Ia supernovae to the problem of improving the measurement of the Hubble constant at about the same time the HZT was attempting to discover supernovae at high redshift. Correction for dust extinction was critical for an unbiased Hubble constant estimate, so a reddening correction was also important for measuring the deceleration parameter. This contrasted with the more statistical approach of the SCP: find a large number of high-redshift supernovae and check that their characteristics are the same as nearby events.

5

The Initial Results

The SCP’s first cosmological results (Perlmutter et al. 1997) analyzed the seven supernovae from 1992 to 1994. The paper also described an original method call “stretch” to parameterize light curve shapes and correct for the Phillips relation. With a small number of supernovae, the statistical uncertainties were large, but the results pointed to a universe with a high matter density and with no significant cosmological constant. Leibundgut et al. (1996) analyzed the light curve of the first HZT supernova, but cosmological results were slowed by poor weather during observing runs at the end of 1995. The publication of the initial SCP results was a blow to the HZT effort: it appeared the best HZT could do was to confirm the high matter density seen by the SCP. The race to extend the Hubble relation to high redshift caught the attention of the Director of the Space Telescope Science Institute. R. Williams offered both teams Hubble Space Telescope (HST) time to follow-up on their ground-based supernova discoveries. The field of view of HST was too small to be used to search for new supernovae, but the exquisitely sharp images provided by HST meant that supernova brightness measurements could be done with high precision. Coordinating a groundbased search with the weekly scheduling of HST meant that the space observations would miss the peak of the supernova light curves and only get data as the event faded. Still, the decline of the light curve held important information on the Phillips relation and corrections needed to get accurate distances to each supernova. By the late 1990s, wide-field mosaic cameras on large telescopes made finding high-redshift supernovae very efficient. Both teams found enough supernovae in the spring of 1997 to feed HST schedule and quickly began analyzing the images from both the ground and space. There was pressure to publish the results quickly and look good for the next HST proposal cycle. The SCP focused on one supernova that HST observed at a record redshift of 0.83. This was a supernova that exploded when the universe was about half its present age, and the paper was published in the flashy journal Nature in January 1998. The supernova’s distance and the precision of the HST data had an enormous impact on the SCP cosmological results. Instead of a universe with a high matter density, the addition of this single supernova to the 1997 data set suggested a better fit to a low deceleration rate and a low matter density (Perlmutter et al. 1998).

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The HZT was also hustling to analyze and publish their HST results as well as all the other supernovae discovered since 1995. HST observed four supernovae identified in the spring 1997 search runs with the Canada-France-Hawaii Telescope (CFHT) using their new large format mosaic camera. Two of the supernovae were found to be type Ia events at redshifts between 0.4 and 0.5 and a third appeared to be a type Ia supernova at a record redshift of 0.97. The final candidate had been misclassified and turned out to be a useless type II event. But the three type Ia supernovae when combined with the HZT’s first discovery, SN 1995K, provided clear evidence for a small deceleration rate meaning a low matter density universe (Garnavich et al. 1998a). With the help of HST, both teams came to agree on a low matter density universe and published their results within weeks of each other at the start of 1998.

6

The Discovery

As the competition between the teams heated up, the data analysis advanced well ahead of the publication of team papers. By January of 1998 the teams had published a total of 12 high-redshift supernova light curves but were analyzing six times that many. Based on the initial supernova data, the larger data set was enough to narrow the uncertainties and make a precise estimate of matter density. At the end of 1997, both teams were finding that the average supernova was coming in fainter than expected, fainter than even a low mater density universe could explain. Could this be dust or some error in the way the high-redshift light curves were being compared to their low-redshift cousins? At the American Astronomical Association (AAS) meeting in January of 1998, both teams presented their research at a press conference focusing on recent estimates of the matter density. S. Perlmutter mentioned the SCP’s recent Nature paper result and then showed a preliminary Hubble diagram with 40 high-redshift supernovae. The plot was impressive, but it was clear that the SCP was trying to deal with the systematic problem of dust extinction and had not decided on a result. At the same press conference, P. Garnavich presented the conclusions from the HST paper for the HZT. A. Riess and A. Filippenko were to lead the next paper for the HZT, and Garnavich was forbidden to mention any preliminary results from their larger data set. The AAS press conference was a big success when measured by front-page headlines in major newspapers. The takeaway from the press conference was that we lived in a low matter density universe that would expand forever. J. Glanz, a journalist for Science magazine, suspected that the teams were close to an even bigger result and began to press the SCP and HZT for a conclusion from the rest of their accumulated supernovae. Glanz did not have to wait long. A. Riess and B. Schmidt had been analyzing a total of 16 HZT supernova light curves since the fall of 1997. They were convinced that the sources of error, including dust extinction, were understood. Yet they were not seeing a deceleration in the data. Instead, the supernovae were pointing to an accelerating universe, one that requires a cosmological constant or some kind of dark energy. After they

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convinced each other, they then had to convince the rest of the team. Fortunately, the HZT paper analyzing their HST supernovae had just recently passed the extensive review by the whole team and this smoothed acceptance of the more unsettling acceleration. The SCP was divided about their data, but after the AAS meeting, they too became convinced that dust was not the source of the faint supernovae: it was cosmology. In mid-February, the two teams made scientific presentations at the “Dark Matter 1998” conference in Marina del Rey, CA. A. Filippenko presented the HZT results indicating an accelerating expansion and S. Perlmutter showed the same for the SCP. Based on supernova measurements, the universe had gone from decelerating to accelerating in less than eight months. But the fact that both teams now agreed quickly made this astounding discovery acceptable to most scientists. Word of the discovery of dark energy quickly spread in the press, even before peer review journals could independently consider the analysis. The HZT publication, A. (Riess et al. 1998), appeared in the September issue of the Astronomical Journal, and S. Perlmutter et al. (1999) was published in the June issue of the Astrophysical Journal (Fig. 1).

ng

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Fig. 1 Constraints on the matter density (M ) and dark energy density (ƒ / based on the HZT supernova discoveries combined with cosmic microwave background radiation measurements available in 1998. The intensity of the color scale indicates increasing joint probability for the matter density and cosmological constant values shown on the axes. The black region shows where the dark energy density would be too large to permit a Big Bang universe (From Garnavich et al. 1998b)

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Conclusions

The brightness of high-redshift type Ia supernovae provided the first direct evidence that the universe has an accelerating expansion rate. This accelerated expansion is likely due to a dark energy that now dominates over matter. Since this discovery, a wide variety of complementary observations have confirmed the existence of dark energy, although its true nature remains uncertain. The discovery of dark energy in 1998 came as a surprise, although the idea of a uniform, unchanging energy density had been around since Einstein. The speed in which dark energy was incorporated into the standard cosmological picture suggests that the discovery arrived at a time when the matter-only model was under stress. The work of the High-Z Team and the Supernova Cosmology Project has been recognized as a fundamental advancement in understanding the universe and the discovery was awarded many prizes including the 2011 Physics Nobel Prize.

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Cross-References

 History of Supernovae as Distance Indicators  Low-z Type Ia Supernova Calibration  The Hubble Constant from Supernovae  The Infrared Hubble Diagram of Type Ia Supernovae  The Peak Luminosity–Decline Rate Relationship for Type Ia Supernovae Acknowledgements The author is grateful to Brian Schmidt and the High-Z Supernova Search Team.

References Garnavich PM, Kirshner RP, Challis P et al (1998a) Constraints on cosmological models from hubble space telescope observations of high-z supernovae. Astrophys J 493:L53 Garnavich PM, Jha S, Challis P et al (1998b) Supernova limits on the cosmic equation of state. Astrophys J 509:74 Hamuy M, Maza J, Phillips MM et al (1993) The 1990 Calán/Tololo supernova search. Astron J 106:2392 Hamuy M, Phillips MM, Suntzeff NB et al (1996) The absolute luminosities of the Calan/Tololo Type IA supernovae. Astron J 112:2391 Kowal CT (1968) Absolute magnitudes of supernovae. Astron J 73:1021 Leibundgut B, Tammann GA (1990) Supernova studies. III – the calibration of the absolute magnitude of supernovae of type IA. Astron Astrophys 230:81 Leibundgut B, Schommer R, Phillips M et al (1996) Time dilation in the light curve of the distant type Ia supernova 1995K. Astrophys J 446:21 Norgaard-Nielsen HU, Hansen L, Jorgensen HE, Aragon Salamanca A, Ellis RS (1989) The discovery of a type IA supernova at a redshift of 0.31. Nature 339:523 Ostriker JP, Steinhardt PJ (1995) The observational case for a low-density universe with a non-zero cosmological constant. Nature 377:600

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Perlmutter S et al (1997) Measurements of the cosmological parameters omega and lambda from the first seven supernovae at z > 0.35. Astrophys J 483:565 Perlmutter S et al (1998) Discovery of a supernova explosion at half the age of the universe and its cosmological implications. Nature 391:51 Perlmutter S et al (1999) Measurements of omega and lambda from 42 high redshift supernovae. Astrophys J 517:565 Phillips MM (1993) The absolute magnitudes of type Ia supernovae. Astrophys J Lett 413:L105 Pskovskii YuP (1984) Photometric classification and basic parameters of type I supernovae. Soviet Astron 28:658 Riess AG, Press WH, Kirshner RP (1996) A precise distance indicator: type IA supernova multicolor light-curve shapes. Astrophys J 473:88 Riess AG, Filippenko AV, Challis P et al (1998) Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron J 116:1009 Sandage A (1961) The ability of the 200-INCH telescope to discriminate between selected world models. Astrophys J 133:355 Schmidt BP, Suntzeff NB, Phillips MM et al (1998) The high-Z supernova search: measuring cosmic deceleration and global curvature of the universe using type IA supernovae. Astrophys J 507:46

Confirming Cosmic Acceleration in the Decade That Followed from SNe Ia at z > 1

106

Adam G. Riess

Abstract

In the decade after the discovery of acceleration, the Hubble Space Telescope (HST) was used to find type Ia supernovae at z > 1 to test for astrophysical dimming an alternative explanation for acceleration. These objects were discovered during 14 epochs of reimaging of the GOODS fields North and South with the Advanced Camera for Surveys on HST. The full sample of 23 SNe Ia at z 1, 13 spectroscopically confirmed, provided the highest-redshift sample known to date and first traced the history of cosmic expansion over the last 10 billion years. The data are consistent with ˝M D 0:3; ˝ D 0:7 and inconsistent with a simple model of evolution or dust as an alternative to dark energy. Combined with previous SNe Ia, we found H(z) at discrete, uncorrelated epochs, reducing the uncertainty of H(z > 1) from 50 % to under 20 %, strengthening the evidence for a cosmic jerk the transition from deceleration in the past to acceleration in the present. These data provided the first meaningful constraint on the darkenergy equation-of-state parameter at z 1. The result remained consistent with a cosmological constant (w.z/ D 1) and ruled out rapidly evolving dark energy (d w=d z  1). The defining property of dark energy, its negative pressure, was present at z > 1, in the epoch preceding acceleration, with 98 % confidence in our primary fit. Moreover, the z > 1 sample-averaged spectral energy distribution was found to be consistent with that of the typical SN Ia over the last 10 Gyr.

Contents 1 2 3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Higher-z SNe Ia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alternatives to Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A.G. Riess Space Telescope Science Institute, AURA, Johns Hopkins University, Baltimore, MD, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_105

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4 Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2619 2620 2621 2621

Introduction

This chapter is largely based on the work by the Higher-Z Team through a series of large Hubble Space Telescope projects executed between 2003 and 2007 with a complete description of the work now published in Riess et al. (2007). The accelerating cosmic expansion first inferred from observations of distant type Ia supernovae (SNe Ia; Riess et al. 1998; Perlmutter et al. 1999) indicates unexpected gravitational physics, frequently attributed to the dominating presence of a “dark energy” with negative pressure. Increasingly incisive samples of SNe Ia at z < 1 have reinforced the significance of this result (Tonry et al. 2003; Knop et al. 2003; Barris et al. 2004; Conley et al. 2006; Astier et al. 2006; Conley 2011; Sullivan et al. 2011; Suzuki et al. 2012; Betoule et al. 2014; Rest et al. 2014; Scolnic et al. 2014). Using the new Advanced Camera for Surveys (ACS) and refurbished NICMOS camera on the Hubble Space Telescope (HST), our collaboration secured observations of a sample of the mostdistant known SNe Ia. These half-dozen SNe Ia, all at z > 1:25, helped confirm the reality of cosmic acceleration by delineating the transition from preceding cosmic deceleration during the matter-dominated phase and by ruling out simple sources of astrophysical dimming (Riess et al. 2004b, hereafter R04). The expanded sample of 23 SNe Ia at z 1 presented here is now used to begin characterizing the early behavior of dark energy. Other studies independent of SNe Ia now strongly favor something like dark energy as the dominant component in the mass-energy budget of the Universe. Perhaps most convincingly, observations of large-scale structure and the cosmic microwave background radiation provide indirect evidence for a dark-energy component (e.g., Spergel et al. 2007). Measurements of the integrated Sachs-Wolfe effect (e.g., Fosalba et al. 2003; Afshordi et al. 2004; Boughn and Crittenden 2004; Nolta et al. 2004; Scranton et al. 2005) more directly suggest the presence of dark energy with a negative pressure. Additional, albeit more tentative, evidence is provided by observations of X-ray clusters (Allen et al. 2004) and baryon oscillations (e.g., Eisenstein et al. 2005). The unexplained existence of a dominant, dark-energy-like phenomenon presents a stiff challenge to the standard model of cosmology and particle physics. The apparent acceleration may result from exotic physics such as the repulsive gravity predicted for a medium with negative pressure or from entirely new physics. The explanation of strongest pedigree is Einstein’s famous “cosmological constant”  (i.e., vacuum energy; Einstein 1917), followed by a decaying scalar field similar to that already invoked for many inflation models (i.e., quintessence – Wetterich 1995; Caldwell et al. 1998; Peebles and Ratra 2003). Competitors include the Chaplygin

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2617

gas (Benot et al. 2002), topological defects, and a massless scalar field at low temperature. Alternatively, alterations to general relativity may be required as what occurs from the higher-dimensional transport of gravitons in string theory models (Deffayet et al. 2002) and braneworlds or by finely tuned, long-range modifications (e.g., Cardassian type, Freese 2005; or Carroll et al. 2004; see Szydlowski et al. 2006 for a review). Empirical clues are critical for testing hypotheses and narrowing the allowed range of possible models. SNe Ia remain one of our best tools for unraveling the properties of dark energy because their individual measurement precision is unparalleled and they are readily attainable in sample sizes of order 102 , statistically sufficient to measure dark-energy-induced changes to the expansion rate of 1 %. Specifically, the equation-of-state parameter of dark energy, w (where P D wc 2 ), determines both the evolution of the density of dark energy, Z

1

DE D DE;0 expf3 a

da .1 C w.a//g; a

and its gravitational effect on expansion, 4 G aR D .1 C 3w.a//; a 3 where DE;0 is the present dark-energy density. Measuring changes in the scale factor, a, from the present time, t0 , to the time t at redshift, z, or from the distance and redshift measurements of SNe Ia, dl .z/ D c.1 C z/

Z t

t0

dt 0 D a.t 0 /

Z

z 0

d z0 ; H .z0 /

constrains the behavior of w.a/ or w.z/ and is most easily accomplished at z < 2 during the epoch of dark-energy dominance. Here dl is the luminosity distance derived from the brightness of a standard candle. Ideally, we seek to extract the function w.z/ for dark energy or its mean value at a wide range of epochs. Alternatively, we might constrain its recent value w0  w.z D 0/ and a derivative, d w=d z  w0 , which are exactly specified for a cosmological constant to be (1,0). Most other models make less precise predictions. For example, the presence of a “tracker” dark-energy field whose evolution is coupled to the (decreasing) dark matter or radiation density may be detected by a measured value of w0 > 0. In truth, we know almost nothing of what to expect for w.z/, so the safest approach is to assume nothing and measure w.z/ across the redshift range of interest. SN Ia at z > 1 are crucial to constrain variations of w with redshift. These measurements can only be made from space, and we report here on that endeavor. We have discovered and measured 21 new SN Ia with HST and used them to constrain the properties of the dark energy.

2618

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A.G. Riess

Higher-z SNe Ia

In Fig. 1 we show the Hubble diagram of distance moduli and redshifts for all of the HST-discovered SNe Ia in the Gold and Silver sets from our program. The new SNe Ia span a wide range of redshift (0:21 < z < 1:55), but their most valuable contribution to the SN Ia Hubble diagram remains in the highest-redshift region where they now well delineate the range at z 1 with 23 SNe Ia, 13 new objects since R04. This territory remains uniquely accessible to HST, which has discovered the dozen highest-redshift SNe Ia known, and its exploration is the focus of the rest of this chapter. In the inset to Fig. 1, we show the residual Hubble diagram (from an empty Universe) with the Gold data uniformly binned. Here and elsewhere, we will utilize uniform, unbiased binning achieved with a fixed value of nz, where z is the bin width in redshift and n is the number of SNe in the bin. The last bin ends abruptly with the highest-redshift SN; thus, its nz value is smaller than the rest. In Fig. 1 we use nz D 6 which yields seven bins for our sample. Although binning is for illustrative purposes in the Hubble diagram, there are some specific advantages of binning such as the removal of lensing-induced asymmetrical residuals by flux averaging (Wang 2005) and the ease of accounting for systematic uncertainties introduced by zeropoint errors in sets of photometric passbands used at similar redshifts.

HST Discovered Ground Discovered

45

35

high

0.5

Δ(m-M) (mag)

μ

Binned Gold data

40

ay d

ust

z

tion ~ Evolu

pure acceleration: q(z)=-0.5

w=-1.2, dw

/dz=-0.5

0.0

ΩM =1

.0, Ω

Λ

-0.5

30

z gr

w=-0.8

, dw/dz

=0.0

Empty (Ω=0) ΩM=0.27, ΩΛ=0.73

0.0

0.5

0.5

1.0 z

1.0 z

~ pure

=+0.5

dece

lerati on: q

(z)=0

1.5

1.5

.5

2.0

2.0

Fig. 1 MLCS2k2 SN Ia Hubble diagram. SNe Ia from ground-based discoveries in the Gold sample are shown as diamonds, HST-discovered SNe Ia are shown as filled symbols. Overplotted is the best fit for a flat cosmology: ˝M D 0:27, ˝ D 0:73. Inset: Residual Hubble diagram and models after subtracting empty Universe model. The Gold sample is binned in equal spans of nz D 6 where n is the number of SNe in a bin and z is the redshift range of the bin

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The distance-redshift relation of SNe Ia is one of few powerful tools available in observational cosmology. A number of different hypotheses and models can be tested with it, including kinematic descriptions of the expansion history of the Universe, the existence of mass-energy terms on the right-hand side of the Friedman equation, and the presence of astrophysical sources of contamination. Testing all interesting hypotheses is well beyond the scope of this chapter and is best left for future work. Instead, we now undertake a few narrowly posed investigations.

3

Alternatives to Dark Energy

After the detection of the apparent acceleration of cosmic expansion (and dark energy) by Riess et al. (1998) and Perlmutter et al. (1999), alternative hypotheses for the apparent faintness of high-redshift SNe Ia were posed. These included extragalactic gray dust with negligible telltale reddening or additional dispersion (Rana 1979, 1980; Aguirre 1999a, b) and pure luminosity evolution (Drell et al. 2000). In R04 we found that the first significant sample of SNe Ia at z > 1 from HST rejected with high confidence the simplest model of gray dust by Goobar et al. (2002), in which a smooth background of dust is present (presumably ejected from galaxies) at a redshift greater than the SN sample (i.e., z > 2) and diluted as the Universe expands. This model and its opacity were invented to match the 1998 evidence for dimming of supernovae at z  0:5 without invoking dark energy in a Universe with ˝m D 1. This model is shown in the inset of Fig. 1. The present Gold sample (at the best fitting value of H0 ) rejects this model at even higher confidence (2 D 194, i.e., 14  ), beyond a level worthy of further consideration.

4

Dark Energy

Strong evidence suggests that high-redshift SNe Ia provide accurate distance measurements and that the source of the apparent acceleration they reveal lies in the negative pressure of a “dark-energy” component. Proceding from this conclusion, our hard-earned sample of SNe Ia at z > 1:0 can provide unique constraints on its properties. Strong motivation for this investigation comes from thorough studies of high-redshift and low-redshift SNe Ia, yielding a consensus that there is no evidence for evolution or intergalactic gray dust at or below the current statistical constraints on the average high-redshift apparent brightness of SN Ia (see Filippenko 2004, 2005 for recent reviews). We summarize the key findings here. (1) Empirically, analyses of SN Ia distances versus host stellar age, chemical abundance, morphology, and dust content indicate that SN Ia distances are relatively indifferent to the evolution of the Universe (e.g., Riess et al. 1999; Sullivan et al. 2003; Astier et al. 2006; Wang and Mukherjee 2006). (2) Detailed examinations of the distance-independent properties of SNe Ia (including the far-UV flux, e.g., as presented in the last section) provide strong evidence for uniformity across redshift

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A.G. Riess

and no indication (thus far) of redshift-dependent differences (e.g., Sullivan et al. 2005; Howell et al. 2005; Blondin et al. 2006). (3) SNe Ia are uniquely qualified as standard candles because a well-understood, physical limit (the Chandrasekhar limit) appears to explain the homogeneity for their majority (weirdos, Iax, and a handful of possible super-Chandra SNe excluded). Based on these studies, we adopt a limit on redshift-dependent systematics is to be 5 % per z D 1 at z > 0:1 and make quantitative use of this here. Many have studied the constraint placed by the redshift-magnitude relation of SNe Ia on the parameter combination ˝M -w, where w (assumed to be constant) is the dark-energy equation-of-state parameter. There are few models for dark energy that predict an equation of state that is constant, different from the cosmological constant, and not already ruled out by the data. On the other hand, a prominent class of models does exist whose defining feature is a time-dependent dark energy (i.e., quintessence). While the rejection of w D 1 for an assumed constant value of w would invalidate a cosmological constant, it is also possible that apparent consistency with w D 1 in such an analysis would incorrectly imply a cosmological constant. For example, if w.z/ is rising, declining, or even sinusoidal, a measured derivative could be inconsistent with zero, while the average value remains near 1. Therefore, when using w.z/ to discriminate between darkenergy models, it is important to allow for time-varying behavior, or else valuable information may be lost. Here, we seek to constrain the value of w.z > 1/ and bound its derivative across the range 0:2 < z < 1:3. This is unique information afforded by the HST-discovered SN Ia sample. Finally, we may consider whether three additional parameters to describe w.z/ are actually needed to improve upon a flat,  cold dark matter (CDM) model fit to the data. To determine this we can calculate the improvement to the fit, 2eff  .2lnL/ D 2lnL.w D 1/  2lnL.wi D Wi /;

(1)

with i additional free parameters. For the weak, strong, and strongest priors, we find an improvement of 2eff D 4, 5.5, and 5.5, respectively, for the three additional degrees of freedom, in no case requiring the additional complexity in dark energy (improvements of >14 would be noteworthy). Likewise, there is no improvement at all for the Akaike information criterion (i.e., AIC D 2  2i ; Liddle 2004) with changes of 2, 0:5, and 0:5, respectively, which fail to overcome the penalty of increased complexity in the model.

5

Conclusions

(1) We present 21 new HST-discovered SNe Ia and an improved calibration of the previous sample from R04. Together this sample contains 23 SNe Ia at z 1, extending the Hubble diagram over 10 Gyr. (2) We derive uncorrelated, model-independent estimates of H .z/ which well delineate current acceleration and preceding deceleration. The HST-discovered SNe Ia measure H .z > 1/ to slightly better than 20 % precision.

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(3) The full HST-discovered SN Ia sample, presented here, provides a factor of two improvements over our present ability to constrain simple parameterizations of the equation-of-state parameter of dark energy (w) and its evolution. (4) Stronger priors and tighter constraints on the preferred cosmological model can be extracted from independent measurements tied to the surface of last scattering, but the use of these requires assumptions about the behavior of dark energy across a wide range of redshift (1:8 < z < 1089). The strongest of these priors, like the simplest dark-energy parameterizations, appears unjustified in the presence of our current ignorance about dark energy. Assuming the effect of dark energy at z > 1:8 is minimal, we derive meaningful constraints on the early properties of dark energy: w.z > 1/ D 0:8C0:6 1:0 and w.z > 1/ < 0, i.e., negative pressure, at 98 % confidence. (5) At present, we find that the use of more than one parameter, i.e., a constant, to describe w.z/ does not provide a statistically significant improvement to the fit of the redshift-magnitude relation over the use of a simple cosmological constant. (6) An analysis of the z > 1 sample-averaged spectrum shows it to be consistent with the mean spectrum of SNe Ia over the last 10 Gyr, failing to reveal direct evidence for SN Ia evolution.

6

Cross-References

 Discovery of Cosmic Acceleration  History of Supernovae as Distance Indicators  The Peak Luminosity-Decline Rate Relationship for Type Ia Supernovae Acknowledgements We are grateful to Dorothy Fraquelli, Sid Parsons, Al Holm, Tracy Ellis, Richard Arquilla, and Mark Kochte for their help in assuring rapid delivery of the HST data. We also wish to thank Ryan Chornock, Anton Koekemoer, Ray Lucas, Max Mutchler, Sherie Holfeltz, Helene McLaughlin, Eddie Bergeron, and Matt McMaster for their help. Financial support for this work was provided by NASA through programs GO-9352, GO-9728, GO-10189, and GO10339 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. Some of the data presented herein were obtained with the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA; the Observatory was made possible by the generous financial support of the W. M. Keck Foundation.

References Aguirre AN (1999a) ApJ 512:L19 Aguirre AN (1999b) ApJ 525:583 Afshordi N, Loh Y-S, Strauss MS (2004) Phys Rev D 69:083524 Allen SW, Schmidt RW, Ebeling H, Fabian AC, van Speybroeck L (2004) MNRAS 353:457 Astier P et al (2006) A&A 447:31 Barris B et al (2004) ApJ 602:571 Benot MC Bertolami O, Sen AA (2002) PhRvD 66(4):3507 Betoule M et al (2014) A&A 568:A22

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Blondin S et al (2006) AJ 131:1648 Boughn S, Crittenden R (2004) Nature 427:45 Caldwell RR, Davé R, Steinhardt PJ (1998) Ap&SS 261:303 Carroll SM, Duvvuri V, Trodden M, Turner MS (2004) Phys Rev D 70:043528 Conley A et al (2006) ApJ 644:1 Conley A et al (2011) ApJS 192:1 Deffayet C, Dvali G, Gabadadze G (2002) Phys Rev D 1:65044023 Drell PS, Loredo TJ, Wasserman I (2000) ApJ 530:593 Einstein A (1917) SPAW 142:142–152 Eisenstein DJ et al (2005) ApJ 633:560 Filippenko AV (2004) Evidence from type Ia supernovae for an accelerating Universe and dark energy. In: Freedman WL (ed) Measuring and modeling the universe. Carnegie Observatories astrophysics series, vol 2. Cambridge University Press, Cambridge, p 270 Filippenko AV (2005) Type Ia supernovae and cosmology. In: Sion SVennes EM, Vennes S, Shipman HL (eds) White dwarfs: cosmological and galactic probes. Springer, Dordrecht, p 97 Fosalba P et al (2003) ApJ 597:L89 Freese K (2005) New Astron Rev 49:103 Goobar A, Bergstrom L, Mörtsell E (2002) A&A 384:1 Howell DA et al (2005) ApJ 634:1190 Knop R et al (2003) ApJ 598:102 Liddle AR (2004) MNRAS 351:49 Nolta MR et al (2004) ApJ 608:10 Peebles PJ, Ratra B (2003) Rev Mod Phys 75:559 Perlmutter S et al (1999) ApJ 517:565 Rana NC (1979) Ap&SS 66:173 Rana NC (1980) Ap&SS 71:123 Rest A et al (2014) ApJ 795:44 Riess AG et al (1998) AJ 116:1009 Riess AG et al (1999) AJ 118:2668 Riess AG et al (2004a) ApJ 600:L163 Riess AG et al (2004b) ApJ 607:665 (R04) Riess AG et al (2007) ApJ 659:98 Scolnic D et al (2014) ApJ 795:45 Scranton R et al (2005) ApJ 633:589 Spergel et al (2007) ApJS 170:377 Sullivan M et al (2003) MNRAS 340:1057 Sullivan M et al (2011) ApJ 737:102 Suzuki N et al (2012) ApJ 746:85 Szydlowski M, Kurek A, Krawiec A (2006) Top ten accelerating cosmological models. arXiv:astroph/0604327 Tonry JT et al (2003) ApJ 594:1 Wang Y (2005) New Astron Rev 49:97 Wang L et al (2006) ApJ 641:50 Wang Y, Mukherjee P (2006, in press) ApJ 650:1. arXiv:astro-ph/0604051 Wetterich C (1995) A&A 301:321

Characterizing Dark Energy Through Supernovae

107

Tamara M. Davis and David Parkinson

Abstract

Type Ia supernovae are a powerful cosmological probe that gave the first strong evidence that the expansion of the universe is accelerating. Here we provide an overview of how supernovae can go further to reveal information about what is causing the acceleration, be it dark energy or some modification to our laws of gravity. We first review the methods of statistical inference that are commonly used, making a point of separating parameter estimation from model selection. We then summarize the many different approaches used to explain or test the acceleration, including parametric models (like the standard model, CDM), nonparametric models, dark fluid models such as quintessence, and extensions to standard gravity. Finally, we also show how supernova data can be used beyond the Hubble diagram, to give information on gravitational lensing and peculiar velocities that can be used to distinguish between models that predict the same expansion history.

Contents 1 2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statistical Inference: Model Testing vs. Parameter Fitting . . . . . . . . . . . . . . . . . . . . . . . 2.1 Parameter Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Model Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Variety of Models to be Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Standard CDM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Parametric Models, Simple Extensions to CDM . . . . . . . . . . . . . . . . . . . . . . . .

2624 2625 2626 2627 2627 2628 2629

T.M. Davis () and D. Parkinson School of Mathematics and Physics, University of Queensland, Brisbane, QLD, Australia ARC Centre of Excellence for All-sky Astrophysics (CAASTRO), Brisbane, QLD, Australia e-mail: [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_106

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T.M. Davis and D. Parkinson

3.3 Nonparametric Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Alternative Physical Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Models That Alter Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Beyond the Hubble Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Peculiar Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2631 2632 2634 2637 2638 2639 2640 2641 2641

Introduction

Discovering that the universe is accelerating is one thing. Determining what is causing the acceleration is quite another. Ever since type Ia supernovae confirmed (Perlmutter et al. 1999; Riess et al. 1998) earlier hints (Efstathiou et al. 1990; Krauss and Turner 1995; Ostriker and Steinhardt 1995; Yoshii and Peterson 1995) that the universe was accelerating, cosmologists have focused on determining why. Whatever the cause, we give it the name dark energy. Dark energy covers a wide range of possible explanations, from the energy of the vacuum through to beyond-standard theories of gravity. In very general terms, one can split explanations of the acceleration into those that modify gravity, i.e., change the G term in the Einstein equation, G D 8 T ;

(1)

and those that modify the contents of the universe, i.e., change the T term. In some cases, the distinction is operationally irrelevant. For example, the cosmological constant, introduced by Einstein such that G ! G C g , is exactly equivalent to adding a vacuum energy to T , where the cosmological constant is related to the energy density of the vacuum  D 8 vac . Some researchers use modified gravity to distinguish explanations that change the theory of gravity from those that introduce a new component to the stress-energy-momentum tensor of general relativity (T ), but here we will stick to dark energy to generically cover all possibilities. In this chapter, we aim to equip you with the tools you require to test new cosmological models against supernova data. To that end, we review the techniques available to determine which is the best model, an aim that differs from finding the best-fit parameters within a model (Sect. 2). We then summarize the range of models currently under consideration (and some classics that have already been ruled out; Sect. 3). We conclude by looking at how supernovae are being used to test cosmology through the inhomogeneities in the Hubble diagram caused by peculiar velocities and gravitational lensing (Sect. 4).

107 Characterizing Dark Energy Through Supernovae

2

2625

Statistical Inference: Model Testing vs. Parameter Fitting

The supernova data, like any measurement of cosmological distances, cannot be used to determine the properties of the universe directly. In this sense, the universe cannot be “weighed” in the manner of an object or particle on Earth, since the properties of dark energy and dark matter, or the nature of the acceleration, are classic examples of an inverse problem – we start with a set of results (in this case the magnitudes of distant supernovae) and then compare them with predictions from some assumed causes. This is opposite to a forward problem, which starts with a set of causes, and then computes the results. Statistical inference of this type is commonly done in a Bayesian framework, where the probabilities associated with causes as well as results can be evaluated. Bayesian statistics provides two complementary tools: • Parameter fitting, where the data is used to evaluate the probabilities associated with the parameters of a given assumed model • Model selection, where the data is used to choose between different models or explanations of the data To determine which model best explains dark energy, we need to test each model against data and rank them based on some model selection statistic. Rather than trying to find the best-fitting parameters within a model, we are trying to determine a more fundamental question – whether the model itself is a good one. Parameter fitting can reveal weaknesses in a model when the model is unable to reproduce the measurements. However, it says little about whether that model outperforms another model when both are good fits. The discovery of the accelerating universe was not technically a discovery of acceleration, but rather a discovery that a model that included cosmological constant-like dark energy outperformed a model with only matter and radiation. (Direct detection of the acceleration may be possible in the future by longterm monitoring of the redshift evolution of extragalactic spectra, known as the “Sandage-Loeb” effect; Loeb 1998; Sandage 1962). Prior to the supernova data, the preferred model for our universe was general relativity with cold dark matter (CDM). To calculate the expansion history in such a model, you only need to know the matter density m and the Hubble constant H0 , often written as h D H0 =100 km s1 Mpc1 . Type Ia supernovae proved difficult to fit with such a model. By adding one parameter, i.e., a cosmological constant ƒ , the new model (CDM) was a much better fit. In the CDM model the universe accelerates, thus the discovery of “acceleration.” However, a model with an extra parameter will always be able to outperform a model that has a subset of its parameters, because the extra flexibility can only improve the fit. Whether the extra parameter is justified requires some assessment of model selection, i.e., is the more complex model enough of a better fit to justify

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the addition of the extra parameter? In the case of ƒ , the answer was a most resounding “yes!" Here we will briefly summarize the methods by which such statements are quantified, both parameter fitting and model selection.

2.1

Parameter Fitting

In Bayesian statistics, the parameter likelihood L.f g/ D P .Djf g/ is the probability of the data (the “results”) given some parameter values (f g, the “causes”). What we are usually trying to figure out is the reverse of this – the likelihood of the parameter values given the data – which is known as the posterior P .f gjD/. The two are not exactly the same, but are related to each other through Bayes’ theorem, which incorporates any prior knowledge that should be included in the calculation P .f g/: P .f gjD/ / P .Djfg/P .fg/ :

(2)

For data with a large number of measurements (such as supernovae, where a large number of photons are incident on the detector), the likelihood function P .Djf g/ will converge to a Gaussian, through the central limit theorem. In this case, the likelihood can be evaluated through a 2 calculation, since the 2 is proportional to the log of the likelihood: 2 =2

L D e 

:

(3)

The value of 2 in the simplest case of independent data points for a particular data/model combination is given by 2 D

X  model;i  i 2 ; i i

(4)

where model;i is the value for data point i predicted by the model and i ˙ i is the i th data point and uncertainty. We then evaluate the value of 2 at every point in the parameter space fg of the model being tested. Once the 2 has been computed across the range of parameter values, it can be used to determine the likelihood L.fg/. Then the prior can be applied to determine the posterior probability distribution of the parameters, given the data. There are many different approaches to sampling the parameter space and generating the posterior statistics. For example, a grid search can become computationally expensive and inefficient as the dimension of the search space becomes large, and so adaptive or Monte Carlo methods are used instead.

107 Characterizing Dark Energy Through Supernovae

2.2

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Model Testing

Finding the best-fit parameters in a model is not enough; one should also always test whether the best fit is a good fit. The reduced 2 is a simple way to get a feel for which model best describes the data but alone is not enough. While it gives a rough estimate of whether a particular model is a good fit to the data, it does poorly at comparing models when those models have differing numbers of free parameters. For example, adding a cosmological constant to the CDM model to make it CDM gave the model extra flexibility, so it is guaranteed to be a better fit than CDM alone. Thus, a lower 2 =dof (where dof is the number of degrees of freedom in fitting the data, which can normally be evaluated as the number of independent data points minus the number of model parameters) is not a good enough criterion on its own to judge the relative merits of a model. Bayesian evidence quantifies how well a model describes the data weighted by the amount of parameter space it could have covered. A simpler model has less parameter space, so if it is able to fit the data as well as a more complex model, then it will be preferred by the Bayesian evidence calculation. In essence this is quantifying Occam’s razor. An example of the use of the Bayesian evidence to choose between parameterizations for the dark energy equation of state is given in Liddle et al. (2006). Information criteria (IC) are another method to penalize more complex models. They simply ask whether a parameter is worthwhile adding to a model by comparing the best-fit 2 before and after the parameter has been added. There are several options including the Akaike IC and the Bayesian IC, which differ slightly in their level of penalty for adding extra parameters (Liddle 2007). An example of these IC applied to supernova cosmology can be found in Davis et al. (2007).

3

The Variety of Models to be Tested

Models of dark energy take many forms. After establishing the basics of the standard model (Sect. 3.1), we begin by describing parametric models that consider dark energy time evolution following particular functional forms (Sect. 3.2) and then consider nonparametric models that allow more flexible time-varying dark energy (Sect. 3.3). These are both methods driven by observation, where the functional forms and methods are motivated by the desire to generically test whether dark energy varies with time or remains consistent with a cosmological constant. We then go on to describe models driven by theory, such as dark fluid models, f .R/ gravity, and braneworld models (Sects. 3.4 and 3.5). These make more specific predictions for how dark energy could possibly vary with time or position.

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The Standard CDM Model

The standard cosmological model, CDM, is an on-average homogeneous, isotropic universe that is spatially flat, consisting of matter, radiation, and a cosmological constant. For late-time measurements, the radiation is negligible, so the contents of the universe are completely designated by a single parameter, the matter density m D m =crit , which is defined relative to the critical density crit , and includes both luminous matter and cold (nonrelativistic) dark matter (CDM). Since the universe in this model is flat, the cosmological constant is simply given by ƒ D 1  m . This standard CDM model belongs to a more general family of models with non-zero curvature, characterized by the Friedmann-Robertson-Walker (FRW) metric, which describes spacetime in an on-average homogeneous and isotropic universe. The metric is given by

 ds 2 D c 2 dt 2 C R2 .t / d2 C Sk2 ./.d 2 C sin2  d 2 / :

(5)

Here t is cosmological time,  is comoving distance, and  and  are the angular position in spherical coordinates. The scale factor R.t / is often normalized to its value at the present day a.t / D R.t /=R0 and Sk ./ D sin./; ; sinh./ in closed, flat, and open geometries, respectively. The Hubble parameter is defined as the ratio P of the rate of change of scale factor to the scale factor itself, H .t / D R=R D a=a, P where overdot represents differentiation with respect to time. More often H .t / is replaced with H .z/ since it is computationally and observationally easier to represent time by the redshift of a galaxy that emitted the light we now see at that time. Comoving distance is Z

zN

d .Nz/ D R0 .Nz/ D c 0

dz ; H .z/

(6)

where zN is the cosmological redshift (with no contribution from peculiar velocities or lensing). Luminosity distance, which is the distance measured by supernovae, is related to comoving distance by dL .z/ D .1 C z/R0 Sk ..Nz// :

(7)

Note the two different redshifts in this equation. The comoving distance is governed by the cosmological redshift, but the pre-factor (that arises due to dilution of photon number counts and beaming) is sensitive to the observed redshift. Using the cosmological redshift in both terms gives negligible error at the level of current experiments, but using the observed redshift in both gives significant errors (Calcino 2015). By inserting the stress-energy-momentum equation relevant for an isotropic, homogeneous, perfect fluid, into Einstein’s equations, one can derive Friedmann’s

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equation, which governs the dynamics of the expansion. Taking into account many contributions to the energy density of the universe (˝i ), the Friedmann equation is concisely expressed as H 2 .z/ D H02

X

˝i .1 C z/3.1Cwi / ;

(8)

i

where the equation of state parameter, w D p=, is the ratio of pressure to density of each component (w D 13 ; 0; 1 for radiation, matter, and cosmological constant, respectively). In the CDM model that becomes H .z/ D H0 Œm a3 C k a2 C ƒ 1=2 . Note P that in non-flat universes, it is important to include a curvature term k D 1  ˝i , with wk D  13 . With these basics established, we now move on to extensions and variations on this model.

3.2

Parametric Models, Simple Extensions to CDM

The simplest alternative to a cosmological constant, where the energy density is constant with time, would be some time-varying dark energy. Without reference to any physical model, this is normally parameterized by wDE , which characterizes the equation of state of dark energy (DE). For an arbitrary equation of state, where wDE can take any value as a function of time or scale factor, the energy density can be found by solving the continuity equation, to give

DE .Nz/ D

0 DE

(Z exp 0

zN

3.1 C wDE .z// dz 1Cz

) :

(9)

If the equation of state is constant with redshift, then this simply becomes 0 DE .Nz/ D DE .1 C zN/3.1CwDE / :

(10)

The cosmological constant is the only model that predicts an equation of state w D 1 for all epochs, though we will see later that some models can predict an equation of state very close to that of  at late times (often by design!). Because of this, any decisive detection of wDE ¤ 1 at any epoch would automatically rule out the cosmological constant as a convincing explanation for the acceleration. Current constraints place wDE very close to 1. A data compilation that includes cosmic microwave background temperature and polarization data from the Planck surveyor; baryon acoustic oscillation data from 6dFGS, SDSS-MGS, BOSS-LOWZ, and CMASS-DR11; supernova data from the joint light-curve analysis; and H0 measurements from Cepheids gives a combined constraint on a constant equation of state of w D 1:019C0:075 0:080 at 95 % confidence (Planck Collaboration et al. 2015).

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Table 1 A number of different parameterizations for the scale factor or redshift dependence of the dark energy equation of state Parameterization Linear in redshift

Reference Huterer and Turner (1999), Weller and Albrecht (2001) Chevallier and Polarski (2001), Linder (2003) Jassal et al. (2005)

w.z/ D w0 C w1 z

w.a/ D w0 C wa .1  a/ z D w0 C w1 1Cz z scale w.a/ D w0 C wa .1Cz/ 2

Linear in scale factor

Nonlinear in factor Logarithmic in red- w.z/ D w0 C w1 ln.1 C z/ shift A steplike function

Hybrid model

w.z/ D w0 C

Efstathiou (1999)

w1 w0 1CexpŒ.zzt /= a1= Œ1.a=a /1=  .w0  wa / 1a1= t

D wa C ( w0 C w1 z w.z/ D w0 C w1

if if

z 0

Starobinsky (2007)

0 < n < 1, R0 &  > 0 Amendola et al. (2007) R0 &  > 0

 fR R  r r fR 

R0 ; n; c1 & c2 > 0

Appleby and Battye (2007), Tsujikawa (2008)

 f .R/  fR g D 8 GT ; 2

(18)

where fR D @f .R/=@R and   r ˛ r˛ . Once the function f .R/ is chosen, then the Friedmann-Robertson-Walker metric, Ricci scalar, and Ricci tensor can be inserted into Eq. 18, and the modified Friedmann equation can be derived. In order to choose a viable f .R/ function, there are a number of stability conditions that must be considered, including no antigravity, which holds that f0 R > 0 for R R0 , where R0 is the present value of the Ricci scalar; consistency with local gravity tests, where the second derivative f0 RR > 0 for R R0 and f .R/ ! R  2 for R  R0 ; and stability of the late-time de Sitter point: Rf Rf where 0 < f00 RR < 1 at r D  f0 R D 2 (Amendola et al. 2007). R A list of some of the proposed f .R/ models that satisfy these conditions is given in Table 2. All of these models contain a threshold value of the Ricci scalar R0 , which has to be tuned to the correct value in order to manifest the observed late-time acceleration. So these models also suffer from the fine-tuning problem of the cosmological constant. In a sense, all of these models have been “designed” to recover the observed acceleration. However, they should not be considered as final theories, but rather as “effective theories” that phenomenologically describe some undiscovered new explanation or theory of gravity.

3.5.2 Braneworld Models The idea of “branes” (short for membranes) as lower-dimensional objects in a higher-dimensional space first arose out of string theory. In Kaluza-Klein theory, all extra dimensions are compactified, but in braneworld models, a three(spatial)dimensional brane is embedded in a 5D bulk with large extra dimensions. In these models, standard model particles are open strings, whose ends must be fixed on a brane, whereas gravitons (which are closed strings) are allowed to propagate in the bulk. Thus, it may be possible to generate acceleration by having gravity “leak” out of the brane into the bulk (Deffayet et al. 2002).

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The DGP braneworld model proposed by Dvali et al. (2000) consists of three branes embedded in a Minkowski bulk spacetime with infinitely large extra dimensions. In the standard DGP model, 4D gravity (Newton’s law) is recovered on small distances, whereas the effect for the 5D gravity manifests as a modification only on large distances. There is a solution to the DGP model that is “self-accelerating,” requiring no extra dark fluid to generate the observed acceleration. For a flat geometry, the modified Friedmann equation is given by H 2  2

G.4/ 8 G.4/ H D ; G.5/ 3

(19)

where G.4/ is the value of Newton’s gravitational constant induced on the brane, whereas G.5/ is the value of the gravitational constant in the higher-dimensional bulk and  D ˙1, depending on how the scale factor a is changing with respect to the extra-dimensional coordinate distance. For  D C1, and a universe dominated by nonrelativistic matter, the expansion approaches a de Sitter (accelerating) solution: H ! HdS D 2

G.4/ : G.5/

(20)

By tuning the value of the five-dimensional gravitational constant G.5/ , such that the ratio is of the order of the present Hubble radius H01 , we recover a late-time acceleration on the correct timescale to fit the observed value. This particular braneworld model seems like the most “natural” model to explain the acceleration, as it requires no value of the cosmological constant to be inserted by hand, and allows us to learn something about extra dimensions that is beyond the ability of current particle accelerators. However, the effective value of the equation of state today, w0 , is required in this theory to be approximately (Maartens and Majerotto 2006) weff D 

1 : 1 C ˝m

(21)

For a value of ˝m ' 0:3, this gives us weff ' 0:77, which is excluded by current data. Furthermore, a perturbation theory analysis shows that the original DGP model contains a ghost instability – that is a term with negative kinetic energy that creates a vacuum instability (Gorbunov et al. 2006). Thus, the DGP model is ruled out by both theory and experiment.

3.5.3 Galileon Models Galileon scalar fields are those that are invariant under a shift symmetry in field space, @ ! @ C c , where  is the scalar field. These theories can be considered as fully covariant forms of the DGP theory (see the previous Sect. 3.5.2), and, because of their symmetry, have the advantage that the field equations will

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be at most second order (Deffayet et al. 2009). In fact there are only five possible Lagrangians for the Galileon that remain second order when coupled to gravity and do not introduce ghost instabilities (Nicolis et al. 2009). The Galileon scalar contains a natural screening mechanism, the Vainshtein effect, where nonlinear effects decouple it from the matter sector. Thus the Galileon has no effect on the expansion rate during nucleosynthesis and recombination and only becomes important at late times (Chow and Khoury 2009). At late times the stable, self-accelerating branch has a very negative equation of state, w < 1. While it is possible to find regions of the Galileon parameter space that match the measured background history, there is then a tension between predictions for and measurements of the growth of structure (Appleby and Linder 2012).

4

Beyond the Hubble Diagram

If the expansion history remains consistent with CDM, then there is no way even in principle to use the Hubble diagram to distinguish between many models of dark energy because they can all reproduce the CDM expansion (as they are designed to do). However, structure formation can differ even in models that predict the same expansion history. Therefore, we look to the growth of structure, and lensing of light around that structure, to find signals that distinguish between models. In order to model the formation of structure, and the distortion of light by these structures, we need a metric that can model inhomogeneities. Using the conformal Newtonian gauge, we can consider perturbations to the Friedmann-RobertsonWalker metric, a temporal perturbation given by and a spatial perturbation given by ˚ such that

 ds 2 D a2 .1 C 2* /d 2 C .1  2˚/d xN 2 ;

(22)

where a is the scale factor, is the conformal time, and xN is the vector of spatial coordinates. In general relativity (and in the absence of any large-scale anisotropic stress) * D ˚, so there is no distinction between the spatial and temporal metric perturbations. However, other theories allow more flexibility, and this is a particularly interesting split because different measurable phenomena behave differently in the two components. For example, lensing is sensitive to both the time and space components, but clustering of matter is purely spatial. Supernovae can trace large-scale structure, both because they are good distance indicators (useful for peculiar velocities) and because they are good standard candles (useful for lensing magnification). Peculiar velocities dominate the dispersion at low redshifts (z . 0:3), whereas lensing dominates at higher redshifts. As data quality improves, both of these effects need to be taken into account to achieve unbiased cosmological constraints from the Hubble diagram. More interestingly, though, they can be used as a signal in their own right to distinguish between different theories explaining dark energy and dark matter. In this section, we discuss how supernovae can be used to make these two different types of measurements.

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Peculiar Velocities

Peculiar velocities, like the acceleration, cannot be directly measured, since all that can be taken from a galaxy spectrum is the total redshift. They are inferred by comparing a precise measurement of distance (e.g., using a supernova as a standard candle) to the distance expected given the object’s redshift (though in practice, we usually do not bother to convert the observables to distances, but work directly in terms of the discrepancies in magnitude). In a homogeneous universe, where all objects sit in the Hubble flow, there would be no difference, but in an inhomogeneous universe, discrepancies arise due to an extra redshift (or blueshift) created by local motion. Denoting the cosmological redshift, zN, and the peculiar velocity redshift, zp , the observed redshift, z, is given by .1 C z/ D .1 C zN/.1 C zp /:

(23)

Traditionally supernova cosmology analyses that fit the magnitude-redshift relation exclude or down-weight nearby supernovae at z < 0:02, because closer than that the contribution from peculiar velocities (which are 300 km s1 ) exceeds 5 % and due to correlations between supernova motions the error can be systematic (particularly for surveys covering small regions of sky). Peculiar velocity measurements are often made using galactic distance measures like Tully-Fisher (Tully and Fisher 1977) and fundamental plane (Djorgovski and Davis 1987; Dressler et al. 1987). While these methods have the advantage of large numbers, the errors associated with them are often large and very non-Gaussian, leading to biases that need to be carefully accounted for (Johnson et al. 2014; Scrimgeour et al. 2016). Supernovae on the other hand have much tighter and more Gaussian probability distributions, making them excellent tools for peculiar velocities. Velocity perturbations are generated by density perturbations through the gradient of the gravitational potential r. Since the distribution of matter can be modelled/measured as a power spectrum, the distribution of velocities can also be described using a power spectrum. Peculiar velocities are particularly useful because the motion of galaxies is induced by the entire density field, including dark matter, so they are not limited in the manner of galaxy surveys, which only directly trace the density of visible matter. Moreover, peculiar velocities are sensitive to very large-scale density fluctuations, beyond the scale that is easy testable in galaxy redshift surveys that measure clustering (Johnson et al. 2014). By measuring the power spectrum of galaxy motions, you get a direct measurement of how quickly structures are growing. This is a useful measure to observationally distinguish between different theories (Jennings et al. 2012; Koda et al. 2013). There are several ways in which peculiar velocities can be compared to models. Peculiar velocities manifest themselves as a scatter in the Hubble diagram, but the scatter is not random. This could be a source of systematic error, since supernovae that are part of the same velocity field will have related offsets in redshift. Using

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a model power spectrum, one can predict the strength of correlations in supernova magnitudes (Davis et al. 2011; Hui and Greene 2006). This allows you to remove the impact of peculiar velocities on the magnitude-redshift cosmology estimates by using the covariance matrix to down-weight the supernovae that should have correlated velocities (the detailed equations can be found in Davis et al. 2011). However, if you want to compare the strength of the correlations to theory, and so use the size of the velocities as a cosmological probes, it is possible to calculate the covariance matrix generated by the peculiar velocities for various models and find the one that best fits the data. This is almost reversing what is usually done in Eq. 3, because the model does not go into the distances, but into the covariance matrix, e.g., 0 1 X 1 1 .v/1 LD exp @ vi .x/ N Cij vj .x/ N A: j2 C .v/ j1=2 2 ij

(24)

Here the measured values of the velocity along the line of sight, v, at positions, x, N are being compared to the predicted correlations between them, as quantified by the inverse of the velocity covariance matrix for those positions C .v/ . For details on how to calculate the covariance matrix for different theoretical models, see Johnson et al. (2014). Yet another method is to compare measured peculiar velocities to the predicted peculiar velocities inferred from maps of the density of galaxies (e.g., Carrick et al. 2015; Springob et al. 2016, 2014). This has been successful but encounters limitations because the fluctuation modes that affect velocities are often larger than encapsulated in the density data.

4.2

Lensing

It has long been known that supernova light is magnified and demagnified as it rides the rollercoaster of curved space en route from the supernova to our telescopes (Dodelson and Vallinotto 2006; Frieman 1996; Holz 1998). Dense lines of sight cause light to converge and result in magnification, while emptier lines of site cause light to diverge and demagnify. The strength of matter clustering as a function of redshift is sensitive to the cosmological parameters (particularly the matter density) and to the law of gravity. Therefore, measuring the lensing distribution can be used to measure cosmological parameters and test for deviations from standard gravity (e.g., see Wang 1999,Fig. 5 for a plot of magnification probability for various cosmologies). Since clusters and filaments take up a relatively small volume compared to the voids between them, there are more under-dense lines of sight than over-dense ones. So the signature of lensing is an asymmetric scatter about the Hubble diagram, with the median peaking on the faint side. The signal increases with redshift, because the

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lines of sight are longer. Typically we would expect additional magnitude dispersion due to lensing up to a maximum of 0:04 mag for supernovae at z < 1. This asymmetric distribution does not bias the Hubble diagram, since the number of photons must be conserved. While many supernovae are slightly demagnified, a small number are highly magnified, and the mean is unaffected. Biases only arise if the sample is incomplete (which can occur, e.g., due to Malmquist bias losing faint galaxies or because highly lensed supernovae are obscured by the dust in the galaxies that would have magnified them). The magnification is related to the convergence  and can be estimated once we know the Hubble constant, the matter density, the total density, the distance to the supernova, and the density distribution along the line of sight. See Eq. 6.16 in Bartelmann and Schneider (2001) for details and Smith et al. (2014) for a practical implementation. Two ways of measuring the effect of lensing on supernova magnitudes are to: 1. Measure the asymmetry in the scatter about the Hubble diagram (fit to moments of the distribution). 2. Measure the cross-correlation between supernova magnitudes and foreground densities. Detecting the signal of lensing requires many supernovae, so early attempts at both techniques gave varied results on the small supernova data sets available. Measuring the moments in the distribution was attempted by Wang (2005) and Castro and Quartin (2014), but careful modelling of the supernova magnitude measurements is required to rule out systematic error due to asymmetric observational uncertainties. Cross-correlating supernova brightnesses with foreground densities has been performed by Williams and Song (2004), Ménard and Dalal (2005), Jönsson et al. (2007), Jönsson et al. (2010), Kronborg et al. (2010), and Karpenka et al. (2013), and it is clear that modelling the mass distribution along the line of sight is important (e.g., Mörtsell et al. 2001). The statistically most robust analysis to date (made using the largest sample of supernovae) was performed by Smith et al. (2014), who found a positive but statistically marginal result (significance of 1.7 ). With upcoming surveys such as the Dark Energy Survey and the Large Synoptic Survey Telescope expecting to measure thousands of type Ia supernovae, the effect of lensing will be important to take into account for the standard Hubble diagram cosmological measurement and will be strong enough to use these techniques to treat the lensing dispersion distribution as signal in its own right.

5

Conclusions

This chapter reviewed some of the many varied models that try to explain the acceleration of the expansion of the universe (dark energy) and the ways in which we can test them. Supernovae provide excellent measurements of the expansion history of the universe, but also can be used to measure the structure within it through

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measurements of peculiar velocities and gravitational lensing. These latter features enable supernovae to distinguish between dark energy models that predict the same expansion history but differ in their predictions for growth of structure, in a way complementary to other large scale structure probes. At the moment, no theory to explain dark energy stands out as particularly compelling in relation to the others. Therefore, strong investment in theoretical efforts is required, and our observational efforts must keep looking for more precision and new ways to test dark energy, so we can provide compelling directions in which to guide theory.

6

Cross-References

 Confirming Cosmic Acceleration in the Decade That Followed from SNe Ia at

z>1  Discovery of Cosmic Acceleration  The Peak Luminosity-Decline Rate Relationship for Type Ia Supernovae  Type Ia Supernovae Acknowledgements We thank Edward Macaulay and Bonnie Zhang for helpful comments while this was under preparation. DP is supported by an Australian Research Council Future Fellowship (grant number FT130101086). Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020.

References Amendola L (2000) Coupled quintessence. Phys Rev D 62:043511. arXiv:astro-ph/9908023 Amendola L, Gannouji R, Polarski D, Tsujikawa S (2007) Conditions for the cosmological viability of f(R) dark energy models. Phys Rev D 75:083504. arXiv:gr-qc/0612180 Amendola L, Tsujikawa S (2010) Dark energy: theory and observations. Cambridge University Press, New York Appleby S, Battye R (2007) Do consistent F(R) models mimic general relativity plus ? Phys Lett B 654:7. arXiv:0705.3199 Appleby S, Linder EV (2012) Trial of Galileon gravity by cosmological expansion and growth observations. J Cosmo Astropart Phys 8:026. arXiv:1204.4314 Armendariz-Picon C, Mukhanov V, Steinhardt PJ (2001) Essentials of k-essence. Phys Rev D 63:103510. arXiv:astro-ph/0006373 Bartelmann M, Schneider P (2001) Weak gravitational lensing. Phys Rep 340:291. arXiv:astroph/9912508 Bassett BA, Kunz M, Parkinson D, Ungarelli C (2003) Condensate cosmology: dark energy from dark matter. Phys Rev D 68:043504. arXiv:astro-ph/0211303 Calcino J (2015) The effect of redshift bias on cosmology. Honours thesis, The University of Queensland Caldwell RR (2002) A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state. Phys Lett B 545:23. arXiv:astro-ph/9908168 Capozziello S, Lazkoz R, Salzano V (2011) Comprehensive cosmographic analysis by Markov chain method. Phys Rev D 84:124061

2642

T.M. Davis and D. Parkinson

Carrick J, Turnbull SJ, Lavaux G, Hudson MJ (2015) Cosmological parameters from the comparison of peculiar velocities with predictions from the 2MCC density field. Mon Not R Astron Soc 450:317 Castro T, Quartin M (2014) First measurement of  8 using supernova magnitudes only. Mon Not R Astron Soc 443:L6. arXiv:1403.0293 Cattoën C, Visser M (2008) Cosmographic hubble fits to the supernova data. Phys Rev D 78:063501 Chevallier M, Polarski D (2001) Accelerating universes with scaling dark matter. Int J Mod Phys D 10:213. arXiv:gr-qc/0009008 Chow N, Khoury J (2009) Galileon cosmology. Phys Rev D 80:024037. arXiv:0905.1325 Corasaniti PS, Kunz M, Parkinson D, Copeland EJ, Bassett BA (2004) Foundations of observing dark energy dynamics with the Wilkinson microwave anisotropy probe. Phys Rev D 70:083006 Daly RA, Djorgovski SG (2003) A model-independent determination of the expansion and acceleration rates of the universe as a function of redshift and constraints on dark energy. Astrophys J 597:9. arXiv:astro-ph/0305197 Daly RA, Djorgovski SG (2004) Direct determination of the kinematics of the universe and properties of the dark energy as functions of redshift. Astrophys J 612:652. arXiv:astroph/0403664 Daly RA, Djorgovski SG, Freeman KA, Mory MP, O’Dea CP, Kharb P, Baum S (2008) Improved constraints on the acceleration history of the universe and the properties of the dark energy. Astrophys J 677:1. arXiv:0710.5345 Davis TM, Hui L, Frieman JA, Haugbølle T, Kessler R, Sinclair B et al (2011) The effect of peculiar velocities on supernova cosmology. Astrophys J 741:67. arXiv:1012.2912 Davis TM, Mörtsell E, Sollerman J, Becker AC, Blondin S, Challis P et al (2007) Scrutinizing exotic cosmological models using ESSENCE supernova data combined with other cosmological probes. Astrophys J 666:716. arXiv:arXiv:astro-ph/0701510 de Putter & Linder (2008) To bin or not to bin: Decorrelating the cosmic equation of state. Astroparticle Physics, 29, 424 De Felice A, Nesseris S, Tsujikawa S (2012) Observational constraints on dark energy with a fast varying equation of state. J Cosmo Astropart Phys 5:029. arXiv:1203.6760 Deffayet C, Dvali G, Gabadadze G (2002) Accelerated universe from gravity leaking to extra dimensions. Phys Rev D 65:044023. arXiv:astro-ph/0105068 Deffayet C, Esposito-Farèse G, Vikman A (2009) Covariant galileon. Phys Rev D 79:084003. arXiv:0901.1314 Djorgovski S, Davis M (1987) Fundamental properties of elliptical galaxies. Astrophys J 313:59 Dodelson S, Vallinotto A (2006) Learning from the scatter in type Ia supernovae. Phys Rev D 74:063515. arXiv:astro-ph/0511086 Dressler A, Lynden-Bell D, Burstein D, Davies RL, Faber SM, Terlevich R, Wegner G (1987) Spectroscopy and photometry of elliptical galaxies. I – A new distance estimator. Astrophys J 313:42 Dvali G, Gabadadze G, Porrati M (2000) 4D gravity on a brane in 5D Minkowski space. Phys Lett B 485:208. arXiv:hep-th/0005016 Efstathiou G (1999) Constraining the equation of state of the universe from distant type Ia supernovae and cosmic microwave background anisotropies. Mon Not R Astron Soc 310:842. arXiv:astro-ph/9904356 Efstathiou G, Sutherland WJ, Maddox SJ (1990) The cosmological constant and cold dark matter. Nature 348:705 Frieman JA (1996) Weak lensing and the measurement of q0 ; from type Ia supernovae. Comments Astrophys 18:323. arXiv:astro-ph/9608068 Gorbunov D, Koyama K, Sibiryakov S (2006) More on ghosts in the Dvali-Gabadaze-Porrati model. Phys Rev D 73:044016. arXiv:hep-th/0512097 Hannestad S, Mörtsell E (2004) Cosmological constraints on the dark energy equation of state and its evolution. J Cosmol Astro-Part Phys 9:1. arXiv:astro-ph/0407259

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Holsclaw T, Alam U, Sansó B, Lee H, Heitmann K, Habib S, Higdon D (2010) Nonparametric reconstruction of the dark energy equation of state. Phys Rev D 82:103502. arXiv:1009.5443 Holz DE (1998) Lensing and high-z supernova surveys. Astrophys J Lett 506:L1. arXiv:astroph/9806124 Hu W, Sawicki I (2007) Models of f(R) cosmic acceleration that evade solar system tests. Phys Rev D 76:064004. arXiv:0705.1158 Hui L, Greene PB (2006) Correlated fluctuations in luminosity distance and the importance of peculiar motion in supernova surveys. Phys Rev D 73:123526. arXiv:astro-ph/0512159 Huterer D, Turner MS (1999) Prospects for probing the dark energy via supernova distance measurements. Phys Rev D 60:081301. arXiv:astro-ph/9808133 Jassal HK, Bagla JS, Padmanabhan T (2005) WMAP constraints on low redshift evolution of dark energy. Mon Not R Astron Soc 356:L11. arXiv:astro-ph/0404378 Jennings E, Baugh CM, Li B, Zhao G-B, Koyama K (2012) Redshift-space distortions in f(R) gravity. Mon Not R Astron Soc 425:2128. arXiv:1205.2698 Johnson A, Blake C, Koda J, Ma Y-Z, Colless M, Crocce M et al (2014) The 6dF galaxy velocity survey: cosmological constraints from the velocity power spectrum. Mon Not R Astron Soc 444:3926–3947 Jönsson J, Dahlén T, Goobar A, Mörtsell E, Riess A (2007) Tentative detection of the gravitational magnification of type Ia supernovae. J Cosmo Astropart Phys 6:002. arXiv:astro-ph/0612329 Jönsson J, Sullivan M, Hook I, Basa S, Carlberg R, Conley A et al (2010) Constraining dark matter halo properties using lensed supernova legacy survey supernovae. Mon Not R Astron Soc 405:535. arXiv:1002.1374 Kamenshchik A, Moschella U, Pasquier V (2001) An alternative to quintessence. Phys Lett B 511:265. arXiv:gr-qc/0103004 Karpenka NV, March MC, Feroz F, Hobson MP (2013) Bayesian constraints on dark matter halo properties using gravitationally lensed supernovae. Mon Not R Astron Soc 433:2693. arXiv:1207.3708 Khoury J, Weltman A (2004) Chameleon cosmology. Phys Rev D 69:044026. arXiv:astroph/0309411 Koda J, Blake C, Davis T, Magoulas C, Springob CM, Scrimgeour M et al (2014) Are peculiar velocity surveys competitive as a cosmological probe? Mon Not Roy Astron Soc 445:4267 Kolb EW, Marra V, Matarrese S (2010) Cosmological background solutions and cosmological backreactions. Gen Relat Gravit 42:1399 Krauss LM, Turner MS (1995) The cosmological constant is back. Gen Relat Gravit 27:1137. arXiv:astro-ph/9504003 Kronborg T, Hardin D, Guy J, Astier P, Balland C, Basa S et al (2010) Gravitational lensing in the supernova legacy survey (SNLS). Astron Astrophys 514:A44. arXiv:1002.1249 Lazkoz R, Alcaniz J, Escamilla-Rivera C, Salzano V, Sendra I (2013) BAO cosmography. J Cosmolo Astropart Phys (2013):005 Liddle AR (2007) Information criteria for astrophysical model selection. Mon Not R Astron Soc 377:L74. arXiv:astro-ph/0701113 Liddle AR, Mukherjee P, Parkinson D, Wang Y (2006) Present and future evidence for evolving dark energy. Phys Rev D 74:123506. arXiv:astro-ph/0610126 Linder EV (2003) Exploring the expansion history of the universe. Phys Rev Lett 90:091301. arXiv:astro-ph/0208512 Loeb A (1998) Direct measurement of cosmological parameters from the cosmic deceleration of extragalactic objects. Astrophys J Lett 499:L111. arXiv:astro-ph/9802112 Maartens R, Majerotto E (2006) Observational constraints on self-accelerating cosmology. Phys Rev D 74:023004. arXiv:astro-ph/0603353 Ménard B, Dalal N (2005) Revisiting the magnification of type Ia supernovae with SDSS. Mon Not R Astron Soc 358:101. arXiv:astro-ph/0407023 Mörtsell E, Gunnarsson C, Goobar A (2001) Gravitational lensing of the farthest known supernova SN 1997ff. Astrophys J 561:106. arXiv:astro-ph/0105355

2644

T.M. Davis and D. Parkinson

Nicolis A, Rattazzi R, Trincherini E (2009) Galileon as a local modification of gravity. Phys Rev D 79:064036. arXiv:0811.2197 Ostriker JP, Steinhardt PJ (1995) The observational case for a low-density universe with a non-zero cosmological constant. Nature 377:600 Perlmutter S, Aldering G, Goldhaber G, Knop RA, Nugent P, Castro PG et al (1999) Measurements of omega and lambda from 42 high-redshift supernovae. Astrophys J 517:565. arXiv:astroph/9812133 Planck Collaboration: Ade PAR, Aghanim N, Arnaud M, Ashdown M, Aumont J, Baccigalupi C et al (2015) Planck 2015 results. XIII. Cosmological parameters. ArXiv e-prints, arXiv:1502.01589 Räsänen S (2004) Dark energy from back-reaction. J Cosmolo Astropart Phys 2004(02):003 Ratra B, Peebles PJE (1988) Cosmological consequences of a rolling homogeneous scalar field. Phys Rev D 37:3406 Riess AG, Filippenko AV, Challis P, Clocchiatti A, Diercks A, Garnavich PM et al (1998) Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astrophys J 116:1009. arXiv:astro-ph/9805201 Sandage A (1962) The change of redshift and apparent luminosity of galaxies due to the deceleration of selected expanding universes. Astrophys J 136:319 Scrimgeour MI, Davis TM, Blake C, Staveley-Smith L, Magoulas C, Springob CM et al (2016) The 6dF galaxy survey: bulk flows on 50–70 h1 Mpc scales. Mon Not R Astron Soc 455:386. arXiv:1511.06930 Shafieloo A, Alam U, Sahni V, Starobinsky AA (2006) Smoothing supernova data to reconstruct the expansion history of the Universe and its age. Mon Not R Astron Soc 366:1081. arXiv:astroph/0505329 Smith M, Bacon DJ, Nichol RC, Campbell H, Clarkson C, Maartens R et al (2014) The effect of weak lensing on distance estimates from supernovae. Astrophys J 780:24. arXiv:1307.2566 Sollerman J, Mörtsell E, Davis TM, Blomqvist M, Bassett B, Becker AC et al (2009) FirstYear sloan digital sky survey-II (SDSS-II) supernova results: constraints on nonstandard cosmological models. Astrophys J 703:1374. arXiv:0908.4276 Springob CM, Hong T, Staveley-Smith L, Masters KL, Macri LM, Koribalski BS et al (2016) 2MTF – V. Cosmography, ˇ, and the residual bulk flow. Mon Not R Astron Soc 456:1886. arXiv:1511.04849 Springob CM, Magoulas C, Colless M, Mould J, Erdo˘gdu P, Jones DH et al (2014) The 6dF galaxy survey: peculiar velocity field and cosmography. Mon Not R Astron Soc 445:2677. arXiv:1409.6161 Starobinsky AA (2007) Disappearing cosmological constant in f(R) gravity. Soviet J Exp Theor Phys Lett 86:157. arXiv:0706.2041 Tsujikawa S (2008) Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints. Phys Rev D 77:023507. arXiv:0709.1391 Tsujikawa S (2013) Quintessence: a review. Class Quantum Gravity 30:214003. arXiv:1304.1961 Tully RB, Fisher JR (1977) A new method of determining distances to galaxies. Astron Astrophys 54:661 Upadhye A, Ishak M, Steinhardt PJ (2005) Dynamical dark energy: current constraints and forecasts. Phys Rev D 72:063501. arXiv:astro-ph/0411803 Visser M (2004) Jerk, snap and the cosmological equation of state. Class Quantum Gravity 21:2603 Wang Y (1999) Analytical modeling of the weak lensing of standard candles. I. Empirical fitting of numerical simulation results. Astrophys J 525:651. arXiv:astro-ph/9901212 Wang Y (2005) Observational signatures of the weak lensing magnification of supernovae. J Cosmo Astropart Phys 3:005. arXiv:astro-ph/0406635 Weller J, Albrecht A (2001) Opportunities for future supernova studies of cosmic acceleration. Phys Rev Lett 86:1939. arXiv:astro-ph/0008314 Wetterich C (1988) Cosmology and the fate of dilatation symmetry. Nucl Phys B 302:668 Williams LLR, Song J (2004) Weak lensing of the high-redshift SNIa sample. Mon Not R Astron Soc 351:1387. arXiv:astro-ph/0403680

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Wiltshire DL (2007) Cosmic clocks, cosmic variance and cosmic averages. New J Phys 9:377. arXiv:gr-qc/0702082 Wiltshire DL (2009) Average observational quantities in the timescape cosmology. Phys Rev D 80:123512. arXiv:0909.0749 Yoshii Y, Peterson BA (1995) Interpretation of the faint galaxy number counts in the K band. Astrophys J 444:15 Zunckel C, Trotta R (2007) Reconstructing the history of dark energy using maximum entropy. Mon Not R Astron Soc 380:865. arXiv:astro-ph/0702695

Supernova Cosmology in the Big Data Era

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Richard Kessler

Abstract

Here we describe large “Big Data” Supernova (SN) Ia surveys, past and present, used to make precision measurements of cosmological parameters that describe the expansion history of the universe. In particular, we focus on surveys designed to measure the dark energy equation of state parameter w and its dependence on cosmic time. These large surveys have at least four photometric bands, and they use a rolling search strategy in which the same instrument is used for both discovery and photometric follow-up observations. These surveys include the Supernova Legacy Survey (SNLS), Sloan Digital Sky Survey II (SDSSII), Pan-STARRS 1 (PS1), Dark Energy Survey (DES), and Large Synoptic Survey Telescope (LSST). We discuss the development of how systematic uncertainties are evaluated, and how methods to reduce them play a major role is designing new surveys. The key systematic effects that we discuss are (1) calibration, measuring the telescope efficiency in each filter band, (2) biases from a magnitude-limited survey and from the analysis, and (3) photometric SN classification for current surveys that don’t have enough resources to spectroscopically confirm each SN candidate.

Contents 1 2 3 4 5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of Fitting Light Curves and Hubble Diagrams . . . . . . . . . . . . . . . . . . . . . . . . Big Data Surveys: Past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Present and Future Big Data Surveys: DES and LSST . . . . . . . . . . . . . . . . . . . . . . . . . . Big Data Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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R. Kessler () Department of Astronomy and Astrophysics, Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL, USA e-mail: [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_107

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5.2 Bias Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Photometric Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

As described in previous sections of this handbook, observations of a few dozen type Ia supernovae (SNe Ia) were used to discover cosmic acceleration (Perlmutter et al. 1999; Riess et al. 1998). After standardizing the rest-frame supernova (SN) brightness to within about 15 %, corresponding to 7 % precision in distance, the observed brightness of distant SNe Ia at redshift z  0:5 (5 billion light years away) was compared to nearby SNe Ia at redshift z < 0:1. The key finding was that the distant SNe Ia are 30 % fainter than expected from a model of the universe containing only matter and undergoing gravitational contraction. The unexpected faintness led to the conclusion that cosmic acceleration has pushed these distant SNe Ia further away, contrary to the long-held conventional wisdom of cosmic deceleration. In the early years of studying type Ia supernovae (SNe Ia), observing and spectroscopically confirming each SN Ia required serious effort to coordinate resources with multiple instruments. Given the rarity and difficulty in acquiring these gems, many of the early pioneers knew their SNe Ia by name and could rattle off detailed information about the SN properties just like they could describe their own child. It is still quite common to hear astronomers describing newly discovered SNe Ia with comparisons such as “this one is 1991T-like” or “2002cx-like.” As samples become larger, the individuality of each SNe Ia becomes less important, and instead we focus more on their bulk properties. In spite of the name of this section title, “Big Data” is not a standard term used by astronomers studying SNe Ia. I will therefore arbitrarily define surveys in the Big Data era as having the following features: 1. they work in “rolling-search” mode, meaning that the same telescope is used for both discovery and following each light curve through broadband filters. 2. SN Ia light curves are measured in at least three broadband filters, giving twocolor measurements. 3. The transient search is associated with a wide-area survey using the same instrument. The advantage of feature (1) is that the earliest light curve points are observed with the same high-quality instrument, and one can recover early and late epochs where the SN is too faint to pass the detection threshold. Other advantages of using a single instrument are to simplify the calibration and to predict the effect of selection

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biases that favor brighter objects. The advantage of (2) is that since correcting the SN brightness for color is the main source of astrophysical uncertainty, having two nearly independent color measurements allows for important systematic checks. The advantage of (3) is that the associated wide-area survey typically results in more effort and resources for calibration, which is currently the largest source of systematic uncertainty. Ironically, the amount of data is not listed as a criteria for Big Data. Instead, the three definitions are related to data quality. In short, to improve measurements of cosmological parameters with SNe Ia, it is the improving data quality that drives larger data samples. Other notable aspects of Big Data include multiyear observing campaigns that require a dedicated team with a long-term commitment, large-scale computing platforms to process hundreds of Gb of new data in less than a day in order to find targets for spectroscopic follow-up observations, and extensive monitoring with fake SNe Ia overlaid near galaxies on real images. An outline of this article is as follows. A brief overview of light curve fitting and the SN Ia Hubble diagram is given in Sect. 2. Past Big Data surveys are reviewed in Sect. 3, and current and future surveys are described in Sect. 4. The main systematic uncertainties are discussed in Sect. 5, including calibration, selection biases, and photometric classification.

2

Overview of Fitting Light Curves and Hubble Diagrams

The Big Data discussions rely on the concept of light curve fitting (LC fitting) and Hubble diagram (HD), so here we give a brief overview of these concepts. The main goal of an LC fit is to determine the SN Ia color, stretch, and brightness; the color and stretch parameters are then used to standardize the brightness to within 15 %, and this 15 % irreducible scatter is from intrinsic brightness variations that do not correlate with other observables. The stretch is the relative light curve width compared to the average width of all SNe Ia, and the color parameter is roughly the B  V color at peak brightness. The wavelength dependence of SN Ia luminosities, known as a color law, is used to determine the color parameter. Typical light curve fits are shown in Fig. 1 for SDSS-II. Since observed SN light has been redshifted, the measured broadband magnitudes are combined with an average SN Ia spectrum to compute rest-frame magnitudes. The conversion factor between an observer-frame and rest-frame magnitude is referred to as K-correction (Nugent et al. 2002). To standardize the SN Ia magnitude, a linear function of the stretch and color works well. Quadratic terms have been tried, but not convincingly found. The linear coefficients for stretch and color, along with the color law, are determined from a process known as “training.” The training sample usually contains the highest quality light curves and those with good-quality spectra. For some of the early SN cosmology results (before Big Data), the color law was often assumed to be the same as that for the Milky Way (Galactic reddening law). Training with the SALT-II

Fig. 1 Light curve fits for 4 SNe Ia from SDSS-II (Kessler et al. 2009a), with redshift shown above each panel. Black points are the measured fluxes, and green curves show the best-fit light curve model

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method (Guy et al. 2010) on larger samples, however, showed that the empirically determined color law is quite different in the ultraviolet (UV) region, which has a significant effect on higher-redshift SNe. The determination of cosmological parameters comes from fitting a SN Ia Hubble diagram (HD), which is a plot of distance modulus (, defined below) versus redshift. Consider an ideal situation of measuring bolometric mags (mobs ) with 100 % efficiency and no Galactic extinction, and each SN Ia rest-frame mag (Mrest ) is fixed to a constant value: in this scenario the distance modulus is given by  D mobs  Mrest , the difference between the observed mag through a telescope and the rest-frame mag that would be observed at a distance of 10 kpc. In a universe with no expansion, no curvature, and a SN at distance D from Earth,  is simply related to the inverse-square law,  D 2:5 logŒ.10pc=D/2  D 5 log.D=10pc/:

(1)

Note that  D 0 at 10 pc, and it is defined to increase with distance. In an expanding universe, the distance D is replaced with the luminosity distance, DL , !  which depends on the redshift (z) and cosmological parameters ( C ), Z DL D c.1 C z/

!  d z=H .z; C /;

 D 5 log.DL =10pc/:

(2)

!  !  H .z; C / is the Hubble parameter as a function of redshift, C is an arbitrary set of fundamental parameters that describe cosmic expansion, and c is the speed of light. The Hubble parameter is most commonly expressed as

1=2 !  0 H .z; C / D H .z; ˝M ; ˝ ; w/ D H0 ˝0 .1 C z/3.1Cw/ C ˝M .1 C z/3

(3)

0 where ˝M ; ˝0 are today’s energy density of dark matter and dark energy, respectively, and w is the dark energy equation of state parameter. Note that w D 1 corresponds to a cosmological constant because ˝ .z; w D 1/ D ˝0 never changes. The radiation density today is ˝  105 and is small enough to be ignored in SN analyses. To summarize, measurements of redshift (z) and distance modulus () for each SN Ia are used to construct an HD, and the HD is fit to Eqs. 2 and 3 in order to determine ˝M , ˝ , and w. A flatness prior is often used in which there is no curvature and thus ˝M C ˝ D 1; this prior is based on measurements of the cosmic microwave background. Measuring an accurate redshift from spectroscopic features is relatively straightforward with adequate signal to noise, but measuring a distance with  D mobs  Mrest is overly simplistic because (1) the telescope efficiency depends on observed wavelength, (2) emitted light is redshifted when reaching Earth, (3) SN light reddens as it passes through dust in the host galaxy, (4) SN light reddens as it passes through Milky Way dust, (5) SN mag changes with time, and (6) Mrest varies with each SN Ia

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and requires an empirical correction based on color and stretch. A full description of determining  is beyond the scope of this section, but for the discussion that follows, we assume that the above effects have been accounted for.

3

Big Data Surveys: Past

We begin with the Supernova Legacy Survey (Astier et al. 2006,SNLS) that collected data from 2003 to 2008 using the 3.5 m Canada-France-Hawaii Telescope (CFHT). SNLS covered four 1-deg2 patches and was designed to measure accurate light curves for high redshift SNe Ia, 0:3 z 1. They used four broadband filters, denoted gri z, with central wavelengths 4900, 6300, 7690, and 8840 Å, respectively. At their lowest redshift (z D 0:3), the g band central wavelength maps to 3800 Å in the rest frame, which is well within the range of SN Ia light curve models. At their highest redshift (z D 1), the g band corresponds to 2500 Å in the rest frame, which is too far in the ultraviolet (UV) to be useful for light curve fitting; in practice the g-band is useful up to redshifts z 0:6. The remaining three bands (ri z) are useful for light curve fitting over the entire redshift range, thus satisfying the two-color requirement. While there are two colors available over the entire redshift range, note that at z D 1, the rest-frame wavelength range is compressed to 3150–4420 Å, which covers only the bluest region of the 3000–7000 Å wavelength range spanned by the SALT-II model (Guy et al. 2010). This limited wavelength coverage at higher redshifts results in larger uncertainties on the fitted parameters. Shortly after SNLS began, the Sloan Digital Sky Survey II (SDSS-II) used the 2.5 m telescope at the Apache Point Observatory to repeatedly search 300 deg2 in the fall seasons of 2005–2007. They discovered and measured light curves for SNe Ia in the redshift range z < 0:4 (Frieman et al. 2008) using five broadband filters (ugri z), although the sensitivity in the u and z bands was far less than in the gri bands. To monitor efficiencies from software selection and human scanners, this is the first Big Data survey that injected fake SNe Ia onto images during the survey in order to provide immediate feedback on the performance of discovering new SNe. Both SDSS-II and SNLS discovered and spectroscopically confirmed about 500 SNe Ia. Each team combined a subset of their SN sample with SN samples in the literature and with SDSS results on baryon acoustic oscillations (Eisenstein et al. 2005). They independently published their own cosmology results measuring ˝M and the dark energy equation of state parameter w and found w consistent with 1 to within about 10 % (Astier et al. 2006; Conley et al. 2011; Kessler et al. 2009a). These results included a detailed treatment of systematic uncertainties. Two noteworthy advances are calibration and bias corrections from simulations. The calibration is needed to accurately compare fluxes measured in different passbands within SDSS-II, SNLS, and the other survey instruments providing lower-redshift SNe Ia (see Sect. 5.1 below). While both teams worked for years to reach 1 % precision on their calibration, their results were nonetheless systematics limited by calibration.

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The second major improvement in these measurements is the use of detailed Monte Carlo simulations to measure and correct for biases (see Sect. 5.2 below). The largest effect is the well-known Malmquist bias in which intrinsically brighter objects are selected at higher redshift, resulting in a redshift-dependent bias in the Hubble diagram. Subtle fitting biases may also be present. The SNLS approach was to fully analyze images with roughly a million fake SNe Ia overlaid near galaxies (Perrett et al. 2010). The SDSS approach was to use a much smaller number of fakes to characterize the software detection efficiency vs. signal to noise and to analytically characterize the instrumental performance (Kessler et al. 2009b). The SNLS simulation has the advantage of being a more faithful representation of real data at the cost of requiring large amounts of computing. The SDSS approach has the advantage of speed, allowing for many iterations with different SN models and assumptions, and it can be used on arbitrary surveys without acquiring their images. Both teams realized that their cosmology results were systematics limited and that adding more data would be of little use without making fundamental improvements to the analysis. These two teams joined forces in 2010, and in a joint analysis, they produced a Hubble diagram with 740 SNe Ia (Fig. 2) and reduced the w-uncertainty to 6 % (Betoule et al. 2014). Their first major improvement was to compare stellar magnitudes in fields observed by both SDSS-II, SNLS, and the

m = mB – M(G) + aX1 – bC

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Hubble Space Telescope (HST), where the stars measured with HST are used as the standard reference for all SN magnitude measurements (Sect. 5.1). This effort led to reducing the calibration uncertainty by about a factor of 2 (Betoule et al. 2013), which reduces the overall w-uncertainty by 20 %. The second major improvement was to use simulations to rigorously evaluate systematic uncertainties from the 15 % irreducible (intrinsic) Hubble scatter and from the so-called “training” process that determines the parameters used to standardize the SN Ia luminosity as a function of its stretch and color. Cosmology fitting programs have always added the intrinsic scatter (int ) in quadrature with the measured uncertainties, and this is equivalent to assuming that the intrinsic scatter for a given SN Ia is characterized by a single number at all wavelengths and epochs. It is unlikely that the SN Ia brightness varies in such a simple manner, and thus the joint analysis team analyzed simulations with several different intrinsic scatter models that include significant wavelength variations. The other systematic effect, SN Ia training, is a very complex process for which previous training uncertainties were either ignored or based on educated guesses. Using the SALT-II light curve model, Mosher et al. (2014) used detailed simulations to evaluate the combined effect of training, light curve fitting, and using int in the cosmology fitting. They found a w-uncertainty of 0.02, well below the current constraints, but these effects could become important in future surveys with reduced uncertainties. The most recent Big Data survey to finish is Pan-STARRS 1 (Kaiser et al. 2002,PS1), which repeatedly observed 70 deg2 with a 1.8 m telescope in Hawaii. As with previous results, their first cosmology result was based on spectroscopically confirmed SNe Ia, and the precision was limited by calibration uncertainties. An interesting contribution of PS1 is their 3 sky calibration for which bright stars (mag < 21) in 3/4 of the sky are calibrated to within 0:005 mag (Schlafly et al. 2012). Scolnic et al. (2015) used this 3 calibration to propose a new “Supercal” method for SN Ia samples that overlap PS1. Instead of comparing tertiary stars (near each SN Ia) to HST spectrophotometric standards, they compare to stars measured by PS1. While the HST calibration may have a larger uncertainty, the relative uncertainty among the SN Ia samples can in principle be reduced to the 0:005 mag level after applying calibration offsets to correct for discrepancies. Scolnic et al. (2015) compared PS1 against star catalogs from SDSS, SNLS, CSP, and numerous low-z samples; most of the offsets are consistent with the reported 0.01 mag uncertainties, but discrepancies up to 0.03 mag were found. Applying these mag offsets to each non-PS1 sample, the equation of state parameter w changes by nearly 0.03 or half the current uncertainty.

4

Present and Future Big Data Surveys: DES and LSST

The Dark Energy Survey (DES) began a 5-year program in 2013 that includes a deep transient search over ten fields covering 30 deg2 . This survey uses the 4 m Blanco telescope at CTIO with a new 500 megapixel camera (Flaugher et al. 2015) featuring

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Fig. 3 Total transmission for DES filters and telescope (shaded) compared with transmissions from SNLS (dashed), a previous generation survey

a 3 deg2 field of view and 62 CCDs with enhanced sensitivity in the near infrared as shown in Fig. 3. The improved sensitivity in the i and z bands should result in finding more SNe at higher redshifts. Compared to a similar predecessor, SNLS, the DES-SN search covers 7 more area and has significantly better sensitivity in the z band. However, with limited spectroscopic resources, it is expected that the size of the spectroscopically confirmed subset in DES-SN will be similar to that in SNLS (400). To take advantage of the increased SN statistics, DES-SN will rely on photometric classification for the majority of SNe Ia (see Sect. 5.3 for more details). Although DES-SN will spectroscopically confirm only a small subset of SNe Ia, there are large multi-fiber spectroscopic programs to measure accurate host-galaxy redshifts for most of the SNe. To improve calibration, DES has two new systems in its arsenal. First, the telescope transmission versus wavelength, denoted T./, and out-of-band leakage are measured with a “DECal” system in which an artificial source of monochromatic light is sent into the telescope. Around the telescope entrance, there are NISTcalibrated photodiodes whose efficiency vs. wavelength is well known. The ratio of CCD signal to photodiode signal is a measure of the combined transmission of the telescope mirror, filters, and CCDs. Note that the definition of magnitude is sensitive to the shape of T./ and not the absolute transmission, and therefore there is no need to track the flux ratio of light entering the telescope and photodiodes. In other words, the photodiodes can be placed at an arbitrary distance from the light source as long as the DECal equipment does not move during a measurement of T./. T./ is typically measured with a 2 nm bandpass and in 2 nm steps and covers the gri z wavelength range 300 <  < 1100 nm. Naively such measurements would take place during daytime, but due to light leaks in the dome, the T./ measurements

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are performed on cloudy nights. This transmission function is measured as a function of position on the focal plane; the rising and falling edges shift by several nanometers over the focal plane, and using this information is critical to achieve sub-percent calibration. The second new system is an atmospheric telescope, called “AtmCam,” which measures changes in the atmosphere transmission (Li et al. 2012; Stubbs et al. 2007). The motivation for AtmCam is illustrated in Fig. 4: it is primarily to measure the effect of changes in precipitable water vapor (PWV), which can affect the z band calibration at the level of 0.01 mag. The Large Synoptic Survey Telescope (LSST Science Collaboration et al. 2009,LSST) is currently under construction and will be a significantly more powerful instrument than its predecessors. It will have an 8 m mirror (4 more area than

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Fig. 5 For each labeled instrument, the size of the square or circle illustrates the field of view, or sky area, covered by a single telescope exposure. The moon, M31 galaxy, and a 1 degree arrow are shown for scale. The telescope mirror size (in meters) is indicated for each instrument

DES) nearly 10 deg2 field of view (3 larger than DES) and advanced calibration systems to measure efficiency variations in the telescope and atmosphere. Current expectations are that tens of thousands of high-quality SN Ia light curves will be measured in the ugri zY bands. Numerous independent Hubble diagrams can be made with different systematic selections such as host-galaxy properties, SN Ia color, classification probability, etc. Comparing so many high-statistics Hubble diagrams will provide unique and critical information about systematic uncertainties. To illustrate the improving sky coverage of large surveys, Fig. 5 shows the field of view (FoV) for past, current, and future surveys. The LSST era will be spectacular, as it has a significant increase in both the FoV and the mirror size. An additional improvement, not shown in the figure, is the improved near-IR sensitivity.

5

Big Data Issues

Large SN Ia data samples bring many new challenges, some of which were described in previous sections. Here we discuss three major challenges in more detail: (1) calibration, (2) selection and fitting biases, and (3) photometric classification.

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Calibration

Since calibration is currently the largest source of systematic uncertainty for the SN Ia Hubble diagram, improving the calibration is essential for improving measurements of cosmological parameters with SNe Ia. This section is far too short to give a proper treatment, so we recommend an excellent paper by Regnault et al. (2009) for those ready to dive into the details. Here we give a brief introductory overview of the calibration issues. In many branches of science, the physical units of measurement (e.g., electron Volt, kilogram, meter) are so well calibrated that we can easily forget the underlying physical property for which these units are based. For example, if you want to measure gravitational acceleration using g D d =t 2 (distance divided by time squared), the precision is most likely determined by your budget to acquire accurate devices to measure distance and time. It is highly unlikely that you would ever need to know how units of distance and time are defined: how far light travels in a short time interval and radiation frequency from cesium 133. In contrast to these extremely well-defined units, astronomical magnitudes are based on comparing to a bright star, known as a “primary standard,” whose absolute brightness may not be known with the desired precision. This means that SN Ia flux measurements can be measured with better (sub-percent) precision than the primary standard. So while astronomical analyses never need to examine how the meter or second is defined, defining the brightness of a primary standard is always under scrutiny. Recall that the essential goal is to compare SN magnitudes at low and high redshift. For example, at z D 0:05, the rest-frame 4400 Å flux is observed in the g band, while at z D 0:50 this same flux is observed in the r band. Thus, comparing fluxes at these two redshifts requires a precise knowledge of the g and r band efficiencies: this is calibration. More generally, for a given rest-frame flux, the observed flux is measured in different filter bands at different redshifts, and the efficiency of each filter passband must be accurately measured. Note that calibration compares fluxes in different bands on the same telescope or from different telescopes. For example, SDSS, SNLS, and PS1 all have SDSS-like gri z filters. However, the transmission is slightly different on each telescope, and therefore measured transmissions are needed to correct one set of observations to accurately compare with another. Since the gri z filter transmissions are quite similar on each telescope (SDSS,SNLS,PS1), there is a relatively small uncertainty in comparing magnitudes among these telescopes. However, the low-z SN Ia sample was measured mostly with Bessell-like UBVRI filters which are quite different than gri z; accurately calibrating the UBVRI and gri z filter systems at the percent level has been a major challenge. Ideally, the telescope+atmosphere efficiency vs. wavelength would be measured well enough for sub-percent calibration, but previous surveys have not been able to do this. They have therefore relied on a relative calibration with respect to a primary spectrophotometric standard for which an accurate spectrum is known: Vega or BD +1 7 as measured by the Hubble Space Telescope (HST). SN fluxes are first compared to nearby “tertiary” stars as illustrated in Fig. 6. Ideally the same

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Fig. 6 Illustration of calibration between SNe observed in different fields. The red symbols represent the SN, and the arrows represent the calibration paths

survey instrument would be used to observe the HST standard, but this is difficult without saturating the CCDs. Vega is hopelessly bright for large telescopes, but BD + 17 (mag 10) has been observed with very short (1 s) exposures. Bohlin and Landolt (2015), however, have recently shown that the BD + 17 mag has been slowly changing at the level of 0.01 mag per year, and thus it is likely part of a binary system. Current projects are looking for more stable spectrophotometric standards measured with the Hubble Space Telescope (HST). While more recent surveys use BD + 17 which can be directly observed with short exposures, Vega-based observations are more common, particular for older SN surveys. A Vega calibration relies on a network of well-measured secondary stars known as “Landolt standards” (Landolt and Umoto 2007) and also on Landolt’s measurements of Vega mags. This Landolt technique was used for many of the low-z SNe Ia1 and leads to calibration difficulties because the filter transmissions for the Landolt observations are not well known. These UBVRI transmissions are approximately like those in Bessell (1990), and there has been significant effort in determining “effective Landolt filters transmissions” as well as the associated uncertainty. In addition to stellar references and filter transmissions, uniformity is another major issue. Ideally, 1000 photons hitting a CCD pixel will give the same signal

1 Most of the low-z SNe Ia used in cosmology analyses are from the Center for Astrophysics (Hicken et al. 2009,CfA), Carnegie Supernova Project (Contreras et al. 2010,CSP), and Lick Observatory Supernova Search (Ganeshalingam et al. 2013,LOSS).

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(number of electrons) regardless of where the pixel is located. In practice, however, each pixel has a different response and must be corrected. In principle, illumination flats correct each pixel to yield a uniform response. This works well on small scales (few pixels), but is not accurate over large scales because the flat illumination is not sufficiently uniform. The standard uniformity method is to observe stars in dense stellar fields and to make many dithered observations so that a given star is observed at many different locations on the focal plane. Flats and stellar field observations can be used to correct CCD response variations over the focal plane, but there is another uniformity challenge for scales much larger than the telescope field of view. SN surveys typically observe several different telescope pointings, some of which are separated by tens of degrees and thus have no overlap. With no common stars to observed in well-separated pointings, the challenge here is to determine a uniform zero point in each pointing. The standard technique is to interleave observations of the SN fields with observations of secondary (e.g., Landolt) or primary standards. In previous surveys the filter transmissions were rarely measured or not measured at all. Even if the transmissions are measured before a survey begins, aging effects can cause significant and unknown changes over time. There are two specific examples to illustrate this problem. First, Doi et al. (2010) remeasured the SDSS filter transmissions and found a significant change in the u band. The second case is when the SNLS i band filter was dropped in 2008 and then replaced. To track potential time-dependent changes in the telescope transmissions, newer surveys (see DES and LSST in Sect. 4) are employing on-site calibration systems which repeatedly measure telescope transmissions throughout the survey. In addition, atmospheric monitoring has also been added since atmospheric changes can be significantly larger and more frequent than those from the telescope.

5.2

Bias Corrections

SN Ia samples are effected by selection biases, primarily from Malmquist bias in which brighter SNe are preferentially selected. Additional biases can be introduced from light curve training and fitting (Sect. 2), fitting the Hubble diagram for cosmological parameters and from core collapse (CC) contamination in a photometrically classified sample (Sect. 5.3). The impact of these biases can be evaluated with a Monte Carlo simulation (MC) of SNe Ia, which is analyzed in exactly the same manner as the data. The basic philosophy of the MC is as follows. First, a light curve model is used to randomly select a set of SN Ia properties: stretch, color, and time of explosion or peak brightness. Next, a volumetric rate model is used to select a random redshift, and a cosmology model is used to determine the distance modulus to dim the apparent brightness of the SN. The MC uses the SN properties and distance modulus to predict the flux and uncertainty that would be measured at each survey observation date (epoch). The measured zero point at each epoch is used to convert the SN magnitude into a CCD flux. The measured sky noise and point spread function (PSF) are used to predict the flux uncertainty. In short, the

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Fig. 7 For the SDSS + SNLS joint analysis (Betoule et al. 2014), MC prediction for distancemodulus bias (  true ) vs. redshift

survey information is used to accurately predict what the telescope would observe for a set of randomly generated SNe Ia. To simulate CC SNe, there are no empirical stretch and color relations as with SNe Ia. Instead, well-measured CC light curves are used to create a set of interpolated templates, and a peak luminosity function is assumed, such as from Li et al. (2011). K-corrections are applied to predict the broadband magnitudes at arbitrary redshift. More details of CC simulations are in Kessler et al. (2010) and Bernstein et al. (2012). The MC is commonly used to predict and correct the Hubble diagram bias as shown in Fig. 7 for the joint SDSS + SNLS analysis. Checking the validity of the MC is tricky and involves examining data/MC comparisons of many distributions such as the fitted light curve parameters and quantities sensitive to signal to noise. The critical MC cross-check is to compare the fitted color vs. redshift as shown in Fig. 8 for several SN Ia samples that have been used in recent cosmology analyses. The average color decreases at higher redshifts where surveys preferentially select brighter events that tend to be bluer. The low-z sample is different because it is not from a rolling search and is instead based on follow-up observations of SNe discovered by other SN search programs. While the follow-up observations provide the zero point, sky noise, and PSF needed to perform a simulation, this information is not available for the low-z SN searches, and therefore the selection bias cannot be simulated from first principles. Although the exact low-z SN search cannot be simulated, two extreme cases can be simulated.

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Fig. 8 Fitted SALT-II color average vs. redshift for SN Ia samples used in recent cosmology analyses. Solid black circles are the data, and the lines are MC predictions using SNANA (Kessler et al. 2009b). The two MC predictions for the low-z sample are described in the text. SDSS and SNLS plots are from their joint analysis; low-z and PS1 plots are from Scolnic et al. (2014)

The first case is a volume-limited search that is naively expected because low-z searches are largely based on targeting known galaxies. The redshift dependence on the average color and stretch is assumed to be real physical properties of SN Ia, and the search instrument is assumed to have sufficient depth to find all low-z SNe. The second case is a magnitude-limited survey as suggested by the observed trend of decreasing color with redshift. In this case, an artificial telescope is tuned so that Malmquist bias causes the redshift dependence of color and stretch. Each MC simulation has been used to predict the low-z bias (low-z panel in Fig. 8), and the difference between these two low-z bias estimates is included in the systematic uncertainty budget (Betoule et al. 2014; Scolnic et al. 2014). The resulting bias uncertainty is 0.01 mag for the low-z sample.

5.3

Photometric Classification

While previous SN Ia cosmology results were based on spectroscopically confirmed samples, increasingly large imaging surveys will find many more SNe Ia than spectroscopic resources can confirm. To take advantage of these large samples in the future (PS1, DES, LSST), we are entering a new era in which high-statistics

Fig. 9 For a DES-SN simulation, SALT-II gri z light curve fits are shown for SNe of Type Ia (left), Type IIP (middle), and Type Ic (right). In the top panels, the generated redshift is z D 0:05, and the z band fit-model uncertainty is large because this wavelength range is well outside the valid range of the SALT-II model. In the bottom panels, the same SNe are generated at z D 0:40. Above each light curve, the best-fit chi-squared per degree of freedom is shown. The SN Ia

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Fig. 9 (continued) fit is good at both redshifts. The SN IIP fit is bad at both redshifts. The SN Ic fit is bad at low redshift and good at z D 0:40, illustrating a potential source of contamination in a photometrically classified samplex

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Fig. 10 For simulated SNe in the Dark Energy Survey, the SALT-II light curve fit probability distribution is shown for SNe Ia (solid black histogram) and for SNe CC (dashed red)

SN Ia Hubble diagrams will rely on “photometric classification” to identify SNe Ia using light curves without spectra. The first challenge is to reject contamination from the much more numerous CC SNe. About 70 % of CC SNe are Type II; these are relatively easy to distinguish from SNe Ia because Type II SNe are much dimmer, and their relatively flat light curve shape is quite different. Type Ib/c and a small fraction of Type II, however, can be photometrically similar to SNe Ia and are considered to be the most serious contamination. Figures 9 and 10 illustrate the CC contamination for a DES-SN simulation that includes SNe Ia based on the SALT-II model and CC SNe as described in Sect. 5.2 and in Kessler et al. (2010) and Bernstein et al. (2012). All simulated SNe are fit with the SALT-II light curve model. Fig. 9 shows a light curve fit for a typical SN type Ia, II, and Ic; the SN II fit is poor at both redshifts, but the SN Ic fit has a good 2 at the higher redshift and can thus contribute to the contamination. For a larger simulation that samples the SN CC luminosity function, a fit probability (Pfit : see Fig. 10) for each light curve is computed from the fit2 and the number of degrees of freedom. Most of the Type II light curves are much broader (and fainter) and those from SNe Ia, and thus Pfit ' 0 resulting in easy rejection. The Pfit distribution for Type Ib/c, and a small fraction of Type II, overlaps the SN Ia Pfit distribution and results in contamination at the few percent level. Continued efforts on photometric classification will hopefully reduce the CC contamination well below these initial estimates. A promising classification methodology is “machine-learning,” which includes techniques such as nearest neighbors, random forests, and neural networks. The caveat, however, is that these methods rely on a training sample. While the spectroscopically confirmed SN Ia training sample is plentiful, there are many fewer confirmed CC SNe with well-measured light curves.

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In addition to contamination, another challenge with photometric classification is to correctly identify the host galaxy (Gupta et al. 2016). While there are not enough spectroscopic resources to classify every SN, multi-fiber spectrographs can be used to measure accurate spectroscopic redshifts for most of the SN host galaxies, provided that the correct host galaxy is identified.

6

Conclusions

Using SNe Ia to precisely measure cosmological parameters is one of the most challenging experimental endeavors. It requires a dedicated team working over many years to collect data and to understand the instrumental performance in exquisite detail in order to distinguish astrophysical effects from instrumental effects. SN Ia cosmology has reached a level where results are systematics limited, so the brute-force method of building bigger telescopes with longer observing programs will not be sufficient to significantly improve cosmological constraints. More data must be accompanied by a reduction in systematic uncertainties. The good news is that the need to reduce systematic uncertainties is well recognized, and it has driven the design of large new surveys (e.g., DES, LSST), particularly in the development of new calibration equipment and techniques. Finally, I wish to thank a few of my younger colleagues for carefully reading this article and providing useful feedback: Dan Scolnic, Rachel Cane, and James Lasker.

7

Cross-References

 Characterizing Dark Energy Through Supernovae  Confirming Cosmic Acceleration in the Decade That Followed from SNe Ia at

z>1  Discovery of Cosmic Acceleration  History of Supernovae as Distance Indicators  Low-z Type Ia Supernova Calibration  The Hubble Constant from Supernovae  The Infrared Hubble Diagram of Type Ia Supernovae  The Peak Luminosity-Decline Rate Relationship for Type Ia Supernovae

References Astier P, Guy J, Regnault N, Pain R, Aubourg E, Balam D, Basa S, Carlberg RG, Fabbro S, Fouchez D, Hook IM, Howell DA, Lafoux H, Neill JD, Palanque-Delabrouille N, Perrett K, Pritchet CJ, Rich J, Sullivan M, Taillet R, Aldering G, Antilogus P, Arsenijevic V, Balland C, Baumont S, Bronder J, Courtois H, Ellis RS, Filiol M, Gonçalves AC, Goobar A, Guide D, Hardin D, Lusset V, Lidman C, McMahon R, Mouchet M, Mourao A, Perlmutter S, Ripoche P, Tao C, Walton N (2006) The supernova legacy survey: measurement of ˝M , ˝ , and w from the first year data set. Astron Astrophys 447:31–48

108 Supernova Cosmology in the Big Data Era

2667

Bernstein JP, Kessler R, Kuhlmann S, Biswas R, Kovacs E, Aldering G, Crane I, D’Andrea CB, Finley DA, Frieman JA, Hufford T, Jarvis MJ, Kim AG, Marriner J, Mukherjee P, Nichol RC, Nugent P, Parkinson D, Reis RRR, Sako M, Spinka H, Sullivan M (2012) Supernova simulations and strategies for the dark energy survey. Astrophys J 753:152 Bessell MS (1990) UBVRI passbands. PASP 102:1181–1199 Betoule M, Marriner J, Regnault N, Cuillandre JC, Astier P, Guy J, Balland C, El Hage P, Hardin D, Kessler R, Le Guillou L, Mosher J, Pain R, Rocci PF, Sako M, Schahmaneche K (2013) Improved photometrci calibration of the SNLS and SDSS SN surveys. Astron Astrophys 552:124 Betoule M, Kessler R, Guy J, Mosher J, Hardin D, Biswas R, Astier P, El-Hage P, Konig M, Kuhlmann S, Marriner J, Pain R, Regnault N, Balland C, Bassett BA, Brown PJ, Campbell H, Carlberg RG, Cellier-Holzem F, Cinabro D, Conley A, D’Andrea CB, DePoy DL, Doi M, Ellis RS, Fabbro S, Filippenko AV, Foley RJ, Frieman JA, Fouchez D, Galbany L, Goobar A, Gupta RR, Hill GJ, Hlozek R, Hogan CJ, Hook IM, Howell DA, Jha SW, Le Guillou L, Leloudas G, Lidman C, Marshall JL, Möller A, Mourão AM, Neveu J, Nichol R, Olmstead MD, PalanqueDelabrouille N, Perlmutter S, Prieto JL, Pritchet CJ, Richmond M, Riess AG, Ruhlmann-Kleider V, Sako M, Schahmaneche K, Schneider DP, Smith M, Sollerman J, Sullivan M, Walton NA, Wheeler CJ (2014) Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS SN samples. Astron Astrophys 568:22 Bohlin RC, Landolt AU (2015) The CALSPEC stars P177D and P330E. Astronon J 149:122 Conley A, Guy J, Sullivan M, Regnault N, Astier P, Balland C, Basa S, Carlberg RG, Fouchez D, Hardin D, Hook IM, Howell DA, Pain R, Palanque-Delabrouille N, Perrett KM, Pritchet CJ, Rich J, Ruhlmann-Kleider V, Balam D, Baumont S, Ellis RS, Fabbro S, Fakhouri HK, Fourmanoit N, González-Gaitán S, Graham ML, Hudson MJ, Hsiao E, Kronborg T, Lidman C, Mourao AM, Neill JD, Perlmutter S, Ripoche P, Suzuki N, Walker ES (2011) Supernova constraints and systematic uncertainties from the first three years of the supernova legacy survey. Astrophys J Suppl 192:1 Contreras C, Hamuy M, Phillips MM, Folatelli G, Suntzeff NB, Persson SE, Stritzinger M, Boldt L, González S, Krzeminski W, Morrell N, Roth M, Salgado F, José Maureira M, Burns CR, Freedman WL, Madore BF, Murphy D, Wyatt P, Li W, Filippenko AV (2010) The carnegie supernova project: first photometry data release of low-redshift type Ia supernovae. Astronon J 139:519–539. doi:10.1088/0004-6256/139/2/519 Doi M, Tanaka M, Fukugita M, Gunn JE, Yasuda N, Ivezi´c Ž, Brinkmann J, de Haars E, Kleinman SJ, Krzesinski J, French Leger R (2010) Photometric response functions of the sloan digital sky survey imager. Astronon J 139:1628–1648 Eisenstein DJ, Zehavi I, Hogg DW, Scoccimarro R, Blanton MR, Nichol RC, Scranton R, Seo HJ, Tegmark M, Zheng Z, Anderson SF, Annis J, Bahcall N, Brinkmann J, Burles S, Castander FJ, Connolly A, Csabai I, Doi M, Fukugita M, Frieman JA, Glazebrook K, Gunn JE, Hendry JS, Hennessy G, Ivezi´c Z, Kent S, Knapp GR, Lin H, Loh YS, Lupton RH, Margon B, McKay TA, Meiksin A, Munn JA, Pope A, Richmond MW, Schlegel D, Schneider DP, Shimasaku K, Stoughton C, Strauss MA, SubbaRao M, Szalay AS, Szapudi I, Tucker DL, Yanny B, York DG (2005) Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies. Astrophys J 633:560–574 Flaugher B, Diehl HT, Honscheid K, Abbott TMC, Alvarez O, Angstadt R, Annis JT, Antonik M, Ballester O, Beaufore L, Bernstein GM, Bernstein RA, Bigelow B, Bonati M, Boprie D, Brooks D, Buckley-Geer EJ, Campa J, Cardiel-Sas L, Castander FJ, Castilla J, Cease H, Cela-Ruiz JM, Chappa S, Chi E, Cooper C, da Costa LN, Dede E, Derylo G, DePoy LD, de Vicente J, Doel P, Drlica-Wagner A, Eiting J, Elliott AE, Emes J, Estrada J, Fausti Neto A, Finley DA, Flores R, Frieman J, Gerdes D, Gladders MD, Gregory B, Gutierrez GR, Hao J, Holland SE, Holm S, Huffman D, Jackson C, James DJ, Jonas M, Karcher A, Karliner I, Kent S, Kessler R, Kozlovsky M, Kron RG, Kubik D, Kuehn K, Kuhlmann S, Kuk K, Lahav O, Lathrop A, Lee J, Levi ME, Lewis P, Li TS, Mandrichenko I, Marshall JL, Martinez G, Merritt KW, Miquel R, Muñoz F, Neilsen EH, Nichol RC, Nord B, Ogando R, Olsen J, Palaio N, Patton K, Peoples J, Plazas AA, Rauch J, Reil K, Rheault JP, Roe NA, Rogers H, Roodman A, Sanchez E, Scarpine

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R. Kessler

V, Schindler RH, Schmidt R, Schmitt R, Schubnell M, Schultz K, Schurter P, Scott L, Serrano S, Shaw TM, Smith RC, Soares-Santos M, Stefanik A, Stuermer W, Suchyta E, Sypniewski A, Tarle G, Thaler J, Tighe R, Tran C, Tucker D, Walker AR, Wang G, Watson M, Weaverdyck C, Wester W, Woods R, Yanny B (2015) The DES collaboration, the dark energy camera. Astronon J 150:150 Frieman JA, Bassett B, Becker A, Choi C, Cinabro D, DeJongh F, Depoy DL, Dilday B, Doi M, Garnavich PM, Hogan CJ, Holtzman J, Im M, Jha S, Kessler R, Konishi K, Lampeitl H, Marriner J, Marshall JL, McGinnis D, Miknaitis G, Nichol RC, Prieto JL, Riess AG, Richmond MW, Romani R, Sako M, Schneider DP, Smith M, Takanashi N, Tokita K, van der Heyden K, Yasuda N, Zheng C, Adelman-McCarthy J, Annis J, Assef RJ, Barentine J, Bender R, Blandford RD, Boroski WN, Bremer M, Brewington H, Collins CA, Crotts A, Dembicky J, Eastman J, Edge A, Edmondson E, Elson E, Eyler ME, Filippenko AV, Foley RJ, Frank S, Goobar A, Gueth T, Gunn JE, Harvanek M, Hopp U, Ihara Y, Ivezi´c Ž, Kahn S, Kaplan J, Kent S, Ketzeback W, Kleinman SJ, Kollatschny W, Kron RG, Krzesi´nski J, Lamenti D, Leloudas G, Lin H, Long DC, Lucey J, Lupton RH, Malanushenko E, Malanushenko V, McMillan RJ, Mendez J, Morgan CW, Morokuma T, Nitta A, Ostman L, Pan K, Rockosi CM, Romer AK, Ruiz-Lapuente P, Saurage G, Schlesinger K, Snedden SA, Sollerman J, Stoughton C, Stritzinger M, Subba Rao M, Tucker D, Vaisanen P, Watson LC, Watters S, Wheeler JC, Yanny B, York D (2008) The sloan digital sky survey-II supernova survey: technical summary. Astronon J 135:338–347 Ganeshalingam M, Li W, Filippenko AV (2013) Constraints on dark energy with the LOSS SN Ia sample. MNRAS 433:2240–2258. doi:10.1093/mnras/stt893 Gupta RR, Kuhlmann S, Kovacs E, Spinka H, Kessler R, Goldstein DA, Liotine C, Pomian K, D’Andrea CB, Sullivan M, Carretero J, Castander FJ, Nichol RC, Finley DA, Fischer JA, Foley RJ, Kim AG, Papadopoulos A, Sako M, Scolnic DM, Smith M, Tucker BE, Uddin S, Wolf RC, Yuan F, Abbott TMC, Abdalla FB, Benoit-Levy A, Bertin E, Brooks D, Carnero Rosell A, Carrasco Kind M, Cunha CE, da Costa LN, Desai S, Doel P, Eifler TF, Evrard AE, Flaugher B, Fosalba P, Gaztanaga E, Gruen D, Gruendl R, James DJ, Kuehn K, Kuropatkin N, Maia MAG, Marshall JL, Miquel R, Plazas AA, Romer AK, Sanchez E, Schubnell M, Sevilla-Noarbe I, Sobreira F, Suchyta E, Swanson MEC, Tarle G, Walker AR, Wester W (2016) Host galaxy identification for supernova surveys. ArXiv e-prints Guy J, Sullivan M, Conley A, Regnault N, Astier P, Balland C, Basa S, Carlberg RG, Fouchez D, Hardin D, Hook IM, Howell DA, Pain R, Palanque-Delabrouille N, Perrett KM, Pritchet CJ, Rich J, Ruhlmann-Kleider V, Balam D, Baumont S, Ellis RS, Fabbro S, Fakhouri HK, Fourmanoit N, González-Gaitán S, Graham ML, Hsiao E, Kronborg T, Lidman C, Mourao AM, Perlmutter S, Ripoche P, Suzuki N, Walker ES (2010) The supernova legacy survey 3year sample: type Ia SN photometric distances and cosmological constraints. Astron Astrophys 523:7 Hicken M, Wood-Vasey WM, Blondin S, Challis P, Jha S, Kelly PL, Rest A, Kirshner RP (2009) Improved dark energy constraints from ˜100 new CfA supernova type Ia light curves. Astrophys J 700:1097–1140. doi:10.1088/0004-637X/700/2/1097 Kaiser N, Aussel H, Burke BE, Boesgaard H, Chambers K, Chun MR, Heasley JN, Hodapp KW, Hunt B, Jedicke R, Jewitt D, Kudritzki R, Luppino GA, Maberry M, Magnier E, Monet DG, Onaka PM, Pickles AJ, Rhoads HHP, Simon T, Szalay A, Szapudi I, Tholen DJ, Tonry JL, Waterson M, Wick J 2002 Pan-STARRS: a large synoptic survey telescope array, In: Tyson JA, Wolff S (eds) survey and other telescope technologies and discoveries, vol 4836. Society of Photo-optical Instrumentation Engineers, Bellingham, pp 154–164. doi:10.1117/12.457365 Kessler R, Becker AC, Cinabro D, Vanderplas J, Frieman JA, Marriner J, Davis TM, Dilday B, Holtzman J, Jha SW, Lampeitl H, Sako M, Smith M, Zheng C, Nichol RC, Bassett B, Bender R, Depoy DL, Doi M, Elson E, Filippenko AV, Foley RJ, Garnavich PM, Hopp U, Ihara Y, Ketzeback W, Kollatschny W, Konishi K, Marshall JL, McMillan RJ, Miknaitis G, Morokuma T, Mörtsell E, Pan K, Prieto JL, Richmond MW, Riess AG, Romani R, Schneider DP, Sollerman J, Takanashi N, Tokita K, van der Heyden K, Wheeler JC, Yasuda N, York D (2009a) First-Year sloan digital sky survey-II supernova results: hubble diagram and cosmological parameters. Astrophys J Suppl 185:32–84

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Kessler R, Bernstein JP, Cinabro D, Dilday B, Frieman JA, Jha S, Kuhlmann S, Miknaitis G, Sako M, Taylor M, Vanderplas J (2009b) SNANA: a public software package for supernova analysis. PASP 121:1028–1035 Kessler R, Bassett B, Belov P, Bhatnagar V, Campbell H, Conley A, Frieman JA, Glazov A, González-Gaitán S, Hlozek R, Jha S, Kuhlmann S, Kunz M, Lampeitl H, Mahabal A, Newling J, Nichol RC, Parkinson D, Philip NS, Poznanski D, Richards JW, Rodney SA, Sako M, Schneider DP, Smith M, Stritzinger M, Varughese M (2010) Results from the supernova photometric classification challenge. PASP 122:1415–1431 Landolt A, Umoto A (2007) Optical multicolor photometry of spectrophotometric standard stars. Astron J 133:768 Li T, DePoy DL, Kessler R, Burke DL, Marshall JL, Wise J, Rheault JP, Carona DW, Boada S, Prochaska T, Allen R (2012) aTmcam: a simple atmospheric transmission monitoring camera for sub 1 % photometric precision. In: Society of photo-optical instrumentation engineers (SPIE) conference series. Society of Photo-Optical Instrumentation Engineers (SPIE) conference series, vol 8446, p 2 Li W, Leaman J, Chornock R, Filippenko AV, Poznanski D, Ganeshalingam M, Wang X, Modjaz M, Jha S, Foley RJ, Smith N (2011) Nearby supernova rates from the lick observatory supernova search – II. The observed luminosity functions and fractions of supernovae in a complete sample. MNRAS 412:1441–1472 LSST Science Collaboration, Abell PA, Allison J, Anderson SF, Andrew JR, Angel JRP, Armus L, Arnett D, Asztalos SJ, Axelrod TS, et al (2009) LSST science book, Version 2.0. arXiv:0912.0201 Mosher J, Guy J, Kessler R, Astier P, Marriner J, Betoule M, Sako M, El-Hage P, Biswas R, Pain R, Kuhlmann S, Regnault N, Frieman JA, Schneider DP (2014) Cosmological parameter uncertainties from the SALT-II type Ia SN lightcurve models. Astrophys J 793:16 Nugent P, Kim A, Perlmutter S (2002) K-Corrections and extinction corrections for type Ia supernovae. PASP 114:803–819 Perlmutter S, Aldering G, Goldhaber G, Knop RA, Nugent P, Castro PG, Deustua S, Fabbro S, Goobar A, Groom DE, Hook IM, Kim AG, Kim MY, Lee JC, Nunes NJ, Pain R, Pennypacker CR, Quimby R, Lidman C, Ellis RS, Irwin M, McMahon RG, Ruiz-Lapuente P, Walton N, Schaefer B, Boyle BJ, Filippenko AV, Matheson T, Fruchter AS, Panagia N, Newberg HJM, Couch WJ, Project TSC (1999) Measurements of omega and lambda from 42 high-redshift supernovae. Astrophys J 517 565–586. doi:10.1086/307221 Perrett K, Balam D, Sullivan M, Pritchet C, Conley A, Carlberg R, Astier P, Balland C, Basa S, Fouchez D, Guy J, Hardin D, Hook IM, Howell DA, Pain R, Regnault N (2010) Real-time analysis and selection biases in the supernova legacy survey. Astron J 140:518–532 Regnault N, Conley A, Guy J, Sullivan M, Cuillandre JC, Astier P, Balland C, Basa S, Carlberg RG, Fouchez D, Hardin D, Hook IM, Howell DA, Pain R, Perrett K, Pritchet CJ (2009) Photometric calibration of the supernova legacy survey Fields. Astron Astrophys 506:999–1042 Riess AG, Filippenko AV, Challis P, Clocchiatti A, Diercks A, Garnavich PM, Gilliland RL, Hogan CJ, x Jha AV, Kirshner RP, Leibundgut B, Phillips MM, Reiss D, Schmidt BP, Schommer RA, Smith RC, Spyromilio J, Stubbs C, Suntzeff NB, Tonry J (1998) Observational evidence from SN for an accelerating universe and a cosmological constant. Astron J 116:1009–1038 Schlafly EF, Finkbeiner DP, Juri´c M, Magnier EA, Burgett WS, Chambers KC, Grav T, Hodapp KW, Kaiser N, Kudritzki RP, Martin NF, Morgan JS, Price PA, Rix HW, Stubbs CW, Tonry JL, Wainscoat RJ (2012) Photometric calibration of the first 1.5 years of the pan-STARRS1 survey. Astrophys J 756:158 Scolnic D, Rest A, Riess A, Huber ME, Foley RJ, Brout D, Chornock R, Narayan G, Tonry JL, Berger E, Soderberg AM, Stubbs CW, Kirshner RP, Rodney S, Smartt SJ, Schlafly E, Botticella MT, Challis P, Czekala I, Drout M, Hudson MJ, Kotak R, Leibler C, Lunnan R, Marion GH, McCrum M, Milisavljevic D, Pastorello A, Sanders NE, Smith K, Stafford E, Thilker D, Valenti S, Wood-Vasey WM, Zheng Z, Burgett WS, Chambers KC, Denneau L, Draper PW, Flewelling H, Hodapp KW, Kaiser N, Kudritzki RP, Magnier EA, Metcalfe N, Price PA, Sweeney W, Wainscoat R, Waters C (2014) Systematic uncertainties associated with

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the cosmological analysis of the first pan-STARRS1 type Ia supernova sample. Astrophys J 795:45 Scolnic D, Casertano S, Riess AG, Rest A, Schlafly E, Foley RJ, Finkbeiner D, Tang C, Burgett WS, Chambers KC, Draper PW, Flewelling H, Hodapp KW, Huber ME, Kaiser N, Kudritzki RP, Magnier EA, Metcalfe N, Stubbs CW (2015) Supercal: cross-calibration of multiple photometric systems to improve cosmological measurements with type Ia supernovae. ArXiv:1508.05361 (Accepted for publication in ApJ) Stubbs CW, High FW, George MR, DeRose KL, Blondin S, Tonry JL, Chambers KC, Granett BR, Burke DL, Smith RC (2007) Toward more precise survey photometry for panSTARRS and LSST: measuring directly the optical transmission spectrum of the atmosphere. PASP 119:1163–1178

Cosmology with Type IIP Supernovae

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Peter Nugent and Mario Hamuy

Abstract

Type IIP supernovae (SNe IIP) are among the most well-understood cosmic explosions. Not only do we have direct observations of nearly a score of their progenitors prior to the supernova event, the explosion itself is well understood to be that of a single red supergiant star undergoing core collapse and depositing 1051 ergs of energy into its atmosphere. While the past two decades have been dominated by the success of using Type Ia supernovae as standardized candles, over the same time SNe IIP have seen a marked increase and improvement in their use as cosmological probes. Here we review the variety of methods currently in use to make SNe IIP cosmic rulers for measuring distances across the observable universe. These methods span the range of highly detailed comparisons with explosion models to those which are purely photometric.

Contents 1 2 3 4 5 6 7

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EPM: Expanding Photosphere Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SEAM: Spectral Expanding Atmosphere Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SCM: Standard Candle Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PPM: Photospheric Magnitude Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCM: Photometric Candle Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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P. Nugent () Lawrence Berkeley National Laboratory, UC Berkley Department of Astronomy, Berkeley, CA, USA e-mail: [email protected]; [email protected] M. Hamuy Astronomy Department, University of Chile, Santiago, Chile Millennium Institute of Astrophysics, Santiago, Chile e-mail: [email protected]; [email protected]; [email protected] © Springer International Publishing AG 2017 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernovae, https://doi.org/10.1007/978-3-319-21846-5_108

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8 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Perhaps the most stunning discovery in cosmology around the turn of this century has been the observation that the expansion of the universe is accelerating, propelled by a mysterious dark energy. The only direct evidence for this conclusion is distance measurements to Type Ia supernovae (SNe Ia) performed by several independent teams starting with the observations by Riess et al. (1998) and Perlmutter et al. (1999). This discovery has since been verified independently through several other methods, most notably via observations of the mass density of the universe via baryon acoustic oscillations (Anderson et al. 2012) coupled with measurements of the geometry of the universe via the CMB (Planck Collaboration et al. 2014). The mystery of dark energy lies at the crossroads of astronomy and fundamental physics, the former tasked with measuring it and the latter saddled with explaining it. The astronomical community must do all it can to perform innovative and independent tests of dark energy. SNe II as cosmological probes have lagged behind their brighter and better calibrated cousins, SNe Ia, but their status in cosmology is rising. Recent studies have utilized new samples of SNe II and demonstrated that a subset of SNe II, the SNe IIP, have outstanding cosmological utility. Unlike the other members of the core-collapse supernova family, SNe IIP maintain a massive hydrogen envelope prior to explosion. The shock from core collapse rips through this envelope, and the expansion of the atmosphere coupled with a slowly receding hydrogen recombination wave powers a 100 day plateau phase of the optical light curve from which these SNe II gain the moniker “P.” From analyses of their optical light curves and spectra (Chugai 1994), they evidently suffer little subsequent interaction with the surrounding medium – they are the result of the putative red supergiant exploding into a near vacuum. Recent results from spectropolarimetric studies also suggest that, at least during the plateau epoch, the ejecta and electron-scattering photosphere are quite spherical (Leonard and Filippenko 2001). Given this, SNe IIP have the potential to be excellent distance indicators and are unlikely to suffer similar systematics as those which have been encountered by SNe Ia (Cao et al. 2015; Dilday et al. 2012; Sullivan et al. 2010). Here we review a variety of current methods in measuring distances to SNe IIP and the underlying theory behind them.

2

EPM: Expanding Photosphere Method

Because SNe IIP possess nearly blackbody atmospheres, it is possible to use their observed fluxes and temperatures to derive their angular sizes which, in combination with the physical radii derived from spectroscopic observations, afford the possibility of estimating distances. This technique is known as the “expanding photosphere method,” hereafter. Kirshner and Kwan (1974) first applied this

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method, assuming that SNe IIP emitted like perfect blackbodies. Later on, the method was refined by incorporating distance correction factors (a.k.a. “dilution factor” and denoted by ) that account for the departure of the SN atmosphere from a blackbody. Assuming that continuum radiation arises from a spherically symmetric photosphere, a photometric measurement of its color and magnitude determines its angular radius , s R f D D ; (1) 2 D  B .T /100:4ŒAh ./CAG ./ where R is the photospheric radius, D is the luminosity distance to the SN, B .T / is the Planck function at the color temperature of the blackbody radiation in the SN rest frame, f is the observed flux density, Ah ./ is the dust extinction in the host galaxy, and AG ./ is the foreground extinction in the galaxy. The factor  accounts for the fact that a real SN does not radiate like a blackbody at a unique color temperature. The SN atmosphere has a large ratio of scattering to absorptive opacity, a ratio which varies with wavelength due to line blanketing and varying continuous absorption. The result is that the photosphere, which lies at a larger radius than the thermalization depth where the color temperature is set, radiates less strongly than a blackbody at that temperature, and the color temperature itself depends upon the photometric bands employed to measure it. The role of  is to convert the observed angular radius into the photospheric angular radius, defined as the region of total optical depth D 2=3 or the last scattering surface. A measurement of the photospheric radius R can then convert the angular radius to the distance to the SN. Because SNe are strong point explosions, they rapidly attain a state of homologous expansion in which the radius at a time t is given by R D R0 C v.t  t0 /;

(2)

where v is the photospheric velocity measured from spectral lines, t0 is the time of explosion, and R0 is the initial radius of the shell. Combining these equations, and neglecting R0 which rapidly becomes insignificant owing to the rapid expansion (typically v 109 cm s1 ), i .ti  t0 / :  vi D

(3)

This equation shows that photometric and spectroscopic data at two or more epochs are needed to solve for D and t0 . Clearly, the determination of distances relies on our knowledge of  . The first theoretical dilution factors were computed by Eastman et al. (1996) (E96) from detailed non-LTE models of SNe IIP encompassing a wide range in luminosity, density structure, velocity, and composition. They found that the most important variable determining  was the effective temperature; for a given temperature, 

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Fig. 1 Dilution factors as a function of color temperature, computed from E96 (blue dots) and D05 (red dots) atmosphere models for three filter subsets (From Jones et al. 2009)

changed by only 5–10 % over a very large variation in the other parameters. More recently, Dessart and Hillier (2005) (D05) computed dilution factors using their own set of non-LTE SN models. Although the D05 dilution factors present the same pattern with temperature as E96, they are systematically higher than E96 by 15 %. The origin of these differences is unclear. In practice, EPM involves measuring the photometric angular radius of the SN (Eq. 1) by fitting Planck curves B .T / to observed broadband magnitudes. Here S is the filter combination used, e.g., S D BV ; V I ; BV I ; . . . With two wavelengths the solution is exact. For >3 wavelengths, a method of least squares must be used to find the color temperature and the parameter  . The dilution factor must be determined for the same photometric system employed in the observations. Figure 1 shows  factors for three filter combinations, where the systematic differences between E96 (blue dots) and D05 (red dots) atmosphere models can be clearly seen. The application of the EPM can be exemplified from the well-observed SN 1999em. Using BV I magnitudes and photospheric velocities derived from H ˇ, Jones et al. (2009) computed the EPM quantity =v as a function of time for three filter subsets and the two sets of dilution factors (E96 and D05). As expected from Eq. 3, Fig. 2 shows that =v increases linearly with time. A least-squares fit permits one to solve for D and t0 , yielding in this case, D D 9:3 ˙ 0:5 Mpc and D D 13:9 ˙ 1:4 Mpc using the E96 and D05 models, respectively. A valuable external comparison can be made with the Cepheid distance to NGC 1637, the host galaxy of SN 1999em, namely, D D 11:7 ˙ 1:0 Mpc (Leonard et al. 2003).

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Fig. 2 The ratio =v (Eq. 3) as a function of time for SN 1999em using the BV, BVI, and VI filter sets. The ridge line corresponds to unweighted least-squares fits to the derived EPM quantities. The upper and lower panels show the results using E96 and D05 dilution factors, respectively (From Jones et al. 2009)

While the D05 models yield consistent distances with the Cepheid distance, the E96 models lead to significantly lower distances. Independent EPM analysis of SN 1999em can be found in Hamuy et al. (2001), Leonard et al. (2002), and Dessart and Hillier (2006). Using 12 well-observed SNe, Jones et al. (2009) constructed the Hubble diagrams shown in Fig. 3. The top one corresponds to the V I filter subset and the E96 models, while the bottom one was obtained with the D05 models. As expected, there is a systematic difference in the H0 values obtained with the E96 (H0 D 91 km s1 Mpc1 ) and D05 models (H0 D 52 km s1 Mpc1 ) owing to the systematic differences in the dilution factors. The internal precision of each of these implementations is 0:3  0:4 mag, which implies an internal precision 0:15  0:2 % in distance. One great advantage of distances determined by EPM is that they are independent of the “cosmic distance ladder.” Photometric and spectroscopic observations at two epochs and a physical model for the SN atmosphere lead directly to a distance. Moreover, additional observations of the same SN are essentially independent

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1000

Fig. 3 (Top) Hubble diagram using the V I filter subset and E96 dilution factors. (bottom) Same as above but with D05 models (From Jones et al. 2009)

distance measurements as the properties of the photosphere change over time. This provides a valuable internal consistency check. However, the method requires us to know the dilution factors, which are still affected by systematic uncertainties. Additional analysis of individual SNe can be found in Schmidt et al. (1994a), Takáts and Vinkó (2006), Vinkó et al. (2012), and Takáts et al. (2015), whereas Schmidt et al. (1992, 1994b), and Bose and Kumar (2014) provide studies of 10, 5 and 8 SNe, respectively.

3

SEAM: Spectral Expanding Atmosphere Method

In the (SEAM), observed spectra and photometry are combined with detailed theoretical modeling of the observed spectral energy distribution of individual SNe to accurately determine their luminosities and hence the distances to these stellar explosions. While the SEAM is similar to the EPM in spirit, it avoids the use of dilution factors and color temperatures as described in Sect. 2 as one fits individual SNe epoch by epoch. Velocities are determined accurately by fitting the

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synthetic to the observed spectra. The radius is still determined by the relationship R D vt which is an excellent approximation given SNe IIP reach homologous expansion quickly after explosion. The explosion time is found by demanding selfconsistency between multiple epochs. This method is in the spirit of the Baade method (Baade 1926; Branch et al. 1981; Kirshner and Kwan 1974) and the more detailed expanding photosphere method of Eastman and collaborators (Eastman and Kirshner 1989; Schmidt et al. 1992). The SEAM uses all the spectral information available in the observed spectra simultaneously; hence, the determination of the underlying parameters is more robust than the use of generalized dilution factors in the EPM. Since the spectral energy distribution is known completely from the calculated synthetic spectra, one can just integrate the spectrum in a given photometric band to determine the absolute luminosity and compare to the observed apparent magnitude to measure the distance modulus. Extinction corrections are usually determined by fitting the earliest observations which, due to the very high temperatures, are in the Jeans’ tail and thus sensitive to extinction by dust (Baron et al. 2000). Codes which have been used to carry out this line of work include CMFGEN (Dessart et al. 2008) and PHOENIX (Baron et al. 2004). In general, these codes solve the fully relativistic radiation transport equation along with the non-LTE rate equations (for some ions) while ensuring radiative equilibrium (energy conservation). Use of these codes have led to some excellent fits to many different types of SNe (Baron et al. 1995; Dessart et al. 2011; Mitchell et al. 2002; Nugent et al. 1995); however, given the low polarization seen during the plateau phase (Leonard and Filippenko 2001), implying a nearly spherical atmosphere, coupled with the facts that the ejecta are dominated by hydrogen and their progenitors are well understood (Smartt et al. 2009), SNe IIP make ideal SNe for the application of the SEAM. The SEAM allows one to measure supernova luminosities with the following two assumptions: (1) homologous expansion, v / r, from which it follows that the velocity of a given matter element is constant and hence that the position of a reference radius is given by v0 tR , where v0 is determined by the spectral fit. (2) A high-quality fit to the spectrum across several epochs implies that the model parameters were accurately determined. The underlying density profile of the atmosphere and elemental abundances are parameters to be fit and often come from explosion models (Woosley and Heger 2007). However, one often assumes that the atmosphere follows a decaying exponential or power law and the abundances are some fraction of solar. Figure 4 shows a PHOENIX fit to SN 1993W during the plateau phase. The fit is a near perfect match to the spectrum and highlights the effects of metallicity on the overall SED. Both Baron et al. (2004) and Dessart and Hillier (2005) provide excellent fits to several epochs of SN 1999em and find distances via the SEAM in agreement with the Cepheid distance provided by Leonard et al. (2003) with uncertainties on the order of 10–15 %. SEAM has also been applied to the well-observed SNe 2005cs and 2006bp (Dessart et al. 2008). While the SEAM is not currently amenable for

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Fλ(in arbitrary units)

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Fig. 4 PHOENIX fits to SN 1993W a SN IIP observed in the Hubble flow. Here we have varied the metallicity from a tenth solar to solar holding all other parameters fixed. The overall fit to the spectrum is excellent and highly favors the low metallicity model. Deviations in flux are