Asteroids IV 9780816532131, 0816532133

Table of contents :
Cover
Front Matter
Contents
List of Contributing Authors
Scientific Organizing Committee and Acknowledgment of Reviewers
Foreword
Preface
Asteroids: Recent Advances and New Perspectives
The Compositional Structure of the Asteroid Belt
Mineralogy and Surface Composition of Asteroids
Astronomical Observations of Volatiles on Asteroids
Space-Based Thermal Infrared Studies of Asteroids
Asteroid Thermophysical Modeling
Asteroid Photometry
Asteroid Polarimetry
Radar Observations of Near-Earth and Main-Belt Asteroids
Asteroid Models from Multiple Data Sources
The Complex History of Trojan Asteroids
The Active Asteroids
The Near-Earth Object Population: Connections to Comets,Main-Belt Asteroids, and Meteorites
Small Near-Earth Asteroids as a Source of Meteorites
Meteoroid Streams and the Zodiacal Cloud
Identification and Dynamical Properties of Asteroid Families
Asteroid Family Physical Properties
Collisional Formation and Modeling of Asteroid Families
Asteroid Systems: Binaries, Triples, and Pairs
Formation and Evolution of Binary Asteroids
Hayabusa Sample Return Mission
The Dawn Mission to Vesta and Ceres
The Flybys of Asteroids (2867) Šteins, (21) Lutetia, and (4179) Toutatis
Phobos and Deimos
New Paradigms for Asteroid Formation
The Dynamical Evolution of the Asteroid Belt
The Yarkovsky and YORP Effects
Asteroid Differentiation: Melting and Large-Scale Structure
Hydrothermal and Magmatic Fluid Flow in Asteroids
Early Impact History and Dynamical Origin ofDifferentiated Meteorites and Asteroids
Asteroid Surface Alteration by Space Weathering Processes
The Formation and Evolution of Ordinary ChondriteParent Bodies
Sources of Water and Aqueous Activity onthe Chondrite Parent Asteroids
Global-Scale Impacts
Color Section
Modeling Asteroid Collisions and Impact Processes
The Collisional Evolution of the Main Asteroid Belt
Cratering on Asteroids
Asteroid Interiors and Morphology
Asteroid Surface Geophysics
Surveys, Astrometric Follow-Up, and Population Statistics
Orbits, Long-Term Predictions, and Impact Monitoring
Asteroid Impacts and Modern Civilization: Can We Prevent a Catastrophe?
Human Exploration of Near-Earth Asteroids
Index

Citation preview

THE UNIVERSITY OF ARIZONA SPACE SCIENCE SERIES Richard P. Binzel, General Editor Asteroids IV P. Michel, F. E. DeMeo, and W. F. Bottke, editors, 2015, 895 pages Protostars and Planets VI Henrik Beuther, Ralf S. Klessen, Cornelis P. Dullemond, and Thomas Henning, editors, 2014, 914 pages Comparative Climatology of Terrestrial Planets Stephen J. Mackwell, Amy A. Simon-Miller, Jerald W. Harder, and Mark A. Bullock, editors, 2013, 610 pages Exoplanets S. Seager, editor, 2010, 526 pages Europa Robert T. Pappalardo, William B. McKinnon, and Krishan K. Khurana, editors, 2009, 727 pages The Solar System Beyond Neptune M. Antonietta Barucci, Hermann Boehnhardt, Dale P. Cruikshank, and Alessandro Morbidelli, editors, 2008, 592 pages Protostars and Planets V Bo Reipurth, David Jewitt, and Klaus Keil, editors, 2007, 951 pages Meteorites and the Early Solar System II D. S. Lauretta and H. Y. McSween, editors, 2006, 943 pages Comets II M. C. Festou, H. U. Keller, and H. A. Weaver, editors, 2004, 745 pages Asteroids III William F. Bottke Jr., Alberto Cellino, Paolo Paolicchi, and Richard P. Binzel, editors, 2002, 785 pages Tom Gehrels, General Editor Origin of the Earth and Moon R. M. Canup and K. Righter, editors, 2000, 555 pages Protostars and Planets IV Vincent Mannings, Alan P. Boss, and Sara S. Russell, editors, 2000, 1422 pages Pluto and Charon S. Alan Stern and David J. Tholen, editors, 1997, 728 pages

Venus II—Geology, Geophysics, Atmosphere, and Solar Wind Environment S. W. Bougher, D. M. Hunten, and R. J. Phillips, editors, 1997, 1376 pages Cosmic Winds and the Heliosphere J. R. Jokipii, C. P. Sonett, and M. S. Giampapa, editors, 1997, 1013 pages Neptune and Triton Dale P. Cruikshank, editor, 1995, 1249 pages Hazards Due to Comets and Asteroids Tom Gehrels, editor, 1994, 1300 pages Resources of Near-Earth Space John S. Lewis, Mildred S. Matthews, and Mary L. Guerrieri, editors, 1993, 977 pages Protostars and Planets III Eugene H. Levy and Jonathan I. Lunine, editors, 1993, 1596 pages Mars Hugh H. Kieffer, Bruce M. Jakosky, Conway W. Snyder, and Mildred S. Matthews, editors, 1992, 1498 pages Solar Interior and Atmosphere A. N. Cox, W. C. Livingston, and M. S. Matthews, editors, 1991, 1416 pages The Sun in Time C. P. Sonett, M. S. Giampapa, and M. S. Matthews, editors, 1991, 990 pages Uranus Jay T. Bergstralh, Ellis D. Miner, and Mildred S. Matthews, editors, 1991, 1076 pages Asteroids II Richard P. Binzel, Tom Gehrels, and Mildred S. Matthews, editors, 1989, 1258 pages Origin and Evolution of Planetary and Satellite Atmospheres S. K. Atreya, J. B. Pollack, and Mildred S. Matthews, editors, 1989, 1269 pages Mercury Faith Vilas, Clark R. Chapman, and Mildred S. Matthews, editors, 1988, 794 pages Meteorites and the Early Solar System John F. Kerridge and Mildred S. Matthews, editors, 1988, 1269 pages

The Galaxy and the Solar System Roman Smoluchowski, John N. Bahcall, and Mildred S. Matthews, editors, 1986, 483 pages Satellites Joseph A. Burns and Mildred S. Matthews, editors, 1986, 1021 pages Protostars and Planets II David C. Black and Mildred S. Matthews, editors, 1985, 1293 pages Planetary Rings Richard Greenberg and André Brahic, editors, 1984, 784 pages Saturn Tom Gehrels and Mildred S. Matthews, editors, 1984, 968 pages Venus D. M. Hunten, L. Colin, T. M. Donahue, and V. I. Moroz, editors, 1983, 1143 pages Satellites of Jupiter David Morrison, editor, 1982, 972 pages Comets Laurel L. Wilkening, editor, 1982, 766 pages Asteroids Tom Gehrels, editor, 1979, 1181 pages Protostars and Planets Tom Gehrels, editor, 1978, 756 pages Planetary Satellites Joseph A. Burns, editor, 1977, 598 pages Jupiter Tom Gehrels, editor, 1976, 1254 pages Planets, Stars and Nebulae, Studied with Photopolarimetry Tom Gehrels, editor, 1974, 1133 pages

Asteroids IV

Asteroids IV Edited by

P. Michel F. E. DeMeo W. F. Bottke With the assistance of

Renée Dotson With 148 collaborating authors

THE UNIVERSITY OF ARIZONA PRESS Tucson in collaboration with LUNAR AND PLANETARY INSTITUTE Houston

About the front cover: “Riding on a Rubble Pile” Numerical simulations of asteroid disruptions indicate that in many cases of asteroid disruption by a collision with another object, fragment ejection velocities are typically slow enough that most of the fragments reassemble, leading to the formation of rubble piles. It occurred to the artist that during such processes, various irregularly shaped rock shards could fall back at very slow velocities (centimeters per second in some cases) and pile up in grotesque formations not seen on Earth. Here, a large, narrow rock shard has come to rest at an angle on another rock at the surface of the rubble pile. This asteroid also has a rubble-pile satellite (upper left), constituting a binary system. Earth and the Moon are in the distance (upper right). Painting copyright William K. Hartmann, acrylic, mixed with basaltic soil from Tucson. About the back cover: Haulani impact crater (diameter 35 km) on asteroid (1) Ceres from Dawn’s Framing Camera with a spatial resolution of ~140 m/pixel. The color mosaic is a cut out of the global mosaic in orthographic projection, obtained in August 2015. Haulani (10°E, 6°N) is shown in colors R = 965 nm, G = 555 nm, B = 438 nm. Absolute reflectance values range between 0.025 and 0.055. This young crater, as indicated by its ray system and lack of impact craters on its floor, contrasts in various bright bluish tones sharply from the surrounding brownish background material. At its center, an irregular remnant central peak at the rim of a central pit exists. The unique colors in the crater indicate excavation and deposition of a subsurface layer of potentially hydrated materials.

The University of Arizona Press in collaboration with the Lunar and Planetary Institute © 2015 The Arizona Board of Regents All rights reserved ∞ This book is printed on acid-free, archival-quality paper. Manufactured in the United States of America 20 19 18 17 16 15 6 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data Names: Michel, Patrick, 1970– editor. | DeMeo, Francesca E., editor. | Bottke, William F. (William Frederick), 1966– editor. Title: Asteroids IV / edited by Patrick Michel, Francesca E. DeMeo, and William F. Bottke ; with the assistance of Renee Dotson ; with 148 collaborating authors. Other titles: University of Arizona space science series. Description: Tucson : The University of Arizona Press ; Houston : Lunar and Planetary Institute, 2015. | Series: The University of Arizona space science series | Includes bibliographical references and index. Identifiers: LCCN 2015024269 | ISBN 9780816532131 (cloth : alk. paper) Subjects: LCSH: Asteroids. Classification: LCC QB651 .A857 2015 | DDC 523.44—dc23 LC record available at http://lccn.loc. gov/2015024269

Contents List of Contributing Authors ............................................................................................................................................ xiii Scientific Organizing Committee and Acknowledgment of Reviewers ........................................................................... xiv Foreword ............................................................................................................................................................................. xv Preface ............................................................................................................................................................................. xvii PART 1: INTRODUCTION Asteroids: Recent Advances and New Perspectives P. Michel, F. E. DeMeo, and W. F. Bottke .................................................................................................................... 3 PART 2: PHYSICAL AND COMPOSITIONAL PROPERTIES 2.1. Asteroid Composition and Physical Properties The Compositional Structure of the Asteroid Belt F. E. DeMeo, C. M. O’D. Alexander, K. J. Walsh, C. R. Chapman, and R. P. Binzel .............................................. 13 Mineralogy and Surface Composition of Asteroids V. Reddy, T. L. Dunn, C. A. Thomas, N. A. Moskovitz, and T. H. Burbine ............................................................... 43 Astronomical Observations of Volatiles on Asteroids A. S. Rivkin, H. Campins, J. P. Emery, E. S. Howell, J. Licandro, D. Takir, and F. Vilas ....................................... 65 Space-Based Thermal Infrared Studies of Asteroids A. Mainzer, F. Usui, and D. E. Trilling ...................................................................................................................... 89 Asteroid Thermophysical Modeling M. Delbo, M. Mueller, J. P. Emery, B. Rozitis, and M. T. Capria ........................................................................... 107 Asteroid Photometry J.-Y. Li, P. Helfenstein, B. J. Buratti, D. Takir, and B. E. Clark ............................................................................. 129 Asteroid Polarimetry I. Belskaya, A. Cellino, R. Gil-Hutton, K. Muinonen, and Y. Shkuratov ................................................................. 151 Radar Observations of Near-Earth and Main-Belt Asteroids L. A. M. Benner, M. W. Busch, J. D. Giorgini, P. A. Taylor, and J.-L. Margot ....................................................... 165 Asteroid Models from Multiple Data Sources J. Ďurech, B. Carry, M. Delbo, M. Kaasalainen, and M. Viikinkoski ..................................................................... 183 2.2. Populations The Complex History of Trojan Asteroids J. P. Emery, F. Marzari, A. Morbidelli, L. M. French, and T. Grav ....................................................................... 203 The Active Asteroids D. Jewitt, H. Hsieh, and J. Agarwal ........................................................................................................................ 221 The Near-Earth Object Population: Connections to Comets, Main-Belt Asteroids, and Meteorites R. P. Binzel, V. Reddy, and T. L. Dunn ..................................................................................................................... 243 ix

Small Near-Earth Asteroids as a Source of Meteorites J. Borovička, P. Spurný, and P. Brown ..................................................................................................................... 257 Meteoroid Streams and Zodiacal Dust P. Jenniskens .............................................................................................................................................................. 281 2.3. Families Identification and Dynamical Properties of Asteroid Families D. Nesvorný, M. Brož, and V. Carruba .................................................................................................................... 297 Asteroid Family Physical Properties J. R. Masiero, F. E. DeMeo, T. Kasuga, and A. H. Parker ..................................................................................... 323 Collisional Formation and Modeling of Asteroid Families P. Michel, D. C. Richardson, D. D. Durda, M. Jutzi, and E. Asphaug ................................................................... 341 2.4. Multiple Systems Asteroid Systems: Binaries, Triples, and Pairs J.-L. Margot, P. Pravec, P. Taylor, B. Carry, and S. Jacobson ............................................................................... 355 Formation and Evolution of Binary Asteroids K. J. Walsh and S. A. Jacobson ................................................................................................................................ 375 PART 3: SPACE MISSIONS Hayabusa Sample Return Mission M. Yoshikawa, J. Kawaguchi, A. Fujiwara, and A. Tsuchiyama ............................................................................. 397 The Dawn Mission to Vesta and Ceres C. T. Russell, H. Y. McSween, R. Jaumann, and C. A. Raymond ............................................................................ 419 The Flybys of Asteroids (2867) Šteins, (21) Lutetia, and (4179) Toutatis M. A. Barucci, M. Fulchignoni, J. Ji, S. Marchi, and N. Thomas .......................................................................... 433 Phobos and Deimos S. L. Murchie, P. C. Thomas, A. S. Rivkin, and N. L. Chabot ................................................................................. 451 PART 4: EVOLUTIONARY PROCESSES 4.1. Dynamical Evolution New Paradigms for Asteroid Formation A. Johansen, E. Jacquet, J. N. Cuzzi, A. Morbidelli, and M. Gounelle .................................................................. 471 The Dynamical Evolution of the Asteroid Belt A. Morbidelli, K. J. Walsh, D. P. O’Brien, D. A. Minton, and W. F. Bottke ........................................................... 493 The Yarkovsky and YORP Effects D. Vokrouhlický, W. F. Bottke, S. R. Chesley, D. J. Scheeres, and T. S. Statler ...................................................... 509 4.2. Differentiation Asteroid Differentiation: Melting and Large-Scale Structure A. Scheinberg, R. R. Fu, L. T. Elkins-Tanton, and B. P. Weiss ................................................................................ 533 x

Hydrothermal and Magmatic Fluid Flow in Asteroids L. Wilson, P. A. Bland, D. Buczkowski, K. Keil, and A. N. Krot ............................................................................. 553 Early Impact History and Dynamical Origin of Differentiated Meteorites and Asteroids E. R. D. Scott, K. Keil, J. I. Goldstein, E. Asphaug, W. F. Bottke, and N. A. Moskovitz ....................................... 573 4.3. Physical Evolution Asteroid Surface Alteration by Space Weathering Processes R. Brunetto, M. J. Loeffler, D. Nesvorný, S. Sasaki, and G. Strazzulla .................................................................. 597 The Formation and Evolution of Ordinary Chondrite Parent Bodies P. Vernazza, B. Zanda, T. Nakamura, E. Scott, and S. Russell ................................................................................ 617 Sources of Water and Aqueous Activity on the Chondrite Parent Asteroids A. N. Krot, K. Nagashima, C. M. O’D. Alexander, F. J. Ciesla, W. Fujiya, and L. Bonal ..................................... 635 4.4. Collisions Global-Scale Impacts E. Asphaug, G. Collins, and M. Jutzi ....................................................................................................................... 661 Modeling Asteroid Collisions and Impact Processes M. Jutzi, K. Holsapple, K. Wünneman, and P. Michel ............................................................................................ 679 The Collisional Evolution of the Main Asteroid Belt W. F. Bottke, M. Brož, D. P. O’Brien, A. Campo Bagatin, A. Morbidelli, and S. Marchi ...................................... 701 4.5. Surface Geology and Geophysics Cratering on Asteroids S. Marchi, C. R. Chapman, O. S. Barnouin, J. E. Richardson, and J.-B. Vincent .................................................. 725 Asteroid Interiors and Morphology D. J. Scheeres, D. Britt, B. Carry, and K. A. Holsapple ......................................................................................... 745 Asteroid Surface Geophysics N. Murdoch, P. Sánchez, S. R. Schwartz, and H. Miyamoto ................................................................................... 767 PART 5: GROUNDBASED SURVEYS, HAZARDS, AND FUTURE EXPLORATION Surveys, Astrometric Follow-Up, and Population Statistics R. Jedicke, M. Granvik, M. Micheli, E. Ryan, T. Spahr, and D. K. Yeomans ......................................................... 795 Orbits, Long-Term Predictions, and Impact Monitoring D. Farnocchia, S. R. Chesley, A. Milani, G. F. Gronchi, and P. W. Chodas .......................................................... 815 Asteroid Impacts and Modern Civilization: Can We Prevent a Catastrophe? A. W. Harris, M. Boslough, C. R. Chapman, L. Drube, P. Michel, and A. W. Harris ............................................ 835 Human Exploration of Near-Earth Asteroids P. A. Abell, B. W. Barbee, P. W. Chodas, J. Kawaguchi, R. R. Landis, D. D. Mazanek, and P. Michel ................ 855 Index

��������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 881

xi

List of Contributing Authors Abell P. A. 855 Agarwal J. 221 Alexander C. M. O’D. 13, 635 Asphaug E. 341, 573, 661 Barbee B. W. 855 Barnouin O. S. 725 Barucci M. A. 433 Belskaya I. 151 Benner L. A. M. 165 Binzel R. P. 13, 243 Bland P. A. 553 Bonal L. 635 Borovička J. 257 Boslough M. 835 Bottke W. F. 3, 493, 509, 573, 701 Britt D. 745 Brown P. 257 Brož M. 297, 701 Brunetto R. 597 Buczkowski D. 553 Buratti B. 129 Burbine T. H. 43 Busch M. W. 165 Campins H. 65 Campo Bagatin A. 701 Capria M. T. 107 Carruba V. 297 Carry B. 183, 355, 745 Cellino A. 151 Chabot N. L. 451 Chapman C. R. 13, 725, 835 Chesley S. R. 509, 815 Chodas P. W. 815, 855 Ciesla F. J. 635 Clark B. E. 129 Collins G. 661 Cuzzi J. N. 471 Delbo M. 107, 183 DeMeo F. E. 3, 13, 323 Drube L. 835 Dunn T. L. 43, 243 Durda D. D. 341 Durech J. 183 Elkins-Tanton L. T. 533 Emery J. P. 65, 107, 203 Farnocchia D. 815 French L. M. 203 Fu R. R. 533 Fujiwara A. 397

Fujiya W. 635 Fulchignoni M. 433 Gil-Hutton R. 151 Giorgini J. D. 165 Goldstein J. I. 573 Gounelle M. 471 Granvik M. 795 Grav T. 203 Gronchi G. F. 815 Harris A. W. (DLR) 835 Harris A. W. (USA) 835 Helfenstein P. 129 Holsapple K. A. 679, 745 Howell E. S. 65 Hsieh H. 221 Jacobson J. A. 375 Jacobson S. 355 Jacquet E. 471 Jaumann R. 419 Jedicke R. 795 Jenniskens P. 281 Jewitt D. 221 Ji J. 433 Johansen A. 471 Jutzi M. 341, 661 Kaasalainen M. 183 Kasuga T. 323 Kawaguchi J. 397, 855 Keil K. 553, 573 Krot A. N. 553, 635 Landis R. R. 855 Li J.-Y. 129 Licandro J. 65 Loeffler M. J. 597 Mainzer A. 89 Marchi S. 701, 725 Marchin S. 433 Margot J.-L. 165, 355 Marzari F. 203 Masiero J. R. 323 Mazanek D. D. 855 McSween H. Y. 419 Michel P. 3, 341, 679, 835, 855 Micheli M. 795 Milani A. 815 Minton D. A. 493 Miyamoto H. 767 Morbidelli A. 203, 471, 493, 701 Moskovitz N. A. 43, 573 Mueller M. 107

xiii

Muinonen K. 151 Murchie S. L. 451 Murdoch N. 767 Nagashima K. 635 Nakamura T. 617 Nesvorný D. 297, 597 O’Brien D. P. 493, 701 Parker A. H. 323 Pravec P. 355 Raymond C. A. 419 Reddy V. 43, 243 Richardson D. C. 341 Richardson J. E. 725 Rivkin A. S. 65, 451 Rozitis B. 107 Russell C. T. 419 Russell S. 617 Ryan E. 795 Sánchez P. 767 Sasaki S. 597 Scheeres D. J. 509, 745 Scheinberg A. 533 Schwartz S. R. 767 Scott E. R. D. 573, 617 Shkuratov Y. 151 Spahr T. 795 Spurný P. 257 Statler T. S. 509 Strazzulla G. 597 Takir D. 65, 129 Taylor P. A. 165, 355 Thomas C. A. 43 Thomas N. 433 Thomas P. C. 451 Trilling D. E. 89 Tsuchiyama A. 397 Usui F. 89 Vernazza P. 617 Viikinkoski M. 183 Vilas F. 65 Vincent J.-B. 725 Vokrouhlický D. 509 Walsh K. J. 13, 375, 493 Weiss B. P. 533 Wilson L. 553 Wünneman K. 679 Yeomans D. K. 795 Yoshikawa M. 397 Zanda B. 617

Scientific Organizing Committee

The editors thank the following for their assistance in the planning stages of this book: Paul Abell Erik Asphaug Olivier Barnouin Peter Brown Thomas H. Burbine Humberto Campins Clark Chapman Beth Clark Guy Consolmagno Linda Elkins-Tanton Joshua Emery

Peter Jeniskens Alan W. Harris (DLR) Alan W. Harris (USA) Keith Holsapple Amy Mainzer Joseph Masiero Alessandro Morbidelli Karri Muinonen David Nesvorný Michael Nolan David Polishook

Vishnu Reddy Derek C. Richardson Andrew Rivkin Daniel Scheeres Edward R. D. Scott Giovanni Valsecchi Joseph Veverka David Vokrouhlický Benjamin Weiss Donald Yeomans

Acknowledgment of Reviewers

The editors gratefully acknowledge the following individuals, as well as several anonymous reviewers, for their time and effort in reviewing chapters in this volume: Conel M. O’D. Alexander Erik Asphaug Olivier Barnouin Richard Binzel Mike Brown Thomas Burbine Bobby Bus Adriano Campo Bagatin Alberto Cellino Clark Chapman Andy Cheng Fred Ciesla Beth Clark Edward Cloutis Gareth Collins Guy Consolmagno Matija Cuk Julia de Leon Marco Delbo Elisabetta Dotto Tasha Dunn Sonia Fornasier Kathryn Garnder-Vandy Jerome Gattacceca Lee Graham Simon Green Bruce Hapke Paul Hardersen

Alan Harris (DLR) Alan Harris (USA) Carl Hergenrother Takahiro Hiroi Joshua Hopkins Kevin R. Housen Henry Hsieh Boris Ivanov Ralf Jaumann Robert Jedicke Klaus Keil Tomas Kohout Katherine Kretke Dante Lauretta Guy Libourel Anny-Chantal Levasseur-Regourd Dmitrij Lupishko Franck Marchis Jean-Luc Margot Francesco Marzari Joseph Masiero Jay McMahon Hap McSween David Minton David Morrison Nick Moskovitz Thomas Mueller Karri Muinonen

xiv

Akiko M. Nakamura David Nesvorný David O’Brien Alex Parker Jean-Marc Petit Carle Pieters Olga Popova Petr Pravec Sean Raymond Derek C. Richardson Pascal Rosenblatt Ben Rositzis Alan Rubin David P. Rubincam Gal Sarid Dan Scheeres Michael K. Shepard Colin Snodgrass Lydie Staron Paolo Tanga Kleomenis Tsiganis Giovanni B. Valsecchi Jérémie Vaubaillon Paul Wiegert Don Yeomans Edward Young Mike Zolensky

Foreword In the founding volume of what would become the Space Science Series, Tom Gehrels (1925–2011) wrote, “We are now on the threshold of a new era of asteroid studies” (Gehrels, 1971). These words once again trumpet the state of the field four decades later with the release of Asteroids IV. Yet why do asteroids captivate our curiosity in a way that so greatly exceeds their small total mass relative to the rest of our solar system? It is because asteroids matter. Now more than ever before, we realize how much asteroids matter to scientists, to explorers, and to the future of humanity. As evidenced throughout this volume, scientists across broad disciplines recognize that understanding asteroids is essential to discerning the basic processes of planetary formation, including how their current distribution bespeaks our solar system’s cataclysmic past. For explorers, the nearest asteroids beckon as the most accessible milestones in interplanetary space, offering spaceflight destinations easier to reach than the lunar surface. For futurists, the prospects of asteroids as commercial resources tantalize as a twenty-first-century gold rush, albeit with far greater challenges and less certain rewards than faced by nineteenth-century pioneers. For humanity as a whole, it is not a question of if — but when — the next major impact will occur. While the disaster probabilities are thankfully small during any one lifespan (and miniscule within the time horizons typically considered by funding agencies), fully cataloging and characterizing the potentially hazardous asteroid population remains unfinished business. While the motivation to “know thy enemy” may ultimately prompt a dedicated spacebased asteroid survey, the richness of the overall scientific return and their exploration/utilization potential will prove that these little worlds are actually our friends. Asteroids IV sets the scientific foundation upon which all these topics and more will continue to be built upon for the foreseeable future. Herein our expert authors lay out what we know, how we know it, and where we go from here. Through this approach, our collective goal is to provide a gateway for new researchers and students of all ages to enter this field by ascertaining the current state. Challenge what doesn’t make sense, resolve what is contentious, and most importantly, fearlessly pursue new ideas that can break through to new paradigms in our understanding. Dare boldly enough to be wrong while being modest enough to reshape or abandon ideas that fail. Only in this way can we soar through the threshold on which we currently stand. It is my privilege to thank the editors, scientific organizing committee, and authors who crafted this work. Leading the effort with boundless energy and enthusiasm is Patrick Michel. Shining throughout is the careful organization and integrative thinking of Francesca DeMeo. Holding this project steady by his Asteroids III editorial experience, Bill Bottke brought his creative thinking as the capstone. Less visible, but whose quality and presence grace every page, are Renée Dotson and colleagues at the Lunar and Planetary Institute (LPI), who brought this volume to physical reality. The ongoing success of the Space Science Series would not be possible without the unfailing support of LPI Director Dr. Stephen Mackwell and the professionalism of the University of Arizona Press. Richard P. Binzel Space Science Series General Editor Cambridge, Massachusetts August 2015 REFERENCES

Gehrels T. (1971) Preface to Physical Studies of Minor Planets (T. Gehrels, ed.). NASA SP-267, U.S. Government Printing Office, Washington, DC. 687 pages. xv

Preface Asteroids are fascinating worlds. Considered the building blocks of our planets, many of the authors of this book have devoted their scientific careers to exploring them with the tools of our trade: ground- and spacebased observations, in situ space missions, and studies that run the gamut from theoretical modeling efforts to laboratory work. Like fossils for paleontologists, or DNA for geneticists, they allow us to construct a veritable time machine and provide us with tantalizing glimpses of the earliest nature of our solar system. By investigating them, we can probe what our home system was like before life or even the planets existed. The origin and evolution of life on our planet is also intertwined with asteroids in a different way. It is believed that impacts on the primordial Earth may have delivered the basic components for life, with biology favoring attributes that could more easily survive the aftermath of such energetic events. In this fashion, asteroids may have banished many probable avenues for life to relative obscurity. Similarly, they may have also prevented our biosphere from becoming more complex until more recent eras. The full tale of asteroid impacts on the history of our world, and how human life managed to emerge from myriad possibilities, has yet to be fully told. The hazard posed by asteroid impacts to our civilization is low but singular. The design of efficient mitigation strategies strongly relies on asteroid detection by our ground- and spacebased surveys as well as knowledge of their physical properties. A more positive motivation for asteroid discovery is that the proximity of some asteroids to Earth may allow future astronauts to harvest their water and rare mineral resources for use in exploration. A key goal of asteroid science is therefore to learn how humans and robotic probes can interact with asteroids (and extract their materials) in an efficient way. We expect that these adventures may be commonplace in the future. Asteroids, like planets, are driven by a great variety of both dynamical and physical mechanisms. In fact, images sent back by space missions show a collection of small worlds whose characteristics seem designed to overthrow our preconceived notions. Given their wide range of sizes and surface compositions, it is clear that many formed in very different places and at different times within the solar nebula. These characteristics make them an exciting challenge for researchers who crave complex problems. The return of samples from these bodies may ultimately be needed to provide us with solutions. In the book Asteroids IV, the editors and authors have taken major strides in the long journey toward a much deeper understanding of our fascinating planetary ancestors. This book reviews major advances in 43 chapters that have been written and reviewed by a team of more than 200 international authorities in asteroids. It is aimed to be as comprehensive as possible while also remaining accessible to students and researchers who are interested in learning about these small but nonetheless important worlds. We hope this volume will serve as a leading reference on the topic of asteroids for the decade to come. We are deeply indebted to the many authors and referees for their tremendous efforts in helping us create Asteroids IV. We also thank the members of the Asteroids IV scientific organizing committee for helping us shape the structure and content of the book. The conference associated with the book, “Asteroids Comets Meteors 2014” held June 30–July 4, 2014, in Helsinki, Finland, did an outstanding job of demonstrating how much progress we have made in the field over the xvii

last decade. We are extremely grateful to our host Karri Muinonnen and his team. The editors are also grateful to the Asteroids IV production staff, namely Renée Dotson and her colleagues at the Lunar and Planetary Institute, for their efforts, their invaluable assistance, and their enthusiasm; they made life as easy and pleasant as possible for the editors, authors, and referees. They also thank Richard Binzel, the General Editor of the Space Science Series, for his strong support and advice during this process, as well as the staff at the University of Arizona Press. Finally, editor Patrick Michel would like to thank his wife Delphine, who married him on June 14, 2013, almost at the birth of the book process. He is grateful that she was willing to put up with him as he spent many of his nights and weekends working on the book. Thanks to her support, their trajectories are as bounded as a perfectly stable asteroid binary system, and this was probably the best way to experience from the start what her life would be like with a researcher! Co-editor Bottke would also like to thank his wife Veronica and his children Kristina-Marie, Laura, and Julie, who make up his own favorite asteroid family. Since Asteroids III, the size distribution of the family members has been steadily changing, and who knows how many tiny new members it will contain by Asteroids V! Co-editor DeMeo would like to thank her husband Alfredo for his support and encouragement throughout the process of creating this book. They met at the beginning of her career in research, becoming an asteroid pair and now continuing on the same orbit in life. Patrick Michel, Francesca DeMeo, and William F. Bottke August 2015

xviii

Michel P., DeMeo F. E., and Bottke W. F. (2015) Asteroids: Recent advances and new perspectives. In Asteroids IV (P. Michel et al., eds.), pp. 3–10. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch001.

Asteroids: Recent Advances and New Perspectives Patrick Michel

Lagrange Laboratory, Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS

Francesca E. DeMeo

Massachusetts Institute of Technology

William F. Bottke

Southwest Research Institute

1. INTRODUCTION

• W  hich classes of meteorites come from which classes of asteroids, and how diverse were the components from which asteroids were assembled? • Did asteroid differentiation involve near-complete melting to form magma oceans, or modest partial melting? • What are the internal structures of Jupiter’s Trojan asteroids? Are there systematic chemical or isotopic gradients in the solar system, and if so, what do they reveal about accretion? • Do we have meteoritic samples of the objects that formed the dominant feeding zones for the innermost planets? • How did Earth get its water and other volatiles? What is the mechanical process of accretion up to and through the formation of meter-size bodies? • Which classes of asteroids participated in the late heavy bombardment of the inner planets and the Moon, and how did the current population of asteroids evolve in time and space? • What are the sources of asteroid groups (e.g., Trojans) that remain to be explored by spacecraft? It is clear that the solutions to these questions will allow us to glean insights into many fundamental planetary science problems, in particular those connected to the formation and evolution of our solar system. Since the last book in this series, Asteroids III, we have made tremendous advances in our knowledge of asteroids, thanks to the combined efforts of ground- and spacebased observations, space mission rendezvous and flybys, laboratory analysis of returned samples, and theoretical and numerical modeling. In Asteroids IV, major strides have been made in the long journey that will eventually lead us to a much deeper understanding of our planetary ancestors. In the words of the classic Californian science fiction radio show Hour 25, our progress has all of us now “standing on the verge of new worlds, new ideas, and new adventures.” This book reviews these major advances in 42 chapters, with the aim of being as exhaustive as possible while also

Asteroids are thought to be leftover planetesimals that are closely related to the precursor bodies that formed both the terrestrial planets and the cores of the giant planets. The most primitive ones contain a record of the original composition of the solar nebula in which the planets formed. The organic matter and properties of water that some contain provide us with critical clues about how life started on Earth. Moreover, some of them cross the trajectory of our planet and therefore pose a risk to humanity. The sizes, shapes, and rotational, internal, and surface properties of asteroids are the outcome of collisional and dynamical evolution that has molded them since they formed. Understanding the processes they experienced, how these mechanisms changed their properties, and how these factors in turn influenced their evolution can serve as a tracer to tell us the story of the solar system. In 2005, the European Space Agency published its report Cosmic Vision: Space Science for Europe in 2015–2025, which contained two questions related to asteroid research: (1) what are the conditions for planet formation and the emergence of life? (2) How does the solar system work? Similarly, in 2012, the committee on the planetary science decadal survey appointed by the U.S. National Research Council published a list of questions intimately related to asteroid research. We repeat here those that help put into context the work that is presented throughout Asteroids IV: (1) What were the initial stages, conditions, and processes of solar system formation and the nature of the interstellar matter that was incorporated? (2) What solar system bodies endanger Earth’s biosphere, and what mechanisms shield it? In addition, the decadal survey indicated the goals for research on primitive bodies for the next decade: (1) Decipher the record in primitive bodies of epochs and processes not obtainable elsewhere, and (2) understand the role of primitive bodies as building blocks for planets and life. Important questions related to asteroids in various areas were then indicated, some of which include: 3

4   Asteroids IV remaining accessible to students and researchers who are interested to learn about these fascinating bodies and what they tell us about solar system history. Here we introduce the major concepts and topics of this book and highlight some of the major advances that have been made since Asteroids III. This introduction does not include references except from the chapters themselves. 2. ASTEROID FORMATION AND SOLAR SYSTEM EVOLUTION Many major improvements have been achieved in solar system dynamical studies since Asteroids III. As discussed in the review chapter by Johansen et al., new modeling work on the very early phases of planetesimal growth, together with constraints derived from meteorites and protoplanetary disks, have inspired next-generation scenarios of how the largest asteroids originated. Simulations of the evolution of turbulent gas and dust in protoplanetary disks demonstrate that 100- to 1000-km-diameter asteroids may have formed directly from the gravitational collapse of small particles that organize themselves in dense filaments and clusters. Although many open questions remain, these models provide a potential solution to the long-standing issue regarding the passage from centimeter-sized particles to asteroidal bodies in planetary growth studies, bypassing the long-standing “meter-size barrier.” In effect, laboratory experiments have shown that micro‑ meter-scale dust readily aggregates into millimeter- or even pebble-sized agglomerates. On the largest scales, impact simulations have shown that self-gravity among two colliding protoplanets ensures net growth, although the efficiency of two planetesimals combining is often less than 100% (see the chapter by Asphaug et al.). The situation is still murky for objects ranging in size from millimeters to kilometers. In fact, macroscopic dust particles (millimeter or larger) have poor sticking properties in particle-particle collisions, while gravity between the components is too low to act as a “glue” between them. Johansen et al. discuss how the self-gravity of a sufficiently massive particle clump may be capable of growing bodies in this size range. Several dynamical scenarios have also emerged to describe the early phases of the solar system, with the observed properties of the asteroid belt acting as a constraint (see chapter by Morbidelli et al.). They indicate that the asteroid belt has been sculpted by one or possibly a series of processes, and that this evolution can be characterized by three phases. The first phase starts during the lifetime of the gaseous protoplanetary disk when the giant planets formed. Here the giant planets may have undergone migration as they gravitationally interacted with the solar nebula. One of the new scenarios describing this phase, which involves the migration of Jupiter through the asteroid belt, is called the “Grand Tack.” It is capable of producing dynamical excitation among the existing asteroids, forcing many out of the region where the main belt currently lies, while also introducing new lowalbedo asteroids into the main belt from the Jupiter-Saturn

zone. This could have left the population in a state similar to the observed main belt, with a low-mass population having a wide range of eccentricities, inclinations, and compositions. The second phase occurs later, possibly as late as ~4 G.y. ago or nearly 500 m.y. after the removal of the gaseous protoplanetary disk. Once again, the giant planets became temporarily unstable, such that some of them may have strongly interacted with a large primordial disk of comet-like planetesimals located in the outer reaches of the solar system. This allowed the giant planets to migrate from an initial resonant and compact configuration to their current configuration. The instability may also have led to the additional loss of asteroids from the main-belt region. The so-called “Nice model” provides a description of this evolutionary phase. The strength of this model is that it naturally reproduces various observed constraints within a single model, such as the current semimajor axes, eccentricities, and inclinations of giant planets; the curious existence of Trojan asteroids, a population that is reviewed by Emery et al.; and the structure of the Kuiper belt beyond Neptune. The Nice model also provides a possible explanation to the origin of the so-called late heavy bombardment, which some argue produced numerous younger basins on the Moon and terrestrial planets. The studies of these first two phases provide us with new insights into how and where planets formed, with implications for the dynamical history of the asteroid belt and the diversity of compositions observed in the relatively narrow ~1-AU-wide main asteroid belt, as reviewed by DeMeo et al. These new scenarios together describe an evolutionary process that could lead to a solar system with properties that are consistent with the observed one. The aforementioned constraints, however, are challenging, and it is possible that the new scenarios will founder as they are tested in detail. Therein lies the new science that will comprise Asteroids V in the decade or more to come. The third phase, reviewed by Morbidelli et al., covers the interval between late giant planet migration until today. Potentially as much as half the asteroid population was lost via depletion taking place at unstable resonances with the giant and terrestrial planets, mostly during the subsequent 100 m.y. after late planet migration took place. Additional constraints on these ideas come from models of the collisional evolution of the asteroid belt. As reviewed by Bottke et al., the latest generation of model results suggests that the main belt’s wavy size-frequency distribution describes a primordial population dominated by 100-km-diameter and larger objects (see Johansen et al.) that undergoes sufficient comminution to create much of the observed population of 100 km) where they comprise only 6% of the total mass, but they make up a quarter of the mass at medium sizes (20 km < D < 100 km), and are almost equal to the S-complex by mass at the smallest sizes (5 km < D < 20 km). At the same time, the fractions of medium-sloped spectral types (M and P) decrease at smaller sizes. Newly discovered in the inner main belt are D-type asteroids defined by their very red spectral slopes, which had only previously been seen at larger distances aside from a few near-Earth objects (NEOs) that have dynamical origins in the outer belt and beyond (Carvano et al., 2010; DeMeo and Carry, 2014; DeMeo and Binzel, 2008). These objects are discussed later in section 5.2. An interesting effect of viewing the inner main belt by mass (previous analyses have viewed such statistics by number, not by mass) is the relative insignificance of the Vesta family, the products of a large collision with Vesta, in the inner belt

Fig 3. The distribution of asteroid classes by mass in distinct size ranges and distances from the Sun. Asteroid mass is grouped according to objects within four size ranges, with diameters of 100–1000 km, 50–100 km, 20–50 km, and 5–20 km. Seven zones are defined as in Fig. 1: Hungaria, inner belt, middle belt, outer belt, Cybele, Hilda, and Trojan. The total mass of each zone at each size is labeled and the pie charts mark the fractional mass contribution of each unique spectral class of asteroid. The total mass of Hildas and Trojans are underestimated because of discovery incompleteness. The top row is consistent with results from Gradie and Tedesco (1982) and Gradie et al. (1989). Figure from DeMeo and Carry (2014).

18   Asteroids IV (Binzel and Xu, 1993). Indeed, when excluding Vesta inself, only a handful of all Vesta family members, called vestoids, are larger than 5 km, so their mass contribution even among 5–20-km-diameter bodies is miniscule [1% of that size range and region (DeMeo and Carry, 2014)]. Vestoids are significant contributors to the inner belt in terms of the total number observed (Parker et al., 2008; Masiero et al., 2013), but it is their high albedo, close distance, and spectral distinctiveness that have biased their discovery and classification. In the middle main belt (2.5–2.82 AU), (1)  Ceres (Ctype in the Bus-DeMeo taxonomy) and (2) Pallas (B-type) are the largest objects and they comprise roughly 31% and 7%, respectively, of the entire main belt by mass. The broad taxonomic makeup of the inner and middle belt at the smallest sizes is essentially identical. In the outer main belt (2.82–3.3 AU), the C-complex dominates by mass, with (10) Hygiea being the largest and most massive member. Despite the fact that the relative fraction of S-complex asteroids is small in the outer main belt, their total mass is still quite significant given that the mass in the outer belt is 2–10× greater than in the inner belt at each size range. A- and V-types, respectively olivine-dominated and basaltic asteroids, are present in small numbers throughout the main belt, aside from those associated with Vesta (Lazzaro et al., 2000; Moskovitz et al., 2008; Sanchez et al., 2014). Their discovery in the middle and outer belts was surprising since differentiated bodies or fragments of them were not expected in the context of the classical understanding of asteroid differentiation. Significant advances have been made since Asteroids III in understanding the complexity of both the asteroid differentiation process and the mechanisms that displace material throughout the solar system (see the chapters by Scheinberg et al., Scott et al., and Morbidelli et al. in this volume). Families play a very important role in the architecture and composition of the main belt. The chapter by Masiero et al. in this volume covers this topic in detail. It will be valuable for future work to incorporate the size-frequency distribution of asteroid families into studies of the radial distance distribution of asteroids in the main belt to fully interpret the results, particularly at small asteroid sizes. The taxonomic makeup of the largest Hildas (~4 AU) and Trojans (5.2 AU) remain predominantly P-type and D-type, respectively. The trends at smaller sizes are discussed in section 5.2. The chapter by Emery et al. in this volume is dedicated to the Trojan population, covering the compositional and physical characteristics as well as the dynamical history. 3. THE DYNAMICAL PERSPECTIVE 3.1. Dynamical Tools Determination of an asteroid’s orbit immediately tells you where it is currently spending its time in the solar system, and the combination of the distributions of known orbits and

physical properties provide powerful clues to the evolution of the solar system (questions A2 and A3 in Appendix A). However, there are many more asteroids with known orbits than there are with physical characterization, and at times we are left to gain context based on their orbits alone. The dominant perturber in the solar system is Jupiter, and its effects are made clear by the large depleted Kirkwood gaps in the asteroid population owing to its mean-motion resonances. Given the dominance of Jupiter’s perturbations for asteroid orbits, one can take advantage of its similarity to the restricted three-body problem to generate some quasiconserved quantities. The most common measure is the Tisserand parameter TJ, which is calculated with respect to Jupiter and can help to distinguish between different classes of small body orbits. This is primarily used to separate Jupiter-family comets (2  < TJ < 3) from nearly isotropic comets (TJ < 2), but is also commonly used to try to uncover dormant comets in the NEO population (Levison et al., 1994; Bottke et al., 2002b; DeMeo and Binzel, 2008) and separate main-belt comets from the ordinary comet population (see the chapter by Jewitt et al. in this volume). Orbits are typically calculated and reported for what the asteroid’s Keplerian orbit would be at a specific epoch in the presence only of the Sun. This calculated “osculating orbit” does not incorporate any information about short- or long-term oscillations of the orbit owing to the perturbations of the giant planets. The “proper elements” of an asteroid represent quasi-integrals of motion, meaning that they are nearly constant in time, and can be calculated or estimated using various numerical and analytical tools (Knežević et al., 2002). The difference between an asteroid’s osculating and proper orbital elements can be substantial — tens of percent in a, e, and i. The proper elements of an asteroid are representative of its long-term orbit and are essential in studies of dynamically related clusters or families of asteroids (see the chapter by Nesvorný et al. in this volume; Bendjoya et al., 2002; Zappalà, 2002). An important dynamical process affecting the entire main asteroid belt is the Yarkovsky effect (see Bottke et al., 2002a, 2006). This is a size-dependent drift in a body’s semimajor axis caused by the reemission of absorbed solar radiation. It is the main driver that pushes main-belt asteroids into resonances and they can then become NEOs or be driven to extreme orbits that could have them impact a planet or the Sun, or be ejected from the solar system. Smaller objects move more rapidly, where drift rates scale roughly as 1/D, which means that where we find smaller objects now may simply be a waypoint on a drift across the asteroid belt (where a 1-km body might drift roughly 10–4 AU in 1 m.y.). A similar point of confusion for small objects is that the collisional lifetimes are much shorter than the age of the solar system at sizes smaller than 10–30 km (see the chapter by Bottke et al. in this volume). Between the effects of the Yarkovsky drift and collisional evolution, we can really trust the orbits of only the 500 or so largest bodies (D > 50 km) as tracers of the early structures of the asteroid belt.

DeMeo et al.:  The Compositional Structure of the Asteroid Belt   19

As the Yarkovsky effect pushes asteroids around, some will inevitably reach an orbital resonance [a mean-motion resonance with Jupiter or other powerful secular resonances (see Nesvorný et al., 2002)]. While the effects of this may vary, a typical response is an increase in the asteroid’s orbital eccentricity. As the eccentricity increases to large values, it can cause the body to cross the orbit of Jupiter, which can easily result in its ejection from the solar system. If the asteroid first has an interaction with the terrestrial planets, it is possible that its orbit can be altered in a way to pull it out of the main asteroid belt and reside almost entirely within the inner solar system. In near-Earth space, the orbital dynamics are controlled by the chaotic interactions with the terrestrial planets and thus the population is transient, with only a 10-m.y. lifetime (Gladman et al., 2000). Numerical models of the evolution from the main belt to near-Earth orbits have largely recovered the flux of bodies moving through different resonant passageways and can explain the size of the NEO population (Bottke et al., 2000, 2002b). Furthermore, the NEO model of Bottke et al. (2002b) provides a dynamical tool to make statistical links between NEAs and the most likely resonant pathway they traveled from the main asteroid belt. Some NEOs can be probabilistically linked to specific regions of the main belt, allowing for links to be made between bodies and their regions or possible parent asteroid families (e.g., Campins et al., 2010). Even the orbits of the largest bodies have likely been altered substantially early in solar system history. As models of solar system evolution have matured, the effects of the possible “late” (after ~400 m.y. or so) movements of the giant planets have been studied in the most detail (see the chapter by Morbidelli et al. in this volume). Specifically, some traces of giant planet migration are still found in the main asteroid belt by way of depletions near primordial mean-motion resonances with Jupiter (Minton and Malhotra, 2009), although some types of migrations can be ruled out by clear patterns of depletion and orbital changes that would still be noticeable in today’s asteroid belt (Morbidelli et al., 2010). As the possible late migration of the giant planets has been studied in more detail, it is clear that many small bodies could be affected. The violent instability of the giant planets has been found to provide ideal dyanamical pathways to capture the Trojan asteroids at Jupiter (Morbidelli et al., 2005; Nesvorný et al., 2013), capture the irregular satellites of the giant planets (Nesvorný et al., 2014), implant D- and P-type asteroids from the primordial Kuiper belt into the main asteroid belt (Levison et al., 2009), and sculpt the Kuiper belt (Levison et al., 2008; Batygin et al., 2012). An example of the effects that planetary migration would have on small bodies and the asteroid belt is shown in Fig. 4. The distribution of asteroid orbits, their physical properties, and the total mass depletion in the asteroid-belt region are all used as constraints on early solar system evolution, as discussed below (and in more detail in the chapter by Morbidelli et al.).

3.2. Dynamical Overview of the Main Belt The asteroid belt today is estimated to contain approximately ~5  × 10–4  Earth masses (M⊕), which is approximately 3× the mass of its most massive asteroid, (1) Ceres (Krasinsky et al., 2002). This is in contrast to the nearly 1 M⊕ of material that would be expected to inhabit this region given a smooth distribution of the solid material found in the planets (Weidenschilling, 1977). Similarly, classical models of planetesimal formation suggest that the current mass in the asteroid belt today would not be enough to have grown the largest asteroids, and thus there has been a depletion of mass since the asteroid belt formed (see Weidenschilling and Jackson, 1993). As discussed in detail in the chapter by Morbidelli et al. (and below), there are multiple proposed methods to remove so much mass from the asteroid belt, and there are also new models for planetesimal formation that may allow the formation of large asteroids directly from small “pebbles” in the solar nebula (see the chapter by Johansen et al. in this volume). The orbital distribution of the asteroid belt finds that most of the dynamically stable phase space of a, e, i is filled, with orbital eccentricities ranging from 0 to 0.35 and inclinations from 0° to about 30°. Meanwhile, every theory for planetesimal formation relies on the damping effects of the gaseous solar nebula to reduce relative velocities and increase accretion rates (see the chapter by Johansen et al.). This implies that, at least immediately following their formation, planetesimals would have been on circular and coplanar orbits and were dynamically excited into their current orbits at some later time. The loss of mass, observed dynamical excitement, and taxonomic mixing are presumed to be closely linked to the dynamical evolution of the solar system — including the formation and migration of the terrestrial and giant planets. As described in more detail in the chapter by Morbidelli et al., models typically attack all three constraints with one mechanism. Studies of sweeping secular resonances due to the dissipation of the solar nebula suffer dual problems of needing long (20 m.y.) timescales of gas dissipation to deplete enough bodies, and then typically failing to reproduce the inclination distributions (see O’Brien et al., 2007). The inclination distribution is also a problem for models that invoke stranded planetary embryos that excite and deplete the primordial asteroid belt (see O’Brien et al., 2006). Here there is depletion of low-inclination bodies owing to their low-velocity encounters with planetary embryos, and again a mismatch with the observed distributions. Collisional processes are also important constraints. While even very massive asteroid belts (e.g., with 1000 times more mass than today) would have collisionally ground away most mass and reached a total mass similar to that found today (Chapman and Davis, 1975), the remnants and scars of such dramatic and long-term collisional evolution would likely be more visible in our studies today (see also the chapter by Bottke et al.). Partly due to the inability of models to simultaneously match constraints with the terrestrial planets (the mass of

20   Asteroids IV 1

10

Accretion disk

0.4

Grand Tack Model

0.2 Radial mixing

Mass removal

0.6

800 Second mass removal

900

LHB Nice Model

Time Since the Beginning of the Solar System (m.y.)

0

100

1000

Main Belt

Kuiper Belt

4600 1

Trojans

10

100

Semimajor Axis (AU) Fig 4. This cartoon depicts major components of the dynamical history of small bodies in the solar system based on models. These models may not represent the actual history of the solar system, but are possible histories. The figure displays periods of radial mixing, mass removal, and planet migration — ultimately arriving at the current distribution of planets and small-body populations. Figure from DeMeo and Carry (2014).

Mars) and with the asteroid belt (orbital distributions and water delivery), a recently proposed model, the Grand Tack model, invokes a scattering implantation of nearly the entire asteroid belt population from different parent populations (Walsh et al., 2011). This dramatic migration of the giant planets causes widespread depletion and then mixing of remnant populations into the dynamically stable asteroid belt. When Jupiter is migrating inward, it completely depletes all objects native to the current asteroid belt. During its outward migration it scatters some remnants of this population back into the asteroid belt, and then during the outermost stretches of its migration it also scatters in bodies from more primitive reservoirs between and beyond the formation region of the giant planets. This mechanism is distinct from others as it implies separate parent populations for some of the major different compositional classes found in the asteroid belt, and also because it results in a low-mass asteroid belt from

very early on in solar system history. While it provides firstorder matches to these three asteroid belt constraints (mass depletion, orbital distributions, and taxonomic distributions), they were not a prediction of the model — rather, they were a necessary constraint for the model to be viable. Going forward, each of these can be investigated more closely and hopefully limit or rule out some of the free parameters in the current Grand Tack scenario (growth and migration parameters of the giant planets). Already, the Grand Tack model relies on some assistance from what is thought to follow in solar system history. The eccentricity distribution in the Grand Tack model is elevated compared to what is observed today (Walsh et al., 2012). However, the motion of the giant planets during the “Nice model,” which might have happened roughly 400 m.y. later, will alter the orbits of the asteroid belt while having minimal affect on taxonomic distributions or total mass

DeMeo et al.:  The Compositional Structure of the Asteroid Belt   21

[eccentricities are the primary orbital element altered, and total mass is only depleted by a factor of 2–3 (Morbidelli et al., 2010), although the Nice model is credited with implanting D- and P- types bodies in the main belt]. In fact, Minton and Malhotra (2011) find that a very excited asteroid belt (elevated eccentricities) is a good fit when considering very simple models of giant planet migration that could come later. However, the models regarding later giant planet migration is a field of active study, and so each new iteration may require a reinvestigation of this aspect of the Grand Tack model’s asteroid belt fits. If the Grand Tack model relies on later events, it begs the question of how much we can use different mechanisms to explain different constraints — and are there ways to mesh asteroid belt constraints with other models of planet formation? Already planet-formation models are increasingly using the asteroid belt as a constraint for their model outcomes, both for delivering water-rich asteroid material to the growing planets (Morbidelli et al., 2000), and also for using their orbits to rule out other modes of planet migration (Minton and Malhotra, 2009; Walsh and Morbidelli, 2011). Meanwhile, recent advances in planetesimal formation (see the chapter by Johansen et al. in this volume) imply the possibility of a different initial distribution of mass in the early solar system than previously considered. It is possible that planetesimal formation relies on clumps of “pebbles” collapsing, which could lead to a small number of planetesimals amid a huge number of remnant pebbles — where only a few of the formed planetesimals are large enough to rapidly accrete the remaining pebbles (see Ormel and Klahr, 2010). One could envision scenarios in which the asteroid belt never had much mass, and thus dynamical and taxonomic stirring would be constraints independent of mass loss. 4. THE METEORITE PERSPECTIVE 4.1. Meteorite Composition Tools The parent asteroids of most meteorites would have formed at different times and/or places in an evolving solar nebula. This will have had profound effects on the initial compositions and subsequent histories of the asteroids that are reflected in the way meteorites are classified. Radial thermal gradients in the disk will have dictated gross differences in compositions upon accretion, such as rock/ice ratios. However, it is evident from the meteorite record that more transient processes were also important in the thermal processing of dust and that radial transport brought together materials with different thermal histories. The thermal processing of dust has left its imprint on the major- and trace-element compositions that show clear variations associated with their volatility. Estimates of the relative volatilities of the elements are traditionally based on thermodynamic equilibrium calculations of their 50% condensation temperatures from a gas of solar composition at a total pressure of 10–4 bar (e.g., Lodders, 2003). There

is also evidence in meteorites for the fractionation of elements in the nebula according to their chemical affinities (lithophile — rock-loving, siderophile — Fe-metal-loving, and chalcophile — sulfide-loving). Physical processes that separated solid/melt from gas and silicates from metal seem the most likely causes for these variations. After accretion, asteroids were subject to internal heating, largely due to the decay of the short-lived radionuclide 26Al (t1/2  ≈ 720,000  yr) that was inherited from the protosolar molecular cloud. Thus, asteroids that formed early will tend to have been more internally heated than those that formed later, although other parameters will also have influenced internal temperatures. The least-heated meteorites (3–4 m.y. after CAIs. Chondrules in the CB chondrites, which are different from those in other

24   Asteroids IV chondrite groups, have average ages of 4.6 ± 0.5 m.y. after CAIs (2s standard error) and seem to have formed in an impact (Krot et al., 2005; Yamashita et al., 2010). Taken at face value, these chondrule ages imply that all chondrite parent bodies formed >3–4  m.y. after CAIs. However, the apparent spreads in chondrule ages are problematic. Chondrules in a particular chondrite group exhibit a limited range or physical and chemical properties that vary from group to group. At the levels of turbulence that are thought to exist in disks, even in a so-called dead zone, chondrules would be mixed over many astronomical units on timescales of 1–3  m.y. (Alexander, 2005; Alexander and Ebel, 2012; Cuzzi et al., 2010). Thus, either chondrite formation was dispersed over a large fraction of the solar nebula, as in the Grand Tack and Nice models, or the quoted ranges in chondrule ages are not real. The latter must be ruled out before concluding the former. Indeed, it has been suggested that most of the reported ranges in Al-Mg ages simply reflect the uncertainties in the measurements (i.e., most chondrules in a chondrite group could have the same age or a narrow range of ages) (Alexander and Ebel, 2012; Kita and Ushikubo, 2012), and that the youngest ages, indeed perhaps all chondrule ages, have been disturbed by parent-body processes (Alexander, 2005; Alexander and Ebel, 2012). It remains to be seen if the range in chondrule Pb-Pb ages also reflect parent-body disturbance. Given that parent-body processes can disturb the radiometric systems that are used to date chondrules, it is essential to study only the least-metamorphosed and aqueously altered members of a chondrite group. Even in these chondrites, it is essential to take care to select only those chondrules that can be shown to have undergone no secondary modification. The most careful Al-Mg study of chondrule ages conducted to date has been for the ungrouped carbonaceous chondrite Acfer 094, where 9 of the 10 chondrule ages are within error of a mean of 2.3+−00..53 m.y. (26Al/27Al  = 5.7  ± 1.0  × 10–6) after CAIs (Ushikubo et al., 2013). Selecting only similar (type I) chondrules from a previous study of a primitive CO (Kurahashi et al., 2008) gives a mean age of 2.0+−00..32 m.y. (26Al/27Al = 7.1 ± 0.8 × 10–6) after CAIs. The Al-Mg system is more susceptible to modification in the chondrules analyzed in Semarkona, the ordinary chondrite that has been least affected by parent-body processes, but the chondrules have a mean age of 2.0+−00..53 m.y. (26Al/27Al = 7.3  ± 1.4  × 10–6) after CAIs (Kita et al., 2000; Villeneuve et al., 2009), which is very similar to those for CO and Acfer 094 chondrules. This Semarkona average chondrule age is consistent with an average age of 1.7 ± 0.7 m.y. after CAIs for H-chondrite chondrules obtained using the 182Hf-W system (Kleine et al., 2008). Additional constraints on the timing of accretion can potentially come from the thermal histories of chondrites since the abundance of the radioactive heat source, 26Al, will have been a function of accretion time. Modeling of mineral ages with different closure temperatures during metamorphism has been used to estimate the accretion time (≥ 2–3 m.y. after

CAIs) and size (~100  km in diameter) of the H ordinary chondrite parent body (Harrison and Grimm, 2010; Henke et al., 2013; Kleine et al., 2008; Trieloff et al., 2003). Alternatively, assuming that the maximum peak temperatures estimated for any member of a chondrite group represents the peak central temperature achieved in their parent body, along with a diameter of 60 km, Sugiura and Fujiya (2014) estimated accretion ages for all chondrite groups (Table 4), including one for the ordinary chondrites of ~2.1 m.y. after CAIs. If this accretion age for the ordinary chondrites is approximately correct, it constitutes further evidence that many measured chondrule ages (e.g., those >2.1 m.y.) are disturbed. Such estimates depend on many assumptions, not the least of which are that we have samples from all depths in the chondrite parent bodies, that the peak temperatures have been accurately determined, that accretion temperatures and initial water ice contents are known, and that the parent body sizes are known. A lack of samples from the deep interior of the CO parent body, for example, could explain why the estimated accretion age of the COs (~2.7 m.y. after CAIs) is younger than for the ordinary chondrites despite their average chondrule ages being so similar. Further complicating these estimates, some have questioned the simple internal heating models and argue that at least the ordinary chondrite parent bodies are rubble piles produced by early collisions while the bodies were still hot (Ganguly et al., 2013; Scott et al., 2014). Also, there is the suggestion that the CV chondrites, at least, formed in the presence of magnetic fields generated by dynamos in their planetesimal cores (Weiss and Elkins-Tanton, 2013), i.e., that these chondrites are the unheated crusts of differentiated bodies. If true, the accretion age of the CV parent body would have to have been significantly earlier than estimated by Sugiura and Fujiya (2014). However, to date, no achondrites or iron meteorites have been linked to the CVs. Constraints on the timing of aqueous alteration can be established in some chondrites because two products of alteration, fayalitic olivine and carbonates, incorporated short-lived 53Mn. Fayalitic olivine in ordinary chondrites formed at 2.4+−11..83 after CAIs, while in CV and CO chondrites it formed at 4.2+−00..87 and 5.1+−00..54 after CAIs, respectively (Doyle et al., 2015). Four to 5  m.y. after CAIs is also about the time that carbonates formed in CM and CI chondrites and the ungrouped chondrite Tagish Lake (Fujiya et al., 2012, 2013; Jilly et al., 2014). Thermal modeling suggests that the parent bodies of these meteorites formed 3–4 m.y. after CAIs. Thermal modeling of differentiated bodies is even more problematic than for chondrites because, for instance, the initial bulk composition is not known, and how the melts segregate within the bodies can have a profound affect on thermal histories (e.g., Moskovitz and Gaidos, 2011; Neumann et al., 2014). Nevertheless, models of varying degrees of sophistication have been used to estimate their accretion times. For instance, core formation on the IIAB, IIIAB, IVA, IVB, and IID iron meteorite parent bodies occurred at 0.7 ± 0.3, 1.2 ± 0.3, 1.4 ± 0.5, 2.9 ± 0.5, and 3.1 ± 0.8 m.y.

DeMeo et al.:  The Compositional Structure of the Asteroid Belt   25

TABLE 4. Average ages and estimates of the accretion ages of chondrites and various nonchondrites from Sugiura and Fujiya (2014) unless otherwise indicated. Group

Chondrules

Time After CV CAI

Other

Chondrites       E   1.8 ± 0.1   2.0 + 0.5, –0.3*, 1.7 ± 0.7† O 2.1 ± 0.1, ≥2–3‡   R   2.1 ± 0.1   2.6 ± 0.2   CK   CO 2.0 + 0.3, –0.2§ 2.7 ± 0.2   CV   3.0 ± 0.2   3.5 ± 0.5   CI, CM, CR, TL   Nonchondrites       Angrites — 0.5 ± 0.4 ≤1.5¶ HEDs — 0.8 ± 0.3 ≤2.5 ± 1**, ≤0.6 + 0.5, –0.4††, 50–100 km) S-type asteroids than the three needed to explain the three ordinary chondrite groups.

Based on the meteorite record and the assumption that each meteorite group comes from a single parent body, there are at least 100–150 distinct parent bodies.

1. How many original parent bodies are represented in the asteroid belt?

B. Asteroid and Meteorite Compositions

Where: Links between asteroids and meteorites help constrain the conditions and location of formation. Dynamical models link where the asteroids are located now to where they originally formed. When: Recent advances dating mateorites have constrained formation ages. For example, igneous meteorites have crystallization ages older than chondritic ones. So bodies that melted, melted early. Bodies that did not melt formed later. How: A second leading theory on formation, through streaming instability, has emerged since Asteroids III.

1. Where, when, and how did they form?

 A. Formation and Physical Evolution of Asteroids

Further research on meteorite composition will yield better understanding of parent bodies. For example, high-precision isotopic measurements may reveal if the OCs separate and demand more than three bodies. Sample return will provide insight, as will a review of how many primary parent bodies (those > 50–100 km) there are in each spectral class.

Meteor observation networks will provide insight on source bodies for meteorites. Continued work linking large main-belt asteroids to meteorites.

Burbine et al. (2002)

Burbine et al. (2002)

Section 3, this chapter; Morbidelli, Vokrouhlický, Bottke

Brunetto, Krot, Scheinberg, Scott, Wilson, Bottke, Asphaug, Jutzi

Continued work on collisional and thermal modeling, studies of families, spacecraft measurements including surface (crater) observations. In situ measurements and sample return of non-OClike bodies. Density measurements to understand interiors. Identify the current spread in semimajor axis of each compositional group and use it to constrain the different migration scenarios. Search for and characterize interlopers for composition. Orbital and mass constraints also continue to inform dynamical history.

Section 4, this chapter, Johansen

Isotopic evidence points to carbonaceous chondrites being different from all others. But they are not all more water-rich, and their water H isotopes are not comet/Enceladus-like. Ages of chondrules and secondary minerals can be used to estimate chondrite formation ages. The almost ubiquitous presence of chondrules suggests that they may have played a role in planetesimal formation.

Related Question Possible Solutions What Next? Chapters

APPENDIX A: MAJOR OUTSTANDING ASTEROID COMPOSITIONAL QUESTIONS

32   Asteroids IV

Comparison of meteorites with micrometeorites and breccias suggests meteorites may be fairly representative samples of the major types of asteroids. We still find new types of meteorites (and presumably parent bodies), but differences tend to be subtle. However, the inherent “top-heavy” asteroid size distribution means that rare, large collisions stochastically dominate the ejected fragments by mass, resulting in an inherent possibility of large devations from direct representation of asteroid types by meteorite collections. If there is more diversity in the spectra of main-belt asteroids than meteorites, could much of this diversity be due to regolith processes (grain size and density sorting) and space weathering? Also, there are biases associated with delivery efficiency from different resonances and the robustness of the samples as they past through Earth’s atmosphere.

A few connections are robust: OCs make up part of the S class. HEDs are linked with V-types and the largest group of isotopically linked HEDs are concluded to be from Vesta. Isotopically distinct HEDs, as well as the diversity of other achondrites, point to a wide diversity of differentiation processes that remain poorly understood. The CMs may be linked with Ch and Cgh asteroids. The weaker and fewer bands present in an asteroid spectrum, the less confident we are of its composition. The C and X complexes could be extremely compositionally diverse, but observations are also affected by varying grain size, phase angle, regolith gardening, space weathering, etc. Shock darkening, which also mutes absorption bands, can also disguise the compositional identity of asteroid surfaces.

3. How well do meteorites sample the asteroids?

4. How robust are our asteroid-meteorite links?

B. Asteroid and Meteorite Compositions (continued) Borovićka, Jenniskens, Binzel

Vernazza, Brunetto, Yoshikawa, Reddy, Burbine et al. (2002)

Characterize asteroids at sizes relevant to meteorite falls (~5–50 m) to compare with the meteorite collection. IDPs, micrometeorites, and clasts in meteorite regoliths provide alternative samplings of the asteroid belt — how similar are they to the meteorites?

Dynamical study of asteroid families has the potential for addressing this question. By determining the ages of families and comparing with meteorite shock ages, and by following the plausible dynamical routes from family to Earth, current best guesses of associations of some meteorite types with families might become more robust. The mid-IR may be the next frontier for groundbased observational studies. Meteorite studies of spectral effects not related to composition are needed. Asteroid sample return will provide valuable insight for featureless asteroids. Serendipitous observation and recovery of objects such as 2008 TC3 will also provide “free sample return.”

Related Question Possible Solutions What Next? Chapters

APPENDIX A (continued)

DeMeo et al.:  The Compositional Structure of the Asteroid Belt   33

Section 5.3, this chapter; Borovićka, Bottke?

Section 5.5, this chapter; Vernazza, Brunetto, Binzel, Yoshikawa

Margot, Scheeres, Barucci

Implementation of ATLAST-like telescopic surveys of asteroids/ meteoroids on their final approach to Earth and increased video surveillance and recovery of fall samples to understand the prevalence of and compositions of these mixes. Physical measurements of the smallest asteroids (5–100-m). Sample return of small asteroids will also provide constraints.

This question is solved. The follow up questions are: What S-type asteroids are not OCs? What meteorites do they supply? How does the space environment affect other asteroid types?

Density measurements particularly from multiple systems. The porosity of asteroid interiors must be better constrained as well.

Collisional or accretional processes (or both) could potentially bring 6. What is the diversity such diverse materials together. of compositions within individual small asteroids? What processes mix wildly different meteorite types into a single tiny body (e.g., Almahatta Sitta, Kaidun)? When did the mixing occur?

Binzel

Survey main-belt asteroids at sizes similar to NEOs (~1 km). Study dynamical and compositional links between NEOs and main-belt families and specific regions. Dynamics need to be calibrated by observations. New understanding of differentiation processes is also relevant.

Space weathering is the primary reason for the spectral mismatch. Laboratory experiments plus ground- and spacebased asteroid measurements made great progress. Hayabusa’s sample return of Itokawa provided conclusive evidence. Other factors affecting spectral slope include grain properties and observational phase angle.

Density measurements and asteroid families currently provide the most information about asteroid interiors. How compositionally homogenous or differentiated the medium to large asteroids are is largely unknown.

7. The ordinary chondrite paradox: Why does the most common asteroid type, S-type, not match the most common meteorite type, OC?

8. What are the interior compositions of asteroids?

5. How well do NEOs represent the main belt and beyond?

We now understand that dynamical and weathering processes can be relatively fast, suggesting that NEO flux is just a current snapshot, influenced by stochastic events like more recent disruption events. Size might also matter, and the speed at which an asteroid’s orbit drifts due to the Yarkovsky effect increases with proximity to the Sun and with decreasing diameter. Yarkovsky is more effective at the small sizes (10 m or smaller) that might dominate meteorite samples. Additionally, size-dependent delivery mechanisms (Yarkovsky) mean that different size ranges could be dominated by specific asteroid families. NEO lifetimes and the NEO delivery models have helped link NEOs to their main-belt source regions.

B. Asteroid and Meteorite Compositions (continued)

Related Question Possible Solutions What Next? Chapters

APPENDIX A: (continued)

34   Asteroids IV

4. Where is the water in the asteroid belt? How much is there? Where did these water-rich asteroids form?

Current evidence: main-belt comets, activated asteroids, water absorptions, Ceres outgassing, and possible exposures of ice on Ceres.

(c) “Battered to bits” — this theory is currently less favored. Collisional modeling, crater counts, and observational evidence do not support an aggressive regime of collisional destruction and battering. (d) Previous theories postulated olivine was hidden by weathering processes. Recent progress on on space weathering disproves this hypothesis.

(b) The parents of these cores formed in the terrestrial planet region. They were destroyed and only the strongest metallic fragments were subsequently delivered to their current locations in the main belt.

Discover additional active asteroids and explore asteroidcomet connections. Continue studies of extinct or dormant comets among NEOs. Visit and map surfaces such as by the Dawn, OSIRIS-REx, and Hayabusa-2 missions. Also, density measurements, radar sounding by spacecraft, etc., might reveal ice buried beneath thick surficial lag deposits.

Further study of dynamical solutions and differentiation modeling. Continued study of meteorites to understand differentiation. Continued search for differentiation in families, including metal within large families.

(a) Asteroids differentiate differently than expected — perhaps they don’t form large olivine-rich mantles and pyroxene-rich crusts.

3. The missing mantle problem: Where is all the missing mantle material? Additional questions: Why are V- and A-types scattered throughout the entire main belt?

Jewitt, Rivkin, Krot, Binzel

Section 5.4, this chapter; Scheinberg, Wilson, Scott

Section 5.2, this chapter

Additional study of the size distribution of families in the inner belt. Groundbased imaging and shape models plus mission visits to primitive bodies. Constrain how prevalent shocking is in the main belt. Larger samples of small asteroids in the main belt (1–20 km) will help determine the distribution at smaller sizes.

Sections 2.2, 2.3, 5.1, this chapter; Morbidelli, Johansen, Emery

Progress on early solar system environment models and asteroid formation models. The best although impractical way to solve this is a mineralogical and isotopic assay of dozens of asteroids and comets.

Recent work has explored the change in relative abundance of asteroid types as a function of size. Many factors still need to be taken into account, such as (1) the size-frequency distribution of families, (2) the difference in collisional lifetimes per asteroid class, and (3) the fact that some compositions are masked at smaller sizes due to processes such as collisions and “shocking.”

(b) It is the result of a transplantation of one or more groups of asteroids that formed elsewhere. (3) Hildas and Trojans actually are more compositionally diverse than they appear, but they have significant quantities of low-albedo materials that render diagnostic spectral features nearly invisible.

(a) It is a primordial remnant from the temperature and compositional gradient in the disk.

2. How does the distribution of asteroids change as a function of size? What is the significance of that distribution?

1. What is the source of the compositional gradient in the main belt? Why are the Hildas and Trojans compositionally homogeneous compared to the main belt?

C. Asteroid Compositional Distributions

Related Question Possible Solutions What Next? Chapters

APPENDIX A: (continued)

DeMeo et al.:  The Compositional Structure of the Asteroid Belt   35

Beyond the scope of this book

Beyond the scope of this book

Harris, Jedicke, Farnocchia

Continue with current progress on crater studies, dynamical studies including migration.

Identify and characterize extrasolar asteroid belts (evolved debris disks). Survey different planetary system architectures including asteroid belt distances and masses. Identify and characterize dusty white dwarf systems, and link those systems to the expected properties of precursor planetary systems. Understand the link or the gradient between comets and wet asteroids. Measure the D/H ratio of a wider array of waterrich small bodies. Dynamical studies of delivery. Understand consequences of delivery of too much water. Studies of impact and water retention on Earth. Studies of ocean-forming mechanisms unrelated to small-body delivery. Discover 90% of PHAs down to 140 m. Understand the size of the small NEA population (75 wt% (Cloutis and Gaffey, 1991).

types have been developed in recent years (e.g., Burbine et al., 2009; Reddy et al., 2012c; Sanchez et al., 2012). The first step in temperature correction of asteroid spectral band parameters is an estimation of the subsolar equilibrium surface temperature, T (Burbine et al., 2009) 14

3. NONCOMPOSITIONAL SPECTRAL EFFECTS Prior to mineralogical interpretation, spectral band parameters of S-type and V-type asteroids must be corrected for noncompositional effects, such as temperature, phase angle, and grain size. Phase angle is defined as the Sun-targetobserver angle, and is typically less than 25° for main-belt asteroids but can be much higher for near-Earth asteroids. With increasing or decreasing phase angle the slope of a reflectance spectrum generally becomes redder or bluer respectively, an effect known as phase reddening. Particle size primarily affects the depth and slope of an absorption feature and overall reflectance, with absorption bands reaching the greatest depth at a grain size bin that provides maximum spectral contrast (deepest absorption bands). Larger particle size typically means deeper bands, bluer (more negative) spectral slope, and lower overall reflectance. Analysis of particles returned by the Hayabusa spacecraft from near-Earth asteroid (25143) Itokawa have shown that a majority of the 1534 particles have a size range between 3 and 40 µm, with most of them smaller than 10  µm (Nakamura et al., 2011). This would suggest that spectra of laboratory meteorite samples with grain sizes 40° (Helfenstein, 1988).

Li et al.:  Asteroid Photometry   131

2. OVERVIEW OF THEORIES 2.1. Basic Concepts

Magnitude

2

4

S-type C-type V-type

Model Model Model

6

8

0

50

100

Solar Phase Angle Fig. 2. The phase functions of three asteroid classes, all normalized at zero degree phase angle. The lines at phase angles less than ~30° are the respective best-fit models using the data from Helfenstein and Veverka (1989) for S and C types (Asteroids II book), and a composite Vesta curve from Hicks et al. (2014) for V types. Data from Mathilde (Clark et al., 1999) and Bennu (B-type) (Takir et al., 2015) are used for additional C types beyond 30° phase angle. Data for Gaspra (Helfenstein et al., 1994), Lutetia (Masoumzadeh et al., 2014), and Eros (Li et al., 2004) are used for S types beyond 30° phase angle.

In this chapter, we will focus on disk-resolved photometric studies of asteroids based on photometric theories and high-resolution data returned by asteroid exploration missions. Photometric modeling based primarily on groundbased photometric surveys have been thoroughly reviewed in previous Asteroids books in this series (Bowell and Lumme, 1979; Bowell et al., 1989; Helfenstein and Veverka, 1989; Muinonen et al., 2002). It is important to keep in mind that physical laws dictate that the photometric signatures from planetary surfaces necessarily correlate with polarimetric signatures. In this chapter we strictly limit the scope of our discussion to asteroid photometry, and readers are referred to a companion chapter in this volume by Belskaya et al. for a comprehensive review on asteroid polarimetry. In section 2, we will review the basic concepts of photometric measurements and models, the most recent developments in theoretical models, and the controversy about several analytical models. In section 3, we will summarize observational results reported over the past decade, focusing on disk-resolved photometry based on spacecraft observations. We will then discuss applications and implications of photometric modeling to the study of general asteroid properties in section 4. In section 5, we provide a summary and a perspective on the future of asteroid photometry for the next decade to come.

The fundamental quantity of light-scattering characteristics of a surface is reflectance. Several different quantities of reflectance and albedo exist under various illumination and observing conditions. Here we follow the definitions and conventions described in Hapke (2012b). Generally, reflectance is defined by the ratio of scattered radiance (or intensity) to incident irradiance (or flux), while albedo is defined with respect to an ideal surface that scatters all incident light isotropically (or a perfectly scattering Lambert surface). Reflectance quantities use two adjectives as prefixes to specify the collimation of incident light and the measurement conditions for scattered light, such as directional-directional reflectance, directional-hemispherical reflectance, etc. In the case where the two adjectives are the same, a prefix bi- is used, e.g., bidirectional reflectance. The most commonly used quantities in light-scattering theories and measurements are listed in Table 1. Here we describe a few of the most important quantities. Bidirectional reflectance, r, is an idealized quantity, because the incident irradiance, J, is assumed to be strictly col­‑ limated (Fig. 1). For observations of most asteroids, the apparent angular size of the Sun is 1 AU from the Sun), so the collimation assumption for incident irradiance is a good approximation except for at near-zero phase angle, where the finite size of the Sun rounds off the peak. The measurements of scattered intensity are made at the pixel scale of the camera or spectrometer, which is typically less than a few tens of milliradians per pixel. J has a unit of [W m–2] or [W m–2 per unit wavelength or per unit frequency]. The scattered radiance, I, has a unit of [W m–2 sr–1] or [W m–2 sr–1 per unit wavelength or unit frequency]. Therefore, bidirectional reflectance has a unit of [sr–1]. Radiance factor (or RADF), R, and reflectance factor (or REFF) are often used in laboratory measurement by ratioing the reflected light from the sample to that from a reference surface, which is usually close to a Lambert disk. A Lambert surface has a bidirectional reflectance rL(0,e,e) = 1/p in any direction, with a unit of [sr–1]. Therefore, both RADF and REFF are dimensionless. Note that non-isotropic scattering, especially a phenomenon known as the “opposition effect” near zero phase (a nonlinear increase of reflectance as phase angle approaches 0°; see section 2.3), can make a surface brighter than a perfectly scattering Lambert surface, producing RADFs greater than unity. RADF is equivalent to the commonly used but often confusing notation I/F, which is usually annotated in the literature as “I is the scattered radiance, and pF is the incident solar irradiance.” Note, however, that the p here originates from the division of the bidirectional reflectance quantity of a perfectly scattering Lambert surface, which is 1/p with a unit of [sr–1]. As such, the p actually has a unit of [sr]. Therefore, F has a unit of radiance rather than irradiance, making I/F dimensionless.

132   Asteroids IV TABLE 1. The definitions of some commonly used reflectance quantities. Quantity

Definition

Formula

Ref.*

Bidirectional reflectance

Ratio of the scattered radiance toward (i, e, a) to the collimated incident irradiance

r(i,e, a) = I(i,e,a)/J [ster–1]

p. 195

Bidirectional reflectance distribution function (BRDF)

Ratio of the scattered radiance toward (i, e, a) to the collimated power incident on a unit area of the surface

BRDF = I(i,e,a)/Jµ0 = r/µ0 [ster–1]

p. 263

Radiance factor (RADF)

Ratio of the bidirectional reflectance of a surface to that of a perfectly scattering surface† illuminated at normal direction

RADF = pr(i,e,a) = [I/F]

p. 264

Reflectance factor (or reflectance coefficient, REFF)

Ratio of the reflectance of a surface to that of a perfectly diffused surface under the same conditions of illumination and viewing

REFF = pr/µ0 = [I/F]/µ0

p. 263

Lambertian albedo

Ratio of the total scattered irradiance toward all directions from a Lambert surface to incident power per unit area

AL = PL/Jµ0 Perfectly scattering surface has AL = 1

p. 187

Normal albedo

Ratio of the reflectance of a surface observed at zero phase angle from an arbitrary direction to that of a perfectly diffuse surface located at the same position, but illuminated and observed perpendicularly

An = pr(e,e,0)

p. 296

Geometric albedo (physical albedo)

Ratio of the integral brightness of a body at zero phase angle to the brightness of a perfect Lambert disk of the same size and at the same distance, but illuminated and observed perpendicularly. It is the weighted average of the normal albedo over the illuminated area of the body

Ap =

Bond albedo (spherical albedo, or global albedo)

Total fraction of incident irradiance scattered by a body into all directions

AS =

Bolometric albedo (radiometric albedo)

Average of the spectral albedo AS(λ) weighted by the spectral irradiance of the Sun JS(λ)

Ab

∫2p r(e,e,0)µdW‡

∫ =

∫ ∫ 2p

∞

0

2p

∫

∫

p

0

r ( i, e, a )mdW e dWi

p. 301

AS ( l ) J S ( l ) dl ∞

0

q=2

Phase integral

1 p

p. 298

p. 302

J S ( l ) dl

F p ( a ) sin a da

p. 302

Page numbers in Hapke (2012b). 1 Perfectly scattering Lambert surface has r = �µ0. ‡ dW = 2psin e de = –2pdµ. * †

Other important concepts include geometric albedo (or physical albedo) and Bond albedo (or spherical albedo). Similar to RADF, geometric albedo, AP, is defined with respect to a perfectly scattering Lambert surface. The use of geometric albedo simplifies the modeling of the diskintegrated brightness of an object at any phase angle, which can now be expressed as the product of AP and its diskintegrated phase function, F(a), normalized to unity at zero phase angle. Note that, similar to RADF, for extremely bright and strongly backscattering objects, the geometric albedo can approach or exceed unity. For example, the geometric albedo of Enceladus is 1.38, Tethys 1.23, and Dione 1.00 (Verbiscer et al., 2007).

Bond albedo, AB (also known as the spherical Bond albedo), is a key quantity to measure the ability of an object to absorb incident energy, therefore critical for understanding energy balance and volatile transport on a planetary body. By definition, Bond albedo cannot exceed unity. Since Bond albedo is an integrated quantity of the disk-averaged reflectance, it can be expressed as AB = APq



(2)



where q is the phase integral, defined as

q=2

∫

p

0

F ( a ) sin a da



(3)

Li et al.:  Asteroid Photometry   133

Important for thermal modeling is the bolometric Bond albedo, which is the average Bond albedo over wavelength, weighted by the solar spectrum, F⊙(l) AB

∫ =

∞

0

A B ( l ) F ( l ) dl

∫

∞

0

F ( l ) dl

(4)

Because the solar spectrum peaks at about 500 nm with about half of the total flux in the visible wavelengths, the V-band Bond albedo is often taken as an approximation to the bolometric Bond albedo for asteroids. 2.2. Empirical Models Sophisticated modern photometric models need to describe two types of photometric data: “whole-disk” or “disk-integrated” observations and “disk-resolved” or “surface-resolved” reflectance measurements when they are available; the latter most often obtained from spacecraft-borne instruments. Diskresolved photometric measurements provided a new ability to detect the photometric effects of physical phenomena like macroscopic surface texture much more reliably and unambiguously than could be achieved with whole-disk data. Surface-resolved photometric models that are applied to asteroid observations seek to relate the local scene viewing and illumination geometry to the radiance factor, RADF, or, more simply, R. In the simplified treatment of the empirical equations to model R, such as that of Lambert (1759) and Minnaert (1941), the dependence of reflectance on i and e, usually called the disk-function or limb-darkening function, d(i,e), is often separated from the dependence on phase angle, called the surface phase function, f(a). The RADF of a surface is expressed as

R = d ( i, e ) f ( a )



(5)

Sometimes a scaling factor is added to equation (5), so that the surface phase function can be normalized, e.g., to unity at zero phase angle. Generally, the disk-function is affected by the amount of multiple scattering (therefore albedo) and surface roughness. The phase function includes the effects of single-scattering phase function, opposition surge (see section 2.3), roughness, and multiple scattering. Historically, this separation is a result of the lack of surface-resolved data before spacecraft missions, where the only available geometric variable was phase angle. Modern photometric theories indicate that when multiple scattering is not significant (i.e., for relatively dark surfaces), the disk-function and phase function can be separated in functional forms. The most commonly used empirical photometric models are listed in Table 2. Most empirical photometric models specify the disk-function, including the Lambert model (Lambert, 1759), the Lommel-Seeliger (LS) model (Seeliger, 1887), the Minnaert model (Minnaert, 1941), and the lunarLambert model (e.g., Buratti and Veverka, 1983; McEwen, 1991, 1996), while leaving the phase function implicit or

unspecified. These models can describe surfaces with a wide range of different albedos. Generally, high-reflectance objects with geometric albedo close to or greater than unity are well described by the Lambert model, although essentially no asteroids scatter light following the Lambert law because the majority have albedos 21 are assigned basic shapes due to the difficulty in obtaining sufficient resolution in radar images. Those with shapes assigned often appear irregular either with angular shapes or highly specular reflections from facets. The spin distribution of NEAs estimated from radar observations closely matches the spin distribution determined from optical light curves (Fig. 6; see the chapter by Scheeres et al. in this volume for a different version of this figure). Light curves are biased against small, slowly rotating bodies because of their inherent faintness, which often limits their observability and hence the opportunity to confidently record an entire rotation period on the scale of many tens of hours. Radar observations detect an apparent spin rate based on the instantaneous echo bandwidth, which does not require one to observe an entire rotation. Thus, radar should detect a small, slowly rotating body as a narrow echo. The distinct change in the shape and spin distributions of the NEA population at H = 21 or 22 (100- to 200-m diameters) may indicate fundamental structural changes at this scale.

Diameter 100 m

1 km

10 km

103

Frequency (1/d)

10 s

Radar Optical

90 s

100

15 m

10

2.4 h

1

24 h 240 h

0.1 0.01

Period

10 m

104

30

25

20

25

10

3.5.2. Abundance of contact binary near-Earth asteroids. Radar imaging since completion of the upgrade at Arecibo in 1999 revealed more than 30 NEAs that are deeply bifurcated (Benner et al., 2006; Brozovic et al., 2010; Magri et al., 2011). Benner et al. (2006) found that at least ~10% of NEAs >200 m in diameter are candidate contact binaries, where a contact binary is defined as “an asteroid consisting of two lobes that are in contact, [and] have a bimodal mass distribution, that may once have been separate.” By this definition, objects such as Itokawa and Toutatis that have two components with substantial size differences, and thus lack bimodal mass distributions, were not classified as contact binaries. The definition of a contact binary is necessarily subjective, and due to considerable subsequent research on the formation and evolution of Itokawa and radar imaging of hundreds of additional NEAs, we now relax the definition to include objects that are obviously bifurcated, have components that can be significantly different in size (with size ratios of at least 4:1), and mass distributions that aren’t bimodal. With this revised definition, the fraction of candidate contact binaries imaged by radar has grown to ~14% (Taylor et al., 2012). Given that true binaries comprise ~16% of the NEA population above ~200 m in diameter (Margot et al., 2002), this implies that the abundances of contact binaries and true binaries are comparable and that these objects together constitute ~30% of the NEA population >200 m in diameter. Figure 7 shows an example: the three-dimensional model of 1996 HW1, which was imaged at Arecibo in 2008 and is one of the most deeply bifurcated NEAs observed to date (Magri et al., 2011). These contact binary objects display considerable dynamic range in long axis lengths, spectral classes, and spin states. The largest is (192642) 1999 RD32, with a long axis of ~6 km, and the smallest is 2013 JR28, with a long axis of ~100 m. The fastest rotator is (4769) Castalia with a rotation period of 4 h, and the slowest, 2002 FC and 2004 RF84, have unknown rotation periods of days to weeks. None of the contact binaries rotate as fast as the rapidly spinning primaries of most NEA binaries and triples (see the chapter by Margot et al. in this volume). Some of the contact binaries rotate at rates close to where they could separate if spun up slightly (Benner et al., 2006; Scheeres, 2007). A significant (but not yet quantified) fraction are non-principal-axis rotators.

100 d

H Magnitude Fig. 6. Spin-rate distribution of near-Earth asteroids as determined by optical and radar techniques (Taylor et al., 2012). Optical data (gray squares) are periods from the Warner lightcurve database [Warner et al. (2009), September 2014 update] with quality factors U ≥ 2; radar data (black diamonds) are estimated from echo bandwidths observed at Arecibo. There is broad agreement between the two techniques despite different observational biases, including the lack of slowly rotating small bodies. Diameters are computed from absolute magnitudes by assuming an optical albedo of 0.2.

Fig. 7. Principal axis views of the 1996 HW1 shape model (adapted from Magri et al., 2011). This is one of the most bifurcated NEAs modeled to date using delay-Doppler radar images.

174   Asteroids IV How did such objects form and why are they so abundant? Plausible formation mechanisms are by low-velocity collisions; collapse of true binaries through tidal friction or as a result of orbital perturbations during close planetary encounters; by spinup due to YORP; or by partial disruption during close planetary flybys. Combinations of the factors above may be necessary to explain the slowest rotators. 3.5.3. Binary near-Earth asteroids. Binary asteroids are a field of vigorous research and are treated in considerable detail in the chapter by Margot et al. in this volume. In this chapter we mention them only to illustrate points that also apply to broader trends within the NEA population. 3.5.4. Equatorial ridges. Evidence for equatorial bulges appears in radar images for many rapidly rotating NEAs >200 m in diameter, some relatively slow rotators, and for most of the primaries in binary and triple NEA systems. The first clear case was the primary of binary (66391) 1999 KW4 (Ostro et al., 2006), which exhibited a “double exposure” appearance at its leading edge that corresponded to the sharp edge of its ridge. Bulges have since been seen in models for (311066) 2004 DC (Taylor, 2009), 2008 EV5 (Busch et al., 2011), (136617) 1994 CC (Brozovic et al., 2011), 2005 YU55 (Busch et al., 2012), the primary of (185851) 2000 DP107 (Naidu et al., 2015), and in radar images of numerous other NEAs for which shape models are not yet available. Figure 8 shows renderings of shape models for selected objects with bulges. The ridges are thought to form via YORP-induced spinup acting on an object with a rubble-pile internal structure (Harris et al., 2009; Walsh et al., 2008; see also the chapter by Scheeres et al. in this volume). Although no formal estimate of their abundance is available, radar observations and three-dimensional modeling indicate that NEAs with equatorial ridges are relatively common. In more detail, the delay-Doppler signature of objects with oblate vs. spheroidal shapes are discussed by Busch et al. (2011) and applied to 2008 EV5. In addition to the appearance of shape models, direct evidence for oblate shapes comes from images of 2013 WT44, which was observed at a subradar latitude close to a pole.

Fig. 8. Model renderings of four NEAs with evidence for oblate shapes. Each model is viewed along the + and – y-axes.

Figure  9 compares the radar images of 2013  WT44 with a high-latitude view of the 1999 KW4 model (Ostro et al., 2006) to illustrate the appearance of the equatorial ridge from a nearly pole-on perspective. The 2013 WT44 images show a flat polar region, a roughly cone-shaped hemisphere, and a “doubly curved” trailing edge region that shows the entire circumference of an equatorial ridge tilted relative to the radar line-of-sight. 3.5.5. Radar evidence for impact craters. Features suggesting impact craters have been seen on numerous NEAs imaged by radar starting with (4179) Toutatis in 1992 (Ostro et al., 1995; see also Hudson et al., 2003). The candidate craters generally take the form of circular to ellipsoidal radar-dark features from tens of meters to more than 2 km in extent. Interpretation of radar-dark features is hampered by the counterintuitive nature of delay-Doppler images, the resolution, SNRs, and rotational coverage of the data. Deep concavities are visible along the leading edges of other objects, but do not appear as radar-dark regions. Concavities are also evident in some shape models and may represent craters but their origins are not clear. Candidate craters appear in radar images of many objects such as (4183) Cuno, (33342) 1998 WT24 (Busch et al., 2008), (53319) 1999 JM8 (Benner et al., 2002), and (185851) 2000 DP107 (Naidu et al., 2015). Table 1 lists NEAs imaged by radar that show evidence for impact craters. Figure 10 shows Arecibo images of (136849) 1998 CS1, which has a number of radar-dark features suggesting impact craters, and Fig. 2 shows images of 2005 YU55, which has several small ellipsoidal radar-dark regions and a small concavity on its leading edge. Craters are conspicuously absent in radar images of many other NEAs, perhaps because such features are not present, due to limited viewing geometry, or perhaps because the SNRs and resolution are insufficient.

Fig. 9. Comparison between observations of binary NEA 2013 WT44 and a synthetic radar image of binary 1999 KW4 viewed at a high subradar latitude. Left: Goldstone delayDoppler image of 2013 WT44 obtained on March 20, 2014. Resolution = 18.75 m × 0.5 Hz. Right: Plane-of-sky renderings of the 1999 KW4 shape models viewed from a subradar latitude of 80°. Middle: Synthetic radar image of 1999 KW4 generated using the geometry of the models shown on the right. In the synthetic image, upper and lower arrows point to echoes from the near and far edges of the equatorial bulge.

Benner et al.:  Radar Observations of Near-Earth and Main-Belt Asteroids   175

TABLE 1. NEAs with radar-detected craters. Asteroid

H

(1580) Betulia 14.5 (4179) Toutatis 15.3 14.4 (4183) Cuno (33342) 1998 WT24 17.9 (52760) 1998 ML14 17.5 (53319) 1999 JM8 15.2 (136849) 1998 CS1 17.6 (185851) 2000 DP107 18.2 (304330) 2006 SX217 18.9 (308635) 2005 YU55 21.9 (388188) 2006 DP14 18.9 2010 JL33 17.7

3.5.6. Radar evidence for boulders on near-Earth asteroid surfaces. Delay-Doppler radar observations of numerous NEAs have revealed many small clusters of radarbright pixels in some of the highest SNR images obtained at Arecibo and Goldstone. Many of the spots persist as the asteroids rotate, so the bright pixels are not receiver noise, self noise, or artifacts. Clusters of bright pixels appear primarily in high-resolution radar images with resolutions of 4–19 m/pixel and suggest that these are features a few tens of meters in extent or smaller. Many spots appear near the trailing edges of the images and are uprange from radar shadows, implying that the source for some of the features is small-scale topography. Figures 2 and 3 show images of 2005 YU55 and 2014 HQ124, NEAs that have conspicuous and widespread radar-bright spots. To date, small groups of bright pixels have been seen on at least 14 NEAs, establishing that these features are relatively common. Benner et al. (2014a) suggest that the bright pixels are echoes from surface and near-surface boulders, which have also been seen on each of the three NEAs imaged at close range by spacecraft: (433) Eros [Near Earth Asteroid Rendezvous (NEAR)], (25143) Itokawa (Hayabusa), and (4179) Toutatis (Chang’e-2). These asteroids have also been imaged by radar, but the SNRs and/or resolutions were insufficient to reveal boulders with Eros and Itokawa. However,

radar images of Toutatis obtained in 2012 reveal spots that can be linked with boulders in the Chang’e-2 spacecraft images. Of the objects with evidence for boulders, 1999 RD32 is the largest, with a long axis of ~6 km, and 2014 BR57 is the smallest, with a diameter of about 80 m. 3.5.7. Circular polarization ratio correlations with spectral class. Benner et al. (2008) conducted a survey of more than 200 NEAs detected by radar and found distinct correlations between their circular polarization ratios (abbreviated as “SC/OC”) and some spectral classes. E- and V-class NEAs have high SC/OC values, a trend that is mirrored among the handful of E-class MBAs that have also been detected to date by radar (Shepard et al., 2008b, 2011). In contrast, SQ-class and optically dark NEAs show circular polarization ratios that vary from ~0.1 to ~0.5 but otherwise show no obvious trends. Fifty-six percent of the NEAs in which SC/OC > 0.5 in the sample have unknown spectral classes, and if all of them turn out to be E- or V-class objects, that implies that EV-class NEAs are much more abundant in the near-Earth population than has been previously realized. Since the study by Benner et al. (2008) was published, the sample of NEAs observed by radar has more than doubled and the pattern of high SC/OC values among E- and V-class objects has persisted (Springmann et al., 2013). How are we to understand these correlations? Benner et al. (2008) speculated that this could possibly “be due to the intrinsic mechanical properties of different mineralogical assemblages but also may reflect very different formation ages and collisional histories.” The fact that the trend of high SC/OC appears to remain across a wide range of diameters, including inner MBAs up to several tens of kilometers in diameter, suggests that there is at least a component due to composition. Virkki et al. (2014) modeled the effects of electric permittivity and the size of surface structure on asteroid radar circular polarization ratios and radar albedos. They find that obtaining SC/OC > 1 at 3.5 and 13 cm wavelengths requires a high refractive index (n > 2), which may explain the high polarization ratios observed among basaltic V-class objects because basalt has a relatively high refractive index. In general, SC/OC > 0.5 occurs from surfaces with scatterers from one to a few times larger than the radar wavelength, although this is also a function of the refractive index and thus composition. Fundamentally, though, asteroid surfaces with high SC/OC are still not well understood. 4. RESULTS FOR SELECTED ASTEROIDS 4.1. (101955) Bennu

Fig. 10. Arecibo images of (136849) 1998 CS1 obtained on January 18, 2009. Resolution is 7.5 m × 0.09 Hz. Rotation is counterclockwise.

Nolan et al. (2013) estimated the shape of Bennu based on Arecibo and Goldstone imaging in 1999 and 2005 (Fig.  11). Bennu is an optically dark spheroid with major axes of 565 × 535 × 508 m, a sidereal rotation period of 4.3 h, a modest equatorial ridge, evidence for a relatively large boulder in the southern hemisphere, and broad-scale near-surface roughness features.

176   Asteroids IV

Fig. 11. Renderings of the three-dimensional model of (101955) Bennu (adapted from Nolan et al., 2013) viewed along the x- and y-axes.

Bennu is the target of the OSIRIS-REx mission, which will provide a stringent test for the shape-modeling process when the spacecraft arrives in October 2018. Chesley et al. (2014) report detection of the Yarkovsky effect for Bennu through radar astrometry obtained in 1999, 2005, and 2011 and optical astrometry from 1999 to 2013. This yields estimates of the mass and bulk density that are invaluable for planning the OSIRIS-REx mission. The density, r = 1.3 kg m–3, implies a macroporosity of ~40% and suggests a rubble-pile internal structure. Bennu has one of the highest impact probabilities known, and, due to frequent close Earth encounters, will probably require orbital monitoring indefinitely (Milani et al., 2009). 4.2. (4660) Nereus Nereus had been identified as a potential spacecraft target since its discovery because of the low DV required for a rendezvous. Nereus was an early target for the NEAR mission and the original target for the Hayabusa mission. Arecibo and Goldstone images of Nereus obtained in 2002 enabled Brozovic et al. (2009) to reconstruct a three-dimensional model, which resembles an ellipsoid with principal axis dimensions X = 510 ± 20 m, Y = 330 ± 20 m, and Z = 241+−80 10 m, and features two prominent facets. 4.3. (214869) 2007 PA8 Goldstone imaged 2007 PA8 on 16 days in 2012. The images achieved range resolutions as fine as 3.75 m, placed thousands of pixels on the asteroid, and revealed an elongated, asymmetric object (Fig. 12) (Brozovic et al., in preparation). The surface has angularities, facets, and a concavity >200 m in diameter. Shape modeling yields an effective diameter of 1.35 ± 0.05 km, and elongation (long/intermediate axis ratio) = 1.4. The modeling revealed that 2007 PA8 is a nonprincipal-axis rotator in short-axis mode with an average period of precession by the long axis around the angular momentum vector of 4.26 ± 0.02 d and an oscillatory period

Fig. 12. Images of (214869) 2007 PA8 obtained at Goldstone during October–November 2012. Range resolutions are 18.75 m on October 31 and November 11–13; 7.5 m on November 2, 3, and 8; and 3.75 m on November 5 and 6. The highest resolutions were obtained on dates when the asteroid was closest to Earth and the signal-to-noise ratios were strongest. Each panel has the same delay-Doppler dimensions.

around the long axis of 20.55 ± 3.75 d. The amplitude of rolling around the long axis is 42 ± 7°. 2007 PA8 is the second confirmed short-axis mode non-principal-axis rotator found in the NEA population, after Apophis (Pravec et al., 2014). 4.4. (162421) 2000 ET70 Arecibo images of 2000 ET70 place thousands of pixels on the object (Fig.  13) (Naidu et al., 2013). The threedimensional physical model has dimensions of 2.6 × 2.2 × 2.1 km, a retrograde spin state with a 9-h period, and an unusually low optical albedo of ~2%. The northern hemisphere has dramatic ridges oriented approximately perpendicular to the long axis, but the southern hemisphere is much more rounded, a global shape dichotomy that is uncommon among NEAs imaged by radar to date. 4.5. (308635) 2005 YU55 2005 YU55 approached within 0.0022 AU (0.85 lunar distances) in November 2011, the closest approach of a known asteroid >300 m in diameter since 1982 (2012 TY52) and until 2028 (2001 WN5). This provided an extraordinary opportunity for radar imaging, and extensive observations were obtained at Goldstone, Arecibo, the Green Bank Telescope, and elements of the VLBA over two weeks (Busch et al., 2012). The SNRs were among the highest ever obtained for any NEA and resulted in radar images with resolutions as fine as 3.75 m in range (Fig. 2). The images reveal a rounded object whose surface has many small radar-bright spots, suggesting numerous boulders, and radar-dark regions that may be impact craters. Modeling indicates that the shape

Benner et al.:  Radar Observations of Near-Earth and Main-Belt Asteroids   177

the target for the proposed European Space Agency’s Marco Polo-R mission and is a leading candidate for NASA’s proposed Asteroid Redirect Mission. 4.8. (33342) 1998 WT24 1998 WT 24 approached within five lunar distances (0.0125 AU) in December 2001, when it was the strongest asteroid radar target ever observed up to that point. This asteroid was observed extensively at Goldstone and Arecibo and yielded a detailed three-dimensional model (Busch et al., 2008). The images show a rounded object with a conspicuous radar-bright spot several pixels in extent that persists over multiple rotations. The asteroid has a diameter of 415 ± 40 m and the shape is dominated by three large basins that may be impact craters. 4.9. (29075) 1950 DA Fig. 13. Selected Arecibo images, fits, and plane-of-sky views of the 2000 ET70 shape model (Naidu et al., 2013).

is close to spheroidal with maximum dimensions of 360 ± 40 m in all directions. The shape has a ridge roughly parallel to the equator that resembles ridges seen on other rapidly rotating spheroidal NEAs imaged by radar, but unlike those other objects, 2005 YU55 is a relatively slow rotator with a period of ~19 h. 4.6. 2014 HQ124 Bistatic Goldstone-Arecibo X-band images of 2014 HQ124 achieve a resolution of 3.75  m × 0.00625  Hz (Fig.  3) and provide some of the most detailed radar views obtained for any near-Earth object (Benner et al., 2014b). 2014 HQ124 is a slowly rotating object that is elongated, bifurcated, and angular with a long axis of at least 400 m. The larger lobe has a narrow, sinuous, ~100-m-long radar-dark feature that may be a scarp or perhaps a fault. These observations were the first test of new data-taking equipment at Arecibo that can acquire images at 3.75 m resolution using transmissions from Goldstone. Radar astrometry increased the interval of reliable Earth encounter predictability by a factor of 2 to ~900 years. 4.7. (341843) 2008 EV5 Busch et al. (2011) observed 2008 EV5 with Arecibo, Goldstone, and the VLBA during the asteroid’s passage within 0.022 AU in December 2008. Radar speckle tracking indicates retrograde rotation; this is the first NEA where that technique was used successfully. The object has a diameter of 400 ± 50 m, a prominent ridge parallel to its equator, and a concavity about 150 m in diameter (Fig. 8). The concavity may be an impact crater; if so, then its ejecta may have produced some of the numerous boulders that are suggested by radar bright spots near the south pole. This object was

1950 DA is a type case highlighting the importance of radar astrometry and shape modeling for predicting asteroid trajectories and the interaction between orbits, shapes, and spin states due to the Yarkovsky effect. 1950 DA was discovered in 1950, lost until 2000, and then observed extensively at Arecibo and Goldstone during a close approach in March 2001. Radar astrometry indicated that 1950 DA will approach Earth in 2880, and the outcome of this approach depends on the magnitude and direction of the Yarkovsky acceleration. Due to the uncertainties in unmeasured physical parameters, Giorgini et al. (2002) included uncertainties in the Earth impact probability by expressing it as an interval, concluding that “the maximum probability of impact is best expressed as being between 0 and 0.33%.” Shape modeling by Busch et al. (2007) generated two pole solutions and two corresponding shapes: one that is roughly spheroidal and ~1.2 km in diameter, and a second that is oblate, ~1.2 km from pole to pole, and ~1.6 km across at the equator (Busch et al., 2007). The data were insufficient to determine if 1950 DA spins prograde or retrograde, producing an ambiguity in the asteroid’s future trajectory and thus in the impact probability. Farnocchia and Chesley (2014) utilized additional optical astrometry, and remeasured radar astrometry from 2001 and new radar ranging from Arecibo in 2012 to further improve the orbit. The main source of uncertainty remains the Yarkovsky effect, which was detected at the ~5s level. Utilizing a statistical model of the Yarkovsky effect, they found that, due to the sign of the orbital drift, prograde rotation is ruled out. This appears to be the first time that a pole direction ambiguity has been resolved by detection of the Yarkovsky effect, which was predicted by Busch et al. (2007). Rozitis et al. (2014) adopted the retrograde shape model from Busch et al. (2007) and used thermal modeling of Wide-field Infrared Survey Explorer (WISE) spacecraft data to estimate 1950 DA’s thermal inertia and bulk density. They state that the asteroid’s rapid spin (2.1 h) implies a need

178   Asteroids IV for cohesive forces to prevent rotational breakup. Rozitis et al.’s (2014) work hinges on the 5s Yarkovsky effect detection reported by Farnocchia and Chesley (2014) and on the retrograde shape model without regard to the uncertainties in that model. However, more recently, Hirabayashi and Scheeres (2015) find that cohesion is necessary over a much wider range of densities, indicating that a change in density estimate will not substantively impact the main conclusions of Rozitis et al. (2014) (see the chapter by Scheeres et al. in this volume). Future radar and optical astrometry can refine estimates of 1950 DA’s Yarkovsky effect drift, improve estimates of the asteroid’s future trajectory, and improve estimates of its bulk density and constraints on its internal structure. The next opportunity for radar observations of 1950 DA is in 2032, when an extensive imaging campaign at Arecibo and Goldstone could provide higher-resolution images than were obtained in 2001. 4.10. (1580) Betulia

objects on the NASA Near-Earth Object Human Spaceflight Accessible Targets Study list (NHATS) (http://neo.jpl.nasa. gov/nhats/) are observed with radar as possible even if the SNRs are very weak. Due to development of the 3.75-m resolution imaging system at Goldstone, it has become possible to obtain delay-Doppler images that can spatially resolve NEAs as small as ~30 m in diameter. This opens up a new capability to investigate the physical properties of a much smaller subset of the NEA population than was previously possible. The first object imaged at 4-m resolution was 2010 AL30 (Slade et al., 2010). More recently, several NEAs such as (367943) Duende (2012 DA14), 2013 ET, and 2014 BR57 have been imaged, revealing a suite of irregular to spheroidal shapes (Fig. 14). Ranging astrometry from tiny NEAs can yield orbits with sufficient precision to detect nongravitational perturbations from solar radiation pressure. If detected, this perturbation yields an estimate of the area/mass ratio. To date, solar radiation pressure perturbations have been detected in the

Magri et al. (2007b) modeled the shape and spin state of Betulia using Arecibo data obtained in 2002 and light curves obtained in 1976 and 1989. They obtain a model that resembles the Kaasalainen et al. (2004) convex-definite shape reconstructed from light curves but is dominated by a prominent concavity in the southern hemisphere. Betulia has an effective diameter of 5.39 ± 0.54 km and a shape that is roughly triangular when viewed along its polar axis. 4.11. (100085) 1992 UY4 Goldstone and Arecibo radar images of 1992 UY4 obtained in 2005 reveal a lumpy, modestly asymmetric, 2-km-diameter object. The surface is characterized by gently undulating topography with many modest concavities. Numerous finescale, radar-bright features are evident at the trailing edges and limbs; one of the most prominent has a visible extent of about 100 m and juts out abruptly from the approaching limb, suggesting a large block similar to the boulder Yoshinodai seen on (25143) Itokawa by the Hayabusa spacecraft (Saito et al., 2006). 4.12. Tiny Near-Earth Asteroids Near-Earth asteroids with diameters 22) comprise approximately one-fourth of all NEAs observed with radar. The fraction of such objects observed by radar has increased ~50% since publication of Asteroids III because more of these objects are being discovered with sufficient advance notice to schedule radar observations, due to greater access to telescope time, and due to more rapid response protocols. Several have been observed within one lunar distance, and one, 2006 RH120, was a temporarily captured satellite of Earth. A further motivation has been acute interest since 2011 in tiny NEAs that could be targets for human missions. To that end, as many

Fig. 14. Goldstone images of two NEAs that are less than 100 m in diameter. Top: (367943) Duende (2012 DA14) imaged on February 16, 2013. Duende has major axes of ~40 × 20 m, an angular shape, and is a non-principal-axis rotator (Moskovitz et al., 2013). Bottom: 2013 ET images from March 10, 2013. 2013 ET appears structurally complex, has a long axis of at least 40 m, and has alternating radardark and radar-bright regions. In each collage, the range resolution is 3.75 m, but the data were double sampled, so each row corresponds to 1.875 m.

Benner et al.:  Radar Observations of Near-Earth and Main-Belt Asteroids   179

motion of one NEA observed by radar: 2006 RH120 in 2007 (P. W. Chodas, personal communication). 5. THE FUTURE The future for asteroid radar observations is potentially very bright if capabilities at least equal to those currently available at Arecibo and Goldstone are maintained. As the number of NEAs discovered has grown rapidly in the last decade, so too have the number of short-term targets of opportunity and targets known well in advance. This trend will only continue as existing surveys upgrade and as new surveys begin. The Large Synoptic Survey Telescope (LSST) could yield vastly more NEA discoveries when it begins routine operations in the 2020s, and with it could come a dramatic increase in radar targets. Due to its sensitivity, it seems likely that many NEAs larger than a few tens of meters in diameter found by LSST will be discovered months or even years before they will be detectable by radar. The number of NEAs observed annually with radar is a fraction of what could be done if a dedicated radar facility were available. Schedules and equipment problems continue to be obstacles for observing on short notice but are less cumbersome than only a few years ago. The net effect is that roughly one-third of NEAs that are potentially detectable with radar are actually being observed. Arecibo could observe many more asteroids if additional telescope time and funding were available. The observatory is already operating the S-band radar at close to the legal limit imposed by local air pollution laws, and a significant increase would require new, lower-emission generators. Due to its extraordinary sensitivity, though, the most effective way to increase the number of NEA radar detections is to augment the number of observations at Arecibo. Demand at Goldstone for spacecraft communications is expected to diminish over the next several years as existing spacecraft cease operations and as future spacecraft switch to NASA’s 34-m antennas for tracking. This could provide an opportunity to observe significantly more asteroids. Although most requests at Goldstone to observe NEAs known well in advance are scheduled, obtaining time on short notice remains challenging because schedules for flight projects are arranged many weeks in advance, and changing schedules on short notice has effects that ripple through the DSN. 5.1. Other Radar Facilities Are there other existing radar facilities that could be utilized to observe NEAs? The 70-m Evpatoria antenna in Crimea has conducted bistatic NEA radar observations utilizing radio telescopes at Effelsberg (Germany), Medicina (Italy), and Irbene (Latvia) as receivers. Evpatoria has also acted as a receiver for Goldstone X-band transmissions of (6489) Golevka (Zaitsev et al., 1997), 1998 WT24 (Di Martino et al., 2004), and 2004 XP14 and could be used for monostatic observations of very close targets if the system

were modernized (B. Shustov, personal communication). Installation of a high-power planetary radar was considered for the new 64-m Sardinia Radio Telescope (Saba et al., 2005) but was not implemented due to the cost. In February 2013, J. Vierinen (personal communication) detected radar echoes from (367943) Duende with the European Incoherent Scatter Scientific Association (EISCAT) facility near Tromso, Norway; this was the first time EISCAT was used for asteroid observations. Nechaeva et al. (2013) observed Duende by using Evpatoria to transmit and Irbene and Medicina to receive. The 37-m X-band and 46-m ultrahigh-frequency (UHF) antennas at Haystack Observatory also detected Duende (P. Erickson and M. Hecht, personal communication). Radar observations of Duende were scheduled at the 35-m Tracking and Imaging Radar (TIRA) facility in Germany, but those observations were canceled due to logistical problems (D. Koschny, personal communication). Although orders of magnitude less sensitive than Goldstone, these facilities could detect a modest number of near-Earth objects annually during very close flybys. 5.2. Future Radar Capabilities A new radar facility began operations in January 2015 on the 34-m DSS-13 antenna at the Goldstone Deep Space Communications Complex. DSS-13 is an experimental test bed that has been equipped with an 80-kW klystron that transmits at C-band (7190 MHz, 4.2 cm). The klystron has a bandwidth of 80 MHz and can achieve a range resolution of up to 1.875 m/pixel, which is twice as fine as the highest resolution at the 70-m DSS-14 Goldstone antenna and four times finer than at Arecibo. DSS-13 is not equipped to receive its own radar echoes, so reception must occur at another facility such as Green Bank, Arecibo, or the 34-m DSS-28 antenna at Goldstone. Bistatic DSS-13/Arecibo and DSS-13/Green Bank observations are significantly less sensitive than observations at DSS-14, but for very strong targets such as 2005 YU55, (367943) Duende, and 2014 HQ124, where the SNR is not a limiting factor, DSS-13 would have been ideal. The new radar at DSS-13 is in its commissioning phase and routine operations are planned by the end of 2015. The 70-m DSS-43 antenna at the Canberra Deep Space Communication Complex in Australia and the 64-m Parkes Radio Telescope could in principle be configured as a bistatic radar system using an existing S-band transmitter on DSS-43 that can radiate 400 kW. This bistatic system might achieve SNRs perhaps ~4% as strong as those at Goldstone and could enable radar observations of very close NEAs at southern declinations that are inaccessible to Goldstone and Arecibo. Proof-of concept tests are planned in late 2015. Farther into the future, one of the 34-m DSN antennas at Canberra could be equipped with an 80-kW, 80-MHz klystron and transmitter identical to the system at DSS-13 (Davarian, 2011). Another concept in the early stages of development is the Ka-Band Objects Observations and Monitoring (KaBOOM) phased-array radar test bed at the Kennedy Space Center (http://www.nasa.gov/directorates/heo/scan/engineering/

180   Asteroids IV technology/KaBOOM.html). KaBOOM is a three-element array with antennas 12 m in diameter. The effective radiated power of an array of transmitters is proportional to N2, where N is the number of array elements (Davarian, 2011), so in principle it is possible use a large number of small antennas radiating low power (~5 kW) to achieve much higher sensitivity than with a single, large dish. The engineering challenges are formidable and it is not yet known if this technique is feasible. 5.3. Greater Automation Observing NEAs with radar remains a labor-intensive process that requires at least three people at the observatory to operate the telescope and transmitter, adjust cables, take data, make key decisions, and update ephemerides. At Arecibo it is still necessary to switch cables and adjust voltage gains when changing setups, a process that in principle could be automated with one electronics box. In the future, one can envision a situation with a nightly queue where the telescope automatically moves from target to target, where software automatically processes the data to determine when a detection has occurred, estimates and reports range-Doppler corrections to the ephemerides, and then slews to the next target. Imaging of high-SNR targets would require more direct human control to maximize the scientific return, but weaker targets could be observed in the automated manner described above. 5.4. Shape Modeling The shape models discussed above demonstrate a clear need for improvements to the shape-modeling procedure. A better estimation algorithm that can fit topographically rugged objects is particularly desirable because features are often visible in radar images that the fits do not adequately reproduce. It would be helpful if a straightforward method of manually adjusting specific vertices on a model were possible in order to fit fine-scale features. Coupled estimation of the shapes and orbits of binaries would also be helpful. Although increasing computer speed is useful, the limiting factor for estimating three-dimensional models is actually the ability of the user to assess the fits. Experience has shown that the human eye is more reliable than the c2 statistic for assessing the quality of fits, but this requires time-consuming visual inspection of many images. Another impediment for augmenting the number of asteroid shape models is the paucity of NEA pole directions. Knowledge of the pole direction dramatically shrinks the time to estimate three-dimensional shapes. Otherwise, pole estimation requires a lengthy grid search may that not yield a unique solution. Radar speckle observations can provide pole directions for the subset of targets with very strong SNRs, and increasing the number of days of radar observations to extend sky motion can help, but the biggest contribution will probably come from obtaining more light curves. Light curves can often provide pole directions when

radar observations cannot, but obtaining light curves can be a major logistical challenge and they are often not available for many NEAs observed by radar. 6. SUMMARY The number of NEAs being observed annually with radar is approaching 100, but that is still only a fraction of the number that could be observed if telescope time, funding, personnel, equipment problems, and the ability to respond to targets of opportunity very rapidly were not issues. Asteroid radar astronomy has made dramatic strides forward since publication of Asteroids III; the field is growing, and it has considerable scientific potential. New discoveries occur frequently, imaging resolutions are approaching the realm of planetary geology, and radar observations have become important in ways that were never imagined only a decade ago. Acknowledgments. We thank D. J. Scheeres and an anonymous reviewer for comments that improved this manuscript. Part of this work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). This material is based in part upon work supported by NASA under the Science Mission Directorate Research and Analysis Programs.

REFERENCES Benner L. A. M. and 10 colleagues (2002) Radar observations of asteroid 1999 JM8. Meteoritics & Planet. Sci., 37, 779–792. Benner L. A. M. and 5 colleagues (2006) Near-Earth asteroid 2005 CR37: Radar images of a candidate contact binary. Icarus, 182, 474–481. Benner L. A. M. and 10 colleagues (2008) Near-Earth asteroid surface roughness depends on compositional class. Icarus, 198, 294–304. Benner L. and 11 colleagues (2014a) Arecibo and Goldstone radar evidence for boulders on near-Earth asteroids. In Asteroids, Comets, Meteors 2014 Book of Abstracts (K. Muinonen et al., eds.), p. 59. Univ. of Helsinki, Finland. Benner L. A. M. and 16 colleagues (2014b) Goldstone and Arecibo radar images of near-Earth asteroid 2014 HQ124. Bull. Am. Astron. Soc., 46, #49.01. Bottke W. F. and 3 colleagues (2002) The effect of Yarkovsky thermal forces on the dynamical evolution of asteroids and meteoroids. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 395–408. Univ. of Arizona, Tucson. Bottke W. F.and 3 colleagues (2006) The Yarkovsky and YORP effects: Implications for asteroid dynamics. Annu. Rev. Earth Planet. Sci., 34, 157–191. Brozovic M. and 10 colleagues (2009) Radar observations and a physical model of asteroid 4660 Nereus, a prime space mission target. Icarus, 201, 153–166. Brozovic M. and 9 colleagues (2010) Radar observations and a physical model of contact binary asteroid 4486 Mithra. Icarus, 208, 207–220. Brozovic M. and 21 colleagues (2011) Radar observations and physical modeling of triple near-Earth asteroid (136617) 1994 CC. Icarus, 216, 241–256. Busch M. W. and 14 colleagues (2007) Physical modeling of near-Earth asteroid (29075) 1950 DA. Icarus, 190, 608–621. Busch M. W. and 9 colleagues (2008) Physical properties of near-Earth asteroid (33342) 1998 WT24. Icarus, 195, 614–621. Busch M. W. and 6 colleagues (2010) Determining asteroid spin states using radar speckles. Icarus, 209, 535–541. Busch M. W. and 12 colleagues (2011) Radar observations and the shape of near-Earth asteroid 2008 EV5. Icarus, 212, 649–660.

Benner et al.:  Radar Observations of Near-Earth and Main-Belt Asteroids   181 Busch M. W. and 16 colleagues (2012) Shape and spin of near-Earth asteroid 308635 (2005 YU55) from radar images and speckle tracking. Asteroids, Comets, Meteors 2012, Abstract #6179. Lunar and Planetary Institute, Houston. Capek D. and Vokrouhlicky D. (2004) The YORP effect with finite thermal conductivity. Icarus, 172, 526–536. Chesley S. R. and 9 colleagues (2003) Direct detection of the Yarkovsky effect via radar ranging to asteroid 6489 Golevka. Science, 302, 1739–1742. Chesley S. R. and 15 colleagues (2014) Orbit and bulk density of the OSIRIS-REx target asteroid (101955) Bennu. Icarus, 235, 5–22. Davarian F. (2011) Uplink arraying for solar system radar and radio science. Proc. IEEE, 99, 783–793. Descamps P. and 18 colleagues (2011) Triplicity and physical characteristics of asteroid (216) Kleopatra. Icarus, 211, 1022–1033. Di Martino M. and 13 colleagues (2004) Results of the first Italian planetary radar experiment. Planet. Space Sci., 52, 325–330. Durech J. and 11 colleagues (2008) Detection of the YORP effect in the asteroid (1620) Geographos. Astron. Astrophys., 489, L25–L28. Emery J. P. and 8 colleagues (2014) Thermal infrared observations and thermophysical characterization of OSIRIS-REx target asteroid (101955) Bennu. Icarus, 234, 17–35. Farnocchia D. and Chesley S. R. (2014) Assessment of the 2880 impact threat from asteroid (29075) 1950 DA. Icarus, 229, 321–327. Farnocchia D. and 5 colleagues (2013a) Near Earth asteroids with measureable Yarkovsky effect. Icarus, 224, 1–13. Farnocchia D. and 7 colleagues (2013b) Yarkovsky-driven impact risk analysis for asteroid (99942) Apophis. Icarus, 224, 192–200. Gaskell R. and 8 colleagues (2008) Gaskell Itokawa Shape Model V1.0. HAY-A-AMICA-5-ITOKAWASHAPE-V1.0, NASA Planetary Data System. Giorgini J. D. and 13 colleagues (2002) Asteroid 1950 DA’s encounter with Earth: Physical limits of collision probability prediction. Science, 296, 132–136. Giorgini J. D. and 4 colleagues (2008) Predicting the Earth encounters of (99942) Apophis. Icarus, 193, 1–19. Harris A. W., Fahnestock E. G., and Pravec P (2009) On the shapes and spins of rubble pile asteroids. Icarus, 199, 310–318. Hirabayashi M. and Scheeres D. (2015) Stress and failure analysis of rapidly rotating asteroid (29075) 1950 DA. Astrophys. J. Lett., in press. Huang J. and 27 colleagues (2013) The ginger-shaped asteroid 4179 Toutatis: New observations from a successful flyby of Chang’e-2. Nature Sci. Rept., 3, 3411. Hudson S. (1993) Three-dimensional reconstruction of asteroids from radar observations. Remote Sensing Rev., 8, 195–203. Hudson R. S. and Ostro S. J. (1994) Shape of asteroid 4769 Castalia (1989 PB) from inversion of radar images. Science, 263, 940–943. Hudson R. S. and Ostro S. J. (1995) Shape and non-principal axis spin state of asteroid 4179 Toutatis. Science, 270, 84–86. Hudson R. S. and 26 colleagues (2000) Radar observations and physical model of asteroid 6489 Golevka. Icarus, 148, 37–51. Hudson R. S., Ostro S. J., and Scheeres D. J. (2003) High-resolution model of asteroid 4179 Toutatis. Icarus, 161, 346–355. Kaasalainen M. and 21 colleagues (2004) Photometry and models of eight near-Earth asteroids. Icarus, 167, 178–196. Kaasalainen M. and 4 colleagues (2007) Acceleration of the rotation of asteroid 1862 Apollo by radiation torques. Nature, 446, 420–422. Lowry S. C. and 10 colleagues (2007) Direct detection of the asteroidal YORP effect. Science, 316, 272–274. Magri C. and 9 colleagues (1999) Mainbelt asteroids: Results of Arecibo and Goldstone radar observations of 37 objects during 1980–1995. Icarus, 140, 379–407. Magri C. and 3 colleagues (2007a) A radar survey of main-belt asteroids: Arecibo observations of 55 objects during 1999–2003. Icarus, 186, 126–151. Magri C. and 6 colleagues (2007b) Radar observations and a physical model of asteroid 1580 Betulia. Icarus, 186, 152–177. Magri C. and 25 colleagues (2011) Radar and photometric observations and shape modeling of contact binary near-Earth asteroid (8567) 1996 HW1. Icarus, 214, 210–227. Margot J. L. and 7 colleagues (2002) Binary asteroids in the near-Earth object population. Science, 296, 1445–1448. Margot J. L. and 4 colleagues (2007) Large longitude libration of Mercury reveals a molten core. Science, 316, 710–714. Margot J. L. and 9 colleagues (2012) Mercury’s moment of inertia from spin and gravity data. J. Geophys. Res., 117, E00L09.

Milani A. and 5 colleagues (2009) Long term impact risk for (101955) 1999 RQ36. Icarus, 203, 460–471. Moskovitz N. and 19 colleagues (2013) The near-Earth asteroid 2012 DA14. Bull. Am. Astron. Soc., 45, #101.03. Naidu S. P. and Margot J. L. (2015) Near-Earth asteroid satellite spins under spin-orbit coupling. Astron. J., 149, 80. Naidu S. P. and 9 colleagues (2013) Radar imaging and physical characterization of near-Earth asteroid (162421) 2000 ET70. Icarus, 226, 323–335. Naidu S. P. and 9 colleagues (2015) Radar imaging and characterization of binary near-Earth asteroid (185851) 2000 DP107. Astron. J., 150, 54. Nechaeva M. and 19 colleagues (2013) First results of the VLBI experiment on radar location of the asteroid 2012 DA14. Baltic Astron., 22, 341–346. Nolan M. C. and 10 colleagues (2013) Shape model and surface properties of the OSIRIS-REx target asteroid (101955) 1999 RQ36 from radar and lightcurve observations. Icarus, 226, 629–640. Nugent C. R. and 3 colleagues (2012) Detection of semi-major axis drifts in 54 near-Earth asteroids: New measurements of the Yarkovsky effect. Astron. J., 144, 60–72. Ostro S. J. (1993) Planetary radar astronomy. Rev. Mod. Phys., 65, 1235–1279. Ostro S. J. and Giorgini J. D. (2004) The role of radar in predicting and preventing asteroid and comet collisions with Earth. In Mitigation of Hazardous Comets and Asteroids (M. J. S. Belton et al., eds.), pp. 38–65. Cambridge Univ., Cambridge. Ostro S. J. and 13 colleagues (1995) Radar images of asteroid 4179 Toutatis. Science, 270, 80–84. Ostro S. J. and 8 colleagues (2000) Radar observations of asteroid 216 Kleopatra. Science, 288, 836–839. Ostro S. J. and 6 colleagues (2002) Asteroid radar astronomy. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 151–168. Univ. of Arizona, Tucson. Ostro S. J. and 15 colleagues (2004) Radar observations of asteroid 25143 Itokawa (1998 SF36) Meteoritics & Planet. Sci., 39, 407–424. Ostro S. J. and 12 colleagues (2005) Radar observations of Itokawa in 2004 and improved shape estimation. Meteoritics & Planet. Sci., 40, 1563–1574. Ostro S. J. and 15 colleagues (2006) Radar imaging of binary near-Earth asteroid (66391) 1999 KW4. Science, 314, 1276–1280. Ostro S. J. and 7 colleagues (2010) Radar imaging of asteroid 7 Iris. Icarus, 207, 285–294. Pravec P. and 58 colleagues (2006) Photometric survey of binary nearEarth asteroids. Icarus, 181, 63–93. Pravec P. and 19 colleagues (2014) The tumbling spin state of (99942) Apophis. Icarus, 233, 48–60. Rivkin A. S. and 4 colleagues (2000) The nature of M-class asteroids from 3 µm observations. Icarus, 145, 351–368. Rozitis B. and 3 colleagues (2013) A thermophysical analysis of the (1862) Apollo Yarkovsky and YORP effects. Astron. Astrophys., 555, A20. Rozitis B., MacLennan E., and Emery J. P. (2014) Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA. Nature, 512, 174–176. Rubincam D. P. (2000) Radiative spin-up and spin-down of small asteroids. Icarus, 148, 2–11. Saba L. and 15 colleagues (2005) The Sardinia Radio Telescope as a radar for the study of near-Earth objects and space debris. Mem. Soc. Astron. Ital. Suppl., 6, 104–109. Saito J. and 33 colleagues (2006) Detailed images of asteroid 25143 Itokawa from Hayabusa. Science, 312, 1341–1344. Scheeres D. J. (2007) Rotational fission of contact binary asteroids. Icarus, 189, 370–385. Scheeres D. J. and 5 colleagues (2005) Abrupt alteration of asteroid 2004 MN4’s spin state during its 2029 Earth flyby. Icarus, 178, 281–283. Shepard M. K. and 18 colleagues (2008a) A radar survey of X- and M-class asteroids. Icarus, 195, 184–205. Shepard M. K. and 9 colleagues (2008b) Radar observations of E-class asteroids 44 Nysa and 434 Hungaria. Icarus, 195, 220–225. Shepard M. K. and 12 colleagues (2010) A radar survey of M- and X-class asteroids. II. Summary and synthesis. Icarus, 208, 221–237. Shepard M. K. and 9 colleagues (2011) Radar observations of asteroids 64 Angelina and 69 Hesperia. Icarus, 215, 547–551. Shepard M. K. and 15 colleagues (2015) A radar survey of M- and X-class asteroids. III. Insights into their compositions, hydration state, and structure. Icarus, 245, 38–55.

182   Asteroids IV Sierks H. and 57 colleages (2011) Images of asteroid 21 Lutetia: A remnant planetesimal from the early solar system. Science, 334, 487–490. Slade M. A. and 6 colleagues (2010) First results of the new Goldstone delay-Doppler radar chirp imaging system. Bull. Am. Astron. Soc., 42, 1080. Slade M. A., Benner L.A.M., and Silva A. (2011) Goldstone Solar System Radar Observatory: Earth-based planetary mission support and unique science results. Proc. IEEE, 99, 757–769. Springmann A. and 3 colleagues (2013) Are the radar scattering properties of near-Earth asteroids correlated with size, shape, or spin? Lunar Planet. Sci. XLIV, Abstract #2915. Lunar and Planetary Institute, Houston. Takahashi Y., Busch M. W., and Scheeres D. J. (2013) Spin state and moment of inertia characterization of 4179 Toutatis. Astron. J., 146, 95. Taylor P. A. (2009) Tidal interactions in binary asteroid systems. Ph.D. thesis, Cornell Univ., Ithaca. Taylor P. A. and 11 colleagues (2007) Increasing spin rate of asteroid 54509 (2000 PH5) a result of the YORP effect. Science, 316, 274–277. Taylor P. A. and 3 colleagues (2012) The shape and spin distributions of near-Earth asteroids observed with the Arecibo radar system. Bull. Am. Astron. Soc., 44, #302.07.

Virkki A., Muinonen K., and Penttila A. (2014) Inferring asteroid surface properties from radar albedos and circular polarization ratios. Meteoritics & Planet. Sci., 59, 86–94. Vokrouhlicky D., Milani A., and Chesley S. R. (2000) Yarkovsky effect on small near-Earth asteroids: Formulation and examples. Icarus, 148, 118–138. Vokrouhlicky D. and 3 colleagues (2005a) Yarkovsky effect opportunities. I. Solitary asteroids. Icarus, 173, 166–184. Vokrouhlicky D. and 3 colleagues (2005b) Yarkovsky effect opportunities. II. Binary systems. Icarus, 179, 128–138. Walsh K. J., Richardson D. C., and Michel P. (2008) Rotational breakup as the origin of small binary asteroids. Nature, 454, 188–191. Warner B. D., Harris A. W., and Pravec P. (2009) Asteroid lightcurve database. Icarus, 202, 134–146. Zaitsev A. and 24 colleagues (1997) Intercontinental bistatic radar observations of 6489 Golevka (1991 JX) Planet. Space Sci., 45, 771–778. Zou X. and 5 colleagues (2014) The preliminary analysis of the 4179 Toutatis snapshots of the Chang’e-2 flyby. Icarus, 229, 348–354.

Ďurech J., Carry B., Delbo M., Kaasalainen M., and Viikinkoski M. (2015) Asteroid models from multiple data sources. In Asteroids IV (P. Michel et al., eds.), pp. 183–202. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch010.

Asteroid Models from Multiple Data Sources Josef Ďurech

Charles University in Prague

Benoȋt Carry

Institut de Mécanique Céleste et de Calcul des Éphémérides

Marco Delbo

Lagrange Laboratory, Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS

Mikko Kaasalainen and Matti Viikinkoski Tampere University of Technology

In the past decade, hundreds of asteroid shape models have been derived using the lightcurve inversion method. At the same time, a new framework of three-dimensional shape modeling based on the combined analysis of widely different data sources — such as optical lightcurves, disk-resolved images, stellar occultation timings, mid-infrared thermal radiometry, optical interferometry, and radar delay-Doppler data — has been developed. This multi-data approach allows the determination of most of the physical and surface properties of asteroids in a single, coherent inversion, with spectacular results. We review the main results of asteroid lightcurve inversion and also recent advances in multi-data modeling. We show that models based on remote sensing data were confirmed by spacecraft encounters with asteroids, and we discuss how the multiplication of highly detailed three-dimensional models will help to refine our general knowledge of the asteroid population. The physical and surface properties of asteroids, i.e., their spin, three-dimensional shape, density, thermal inertia, and surface roughness, are among the least known of all asteroid properties. Apart from the albedo and diameter, we have access to the whole picture for only a few hundreds of asteroids. These quantities are nevertheless very important to understand, as they affect the nongravitational Yarkovsky effect responsible for meteorite delivery to Earth, as well as the bulk composition and internal structure of asteroids.

1. INTRODUCTION The determination of asteroid physical properties is an essential part of the complex process of revealing the nature of the asteroid population. In many cases, this process starts with obtaining observational data, continues with creating a model of the asteroid (i.e., its size, three-dimensional shape, and spin state, in the first approximation), and ends with interpreting new facts based on the model or a set of these. In this sense, modeling is a crucial mid-step between observations and theory. Results based on individual well-studied asteroids can be generalized to other members of the population. On the other hand, a statistically large sample of asteroids with known properties can reveal physical effects that play an important role for the whole population. In this chapter, we will build on the content of the Asteroids III chapter by Kaasalainen et al. (2002a) about asteroid models reconstructed from disk-integrated photometry. Although visual photometry still remains the most important data source of the modeling, the main progress in this field

since Asteroids III has been the addition of complementary data sources. Many of these data sources are disk-resolved, thus containing much more information than disk-integrated data. This shift in paradigm — using photometry not alone but simultaneously with complementary data — was mentioned in the last paragraph of the Asteroids III chapter as “perhaps the most interesting future prospect,” and we are now at this stage. In the following, we will review all data types suitable for inversion, their sources, uncertainties, and how they can be used in modeling. When describing the methods of data inversion and the results obtained by these methods, it is also important to emphasize caveats, ambiguities, and possible sources of errors. Although the description of what can be obtained from different data sources is exciting, the knowledge of what cannot, i.e., the limitations of our datasets, is of the same importance. Omitting this may lead to overinterpretation of results. This chapter is structured as follows. First, we review the main principles of the multimodal inverse problem in

183

184   Asteroids IV section 2. Then, in section 3, we discuss each data type and their contribution to model characteristics and details, and we describe some extensions of the predominant model. In section 4, we discuss the main results based on lightcurve inversion and multimodal asteroid reconstruction. We conclude with prospects for the future in section 5. 2. THEORETICAL ASPECTS OF INVERSION AND DATA FUSION Asteroid physical model reconstruction from multimodal data is, by its very nature, a mathematical inverse problem. It is ill-posed; i.e., the uniqueness and stability properties of the solution are usually not very good unless the data are supported by a number of prior constraints. Furthermore, it is not sufficient just to fit some model to the data numerically and try to probe the solution space with some scheme. Although there are more approaches to the problem of asteroid shape reconstruction, they are usually dealing with only one data type and we mention them in the next section. Here, we describe the problem in a general way in the framework of generalized projections: Our data are various one- or twodimensional projection types of a three-dimensional model, and understanding the fundamental mathematical properties of the inverse projection mapping is essential. This includes a number of theorems on uniqueness, information content, and stability properties (Kaasalainen and Lamberg, 2006; Kaasalainen, 2011; Viikinkoski and Kaasalainen, 2014). Let the projection point x0 in the image plane (plane-ofsky or range-Doppler) of the point x0 on the body be mapped by the matrix A: x0 = Ax0. Define the set I(x) for any x as

I (x) = { x g ( x, x; R , t ) h ( x; M, R , t ) = 1}

(1)



where we have explicitly shown the time t and the adjustable parameters: M for the shape and R for the rotation. The projection point function g(x; x) = 1 if A(R, t)x = x, and g = 0 otherwise. The ray-tracing function h = 1 if x is visible (for occultation, thermal, and radar data), or visible and illuminated (for disk-resolved imaging and photometry in the optical); otherwise h = 0. The set I(x) is numerable and finite. The number of elements in I(x) is at most one for plane-of-sky projections (each point on the projection corresponds to at most one point of the asteroid’s surface); for range-Doppler, it can be more (more points on an asteroid’s surface can have the same distance to the observer and the same relative radial velocity). Generalized projections, i.e., all the data modes presented in section 3, can now be presented as scalar values p(x) in the image field W

p ( x; t ) =

∫

W

f ( x, η )

∑

x ∈I ( η)

S ( x; M, R , L, t )dη

(2)

where L denotes the luminosity parameters (for scattering or thermal properties), and the luminosity function is denoted by S. The function f is the point-spread, pixellation,

or other transfer function of the image field. For interferometry, it is typically the Fourier transform kernel. In fact, the reconstruction process works efficiently by taking the Fourier transform of any image type rather than using the original pixels (Viikinkoski and Kaasalainen, 2014). For lightcurves, f = 1 [and x is irrelevant, p(x) is constant]. The surface albedo is usually assumed to be constant, although its variegation can be included in S by the parameters L if there are high-quality disk-resolved data. In the case of lightcurves only, we can get an indication of non-uniform albedo and compensate for this with a (non-unique) spot model (Kaasalainen et al., 2001). The multimodal inverse problem can be expressed as follows. Let us choose as goodness-of-fit measures some functions di, i = 1, . . . , n, of n data modalities. Typically, d is the usual c2-fit form between pmodel and pobs. Our task is to construct a joint dtot with weighting for each data mode



n

∑l

d tot ( P, D ) = d1( P, D1 ) +

i=2

i −1d i

( P, D i ) ,

D = {Di } (3)

where Di denotes the data from the source i, li–1 is the weight of the source i, and P = {M,R,L} is the set of model parameter values. The best-fit result is obtained by minimizing dtot with nonlinear techniques, typically Levenberg-Marquardt for efficient convergence. Regularization functions r(P) can be added to the sum; these constrain, for instance, the smoothness of the surface to suppress large variations at small scales, the deviation from principal-axis rotation to force the model to rotate around the shortest inertia axis (assuming uniform density), or the gravitational slope, etc. (Kaasalainen and Viikinkoski, 2012). The modality (and regularization) weights li are determined using the maximum compatibility estimate (MCE) principle (Kaasalainen, 2011; Kaasalainen and Viikinkoski, 2012). This yields well-defined unique values that are, in essence, the best compromise between the different datasets that often tend to draw the solution in different directions. Moreover, MCE values of weighting parameters are objective, not dependent on the user’s choice, although their values are usually close to those determined subjectively based on experience. Plotting various choices of weights typically results in an L-shaped curve shown in Fig. 1; the best solution is at the corner of the curve. In this way, the reconstruction from complementary data sources is possible even if no single data mode is sufficient for modeling alone. For practical computations, the surface is rendered as a polyhedron, and S and h are computed accordingly with raytracing (Kaasalainen et al., 2001). Rather than using each vertex as a free parameter, the surface can be represented in a more compact form with spherical harmonics series (for starlike or octantoid shapes) or subdivision control points (Kaasalainen and Viikinkoski, 2012; Viikinkoski et al., 2015). These shape supports are essential for convergence: They allow flexible modifications of the surface with a moderate number of parameters while not getting stuck in local minima

Ďurech et al.:  Asteroid Models from Multiple Data Sources   185 1.2 1

log(χ2LC)

0.8 0.6 0.4 0.2

Optimum MCE weight

0 −0.2 −0.4 0.5

1

1.5

2

2.5

log(χ ) 2 occ

Fig. 1. The level of fit for lightcurves and occultation data for different weighting between the two data types. The optimum weight is around the “corner” of the L-curve. Each dot corresponds to an inversion with a different weight l.

or overemphasizing the role of regularization functions when searching for the best-fit solution. Each shape support has its own characteristic way of representing global and local features. For example, the octantoid parameterization  x ( q, j ) =  x ( q, j ) =  y ( q, j ) =   z ( q, j ) =

ea (q,j ) sin q cos j ea (q,j ) + b (q,j ) sin q sin j e

a ( q ,j ) + c ( q ,j )

cos q

(4)

where a, b, and c are linear combinations of the (real) spherical harmonic functions Y ml (q,j), with coefficients {alm}, {blm}, and {clm}, respectively, are easy to regularize globally while retaining the ability to produce local details. The coordinates (q,j), 0 ≤ q ≤ p, 0 ≤ j < 2p, parameterize the surface on the unit sphere S2 but do not represent any physical directions such as polar coordinates. This inverse problem is a typical example of a case where model and systematic errors dominate over random measurement errors. Thus the stability and error estimation of the solution are best examined by using different model types (Fig. 2). In the case of shape, for example, the reliability of the features on the solution can be checked by comparing the results obtained with two or more shape supports [starlike, octantoid, subdivision (Viikinkoski et al., 2015)]. This yields better estimates than, e.g., Markov chain Monte Carlo sequences that only investigate random error effects within a single model type. A particular feature of the model reconstruction from disk-resolved data is that the result is dominated by the target image boundaries rather than the pixel brightness distribution within the target image. This is because the information is contained in the pixel contrast, which is the largest on the

Fig. 2. Model of (41) Daphne reconstructed from lightcurves and adaptive-optics images using (a) subdivision surfaces and (b) octantoids. The general shape remains stable, even if small-scale features slightly change.

boundary (occultations are special cases of this as they are samples of the boundary contour). This is very advantageous when considering the effect of model errors in luminosity properties (scattering or thermal models): It is sufficient to have a reasonable model, and the result is not sensitive to the parameters L. Thus, for example, Atacama Large Millimeter Array (ALMA) data can be used for efficient reconstruction even with a very approximate semi-analytical Fourier-series thermal model — more detailed models have hardly any effect on the shape solution (section  3.5) (Viikinkoski and Kaasalainen, 2014; Viikinkoski at al., 2015). 3. DATA AND MODELING We describe all data types that can be used, the various ways of collecting data and their accuracy, the typical number of asteroids for which data exist, and expectations for the future. We also discuss a typical result of inversion — the resolution of the model and how many targets can be modeled (Table 1). 3.1. Photometry Disk-integrated photometry is, and will always be, the most abundant source of data, because it is available for essentially every single known asteroid. Because asteroid brightness periodically changes with its rotation, frequency analysis of asteroid lightcurves provides asteroid rotation periods — the basic physical property derivable from time-resolved photometry. The regularly updated Asteroid Lightcurve Database of Warner et al. (2009) (available at http://www.minorplanet.info/lightcurvedatabase.html) now contains rotation periods and other physical parameters for almost 7000 objects, about half of which have a rotation

186   Asteroids IV TABLE 1. List of observation techniques and derivable physical properties. Technique Period Spin Size Shape Thermal Inertia Photometry X X Images X Occultation X Radar X X Radiometry Interferometry X Flyby X X *Ellipsoidal †HST/FGS.

Number of Models

Asteroids III Asteroids IV Asteroids V

X X X X X X X X X X X X X X

30 500 104 5 50 102 5 * 50 102 10 30 102 * 10 20 104 5 † 70 km) from groundbased telescopes (Cruikshank, 1977; Fernandez et al., 2003) and spacebased surveys [Infrared Astronomical Satellite (IRAS) (Tedesco et al., 2002), AKARI (Usui et al., 2011)] revealed visible geometric albedos (pv) of only a few percent, making them among the darkest objects in the solar system. The NEOWISE project (Mainzer et al., 2011) obtained thermal measurements of more than 1700 known Trojan asteroids during its main cryogenic operations from January to October 2010 (Fig. 2) (Grav et al., 2011, 2012). This represented an order of magnitude increase over all previous publications. The NEOWISE observed sample covers almost all the largest objects, providing a sample that is more than 80% complete down to about 10 km. The albedo distribution derived from

0.15

0.10

0.05

0.00

0

20

40

60

80

100

120

140

160

Diameter (km) Fig. 2. The diameter vs. albedo distribution of the jovian Trojan population. From Grav et al. (2012).

Emery et al.:  The Complex History of Trojan Asteroids   207

2.3. Rotational States and Phase Curves Studies of asteroid light curves provide information about important properties such as rotation rates, shape, pole orientation, and surface characteristics. Rotation properties of MBAs have been shown to vary dramatically with size (Pravec and Harris, 2000; Warner et al., 2009). The rotation of MBAs larger than ~50 km in diameter seems to be determined largely by collisions, while that of smaller bodies is shaped primarily by Yarkovsky-O’Keefe-RadzievskiiPaddack (YORP) forces and torques (Pravec et al., 2008). Rotation rates of MBAs between ~0.4 and 10 km exhibit a “spin barrier” corresponding to a rotation period of ~2.2 h (summarized by Warner et al., 2009). Because of their greater heliocentric distance and low geometric albedos, the Trojans have been less studied until recently. The orbital eccentricities of the jovian asteroids are low, with a mean value of 0.074 ± 0.04 (Mottola et al., 2014). They are thus physically isolated from frequent dynamical interactions with other major asteroid groups. While collisions dominate the rotation periods and shapes of large MBAs, factors such as cometary outgassing, tidal braking, and YORP may be significant for the Trojans. Early work by French (1987), Hartmann et al. (1988), Zappala et al. (1989), and Binzel and Sauter (1992) suggested that larger Trojans might have, on average, higher-amplitude light curves (meaning more elongated shapes) than MBAs of a similar size. All these studies, however, were limited to different degrees either by small sample size or by observational biases favoring large amplitudes and short periods. Because determination of the true shape, surface scattering properties, and pole direction of an asteroid requires observations at many aspect angles, most recent studies have focused on rotation periods rather than systematic coverage of lightcurve amplitudes and determination of pole directions. We focus first on studies of rotation periods, and will conclude with what is known about amplitudes and surface properties. The past decade has brought the publication of several studies dedicated to eliminating observational bias in Trojan rotation data. Molnar et al. (2008) and Mottola et al. (2010) investigated medium to large Trojans (60–180 km in diam-

eter), while French et al. (2011, 2012, 2013), Stephens et al. (2012, 2014), and Melita et al. (2010) have focused on Trojans less than 60 km in diameter. All investigators have concluded that a significant population of Trojans rotates slowly, with periods greater than 24 h. Mottola et al. (2014) compared Trojan and MBAs in the size range 60–180 km, and a Kuiper nonparametric statistical test rejects the hypothesis that the two samples belong to the same population at the 5% significance level. For smaller Trojans, the overabundance of slow rotators is even more pronounced. Figure 3, from French et al. (2015), shows the distribution of rotation rates for Trojans less than 30 km in diameter, along with the bestfit Maxwellian curve. The Maxwellian is the distribution that would be expected if the spin vectors were oriented isotropically, with each component of the angular velocity following a Gaussian distribution. The curve has been normalized to 1 at the geometric mean rotation frequency for the sample of f = 1.22 revolutions/day (P = 19.7 h). The excess of slow rotators is obvious. The presence of large numbers of slow and fast rotators has already been observed in MBAs, particularly at small diameters. Pravec et al. (2008), in their study of 268 small MBAs, demonstrated that the observed distribution of rotation frequencies is consistent with the YORP effect as the controlling mechanism (Rubincam, 2000). The YORP effect causes a prograde-rotating asteroid to speed up in its rotation and a retrograde rotator’s rotation to slow. Because the YORP effect scales as (R2/a2), where R is the radius of the asteroid and a is the semimajor axis of its orbit, a Trojan asteroid would be affected by YORP to a similar degree as an MBA that is about twice as large. The slow rotation of MBAs as large as (253) Mathilde, at R = 26 km, has been suggested to be caused by YORP (Rubincam, 2000; Harris, 2004). Thus, Trojans with radii in the 10–15-km range (D = 20–30 km) might be expected to show evidence of YORP, 14 12 10

Number

Fernandez et al. (2003) reported an anomalously high albedo of 0.13–0.18 (depending on model parameters) for (4709) Ennomos, which they suggested might be from a recent impact excavating down to a subsurface ice layer. NEOWISE, AKARI, and IRAS all report radiometric albedos of around 0.075 for Ennomos, and Shevchenko et al. (2014) report occultation and phase curve observations from which they derive an albedo of 0.054. Yang and Jewitt (2007) see no evidence for absorptions due to H2O in near-infrared (NIR) spectra of Ennomos observed on three different nights. Unfortunately, since the rotation period is very close to 12 h [12.2696 ± 0.0005 h (Shevchenko et al., 2014)], they would have been observing nearly the same hemisphere each night. It remains an open question whether Ennomos has a bright spot on its surface.

8 6 4 2 0

0

1

2

3

4

Normalized Spin Rate Fig. 3. Distribution of rotation frequencies of 31 Trojan asteroids with D < 30 km vs. the best-fit Maxwellian curve. Frequencies have been normalized to the geometric mean for this group of  = 1.22 rotations per day (

 = 19.8 h). From French et al. (2015).

208   Asteroids IV and the large numbers of slow rotators in the leftmost bin of Fig. 3 suggest that they are. What about fast rotators? The presence of a “spin barrier” at P ~ 2.2 h has been well documented for MBAs. This represents the critical rotation period, PC, at which a body without internal material strength — a rubble pile — would be spun apart by its centripetal acceleration. This period is



PC  3.3

(1 + A ) r



where PC is in hours, A is the light-curve amplitude in magnitudes, and r is the bulk density of the body (Pravec and Harris, 2000). Figure 2 of Mottola et al. (2014) shows some evidence for an excess of fast rotators among Trojans as compared to the MBA population in the 60–180-km range. The French et al. (2015) study includes 31 welldetermined light curves for sub-30-km Trojans. Currently, no Trojan has been found with a period shorter than that of (129602) 1997 WA12 (D = 12.5 km) at 4.84 h (French et al., 2015). Several other Trojans have periods in the ~5-h range (Mottola et al., 2014; French et al., 2015). The observed light-curve amplitudes give density estimates of ~0.5 g cm–3 if the objects are spinning at the critical period. This value would be consistent with observed comet densities (Lamy et al., 2004). More observations of Trojan rotation periods are encouraged in order to locate the Trojan spin barrier, setting a limit on Trojan densities. The most recent survey of Trojan asteroid light-curve amplitudes remains that of Binzel and Sauter (1992). After correcting for the likely bias in published light curves due to incomplete sampling at all viewing angles, they concluded that the larger Trojans (D > 90 km) have higher average amplitudes, implying a more elongated shape than MBAs in the same size range. What this means in terms of the evolutionary and collisional history of the Trojans is as yet unexplained. Most solar system bodies without atmospheres show an opposition effect (OE) — a sharp, nonlinear brightening near zero phase angle. (The phase angle is the angle between the Sun and Earth, as seen from the object. For Earth’s Moon this corresponds to a full Moon.) High-quality asteroid phase curves generally show a linear slope between phase angles of 5° and 25°, with differing slopes for different albedo asteroids (Belskaya and Shevchenko, 2000). At phase angles less than 5°, an opposition surge is observed; this is now understood as due to coherent backscattering, as it is stronger for higher-albedo surfaces (Muinonen et al., 2002). Phase curves for Trojan asteroids are linear down to phase angles of ~0.1°–0.2° (Shevchenko et al., 2012). This linear behavior differs dramatically from the sharp opposition spikes seen in several Centaurs, and is similar to what is observed for dark outer MBAs and Hilda asteroids (Shevchenko et al., 2012). Shevchenko et al. (2012) attribute the absence of a strong opposition surge to the low albedos of Trojan asteroids. For such low albedos, multiply scattered light, which is required for the coherent-backscatter opposition effect to occur, does not provide a significant contribution to the reflected flux.

2.4. Spectral Properties The first visible-wavelength reflectance spectra of Trojan asteroids were featureless, but the relatively steep, red spectral slopes were excitingly interpreted to indicate the presence of abundant complex organic molecules on the surfaces, masking an ice-rich interior (Gradie and Veverka, 1980). Over the following two decades, reflectance spectroscopy at VNIR wavelengths continued to show a range of spectral slopes, but no absorption features (see Dotto et al., 2008), placing strong constraints on the presence of ice near the surfaces and on the presence and form of organic material. Recent dedicated spectral searches for ices in the Eurybates family (DeLuise et al., 2010), on several large Trojans, including Ennomos (Yang and Jewitt, 2007), and on several of the smaller (D ~ 10–30 km) Trojans for which the NEOWISE survey suggests high albedos (Marsset et al., 2014), as well as a general NIR survey [0.7–2.5 µm (Emery et al., 2011)] still reveal no spectral absorption bands. Yang and Jewitt (2011) reobserved seven large Trojans whose spectra had hinted at a possible broad 1-µm silicate band, but those also turned out to be featureless. Statistical analyses of VNIR colors and spectra have revealed the presence of two distinct spectral groups (Fig. 4), a “red” group consistent with the asteroidal D-type taxonomic class and a “less-red” group consistent with the asteroidal P-type classification (Szabó et al., 2007; Roig et al., 2008; Emery et al., 2011; Grav et al., 2012). Emery et al. (2013) supplemented the NIR sample with 20 additional L5 Trojans, showing that the two spectral groups appear to be equally distributed in the two swarms. The NIR sample is restricted to objects larger than ~70 km, and it is not yet clear if the bimodality extends to smaller sizes (e.g., Karlsson et al., 2009). Emery et al. (2011) suggest that the spectral groups represent two compositional classes that potentially formed in different regions of the solar nebula. Otherwise, no strong correlations between spectral and any physical or orbital parameter are present (Fornasier et al., 2007; Melita et al., 2008; Emery et al., 2011), although Szabó et al. (2007) suggest a weak correlation of color with orbital inclination in the L4 swarm that Fornasier et al. (2007) attribute to the presence of the Eurybates family. Brown et al. (2014) presented spectra in the 2.85–4.0-µm region showing a possible absorption for a few “less-red” Trojans similar to that seen on (24) Themis (Campins et al., 2010; Rivkin and Emery, 2010). The objects that Brown et al. (2014) observed from the “red” group showed no absorption. Mid-infrared (MIR) (5–38  μm) emissivity spectra have been published of four Trojan asteroids [(624) Hektor, (911) Agamemnon, (1172) Aneas, and (617) Patroclus], and all four show strong emissivity peaks near 10 and 20 μm (Emery et al., 2006; Mueller et al., 2010). It is interesting to note that although the emissivity features seen in Patroclus, the only “less-red” object among the four, are in the same location as for the other three Trojans, the spectral contrast is significantly weaker. Whether this is a trend that follows the spectral groups remains to be discovered. From mutual eclipses of the binary

Emery et al.:  The Complex History of Trojan Asteroids   209

Geometric Albedo

0.12 0.10 0.08 0.06 0.04

Avg of redder Trojan group Avg of less-red Trojan group

0.02

0.5

1.0

1.5

2.0

2.5

Wavelength (µm) Fig. 4. Combined visible and NIR average spectra of the two spectral groups. The spectral groups are separated more clearly when both visible and NIR wavelength ranges are considered. These spectra have been scaled to pv = 0.055. From Emery et al. (2011).

components, Mueller et al. (2010) derived a very low thermal inertia (~6–20 J m–2 K–1 s–1/2) for Patroclus. Thermal spectral energy distributions of other (large) Trojans are also consistent with very low thermal inertia surfaces (e.g., Fernandez et al., 2003; Emery et al., 2006), suggesting very fine grained, porous regoliths. Horner et al. (2012) computed a slightly higher thermal inertia of 25–100 m–2 K–1 s–1/2 for (1173) Anchises, but still consistent with a “fluffy” regolith. 2.5. Binarity/Densities Binaries provide invaluable data about the physical nature of asteroids. Two are presently known among the Trojans, and they present intriguing comparisons. (617) Patroclus has a less-red surface, and the two components are nearly equal in size (Merline et al., 2002). The bulk density of the components is 1.08 ± 0.33 g cm–3 (Marchis et al., 2006). The orbit is nearly circular, and the rotation periods appear to be synchronized with the orbital motion, implying that the bodies are in a principal-axis rotation state (Mueller et al., 2010). The 102.5-h period is well explained by tidal braking. (624) Hektor, on the other hand, has a rotation period of 6.924 h and appears to be either a contact binary or one extremely elongated object with a small moon ~12 km in diameter (Marchis et al., 2014). Its bulk density has been determined to be 1.0 ± 0.3 g cm–3 (Marchis et al., 2014), very close to that of the Patroclus system. Hektor has a redder spectrum (Emery et al., 2011), suggesting a possible difference in composition. Analysis of the Hektor system suggests a high-inclination (~166°) and high-eccentricity (~0.3) orbit for the satellite, with an orbital period just between two spin-orbit resonances. This implies that the orbit has not evolved significantly since the formation of the system and is therefore primordial (Marchis et al., 2014). Most recently, Descamps (2015) reanalyzed light-curve data and adaptive

optics images of the Hektor contact binary in terms of a dumbbell shape, finding a better fit to the data and a smaller volume than the previous shape model. This smaller volume results in a higher density estimate of 2.43 ± 0.35 g cm–3. Hektor and Patroclus may therefore have different internal structures as well as belonging to different spectral groups. Searches for other Trojan binaries have been undertaken by several researchers. In a study of light-curve amplitudes, Mann et al. (2007) report two objects with light-curve amplitudes of ~1 mag [(17365) 1978 VF11 and (29314) Eurydamas] and suggest these might be contact binaries. From their survey of 114 Trojans, they estimate that 6–10% of Trojans might be contact binaries. While observing a stellar occultation by (911) Agamemnon, Timerson et al. (2013) detected a brief dip after the main occultation, which they interpret as a potential moonlet. Most recently, Noll et al. (2013) observed eight outer main belt and Trojan asteroids with long rotational periods. No binaries were found, and those authors concluded that binaries are less frequent in the outer main belt and Trojan regions than in the Kuiper belt. 2.6. Physical Interpretation of Observations In some ways, it seems that the Trojans are conspiring to keep the secret of their compositions and physical structure hidden. Nevertheless, the persistent effort of characterization described in the previous sections is paying off. The clearest indication of internal structure comes from the determination that (617) Patroclus and (624) Hektor both have bulk densities near 1 g cm–3. This low density, relative to rock and even carbonaceous chondrites, indicates either a significant low-density component (i.e., ice), a large macroporosity, or, more likely, a combination of the two. However, the interpretation for Hektor’s interior will differ if the latest, higher-density estimate is correct. The distribution of rotation rates and sizes have both been used to argue for a division in which the largest Trojans (D > 80–130 km) are intact, primordial planetesimals, whereas the smaller bodies are collisional fragments (Binzel and Sauter, 1992; Jewitt et al., 2000; Yoshida and Nakamura, 2005, 2008; Grav et al., 2011; Fraser et al., 2014). If the internal compositions are distinct from surface compositions (i.e., if a surface crust hides an ice-rich interior), one would expect the properties of smaller Trojans to be systematically different from those of larger Trojans. The small Trojans are at the limit of current observing capabilities from most characterization techniques, but there does not appear to be a systematic difference between large and small Trojans. The featureless VNIR spectra can be used to assess what is not on Trojan surfaces, but do not give a clear indication of what is on these surfaces. The red VNIR slopes have often been cited as suggestive of abundant organic material. However, Emery and Brown (2003, 2004) argue that the absence of strong absorptions in the 2.85–4.0 µm spectral range strongly limits the types and abundance of organics, and therefore the spectral slopes cannot be due to organics. Rather, they and Emery et al. (2011) demonstrate that the

210   Asteroids IV featureless, low-albedo, red-sloped VNIR spectra can be fit by amorphous and/or space-weathered silicates. Spectral models have been used to place upper limits of only a few weight % of H2O ice on the surfaces (e.g., Emery and Brown, 2004; Yang and Jewitt, 2007). The MIR emissivity spectra that have been published demonstrate convincingly that Trojan surfaces are populated by silicate dust. The large spectral contrast and positive polarity (i.e., that the features appear as peaks rather than valleys) indicate that the dust is very fine-grained (10 µm were recently reported in thermal emission at 25 µm (Arendt, 2014), while kilogram-mass Geminids have been recorded striking the nightside of the Moon (Yanagisawa et al., 2008). Some such bodies might survive passage through Earth’s atmosphere (Madiedo et al., 2013) and could already be present, but unrecognized, in terrestrial meteorite collections.

The Geminid stream mass and dynamical age together could imply ejection of debris from Phaethon, if in steadystate, at rates 30 < Ms/t  < 300 kg s–1. More likely, mass loss from Phaethon is highly variable, with dramatic bursts interspersed with long periods of quiescence. Continued observations of Phaethon, especially at long wavelengths sensitive to large particles, are needed. 2.2. 311P/PanSTARRS (P/2013 P5), TJ = 3.662 311P is an inner-belt asteroid (Table 1) that ejected dust episodically over at least nine months in 2013, creating a remarkable multi-tail appearance (Jewitt et al., 2013c, 2014c; Hainaut et al., 2014; Moreno et al., 2014) (cf. Fig. 4). Interpreted as synchrones (the sky-plane projected positions of dust particles of different sizes released simultaneously from the nucleus), each tail has a position angle linked to the ejection date. The intervals between ejections appear random. The episodic mass loss is unlike that seen in any previously observed comet. This fact alone argues against ice sublimation as the driving agent. An additional consideration is that the orbit of 311P lies near the inner edge of the asteroid belt, in the vicinity of the Flora family. The Floras have been associated with the LL chondrites (Vernazza et al., 2008), which themselves reflect metamorphism to temperatures ~800°C to 960°C (Keil, 2000). It is improbable that water ice could survive in such a body. Impact likewise offers an untenable explanation for activity that occurs episodically over many months. The color of 311P indicates an S-type classification (Jewitt et al., 2013c; Hainaut et al., 2014), consistent with its

224   Asteroids IV

Fig. 3. (3200) Phaethon at perihelion in 2009 and 2012 showing extended emission along the projected Sun-comet line. The insets show the point-spread function of the STEREO camera. Each panel shows a region 490″ square and is the median of ~30 images taken over a one-day period. From Jewitt et al. (2013a).

inner-belt orbit and with the Floras. Flora-family asteroids have a mean visual geometric albedo 0.29 ± 0.09 (Masiero et al., 2013). With this assumed albedo, the nucleus of 311P has a radius rn  ≤ 240 ± 40 m (Jewitt et al., 2013c). This small size, combined with the inner-belt location, renders 311P susceptible to spinup by radiation forces. Specifically, the YORP timescale for 311P is 80% of all falls; see the chapter by Borovička et al. in this volume) has been a vexing problem for decades (Wetherill and Chapman, 1988). Spectral interpretation of S-class asteroids and understanding their compatibility with the olivine/pyroxene mineralogy of

Near-Earth Asteroids

(a)

5–20-km Inner Mail Belt

(b)

(c)

C

S Q X

LL L Iron

C L B

Pallasite HED C

Mesosiderite Martian Enstatite chondrite Ureilite Other Lunar Aubrite

S M

X

P

P D L A V K R M E

K

B

V

D

E A R Q

Fig. 3. Mass distribution for the near-Earth asteroids, Antarctic meteorites, and inner main asteroid belt. Asteroid data are from Binzel et al. (in preparation, 2015), Antarctic data are from the Meteoritical Bulletin database, and the comparably sized main-belt data are from DeMeo and Carry (2014). The two largest nearEarth asteroids, S-types (433) Eros and (1036) Ganymed, dominate the population mass and are not included.

248   Asteroids IV ordinary chondrite meteorites has as its strongest roots the pioneering work by M. J. Gaffey (e.g., Gaffey, 1976; Gaffey et al., 1993; see the chapter by Reddy et al. in this volume) as well as the underlying atomic structure revealed by R. G. Burns (Burns, 1970). In spite of discovering the mineralogical compatibility of these two groups, direct comparison of S-type asteroid spectra with laboratory spectra of ordinary chondrite meteorites shows a distinct mismatch owing to redder slopes and muted absorption bands displayed by the asteroids. Only the Q-type asteroids (McFadden et al., 1985) (see section 2.1) display a compatible spectral match in slope and absorption band strengths. Finding that Q- to S-type spectral classes display a continuum in their transition [Binzel et al. (1996), updated in Fig.  4] bolstered the proposition that some sort of “space-weathering” process (see the chapter by Brunetto et al. in this volume) works to progressively disguise the spectral surface of a “fresh” ordinary chondrite asteroid. The Near-Earth Asteroid Rendezvous mission to the S-type asteroid (433) Eros (Veverka et al., 2000) bolstered the space-weathering interpretation. Elemental abundance measurements of Eros (Trombka et al., 2000) yielded evidence for its likely composition as an ordinary chondrite subject to space-weathering processes (Chapman, 2004). Certainly the mass distributions (Fig. 3) strongly support the S- and Q-type asteroid correspondence with ordinary chondrite meteorites. Ignoring the dominating mass of the two largest NEOs [(1036)  Ganymed and (433) Eros are both S-types, and themselves make up 75% of the total mass], S- and Q-type asteroids account for 75%

1.4

S-type

Relative Reflectance

1.3 Sq-type 1.2 Q-type

1.1 1.0

Ordinary chondrite meteorite

0.9 0.8 0.5

1.0

1.5

2.0

2.5

3.0

Wavelength (µm) Fig. 4. Asteroid reflectance spectral properties display an apparent continuum of increasing slope with decreasing absorption band depth as they transition between Q-, Sq-, and S-types, where this progression is thought to be consistent with the increasing effects of space weathering on ordinary chondrite-like asteroid surfaces. Figure adapted from Binzel et al. (2010).

of the NEO mass. In turn, ordinary chondrite meteorites (the sum of H + L + LL classes) are nearly identical in abundance at 80% of the total mass. Yet accepting this concordance as more than just a coincidence requires a definitive answer to the decades-old lingering question: Are some S-type (and Q-type) asteroids truly compositionally compatible with most ordinary chondrite meteorites? The space engineering triumph of returning a sample from the S-type asteroid (25143)  Itokawa by the Japanese Hayabusa mission (see the chapter by Yoshikawa et al. in this volume) cut the Gordian knot. Interpretation of telescopic spectra of Itokawa (then known by its provisional designation 1998  SF36) in advance of the “MUSES-C” mission (e.g., Abell et al., 2007) included the specific prediction for Itokawa being a space-weathered LL ordinary chondrite (Binzel et al., 2001). Hayabusa’s findings (Nakamura et al., 2011) not only confirmed the 2001 prelaunch LL-chondrite prediction (see the chapter by Reddy et al. in this volume), but also revealed the details of the space-weathering process (Noguchi et al., 2011) being due to nanophase iron, as predicted by Pieters et al. (2000). Emboldened by this predictive success forged by Hayabusa’s ground truth link, mineralogical modeling of the near-Earth asteroid population has proceeded with new confidence. These models have taken differing approaches, including band area analysis (Gaffey et al., 1993, 2002) and mixing models using optical constants for the constituent minerals (Shkuratov et al., 1999). In an assuring way these approaches have yielded consistent, albeit surprising results. Most notably surprising, S-type near-Earth asteroid spectra (after correction for space weathering) are most often analogous to the LL subgroup of the ordinary chondrite meteorite population (Vernazza et al., 2008; Thomas and Binzel, 2010; de Leon et al., 2010; Dunn et al., 2013). While this ordinary chondrite interpretation of asteroid spectra is overall consistent with the predominance of ordinary chondrites among all meteorite falls, the proportion is discordant. From highest-to-lowest metallic iron content, the fall percentages by mass for ordinary chondrite subgroups are H, 27%; L, 42%; LL, 12% of all meteorites (Fig. 3). Thus the epoch of Asteroids IV has its own new problem to solve: Why does the least-common subgroup of ordinary chondrites (LL) dominate the compositions interpreted by asteroid spectral analysis? Significant to the puzzle is that LL chondrites contain the highest proportion of olivine among the three classes, where olivine has a strong signature effect in broadening the absorption feature near 1  µm (see Fig.  4). Thus identifying and modeling olivine abundance from the spectral data would seem to be a secure art. Preferential delivery of the largest NEOs from the olivine-rich Flora region of the inner asteroid belt has been proposed as one explanation (Vernazza et al., 2008) (see section 3). As addressed in the chapter by Reddy et al. in this volume, an explanation may also come through better modeling of space-weathering effects, better understanding of the role of impact shocks in altering spectral properties, or better understanding of temperature or phase-angle effects on asteroid spectra. These

Binzel et al.:  The Near-Earth Object Population   249

noncompositional effects are particularly relevant because olivine-dominated LL chondrites are more likely to show space-weathering effects than L or H chondrites. In addition, significant work remains to be done to clarify spaceweathering effects (and their consequences) across the full range of asteroid taxonomic classes and compositions (see the chapter by Brunetto et al. in this volume). 2.3. Linking Observable Properties to Planetary Encounters With Hayabusa’s returned sample demonstrating space weathering as both a real and significant process affecting asteroid spectra (most notably S-type spectra; see the chapter by Brunetto et al. in this volume), a key question is the timescale for this process. Near-Earth asteroids are particularly diagnostic because the population shows the full range from “fresh” to “weathered” objects (Fig. 4). Binzel et al. (2004; see their Fig. 7) proposed a size-dependence to explain this spectral range in terms of space weathering, where size is a proxy for the surface age. Their explanation: Smaller objects have shorter collision survival lifetimes and hence (on average) younger surface ages. By corollary, a smaller object could have its surface age reset more often as even more frequent significant (even if noncatastrophic) collisions could either recoat the surface with fresh regolith or seismically reset the surface entirely. Under this collisional hypothesis, spectral studies turned to young asteroid families (e.g., Nesvorný et al., 2002; see the chapter by Nesvorný et al. in this volume) and the smallest (and hence youngest) measured main-belt objects (Nesvorný et al., 2005; Mothé-Diniz and Nesvorný, 2008; Thomas et al., 2012). Progressively these studies have found evidence for space weathering taking hold rapidly, with indications for the timescale being shorter than 106 yr (Vernazza et al., 2009). Such short timescales pose a problem for the near-Earth asteroid population: If space weathering is so rapid, how does one explain that 10% of NEAs (the Q-types; see section 2.1 and Fig. 4) appear completely unweathered? In other words, how and why do NEAs get resurfaced at a rate that occurs more frequently than in the main belt — especially when mutual collisions (if this is the responsible resurfacing mechanism) occur more often in the main belt? Nesvorný et al. (2005) insightfully noted that NEAs undergo planetary encounters on a timescale that is even more frequent than their mutual collisions, such that in the face of rapid space-weathering timescales, encounters would play a more important role than collisions for resurfacing. For a sample of nearly 100 S- and Q-type NEAs, Binzel et al. (2010) treated the dynamical history of each object and its spectral properties as independent variables and found a distinct correlation: All fresh “unweathered” Q-types in the sample had the possibility of a recent (within the past 105 yr) Earth encounter, while weathered S-types (having no fresh resurfacing) fully populated the sample whose orbits had no recent Earth encounters. Thus telescopic measurements of near-Earth asteroids yield a geophysical and seismological in-

terpretation that planetary encounters induce tidal distortions and/or seismic shaking processes sufficient to resurface, if not fully reshape, Earth-close-encounter objects (Richardson et al., 1998; see the chapter by Scheeres et al. in this volume). The critical distance or “seismic limit” (residing somewhere beyond the Roche limit and perhaps reaching out to more than 10 Earth radii) at which planetary close encounters could possibly create a detectable surface changing effect remains uncertain: Binzel et al. (2010) interprets a further limit than that calculated by Nesvorný et al. (2010). Thus continuing studies represent a fruitful area for new insights into the bulk geophysical properties of small asteroids and their response to tidal forces (see the chapter by Murdoch et al. in this volume). For example, Binzel et al. (2010) advocate the detailed study (Rosetta-like reconnoitering) of the 2029 Earth encounter by (99942) Apophis at 6  Earth radii; substantial tidal torques altering its rotation are predicted (Scheeres et al., 2005). Yu et al. (2014) estimate that small-scale landslides may occur. However, the overall observable consequences (small scale or large scale) of the tidal effects remain highly uncertain. Here we reemphasize that the 2029 Apophis encounter is a grand experiment in asteroid seismology that nature is performing for us; no other currently foreseen naturally performed case study of asteroid interiors is availing itself so opportunistically. Looking for similar tidal effects beyond Earth, ongoing studies (DeMeo et al., 2014b) indicate that Mars encounters also appear effective. Venus encounters must be similarly effective, but our sample set of “Venus only” encountering objects is presently null owing to the limitations of our Earthbased vantage point for asteroid search programs. Even with the apparent physical evidence for tidal effects in resurfacing, it remains an open question as to how the frequency of “seismic resurfacing” by planetary encounters compares with the frequency at which rapid spin-up due to thermal reradiation (e.g., Walsh et al., 2008; see the chapter by Vokrouhlický et al. in this volume) creates “refreshed” surfaces through mass shedding. What’s more, it is possible that under the conditions of frequent tidal close encounters or thermal reradiation spin-up events, frequent overturn of the surface grains could effectively allow the grains to be “sautéed,” i.e., fully “cooked” by space weathering on all sides. Thus there can be no guarantee that a given surface-shaking event will expose underlying fresh unweathered material. 3. SOURCE REGIONS FOR NEAR-EARTH OBJECTS AND METEORITES With increasing numbers of NEOs and main-belt asteroids having compositional characterization, preliminary attempts at unraveling the source regions for the near-Earth population (including meteorites) are becoming possible. In this section we describe the “Asteroids IV Scenario,” summarized in Table  2, as a framework to be augmented or refuted as future understanding evolves. Essential to this framework is the mineralogical modeling outlined in section  2.2 (see the chapter by Reddy et al. in this volume) and dynamical modeling for asteroid orbital evolution (see the chapter by

250   Asteroids IV Morbidelli et al. in this volume). Here we particularly utilize the dynamical model developed by Bottke et al. (2002) that receives as input the current orbital elements for an individual NEO and evaluates the probability for its origin from each of five source regions: the ν6 secular resonance with Saturn, the intermediate-source Mars-crossing region (IMC), the 3:1 mean-motion resonance at 2.5 AU, the outer belt region (OB) near the 5:2 resonance at 2.82 AU, and the Jupiterfamily comet (JFC) region. (The sum of all model output probabilities for any set of input orbital elements is equal to unity.) Each of these locations is depicted in Fig. 1. Using this model, Bottke et al. (2002) predicted that ~61% of the NEO population comes from the inner main belt (a  < 2.5 AU), ~24% from the central main belt (2.5 < a < 2.8 AU), ~8% from the outer main belt (a > 2.8 AU), and ~6% from Jupiter-family comets. In an attempt to reveal source regions for the NEO population, Binzel et al. (2004) evaluated the Bottke source prob-

abilities for ~400 NEOs and Mars-crossing (MC) objects for which visible and near-infrared spectra had been obtained. For their sample, they found the ν6 resonance contributed 46% of NEOs, the IMC 27%, the 3:1 resonance 19%, the OB 6%, and the JFC 2%. The vast majority of measured objects (~90%) were classified as S-, Q-, X-, and C-complex bodies within the Bus and Binzel (2002) taxonomy. Figure 5 illustrates their results for correlating the taxonomic classes with source regions, where results for major classes are summarized below. 3.1. S-Types, Q-Types, and Ordinary Chondrite Meteorites In comparing the histogram profiles (see Fig. 5) for Sand Q-types, both have very similar distributions across the inner main belt. (For “S-type” we specifically include in this discussion the related subclasses, such as Sq-types.) An

TABLE 2. Specifics for near-Earth object and meteorite sources: The Asteroids IV Scenario. Link

Evidence

Key References

LL ordinary chondrites originate from the Flora region of the inner main belt.

Flora family shows similar olivine-rich compositions. Strong dynamical link of LLcompatible NEOs favor inner main belt source.

Vernazza et al. (2009); Dunn et al. (2013); section 3.1

H ordinary chondrites originate from the mid-region of the asteroid belt.

Hebe argued as a source, but compatible asteroid compositions are broadly abundant from the 3:1 region out to, and spanning, the 5:2 resonance. H-compatible NEOs show 3:1 and 5:2 resonance source region signatures.

Gaffey and Gilbert (1998); Thomas and Binzel (2010); Vernazza et al. (2014); Nedelcu et al. (2014); section 3.1.

Less certain, but emerging ideas for the L ordinary chondrites originating from the Gefion family in the outer main belt.

Gefion family spectra compatible with L chondrites. L-compatible NEOs favor 5:2 region source.

Nesvorny et al. (2009); Binzel et al. (2014, 2015); section 3.1

“Primitive” meteorite classes sample from the outer main belt. Unresolved is the contribution from inner belt C-types.

Interpreted primitive taxonomic C- and D-classes show outer main-belt source region signatures.

Brown et al. (2000); Hiroi et al. (2001); Binzel et al. (2004); Vernazza et al. (2013); section 3.2.

Most V-type NEOs linked to Vesta and to HED meteorites. Isotopically distinct HEDs (rare) and other achondrites indicate multiple differentiated source bodies.

Spectral and dynamical links to Vesta; Dawn in situ measurements. Other small basaltic asteroids in outer belt. Achondrite meteorites are diverse.

McCord et al. (1970); Cruikshank et al. (1991); Binzel and Xu (1993); Lazzaro et al. (2000); Scott et al. (2009); Prettyman et al. (2012); Lucas and Emery (2014); section 3.3

Enstatite achondrites (aubrites) originate from the Hungaria region of the inner main belt.

E- and Xe-type asteroids are spectrally distinct. They show strong orbital and dynamical links to the inner main belt.

Gaffey et al. (1992); Binzel et al. (2004); section 3.3

Extinct Jupiter-family comets reside in NEO orbits having Tisserand (T) values 130 km, individual atoms and molecules directly impact the meteoroid surface. This leads to gradual heating of the meteoroid surface. Under some circumstances, the collision with atmospheric molecules can lead to the release of a meteoric atom from the surface. This process, called sputtering, is a form of slow mass loss at low temperatures (Rogers et al., 2005). It is efficient only at meteoroid velocities larger than 30  km  s–1 (Popova et al., 2007). Intense mass loss starts only when the meteoroid surface is heated to its melting temperature of about 2000 K (Ceplecha et al., 1998). The molten surface layer partly evaporates and is partly lost in the form of liquid droplets, which then continue to evaporate in the hot plasma surrounding the meteoroid in a process

Borovička et al.:  Small Near-Earth Asteroids as a Source of Meteorites   259

called thermal ablation. The hot envelope of heated air and meteoric vapors around the meteoroid is the main source of bolide radiation. The plasma temperature and composition can be studied by the methods of meteor spectroscopy. The typical temperatures are 4000–5000  K (e.g., Borovička, 2005). At these temperatures, the main contributors to the bolide radiation in visible light are meteoric metals, in particular Fe, Mg, Na, Ca, Cr, and Mn. They radiate in the form of atomic emission lines. The atmospheric species (N, O) and some meteoric species (notably Si, S, and C) have no bright lines in the visible range. As a result, their abundance is difficult to determine. Moreover, the composition of meteoric vapors usually does not fully reflect the composition of the meteoroid as some refractory elements, notably Al, Ca, and Ti, are not evaporated completely during thermal ablation, particularly at heights above 30  km (Borovička and Spurný, 1996; Borovička, 2005). Nevertheless, bolide spectroscopy can be used to distinguish the main types of meteoritic material (chondrites, achondrites, irons) in the cases where no meteorite is recovered. There is also a component of higher temperature (~10,000  K) observed in bolide spectra (Borovička, 1994a). The strength of this second component (represented mainly by the lines of Ca+, Mg+, and Si+) increases rapidly with bolide velocity and is not seen in slow bolides. The high-temperature region is probably formed in front of the body, where the interaction of the ablated material and the air flux is the strongest. In the denser atmospheric layers, atmospheric molecules do not directly impact the meteoroid surface. The free molecular regime changes into the continuous flow (Popova, 2004), which can be treated within the framework of gas hydrodynamics. A shock wave forms at the boundary between the envelope protecting the meteoroid and the incoming flow of the atmosphere. According to models, the temperature of the shock-heated air can reach tens of thousands of degrees (Artemieva and Shuvalov, 2001). The interaction with the atmosphere leads to loss of mass, deceleration, and, in many cases, fragmentation of the meteoroid. The classical meteor equations describe the deceleration and mass loss (ablation) of a single (nonfragmenting) meteoroid (Bronshten, 1983; Ceplecha et al., 1998). In this treatment, the meteoroid with mass m, crosssection S, moving with a velocity v, encounters atmosphere of mass Srvdt, where r is the density of atmosphere and dt is the considered time interval. The momentum of the encountered atmosphere is Srv2dt and the kinetic energy is 12 Srv3dt. From the conservation of momentum, we have the drag equation describing deceleration of the meteoroid m dv/dt = –GSrv2 where G (sometimes written as CD /2) is the drag coefficient. The energy is consumed in mass loss according to the ablation equation dm/dt = –LSrv3/2Q

where L is the heat transfer coefficient and Q is the energy necessary to ablate a unit mass of the meteoroid. These equations are usually rewritten by introducing the shape factor A = Sm–2/3d2/3, where d is the bulk density of the meteoroid, and the ablation coefficient is s = L/2QG, the latter of which can be directly inferred from observations. More details and the analytical integrals of the above equations (assuming constant coefficients) can be found in Ceplecha et al. (1998). Theoretical models of meteoroid ablation were discussed by, e.g., Baldwin and Schaeffer (1971), Biberman (1980), Svetsov et al. (1995), Golub’ et al. (1996), and Nemtchinov et al. (1997). The single-body approach is rarely applicable for the entirety of the bolide’s flight. Meteoroid fragmentation in the atmosphere is a complex process that is not possible to predict exactly but is ubiquitous. It depends on the structural properties of each individual meteoroid and occurs in various forms, i.e., chipping off a small part of the body, disruption into two or more fragments of similar sizes, catastrophic disruption into large numbers of small fragments, etc. Fragmentation is often a multi-stage process, whereby fragments arising from early fragmentation episodes disrupt again later. If this process has some regularity, it is called progressive fragmentation. The term quasicontinuous fragmentation refers to a process when small fragments (dust) are released from the main body almost continuously. This is the dominant fragmentation mode for a kind of weak millimeter-sized population of meteoroids of cometary origin (Borovička et al., 2007). For a given bolide velocity, the structurally weaker is the meteoroid, the higher in altitude the fragmentation starts. Some types of fragmentation can be induced thermally; nevertheless, in most cases (especially when large fragments are involved or when catastrophic disruption occurs) the breakup is likely due to aerodynamic loading. In this process, the dynamic pressure acting at the front surface of the meteoroid is p = Grv2, while the pressure at the rear side is zero, and the difference in the pressures causes structural failure of the meteoroid. Fragmentation occurs when p exceeds the strength of the meteoroid [see Holsapple (2009) for various definitions of strength]. In estimating the dynamic pressure at breakup, the factor G, on the order of unity, is often neglected and the meteoroid strength is estimated as rv2. The velocity, v, is easily measurable from meteor data, but the determination of the fragmentation height (and thus the corresponding atmospheric density, r) is often difficult. This can be done by a number of methods (geometric, photometric, dynamic, acoustic), depending on the type of available data and the type of fragmentation (Ceplecha et al., 1993; Trigo-Rodríguez and Llorca, 2006; Popova et al., 2011). The radiation of the bolide is assumed to be proportional to the instantaneous loss of kinetic energy, as expressed by the luminosity equation I = –t( 12 v2 dm /dt + mv dv/dt) where I is the radiative output and t is the luminous efficiency (which may depend on meteoroid velocity, mass, composition,

260   Asteroids IV and height in the atmosphere). For cases including fragmentation, the total output is the sum of contributions of all fragments. When a large number of fragments is released, a sudden increase in brightness, called a flare, occurs due to the increase of the meteoroid total cross-section. Thermal ablation stops when the meteoroid velocity decreases below about 3 km s–1. The end of the bolide therefore occurs when either all mass has been ablated and no macroscopic fragments remain or the velocity of all fragments decreases below this ablation limit. In the latter case, the fragments continue to fall during a period called dark flight. Their surface gradually cools and no light is emitted (except perhaps a faint infrared glow at the beginning). Typically, the velocity drops below the ablation limit at a height somewhere between 10 km and 30 km, depending mainly on the initial meteoroid mass and its fragmentation in the atmosphere. The deceleration continues during dark flight. The fragments follow a ballistic trajectory that turns into a nearly vertical fall, influenced by atmospheric winds (Ceplecha, 1987). When they reach the ground, the fragments are called meteorites. Typical impact speeds are in the range 10–100  m  s–1 for meteorites of 0.1–100 kg. Fresh meteorites are characterized by a dark fusion crust representing a resolidified layer of molten material acquired during the latter stages of ablation (Genge and Grady, 1999). Sometimes a part of the fusion crust is missing, suggesting that fragmentation continues to occur during the dark flight. In rare cases of large, strong meteoroids, the deceleration may not be sufficient to convert the flight into free fall. If the body hits the ground with a velocity larger than about 0.5–1 km s–1, it generates a shock wave in the ground resulting in crater formation. An impact crater much larger than the impactor is then formed (Holsapple, 1993). The radiation is not the only demonstration of meteoroid flight through the atmosphere. The supersonic flight generates a cylindrical blast wave, which can be heard on the ground and, if the amplitude and the seismic characteristics of the ground are appropriate, seismic waves may be excited (Edwards et al., 2008). Meteoroid fragmentation events can generate spherical blast waves. These waves travel in the atmosphere with the speed of sound (~300  m  s–1), so they reach the ground tens of seconds to minutes after the bolide, depending on the range of the bolide. Non-audible sound waves of low frequency, termed infrasound, attenuate particularly slowly in the atmosphere and can be detected with special detectors over large distances, in some cases for tens of thousands of kilometers (Ens et al., 2012). Eyewitnesses of bolides sometimes report another type of sound (variously described as a hissing, popping, or crackling) heard simultaneously with the bolide. The origin of these electrophonic sounds is not well understood but they are believed to be transmitted as very low frequency/extremely low frequency (VLF/ELF) electromagnetic waves and converted into audible sound by the vibration of objects in the vicinity of the observer (Keay, 1992). Recently, radio emissions at frequencies 20–40  MHz were reported from fireball trails (Obenberger et al., 2014).

Bolides, but also quite faint meteors, produce ionization trails in the atmosphere. The lifetimes of the trails vary from a fraction of second to many minutes. They reflect electromagnetic radiation, which is used for the detection of meteors by radars (Ceplecha et al., 1998, Jones et al., 2005). High-power, large-aperture (HPLA) radars are able to detect the plasma that forms in the vicinity of tiny meteoroids (Close et al., 2007). For larger bodies, this so-called head echo can also be detected by normal meteor radars (Brown et al., 2011). 3. FIREBALL OBSERVATIONS In this section we provide a brief overview of bolide observa‑ tions and the basic methods of data analysis. 3.1. Observation Methods Bolides, and particularly superbolides, are conspicuous phenomena on the sky (Fig. 1) and often draw the attention of the public. They can also be detected by various instruments  — optical cameras, photoelectric sensors, radars, acoustic and seismic detectors, or satellite-based sensors. Optical imaging cameras provide the most straightforward data about the bolide trajectory, velocity, and luminosity. The bolide must be imaged from at least two widely separated (optimally about 100  km apart) sites to reconstruct the trajectory. Inspired by success with the Příbram bolide, whole networks of cameras have been established to capture similar events and to characterize the population of large meteoroids. The network, which started in Czechoslovakia in 1963 (Ceplecha and Rajchl, 1965) and was joined by Germany in 1968 (Ceplecha et al., 1973; Oberst et al., 1998), formed the European Fireball Network (EN), which remains in operation today. The network originally used low-resolution all-sky mirror cameras recording on photographic film. The Czech portion has been modernized in several stages following the advancement of technology: Mirrors have been replaced by fish-eye lenses providing

Fig. 1. Image of a very bright bolide EN 210199 taken by the photographic all-sky camera at Lysá hora, Czech Republic. Stars form circles around the North Pole during a long exposure. Only part of the all-sky image is shown.

Borovička et al.:  Small Near-Earth Asteroids as a Source of Meteorites   261

(Jenniskens, 2007). The Spanish Meteor Network uses video cameras to obtain low-resolution spectra of bolides (Madiedo et al., 2013a,b, 2014a). Detailed light curves of bolides can be studied by radiometers, i.e., photoelectric or semiconductor devices, which do not image the bolide, but measure the total scattered sky light as a function of time (Fig. 3). Radiometers are part of AFOs and DAFOs in central Europe and of AFOs in Australia and

Fig. 2. Photographic grating spectrum of a lower part of the Benešov bolide EN 070591. The spectrum was taken from the Ondřejov Observatory, Czech Republic. The zero order (direct image) is on the left, the first order and part of the second order are on the right. The fireball flew from the top to the bottom. The exposure was interrupted by a rotating shutter. See Borovička and Spurný (1996) for more detailed description of the spectrum. Benešov is the only bolide with both recovered meteorites and recorded spectrum.

2400

Intensity (arbitrary units)

higher resolution after 1975 (Ceplecha, 1986), manually operated cameras were replaced by Autonomous Fireball Observatories (AFO) beginning in 2001 (Spurný et al., 2007), and film versions are currently being replaced by digital versions (the Digital AFO, or DAFO). The Australian Desert Fireball Network, which has operated since 2005 (Bland et al., 2012), also uses AFO. The Prairie Network operated in the United States (U.S.) from 1963 to 1975 and used batteries of high-resolution photographic cameras (McCrosky and Boeschenstein, 1965). This was also the case for the Meteorite Observation and Recovery Project (MORP) in Canada, which was active from 1971 to 1985 (Halliday et al., 1978, 1996). The three early networks were compared by Halliday (1973). The Tajikistan Fireball Network operated in 2009–2012 (two stations have been in operation since 2006 until now) and used manually operated fish-eye film cameras together with digital cameras (Kokhirova et al., 2015). There are also networks based on video cameras, either all-sky versions used in the Southern Ontario Meteor Network, operated in Canada since 2004 (Brown et al., 2010); in the NASA fireball network operated in the U.S. since 2008 (Cooke and Moser, 2012), and in the Slovak Video Meteor Network, which started with two stations in 2009 (Tóth et al., 2012), or various types of wide field cameras. The latter is the case of the Spanish Meteor Network dating back to 1997 (Trigo-Rodríguez et al., 2001) and the Polish Fireball Network operated since 2004 (Olech et al., 2006). The video-based networks provide lower resolution and thus lower precision of data than photographic networks. Video cameras are usually more sensitive and capture fainter meteors, while bright bolides are saturated and hardly measurable. The quality and reliability of the data critically depends on the quality of the astrometric procedures. Amateur astronomers in many countries now operate video cameras optimized for fainter meteors (e.g., Molau and Rendtel, 2009; SonotaCo, 2009). The International Meteor Organization (http://www.imo.net) plays an important role in coordinating and popularizing these activities. Occasionally, faint-meteor cameras also capture meteorite falls, as was the case for the Slovenian and Croatian Meteor Networks (Spurný et al., 2010; Šegon et al., 2011) and the professional Cameras for Allsky Meteor Surveillance (CAMS) system in California (Jenniskens et al., 2014). Optical cameras can be used as meteor spectrographs by putting a diffraction element (prism or grating) in front of the lens. Such objective spectrographs do not need any slit, since meteors are line objects and their monochromatic images form the spectrum. Large-format photographic film cameras with rather long focal length have been used to obtain high-resolution spectra of bright bolides (Fig. 2). The description and analysis of such detailed spectra, containing more than 100 emission lines, was published in a number of papers (e.g., Halliday, 1961; Ceplecha, 1971; Borovička, 1993, 1994b). High-resolution photographic spectrographs are still in use at Ondřejov Observatory. A more sensitive charge-coupled-device (CCD) spectrograph (but having a smaller field of view) was used during the Leonid campaign

DN050513 Light Curve Forrest T0 = 12h26m49s UT

2000 1600 1200 800 400 0 0

1

2

3

4

5

6

7

Relative Time (s) Fig. 3. Radiometric light curve of bolide DN 050513 taken by the Autonomous Fireball Observatory at Forrest station in Australia. The sampling rate was 500 Hz. The high amplitude and high frequency variations during the bright phase are real. The amplitude of the noise was much lower, as can be seen at the edges of the curve. DN 050513 was a type I meteorite-dropping bolide (meteorites landed in an inaccessible area and were not recovered).

262   Asteroids IV provide the light curves with either 500 or 5000 samples per second (Spurný and Ceplecha, 2008). Radiometric light curves of superbolides are also detected globally as a byproduct of satellite-based systems constructed for different purposes. These systems provide global detection of superbolides, with radiometric measurements establishing bolide time and radiant power (Tagliaferri et al., 1994). The total energy of the event may also be estimated under a number of assumptions. A complimentary system provides estimates of the location and in some cases the velocity/altitude or fragmentation height of superbolides. Meteorological and scientific satellites have also detected bolides in flight or their remnant dust/aerosol clouds (Borovička and Charvát, 2009; Klekociuk et al., 2005; Rieger et al., 2014). In addition to systems exploiting the electromagnetic emission of bolides, the atmospheric shock waves produced by fireballs may be detected (Edwards, 2010). At large distances from the bolide, these shocks are detectable as infrasound, which is sound below ~20 Hz. Bolide infrasound is detectable by microbarographs, which are instruments able to record coherent pressure amplitudes as low as one part in 108 of the ambient atmospheric pressure. When three or more such sensors are deployed within a region on the order of 1 km in size, the resulting sensor array can efficiently distinguish coherent sources from noise based on cross-correlation of the pressure signals and measured signal arrival direction and elevation (Christie and Campus, 2010). Since approximately 2000, the International Monitoring System (IMS) of the Comprehensive-Test Ban Treaty Organization (CTBTO) has operated infrasound arrays on a global scale. As of 2014, some 47 stations (of a projected network of 60) are operating and provide nearly global detection capability for kilotonscale superbolides. In contrast to infrasound observations, which directly detect the very small pressure perturbation from bolides at ranges of thousands of kilometers, seismographs respond to the bolide air waves coupled to the solid Earth. The low efficiency of seismo-acoustic coupling implies that airwaves are normally only directly detectable seismically within a few hundred kilometers of a bolide. For very energetic bolides, surface-coupled waves may also be produced (Edwards et al., 2008). The principle advantage of seismic bolide measurements are the tens of thousands of seismic stations operated globally that provide dense coverage in some areas, sometimes allowing multiple seismo-acoustic detections of a single bolide, which can provide information on trajectory and fragmentation points (e.g., Borovička and Kalenda, 2003; Pujol et al., 2006). Radar may also be used in several modes to characterize bolides. Direct detection of the radar head echo associated with the fireball, whereby radio waves are reflected off electrons in the region of the fireball head, can be used to estimate the velocity of the bolide as well as compute its trajectory (Brown et al., 2011) and, in principle, its mass. The main limitation of this observational mode is the large power aperture (or large radar cross section) needed to detect such head echoes, which effectively limit detectability to small

regions in the atmosphere near the radar (Kero et al., 2011). The ionization trail left behind from a bolide is more easily detected than the corresponding head echo (Ceplecha et al., 1998) — this provides some limited information on the location of the bolide and may be used to place constraints on its ablated mass. Recently, weather radars (Fries and Fries, 2010) have been shown to be effective at detecting the debris plume from a bolide in the form of material in dark flight. These Doppler radars are able to detect macroscopic-sized fragments as well as finer dust drifting to Earth, typically at altitudes 3000  kg  m–3.

264   Asteroids IV Meteoroid densities are not directly measurable from bolide data; nevertheless, statistical arguments led Ceplecha and McCrosky to the conclusion that type II bolides correspond to carbonaceous chondrites of densities ~2000  kg  m–3, and IIIA and IIIB are two types of cometary material of densities of about 750 kg m–3 and 300 kg m–3, respectively (Ceplecha, 1988). The latter two types disintegrate high in the atmosphere and do not provide meteorites. The bolide end height is easily measurable and the PE criterion is still used today. A complementary method of classification uses the apparent ablation coefficient of the fireball. It is obtained by fitting the bolide dynamics without considering fragmentation. Typical values are 0.014, 0.042, 0.1, and 0.21  s2  km–2 (or kg  MJ–1) for fireball types  I, II, IIIA, and IIIB, respectively (Ceplecha, 1988; Ceplecha et al., 1998). However, as shown by Ceplecha and ReVelle (2005), if fragmentation is taken into account, the obtained intrinsic ablation coefficient is nearly the same for all four types and is quite low, about 0.005  s2  km–2. This suggests that the composition of the material is similar in all cases (mostly silicates) and the main differences are in the bulk density, porosity, and mechanical strength, which determines the degree of meteoroid fragmentation. Note that iron meteoroids are not considered in this scheme, since they are quite rare and we do not have enough bolide data to characterize them as a population. In fact, iron meteoroids are not easily recognizable without spectral observation or recovered meteorites. They have a higher density than stony meteoroids (~7800  kg  m–3) and probably also have a larger intrinsic ablation coefficient because of lower melting temperature and higher thermal conductivity (ReVelle and Ceplecha, 1994). Finally, if discrete fragmentation points are identified on the fireball trajectory, the dynamic pressure acting on the meteoroid at that point can be used to classify the meteoroid. The fragile IIIB bodies often disrupt catastrophically at pressures of several to several tens of kilopascals accompanied by conspicuous flares (Borovička and Spurný, 1996; Borovička et al., 2007; Madiedo et al., 2014a). The type I bodies usually fragment into macroscopic pieces, often several times consecutively, at pressures from a few tenths to a few megapascals (Ceplecha et al., 1993; Popova et al., 2011). The heliocentric orbit of the meteoroid can be computed from the time of entry, direction of flight (radiant coordinates), and velocity. The corrections to Earth gravity and Earth rotation must be applied. The corrected radiant and velocity are called geocentric. An analytical method of orbit computation was presented by Ceplecha (1987). Clark and Wiegert (2011) presented a computationally more demanding numerical method and showed that Ceplecha’s formulation remains valid except in rare particular cases. 4. METEORITE ANALYSES RELEVANT TO FIREBALL STUDIES Meteorites, when recovered, are subject to detailed mineralogical, chemical, physical, and isotopic analyses in the

laboratory. Some of them are directly relevant to fireball studies because they provide either independent estimates of some parameters or supplementary information. In interplanetary space, meteoroids are bombarded by energetic particles of solar and galactic cosmic rays. The interaction of cosmic rays with atoms in the meteoroid leads to the formation of atomic nuclei that are otherwise only rare or absent in the meteoric material, namely noble gases and short-lived radionuclides (Verchovsky and Sephton, 2005; Eugster et al., 2006). Cosmic rays penetrate a few meters inside the meteoroid. The measurement of the concentration of selected nuclides, in particular 60Co, 10Be, 21Ne, and 22Ne, can be used to estimate the pre-atmospheric radius of the meteoroid and the depth of the measured sample inside the meteoroid. Note, however, that the calculations are model dependent and rely on derived nuclide production rates (Leya and Masarik, 2009). The correspondence with the fireballdetermined pre-atmospheric mass of the meteoroid is not always good (Popova et al., 2011). The cosmogenic nuclides can be also used to estimate the cosmic-ray exposure (CRE) age of the meteoroid. This is the time for which the meteoroid was exposed to cosmic rays, i.e., the time elapsed since the meteoroid was excavated from a deeper depth in its parent body. Lunar meteorites and carbonaceous chondrites have the shortest CRE ages (about 1 m.y. on average), while the CRE ages of iron meteorites are the longest (hundreds of million years) (see Eugster et al., 2006). The measurement of physical properties of meteorites is also important for modeling the meteoroid flight in the atmosphere. Densities and porosities of meteorites of various types were published in a series of papers (Macke et al., 2011, and references therein). Thermal conductivities (Opeil et al., 2012) and heat capacities (Consolmagno et al., 2013) were also measured. Other measurements of these quantities were obtained by Beech et al. (2009) and their application to meteor physics was discussed. The measurements of tensile and compressive strengths of meteorites are still rare because a destructive analysis is needed. Published values were compiled by Popova et al. (2011) and Kimberley and Ramesh (2011). 5. INSTRUMENTALLY OBSERVED METEORITE FALLS Instrumental observations of fireballs that produce meteorite falls and finds are of great scientific interest and importance because meteorites provide us with a surviving physical record of the formation of our solar system, and a direct link to their parent bodies. But most meteorites are also unique — as geological materials — in that they come with virtually no spatial context to aid us in interpreting that record. Reliable orbital information for meteorite falls is known for only 22 cases. This is a tiny fraction of the tens of thousands of meteorites that are known. For this reason, every new fireball with precise orbital data that produces a meteorite gives us invaluable information.

Borovička et al.:  Small Near-Earth Asteroids as a Source of Meteorites   265

Similarly important is the study of processes accompanying the atmospheric flight of the meteoroid producing a meteorite fall. From every new instrumentally documented fall we learn much to help refine our methods and models. On the other hand, the known properties of the meteorite, such as density, mass, shape, composition, structure, etc., facilitate reverse calibration of other data from fireballs that do not produce meteorites. This provides information on the physical properties of meteoroids not likely contained in our meteorite collections. Basic data about all instrumentally documented meteorite falls (22 cases so far) are shown in Tables  1–3, where details about their orbital data, atmospheric trajectory data, and meteorite data are collected. When comparing the data, it must be realized that the data were obtained under various circumstances (day/night, different ranges to the bolide) and by widely different techniques. The techniques are listed in the last column of Table 1. Only in a minority of cases (eight) was the fireball trajectory fully determined from professional photographic or video networks aimed at fireball observations. In seven cases, only casual videos and photographs were available. In four cases, a combination of the two or video cameras aimed at fainter meteors were used. Tagish Lake and Almahata Sitta fireballs were not imaged in flight from the ground at all; instead, satellite data and dust cloud images were used. In the case of Almahata Sitta, the orbit was precisely known from pre-impact observation of the meteoroid. To some extent the atmospheric trajectory could be determined from that data as well. It is difficult to link specific meteorites with individual parent asteroids with some certainty. The orbit measured for any particular meteorite-producing fireball is heavily evolved from the original orbit of the parent asteroid. As a result, linking individual fireballs with specific asteroids is generally not possible. Rather, classes of meteorites and source regions in the main asteroid belt can be statistically associated using the orbit distribution of many meteorites and models of main-belt to near-Earth asteroid (NEA) delivery (Bottke et al., 2002a). We tried to evaluate the quality of various aspects of fireball data in the thirteenth column of Table 1. The trajectory (direction of flight, geographical coordinates, heights), dynamics (deceleration along trajectory), photometry (absolute brightness, shape of the light curve), and heliocentric orbit (dependent on the precision of the radiant, initial velocity, and time of the fireball) were evaluated on scale of 1–5 (1– means between 1 and 2, etc.). Overall, Tagish Lake, Buzzard Coulee, and Sutter’s Mill have less-reliable data. The number of digits for orbital elements in Table  1 is given so that the published error is on the last digit. Most orbits are Apollo-type; only one is an Aten-type. The inclinations are mostly low (the median value is about 5°) but go up to 32°. All aphelia lie within the orbit of Jupiter, although the Tisserand parameters (TJ) of Maribo and Sutter’s Mill are lower than 3. These two fireballs had the largest entry velocity (V∞ in Table 2). The other values given in Table 2

are the observed terminal velocity (VE), the best estimate of the initial mass of the meteoroid (m∞), the maximal absolute magnitude of the fireball (Mmax), the slope of the trajectory (the slope is changing along the trajectory due to Earth’s curvature, so only rough values are given), the observed begin‑ ning height (HB), the height of maximum brightness (Hmax), the terminal height (HE), the total length of the trajectory (L); the duration of the fireball (T), the total energy (E) in kilotons of TNT (1 kt TNT = 4.185 × 1012 J), and the maximal encountered dynamic pressure (Pmax). The observed beginnings of the fireballs (and thus also the lengths and durations) strongly depend on the technique and, in the case of casual records, also on pure chance. We therefore also list in some cases values from visual observations. The terminal heights are affected by observation effects to a lesser extent because the drop of brightness at the end is usually steeper. It can be seen that meteorites were observed to fall from meteoroids of a wide range of masses, causing fireballs that are different by orders of magnitude in terms of energy and brightness. At the lower end, there were meteoroids of initial masses of only a few dozens of kilograms causing fireballs of absolute magnitude of about –10 or slightly more. Some meteorite falls were produced by large (>meter-sized) meteoroids associated with superbolide events, which occur globally every two weeks (Brown et al., 2002a, 2013a). As a result, only a very small number of these events have detailed atmospheric flight observed. Our sample includes several superbolides with good dynamic and photometric data (such as Benešov, Košice, and Chelyabinsk). In these instances we can obtain insight into the internal structure of the pre-atmospheric meteoroid, for comparison with the physical structure of asteroids as determined from other kinds of observations. One of the measurable values is the mechanical strength expressed by the dynamic pressure at fragmentation. The enlarged sample confirms the conclusions of Popova et al. (2011) about the low strengths of interplanetary meteoroids and small asteroids. The relatively large value for Chelyabinsk (18 MPa) concerns only a very minor part of the body. The majority of the material was, in fact, destroyed under 1–5 MPa (Borovička et al., 2013b). Data on types and masses of recovered meteorites are compiled in Table 3. Some of the large meteoroids disrupted heavily in the atmosphere and produced large numbers of small meteorites. This was the case for not only all three carbonaceous chondrite meteorites (which were made of relatively weak rock) and two mineralogically heterogeneous bodies (Almahata Sitta and Benešov), but also for ordinary chondrite bodies like Košice. The opposite example is Carancas, discussed in the next section. But there are bodies also in our sample that did not fragment very heavily (e.g., Morávka, Příbram, and, in particular, Neuschwanstein). Chelyabinsk fragmented extensively; nevertheless, one large (600 kg) piece survived intact to the ground. In the next section, we discuss in greater detail some particularly notable meteorite falls that were caused by large meteoroids.



1, 2–, 3, 1 1, 1, 1–, 2 1, 1–, 1, 1 1, 1, 1–, 1 2–, 3, 3-, 2- 3–, 4–, 4, 3- 2, 2, 3–, 2- 1, 1–, 2, 1 2–, 4, 3, 3 2, 2–, 3–, 2- 1, 1, 1, 1 3, 4–, 4–, 1‡ 3–, 4, 5, 3– 2–, 3, 2, 3 2–, 3, 2–, 2- 1, 2, 1–, 1 2–, 2–, 2, 3 1, 1, 1, 1 1–, 2, 2, 1- 3, 4, 4–, 3- 2–, 2–, 3, 2 1–, 2, 2, 1-

P P P P CV,CP CTP, I, S, Sa CV, I, S, Sa P, S, I, PE CV, I, S, Sa CV, CP, I, S P, PE I, Sa, T, CTP CV, I P, CV, R, PE P, V, PE, I, S V, I, R, RD CV, PE, I, S P, PE P, PE, V CV,CP,I,S,RD V, I, CP CV, CP,I,S,Sa

Techniques†

All angular orbital values are in J2000.0 equinox.

† Instrumental

*

Quality coefficient describes the achieved reliability in determination of the atmospheric trajectory (T), dynamics (D), light curve and photometry (P), and heliocentric orbit (O); 1 = best, 5 = worst. techniques used for the data acquisition: P = dedicated photographic network, CV = casual video, V = dedicated video network, I = infrasound, S = seismic, Sa = satellite, R = meteor radar, PE = fast photoelectric photometer, T = telescope (pre-atmospheric observation of the meteoroid), RD = weather Doppler radar, CP = casual photograph, CTP = casual trail photograph. ‡ The most precise orbit thanks to the pre-atmospheric observations; however, very limited precision in the atmospheric trajectory, dynamics, and photometry determination.

3.16 4.14 3.81 3.08 4.47 3.66 3.70 3.16 3.08 3.30 6.88 4.93 5.04 2.91 4.01 3.50 3.02 3.14 4.30 2.81 3.56 3.97

Geocentric Radiant Vg Quality* a (AU) e q (AU) Q (AU) w (deg) W (deg) i (deg) TJ ag (deg) dg (deg) (km s–1) T/D/P/O

Příbram 192.338 17.467 17.431 2.401 0.6711 0.78951 4.012 241.750 17.7915 10.482 Lost City 315.0 39.1 9.2 1.66 0.417 0.967 2.35 161.0 283.8 12.0 Innisfree 6.66 66.21 9.4 1.872 0.4732 0.986 2.758 177.97 317.52 12.27 Benešov 227.617 39.909 18.081 2.483 0.6274 0.92515 4.040 218.370 47.001 23.981 Peekskill 209.0 –29.3 10.1 1.49 0.41 0.886 2.10 308.0 17.030 4.9 Tagish Lake 90.4 29.6 11.3 1.98 0.55 0.884 3.08 224.4 297.901 2.0 Morávka 250.1 54.96 19.6 1.85 0.47 0.9823 2.71 203.5 46.258 32.2 Neuschwanstein 192.33 19.54 17.51 2.40 0.670 0.7929 4.01 241.20 16.827 11.41 Park Forest 171.8 11.2 16.1 2.53 0.680 0.811 4.26 237.5 6.1156 3.2 Villalbeto de la Peña 311.4 –18.0 12.9 2.3 0.63 0.860 3.7 132.3 283.671 0.0 Bunburra Rockhole 80.73 –14.21 6.743 0.8529 0.2427 0.6459 1.05991 210.04 297.595 8.95 Almahata Sitta 348.1 7.6 6.45 1.3082 0.31206 0.89996 1.7164 234.449 194.101 2.542 Buzzard Coulee 290.1 77.0 14.2 1.25 0.228 0.9612 1.53 211.3 238.937 25.0 Maribo 124.7 19.7 25.8 2.48 0.807 0.479 4.5 279.2 297.122 0.11 Jesenice 159.9 58.7 8.3 1.75 0.431 0.9965 2.51 190.5 19.196 9.6 Grimsby 242.6 54.97 17.9 2.04 0.518 0.9817 3.09 159.9 182.956 28.1 Košice 114.3 29.0 10.3 2.71 0.647 0.957 4.5 204.2 340.072 2.0 Mason Gully 148.36 9.00 9.322 2.556 0.6158 0.98199 4.130 19.00 203.214 0.895 Križevci 131.22 19.53 14.46 1.544 0.521 0.7397 2.35 254.4 315.55 0.640 Sutter’s Mill 24.0 12.7 26.0 2.59 0.824 0.456 4.7 77.8 32.77 2.4 Novato 268.1 –48.9 8.21 2.09 0.526 0.9880 3.2 347.37 24.9414 5.5 Chelyabinsk 333.82 0.28 15.14 1.72 0.571 0.738 2.70 107.67 326.459 4.98

Name

TABLE 1. Instrumentally observed meteorite falls — Orbital data.

266   Asteroids IV



1959/04/07 1970/01/04 1977/02/06 1991/05/07 1992/10/09 2000/01/18 2000/05/06 2002/04/06 2003/03/27 2004/01/04 2007/07/20 2008/10/07 2008/11/21 2009/01/17 2009/04/09 2009/09/26 2010/02/28 2010/04/13 2011/02/04 2012/04/22 2012/10/18 2013/02/15

Date (UT) (yyyy/mm/dd) 19:30:20 2:14 2:17:38 23:03:44 23:48 16:43:42 11:51:51 20:20:13.5 5:50:26 16:46:45 19:13:53.24 2:45:40 0:26:40 19:08:32.73‡ 0:59:40.5 1:02:58.40 22:24:46.6 10:36:12.68‡ 23:20:39.9 14:51:12 2:44:29.9 3:20:21

Time* (UT) 20.886 14.150 14.54 21.256 14.72 15.8 22.5 20.95 19.5 16.9 13.365 12.4 18.0 28.3 13.78 20.91 15.0 14.648 18.21 28.6 13.67 19.03

— 3.4 2.7 5.0 5 9 3.8 2.4 — 7.8 5.68 — — — — 3.1 4.5 4.1 4.5 19 — 3.2

V∞ VE (km s–1) (km s–1) 1300 163 51 3500 10,000 56,000 1500 300 11,000 600 22 40,000 8,000 1500 170 30 3500 14 50 40,000 80 12 × 106

–19 –11.6 –12.1 –19.5 –16 –22 –20 –17.2 –21.7 –18 –9.6 100 Villalbeto de la Peña ESP D(E) 36 Bunburra Rockhole AUS N(M) 3 Almahata Sitta (2008 TC3) SDN N(M) >650 Buzzard Coulee CAN N(E) ≥2500 Maribo DNK N(E) 1 Jesenice SVN N 3 Grimsby CAN N(E) 13 Košice SVK N 218 AUS N(E) 1 Mason Gully Križevci HRV N 1 USA D 77 Sutter’s Mill Novato USA N(E) 6 Chelyabinsk RUS D(M) >1000

H5 5.6 (~7**) H5 17.342 L5 4.58 LL3.5, H5, PA 0.0116 H6 12.4 C2 ~10 H5–6 1.40 EL6 6.226 L5 ~30 L6 5.2 Euc-anom 0.339 EL, EH, H, L, LL, CB, R ~11 Ure-Anom H4 >50 CM2 0.026 L6 3.61 H4–6 0.215 H5 11.28 H5 0.0245 H6 0.291 CM2 0.943 L6 0.363 LL5 >730§§

Estimated Meteorite Coordinates‡ Terminal (deg) Mass (kg) Longitude Latitude

No. of Meteorite Recovered Day/Night Name Country* † Fall Meteorites Type(s) Mass (kg)

TABLE 3. Instrumentally observed meteorite falls — Meteorite data.

268   Asteroids IV

Borovička et al.:  Small Near-Earth Asteroids as a Source of Meteorites   269

6. NOTABLE METEORITE-PRODUCING FIREBALLS 6.1. Almahata Sitta (2008 TC3) and Benešov: Heterogeneous Falls The Almahata Sitta meteorite fall (Jenniskens et al., 2009) is unique in many aspects. It was the first meteorite fall that was predicted in advance  — still the only case of this kind. The corresponding meteoroid/asteroid, designed 2008 TC3, was discovered 19  hr before it entered the terrestrial atmosphere. During that time interval, numerous astrometric observations were made from various observatories around the world. Thanks to these data, a precise orbit was computed and the impact trajectory was predicted over the Nubian Desert in the Sudan with a precision of better than 1 km. Moreover, photometric and spectroscopic observations of 2008  TC3 were also made and helped to characterize the body before the atmospheric entry. There was not enough time to set up any fireball cameras in the region of impact. Consequently, available data for the actual fireball are scarce. Nevertheless, the data clearly showed that the meteoroid was a fragile body and disrupted relatively high in the atmosphere. In accordance with this, a large number (~600) of mostly small (0.2–379 g) meteorites were recovered, but no large meteorite was found. Quite surprisingly, the meteorites were of various mineralogical types. This fact completely changed our paradigm that one meteorite fall produces meteorites of one type and that (undifferentiated) asteroids have a certain mineralogical composition, although polymict meteorite breccias were previously known (Bischoff et al., 2010). Shaddad et al. (2010) described over 600 recovered meteorites. Their total mass was 10.7 kg; the individual masses ranged from 0.2 to 379  g. The locations of all meteorites were carefully documented but only a few of the meteorites were analyzed in detail. Of the classified meteorites, the majority were ureilites, i.e., a relatively rare type of achondrite. However, enstatite chondrites and ordinary chondrites were found as well. Kohout et al. (2010) measured magnetic susceptibility of 62 meteorites from that sample. In 25 cases, he found anomalous values suggesting that the meteorites are not ureilites. Bischoff et al. (2010) analyzed a different sample of 40 meteorites from undocumented locations within the Almahata Sitta strewn field and found many different types. The mineralogical measurements of 110 meteorites by various authors were summarized by Horstmann and Bischoff (2014). Of these, 75 were ureilites or ureilite-related, 28 were enstatite chondrites (both EH and EL), 5 were ordinary chondrites (H, L, LL), one was a carbonaceous chondrite (CB), and one was a previously unknown type of chondrite related to R chondrites. Such a variety of meteorite types within one fall is unprecedented. Naturally, the question arises if all meteorites were really part of 2008 TC3 and did not come from unrelated meteorite fall(s) with overlapping strewn fields. The main arguments for common origin are as follows: (1) All meteorites are

similarly fresh looking. (2)  There is no indication that the non-ureilitic meteorites were located in a specific part of the strewn field (Shaddad et al., 2010). (3) The presence of short-lived radionuclides in two non-ureilitic meteorites is evidence for a recent fall, consistent with the association with 2008 TC3 (Bischoff et al., 2010). (4) The analysis of noble gases and radionuclides in two other non-ureilitic meteorites provided the same pre-atmospheric radius and the same CRE age (20 m.y.) as for ureilitic meteorites (Meier et al., 2012). So, although not definitely proven, it is very likely that most, if not all, of the various meteorite types really belonged to the same fall and that 2008 TC3 was therefore a highly heterogeneous body. Although the ureilitic lithology was prevailing, completely different lithologies were present as well. It is worth noting that none of the foreign lithologies was found to be directly embedded within the ureilitic meteorites. It therefore seems that the chondritic material was only loosely bound within the asteroid. From the foregoing it may seem that asteroid 2008 TC3 was a rubble pile, i.e., a conglomerate of rocks bound together only by mutual gravity. However, other data do not support that view. Scheirich et al. (2010) and Kozubal et al. (2011) determined the shape and rotation of 2008 TC3 from pre-impact photometry. The asteroid was an elongated body with axial ratio of approximately 1:0.54:0.36. It was in an excited rotation state with period of rotation of 99.2  s and period of precession of 97.0 s. The absolute dimensions are uncertain due to uncertainties in albedo. The V-band albedo of selected meteorites was measured as 0.046  ± 0.005 by Jenniskens et al. (2009) and as 0.11 by Hiroi et al. (2010). The asteroid dimensions can, in principle, be determined from its mass and density as well. The mass can be inferred from bolide energy, since the entry velocity is well known. The bolide energy was estimated as (6.7 ± 2.1) × 1012 J from infrasound detection in Kenya (Jenniskens et al., 2009). The radiated energy measured by U.S. government sensors was 4 × 1011 J (Jenniskens et al., 2009), which translates to a total energy (2.7–5.1) × 1012 J, depending on the value of luminous efficiency (Borovička and Charvát, 2009). The densities of most of the 45 meteorites measured by Shaddad et al. (2010) were around 2800 kg m–3, but values as high as 3430 kg m–3 and as low as 1590 kg m–3 were found. The bulk density of the asteroid could in principle be even lower if significant macroporosity was present. Combining the possible range of all values, Kozubal et al. (2011) concluded that the most probable mean size was 4.1 m, mass 50,000 kg, albedo 0.05, and bulk density 1800 kg m–3. They did not use the shape model of Scheirich et al. (2010). Kohout at al. (2011) found a mean density of five Almahata Sitta ureilities of 3100 kg m–3. Considering the higher albedo values of Hiroi et al. (2010) as more reliable and assuming significant macroporosity, they concluded that the mass of 2008 TC3 was only between 8000 and 27,000 kg. Welten et al. (2010) estimated the radius × density on the basis of radionuclide measurements to 3000 ± 300  kg  m–2. We consider the following parameters as the most likely: size 6.6 × 3.6 × 2.4 m, volume 22 m3, mean radius 1.74 m, mass 40,000 kg, bulk density 1800 kg m–3,

270   Asteroids IV porosity almost 50% [using grain density 3500 kg m–3 from Kohout et al. (2011)], albedo 0.049, bolide energy 3.1  × 1012 J, and integral luminous efficiency 13%. This implies that the albedo of Hiroi et al. (2010) and the energy derived from infrasound estimates were overestimated. The higher albedo would lead to a smaller mass and thus an even higher conflict with infrasonic energy. On the other hand, if that energy were true, the resulting asteroid density would be too high in comparison with some of the meteorites, and considering the atmospheric behavior of the body or an unrealistically low albedo would be needed. The fast rotation of 2008 TC3 means that the centrifugal force at the surface exceeded self-gravity, and therefore 2008 TC3 was not a classical rubble pile held together only by gravity. Nevertheless, as shown by Sánchez and Scheeres (2014), a cohesive strength of only 25 Pa would be sufficient to bind the body together. Such strength could be provided by van der Waals forces between constituent grains (Sánchez and Scheeres, 2014). However, such a small mechanical strength would lead to the disintegration of the body just at the beginning of atmospheric entry at heights above 100 km. The bolide observations by U.S. government sensors revealed that the bolide exhibited three flares; that in the middle was the brightest and occurred at a height of 37 km (Jenniskens et al., 2009). The Meteosat satellite data confirmed the maximum at 37 km and revealed two earlier flares at 45 km and 53 km (Borovička and Charvát, 2009). Finally, the distribution of meteorites is consistent with their release at a height of 37 km (Shaddad et al., 2010). So the major disruption of 2008 TC3 occurred at a height of 37 km under the dynamic pressure 0.9 MPa. This pressure is within the lower range as compared to other bodies of similar sizes (see Table 2), confirming the fragile nature of 2008 TC3, but it is still much higher that the expected strength of rubble piles. The actual structure of this body remains unclear. In any case, the recovered meteorites of various physical and mineralogical properties represent only a tiny fraction of the original mass, namely the fraction that was the strongest. They were probably embedded within a matrix that mostly disappeared during atmospheric entry. The matrix could be similar to the meteorites with the lowest measured densities, i.e., the porous fine-grained ureilites (Bischoff et al., 2010). The reflectance spectrum of 2008 TC3 was taken in the wavelength range 550–1000 nm (Jenniskens et al., 2009). The spectrum was flat and featureless and 2008 TC3 was classified as F  type. Jenniskens et al. (2010) searched for asteroids of similar spectra. They were not able to identify an asteroid family as the source of 2008  TC3. A similar search was performed by Gayon-Markt et al. (2012), who also discussed the origin of 2008 TC3 and concluded that it is highly improbable that the heterogeneous structure was formed by low-velocity impacts in the current asteroid belt. Horstmann and Bischoff (2014) proposed that the material was formed in the early solar system by a four-stage process: (1) heating and partial melting on the ureilite parent body (UPB), including basaltic magmatism; (2) an impact event that resulted in the catastrophic disruption of the UPB;

(3) rapid cooling of the released mantle material; and (4) reaccretion into smaller daughter asteroids, forming ureilitic “second-generation” asteroids. The foreign (chondritic) fragments were more likely incorporated into them at the fourth stage rather than by subsequent impacts. Finally, 2008 TC3 separated from one of the second-generation ureilitic bodies at 20 Ma. More recently, Goodrich et al. (2015) argued that the proportion of foreign clasts in 2008 TC3 was not larger than in other polymict ureilites and that the same selection of materials as in other polymict ureilites was present. They hypothesized that the immediate parent of 2008  TC3 was also the immediate parent of all other ureilitic meteorites. In contrast to Horstmann and Bischoff (2014), Goodrich et al. (2015) considered it more likely that the foreign fragments were accreted by the 2008 TC3 parent body over long periods of time. Almahata Sitta is not the only heterogeneous meteorite fall. The second confirmed case is Benešov, a fall instrumentally observed and very well documented in 1991 (Spurný, 1994), including a rich bolide spectrum. The search for meteorites was unsuccessful at that time; nevertheless, several papers were devoted to the bolide analysis (e.g., Borovička and Spurný, 1996; Borovička et al., 1998). In the spring of 2011, after a complete reanalysis of all available records (Spurný et al., 2014), the meteorite search was resumed with a revised strategy  — not looking for big pieces but for small ones produced in large amounts from the disruption at a height of 24 km. The new strategy was successful and four weathered meteorites with masses in the predicted range were found with metal detectors exactly in the predicted area (Spurný et al., 2014). Surprisingly, one meteorite was an H chondrite, one was an LL chondrite, and one was an LL chondrite with an embedded achondritic clast (the fourth meteorite could not be classified because of its small size and weathering stage). The size and location of all four meteorites exactly in the predicted area for corresponding masses, the same degree of weathering and composition consistent with the bolide spectrum, and the extremely low probability of two coincidental falls in the given area means that all the meteorites almost certainly came from the Benešov bolide. The heterogeneous nature of the Benešov meteoroid is supported by its early separation into smaller bodies during atmospheric flight (Borovička et al., 1998). These findings can shed new light on some old meteorite finds. The Galim meteorite fall contained both LL and EH specimens (Rubin, 1997). Other examples of meteorites of different types found close to each other can be found in the Meteoritical Database, e.g., Hajmah (ureilite + L), GaoGuenie (H + CR), and Markovka (H + L). These meteorites were traditionally classified separately, e.g., as Hajmah (a), Hajmah (b), but may in fact come from the same body. Of course, chance alignment in these non-observed falls is also possible. Studies of the surprisingly rich Franconia strewn field, which contains various meteorite types, concluded that they fell at various times (Hutson et al., 2013). On the other hand, there are some meteorites containing foreign clasts on a microscopic scale. The most prominent example

Borovička et al.:  Small Near-Earth Asteroids as a Source of Meteorites   271

is the polymict microbreccia Kaidun, which contains materials of many different meteorite types in millimeter-sized clasts (Zolensky and Ivanov, 2003). Other cases have been summarized by Bischoff et al. (2010).

4.0

6.2. Příbram and Neuschwanstein Meteorite Pair

2.5

The Příbram meteorite fall has a special status among instrumentally recorded falls. This is not only because of the fact that it was the first such case in history (it fell on April 7, 1959) and that it represents the first time that recovered meteorites were directly linked with asteroids, but also because it was the first time when the so-called dark flight (first use of this term, which was invented by Z. Ceplecha) was rigorously computed for individual meteorite trails seen on the photographs (Ceplecha, 1961). This method was crucial for the future recovery of several subsequent events and it also played a fundamental role in the recovery of the second predicted meteorite fall in Europe, Neuschwanstein. Coincidentally, this other extraordinary case actually increased the original significance of the historic Příbram fall. The spectacular Neuschwanstein bolide was recorded by the all-sky cameras of the EN over Austria and Germany exactly 43 years after the Příbram fall. Based on the analysis of EN photographic records, three meteorites of corresponding masses were found exactly in the predicted area (Spurný et al., 2003). However, the uniqueness of this case is not in the successful recovery of meteorites, but in the fact that the heliocentric orbits of both Příbram and Neuschwanstein meteoroids were almost identical, with DSH = 0.025 (Fig. 4). Such close similarity of orbits for two independent meteorite falls with recovered meteorites is unknown among the other 20 meteorite falls having known orbits. Only in the case of Innisfree and Ridgedale (presumed fall) meteorite falls observed in the MORP Canadian fireball network (Halliday, 1987) has a similarly close orbital pair been observed; unfortunately, meteorites were found only for the Innisfree fall. Nevertheless, this case generated the idea of the existence of meteorite streams (Halliday et al., 1990), a notion strongly supported by the unique orbital similarity of the Příbram-Neuschwanstein pair. On the other hand, Příbram and Neuschwanstein falls differ in meteorite composition (Příbram is H5 while Neuschwanstein is EL6) and in CRE ages (Příbram is 12 m.y. while Neuschwanstein is 48 m.y.). Therefore this case has generated wide discussion as to whether the apparent orbital connection between these two meteoroids is real (e.g., Tóth et al., 2011) or only coincidental (Pauls and Gladman, 2005). This question is not yet reliably solved; it seems from other recent instrumental observed falls such as Almahata Sitta or Benešov that the compositional difference should not be a decisive argument against the Příbram and Neuschwanstein connection.

2.0

6.3. Carbonaceous Chondrites: The Weakest Meteorites Three instrumentally recorded fireballs resulted in carbonaceous chondrite meteorite falls. These three falls (Tagish Lake,

3.5 3.0

Mars

1.5

Earth

AU

1.0 0.5

Mercury

0.0



Sun

–0.5

Venus

–1.0 –1.5 –2.0 Přibram Neuschwanstein Chelyabinsk 86039

–2.5 –3.0 –2.0 –1.5 –1.0 –0.5

0.0

0.5

1.0

1.5

2.0

2.5

AU Fig. 4. The orbits of Příbram, Neuschwanstein, and Chel­ yabinsk meteorites and asteroid (86039) 1999 NC43, projected into the plane of ecliptic. The arrow with symbol points to vernal equinox. The orbital similarity of Příbram-Neuschwanstein and Chelyabinsk-1999 NC43 is evident.

Maribo, and Sutter’s Mill) have several common characteristics: They were all large (multi-meter-sized) initial objects and they all showed flight characteristics (early fragmentation, high end heights relative to their mass and speed) indicative of a very fragile structure. While the orbit for Tagish Lake (a C2 ungrouped unusual meteorite) is solidly asteroidal (with TJ = 3.7), the orbits for Maribo and Sutter’s Mill (both CM2 chondrites) are on the borderline between Jupiter-family comets and asteroids. Intriguingly, Maribo and Sutter’s Mill have very similar orbits, suggesting both a common and relatively recent origin on the basis of short CRE ages (Jenniskens et al., 2012). Moreover, these two meteorite falls appear to be associated with fireballs having initial speeds in excess of 28 km s–1. This is substantially higher than the next fastest recovered fall (Morávka, at 22.5 km s–1). As surviving mass from ablation  ∝ exp(–v2), even a small increase in initial speed result in large increases in ablation. This is even more remarkable as these are friable carbonaceous chondrites. The large size of the initial objects and the high altitude of the breakup allowing fragments to decelerate gradually appears to have been critical in survival of a small terminal mass in all three cases. For Tagish Lake, the estimated mass survival

272   Asteroids IV fraction was 15  MPa ram pressure during flight and was initially most likely a few meters in size. Presuming that the crater formed because the meteoroid did not undergo significant fragmentation during flight (highly unusual for a stony meteoroid), this suggests the initial object was largely devoid of cracks and well described as a monolith. This result emphasizes the fact that meteoroid strengths and physical properties vary significantly, a conclusion well summarized as indicating there is no “average” meteoroid (e.g., Ceplecha et al., 1998). The Carancas impact demonstrates that contrary to entry models, which predict that stony meteoroids require in excess of 10 MT of mass to produce high-velocity impact craters on the ground (Bland and Artemieva, 2006), in rare cases much smaller stony objects can impact Earth’s surface hypersonically. As Carancas is the only known example of such a small stony meteorite producing a high-velocity impact crater, it is unclear how common strong (>10 MPa) monolithic meter-sized stony meteoroids are among the NEA population. The energy of formation of the crater was

estimated to be 2–3 t of TNT equivalent (1010 J) based on proximal blast effects (Tancredi et al., 2009) as well as interpretation of the infrasonic signals (Le Pichon et al., 2008; Brown et al., 2008). The crater-forming impact generated a surface wave seismically detected some 50 km from the crater. Based on the estimated crater yield and equivalent seismic magnitude of the surface wave the impact coupling was approximately 0.1%, the first direct measure of crater seismic coupling from an impact (Tancredi et al., 2009). 6.5. Chelyabinsk: The Largest Well-Documented Impact The Chelyabinsk meteorite fall, which occurred in Russia on February 15, 2013, was an event in a fundamentally different category than any other meteorite fall in recent history. It was preceded by an extraordinarily bright superbolide, brighter than the Sun, and accompanied by damaging blast wave. The analysis of the infrasonic, seismic, and satellite data showed that the total energy was ~500  kt TNT, i.e., 2 × 1015 J (Brown et al., 2013a; Popova et al., 2013). This energy is ~30× larger than the energy of the Hiroshima atomic bomb. Although the explosion of an asteroid near the Tunguska River in Siberia in 1908 had much larger energy, estimated to be 5–20 Mt TNT (Vasilyev, 1998; Boslough and Crawford, 2008), no meteorites were recovered. Moreover, only limited data exist about the Tunguska event, which occurred over a very remote region. The Chelyabinsk event, on the other hand, was casually recorded by many video cameras and represented a unique opportunity to study the entry of a body larger than 10 m in size into the atmosphere. From the known energy, entry velocity, and density of the meteorites, the effective diameter of the Chelyabinsk was estimated to be 19 m and the mass was 12,000 t. For such a large initial mass, the mass of material surviving as meteorites was quite small. There was only one large meteorite, which landed in Lake Chebarkul and was later recovered from the lake bottom, having a mass of ~600 kg (Popova et al., 2013). All other meteorites were smaller than 30 kg. Only a few meteorites larger than 1 kg were recovered, although the number of small meteorites was enormous. The total recovered mass is unknown but was probably not larger than 2 t. The percentage of initial mass, which landed as macroscopic (> ~1 cm) fragments, was much smaller than in a typical meteorite fall. It was also smaller than theory predicted for an impacting asteroid of such size (Bland and Artiemeva, 2003, 2006). The analysis of the atmospheric fragmentation revealed that severe destruction of the asteroid occurred between heights 39–30 km, under dynamic pressures of 1–5 MPa. At this early stage 95% of the mass was ablated and converted into dust and small (60%, although most of their data are in Diameter (m) Cumulative Number Impacting Earth Per Annum

Carancas meteoroid, although representing less than 0.01% of the initial mass. These fragmentation pressures are in the same range as found for smaller meteoroids based on observations of the associated fireballs (Popova et al., 2011). This confirms that there is no clear size-strength correlation among stony NEAs over the size range of centimeters to tens of meters. Since the actual strength and thus atmospheric behavior varies from case to case, we do not expect that Chelyabinsk will be representative of all bodies of similar size. Nevertheless, larger bodies are less decelerated, so they are subject to larger pressures when reaching denser atmospheric layers, which may lead to more destructive fragmentation. Some asteroids are believed to be rubble piles/gravitational aggregates with a small strength of ~25  Pa due to van  der  Waals forces between constituent grains (Sánchez and Scheeres, 2014). A priori, we expect rubble-pile meteoroids to separate into their constitutional parts at the very beginning of their atmospheric entry, under pressures of tens to hundreds of pascals. There is no evidence that such a separation occurred in the Chelyabinsk case. Nevertheless, significant loss of mass in the form of dust, probably from the surface layers, started early in flight at heights of >70 km, as demonstrated by the extent of the dust trail deposited in the atmosphere (Borovička et al., 2013b; Popova et al., 2013). The Chelyabinsk case also vividly demonstrates the damage potential of small (tens of meters) NEAs. Although no significant damage was caused by the ground impact, the cylindrical blast wave originating at heights of 25–35  km (Brown et al., 2013a) caused structural damage (one collapsed roof, about 10% of windows broken, many large doors of factory halls fallen). The flying glass and other objects injured 1600 people (Popova et al., 2013).

0.1

106

1

10

105 104 103 102 101 100 10–1 10–2 10–3 10–6

Rabinowitz et al. (2000) NEAT Rabinowitz et al. (2000) Spacewatch Silber et al. (2009 Brown et al. (2002) Harris (2013) Suggs et al. (2014) Halliday et al. (1996) Brown et al. (2013)

10–5

10–4

10–3

10–2

10–1

100

101

102

103

104

Bolide Energy (kT) Fig. 5. Observational estimates of the terrestrial cumulative impact flux (ordinate) as a function of impact energy (abscissa). The light gray line cutting through the plot represents the power-law fit from Brown et al. (2002a) based on satellite impact flash observations (diamonds) approximately representing the interval 0.1–10 kT where data is most complete. The solid circles are an update to these data as given by Brown et al. (2013a) with better statistics at larger sizes for energies >1 kT. Error bars (where shown) represent counting statistics only. These data consist of debiased estimates of the telescopic near-Earth asteroid population and assumed average impact probabilities as given by Rabinowitz et al. (2000) (dark gray squares) from the NEAT survey and Spacewatch (black squares) surveys, where diameters are determined assuming an albedo of 0.1. The LINEAR values at smaller sizes are normalized to early work that established the absolute population for diameters >100 m (Stuart, 2001). Also shown are the estimated impact rate from infrasonic measurements of bolide airbursts from the Air Force Technical Application Centre (AFTAC) acoustic monitoring network as reanalyzed by Silber et al. (2009) (triangles). More recent telescopic debiased estimates from data compiled from all surveys by Harris (2013) are shown as light gray squares. The circles are the equivalent impact rate for Earth as determined from lunar flashes taking into account gravitational focusing (Suggs et al., 2014). Finally, the dark gray line at the top represents the impact rate from the photographic Meteorite Observation and Recovery Project (MORP) clear sky survey as described by Halliday et al. (1996).

274   Asteroids IV the tens of grams mass range, below the level where the Halliday et al. (1996) survey is complete. A larger difference is apparent at the smallest sizes, but the uncertain mass scale in both surveys may be the cause. Due to the rarity of meter-sized impacts (which occur roughly once every two weeks over the entire Earth), groundbased optical systems are not efficient at recording large enough numbers of such events to estimate fluxes. Brown et al. (2002a) used data from spacebased systems to detect impacts on a global scale of multi-meter-sized meteoroids over an eight-year period. Total impact energies were available for 300 events, although individual speeds were not. The resulting cumulative number of impacts per year (N) as a function of energy (E) — in units of kilotons of TNT = 4.18 × 1012 J — was found to follow a power law of the form N = 3.7 E–0.9. This fit is appropriate to energies of 0.1–10 kt or diameters ranging from 1–6 m. An extension to this survey by Brown et al. (2013a) found similar values at these energies, but evidence for fluxes above the power-law curve at larger sizes. Silber et al. (2009) used acoustic records of impacts over a 14-year period to independently estimate fluxes in a similar size range. Their fluxes are systematically higher than the power-law curve from Brown et al. (2002a) but in agreement within uncertainty with the revised values at larger sizes (>6 m) from Brown et al. (2013a). At sizes above 10 m diameter, telescopic population esti‑ mates are widely used to estimate flux. These estimates generally agree well with the extrapolated Brown et al. (2002a) power law, although are somewhat lower than the smallnumber statistic-limited estimates from bolide impacts at these larger sizes. The telescopic survey impact values have underlying uncertainties due to unknown population-wide collision probabilities at smaller sizes and poorly known albedo distribution of smaller NEAs. Given the widely differing sources of uncertainties across all the surveys shown in Fig. 5, the degree of agreement is good. We note that fluxes may also be derived from counting smaller lunar impact craters, and such estimates (e.g., Werner et al., 2002) agree well with the telescopically determined flux curve (Harris, 2013). We chose not to include the estimated flux from small lunar craters due to the controversy surrounding the role and importance of secondary craters at such small sizes (e.g., McEwan and Bierhaus, 2006). Orbital information from telescopic data is only available in quantity for NEAs larger than ~10 m. Unlike the population in the centimeter to tens of centimeter size range, NEA “streams” appear to be non-existent (Schunová et al., 2012), emphasizing both the longer collisional lifetimes of larger NEAs and a probable lack of cometary material among multi-meter-sized bodies. Of the several dozen meter-class impacts recorded in Earth’s atmosphere with orbital and/ or physical information about the strength of the impactor, the majority appear to be stony objects, with only a small number of probable, weak cometary bodies. Only 10% of this impacting population had Tisserand values below 3, emphasizing the likely dominance of asteroidal objects

at these larger sizes. Among the 22 meteorite-producing fireballs, eight appear to have been meter-sized or larger prior to impact. None of these had clearly cometary orbits, although Maribo and Sutter’s Mill (both CM2 carbonaceous chondrites) have orbits similar to 2P/Encke. 8. OPEN QUESTIONS We have shown that bolide observations provide information about physical and chemical properties of asteroidal and cometary fragments in the decimeter to decameter size range; about the processes occurring during their interaction with the atmosphere, including potentially hazardous effects; and about the size-frequency distribution of such events. The obtained pre-impact heliocentric orbits enable the study of likely source regions of meteorites. Nevertheless, there are still open questions that need to be answered by further observations and modeling. In this final section of this chapter, we discuss some of these questions. 8.1. Meteorites from Comets The question of whether some meteorites come from comets has been discussed for a long time (e.g., Öpik, 1968; Padevět and Jakeš, 1993; Campins and Swindle, 1998; Lodders and Osborne, 1999; Gounelle et al., 2008). Some of the earlier studies were motivated by the apparent difficulty of transferring meteoroids from the asteroid belt to Earth, a problem that has now been solved [by orbital resonances and the Yarkovsky effect (see Morbidelli et al., 2002; Bottke et al., 2002b)]. Nevertheless, it was proposed that cometary nuclei may also contain — in addition to ice and dust —macroscopic boulders similar to carbonaceous asteroidal material, e.g., in the “icy-glue” model of Gombosi and Houpis (1986). Although other cometary models seem to be more probable (Weissman and Lowry, 2008), the presence of chondrule-like material in the samples of Comet  81P/Wild  2 returned by the Stardust mission (Nakamura et al., 2008) suggests that material that formed meteorites is present in comets as well, at least in small samples. None of the known meteorite orbits is clearly cometary, although the orbits of Maribo and possibly also Sutter’s Mill are close to the transition between cometary and asteroidal orbits. The carbonaceous chondrites, in particular types CI and CM, would be the primary candidates for cometary origin. These meteorites have been hydrated, while cometary dust is anhydrous, but Gounelle et al. (2008) argued that hydration can occur in cometary interiors. Gounelle et al. (2006) computed the orbit of the Orgueil CI1 meteorite, which fell in France in 1864, and concluded that the aphelion probably lay beyond the orbit of Jupiter. As determination of the orbit was based on visual observations and there is no direct velocity information available, the assumptions about the orbit cannot be completely trustworthy. Trigo-Rodríguez et al. (2009) observed a deeply penetrating fireball (no meteorites were found) and concluded that the orbit was similar to that

Borovička et al.:  Small Near-Earth Asteroids as a Source of Meteorites   275

of Comet C/1919 Q2 Metcalf. Their paper, however, contains a numerical error in orbit computation. When corrected, the orbit is no more similar to the orbit of Comet  Metcalf, although the aphelion still lies beyond Jupiter. However, the orbit is highly sensitive to the value of initial velocity, which was difficult to measure in that particular case. A small change of velocity will make the orbit completely asteroidal. So there remains no clear, unambiguous example of a cometary meteorite fall. 8.2. Meteorites from Meteor Showers Meteor showers are caused by meteoroids of a common origin, in most cases cometary. For many showers, the meteorite survival is hampered by high entry velocity. Until recently, 30 km s–1 was considered a practical upper velocity limit for the occurrence of a meteorite fall (Ceplecha et al., 1998). The fact that the Maribo meteorite almost reached this limit and was made from a soft material suggests that the actual limit may be higher. Some of the low-velocity meteor showers, like the 23.5 km s–1 Draconids originating from Comet  21P/Giacobini-Zinner, contain, however, such fragile material that survival is excluded (Borovička et al., 2007). On the other hand, the Taurid meteor shower (entry speeds ~26–30 km s–1) contains both fragile and strong bodies, some of which seem to be capable of producing meteorites (Brown et al., 2013b). The principal parent body of Taurids is supposed to be Comet 2P/Encke, a comet on a peculiar orbit completely inside Jupiter’s orbit. Both Taurids and Comet 2P/ Encke may be part of a broader “Taurid complex,” which also contains several other showers and possibly several NEAs (see Jenniskens, 2006). Because of this it may be difficult in individual cases to link bolides directly with Comet 2P/Encke. The Geminid shower, on the other hand, is well defined and is one of the most active annual showers. The entry speed is 36 km s–1 and the parent body is (3200) Phaethon, which orbits in the inner solar system and closely approaches the Sun (q  = 0.14 AU, a  = 1.27 AU, i  = 22°). Recently it has been classified as an active asteroid (Jewitt, 2012; Jewitt et al., 2013). Based on the reflectance spectroscopy, asteroid (2) Pallas was identified as the likely parent body of Phaethon (de León et al., 2010). Geminid meteoroids have been known to be relatively dense and strong (e.g., Babadzhanov, 2002; Brown et al., 2013b), but only recently has it been demonstrated that a meteorite-dropping Geminid could occur, although the meteorite was not found (Spurný and Borovička, 2013; Spurný et al., in preparation). Madiedo et al. (2013b) presented similar observations concerning Gemind meteorite survival, but their data were less robust. The recovery of a meteorite originating from Phaethon would undoubtedly be a major milestone. 8.3. Meteorite Streams The very close similarity of orbits of the Příbram and Neuschwanstein meteorites (Spurný et al., 2003) suggested

that they may have a common origin and be part of a meteorite stream. A similar pairing was proposed earlier for the Innisfree meteorite and the Ridgedale bolide (Halliday, 1987). The idea of meteorite streams was also discussed from another perspective by Lipschutz et al. (1997). Meteorite streams are potentially formed by asteroidal collisions. The orbit of Chelyabinsk meteorites was found to be similar to the orbit of asteroid (86039) 1999 NC43, suggesting that the Chelyabinsk body could have been ejected from 1999 NC43 by a collision (Borovička et al., 2013b). In that case, a meteorite stream could exist in Chelyabinsk orbit. However, the typical decoherence time of meteoroid streams in the near-Earth region is only 104–105 yr (Pauls and Gladman, 2005), while the estimated collisional lifetime of asteroids is much longer (Bottke at al., 2005). Meteorite streams should be therefore rare, although some may be expected to exist (Jones and Williams, 2008). In the Příbram-Neuschwanstein case, the search for a related shower of fainter meteors was negative (Koten et al., 2014), implying that the stream, if it exists, contains only large bodies. For Chelyabinsk, the reflectance spectra of the meteorites and 1999 NC43 do not match well, so the association seems to be unlikely (Reddy et al., 2015). Direct evidence of a meteorite stream or an association of a meteorite with its immediate parent body is therefore still missing. Near-Earth asteroids have been also associated with (often unconvincingly) meteor showers or individual fireballs, not necessarily meteorite dropping (e.g., Babadzhanov et al., 2012; Madiedo et al., 2014b, and references therein). If some of these associations are real, they may indicate that the respective NEAs are in fact extinct comets and the stream was formed by cometary activity. 8.4. Structure of Meteoroids and Details of Their Interaction with the Atmosphere The internal structure of meteoroids and their bulk densities are still difficult to infer from bolide observation. Data interpretation is complicated by the fact that the values of luminous efficiencies are not reliably known and the process of meteoroid ablation and fragmentation is not understood in detail. In particular, the structure and frequency of mixed-type meteoroids like Almahata Sitta and Benešov is unknown. There are also unexplained phenomena like periodic variations and high-frequency flickering on fireball light curves (Spurný and Ceplecha, 2008) (see also Fig. 3), large lateral velocities of fragments (Borovička and Kalenda, 2003; Borovička et al., 2013b; Stokan and Campbell-Brown, 2014), and jet-like features on fireball images at high altitudes (Spurný et al., 2000). Acknowledgments. This work was supported by grant no. P209/11/1382 from the Grantová agentura České republiky (GAČR), Praemium Academiae of the Czech Academy of Sciences, the Czech institutional project RVO:67985815, NASA cooperative agreement NNX11AB76A, the Natural Sciences and Engineering Research Council of Canada, and the Canada Research Chairs program.

276   Asteroids IV REFERENCES Artemieva N. A. and Shuvalov V. V. (2001) Motion of a fragmented meteoroid through the planetary atmosphere. J. Geophys. Res., 106, 3297–3310. Babadzhanov P. B. (2002) Fragmentation and densities of meteoroids. Astron. Astrophys., 384, 317–321. Babadzhanov P. B., Williams I. P., and Kokhirova G. I. (2012) NearEarth object 2004CK39 and its associated meteor showers. Mon. Not. R. Astron. Soc., 420, 2546–2550. Baldwin B. and Sheaffer Y. (1971) Ablation and breakup of large meteoroids during atmospheric entry. J. Geophys. Res., 76, 4653–4668. Beech M., Coulson I. M., Nie W., and McCausland P. (2009) The thermal and physical characteristics of the Gao-Guenie (H5) meteorite. Planet. Space Sci., 57, 764–770. Biberman L. M., Bronin S. Y., and Brykin M. V. (1980) Moving of a blunt body through the dense atmosphere under conditions of severe aerodynamic heating and ablation. Acta Astronaut., 7, 53–65. Bischoff A., Horstmann M., Pack A., Laubenstein M., and Haberer S. (2010) Asteroid 2008 TC3 — Almahata Sitta: A spectacular breccia containing many different ureilitic and chondritic lithologies. Meteoritics & Planet. Sci., 47, 1638–1656. Bischoff A., Jersek M., Grau T., Mirtic B., Ott U., Kučera J., Horstmann M., Laubenstein M., Herrmann S., Řanda Z., Weber M., and Heusser G. (2011) Jesenice — A new meteorite fall from Slovenia. Meteoritics & Planet. Sci., 46, 793–804. Bischoff A., Dyl K. A., Horstmann M., Ziegler K., Wimmer K., and Young E. D. (2013) Reclassification of Villalbeto de la Peña — Occurrence of a winonaite-related fragment in a hydrothermally metamorphosed polymict L-chondritic breccia. Meteoritics & Planet. Sci., 48, 628–640. Bland P. A. and Artiemeva N. A. (2003) Efficient disruption of small asteroids by Earth’s atmosphere. Nature, 424, 288–291. Bland P. A. and Artemieva N. (2006) The rate of small impacts on Earth. Meteoritics & Planet. Sci., 41, 607–631. Bland P. A. and 17 colleagues (2009) An anomalous basaltic meteorite from the innermost main belt. Science, 325, 1525–1527. Bland P. A., Spurný P., Bevan A. W. R., Howard K. T., Towner M. C., Benedix G. K., Greenwood R. C., Shrbený L., Franchi I. A., Deacon G., Borovička J., Ceplecha Z., Vaughan D., and Hough R. M. (2012) The Australian Desert Fireball Network: A new era for planetary science. Aust. J. Earth Sci., 59, 177–187. Borovička J. (1990) The comparison of two methods of determining meteor trajectories from photographs. Bull. Astron. Inst. Czech., 41, 391–396. Borovička J. (1993) A fireball spectrum analysis. Astron. Astrophys., 279, 627–645. Borovička J. (1994a) Two components in meteor spectra. Planet. Space Sci., 42, 145–150. Borovička J. (1994b) Line identifications in a fireball spectrum. Astron. Astrophys. Suppl., 103, 83–96. Borovička J. (2005) Spectral investigation of two asteroidal fireballs. Earth Moon Planets, 97, 279–293. Borovička J. (2014) The analysis of casual video records of fireballs. In Proceedings of the International Meteor Conference, Poznań, Poland August 22–25, 2013 (M. Gyssens et al., eds.), pp. 101–105. International Meteor Organization, Mechelen, Belgium. Borovička J. and Ceplecha Z. (1992) Earth-grazing fireball of October 13, 1990. Astron. Astrophys., 257, 323–328. Borovička J. and Charvát Z. (2009) Meteosat observation of the atmospheric entry of 2008 TC3 over Sudan and the associated dust cloud. Astron. Astrophys., 507, 1015–1022. Borovička J. and Kalenda P. (2003) The Morávka meteorite fall: 4. Meteoroid dynamics and fragmentation in the atmosphere. Meteoritics & Planet. Sci., 38, 1023–1043. Borovička J. and Spurný P. (1996) Radiation study of two very bright terrestrial bolides and an application to the Comet S-L 9 collision with Jupiter. Icarus, 121, 484–510. Borovička J. and Spurný P. (2008) The Carancas meteorite impact — Encounter with a monolithic meteoroid. Astron. Astrophys., 485, L1–L4. Borovička J., Spurný P., and Keclíkova J. (1995) A new positional astrometric method for all-sky cameras. Astron. Astrophys. Suppl., 112, 173–178.

Borovička J., Popova O. P., Nemchinov I. V., Spurný P., and Ceplecha Z. (1998) Bolides produced by impacts of large meteoroids into the Earth’s atmosphere: Comparison of theory with observations I. Benešov bolide dynamics and fragmentation. Astron. Astrophys., 334, 713–728. Borovička J., Spurný P., Kalenda P., and Tagliaferri E. (2003) The Morávka meteorite fall: 1. Description of the events and determination of the fireball trajectory and orbit from video records. Meteoritics & Planet. Sci., 38, 975–987. Borovička J., Spurný P., and Koten P. (2007) Atmospheric deceleration and light curves of Draconid meteors and implications for the structure of cometary dust. Astron. Astrophys., 473, 661–672. Borovička J., Tóth J., Igaz A., Spurný P., Kalenda P., Haloda J., Svoreň J., Kornoš L., Silber E., Brown P., and Husárik M. (2013a) The Košice meteorite fall: Atmospheric trajectory, fragmentation, and orbit. Meteoritics & Planet. Sci., 48, 1757–1779. Borovička J., Spurný P., Brown P., Wiegert P., Kalenda P., Clark D., and Shrbený L. (2013b) The trajectory, structure and origin of the Chelyabinsk asteroidal impactor. Nature, 503, 235–237. Borovička J., Spurný P., Šegon D., Andreic Ž., Kac J., Korlević K., Atanackov J., Kladnik G., Mucke H., Vida D., and Novoselnik F. (2015) The instrumentally recorded fall of the Križevci meteorite, Croatia, February 4, 2011. Meteoritics & Planet. Sci., 50, 1244–1259. Boslough M. B. E. and Crawford D. A. (2008) Low-altitude airbursts and the impact threat. Intl. J. Impact Eng., 35, 1441–1448. Bottke W. F., Morbidelli A., Jedicke R., Petit J.-M., Levison H. F., Michel P., and Metcalfe T. S. (2002a) Debiased orbital and absolute magnitude distribution of the near-Earth objects. Icarus, 156, 399–433. Bottke W. F. Jr., Vokrouhlický D., Rubincam D. P., and Brož M. (2002b) The effect of Yarkovsky thermal forces on the dynamical evolution of asteroids and meteoroids. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 395–408. Univ. of Arizona, Tucson. Bottke W. F., Durda D. D., Nesvorný D., Jedicke R., Morbidelli A., Vokrouhlický D., and Levison H. F. (2005) Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion. Icarus, 179, 63–94. (Erratum: Icarus, 183, 235–236.) Bronshten V. A. (1983) Physics of Meteoric Phenomena. Reidel, Dordrecht. 356 pp. (Originally published in Russian, 1981, Nauka, Moscow.) Brown P. G., Ceplecha Z., Hawkes R. L., Wetherill G. W., Beech M., and Mossman K. (1994) The orbit and atmospheric trajectory of the Peekskill meteorite from video records. Nature, 367, 624–626. Brown P. G. and 21 colleagues (2000) The fall, recovery, orbit, and composition of the Tagish Lake meteorite: A new type of carbonaceous chondrite. Science, 290, 320–325. Brown P., Spalding R. E., ReVelle D. O., Tagliaferri E., and Worden S. P. (2002a) The flux of small near-Earth objects colliding with the Earth. Nature, 420, 294–296. Brown P. G., Revelle D. O., Tagliaferri E., and Hildebrand A. R. (2002b) An entry model for the Tagish Lake fireball using seismic, satellite and infrasound records. Meteoritics & Planet. Sci., 37, 661–676. Brown P. G., Pack D., Edwards W. N., Revelle D. O., Yoo B. B., Spalding R. E., and Tagliaferri E. (2004) The orbit, atmospheric dynamics, and initial mass of the Park Forest meteorite. Meteoritics & Planet. Sci., 39, 1781–1796. Brown P., ReVelle D. O., Silber E. A., Edwards W. N., Arrowsmith S., Jackson L. E., Tancredi G., and Eaton D. (2008) Analysis of a craterforming meteorite impact in Peru. J. Geophys. Res.–Planets, 113, E09007, DOI: 10.1029/2008JE003105. Brown P., Weryk R. J., Kohut S., Edwards W. N., and Krzeminski Z. (2010) Development of an all-sky video meteor network in Southern Ontario, Canada: The ASGARD system. WGN, J. Intl. Meteor Org., 38, 25–30. Brown P., McCausland P. J. A., Fries M., Silber E., Edwards W. N., Wong D. K., Weryk R. J., Fries J., and Krzeminski Z. (2011) The fall of the Grimsby meteorite — I: Fireball dynamics and orbit from radar, video, and infrasound records. Meteoritics & Planet. Sci., 46, 339–363. Brown P. G. and 32 colleagues (2013a) A 500-kiloton airburst over Chelyabinsk and an enhanced hazard from small impactors. Nature, 503, 238–241. Brown P., Marchenko V., Moser D. E., Weryk R., and Cooke W. (2013b) Meteorites from meteor showers: A case study of the Taurids. Meteoritics & Planet. Sci., 48, 270–288.

Borovička et al.:  Small Near-Earth Asteroids as a Source of Meteorites   277 Caffee M. and Nishiizumi K. (1997) Exposure ages of carbonaceous chondrites — II. Meteoritics & Planet. Sci., Suppl., 32, A26. Campins H. and Swindle T. D. (1998) Expected characteristics of cometary meteorites. Meteoritics & Planet. Sci., 33, 1201–1211. Ceplecha Z. (1961) Multiple fall of Příbram meteorites photographed. 1. Double-station photographs of the fireball and their relations to the found meteorites. Bull. Astron. Inst. Czech., 12, 21–47. Ceplecha Z. (1971) Spectral data on terminal flare and wake of doublestation meteor No. 38421 (Ondřejov, April 21, 1963). Bull. Astron. Inst. Czech., 22, 219–304. Ceplecha Z. (1979) Earth-grazing fireballs. The daylight fireball of Aug. 10, 1972. Bull. Astron. Inst. Czech., 30, 349–356. Ceplecha Z. (1986) Photographic fireball networks. In Asteroids, Comets, Meteors II (C.-I. Lagerkvist et al., eds.), pp. 575–582. Astronomiska Observatoriet Uppsala, Sweden. Ceplecha Z. (1987) Geometric, dynamic, orbital and photometric data on meteoroids from photographic fireball networks. Bull. Astron. Inst. Czech., 38, 222–234. Ceplecha Z. (1988) Earth’s influx of different populations of sporadic meteoroids from photographic and television data. Bull. Astron. Inst. Czech., 39, 221–236. Ceplecha Z. (1996) Luminous efficiency based on photographic observations of the Lost City fireball and implications for the influx of interplanetary bodies onto Earth. Astron. Astrophys., 311, 329–332. Ceplecha Z. (2007) Fragmentation model analysis of the observed atmospheric trajectory of the Tagish Lake fireball. Meteoritics & Planet. Sci., 42, 185–189. Ceplecha Z. and McCrosky R. E. (1976) Fireball end heights  — A diagnostic for the structure of meteoric material. J. Geophys. Res., 81, 6257–6275. Ceplecha Z. and Rajchl J. (1965) Programme of fireball photography in Czechoslovakia. Bull. Astron. Inst. Czech., 16, 15–22. Ceplecha Z. and ReVelle D. O. (2005) Fragmentation model of meteoroid motion, mass loss, and radiation in the atmosphere. Meteoritics & Planet. Sci., 40, 35–50. Ceplecha Z., Ježková M., Boček J., Kirsten T., and Kiko J. (1973) Data on three significant fireballs photographed within the European network in 1971. Bull. Astron. Inst. Czech., 24, 13–21. Ceplecha Z., Spurný P., Borovička J., and Keclíková J. (1993) Atmospheric fragmentation of meteoroids. Astron. Astrophys., 279, 615–626. Ceplecha Z., Brown P. G., Hawkes R. L., Wetherill G. W., Beech M., and Mossman K. (1996) Video observations, atmospheric path, orbit and fragmentation record of the fall of the Peekskill meteorite. Earth Moon Planets, 72, 395–404. Ceplecha Z., Borovička J., Elford W. G., Revelle D. O., Hawkes R. L., Porubčan V., and Šimek M. (1998) Meteor phenomena and bodies. Space Sci. Rev., 84, 327–471. Ceplecha Z., Spalding R. E., Jacobs C. F., ReVelle D. O., Tagliaferri E., and Brown P. G. (1999) Superbolides. In Meteoroids 1998 (W. J. Baggaley and V. Porubčan, eds.), pp. 37–54. Astronomical Institute of the Slovak Academy of Sciences, Tatranská Lomnica. Chesley S. R., Farnocchia D., Brown P. G., and Chodas P. W. (2015) Orbit estimation for late warning asteroid impacts: The case of 2014 AA. In Aerospace Conference, 2015 IEEE , 8 pp., 7–14 March 2015, DOI: 10.1109/AERO.2015.7119148. Christie D. R. and Campus P. (2010) The IMS Infrasound Network: Design and establishment of infrasound stations. In Infrasound Monitoring for Atmospheric Studies (A. Le Pichon et al., eds.), pp. 29–77. Springer, Berlin. Clark D. L. and Wiegert P. A. (2011) A numerical comparison with the Ceplecha analytical meteoroid orbit determination method. Meteoritics & Planet. Sci., 46, 1217–1225. Close S., Brown P., Campbell-Brown M., Oppenheim M., and Colestock P. (2007) Meteor head echo radar data: Mass-velocity selection effects. Icarus, 186, 547–556. Consolmagno G. J., Schaefer M. W., Schaefer B. E., Britt D. T., Macke R. J., Nolan M. C., and Howell E. S. (2013) The measurement of meteorite heat capacity at low temperatures using liquid nitrogen vaporization. Planet. Space Sci., 87, 146–156. Cooke W. J.and Moser D. E. (2012) The status of the NASA All Sky Fireball Network. In Proceedings of the International Meteor Conference, Sibiu, Romania, 15–18 Sept., 2011 (M. Gyssens and P. Roggemans, eds.), pp. 9–12. International Meteor Organization, Mechelen, Belgium. Daubar I. J., McEwen A. S., Byrne S., Kennedy M. R., and Ivanov B. (2013) The current martian cratering rate. Icarus, 225, 506–516.

de León J., Campins H., Tsiganis K., Morbidelli A., and Licandro J. (2010) Origin of the near-Earth asteroid Phaethon and the Geminids meteor shower. Astron. Astrophys., 513, A26. Dodd R. T. (1981) Meteorites, a Petrologic-Chemical Synthesis. Cambridge Univ., Cambridge. 368 pp. Edwards W. N. (2010) Meteor generated infrasound: Theory and observation. In Infrasound Monitoring for Atmospheric Studies (A. Le Pichon et al., eds.), pp. 361–414. Springer, Berlin. Edwards W. N., Eaton D. W., and Brown P. G. (2008) Seismic observations of meteors: Coupling theory and observations. Rev. Geophys., 46, Article ID 4007, 1–21. Ens T. A., Brown P. G., Edwards W. N., and Silber E. A. (2012) Infrasound production by bolides: A global statistical study. J. Atmos. Solar Terr. Phys., 80, 208–229. Eugster O., Herzog G. F., Marti K., and Caffee M. W. (2006) Irradiation records, cosmic-ray exposure ages, and transfer times of meteorites. In Meteorites and the Early Solar System II (D. S. Lauretta and H. Y. McSween Jr., eds.), pp. 829–851. Univ. of Arizona, Tucson. Fairén A. G. and 15 colleagues (2011) Meteorites at Meridiani Planum provide evidence for significant amounts of surface and near-surface water on early Mars. Meteoritics & Planet. Sci., 46, 1832–1841. Fessenkow V. G., Huzarski R. G., and La Paz L. (1954) On the origin of meteorites. Meteoritics, 1, 208–227. Fries M. and Fries J. (2010) Doppler weather radar as a meteorite recovery tool. Meteoritics & Planet. Sci., 45, 1476–1487. Gayon-Markt J., Delbo M., Morbidelli A., and Marchi S. (2012) On the origin of the Almahata Sitta meteorite and 2008 TC3 asteroid. Mon. Not. R. Astron. Soc., 424, 508–518. Genge M. J. and Grady M. M. (1999) The fusion crusts of stony meteorites: Implications for the atmospheric reprocessing of extraterrestrial materials. Meteoritics & Planet. Sci., 34, 341–356. Golub’ A. P., Kosarev I. B., Nemchinov I. V., and Shuvalov V. V. (1996) Emission and ablation of a large meteoroid in the course of its motion through the Earth’s atmosphere. Solar System Res., 30, 183–197. Gombosi T. I. and Houpis H. L. F. (1986) An icy-glue model of cometary nuclei. Nature, 324, 43–44. Goodrich C. A., Hartmann W. K., O’Brien D. P., Weidenschilling S. J., Wilson L., Michel P., and Jutzi M. (2015) Origin and history of ureilitic material in the solar system: The view from asteroid 2008 TC3 and the Almahata Sitta meteorite. Meteoritics & Planet. Sci., 50, 782–809, DOI: 10.1111/maps.12401. Gorkavyi N., Rault D. F., Newman P. A., Silva A. M., and Dudorov A. E. (2013) New stratospheric dust belt due to the Chelyabinsk bolide. Geophys. Res. Lett., 40, 4728–4733. Gounelle M., Spurný P., and Bland P. A. (2006) The orbit and atmospheric trajectory of the Orgueil meteorite from historical records. Meteoritics & Planet. Sci., 41, 135–150. Gounelle M., Morbidelli A., Bland P. A., Spurný P., Young E. D., and Sephton M. (2008) Meteorites from the outer solar system? In The Solar System Beyond Neptune (M. A. Barucci et al., eds.), pp. 525– 541. Univ. of Arizona, Tucson. Gritsevich M. I. (2009) Determination of parameters of meteor bodies based on flight observational data. Adv. Space Res., 44, 323–334. Gural P. S. (2012) A new method of meteor trajectory determination applied to multiple unsynchronized video cameras. Meteoritics & Planet. Sci., 47, 1405–1418. Haack H., Grau T., Bischoff A., Horstmann M., Wasson J., Sørensen A., Laubenstein M., Ott U., Palme H., Gellissen M., Greenwood R. C., Pearson V. K., Franchi I. A., Gabelica Z., and Schmitt-Kopplin P. (2012) Maribo — A new CM fall from Denmark. Meteoritics & Planet. Sci., 47, 30–50. Halliday I. (1961) A study of spectral line identifications in Perseid meteor spectra. Publ. Dom. Obs. (Ottawa), 25, 3–16. Halliday I. (1973) Photographic fireball networks. In Evolutionary and Physical Properties of Meteoroids (C. L. Hemenway et al., eds.), pp. 1–8. NASA Spec. Publ. 319, Washington, DC. Halliday I. (1987) Detection of a meteorite ‘stream’ — Observations of a second meteorite fall from the orbit of the Innisfree chondrite. Icarus, 69, 550–556. (Erratum: Icarus, 72, 239.) Halliday I., Blackwell A. T., and Griffin A. A. (1978) The Innisfree meteorite and the Canadian camera network. J. R. Astron. Soc. Can., 72, 15–39. Halliday I., Griffin A., and Blackwell A. T. (1981) The Innisfree meteorite fall — A photographic analysis of fragmentation, dynamics and luminosity. Meteoritics, 16, 153–170.

278   Asteroids IV Halliday I., Blackwell A. T., and Griffin A. A. (1989a) The typical meteorite event, based on photographic records of 44 fireballs. Meteoritics, 24, 65–72. Halliday I., Blackwell A. T., and Griffin A. A. (1989b) The flux of meteorites on the Earth’s surface. Meteoritics, 24, 173–178. Halliday I., Blackwell A. T., and Griffin A. A. (1990) Evidence for the existence of groups of meteorite-producing asteroidal fragments. Meteoritics, 25, 93–99. Halliday I., Griffin A. A., and Blackwell A. T. (1996) Detailed data for 259 fireballs from the Canadian camera network and inferences concerning the influx of large meteoroids. Meteoritics & Planet. Sci., 31, 185–217. Harris A. (2013) The value of enhanced NEO surveys. Planetary Defense Conference, IAA-PDC13-05-09. Hildebrand A. R., McCausland P. J. A., Brown P. G., Longstaffe F. J., Russell S. D. J., Tagliaferri E., Wacker J. F., and Mazur M. J. (2006) The fall and recovery of the Tagish Lake meteorite. Meteoritics & Planet. Sci., 41, 407–431. Hildebrand A. R. and 11 colleagues (2009) Characteristics of a bright fireball and meteorite fall at Buzzard Coulee, Saskatchewan, Canada, November 20, 2008. Lunar Planet. Sci. XL, Abstract #2505. Lunar and Planetary Institute, Houston. Hill K. A., Rogers L. A., and Hawkes R. L. (2005) High geocentric velocity meteor ablation. Astron. Astrophys., 444, 615–624. Hiroi T., Jenniskens P., Bishop J. L., Shatir T. S. M., Kudoda A. M., and Shaddad M. H. (2010) Bidirectional visible-NIR and biconical FT-IR reflectance spectra of Almahata Sitta meteorite samples. Meteoritics & Planet. Sci., 45, 1836–1845. Holsapple K. (1993) The scaling of impact processes in planetary sciences. Annu. Rev. Earth Planet. Sci., 21, 333–373. Holsapple K. (2009) On the strength of the small bodies of the solar system: A review of strength theories and their implementation for analyses of impact disruption. Planet. Space Sci., 57, 127–141. Horstmann M. and Bischoff A. (2014) The Almahata Sitta polymict breccia and the late accretion of asteroid 2008 TC3. Chem. Erde– Geochem., 74, 149–183. Hueso R. and 23 colleagues (2013) Impact flux on Jupiter: From superbolides to large-scale collisions. Astron. Astrophys., 560, A55. Hutchison R. (2004) Meteorites, a Petrologic, Chemical and Isotopic Synthesis. Cambridge Univ., Cambridge. 511 pp. Hutson M., Ruzicka A., Jull A. J., Smaller J. E., and Brown R. (2013) Stones from Mohave County, Arizona: Multiple falls in the “Franconia strewn field.” Meteoritics & Planet. Sci., 48, 365–389. Jenniskens P. (2006) Meteor Showers and Their Parent Comets. Cambridge Univ., Cambridge. 790 pp. Jenniskens P. (2007) Quantitative meteor spectroscopy: Elemental abundances. Adv. Space Res., 39, 491–512. Jenniskens P. and 34 colleagues (2009) The impact and recovery of asteroid 2008 TC3. Nature, 458, 485–488. Jenniskens P., Vaubaillon J., Binzel R. P., DeMeo F. E., Nesvorný D., Bottke W. F., Fitzsimmons A., Hiroi T., Marchis F., Bishop J. L., Vernazza P., Zolensky M. E., Herrin J. S., Welten K. C., Meier M. M. M., and Shaddad M. H. (2010) Almahata Sitta (=asteroid 2008 TC3) and the search for the ureilite parent body. Meteoritics & Planet. Sci., 45, 1590–1617. Jenniskens P. and 69 colleagues (2012) Radar-enabled recovery of the Sutter’s Mill meteorite, a carbonaceous chondrite regolith breccia. Science, 338, 1583–1587. Jenniskens P. and 47 colleagues (2014) Fall, recovery and characterization of the Novato L6 chondrite breccia. Meteoritics & Planet. Sci., 49, 1388–1425. Jewitt D. (2012) The active asteroids. Astron. J., 143, 66. Jewitt D., Li J., and Agarwal J. (2013) The dust tail of asteroid (3200) Phaethon. Astrophys. J. Lett., 771, L36. Jones D. C. and Williams I. P. (2008) High inclination meteorite streams can exist. Earth Moon Planets, 102, 35–46. Jones J., Brown P., Ellis K. J., Webster A. R., Campbell-Brown M., Krzemenski Z., and Weryk R. J. (2005) The Canadian Meteor Orbit Radar: System overview and preliminary results. Planet. Space Sci., 53, 413–421. Keay C. S. L. (1992) Electrophonic sounds from large meteor fireballs. Meteoritics, 27, 144–148. Kero J., Szasz C., Nakamura T., Meisel D. D., Ueda M., Fujiwara Y., Terasawa T., Miyamoto H., and Nishimura K. (2011) First results from the 2009–2010 MU radar head echo observation programme for sporadic and shower meteors: The Orionids 2009. Mon. Not. R. Astron. Soc., 416, 2550–2559.

Keuer, D., Singer, W. and Stober G. (2009) Signatures of the ionization trail of a fireball observed in the HF, and VHF range above middleEurope on Jan 17, 2009. In Proceedings of the 12th Workshop on Technical and Scientific Aspects of MST Radar (N. Swarnalingham and W. K. Hocking, eds.), p. 154–158. Kimberley J. and Ramesh K. T. (2011) The dynamic strength of an ordinary chondrite. Meteoritics & Planet. Sci., 46, 1653–1669. Klekociuk A. R., Brown P. G., Pack D. W., Revelle D. O., Edwards W. N., Spalding R. E., Tagliaferri E., Yoo B. B., and Zagari J. (2005) Meteoritic dust from the atmospheric disintegration of a large meteoroid. Nature, 436, 1132–1135. Kohout T., Jenniskens P., Shaddad M. H., and Haloda J. (2010) Inhomogeneity of asteroid 2008 TC3 (Almahata Sitta meteorites) revealed through magnetic susceptibility measurements. Meteoritics & Planet. Sci., 45, 1778–1788. Kohout T., Kiuru R., Montonen M., Scheirich P., Britt D., Macke R., and Consolmagno G. (2011) Internal structure and physical properties of the asteroid 2008 TC3 inferred from a study of the Almahata Sitta meteorites. Icarus, 212, 697–700. Kokhirova G. I., Babadzhanov P. B., and Khamorev U. Kh. (2015) Tajikistan Fireball Network and results of photographic observations. Solar System Res., 49, 275–283. Koten P., Vaubaillon J., Čapek D., Vojáček V., Spurný P., Štork R., and Colas F. (2014) Search for faint meteors on the orbits of Příbram and Neuschwanstein meteorites. Icarus, 239, 244–252. Kozubal M. J., Gasdia F. W., Dantowitz R. F., Scheirich P., and Harris A. W. (2011) Photometric observations of Earth-impacting asteroid 2008 TC3. Meteoritics & Planet. Sci., 46, 534–542. Lauretta D. S. and McSween H. Y. Jr., eds. (2006) Meteorites and the Early Solar System II. Univ. of Arizona, Tucson. 943 pp. Le Pichon A., Antier K., Cansi Y., Hernandez B., Minaya E., Burgoa B., Drob D., Evers L. G., and Vaubaillon J. (2008) Evidence for a meteoritic origin of the September 15, 2007, Carancas crater. Meteoritics & Planet. Sci., 43, 1797–1809. Leya I. and Masarik J. (2009) Cosmogenic nuclides in stony meteorites revisited. Meteoritics & Planet. Sci., 44, 1061–1086. Lipschutz M. E., Wolf S. F., and Dodd R. T. (1997) Meteoroid streams as sources for meteorite falls: A status report. Planet. Space Sci., 45, 517–523. Lodders K. and Osborne R. (1999) Perspectives on the comet-asteroidmeteorite link. Space Sci. Rev., 90, 289–297. Llorca J., Trigo-Rodríguez J. M., Ortiz J. L., Docobo J. A., GarcíaGuiea J., Castro-Tirado A. J., Rubin A. E., Eugster O., Edwards W., Laubenstein M., and Casanova I. (2005) The Villalbeto de la Peña meteorite fall: I. Fireball energy, meteorite recovery, strewn field, and petrography. Meteoritics & Planet. Sci., 40, 795–804. Macke R. J., Consolmagno G. J., and Britt D. T. (2011) Density, porosity, and magnetic susceptibility of carbonaceous chondrites. Meteoritics & Planet. Sci., 46, 1842–1862. Madiedo J. M., Trigo-Rodríguez J. M., Ortiz J. L., Castro-Tirado A. J., Pastor S., de los Reyes J. A., and Cabrera-Caño J. (2013a) Spectroscopy and orbital analysis of bright bolides observed over the Iberian Peninsula from 2010 to 2012. Mon. Not. R. Astron. Soc., 435, 2023–2032. Madiedo J. M., Trigo-Rodríguez J. M., Castro-Tirado A. J., Ortiz J. L., and Cabrera-Caño J. (2013b) The Geminid meteoroid stream as a potential meteorite dropper: A case study. Mon. Not. R. Astron. Soc., 436, 2818–2823. Madiedo J. M., Ortiz J. L., Trigo-Rodríguez J. M., Zamorano J., Konovalova N., Castro-Tirado A. J., Ocaña F., de Miguel A. S., Izquierdo J., and Cabrera-Caño J. (2014a) Analysis of two superbolides with a cometary origin observed over the Iberian Peninsula. Icarus, 233, 27–35. Madiedo J. M., Trigo-Rodríguez J. M., Ortiz J. L., Castro-Tirado A. J., and Cabrera-Caño J. (2014b) Bright fireballs associated with the potentially hazardous asteroid 2007LQ19. Mon. Not. R. Astron. Soc., 443, 1643–1650. McCrosky R. E. and Boeschenstein H. Jr. (1965) The Prairie Meteorite Network. SAO Spec. Rept. 173, Smithsonian Astrophysical Observatory, Cambridge. 23 pp. McCrosky R. E., Posen A., Schwartz G., and Shao C.-Y. (1971) Lost City meteorites, its recovery and a comparison with other fireballs. J. Geophys. Res., 76, 4090–4108. McEwen A. S. and Bierhaus E. B. (2006) The importance of secondary cratering to age constraints on planetary surfaces. Annu. Rev. Earth Planet. Sci., 34, 535–567.

Borovička et al.:  Small Near-Earth Asteroids as a Source of Meteorites   279 Megner L., Siskind D. E., Rapp M., and Gumbel J. (2008) Global and temporal distribution of meteoric smoke: A two-dimensional simulation study. J. Geophys. Res., 113, D03202. Meier M. M. M., Welten K. C., Caffee M. W., Friedrich J. M., Jenniskens P., Nishiizumi K., Shaddad M. H., and Wieler R. (2012) A noble gas and cosmogenic radionuclide analysis of two ordinary chondrites from Almahata Sitta. Meteoritics & Planet. Sci., 47, 1075–1086. Milley E. P. (2010) Physical properties of fireball-producing Earthimpacting meteoroids and orbit determination through shadow calibration of the Buzzard Coulee meteorite fall. M.Sc. thesis, Univ. of Calgary, Calgary. 166 pp. Molau S. and Rendtel J. (2009) A comprehensive list of meteor showers obtained from 10 years of observations with the IMO Video Meteor Network. WGN, J. Intl. Meteor Org., 37, 98–121. Morbidelli A., Bottke W. F. Jr., Froeschlé C., and Michel P. (2002) Origin and evolution of near-Earth objects. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 409–422. Univ. of Arizona, Tucson. Mukhamednazarov S. (1999) Observation of a fireball and the fall of the first large meteorite in Turkmenistan. Astron. Lett., 25, 117–118. Nakamura T., Noguchi T., Tsuchiyama A., Ushikubo T., Kita N. T., Valley J. W., Zolensky M. E., Kakazu Y., Sakamoto K., Mashio E., Uesugi K., and Nakano T. (2008) Chondrule-like objects in short-period Comet 81P/Wild 2. Science, 321, 1664–1667. Nemtchinov I. V., Svetsov V. V., Kosarev I. B., Golub’ A. P., Popova O. P., Shuvalov V. V., Spalding R. E., Jacobs C., and Tagliaferri E. (1997) Assessment of kinetic energy of meteoroids detected by satellite-based light sensors. Icarus, 130, 259–274. Nishiizumi K., Caffee M. W., Hamajima Y., Reedy R. C., and Welten K. C. (2014) Exposure history of the Sutter’s Mill carbonaceous chondrite. Meteoritics & Planet. Sci., 49, 2056–2063. Obenberger K. S., Taylor G. B., Hartman J. M., Dowell J., Ellingson S. W., Helmboldt J. F., Henning P. A., Kavic M., Schinzel F. K., Simonetti J. H., Stovall K., and Wilson T. L. (2014) Detection of radio emission from fireballs. Astrophys. J. Lett., 788, L26. Oberst J., Molau S., Heinlein D., Gritzner C., Schindler M., Spurný P., Ceplecha Z., Rendtel J., and Betlem H. (1998) The “European Fireball Network”: Current status and future prospects. Meteoritics & Planet. Sci., 33, 49–56. Olech A., Żołądek P., Wiśniewski M., Krasnowski M., Kwinta M., Fajfer T., Fietkiewicz K., Dorosz D., Kowalski L., Olejnik J., Mularczyk K., and Złoczewski K. (2006) Polish Fireball Network. In Proceedings of the International Meteor Conference, Oostmalle, Belgium, 15–18 Sept., 2005 (J. Verbert et al., eds.), pp. 53–62. International Meteor Organization, Mechelen, Belgium. Opeil C. P., Consolmagno G. J., Safarik D. J., and Britt D. T. (2012) Stony meteorite thermal properties and their relationship with meteorite chemical and physical states. Meteoritics & Planet. Sci., 47, 319–329. Öpik E. J. (1950) Interstellar meteors and related problems. Irish Astron. J., 1, 80–96. Öpik E. J. (1968) The cometary origin of meteorites. Irish Astron. J., 8, 185–208. Padevět V. and Jakeš P. (1993) Comets and meteorites: Relationship (AGAIN?). Astron. Astrophys., 274, 944–954. Papike J. J., ed. (1998) Planetary Materials. Mineralogical Society of America, Washington, DC. 1039 pp. Pauls A. and Gladman B. (2005) Decoherence time scales for “meteoroid streams.” Meteoritics & Planet. Sci., 40, 1241–1256. Pecina P. and Ceplecha Z. (1983) New aspects in single-body meteor physics. Bull. Astron. Inst. Czech., 34, 102–121. Petaev M. I. (1992) The Sterlitamak meteorite — A new crater-forming fall. Solar Sys. Res., 26, 384–398. Popova O. (2004) Meteoroid ablation models. Earth Moon Planets, 95, 303–319. Popova O. P., Strelkov A. S., and Sidneva S. N. (2007) Sputtering of fast meteoroids’ surface. Adv. Space Res., 39, 567–573. Popova O., Borovička J., Hartmann W. K., Spurný P., Gnos E., Nemtchinov I., and Trigo-Rodríguez J. M. (2011) Very low strengths of interplanetary meteoroids and small asteroids. Meteoritics & Planet. Sci., 46, 1525–1550. Popova O. P. and 59 colleagues (2013) Chelyabinsk airburst, damage assessment, meteorite recovery, and characterization. Science, 342, 1069–1073. Pujol J., Rydelek P., and Ishihara Y. (2006) Analytical and graphical determination of the trajectory of a fireball using seismic data. Planet. Space Sci., 54, 78–86.

Rabinowitz D., Helin E., Lawrence K., and Pravdo S. (2000) A reduced estimate of the number of kilometre-sized near-Earth asteroids. Nature, 403, 165–166. Reddy V. and 17 colleagues (2015) Link between the potentially hazardous Asteroid (86039) 1999 NC43 and the Chelyabinsk meteoroid tenuous. Icarus, 252, 129–143. ReVelle D. O. and Ceplecha Z. (1994) Analysis of identified iron meteoroids: Possible relation with M-type Earth-crossing asteroids? Astron. Astrophys., 292, 330–336. ReVelle D.O. and Ceplecha Z. (2001) Bolide physical theory with application to PN and EN fireballs. In Proceedings of the Meteoroids 2001 Conference, Kiruna, Sweden (B. Warmbein, ed.), pp. 507–512. ESA SP-495, Noordwijk, The Netherlands. ReVelle D. O., Brown P. G., and Spurný P. (2004) Entry dynamics and acoustics/infrasonic/seismic analysis for the Neuschwanstein meteorite fall. Meteoritics & Planet. Sci., 39, 1605–1626. Rieger L. A., Bourassa A. E., and Degenstein D. A. (2014) Odin — OSIRIS detection of the Chelyabinsk meteor. Atmos. Meas. Tech., 7, 777–780. Rogers L., Hill K. A., and Hawkes R. L. (2005) Mass loss due to sputtering and thermal processes in meteoroid ablation. Planet. Space Sci., 53, 1341–1354. Rubin A. E. (1997) The Galim LL/EH polymict breccia: Evidence for impact-induced exchange between reduced and oxidized meteoritic material. Meteoritics & Planet. Sci., 32, 489–492. Sánchez P. and Scheeres D. J. (2014) The strength of regolith and rubble pile asteroids. Meteoritics & Planet. Sci., 49, 788–811. Scheirich P., Ďurech J., Pravec P., Kozubal M., Dantowitz R., Kaasalainen M., Betzler A. S., Beltrame P., Muler G., Birtwhistle P., and Kugel F. (2010) The shape and rotation of asteroid 2008 TC3. Meteoritics & Planet. Sci., 45, 1804–1811. Schunová E., Granvik M., Jedicke R., Gronchi G., Wainscoat R., and Abe S. (2012) Searching for the first near-Earth object family. Icarus, 220, 1050–1063. Šegon D., Korlević K., Andreić Ž., Kac J., Atanackov J., and Kladnik G. (2011) Meteorite-dropping bolide over north Croatia on 4th February 2011. WGN, J. Intl. Meteor Org., 39, 98–99. Shaddad M. H. and 19 colleagues (2010) The recovery of asteroid 2008 TC3. Meteoritics & Planet. Sci., 45, 1557–1589. Silber E. A., ReVelle D. O., Brown P. G., and Edwards W. N. (2009) An estimate of the terrestrial influx of large meteoroids from infrasonic measurements. J. Geophys. Res., 114, E08006. SonotaCo (2009) A meteor shower catalog based on video observations in 2007–2008. WGN, J. Intl. Meteor Org., 37, 55–62. Spurný P. (1994) Recent fireballs photographed in central Europe. Planet. Space Sci., 42, 157–162. Spurný P. and Borovička J. (2013) Meteorite dropping Geminid recorded. In Meteoroids 2013, Abstract #061. Adam Mickiewicz Univ., Poznań, Poland. Available online at http://www.astro.amu.edu. pl/Meteoroids2013/main_content/data/abstracts.pdf. Spurný P. and Ceplecha Z. (2008) Is electric charge separation the main process for kinetic energy transformation into the meteor phenomenon? Astron. Astrophys., 489, 449–454. Spurný P., Betlem H., Jobse K., Koten P., and van’t Leven J. (2000) New type of radiation of bright Leonid meteors above 130 km. Meteoritics & Planet. Sci., 35, 1109–1115. Spurný P., Oberst J., and Heinlein D. (2003) Photographic observations of Neuschwanstein, a second meteorite from the orbit of the Příbram chondrite. Nature, 423, 151–153. Spurný P., Borovička J., and Shrbený L. (2007) Automation of the Czech part of the European fireball network: Equipment, methods and first results. In Near Earth Objects, Our Celestial Neighbors: Opportunity and Risk (A. Milani et al., eds.), pp. 121–130. IAU Symp. 236, Cambridge Univ., Cambridge. Spurný P., Borovička J., Kac J., Kalenda P., Atanackov J., Kladnik G., Heinlein D., and Grau T. (2010) Analysis of instrumental observations of the Jesenice meteorite fall on April 9, 2009. Meteoritics & Planet. Sci., 45, 1392–1407. Spurný P., Bland P. A., Shrbený L., Borovička J., Ceplecha Z., Singelton A., Bevan A. W. R., Vaughan D., Towner M. C., McClafferty T. P., Toumi R., and Deacon G. (2012a) The Bunburra Rockhole meteorite fall in SW Australia: Fireball trajectory, luminosity, dynamics, orbit, and impact position from photographic and photoelectric records. Meteoritics & Planet. Sci., 47, 163–185.

280   Asteroids IV Spurný P., Bland P. A., Borovička J., Towner M. C., Shrbený L., Bevan A. W. R., and Vaughan D. (2012b) The Mason Gully meteorite fall in SW Australia: Fireball trajectory, luminosity, dynamics, orbit and impact position from photographic records. In Asteroids, Comets, Meteors 2012, Abstract #6369. Lunar and Planetary Institute, Houston. Spurný P., Borovička J., Haack H., Singer W., Keuer D., and Jobse K. (2013) Trajectory and orbit of the Maribo CM2 meteorite from optical, photoelectric and radar records. Poster presented at the Meteoroids 2013 conference, Poznań, Poland, August 26–30, 2013. Spurný P., Haloda J., Borovička J., Shrbený L., and Halodová P. (2014) Reanalysis of the Benešov bolide and recovery of inhomogeneous breccia meteorites — old mystery solved after 20 years. Astron. Astrophys., 570, A39. Stokan E. and Campbell-Brown M. D. (2014) Transverse motion of fragmenting faint meteors observed with the Canadian Automated Meteor Observatory. Icarus, 232, 1–12. Stuart J. S. (2001) A near-Earth asteroid population estimate from the LINEAR survey. Science, 294, 1691–1693. Suggs R. M., Moser D. E., Cooke W. J., and Suggs R. J. (2014) The flux of kilogram-sized meteoroids from lunar impact monitoring. Icarus, 238, 23–36. Svetsov V. V., Nemtchinov I. V., and Teterev A. V. (1995) Disintegration of large meteoroids in Earth’s atmosphere: Theoretical models. Icarus, 116, 131–153. Tagliaferri E., Spalding R., Jacobs C., Worden S. P., and Erlich A. (1994) Detection of meteoroid impacts by optical sensors in Earth orbit. In Hazards Due to Comets and Asteroids (T. Gehrels, ed.), pp. 199–221. Univ. of Arizona, Tucson. Tancredi G. and 15 colleagues (2009) A meteorite crater on Earth formed on September 15, 2007: The Carancas hypervelocity impact. Meteoritics & Planet. Sci., 44, 1967–1984. Tóth J., Vereš P., and Kornoš L. (2011) Tidal disruption of NEAs  — A case of Příbram meteorite. Mon. Not. R. Astron. Soc., 415, 1527–1533. Tóth J., Kornoš L., Piffl R., Koukal J., Gajdoš Š., Popek M., Majchrovič I., Zima M., Világi J., Kalmančok D., Vereš P., and Zigo P. (2012) Slovak Video Meteor Network — Status and results: Lyrids 2009, Geminids 2010, Quadrantids 2011. In Proceedings of the International Meteor Conference, Sibiu, Romania, 15–18 Sept.,

2011 (M. Gyssens and P. Roggemans, eds.), pp. 82–84. International Meteor Organization, Mechelen, Belgium. Trigo-Rodríguez J. M. and Llorca J. (2006) The strength of cometary meteoroids: Clues to the structure and evolution of comets. Mon. Not. R. Astron. Soc., 372, 655–660. (Erratum: Mon. Not. R. Astron. Soc., 375, 415.) Trigo-Rodríguez J. M., Fabregat J., Llorca J., Castro-Tirado A., del Castillo A., de Ugarte A., López A. E., Villares F., and RuizGarrido J. (2001) Spanish Fireball Network: Current status and recent orbit data. WGN, J. Intl. Meteor Org., 29, 139–144. Trigo-Rodríguez J. M., Borovička J., Spurný P., Ortiz J. L., Docobo J. A., Castro-Tirado A. J., and Llorca J. (2006) The Villalbeto de la Peña meteorite fall: II. Determination of atmospheric trajectory and orbit. Meteoritics & Planet. Sci., 41, 505–517. Trigo-Rodríguez J. M., Madiedo J. M., Williams I. P., Castro-Tirado A. J., Llorca J., Vítek S., and Jelínek M. (2009) Observations of a very bright fireball and its likely link with comet C/1919 Q2 Metcalf. Mon. Not. R. Astron. Soc., 394, 569–576. Vasilyev N. V. (1998) The Tunguska meteorite problem today. Planet. Space Sci., 46, 129–150. Verchovsky A. B. and Sephton M. A. (2005) Noble gases in meteorites: A noble record. Astron. Geophys., 46, 2.12–2.14. Weissman P. R. and Lowry S. C. (2008) Structure and density of cometary nuclei. Meteoritics & Planet. Sci., 43, 1033–1047. Welten K. C., Meier M. M. M., Caffee M. W., Nishiizumi K., Wieler R., Jenniskens P., and Shaddad M. H. (2010) Cosmogenic nuclides in Almahata Sitta ureilites: Cosmic-ray exposure age, preatmospheric mass, and bulk density of asteroid 2008 TC3. Meteoritics & Planet. Sci., 45, 1728–1742. Werner S. C., Harris A. W., Neukum G., and Ivanov B. A. (2002) The near-Earth asteroid size-frequency distribution: A snapshot of the lunar impactor size frequency distribution. Icarus, 156, 287–290. Weryk R. J. and Brown P. G. (2013) Simultaneous radar and video meteors — II: Photometry and ionisation. Planet. Space Sci., 81, 32–47. Zolensky M. and Ivanov A. (2003) The Kaidun microbreccia meteorite: A harvest from the inner and outer asteroid belt. Chem. Erde– Geochem., 63, 185–246.

Jenniskens P. (2015) Meteoroid streams and the zodiacal cloud. In Asteroids IV (P. Michel et al., eds.), pp. 281–295. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch015.

Meteoroid Streams and the Zodiacal Cloud Peter Jenniskens

SETI Institute and NASA Ames Research Center

In the last decade, considerable progress has been made in charting meteoroid streams at Earth and in understanding the mechanisms of meteoroid stream formation and evolution that ultimately result in the formation of the zodiacal cloud. This has led to the realization that episodic disruption plays a key role in the decay of comets and primitive asteroids. Several ongoing disruption cascades manifest as multiple meteoroid streams at Earth. Evidence is mounting that the recently released meteoroids also fall apart, on timescales of 100 –10,000 yr, into smaller meteoroids that survive for another 105–106 yr to form the zodiacal cloud. The first dynamical models of the zodiacal cloud are being developed to explore the relative importance of the various sources. These show that main-belt asteroids contribute only a small fraction to the cloud. Ironically, the infall to Earth of freshly ejected meteoroids, dominated by the larger meteoroid streams, is currently in significant part from primitive asteroid (3200) Phaethon.

1. INTRODUCTION All asteroids and comets in our solar system are gradually falling apart into meteoroids. These meteoroids move at a high relative speed to other objects in the solar system and are therefore an impact hazard to satellites, a cause of asteroid surface weathering, and create meteors when impacting a planetary atmosphere. Streams of meteoroids provide a history of parent body activity and can warn us about the presence of potentially hazardous objects. Interplanetary matter falls to Earth at a rate of 10,000– 40,000 tons per year, mostly in the form of ~150-µm (10 µm–1 mm)-sized meteoroids (Love and Brownlee, 1993; Ceplecha et al., 1998). They produce the neutral-atomdebris layer (and trails) in our atmosphere, responsible for the sodium airglow (Plane, 2003), and the meteoric smoke particles that condense the ice of noctilucent clouds (Hervig et al., 2012). They are responsible for the interplanetary dust particles (IDP) collected in Earth’s atmosphere, and deliver to Earth’s surface micrometeorites (e.g., Rudraswami et al., 2014), solar wind-implanted 3He (e.g., Farley, 2001), platinum-group elements (Peucker-Ehrenbrink, 2001), and the meteoric iron that enables life in the iron-depleted southern oceans (Plane, 2012). In the past, meteoroids may have supplied origin-of-life organics, directly from surviving organics as well as through impact-induced chemistry in the atmosphere (e.g., Chyba et al., 1990; Maurette, 1998; Jenniskens, 2001; see also Chapter 34 in Jenniskens, 2006. Meteoroids with sizes on the order of the wavelength of light (also called interplanetary dust) scatter light efficiently and cause the visible zodiacal cloud (Leinert et al., 1998).

They are also strong emitters of infrared light when heated (e.g., Levasseur-Regourd and Lasue, 2010; Maris et al., 2011; Krick et al., 2012; Ade et al., 2014). It is these meteoroids that make the presence of minor planets in other solar systems detectable (e.g., Nesvorny et al., 2010; Morlok et al., 2014; Bonsor et al., 2014; Ballering et al., 2014). Larger >1-mm meteoroids are often only detected when they enter Earth’s atmosphere and cause phenomena collectively called a “meteor.” They cause the ionization trains in radio-detected meteors, the bright lights that are our nakedeye observed meteor showers, as well as the occasional fireballs that produce airbursts and meteorites. The largest >1-m meteoroids are the topic of the chapter by Borovicka et al. in this volume. The manner in which these larger meteoroids break in the atmosphere probes the physical properties of small near-Earth asteroids (NEAs), while the surviving meteorites sample their material properties. This chapter is mostly concerned with how active asteroids and the now dormant comets created the meteoroid streams that manifest as meteor showers on Earth and how that matter contributes to the zodiacal cloud and sporadic meteors. Numerous papers on these topics since the 2002 Asteroids III volume and the 2001 review papers on interplanetary dust in Grün et al. (2001a) can be found in conference proceedings of meetings on interplanetary dust by Krueger and Graps (2007); on meteoroids by Trigo-Rodriquez et al. (2008), Cooke et al. (2010), and Jopek et al. (2014); on asteroids, comets, and meteors by Lazzaro et al. (2006); and in abstracts from the Asteroids, Comets, and Meteors (ACM) 2008 meeting in Baltimore, the ACM 2012 meeting in Niigata, and the ACM 2014 meeting in Helsinki, as well

281

282   Asteroids IV as in the annual Proceedings of the International Meteor Conference. This chapter builds upon, and expands on, an earlier synopsis presented in Jenniskens (2006). 2. Nomenclature When discussing the role of asteroids in the production of meteoroids, it is important to understand what is meant by “asteroid.” From an observer’s point of view, that can include both objects from the asteroid main belt and the dormant or mostly inactive comets that originated in the Kuiper belt and Oort cloud (Levison, 1996). It is the instantaneous rate of mass loss and its nature, especially the meteoroid size and size distribution, that determine a telescopic observer’s distinction between an asteroid (star-like) and a comet (fuzzy object). This appearance can change over time. An asteroid can have an associated stream of meteoroids from a period of activity in the past. A “meteoroid” is defined as “a solid object moving in interplanetary space, of a size considerably smaller than an asteroid and considerably larger than an atom or molecule” (Millman, 1963). At what point an “asteroid” becomes a “meteoroid” is not clear. The definitions approved by the International Astronomical Union in the 1960s are now outdated and efforts are underway to come to terms with this. For example, it is custom these days to also use the term “meteoroid” for the object when it no longer moves through space but through Earth’s atmosphere to cause the meteor. The boundary with asteroids is varyingly put at 1 m or 10 m. However, some researchers protested the use of “asteroid” for the 20-m-sized meteoroid responsible for the Chelyabinsk airburst (Popova et al., 2013), as it had not been seen in space prior to impact, while the small boulders seen in space near Comet 103P/ Hartley 2 by the telescopic cameras of NASA’s Deep Impact mission are considered “meteoroids” rather than “asteroids” (A’Hearn et al., 2011). 3. INTERPLANETARY DUST PARTICLES A review of the properties of the IDPs and micrometeorites collected on Earth is given in the chapter on asteroidal dust in the previous Asteroids III book (Dermott et al., 2002a). In summary, ~75% of IDPs collected in Earth’s atmosphere are unequilibrated, fine-grained mixtures of thousands to millions of mineral grains and amorphous components with close to chondritic abundances. The compositions of micrometeorites are similar to CM- and CR-type carbonaceous chondrites, but they are 2× richer in carbon. Some hydrous IDPS are extensively altered by liquid water inside a parent body. However, most are anhydrous, with the pyroxene-rich particles that are complex admixtures of 0.1–5-µm-diameter single-mineral grains (most commonly enstatite and Fe-Ni sulfides), amorphous material, carbonaceous material, and submicrometer spheroidal grains of silicate glass with embedded metal and sulfides (GEMS). Some have very large D/H ratios and other isotopic anomalies, and contain presolar grains.

Clearly, interplanetary dust is dominated by relative primitive materials, not by dust from the ordinary chondrites that are recovered from most meteorite falls. Back in 2002, these materials were thought to be the result of prolonged mechanical mixing in the deep regolith of asteroidal rubble piles in the outer main belt (Dermott et al., 2002a). This view has changed dramatically in recent years with the study of the small cometary dust particles collected from Jupiter-family comet (JFC) 81P/Wild in 2004 during the Stardust mission (e.g., Zolensky et al., 2006; McKeegan et al., 2006; Hanner and Zolensky, 2010). This dust proved to consist of the expected fine-grained (submicrometersized) loosely bound aggregates with a bulk chondritic composition. However, most aggregates also contained large individual crystals of (most commonly) olivine (33%), lowcalcium pyroxene (24%), mixtures of these (10%), and other minerals (33%), mostly Fe-Ni sulfides, formed or altered at temperatures of 1600–2000 K (Zolensky et al., 2012). The cometary dust was even found to have calcium-aluminumrich inclusions (CAIs) and small chondrule fragments (Nakamura et al., 2008; Joswiak et al., 2014), suggesting that high-temperature inner solar system materials reached the young Kuiper belt. Some magnesium-calcium carbonates and a single occurrence of orthorhombic cubanite even suggested that transient liquid water may have existed within the nucleus or in the inner solar system parent bodies from which this dust originated (Mikouchi et al., 2007; Berger et al., 2011; Zolensky et al., 2012). These materials are not unlike those found in primitive carbonaceous chondrite meteorites. Indeed, the recent “Grand Tack” planet-formation models suggest that primitive asteroids and Kuiper belt (JFC) comets could both have initially formed beyond the birth region of the giant planets (Walsh et al., 2011; Morbidelli et al., 2011; Briani et al., 2011; Raymon and Morbidelli, 2014; see also the chapter by Morbidelli et al. in this volume). Are meteoroids from primitive asteroids and JFC-type comets different? Kikwaya et al. (2011) measured similar densities from meteor lightcurves. CM-type meteorites are likely from a main-belt asteroid source (Jenniskens et al., 2012), although the eccentric orbits of CM-type Maribo and Sutter’s Mill resemble that of JFC 2P/Encke (Haack et al., 2011). The CI-type carbonaceous chondrite Orgueil (also aqueously altered) had an even wider JFC-like preatmospheric orbit, but based on the 1864 visual observations of the fireball (Gounelle et al., 2006). How these materials manifest as IDPs in Earth’s atmosphere and micrometeorites on the ground is determined by changes while in the interplanetary medium and the physical conditions during entry (Rietmeijer, 2007). In the interplanetary medium, grains are exposed to solar wind and galactic cosmic rays, causing amorphitization of minerals and polymerization of carbon (e.g., Rietmeijer, 2011). During atmospheric entry, the level and rate of heating is a function of entry speed. This changes the meteoroid density and porosity (Kohout et al., 2014). Because of admixtures of large grains, even the IDPs with nonchondritic

Jenniskens:  Meteoroid Streams and the Zodiacal Cloud   283

abundances could originate from primitive bodies, with frail aggregate material more easily lost during atmospheric entry (Rietmeijer, 2008).

were theoretical predictions validated and refined by observations, such as shown in Fig. 1 (see reviews by Jenniskens, 2006; Williams, 2011). Meteoroid streams are principally first created by small differences in the orbital period of the ejected particles, which cause a comet dust coma to return as a meteoroid stream after one orbit, creating the one-revolution dust trail (Pravec, 1955). Ejection of meteoroids from parent bodies can occur via gas drag from sublimating ices (Whipple, 1950), parent body disruptions (with collisions, spinup, or other causes), impacts by meteoroids on surfaces, centrifugal forces from Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) spinup of the parent body, and even from electrostatic levitation (e.g., Walsh et al., 2008). All common mechanisms tend to result in small relative ejection speeds compared to the heliocentric velocity of the parent body. The hemispherical direction of ejection can either be toward the Sun or be isotropic. Models of ejection from active asteroids follow those for comets (e.g., Whipple, 1950; Crifo and Rodionov, 2000; Vaubaillon et al., 2005; Kelley et al., 2014). The shorter or longer orbital period resulting from the ejection process will cause the particle to return correspondingly sooner or later in future returns (two-revolution, threerevolution, etc., orbit), spreading the trail along the parent body orbit and creating a meteoroid stream (Fig. 1), but not broadening it (Kondrateva and Reznikov, 1985; McNaught

4. METEOROID STREAMS Meteoroid streams provide a historic record of dust formation, and still identify their sources. These sources are not necessarily the active comets we can study today, long known to be a source of meteoroid streams and the zodiacal cloud (Shiaparelli, 1867; Whipple, 1950, 1967). Instead, the meteoroid input can be dominated by discrete massive disruption events that happened some time ago or, alternatively, by a large population of objects that each contribute small amounts of meteoroids that are hard to measure. 4.1. Formation and Evolution of Meteoroid Streams Meteoroid streams are observed as meteor showers on Earth and, in some cases, as dust trails in infrared emission (Davies et al., 1984; Sykes et al., 1986). Significant progress was made in recent years in systematically charting meteoroid streams at Earth (e.g., Brown et al., 2008a,b, 2010; Younger et al., 2009; Jenniskens et al., 2011). Around the time when the Asteroids III book came out in 2002, there was a watershed in understanding the mechanisms of meteoroid stream formation and evolution. Many relevant mechanisms were proposed earlier, but only now

2

(a)

4

1

–0.89

0

209P Earth

–1

0

209P Earth

–2 –4

2

Y(

Zenith Hourly Rate (/h)

0

AU

–4

–2

)

40

– 4 –2

0

2

)

X (AU

4

Model

–4

–2

0

X (AU)

(d)

May 23

–0.90

(c)

May 25

–0.91 –0.92

4

–2

Y (AU)

2

Y (AU)

Z (AU)

Jupiter

–0.88

(b)

Jupiter

2

4

–0.48 –0.47 –0.46 –0.45

X (AU) (d)

30 20 10 0 0

5

10

15

Time (UT, 2014 May 24) Fig. 1. Meteoroid stream model for how the 1903 AD ejecta from weakly active comet 209P/Linear are distributed on May 24, 2014 (top); dust from AD 1803–1924 will be in Earth’s path (bottom, left). From Berárd and Vaubaillon (2013). In the bottom left panel, the predicted activity (solid line, scaled down by factor of 10) is compared to the observed activity (dashed line), with different symbols representing different video (right), visual, and radio-MS data. From Jenniskens (2014).

284   Asteroids IV

4.2. Main-Belt Asteroids as a Source of Meteoroid Streams Main-belt asteroids create meteoroid streams when primitive asteroids have comet-like activity, such as observed for the Geminid shower parent asteroid (3200)  Phaethon (see the chapter by Jewitt et al. in this volume), or when rubblepile asteroids spin up by YORP and fall apart by centrifugal forces (Walsh et al., 2008), if not prevented by cohesion forces (Rozitis et al., 2014). These events could produce dust trails detectable by the Infrared Astronomical Satellite (IRAS) and Spitzer at midinfrared (IR) wavelengths for much longer periods of time than the cometary activity. Two such low-inclined and loweccentricity dust trails may have originated from relatively recent, 4 meteoroids have been identified from CAMS data. Few of the established CMOR showers with TJ > 4 show a concentration in the CAMS orbital-element diagrams, possibly because they are rich in faint meteors. Table 1 lists only those CMORderived streams for which some meteoroids were detected by CAMS (N being the number of meteoroid orbits). These include the e Pegasids (#326, EPG), the b Equuleids (#327, BEQ), and the a Lacertids (#328, ALA). The e Aquilids (#151, EAU) were detected earlier by the Harvard Meteor Radar (Sekanina, 1976). In later work, CMOR also detected a shower called the July b Pegasids (#366, JBP) (Brown et al., 2010). Only the e Pegasids stand out well in Fig. 2.

It is possible that these high-inclination short-semimajoraxis showers are not from main-belt asteroids at all. No main-belt asteroid parent bodies have been identified yet, despite the fact that 9.3% of all 11,853 known NEAs have inclinations >30°, and as much as 25% of the bright H ≤ 18 mag NEAs. Instead, old age and Poynting-Robertson (P-R) drag may have decreased the semimajor axis of initial JFC- or Halley-type-comet-derived dust, without fully dispersing the meteoroids. Many CAMS-detected meteoroids have orbits that straddle the border of asteroids (TJ ≥ 3) and JFC (TJ = 2–3) domains (Fig. 2). The Taurid Complex showers in November, associated with large but weakly active comet 2P/Encke, have TJ ~ 3.2 on average, well into the asteroidal domain, but these meteoroids are fragile, with beginning heights similar to JFCs, higher than those of the Geminids (Fig. 3). Whipple (1940) first proposed that Comet  2P/Encke is the parent body of the Southern Taurids (#2, STA) and the Northern Taurids (#17, NTA). From the widely dispersed longitude of perihelion, these streams are thought to be at least 20–30,000 yr old. One rotation of the nodal line takes about 5900 yr, explaining the twin showers, as well as the associated daytime b Taurids (#173, BTA) and z Perseids (#172, ZPE) (Whipple, 1940; Steel and Asher, 1996). After more asteroids were discovered in Taurid-like orbits, it was proposed that there existed a Taurid complex with a hard-to-understand wide range of semimajor axes (a = 1.66–2.57 AU), proposed to be fragments from a 20-km-sized comet that broke apart 20–30,000 yr ago (Clube and Napier, 1984; Asher et al., 1993; Steel and Asher, 1996). However, a tally made in 2006 concluded that all proposed members up to that point, with the exception of 2P/ Encke, had reflection properties typical of S- or O-class asteroids (Jenniskens, 2006, pp. 462–464). It is now thought that these originally proposed objects are instead asteroids that originated from the inner main belt by ejection from the n6 resonance, a known source of S-class asteroids. More recently, the picture is dramatically changing with both more near-Earth objects (NEOs) being discovered in orbits that resemble 2P/Encke in semimajor axis and more

TABLE 1. High TJ showers.

N a q i w (AU) (AU) (°) (°) (°)

# IAU



Phaethon 4 GEM 221 DSX Toroidal 151 EAU 326 EPG 327 BEQ 328 ALA

Node TJ

4225 1.32 0.143 23.2 324.4 225.8 4.4 14 1.14 0.147 24.3 214.3 6.4 5.0 11 0.83 0.405 64.6 322.8 62.5 6.6 33 0.73 0.144 49.0 337.8 109.3 7.4 35 1.04 0.157 46.5 327.6 84.4 5.3 2 1.07 0.976 77.7 122.2 114.5 5.1

Median orbital elements for N = number of CAMS-observed meteors: a = semimajor axis; q = perihelion distance; i = inclination; w = argument of perihelion; Node = longitude of the ascending node.

286   Asteroids IV clarity about the Taurid stream being composed of multiple streams (Porubcan et al., 2006). A recent analysis of CAMS data shows that the Taurid showers are composed of at least 19 individual streams, 7 of which were assigned to parent body asteroids. Importantly, these streams are not twins, having separate values of the longitude of perihelion, but similar to that of their parent bodies. This implies that individual streams fade rapidly, presumably due to meteoroids falling apart, before their node can significantly rotate away from the parent body (Jenniskens et al., 2015b). Unlike the Taurid complex asteroids proposed in the past, these asteroids all have a narrow range of semimajor axis (a = 2.20–2.35 AU). Of the 17 known asteroids with semimajor axis in this range and with a Taurid (and related c-Orionid) shower’s longitude of perihelion P = 130°–185°, 9 can be associated with one of the Taurid and c-Orionid stream components, most in the 0.3–1-km size range. The current completeness of NEO detections in the this size range is about 64%, in good agreement (Jenniskens et al., 2015b). Another example of a complex of comet fragments, each meteoroid stream detected at Earth still having a nodal line similarly oriented to that of the comet fragments, is the complex of comets and meteoroid streams associated with Comet 96P/Machholz (Sekanina and Chodas, 2005; Jenniskens, 2006; Jenniskens et al., 2015b). 5. THE ZODIACAL CLOUD How important are main-belt asteroids in the formation of the interplanetary dust cloud as a whole? In the Asteroids III chapter on asteroidal dust (Dermott et al., 2002a), much focus was given to the zodiacal dust bands at 2° and 10° ecliptic latitude, because these features can be used to estimate the contribution of dust from asteroids to the zodiacal dust cloud. At the time, the dust bands were thought to be produced in the Eos, Koronis, and Themis families, but a few problems with this interpretation were already noted in Grogan et al. (2001). This perception has changed completely in the past decade. Now, the three main bands are believed to sample an ongoing collisional cascade among the smallest fragments in three recently formed families: Karin, Veritas, and Beagle, which represents collisions between asteroids only 6–8 m.y. ago (Nesvorny et al., 2006a,b, 2008; Kehou et al., 2007; Vokrouhlicky et al., 2008; Espy et al., 2009). Based on the earlier proposed source regions, and assuming that all asteroids contribute similar amounts of meteoroids, Kortenkamp and Dermott (1998) estimated that >75% of infalling matter on Earth originated from main-belt asteroids, and later increased this estimate to as high as 90% (Grogan et al., 2001; Dermott et al., 2002a,b). With some holdouts, this perception has also completely changed in recent years. Now, dynamical models put this fraction at less than 5% (Wiegert et al., 2009; Nesvorny et al., 2010). That also agrees better with the fact that satellites with dust detectors passing through the asteroid belt have never detected

a significant increase of impact rates of small meteoroids (Grün et al., 2001b; Landgraf et al., 2002). Nevertheless, Ipanov et al. (2008) still assigned 30–50% to main-belt asteroids, while the “model A” by RowanRobinson and May (2013) found 22.2% of meteoroids from asteroids originating in the main belt and 7.5% from an isotropic source proposed to be interstellar dust. 5.1. Dormant Comets as the Source of Zodiacal Dust The first dynamical models of the zodiacal cloud were inspired by insight from meteor observations and were made possible by advances in computing techniques, which now make it possible to follow the complex dynamical evolution of clouds of meteoroids. The advance in computing capabilities also has greatly aided the ongoing development of new meteor and meteoroid observing techniques, and has resulted in a better understanding of the observing biases and the astronomical interpretation of meteor observations (e.g., Taylor and McBride, 1997; Galligan and Baggaley, 2004, 2005; Campbell-Brown, 2008; Close et al., 2007). The new models are calibrated to the optical (peak emission, polarization, and Fraunhofer lines) and infrared observations of the zodiacal cloud (e.g., Levasseur-Regourd and Lasue, 2010), but only the meteor observations provide orbital-element distributions of the actual meteoroids. Before discussing the new models, I will first discuss the latest meteor observations. Meteor observations are capable of probing both the small 1-mm grains that carry most mass loss of their source, but are relatively rare and not easily detected by dust detectors or by remote sensing in astronomical observations. The small meteoroids are detected by specular meteor radars, which sample underdense echoes from meteors of magnitude +6 and fainter, and by high-power large-aperture (HPLA) radars that can also detect the head-echoes of small meteoroids. The larger meteoroids are observed as visual and video-detectable meteor showers and fireballs (e.g., Borovicka et al., 2005; Jenniskens et al., 2011), as head echoes by radar (e.g., Kero et al., 2012; Pifko et al., 2013), and as impact flashes on airless bodies such as the Moon (e.g., Suggs et al., 2014). Bright meteors and impact flashes are relatively few, but advances in low-light-level video observations now provide insight into the population of ~1 g–1 kg meteoroids that carry much of a comet’s mass loss. Figure 4 shows the six principal source directions from which sporadic meteors (both small and large) approach Earth (Hawkins, 1956; Taylor, 1997; Jones and Brown, 1993; Younger et al., 2009). Observational and technical biases affect how these sources are sampled. Most easily detected are the fast 40–72 km s–1 meteors approaching from the northern and southern apex sources, which originate from Oort cloud comets (long-period comets with orbital period P > 250 yr and retrograde Halley-type comets with 250 > P > 20 yr). Of intermediate 30–50 km s–1

Jenniskens:  Meteoroid Streams and the Zodiacal Cloud   287

North Toroidal

(a)

North Apex Helion

Antihelion

Helion

South Apex

South Toroidal

(b)

80

Ecliptic Latitude (°)

60 40 20 0 –20 –40 –60 –80 350

300

250

200

150

100

50

0

Ecliptic Longitude (°) Fig. 4. (a) Cartoon showing the sporadic meteoroid source regions identified by Hawkins (1956), Taylor (1997), and Jones and Brown (1993). (b)  An example of measured approach directions of meteoroids to Earth; all +1 to +4 magnitude meteors throughout the year observed in CAMS video observations (Jenniskens et al., 2015).

apparent entry speed are the toroidal sources, which mostly are rich in faint meteors and are prominent in radar observations (Campbell-Brown, 2008; Pokorny et al., 2013). More important for the total mass input in the zodiacal cloud, however, are the slow and therefore hard to see 11–40 km s–1 meteors in the antihelion and helion sources (Fig. 4), which are meteoroids from JFCs and main-belt asteroids. Much effort has gone into debiasing the radar-observed populations (e.g., Taylor, 1997; Jones and Brown, 1993; Galligan and Baggaley, 2002; Nesvorny et al., 2011a; Kero et al., 2012, 2013; Pifko et al., 2013). Both specular and headecho radar observations have strong velocity-dependent biases, because ionization has a complex and steep dependence on speed and altitude. After debiasing for these observational effects, most mass from the larger observed particles, and therefore most mass input into the interplanetary dust cloud, arrives from the antihelion and helion sources. The derived orbital data shows that the meteoroid density falls off with heliocentric distance (r) according to r–1 inside 1 AU and

according to r–2 outside 1 AU, with a weak excess at 2–4 AU (Galligan and Baggaley, 2002; Dikarev et al., 2004, 2005; Jenniskens, 2006). Surprisingly, the sensitive AMOR (+14 limiting magnitude) and not-so-sensitive CMOR (+8 limiting magnitude) radar results show a sporadic population with similar orbital-element distributions, with antihelion source orbits on relatively small a ~ 1.0 orbits (Fig. 5). For CMOR particles to evolve to a = 1 AU orbits by P-R drag requires more time than allowed by the collisional lifetime according to Grün et al. (1985). Nesvorny et al. (2011a) assumed that CMOR-detected particles, about 0.6 mm in size, survived as long as the smaller 0.09-mm-diameter AMORdetected particles, some 3 × 105 yr, about 4–10× as long as calculated by Grün et al. (1985). The same is measured for the CAMS-detected sporadic meteors (Jenniskens et al., 2015a). The debiased distribution of semimajor axis peaks at 2.1–2.8 AU, but has a P-R-evolved component (Fig. 5). These particles survived collisions for 1–3 × 106 yr, 10× longer than calculated by Grün et al. (1985). Above 100 µm, the size frequency distribution of meteoroids falling to Earth falls off steeply to larger sizes. The short lifetime required to explain the relative lack of the CAMS-detected 7-mm-sized meteoroids at Earth (Grün et al., 1985) suggests that these meteoroids disappear on a short timescale of 300–104 yr, not from collisions, but from other processes that disrupt the meteoroids into smaller grains. A small fraction of large grains remains and goes on to evolve by P-R drag (Jenniskens et al., 2015a). Large meteoroids deposited by comets disappear over time, before their streams evolve and dynamically merge with the sporadic background. Freshly deposited comet dust fades over timescales as short as 300 yr for the Leonids of Comet 55P/Tempel-Tuttle and 50 yr for the Camelopardalids of 209P/Linear, needing the scaling down of the model activity in Fig. 1 to match the observations, for example (Jenniskens, 2014). Other meteoroids survive longer, but streams linked to weakly active comets or asteroidal parent bodies are rarely older than about 104 yr, not old enough to differentially rotate the nodal line and create twin showers at their other node (Jenniskens et al., 2015b). CMOR samples large enough particles to recognize the meteoroid streams, being most sensitive to showers rich in faint meteors and with intermediate entry speeds of 20–50 km s–1 (Brown et al., 2008a,b, 2010; Weryk and Brown, 2012). The meteoroid streams of faster, slower, and larger particles are best detected by optical techniques, but bright meteors are much less frequent. Only in recent years have significant numbers of meteoroid trajectories been measured by scaling up multi-station video observations. These surveys are ongoing, but already show the presence of many additional meteoroid streams. CAMS is just one of these surveys [for an overview of other projects, see Jenniskens et al. (2011)]. CAMS detects the +1 to +4 meteors (~1-g- and ~1-cm-sized meteoroids)

288   Asteroids IV 1.0 CAMS CMOR AMOR

Fraction

0.8

0.6

0.4

0.2

0.0

0

1

2

3

4

5

6

Semimajor Axis (AU) Fig. 5. The measured orbital element distribution at Earth for 7-mm-sized (CAMS), 0.6-mm-sized (CMOR), and 0.09-mm-sized (AMOR) meteoroids. The distributions are debiased by correcting for observational effects and mass weighted, but are not corrected for the collisional probability with Earth (Jenniskens et al., 2015a).

approaching from the nightside antihelion source, but not those arriving on the dayside after circling the Sun, called the helion source (Fig. 4). The cameras measure luminosity, with luminous efficiency (=  the fraction of kinetic energy converted into the light detected by the cameras) depending in an uncertain manner on entry speed. Slightly more than a quarter (25.6%) of all CAMSdetected meteors between October 2010 and March 2013 were assigned to 230 meteor showers, of which 86 are newly discovered [listed among the International Astronomical Union (IAU) Meteor Shower Working List numbers 427, 448–502, 506–507, and 623–750]. The IAU keeps a tally of meteor showers and assigns names, numbers, and codes (Jenniskens et al., 2009). So far, only 95 showers are considered “established,” meaning that we can be certain that they exist. Based on the new data, this number is expected to increase. Only a small fraction of these showers has known parent bodies. It was long thought that the lack of parent bodies for most showers meant they had disappeared. This view has now changed dramatically. With a surge in NEO discoveries, it was realized that many meteor shower parent bodies are hiding as asteroid-looking objects. Most are weakly active or dormant comets and a few are primitive asteroids (Jenniskens, 2008). Whipple (1983) was the first to point out that asteroid (3200) Phaethon moves in the Geminid stream (#4, GEM), but that association was long dismissed as a possibly coincidental alignment of orbits. However, Phaethon moves in an eccentric asteroid-like orbit with small perihelion distance (q), which makes a random association unlikely. As said, the stream has a Tisserand parameter with respect to Jupiter TJ = 4.4, well into the asteroid regime with TJ ≥ 3. Phaethon now is known to be occasionally weakly active at

perihelion (Jewitt et al., 2013), and there is no longer doubt that Phaethon is the source of the Geminids. This uncertainty was lifted following the discovery that asteroid 2003 EH1 moves among the highly inclined 72° Quadrantids (#10, QUA) (Jenniskens, 2004). It was then found that asteroid 2005 UD moved in the Sextantid stream (#221, DSX) (Ohtsuka et al., 2006), which is related to the Geminids (Jewitt and Hsieh, 2006; Jenniskens, 2006), and asteroid 2008 ED69 moved among the k Cygnids (#12, KCY) (Jenniskens and Vaubaillon, 2008; Trigo-Rodriguez et al., 2009). Asteroid 2002 EX12, now better known as weakly active Comet 169P/NEAT, was proven to be the parent body of the a Capricornids (#1, CAP) (Wiegert and Brown, 2004; Jenniskens and Vaubaillon, 2010), while 2003 WY25 was identified as a recovered fragment of Comet D/1819 W1 (Blanpain), the source of the Phoenicids (#254, PHO) (Foglia et al., 2005; Jenniskens, 2006). Work on other proposed associations is ongoing (e.g., Babadzhanov et al., 2008, 2012; Rudawska et al., 2012). The situation should be similar on Mars and Venus (Christou, 2010). Typically, the mass of meteoroids in each stream is similar to that of the remaining parent body (Jenniskens, 1994, 2006, 2008a,b). The implication is that the main mass-loss mechanism of JFCs is an episodic disruption, during which they lose about half their mass and create meteoroid streams. Active comets were long known to contribute to the zodiacal cloud (e.g., Whipple, 1967; Zook, 2001), but are insufficient to account for the required steady-state mass input. Active JFCs contribute only about 300 kg s–1 of large meteoroids that contribute to mid-IR emissions (Reach et al., 2007). The required steady-state averaged mass input in the zodiacal cloud is 104–105 kg s–1 (Nesvorny et al., 2011a). Based on the new parent body identifications, we now know that the episodic breakup of mostly dormant comets solves this discrepancy (Jenniskens, 2008a,b). With the more prominent JFC streams today measuring about 2 × 1013 kg (Table 8 in Jenniskens, 2006), there needs to be about 1 such breakup every 30 yr in the inner solar system to maintain the cloud, from a population that is about 2000 dormant comets and 600 active comets (Belton, 2015a). Jupiter-family comets appear to break apart as often as Oort cloud comets (Levison et al., 2002; Belton, 2015) at a rate of about 5 × 10–5 disruptions/yr for an active comet and a factor of 3 less for a dormant comet. Recent disruptions include that of meteoroid stream parents D/1819 V1 (Blanpain) in 1819, 3D/Biela in 1843, and 73P/SchwassmannWachmann 3 in 1995 (Reach et al., 2009). The latter released meteoroids during the 1995 breakup with a cumulative mass index of 0.85–1.00, dominated by particles >1 mm (Vaubaillon and Reach, 2010), and numerous fragments of which one large object survived. Eleven known short-period comets were observed to split in the last 200 yr, amounting to a rate of 1 in 18 years, but not all may have disrupted to the level required. Activity from these events can linger, as in the case of weakly active 2P/Encke, the remnant of the Taurid complex (see below). The activity associated with 2P/Encke and the

Jenniskens:  Meteoroid Streams and the Zodiacal Cloud   289

Taurid complex meteoroid streams is recognized to be a significant contributor to the current helion and antihelion meteor shower sources (Whipple et al., 1967; Wiegert et al., 2009). Discovering the dominant presence of dormant and weakly active comets among our antihelion source meteoroid streams inspired a revisiting of zodiacal cloud models to investigate whether or not mostly dormant comets can be the main source of our zodiacal meteoroids. Only recently have zodical dust cloud models been developed that are based on rigorous dynamical modeling of the meteoroid orbital evolution from their source to their demise in collisions with other meteoroids. All prior zodical cloud models were based on artificial constructs of components with presumed orbital dynamics (e.g., Divine, 1993; Dikarev, 2005; Ipatov et al., 2008; Rowan-Robinson and May, 2013). It was often assumed that main-belt asteroidal dust would evolve by P-R drag into near-circular orbits (e ~ 0.3–0.0), from which they hit Earth at very low entry velocities. However, Doppler radial velocity profiles of Fraunhofer lines in scattered light from the zodiacal cloud show a typical e ~ 0.5 eccentricity of small meteoroids (Ipatov et al., 2008; May, 2008). The new modeling showed that meteoroids evolving from asteroids would increase their eccentricity as required due to the action of resonances, but would not be pumped up to high enough inclinations to account for the observed latitudinal dispersion of the zodiacal cloud (Nesvorny et al., 2010). In contrast, meteoroids ejected by the population of JFCs naturally created the observed width of the zodiacal cloud (Fig. 6) from an initial higher distribution of inclinations, coupled to an increase of inclinations from interactions with Jupiter when still having an aphelion near this planet. It was calculated that Kuiper belt comets in the form of JFCs

contribute more than 90% of all meteoroids in the inner solar system (Nesvorny et al., 2010). Other derived properties for the zodiacal cloud are summarized in Table 2. While deposited initially in JFC-like orbits (e ~ 0.7), the dust does evolve by P-R and solar-wind drag to lower eccentricities (e ~ 0.5) over time, finally hitting Earth with a median speed of ~14 km s–1, slow enough to explain these comets as the dominant source of our micrometeorites (Nesvorny et al., 2010). However, if collisional lifetimes are reversed and small 10–100-µm grains collide more frequently than in the Grün et al. (1985) model, it is possible that the P-R evolution is interrupted and meteoroids move in e ~ 0.3–0.5, as observed. It was earlier assumed that the relative lack of large grains at Earth was because meteoroids with masses >10–6 g (>1 mm) collided with smaller so-called b-meteoroids (radiation-pressure-driven, on hyperbolic orbits, generated deep inside 1 AU) before they had time to evolve from the asteroid belt to Earth. The observed size distribution slope at Earth was explained through a balance between the collisional loss of particles and the dust supply (Gustafson, 1994; Ishimoto, 1998). Collisional lifetimes at 1 AU were estimated at about 60,000 yr for a 1-mm meteoroid and 200,000 years for centimeter-sized grains (Nikolova and Jones, 2001). Collisional lifetimes may in fact be longer if collisions with larger meteoroids dominate their destruction (e.g., Davis et al., 2012). In summary, we now understand that the zodiacal cloud results mainly from episodic disruptions of weakly active and mostly dormant JFCs, followed by the formation of meteoroid streams of millimeter- to centimeter-sized particles, which then fade by meteoroid fragmentation to ~0.15-mm particles, with these smaller particles dynamically evolving to become the zodiacal cloud, until collisions finally shatter

(a)

(b) 60

Flux (MJy sr–1)

Flux (MJy sr–1)

60

40

20

40

20

0

0

–50

0

50

Ecliptic Latitude (°)

–50

0

50

Ecliptic Latitude (°)

Fig. 6. Two models of zodiacal cloud infrared emission (upper solid lines) with 25µm IRAS flux measurements (upper dashed lines, with gray areas prone to residual galactic plane emissions) and the differential of calculated–observed (bottom). (a) The best-fit model with asteroid and Oort cloud comet particles. This model does not fit IRAS observations well. The model profile is too narrow near the ecliptic and too wide overall. (b) A model with a dominant contribution of (mostly dormant and weakly active) JFC particles. From Nesvorny et al. (2010).

290   Asteroids IV TABLE 2. Zodiacal cloud properties. Property

Value Ref.

First stage — sources Mass in young comp. Mean age young comp. Steady state mass input Main-belt asteroids Jupiter-family (=Kuiper belt) comets Oort cloud comets Interstellar (at 1 AU) Dominant size range Second stage — evolved Total dust cross section Total mass Mean age Dominant size range Mass impacting Earth (ø = 1 µm to 5 cm)

~5 × 1015 kg 300–104 yr 104–105 kg s–1 90% by mass Nmin are then treated as meaningful asteroid families. Different researchers made different choices: Nmin = 5 in Zappalà et al. (1990), Nmin = 100 in Parker et al. (2008), and Nmin = 10–20 in most other publications. The two disadvantages of this method are that (1) meaningful asteroid families with N < Nmin members are explicitly avoided, and (2) dcut (Nmin) depends on the population density in proper element space and must be recomputed when a new classification is attempted from ever-growing catalogs. Another approach to this problem is to identify all groups, even if they have only a few members, and establish their statistical significance a posteriori. Those that are

judged to be insignificant are subsequently discarded and do not appear in the final lists. To determine the statistical significance of a group, one can generate mock distributions and apply the HCM to them. For example, the high statistical significance of the Karin family, which is embedded in the much larger Koronis family, can be demonstrated by generating 1000 orbital distributions corresponding to the Koronis family, and applying the HCM to each one (Nesvorný et al., 2002a). With dcut = 10 m s–1, no concentrations in this input can be found containing more than a few dozen members, while the Karin family currently has 541 known members. Therefore, the Karin family is significant at a 0), which is roughly one-fifth of the extension of the whole main belt. In addition, drifting asteroids encounter orbital resonances and can be dispersed by them in eP and iP as well. A good illustration of this is the case of the Flora and Vesta families in the inner main belt. To separate these families from each other down to their smallest members, the scope of the HCM can be restricted by an artificial cut in proper element space. Alternatively, one can first apply the HCM to the distribution of large members, thus identifying the core of each family, and then proceeding by trying to “attach” the small members to the core. This second step must use a lower dcut value than the first step to account for the denser population of smaller asteroids. In practice, this has been done by applying an absolute magnitude cutoff, H*, with H < H* for the core and H > H* for the rest. In the low-i portion of the inner main belt, where the Flora and Vesta families reside, Milani et al. (2014) opted to use H* = 15, and identified cores of families with Nmin = 17 and dcut  = 60  m  s–1, and small members with Nmin = 42 and dcut = 40 m s–1. Another solution to the overlap problem is to consider the physical properties of asteroids. Previously, the spectroscopic observations of members of dynamical families have been used to (1) establish the physical homogeneity of asteroid families (the difference between physical prop-

Nesvorný et al.:  Identification and Dynamical Properties of Asteroid Families   301

2.5. Families in Extended Space Another useful strategy is to include the color and/or albedo information directly in the clustering algorithm. This can be done by first separating the main belt into two (or more) populations according to their color and albedo properties. For example, asteroids in the S-complex can be separated from those in the C/X-complex based on the SDSS colors (Nesvorný et al., 2005), and the high-albedo asteroids can be separated from the low-albedo asteroids based on the albedo measurements of WISE (Masiero et al., 2013). The HCM is then applied to these populations separately. This method is capable of identifying small/ dispersed S-complex families in the C/X-type background, and vice versa, or low-albedo families in the high-albedo background, and vice versa. It can also be useful to characterize the so-called family “halos” (section 6.4). A more general method for including the color/albedo information in the clustering algorithm consists in the application of the HCM in space of increased dimension (e.g., Parker et al., 2008; Carruba et al., 2013a). When considering the proper elements and SDSS colors, the distance in five dimensions can be defined as d22 ≡ d2 + n2a2P (k1(dC1)2 +

(a)

0.15

2.3

2.4

2.5

Semimajor Axis aP (AU)

(b)

0.2

Eccentricity eP

0.2

Eccentricity eP

erties of members of the same family tends to be smaller than the differences between physical properties of different families), and (2) identify large interlopers (asteroids classified as family members based on proper elements but having spectroscopic properties distinct from the bulk of the family). With the color and albedo data from SDSS and WISE (Note 5), the physical homogeneity of asteroid families has been demonstrated to hold down to the smallest observable members (Ivezić et al., 2001; Parker et al., 2008) (see Fig. 1b). A straightforward implication of this result is that the interior of each disrupted body was (relatively) homogeneous, at least on a scale comparable to the size of the observed fragments (~1–100 km) (Note 6). The physical homogeneity of asteroid families can be used to identify interlopers as those members of a dynamical family that have color and/or albedo significantly distinct from the rest of the family. The number density of apparent color/albedo interlopers in a family can then be compared with the number density of the same color/albedo asteroids in the immediate neighborhood of the family. Similar densities are expected if the identified bodies are actual interlopers in the family. If, on the other hand, the density of color/albedo outliers in the family is found to be substantially higher than in the background, this may help to rule out the interloper premise, and instead indicate that (1) the disrupted parent body may have been heterogeneous, or (2) we are looking at two or more overlapping dynamical families with distinct color/albedo properties. Finally, as for (2), it is useful to verify whether the family members with different color/albedo properties also have different proper element distributions, as expected if breakups happened in two (slightly) different locations in proper element space (e.g., the Nysa-Polana complex; see Fig. 2).

0.15

2.3

2.4

2.5

Semimajor Axis aP (AU)

Fig. 2. The Nysa-Polana complex. (a) The HCM applied to this region of the inner main belt reveals a major concentration of asteroids with 2.25 < aP < 2.48 AU and 0.13 < eP < 0.22. The shape of the concentration in the (aP, eP) projection is unusual and difficult to interpret. (b) The WISE albedos of members of the Nysa-Polana complex: black for pV < 0.15 and gray for pV > 0.15. It becomes clear with the albedo information that the Nysa-Polana complex is two overlapping groups with distinct albedos. Furthermore, based on the V-shape criterion (section 4), the low-albedo group is found to consist of two asteroid families [the Polana and Eulalia families (Walsh et al., 2013)]. The vertical feature at aP = 2.42 AU is the 1:2 mean-motion resonance with Mars.

k2(dC2)2), where d is the distance in three-dimensional space of proper elements defined in section  2.2, C1 and C2 are two diagnostic colors defined from the SDSS (Ivezić et al., 2001; Nesvorný et al., 2005), and k1 and k2 are coefficients whose magnitude is set to provide a good balance between the orbital and color dimensions (e.g., Nesvorný et al., 2006b). Similarly, we can define d23  ≡ d2 + n2a2P kp(dpV)2 (in four dimensions) and d24  ≡ d22 + n2a2P kp(dpV)2 (in six dimensions) to include the measurements of albedo pV from WISE. The d4 metric applies the strictest criteria on the family membership, because it requires that the family members have similar proper elements, similar colors, and similar albedos. Note, however, that this metric can only be applied to a reduced set of main-belt asteroids for which the proper elements, colors, and albedos are simultaneously available (presently =25,000; Fig. 1b). 2.6. Very Young Families in Orbital Element Space Short after a family’s creation, when the mutual gravity effects among individual fragments cease to be important, the fragments will separate from each other and find themselves moving on heliocentric orbits. Initially, they will have very tightly clustered orbits with nearly the same values of the osculating orbital angles W, v, and l, where W is the nodal longitude, v is the apsidal longitude, and l is the mean longitude. The debris cloud will be subsequently dispersed by the (1) Keplerian shear (different fragments are ejected with different velocity vectors, have slightly different values of the semimajor axis, and therefore different orbital

302   Asteroids IV

Inclination iP (rad)

Eccentricity eP

0.046

(a)

0.045 0.044 0.043 0.046 0.045 0.044 0.043 2.86

2.865

2.87

Semimajor Axis aP (AU)

Perihelion Longitude (°) Nodal Longitude (°)

periods) and (2) differential precession of orbits produced by planetary perturbations. As for (1), the fragments will become fully dispersed along an orbit on a timescale Tn = p/(a∂n/∂a)(Vorb/dV) = (P/3)(Vorb/dV), where P = 2– 4 yr is the orbital period and dV is the ejection speed. With dV = 1–100 m s–1, this gives Tn = 300–30,000 yr. Therefore, the dispersal of fragments along the orbit is relatively fast, and the clustering in l is not expected if a family is older than a few tens of thousand years. The dispersal of W and v occurs on a timescale Tf = p/(a∂f/∂a)(Vorb/dV), where the frequency f = s or g. For example, ∂s/∂a = –70 arcsec yr–1 AU–1 and ∂g/∂a = 94 arcsec yr–1 AU–1 for the Karin family (a = 2.865 AU). With dV = 15 m s–1 (Nesvorný et al., 2006a) and Vorb = 17.7 km s–1, this gives Ts = 3.8 m.y. and Tg = 2.8 m.y. Since tage > Ts and tage > Tg in this case, the distribution of W and v for the Karin family is not expected to be clustered at the present time (Fig.  3). Conversely, the clustering of W and v would be expected for families with tage < 1 m.y. This expectation leads to the possibility that the families with tage < 1 m.y. could be detected in the catalogs of osculating orbital elements (Marsden, 1980; Bowell et al., 1994), where they should show up as clusters in five-dimensional space of a, e, i, v, and W. The search in five-dimensional space of the osculating orbital elements can be performed

with the HCM method and metric d25 = d2 + (na)2(kW(dW)2 + kv(dv)2), where d = d(a,e,i) was defined in section 2.2, and kW and kv are new coefficients. [Different metric functions were studied by Rožek et al. (2011), who also pointed out that using the mean elements, instead of the osculating ones, can lead to more reliable results.] This method was first successfully used in practice for the identification of the Datura family (Nesvorný et al., 2006c), and soon after for the discovery of the asteroid pairs (Vokrouhlický and Nesvorný, 2008). The Datura family now consists of 15 known members ranging in size from =10-kmdiameter object (1270) Datura to subkilometer fragments. They have W and v clustered to within a few degrees near 98° and 357°, respectively. The age of the Datura family is only 530 ± 20 k.y., as estimated from the backward integration of orbits (Vokrouhlický et al., 2009). Table 1 reports other notable cases of families with tage < 1 m.y. 3. DETECTION OF RECENT BREAKUPS The detection of families with very young formation ages was one of the highlights of asteroid research in the past decade. A poster child of this exciting development is the Karin family, part of the larger Koronis family, that was shown to have formed only 5.8 ± 0.2 m.y. ago (Nesvorný et al., 2002a). The Karin family was identified by the tra-

100

(b)

0 –100

100 0 –100 –107

–8 × 108

–6 × 108

–4 × 106

–2 × 106

0

Time (yr)

Fig. 3. (a) Proper elements of members of the Karin family. The size of each dark symbol is proportional to the diameter of a family member. Light gray dots indicate background bodies near the Koronis family. The black ellipses show the proper orbital elements of test bodies launched at 15 m s–1 from aP = 2.8661 AU, eP = 0.04449, and iP = 0.03692, assuming that f = 30° and w + f = 45°, where f and w are the true anomaly and perihelion argument of the disrupted body at the time of the family-forming collision. (b) The convergence of angles at 5.8 m.y. ago demonstrates that the Karin family was created by a parent asteroid breakup at that time. The plot shows past orbital histories of 90 members of the Karin family: (top) the proper nodal longitude, and (bottom) the proper perihelion longitude. Values of these angles relative to (832) Karin are shown. At t = 5.8 m.y. (broken vertical line), the nodal longitudes and perihelion arguments of all 90 asteroids become nearly the same, as expected if these bodies had initially nearly the same orbits. Adapted from Nesvorný and Bottke (2004).

Nesvorný et al.:  Identification and Dynamical Properties of Asteroid Families   303

TABLE 1. Recently formed asteroid families. Family/Pair

tage

(832) Karin 5.75 ± 0.05 m.y. 10–15 m.y. (158) Koronis(2) (490) Veritas 8.3 ± 0.5 m.y. (656) Beagle ~10 m.y. (778) Theobalda 6.9 ± 2.3 m.y. (1270) Datura 530 ± 20 k.y. (2384) Schulhof 780 ± 100 k.y. (4652) Iannini 2.37 AU) by the Yarkovsky/YORP evolution. (b) A comparison between model results (solid line) and binned Erigone family [gray dots (see Vokrouhlický et al., 2006b)]. The error bars are the square root of the number of bodies in each bin. The x-axis is the distance of family members from the the family center. Based on this result, Vokrouhlický et al. (2006b) estimated that tage = 280+30 −50 m.y. and –1, where the error bars do not include the uncertainty originating from V5 = 26+14  m s −11 uncertain material properties (e.g., density, surface conductivity).

Nesvorný et al.:  Identification and Dynamical Properties of Asteroid Families   307

poorly known bulk density and surface conductivity of the asteroids in question. Including this uncertainty, Masiero et al. (2012) found that the best-fitting age of the Baptistina family can be anywhere between 140 and 320 m.y. The estimated ejection speeds are V5 = 15–50 m s–1, except for the Eos family, which formed in a breakup of a very large parent asteroid (DPB ~ 300 km). These results are consistent with the ejection speeds inferred from the young Karin family, which has V5 = 15 m s–1 for a relatively small parent body [DPB = 35 km (Nesvorný et al., 2006a)]. The ejection speeds contribute by =20% (for oldest Eos) to 50% (for youngest Agnia) to the total family spread in the semimajor axis. Ignoring this contribution, as in equation  (2), would thus lead to an overestimate of tage by =20–50%. While one must therefore be careful in applying equation  (2) to the small/young families that did not have enough time to significantly spread by the YE, the effect of the ejection speeds should be less of an issue for old families. 6. DYNAMICAL EVOLUTION 6.1. Initial State The dynamical evolution of asteroids in families is similar to the dynamical evolution of main-belt asteroids in general. Studying the dynamical evolution of individual families is useful in this context, because we more or less know how the families should look like initially. Things may thus be learned by comparing these ideal initial states with how different families look now, after having dynamically evolved since their formation. The dynamical studies can also often provide an independent estimate of tage. Assuming that dV  Vorb, the initial shape of families in (a, e, i) can be obtained from the Gauss equations (e.g., Zappalà et al., 2002), which map the initial velocity perturbation dV = (VR, VT, VZ), where VR, VT, and VZ are the radial, tangential, and vertical components of the velocity vector, to the change of orbital elements dE = (da, de, di). If the ejection velocity field is (roughly) isotropic, the Gauss equations imply that initial families should (roughly) be ellipsoids in (a, e, i) centered at the reference orbit (a*, e*, i*). The transformation from (a, e, i) to (aP, eP, iP) preserves the shape, but maps (a*, e*, i*) onto (a*P, e*P, i*P) such that, in general, a*P ≠ a*, e*P ≠ e*, and i*P ≠ i*. The shape of the ellipsoids in (aP, eP, iP) is controlled by the true anomaly f and the argument of perihelion w of the parent body at the time of the family-forming breakup. The projected distribution onto the (aP, eP) plane is a tilted ellipse with tightly correlated aP and eP if the breakup happened near perihelion (see Fig. 3a), or tightly anticorrelated aP and eP if the breakup happened near aphelion. The two recently formed families for which this shape is clearly discernible, the Karin and Veritas families, have correlated aP and eP, implying that |f | = 30° (Figs. 3 and 4). The projected initial distribution onto the (aP, iP) plane is an ellipse with horizontal long axis and vertical short axis. The short-to-long axis ratio is roughly given by cos (w + f )

VZ/VT. Thus, breakups near the ascending (w + f = 0) and descending (w + f = p) nodes should produce “fat” ellipses while those with w  + f  = ± p/2 should make “squashed” ellipses with diP  = 0. While the Karin family neatly fits in this framework with w + f = p/4 (Fig.  3), the Veritas family shows large diP values, indicating that the ejection velocity field should have been anisotropic with VZ some =2–4× larger than VT. The reference orbit (a*P, e*P, i*P) is often taken to coincide with the proper orbit of a largest family member. This should be fine for families produced in cratering or mildly catastrophic events, where the orbital elements of the impacted body presumably did not change much by the impact. For the catastrophic and highly catastrophic breakups, however, the largest surviving remnant is relatively small and can be significantly displaced from the family’s center. For example, (832)  Karin, the largest =17-km-diameter member of the Karin family produced by a catastrophic breakup of a =40-km-diameter parent body [mass ratio ~0.08 (Nesvorný et al., 2006a)], is displaced by –0.002 AU from the family center (=20% of the whole extension of the Karin family in aP). This shows that, in general, the position of the largest fragment does not need to perfectly coincide with the family center, and has implications for the V-shape criterion discussed in section 4 (where an allowance needs to be given for a possible displacement). 6.2. Dynamics on Gigayear Timescales An overwhelming majority of the observed asteroid families are not simple Gaussian ellipsoids. While this was not fully appreciated at the time of the Asteroids III book, today’s perspective on this issue is clear: The families were stretched in aP as their members drifted away from their original orbits by the Yarkovsky effect. The asteroid families found in the present main belt are therefore nearly horizontal and elongated structures in (aP, eP) and (aP, iP). This shows that the original ejection velocity field cannot be easily reconstructed by simply mapping back today’s (aP, eP, iP) to (VR, VT, VZ) from the Gauss equations (Note 7). Moreover, many asteroid families have weird shapes that, when taken at face value, would imply funny and clearly implausible ejection velocity fields. A prime example of this, briefly mentioned in section  2.2, is the Koronis family (Bottke et al., 2001). Since the case of the Koronis family was covered in the Asteroids III book (Bottke et al., 2002), we do not discuss it here. Instead, we concentrate on the results of new dynamical studies, many of which have been inspired by the Koronis family case. The dynamical effects found in these studies fall into three broad categories: 1. Members drifting in aP encounter a mean-motion resonance with one of the planets [mainly Jupiter, Mars, or Earth (see Nesvorný et al., 2002c)]. If the resonance is strong enough (e.g., 3:1, 2:1, or 5:2 with Jupiter), the orbit will chaotically wander near the resonance border, its eccentricity will subsequently increase, and the body will be removed from the main belt and transferred onto a planet-crossing

308   Asteroids IV orbit (Wisdom, 1982). If the resonance is weak, or if the asteroid is small and drifts fast in aP, the orbit can cross the resonance, perhaps suffering a discontinuity in eP during the crossing, and will continue drifting on the other side. If the resonance is weak and the drift rate is not too large, the orbit can be captured in the resonance and will slowly diffuse to larger or smaller eccentricities. It may later be released from the resonance with eP that can be substantially different from the original value. The effects of mean-motion resonances on iP are generally smaller, because the eccentricity terms tend to be more important in the resonant potential. The inclination terms are important for orbits with iP  > 10°. A good example of this is the Pallas family, with iP = 33° (Carruba et al., 2011). 2. Drifting members meet a secular resonance. The secular resonances are located along curved manifolds in (aP, eP, iP) space (Knežević et al., 1991). Depending on the type and local curvature of the secular resonance, and asteroid’s da/dt, the orbit can be trapped inside the resonance and start sliding along it, or it can cross the resonance with a noticeably large change of eP and/or iP. A good example of the former case are orbits in the Eos family sliding along the z1 = g–g6 + s–s6 = 0 resonance (Vokrouhlický et al., 2006a). An example of the latter case is the Koronis family, where eccentricities change as a result of crossing of the g + 2g5–3g6 = 0 resonance (Bottke et al., 2001). If the secular resonance in question only includes the g (or s) frequency, effects on eP (or iP) are expected. If the resonance includes both the g and s frequencies, both eP and iP can be affected. If the orbit is captured in a resonance with the g and s frequencies, it will slide along the local gradient of the resonant manifold with changes of eP and iP, depending on the local geometry. 3. Encounters with (1) Ceres and other massive asteroids produce additional changes of aP, eP, and iP (Nesvorný et al., 2002b; Carruba et al., 2003, 2007a, 2012, 2013b; Delisle and Laskar, 2012). These changes are typically smaller than those from the Yarkovsky effect on aP and resonances on eP and iP. They are, however, not negligible. The effect of encounters can be approximated by a random walk (for a discussion, see Carruba et al., 2007a). The mean changes of aP, eP, and iP increase with time roughly as t . The asteroid families become puffed out as a result of encounters, and faster so initially than at later times, because of the nature of the random walk. Also, a small fraction of family members, in some cases perhaps including the largest remnant, can have their orbits substantially affected by a rare, very close encounter. Additional perturbations of asteroid orbits arise from the linear momentum transfer during nondisruptive collisions (Dell’Oro and Cellino, 2007). 6.3. Discussion of Dynamical Studies The case of the Koronis family (Bottke et al., 2001) sparked a great deal of interest in studies of the dynamical evolution of asteroid families on very long timescales. Here we review several of these studies roughly in chronologic

order. The goal of this text is to illustrate the dynamical processes discussed in the previous section on specific cases. Nesvorný et al. (2002b) considered the dynamical evolution of the Flora family. The Flora family is located near the inner border of the main belt, where numerous mean-motion resonances with Mars and Earth produce slow diffusion of ep and ip. The numerical integration of orbits showed how the overall extent of the Flora family in eP and iP increases with time. The present width of the Flora family in eP and iP was obtained in this study after t = 0.5 G.y. even if the initial distribution of fragments in eP and iP was very tight. The Flora family expansion saturates for t > 0.5 G.y., because the Flora family members that diffused to large eccentricities are removed from the main belt by encounters with Mars [the Flora family is an important source of chondritic near-Earth asteroids (NEAs) (Vernazza et al., 2008)]. The present spread of the Flora family in aP, mainly contributed by the Yarkovsky effect, indicates tage ~ 1 G.y. Carruba et al. (2005) studied the dynamical evolution of the Vesta family. The main motivation for this study was the fact that several inner main-belt asteroids, such as (956)  Elisa and (809)  Lundia, have been classified as V-types from previous spectroscopic observations (Florczak et al., 2002), indicating that they may be pieces of the basaltic crust of (4)  Vesta. These asteroids, however, have orbits rather distant from that of (4)  Vesta and are not members of Vesta’s dynamical family even if a very large cutoff distance is used. It was therefore presumed that (1) they have dynamically evolved to their current orbits from the Vesta family, or (2) they are pieces of differentiated asteroids unrelated to (4) Vesta. Carruba et al. (2005) found that the interplay of the Yarkovsky drift and the z2 ≡ 2(g–g6) + s–s6 = 0 resonance produces complex dynamical behavior that can indeed explain the orbits of (956) Elisa and (809) Lundia, assuming that the Vesta family is at least =1 G.y. old. This gives support to assumption (1) above. In a follow-up study, Nesvorný et al. (2008a) performed a numerical integration of 6600 Vesta fragments over 2 G.y. They found that most V-type asteroids in the inner main belt can be explained by being ejected from (4) Vesta and dynamically evolving to their current orbits outside the Vesta family. These V-type “fugitives” have been used to constrain the age of the Vesta family, consistent with findings of Carruba et al. (2005), to tage  > 1 G.y. Since previous collisional modeling of the Vesta family suggested tage < 1 G.y. (Marzari et al., 1999), the most likely age of the Vesta family that can be inferred from these studies is tage ~ 1 G.y. This agrees well with the age of the =500-kmdiameter Rheasilvia basin on (4) Vesta inferred from crater counts [=1 G.y. (Marchi et al., 2012)] (Note 8). Vokrouhlický et al. (2006a) studied the dynamical evolution of the Eos family. The Eos family has a complicated structure in proper element space, leading some authors to divide it into several distinct families (e.g., Milani et al., 2014). Diagnostically, however, the Eos family, although somewhat physically heterogeneous, has the color, albedo, and spectral properties that contrast with the local, predomi-

Nesvorný et al.:  Identification and Dynamical Properties of Asteroid Families   309

nantly C-type background in the outer asteroid belt, which suggests that it is a single family. As we discuss below, the complicated structure of the Eos family arises from the presence of several mean-motion and secular resonances. To start with, Vokrouhlický et al. (2006a) showed that the Eos family members drifting by the Yarkovsky effect into the 7:3 resonance with Jupiter are removed (see Fig. 7). This cuts the family at 2.957 AU. Members drifting with da/ dt > 0, on the other hand, will encounter the 9:4 resonance at 3.03 AU. This resonance, being of higher order and thus weaker, is not an unpenetrable barrier, especially for smaller members with higher drift rates. The estimated fraction of bodies that can cross the 9:4 resonance is 3.03 AU is attributed to perturbations of eP and iP during the 9:4 resonance crossing (Fig. 7). Finally, many orbits in the central part of the Eos family are trapped in the secular resonance z1  ≡ g + s–g6–s6 = 0, and slide along it while drifting in aP (Note 9). Finally, we discuss additional processes whose significance is shadowed by the Yarkovsky effect and resonances, but which can be important in some cases. Nesvorný et al. (2002b) considered encounters with (1)  Ceres and found that the characteristic change of the semimajor axis due to these encounters is Da = 0.001 AU over 100 m.y. Assuming that the scattering effect of encounters can be described by a random walk with Da  ∝ t , the expected changes over 1 G.y. and 4 G.y. are =0.003 AU and =0.007 AU, respectively. The orbital changes were found to be larger for orbits

Eccentricity eP

0.2

7:3

9:4

(a)

11:5

0.15

7:3

similar to that of (1) Ceres, because the orbital proximity leads to lower encounter speeds and larger gravitational perturbations during the low-speed encounters. Carruba et al. (2003) studied the effect of encounters on the Adeona and Gefion families, both located near (1) Ceres in proper element space. They found that the semimajor axis of members of the Adeona and Gefion families can change by up to ~0.01 AU over the estimated age of these families. With similar motivation, Carruba et al. (2007a) considered the effect of encounters of the Vesta family members with (4) Vesta. They found the characteristic changes Da = 0.002 AU, De = 0.002, and Di = 0.06° over 100 m.y. In a follow-up work, Delisle and Laskar (2012) included the effects of 11 largest asteroids. They showed that encounters of the Vesta family members with (4) Vesta and (1) Ceres are dominant, contributing roughly by 64% and 36% to the total changes, respectively. The functional dependence Da = 1.6 × 10–4 t 1 m.y. AU was used in this work to extrapolate the results to longer time intervals. Moreover, Carruba et al. (2013b) studied the influence of these effects on the Pallas, Hygiea, and Euphrosyne families. They showed that the effects of (2) Pallas — the third most massive main-belt asteroid — on the Pallas family are very small, because these asteroids have high orbital inclinations (iP  = 33°), lower frequency of encounters, and higher-than-average encounter speeds. Dell’Oro and Cellino (2007) pointed out that orbits of main-belt asteroids can change as a result of the linear momentum transfer during nondestructive collisions. They found that the expected semimajor axis change from these collisions for a D = 50-km main-belt asteroid is Da ~

9:4

(b)

11:5

7:3

9:4

(c)

11:5

0.15

halo

0.1

0.1

core

0.05

0 2.9

0.2

0.05

2.95

3

3.05

3.1

3.15

Semimajor Axis aP/AU

2.9

2.95

3

3.05

3.1

3.15

Semimajor Axis aP/AU

2.9

2.95

3

3.05

3.1

3.15

0

Semimajor Axis aP/AU

Fig. 7. Dynamical evolution of the Eos family. From left to right, the panels show (a) the observed family and its halo in the (aP, eP) projection, (b) the assumed initial shape of the family, and (c) the family’s structure after 1.7 G.y. In (a), we plot all asteroids with Eos-family colors [0.0 < a* < 0.1 mag and –0.03 < i–z < 0.08 mag; see Ivezić et al. (2001) for the definition of color indexes from the SDSS]. The size of a symbol is inversely proportional to absolute magnitude H. The boxes approximately delimit the extent of the core and halo of the Eos family. In (b), 6545 test particles were distributed with assumed isotropic ejection velocities, V5  = 93 m s–1, f = 150°, and w = 30°. Nearly all initial particles fall within the family core. In (c), an N-body integrator was used to dynamically evolve the orbits of the test particles over 1.7 G.y. The integration included gravitational perturbations from planets, and the Yarkovsky and YORP effects. The vertical lines show the locations of several resonances that contributed to spreading of orbits in eP (7:3, 9:4, and 11:5 with Jupiter, also 3J2S-1 and z1 ≡ g + s – g6 – s6 = 0). Adapted from Brož and Morbidelli (2013).

310   Asteroids IV 10–4 AU over 100  m.y. [with the scaling laws from Benz and Asphaug (1999)]. This is an order of magnitude lower than the change expected from close encounters with large asteroids and comparable to the sluggish drift rate expected from the Yarkovsky effect for D = 50 km. For D < 50 km, the orbital changes from nondestructive collisions sensitively depend on several unknown parameters, such as the SFD of subkilometer main-belt asteroids, but the general trend is such that Da drops with decreasing D [assuming that the cumulative SFD index is 17.5°). Figure 9 shows the orbital location of the notable families in the main belt. The lists of members of the notable families can be downloaded from the PDS node (Note 11). Each list contains (1) the asteroid number, (2) aP, (3) eP, (4) sin iP, and (5) the absolute magnitude H from the Minor Planet Center. Also, for families that have a well-defined V-shape envelope in (aP,H), we fit C0 to this shape (section 4, column 7 in Table 2) and report Cj/C0 for each family member in column 6 of the PDS files. The average albedo of each family was obtained from WISE, and is reported in column 9 of Table 2 (pV). The taxonomic type of families, reported in column 8 of Table 2, was taken from the previous taxonomic classification of families (Cellino et al., 2002) or was deduced from the SDSS colors. Columns 5 and 6 of Table 2 report the estimated diameter of the largest member, DLM, and diameter of a sphere with volume equivalent to that of all fragments, Dfrag. DLM was obtained from AKARI, if available, or from WISE, if available, or was estimated from H and average pV. The largest member and suspected interlopers with |Cj /C0| > 2 were excluded in the estimate of Dfrag. The comparison of DLM and Dfrag helps to establish whether a particular breakup event was catastrophic (Dfrag > DLM) or cratering (Dfrag < DLM), but note that this interpretation may depend on sometimes uncertain membership of the largest family objects. Also, the diameter of the parent body of each family can be estimated

as DPB = (D3LM + D3frag)1/3, but note that this estimate ignores the contribution of small (unobserved) fragments. 7.3. Comparison with Previous Datasets The family synthesis presented here is consistent with the results reported in Nesvorný (2012), Brož et al. (2013), and Carruba et al. (2013a). For example, all families reported in Nesvorný (2012) were found to be real here [except the (46)  Hestia family, which was reclassified as a candidate family; see Note 10]. Nesvorný (2012), however, used very conservative criteria for the statistical significance of a family, and reported only 76 families (or 78 if the Nysa-Polana complex is counted, as it should be, as three families). Using the 2014 catalog of proper elements, albedo information from Masiero et al. (2013), and validating several new families from Milani et al. (2014), we now have 44 families that did not appear in Nesvorný (2012). Almost all families reported in Brož et al. (2013) also appear here [a notable exception is a large group surrounding (1044)  Teutonia that we do not believe to be a real family; see Note 10], but many new cases were added. The correspondence with Carruba et al. (2013a) is also good. Parker et al. (2008) used Nmin = 100 and therefore missed many small families that did not have more than 100 members in the 2008 catalog. Also, given that they used a subset of asteroids with SDSS colors, even relatively large families were unnoticed in this work [e.g., the (752)  Sulamitis family in the inner belt now has 303 members]. The high-i families were not reported in Parker et al. (2008) because they only used the analytic proper elements, which are not available for the high-i orbits. The strength of Parker et al.’s identification scheme was its reliability. Indeed, of all the families reported in Parker et al. (2008), only (1044)  Teutonia, (1296) Andree, and (2007)  McCuskey (part of the Nysa-Polana complex) are not included among the notable families here [Parker et al.’s (110) Lydia family appears here as the (363) Padua family]. Masiero et al. (2013) (hereafter M13) reported 28 new cases and found that 24 old families were lost when compared to the family lists in Nesvorný (2012). Most families not listed in M13 are well-defined families such as Karin, Beagle, Datura, Emilkowalski, Lucascavin, etc. These families were not listed in M13, because they overlap with larger families (and were included in their membership lists in M13) or because they only have a few known members (i.e., fall below Nmin used in M13). On the other hand, we verified that many new cases reported in Masiero et al. (2013) are genuine new families that can be conveniently found with the albedo cutoff [e.g., the (84) Klio, (144) Vibilia, (313) Chaldaea — which is the same as (1715) Salli in M13  — (322)  Phaeo, (623)  Chimarea, (816)  Juliana, and (1668) Hanna families]. These families were included here. In some cases, we found that M13’s new family barely stands out from the background and thus seems uncertain. To stay on the safe side, we therefore report these cases as the candidate families in Note 10. These families may be

C 0 (10–4 AU)

Tax. Type pV

References and Notes

(25) Phocaea

(3) Juno (15) Eunomia

501 502 55 50

150 1684 5670

1989

231 256

(25,587)

Central Main Belt, 2.5 < a < 2.82 AU, i < 17.5° 25 0.5 ± 0.2 S 0.25 100 2.0 ± 0.7 S 0.19

Inner Main Belt, 2.0 < a < 2.5 AU, i > 17° — 2.0 ± 1.0 S 0.22

cratering, relation to H chondrites? continues beyond 5:2?

Carruba (2009b), Carruba et al. (2010)

Inner Main Belt, 2.0 < a < 2.5 AU, i < 17.5° (4) Vesta 50 15252 525 50 1.5 ± 0.5 V 0.35 source of HEDs, two overlapping families? (8) Flora 60 13786 (8,254) — 2.5 ± 0.5 S 0.30 dispersed, source of LL NEAs, Dykhuis et al. (2014) (298) Baptistina 45 2500 21 — 0.25 ± 0.05 X 0.16 related to K/T impact? Bottke et al. (2007) (20) Massalia 55 6424 132 27 0.25 ± 0.05 S 0.22 Vokrouhlický et al. (2006b) (44) Nysa-Polana 50 19073 (135,142,495) — 1.0 ± 0.5 SFC 0.28/0.06 Walsh et al. (2013), Dykhuis and Greenberg (2015) (163) Erigone 50 1776 72 46 0.2 ± 0.05 CX 0.06 Vokrouhlický et al. (2006b) (302) Clarissa 55 179 34 15 0.05 ± 0.01 X 0.05 compact with ears, cratering (752) Sulamitis 55 303 61 35 0.3 ± 0.1 C 0.04 (1892) Lucienne 100 142 11 11 0.15 ± 0.05 S 0.22 (27) Euterpe 65 474 110 16 0.50 ± 0.25 S 0.26 (1270) Datura 10 6 8 3 — S 0.21 Nesvorný et al. (2006c) (21509) Lucascavin 10 3 — — — S — Nesvorný and Vokrouhlický (2006) (84) Klio 130* 330 78 33 0.75 ± 0.25 C 0.07 interloper 12?, Masiero et al. (2013) (623) Chimaera 120 108 43 21 0.3 ± 0.1 CX 0.06 Masiero et al. (2013) (313) Chaldaea 130* 132 (313,1715) — 1.0 ± 0.5 C 0.07 1715 in Masiero et al. (2013) (329) Svea 150 48 70 21 0.3 ± 0.1 CX 0.06 new, near 3:1 (108138) 2001 GB11 20 9 — — — — — new, compact

401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417

701

(153) Hilda 130 409 164 (1911) Schubart 60 352 80 (434) Hungaria 100 2965 10 (624) Hector 50 12 231 (3548) Eurybates 50 218 68 (9799) 1996 RJ 60 7 72 James Bond ∞ 1 (himself) (20961) Arkesilaos 50 37 — (4709) Ennomos 100 30 (1867,4709) (247341) 2001 UV209 100 13 —

Hungarias, Hildas, and Jupiter Trojans — — C 0.04 Brož et al. (2011) 91 — C 0.03 Brož and Vokrouhlický (2008) 24 0.3 ± 0.1 E 0.35 Warner et al. (2009), Milani et al. (2010) — — — — satellite, Marchis et al. (2014), Rozehnal and Brož (2013) 87 — CP 0.06 Roig et al. (2008), Brož and Rozehnal (2011) 26 — — 0.06 Rozehnal and Brož (2013) — — ASP variable Campbell et al. (1995) — — — — Rozehnal and Brož (2013) — — — 0.06 Rozehnal and Brož (2013) — — — 0.09 Rozehnal and Brož (2013)

DLM Dfrag (km) (km)

001 002 003 004 005 006 007 008 009 010

dcut No. of FIN Family Name (m s–1) Members

TABLE 2. Notable asteroid families.

Nesvorný et al.:  Identification and Dynamical Properties of Asteroid Families   313

dcut No. of (m s–1) Members DLM Dfrag (km) (km)

C0 (10–4 AU)

Tax. Type pV

References and Notes

Central Main Belt, 2.5 < a < 2.82 AU, i < 17.5° (continued) — — — — — — — — 46 Hestia moved to candidates 503 (128) Nemesis 50 1302 178 50 0.25 ± 0.05 C 0.05 3827 in Milani et al. (2014), 125 in Cellino et al. (2002) 504 505 (145) Adeona 50 2236 141 78 0.7 ± 0.3 C 0.07 506 (170) Maria 60 2940 (472,170) — 2.0 ± 1.0 S 0.25 (472) Roma in Masiero et al. (2013) (363) Padua 45 1087 91 48 0.5 ± 0.2 X 0.10 Carruba (2009a), also known as the (110) Lydia family 507 508 (396) Aeolia 20 296 46 13 0.075 ± 0.025 X 0.17 compact, young? 509 (410) Chloris 80 424 107 56 0.75 ± 0.25 C 0.06 eroded 510 (569) Misa 50 702 65 57 0.5 ± 0.2 C 0.03 V-shaped subfamily inside 511 (606) Brangane 55 195 36 18 0.04 ± 0.01 S 0.10 compact, 606 offset, interloper? (668) Dora 45 1259 (1734,668) — — C 0.05 668 offset, 1734 in Masiero et al. (2013), V-shaped 512 subfamily 513 (808) Merxia 55 1215 34 28 0.3 ± 0.1 S 0.23 Vokrouhlický et al. (2006b) 514 (847) Agnia 30 2125 (847,3395) — 0.15 ± 0.05 S 0.18 z1 resonance, Vokrouhlický et al. (2006c) (1128) Astrid 60 489 42 29 0.12 ± 0.02 C 0.08 Vokrouhlický et al. (2006b) 515 516 (1272) Gefion 50 2547 (2595,1272) — 0.8 ± 0.3 S 0.20 source of L chondrites? Nesvorný et al. (2009), also known as 93 and 2595 (3815) Konig 55 354 22 34 0.06 ± 0.03 CX 0.04 compact, young? Nesvorný et al. (2003), 342 and 1639 517 offset (1644) Rafita 70 1295 (1658,1587) — 0.5 ± 0.2 S 0.25 1644 probably interloper 518 519 (1726) Hoffmeister 45 1819 (272,1726) — 0.20 ± 0.05 CF 0.04 (272) Antonia in Masiero et al. (2013), but 272 offset (4652) Iannini 25 150 5 10 — S 0.32 1547 offset, compact, Nesvorný et al. (2003) 520 (7353) Kazuya 50 44 11 10 — S 0.21 small clump 521 522 (173) Ino 50 463 161 21 0.5 ± 0.2 S 0.24 also known as 18466, large and dark 173 is probably interloper, ears? (14627) Emilkowalski 10 4 7 3 — S 0.20 Nesvorný and Vokrouhlický (2006) 523 (16598) 1992 YC2 524 10 3 — — — S — Nesvorný and Vokrouhlický (2006) (2384) Schulhof 10 6 12 4 — S 0.27 Vokrouhlický and Nesvorný (2011) 525 526 (53546) 2000 BY6 40 58 8 18 — C 0.06 Milani et al. (2014) (5438) Lorre 10 2 30 — — C 0.05 Novaković et al. (2012) 527 528 (2782) Leonidas 50 135 (4793,2782) — — CX 0.07 new, related to 144? 529 (144) Vibilia 100* 180 142 — — C 0.06 Masiero et al. (2013), PDS list identical to 2782 (322) Phaeo 100* 530 146 72 31 0.3 ± 0.1 X 0.06 Cellino et al. (2002), joins (2669) Shostakovich (2262) Mitidika 100* 531 653 (404,5079) — — C 0.06 dispersed, 404 offset, 2262 has pV = 0.21 532 (2085) Henan 50 1872 18 32 0.75 ± 0.25 L 0.20 2085 offset in iP, 4 families in Milani et al. (2014) 533 (1668) Hanna 60 280 22 32 0.2 ± 0.1 CX 0.05 Masiero et al. (2013) 534 (3811) Karma 60 124 26 24 0.25 ± 0.05 CX 0.05 Milani et al. (2014)

FIN Family Name

TABLE 2. (continued)

314   Asteroids IV

dcut No. of (m s–1) Members DLM Dfrag (km) (km)

C0 (10–4 AU)

Tax. Type pV

relation to the Charis family beyond 5:2? 10955 and 19466 in Milani et al. Milani et al. (2014), includes 396 Cellino et al. (2014) new, compact, diagonal in (aP,eP) new, part above 2.6778 AU down in iP new, compact new, large 387,547,599?

References and Notes

Outer Main Belt, 2.82 < a < 3.7 AU, i < 17° (10) Hygiea 60 4854 428 — — CB 0.06 Carruba et al. (2014) 601 (24) Themis 60 4782 177 230 2.5 ± 1.0 C 0.07 includes 656 Beagle, Nesvorný et al. (2008b) 602 (87) Sylvia 130 255 263 — — X 0.05 Vokrouhlický et al. (2010) 603 (137) Meliboea 85 444 (511,137) — — C 0.05 (511) Davida in Masiero et al. (2013) 604 (158) Koronis 45 5949 (208,158,462) — 2.0 ± 1.0 S 0.15 (208) Lacrimosa in Masiero et al. (2013) 605 (221) Eos 45 9789 (221,579,639) — 1.5 ± 0.5 K 0.13 Vokrouhlický et al. (2006a), Brož and Morbidelli (2013) 606 607 (283) Emma 40 76 122 56 0.3 ± 0.1 C 0.05 affected by the z1 resonance? (293) Brasilia 50 579 (3985) — 0.20 ± 0.05 X 0.18 293 interloper?, also known as (1521) Sejnajoki, 608 Nesvorný et al. (2003) 609 (490) Veritas 30 1294 113 78 0.2 ± 0.1 CPD 0.07 see Section 3 (832) Karin 10 541 17 16 0.03 ± 0.01 S 0.21 see Section 3, Harris et al. (2009) 610 611 (845) Naema 35 301 61 37 0.20 ± 0.05 C 0.08 612 (1400) Tirela 50 1395 (1040,1400) — 0.75 ± 0.25 S 0.07 8 families in Milani et al. (2014) 613 (3556) Lixiaohua 45 756 (3330,3556) — 0.25 ± 0.05 CX 0.04 3330 offset, Novaković (2010) 614 (9506) Telramund 45 468 (179,9506) — — S 0.22 (179) Klytaemnestra in Masiero et al. and Milani et al. (18405) 1993 FY12 615 50 104 9 14 0.08 ± 0.03 CX 0.17

Central Main Belt, 2.5 < a < 2.82 AU, i > 17.5° 801 (2) Pallas 350 128 513 40 — B 0.16 Carruba et al. (2010, 2012), part beyond 5:2 802 (148) Gallia 200 182 81 19 0.5 ± 0.1 S 0.17 large interlopers 803 (480) Hansa 200 1094 56 62 — S 0.26 2 families in Milani et al. (2014) 804 (686) Gersuind 120 415 49 36 — S 0.15 2 families in Milani et al. (2014) 805 (945) Barcelona 150 306 27 19 0.25 ± 0.05 S 0.25 2 families in Milani et al. (2014) 806 (1222) Tina 200 96 26 10 0.10 ± 0.05 X 0.34 in the g–g6 = 0 resonance, Carruba and Morbidelli (2011) (4203) Brucato 200 342 18 44 0.5 ± 0.2 CX 0.06 1263 interloper? Carruba (2010), 4 families in 807 Milani et al. (2014)

Central Main Belt, 2.5 < a < 2.82 AU, i < 17.5° (continued) 535 (2732) Witt 45 1816 11 25 0.75 ± 0.25 S 0.26 536 (2344) Xizang 65 275 17 20 0.3 ± 0.1 — 0.12 537 (729) Watsonia 130 99 52 38 — L 0.13 538 (3152) Jones 40 22 37 11 — T 0.05 539 (369) Aeria 90 272 75 17 0.3 ± 0.1 X 0.17 540 (89) Julia 70 33 147 6 — S 0.19 541 (1484) Postrema 100 108 47 — — CX 0.05

FIN Family Name

TABLE 2. (continued)

Nesvorný et al.:  Identification and Dynamical Properties of Asteroid Families   315

120 120 120 50 50

(31) Euphrosyne (702) Alauda (909) Ulla (1303) Luthera (780) Armenia

901 902 903 904 905

2035 1294 26 163 40

276 191 113 87 98

Tax. Type pV

Outer Main Belt, 2.82 < a < 3.5 AU, i > 17.5° 130 — C 0.06 — 2.5 ± 1.0 B 0.07 28 — X 0.05 56 — X 0.04 22 — C 0.05

Outer Main Belt, 2.82 < a < 3.7 AU, i < 17.5° 45 — C 0.08 50 — CX 0.06 18 0.13 ± 0.03 C 0.07 6 0.075 ± 0.025 S 0.27 28 0.07 ± 0.03 C 0.09 13 0.010 ± 0.005 S 0.14 27 0.50 ± 0.25 C 0.05 55 — X 0.05 23 — X 0.04 23 0.15 ± 0.05 C 0.05 — — X 0.19 — 0.10 ± 0.05 CX 0.05 — — S 0.10 — 0.25 ± 0.05 S 0.21 38 — CX 0.07 — — CX 0.06 26 — C 0.05 35 — S 0.23 33 — CX 0.07 14 — S 0.16 16 — CX 0.05 15 — CX 0.05 31 0.5 ± 0.2 X 0.07 18 0.2 ± 0.1 CX 0.05 — — — — 39 — CX 0.05

C0 (10–4 AU)

also known as (781) Kartivelia compact

Carruba et al. (2014), 3 families in Milani et al. (2014) 276 and 1901 offset, 4 families in Milani et al. (2014)

several large bodies Masiero et al. and Milani et al. Masiero et al. and Milani et al. compact, recent? dispersed, many sizable members Milani et al. (2014) Milani et al. (2014) new new, large 132999 new, 21885 in Milani et al. (2014) new Novaković et al. (2014) Masiero et al. (2013)

also known as 12573

large 1191

36824 interloper? 656 and 90 offset, Nesvorný et al. (2008b) young, Molnar and Haegert (2009)

16286 in Milani et al. (2014), related to Witt family? 778 offset, Novaković (2010)

References and Notes

Columns are (1) Family Identification Number (FIN), (2) family name, (3) cutoff distance (dcut; asterisk denotes dcut used on a subset of asteroids with pV < 0.15), (4) number of family members identified with dcut, (5) largest member(s) in the family [either the number designation of the largest member(s), in parenthesis, if different from the asteroid after which the family is named, or the estimated diameter of the largest member, DLM)], (6) diameter of a sphere with volume equivalent to that of all fragments (Dfrag), (7) C0 parameter defined in section 4, (8) taxonomic type, (9) mean geometric albedo from WISE (pV), and (10) various references and notes. We do not report tage here but note that tage can be estimated from C0 given in column 7 and equation (2). For additional information on asteroid families, see http://sirrah. troja.mff.cuni.cz/˜mira/mp/fams/ (Brož et al., 2013).

80 60 60 120 25 8 120 150 100 120 100 80 95 70 50 70 40 100 80 60 30 60 45 70 10 80

(627) Charis (778) Theobalda (1189) Terentia (10811) Lau (656) Beagle (158) Koronis(2) (81) Terpsichore (709) Fringilla (5567) Durisen (5614) Yakovlev (7481) San Marcello (15454) 1998 YB3 (15477) 1999 CG1 (36256) 1999 XT17 (96) Aegle (375) Ursula (618) Elfriede (918) Itha (3438) Inarradas (7468) Anfimov (1332) Marconia (106302) 2000 UJ87 (589) Croatia (926) Imhilde P/2012 F5 (Gibbs) (816) Juliana

616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641

DLM Dfrag (km) (km)

808 50 376 66 79 63 56 8 148 54 246 34 138 123 134 96 27 34 67 13 144 (3978,7489) 38 (3156,15454) 248 — 58 (15610,36256) 99 165 1466 (1306,375) 63 122 54 21 38 25 58 10 34 50 64 7 93 92 43 50 8 — 76 68

dcut No. of (m s–1) Members

FIN Family Name

TABLE 2. (continued)

316   Asteroids IV

Nesvorný et al.:  Identification and Dynamical Properties of Asteroid Families   317

Eccentricity eP

0.3

0.2

0.1

sin(Inclination iP)

0

0.4

0.2

0

2.5

3

Semimajor Axis aP (AU) Fig. 9. The orbital location of notable families from Table 2. A triangle is placed at the orbit of an asteroid after which the family is named. The label near the triangle shows the designation number of that asteroid.

real, but their statistical significance needs to be carefully tested with the new data. Finally, we compare the family synthesis with Milani et al. (2014) (hereafter M14), who used the newest catalog from all previous works discussed here. They identified many new families that are certain beyond doubt [e.g., (96) Aegle, (618) Elfriede, (2344) Xizang, (3438) Inarradas, (3811) Karma, (7468) Anfimov, and (53546) 2000 BY6; the (96) Aegle and (618) Elfriede families were also reported in M13]. These cases highlight the strength of the M14 identification scheme and are included in the family synthesis in Table 2. Some smaller families located inside bigger families [e.g., the (832)  Karin family in the (158) Koronis family, (656) Beagle in (24) Themis] were not reported in M14. In addition, several families were not reported, presumably because the QRL was set too low to detect them. This happens, most notably, in the 2.82–2.96-AU region (i.e., between the 5:2 and 7:3 resonances), where the number density of asteroids is relatively low (see Figs. 1 and 9). The notable cases in this region include the (81) Terpsichore, (709) Fringilia,

(5567) Durisen, (5614) Yakovlev, (7481) San Marcello, and (10811) Lau families. A possible solution to this issue, in terms of the M14 identification scheme, would be to use a separate QRL level for the 2.82–2.96-AU region. Also, several families were split in M14 into several parts. This affects (8) Flora (split in four parts), (31) Euphrosyne (three parts), (221) Eos (five parts), (702) Alauda (four parts), (1400) Tirela (eight parts), (2085) Henan (four parts), (4203) Brucato (four parts) (here we only list families that were split to three or more parts in M14). 8. CONCLUSIONS It is clear from several different arguments that the list of known families must be largely incomplete. For example, most families with an estimated parent body size below =100–200 km are found to have ages tage  < 1 G.y. (e.g., Brož et al., 2013). In contrast, the rate of impacts in the main belt, and therefore the rate of family-forming events, should have been roughly unchanging with time over the

318   Asteroids IV past =3.5 G.y. (and probably raised quite a bit toward the earliest epochs). So, there must be many missing families with the formation ages tage > 1 G.y. (Note 12). These families are difficult to spot today, probably because they have been dispersed by dynamical processes, lost members by collisional grinding, and therefore do not stand out sufficiently well above the dense main-belt background (they are now part of the background). The significant incompleteness of known families is also indicated by the extrapolation of the number of families detected in the 2.82–2.96-AU zone to the whole main belt. As we hinted on at the end of the last section, the 2.82–2.96AU zone is sparsely populated such that asteroid families can be more easily detected there. Nearly 20 families with iP < 17.5° were identified in this region. In comparison, the 2.96–3.3-AU zone, where =20 families with iP < 17.5° can also be found, is about twice as wide as the 2.82–2.96-AU zone and contains about twice as many large asteroids. A straightforward conclusion that can be inferred from this comparison, assuming everything else is equal, is that the families in the 2.96–3.3-AU zone are (at least) a factor of ~2 incomplete. A similar argument applies to the inner and central belts. This is actually good news for future generations of planetary scientists, because this field is open for new discoveries. Figuring out how to find the missing asteroid families with tage > 1 G.y. will not be easy. One way forward would be to improve our capability to model the dynamical evolution of main-belt asteroids over gigayear timescales, such that we can rewind the clock and track fragments back to their original orbits. The modeling of the Yarkovsky effect could be improved, for example, if we knew the spin states, densities, conductivity, etc., of small main-belt asteroids on an individual basis. Another approach would consist of identifying families based on the physical properties of their members. While this method is already in use, mainly thanks to data from SDSS and WISE, we anticipate that it can be pushed much further, say, with automated spectroscopic surveys, or, in the more distant future, with routine sampling missions. 9. NOTES Note 1 — Alternatively, one can use the frequencies n, g, and s (Carruba and Michtchenko, 2007, 2009), where n is the mean orbital frequency and g and s are the (constant) precession frequencies of the proper perihelion longitude vP and the proper nodal longitude WP, respectively. The use of frequencies, instead of the proper elements, can be helpful for asteroid families near or inside the secular orbital resonances [e.g., the Tina family in the n6 resonance (Carruba and Morbidelli, 2011)]. Note 2  — Additional methods were developed and/or adapted for specific populations of asteroids such as the ones on the high-inclination and high-eccentricity orbits (Lemaître and Morbidelli, 1994) or in orbital resonances (Morbidelli, 1993; Milani, 1993; Beaugé and Roig, 2001; Brož and Vokrouhlický, 2008; Brož and Rozehnal, 2011). Note 3 — http://hamilton.dm.unipi.it/astdys/

Note 4 — See Bendjoya and Zappalà (2002) for a discussion of other clustering algorithms such as the wavelet analysis method (WAM) and D-criterion. The WAM was shown to produce results that are in good agreement with those obtained from the HCM (Zappalà et al., 1994). The D-criterion was originally developed to identify meteorite streams (Southwork and Hawkins, 1963). These methods have not been used for the classification of asteroid families in the past decade, and we therefore do not discuss them here. Note 5 — The SDSS measured flux densities in five bands with effective wavelengths 354, 476, 628, 769, and 925  nm. The WISE mission measured fluxes in four wavelengths (3.4, 4.6, 12, and 22  µm), and combined the measurements with a thermal model to calculate albedos (pV) and diameters (D). The latest public releases of these catalogs include color or albedo data for over 100,000 main-belt asteroids with known orbits, of which about 25,000 have both color and albedo measurements. The catalogs are available at http://www.sdss. org/dr6/products/value added/index.html and http://irsa.ipac. caltech.edu/Missions/wise.html. Note 6 — Most but not all asteroid families are physically homogeneous. The Eos family has the highest diversity of taxonomic classes of any known family (e.g., Mothé-Diniz et al., 2008). This diversity has led to the suggestion that the Eos parent body was partially differentiated. It can also be the source of carbonaceous chondrites (Clark et al., 2009). The Eunomia family may be another case of a relatively heterogeneous family (e.g., Nathues et al., 2005). See Weiss and Elkins-Tanton (2013) for a review. Note 7 — Dell’Oro et al. (2004) attempted to model observed family shapes by Gaussian ellipsoids. The distribution of |f | obtained in this work was strongly peaked near p/2, while a more uniform distribution between 0 and p would be expected if different breakups occurred at random orbital phases. This result was attributed to the Yarkovsky effect. Note 8 — Nesvorný et al. (2008a) found evidence for a large population of V-type asteroids with slightly lower orbital inclinations (iP = 3°–4°) than the Vesta family (iP = 5°). Because these asteroids could not have dynamically evolved from the Vesta family region to their present orbits in =1 G.y., they are presumably fragments excavated from (4) Vesta’s basaltic crust by an earlier impact. Note 9 — Other asteroid families whose long-term dynamics have been studied in detail, listed here in alphabetical order, are the Adeona family [affected in eP and iP by the 8:3 resonance at 2.705 AU (Carruba et al., 2003)], Agnia family [inside the z1 resonance (Vokrouhlický et al., 2006c)], Astrid family [near the border of the 5:2 resonance (Vokrouhlický et al., 2006b)], Eunomia family (Carruba et al., 2007b), Euphrosyne family [located in a region with many resonances, including g–g6 = 0, near the inner border of the 2:1 resonance (Carruba et al., 2014)], Erigone family [cut in the middle by the z2 resonance (Vokrouhlický et al., 2006b)], Gefion family [affected by various resonances near 2.75 AU (Carruba et al., 2003; Nesvorný et al., 2009)], Hilda and Schubart families in the 3:2 resonance with Jupiter (Brož and Vokrouhlický, 2008), Hungaria family [perturbed by 2g–g5–g6 = 0 and other secular resonances below 1.93 AU (Warner et al., 2009; Milani et al., 2010); see also Galiazzo et al. (2013, 2014) for the contribution of Hungarias to the E-type NEAs and Ćuk et al. (2014) for their suggested relation to the aubrite meteorites], Hygiea family (Carruba, 2013; Carruba et al., 2014), Massalia family [the part with

Nesvorný et al.:  Identification and Dynamical Properties of Asteroid Families   319

a P  > 2.42  AU disturbed by the 1:2 resonance with Mars (Vokrouhlický et al., 2006b)], Merxia family [spread by the 3J-1S-1 three-body resonance at aP = 2.75 AU (Vokrouhlický et al., 2006b)], Padua family (Carruba, 2009a), Pallas family (Carruba et al., 2011), Phocaea family (Carruba, 2009b), Sylvia family [(87) Sylvia has two satellites, possibly related to the impact that produced the Sylvia family (Vokrouhlický et al., 2010)], and Tina family (Carruba and Morbidelli, 2011). Note 10 — The candidate families are (929) Algunde, (1296) Andree, (1646)  Rosseland, (1942)  Jablunka, (2007)  McCuskey, (2409)  Chapman, (4689)  Donn, (6246)  Komurotoru, and (13698) 1998 KF35 in the inner belt; (46) Hestia, (539) Palmina, (300163) P/2006 VW139, (3567) Alvema, and (7744) 1986 QA1 in the central belt; and (260) Huberta, (928) Hilrun, (2621) Goto, (1113) Katja, and (8737) Takehiro in the outer belt. We tentatively moved the (46)  Hestia family, previously known as FIN  503, to the family candidate status, because the existence of this group has not been conclusively proven with present data. The previously reported groups around (5) Astraea, (1044) Teutonia, (3110)  Wagman, (4945)  Ikenozenni, (7744)  1986  QA 1 , (8905) Bankakuko, (25315) 1999 AZ8, and (28804) 2000 HC81 seem to align with the z1 = g + s–g6–s6 = 0 resonance and are probably an artifact of the HCM chaining. Note 11 — http://sbn.psi.edu/pds/resource/nesvornyfam.html Note 12 — The list of known families corresponding to parent bodies with D > 200 km, on the other hand, is probably reasonably complete, because the estimated ages of these families appear to be randomly distributed over 4  G.y. (Brož et al., 2013). These largest families can therefore be used to constrain the collisional history of the asteroid belt (see the chapter by Bottke et al. in this volume). Acknowledgments. The work of M.B. was supported by the Czech Grant Agency (grant no.  P209-12-01308S). The work of V.C. was supported by the São Paulo State (FAPESP grant no. 2014/06762-2) and Brazilian (CNPq grant no. 305453/2011-4) Grant Agencies.

REFERENCES Beaugé C. and Roig F. (2001) A semi-analytical model for the motion of the Trojan asteroids: Proper elements and families. Icarus, 153, 391–415. Bendjoya Ph. and Zappalà V. (2002) Asteroid family identification. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 613–618. Univ. of Arizona, Tucson. Benz W. and Asphaug E. (1999) Catastrophic disruptions revisited. Icarus, 142, 5–20. Bottke W. F., Vokrouhlický D., Brož M., et al. (2001) Dynamical spreading of asteroid families by the Yarkovsky effect. Science, 294, 1693–1696. Bottke W. F., Vokrouhlický D., Rubincam D. P., and Brož M. (2002) The effect of Yarkovsky thermal forces on the dynamical evolution of asteroids and meteoroids. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 395–408. Univ. of Arizona, Tucson. Bottke W. F., Durda D. D., Nesvorný D., et al. (2005a) The fossilized size distribution of the main asteroid belt. Icarus, 175, 111–140. Bottke W. F., Durda D. D., Nesvorný D., et al. (2005b) Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion. Icarus, 179, 63–94. Bottke W. F., Vokrouhlický D., Rubincam D. P., and Nesvorný D. (2006) The Yarkovsky and YORP effects: Implications for asteroid dynamics. Annu. Rev. Earth Planet. Sci., 34, 157–191. Bottke W. F., Vokrouhlický D., and Nesvorný D. (2007) An asteroid breakup 160 Myr ago as the probable source of the K/T impactor. Nature, 449, 48–53.

Bottke W. F., Vokrouhlický D., Walsh K. J., Delbo M., Michel P., Lauretta D. S., Campins H., Connolly H. C., Scheeres D. J., and Chelsey S. R. (2015) In search of the source of asteroid (101955) Bennu: Applications of the stochastic YORP model. Icarus, 247, 191–217. Bowell E., Muinonen K., and Wasserman L. H. (1994) A public-domain asteroid orbit data base. Asteroids Comets Meteors 1993, 160, 477. Brož M. and Morbidelli A. (2013) The Eos family halo. Icarus, 223, 844–849. Brož M. and Rozehnal J. (2011) Eurybates — the only asteroid family among Trojans? Mon. Not. R. Astron. Soc., 414, 565–574. Brož M. and Vokrouhlický D. (2008) Asteroid families in the first-order resonances with Jupiter. Mon. Not. R. Astron. Soc., 390, 715–732. Brož M., Vokrouhlický D., Morbidelli A., Nesvorný D., and Bottke W. F. (2011) Did the Hilda collisional family form during the late heavy bombardment? Mon. Not. R. Astron. Soc., 414, 2716–2727. Brož M., Morbidelli A., Bottke W. F., et al. (2013) Constraining the cometary flux through the asteroid belt during the late heavy bombardment. Astron. Astrophys., 551, A117. Campbell M. (1995) Golden Eye. MGM/UA Distribution Company. Carruba V. (2009a) The (not so) peculiar case of the Padua family. Mon. Not. R. Astron. Soc., 395, 358–377. Carruba V. (2009b) An analysis of the region of the Phocaea dynamical group. Mon. Not. R. Astron. Soc., 398, 1512–1526. Carruba V. (2010) The stable archipelago in the region of the Pallas and Hansa families. Mon. Not. R. Astron. Soc., 408, 580–600. Carruba V. (2013) An analysis of the Hygiea asteroid family orbital region. Mon. Not. R. Astron. Soc., 431, 3557–3569. Carruba V. and Michtchenko T.A. (2007) A frequency approach to identifying asteroid families. Astron. Astrophys., 75, 1145–1158. Carruba V. and Michtchenko T. A. (2009) A frequency approach to identifying asteroid families. II. Families interacting with non-linear secular resonances and low-order mean-motion resonances. Astron. Astrophys., 493, 267–282. Carruba V. and Morbidelli A. (2011) On the first nu(6) anti-aligned librating asteroid family of Tina. Mon. Not. R. Astron. Soc., 412, 2040–2051. Carruba V., Burns J. A., Bottke W. F., and Nesvorný D. (2003) Orbital evolution of the Gefion and Adeona asteroid families: Close encounters with massive asteroids and the Yarkovsky effect. Icarus, 162, 308–327. Carruba V., Michtchenko T. A., Roig F., Ferraz-Mello S., and Nesvorný D. (2005) On the V-type asteroids outside the Vesta family. I. Interplay of nonlinear secular resonances and the Yarkovsky effect: The cases of 956 Elisa and 809 Lundia. Astron. Astrophys., 441, 819–829. Carruba V., Roig F., Michtchenko T. A., Ferraz-Mello S., and Nesvorný D. (2007a) Modeling close encounters with massive asteroids: A Markovian approach. An application to the Vesta family. Astron. Astrophys., 465, 315–330. Carruba V., Michtchenko T. A., and Lazzaro D. (2007b) On the V-type asteroids outside the Vesta family. II. Is (21238) 1995 WV7 a fragment of the long-lost basaltic crust of (15) Eunomia? Astron. Astrophys., 473, 967–978. Carruba V., Machuca J. F., and Gasparino H. P. (2011) Dynamical erosion of asteroid groups in the region of the Pallas family. Mon. Not. R. Astron. Soc., 412, 2052–2062. Carruba V., Huaman M. E., Douwens S., and Domingos R. C. (2012) Chaotic diffusion caused by close encounters with several massive asteroids. Astron. Astrophys., 543, A105. Carruba V., Domingos R. C., Nesvorný D., et al. (2013a) A multidomain approach to asteroid families identification. Mon. Not. R. Astron. Soc., 433, 2075–2096. Carruba V., Huaman M. E., Domingos R. C., and Roig F. (2013b) Chaotic diffusion caused by close encounters with several massive asteroids II: The regions of (10) Hygiea, (2) Pallas, and (31) Euphrosyne, Astron. Astrophys., 550, A85. Carruba V., Aljbaae S., and Souami D. (2014) Peculiar Euphrosyne. Astrophys. J., 792, 46–61. Cellino A., Bus S. J., Doressoundiram A., and Lazzaro D. (2002) Spectroscopic properties of asteroid families. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 633–643. Univ. of Arizona, Tucson. Cellino A., Dell’Oro A., and Zappalà V. (2004) Asteroid families: Open problems. Planet. Space Sci., 52, 1075–1086. Cellino A., Dell’Oro A., and Tedesco E. F. (2009) Asteroid families: Current situation. Planet. Space Sci., 57, 173–182.

320   Asteroids IV Cellino A., Bagnulo S., Tanga P., Novaković B., and Delbó M. (2014) A successful search for hidden Barbarians in the Watsonia asteroid family. Mon. Not. R. Astron. Soc. Lett., 439, 75–79. Cibulková H., Brož M., and Benavidez P. G. (2014) A six-part collisional model of the main asteroid belt. Icarus, 241, 358–372. Cimrman J. (1917) On the literal expansion of the perturbation Hamiltonian and its applicability to the curious assemblages of minor planets. Cimrman Bull., 57, 132–135. Clark B. E., Ockert-Bell M. E., Cloutis E. A., Nesvorný D., MothéDiniz T., and Bus S. J. (2009) Spectroscopy of K-complex asteroids: Parent bodies of carbonaceous meteorites? Icarus, 202, 119–133. Ćuk M., Gladman B. J., and Nesvorný D. (2014) Hungaria asteroid family as the source of aubrite meteorites. Icarus, 239, 154–159. Delisle J.-B. and Laskar J. (2012) Chaotic diffusion of the Vesta family induced by close encounters with massive asteroids. Astron. Astrophys., 540, A118. Dell’Oro A. and Cellino A. (2007) The random walk of main belt asteroids: Orbital mobility by non-destructive collisions. Mon. Not. R. Astron. Soc., 380, 399–416. Dell’Oro A., Bigongiari G., Paolicchi P., and Cellino A. (2004) Asteroid families: Evidence of ageing of the proper elements. Icarus, 169, 341–356. Dermott S. F., Nicholson P. D., Burns J. A., and Houck J. R. (1984) Origin of the solar system dust bands discovered by IRAS. Nature, 312, 505–509. Dermott S. F., Kehoe T. J. J., Durda D. D., Grogan K., and Nesvorný D. (2002) Recent rubble-pile origin of asteroidal solar system dust bands and asteroidal interplanetary dust particles. Asteroids Comets Meteors, 500, 319–322. Durda D. D., Bottke W. F., Enke B. L., Merline W. J., Asphaug E., Richardson D. C., and Leinhardt Z. M. (2004) The formation of asteroid satellites in large impacts: Results from numerical simulations. Icarus, 170, 243–257. Durda D. D., Bottke W. F., Nesvorný D., et al. (2007) Size-frequency distributions of fragments from SPH/ N-body simulations of asteroid impacts: Comparison with observed asteroid families. Icarus, 186, 498–516. Dykhuis M. and Greenberg R. (2015) Collisional family structure within the Nysa-Polana complex. Icarus, in press, arXiv:1501.04649. Dykhuis M. J., Molnar L., Van Kooten S. J., and Greenberg R. (2014) Defining the Flora family: Orbital properties, reflectance properties and age. Icarus, 243, 111–128. Farley K. A., Vokrouhlický D., Bottke W. F., and Nesvorný D. (2006) A late Miocene dust shower from the break-up of an asteroid in the main belt. Nature, 439, 295–297. Florczak M., Lazzaro D., and Duffard R. (2002) Discovering new V-type asteroids in the vicinity of 4 Vesta. Icarus, 159, 178–182. Fujiwara A., Cerroni P., Davis D., Ryan E., and di Martino M. (1989) Experiments and scaling laws for catastrophic collisions. In Asteroids II (R. P. Binzel et al., eds.), pp. 240–265. Univ. of Arizona, Tucson. Galiazzo M. A., Bazsó Á., and Dvorak R. (2013) Fugitives from the Hungaria region: Close encounters and impacts with terrestrial planets. Planet. Space Sci., 84, 5–13. Galiazzo M. A., Bazsó Á., and Dvorak R. (2014) The Hungaria asteroids: Close encounters and impacts with terrestrial planets. Mem. Soc. Astron. Ital. Suppl., 26, 38. Gil-Hutton R. (2006) Identification of families among highly inclined asteroids. Icarus, 183, 93–100. Harris A. W., Mueller M., Lisse C. M., and Cheng A. F. (2009) A survey of Karin cluster asteroids with the Spitzer Space Telescope. Icarus, 199, 86–96. Hirayama K. (1918) Groups of asteroids probably of common origin. Astron. J., 31, 185–188. Ivezić Ž., Tabachnik S., Rafikov R., et al. (2001) Solar system objects observed in the Sloan Digital Sky Survey commissioning data. Astron. J., 122, 2749–2784. Knežević Z. and Milani A. (2000) Synthetic proper elements for outer main belt asteroids. Cel. Mech. Dyn. Astron., 78, 17–46. Knežević Z. and Pavlović R. (2002) Young age for the Veritas asteroid family confirmed? Earth Moon Planets, 88, 155–166. Knežević Z., Milani A., Farinella P., Froeschle Ch., and Froeschle Cl. (1991) Secular resonances from 2 to 50 AU. Icarus, 93, 316–330.

Knežević Z., Lemaître A. and Milani A. (2002) The determination of asteroid proper elements. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 603–612. Univ. of Arizona, Tucson. Lemaître A. and Morbidelli A. (1994) Proper elements for highly inclined asteroidal orbits. Cel. Mech. Dyn. Astron., 60, 29–56. Low F. J., Young E., Beintema D. A., Gautier T. N., et al. (1984) Infrared cirrus — New components of the extended infrared emission. Astrophys. J., 278, 19–22. Mainzer A., Grav T., Masiero J., et al. (2011) NEOWISE studies of spectrophotometrically classified asteroids: Preliminary results. Astrophys. J., 741, 90–115. Marchi S., McSween H. Y., O’Brien D. P., et al. (2012) The violent collisional history of asteroid 4 Vesta. Science, 336, 690. Marchis F., and 11 colleagues (2014) The puzzling mutual orbit of the binary Trojan asteroid (624) Hektor. Astrophys. J. Lett., 783, L37. Marsden B. G. (1980) The Minor Planet Center. Cel. Mech. Dyn. Astron., 22, 63–71. Marzari F., Farinella P., and Davis D. R. (1999) Origin, aging, and death of asteroid families. Icarus, 142, 63–77. Masiero J. R., Mainzer A. K., Grav T., et al. (2011) Main belt asteroids with WISE/NEOWISE. I. Preliminary albedos and diameters. Astrophys. J., 741, 68–88. Masiero J. R., Mainzer A. K., Grav T., Bauer J. M., and Jedicke R. (2012) Revising the age for the Baptistina asteroid family using WISE/NEOWISE data. Astrophys. J., 759, 14–28. Masiero J. R., Mainzer A. K., Bauer J. M., et al. (2013) Asteroid family identification using the hierarchical clustering method and WISE/NEOWISE physical properties. Astrophys. J., 770, 7–29. Michel P., Benz W., Tanga P., and Richardson D. C. (2001) Collisions and gravitational reaccumulation: Forming asteroid families and satellites. Science, 294, 1696–1700. Michel P., Benz W., and Richardson D. C. (2003) Disruption of fragmented parent bodies as the origin of asteroid families. Nature, 421, 608–611. Michel P., Benz W., and Richardson D. C. (2004) Catastrophic disruption of pre-shattered parent bodies. Icarus, 168, 420–432. Michel P., Jutzi M., Richardson D. C., and Benz W. (2011) The asteroid Veritas: An intruder in a family named after it? Icarus, 211, 535–545. Migliorini F., Zappalà V., Vio R., and Cellino A. (1995) Interlopers within asteroid families. Icarus, 118, 271–291. Milani A. (1993) The Trojan asteroid belt: Proper elements, chaos, stability and families. Cel. Mech. Dyn. Astron., 57, 59–94. Milani A. and Farinella P. (1994) The age of the Veritas asteroid family deduced by chaotic chronology. Nature, 370, 40–42. Milani A. and Knežević Z. (1990) Secular perturbation theory and computation of asteroid proper elements. Cel. Mech., 49, 347–411. Milani A. and Knežević Z. (1994) Asteroid proper elements and the dynamical structure of the asteroid main belt. Icarus, 107, 219–254. Milani A., Knežević Z., Novaković B., and Cellino A. (2010) Dynamics of the Hungaria asteroids. Icarus, 207, 769–794. Milani A., Cellino A., Knežević Z., et al. (2014) Asteroid families classification: Exploiting very large datasets. Icarus, 239, 46–73. Minton D. and Malhotra R. (2009) A record of planet migration in the main asteroid belt. Nature, 457, 1109–1111. Molnar L. A. and Haegert M. J. (2009) Details of recent collisions of asteroids 832 Karin and 158 Koronis. AAS/Division for Planetary Sciences Meeting Abstracts, 41, #27.05. Morbidelli A. (1993) Asteroid secular resonant proper elements. Icarus, 105, 48–66. Morbidelli A., Brasser R., Gomes R., Levison H. F., and Tsiganis K. (2010) Evidence from the asteroid belt for a violent past evolution of Jupiter’s orbit. Astron. J., 140, 1391–1401. Mothé-Diniz T., Roig F., and Carvano J. M. (2005) Reanalysis of asteroid families structure through visible spectroscopy. Icarus, 174, 54–80. Mothé-Diniz T., Carvano J. M., Bus S. J., et al. (2008) Mineralogical analysis of the Eos family from near-infrared spectra. Icarus, 195, 277–294. Nathues A., Mottola S., Kaasalainen M., and Neukum G. (2005) Spectral study of the Eunomia asteroid family. I. Eunomia. Icarus, 175, 452–463. Nesvorný D. (2010) Nesvorny HCM Asteroid Families V1.0. EAR-AVARGBDET-5-NESVORNYFAM-V1.0, NASA Planetary Data System.

Nesvorný et al.:  Identification and Dynamical Properties of Asteroid Families   321 Nesvorný D. (2012) Nesvorny HCM Asteroid Families V2.0. EAR-AVARGBDET-5-NESVORNYFAM-V2.0, NASA Planetary Data System. Nesvorný D. and Bottke W. F. (2004) Detection of the Yarkovsky effect for main-belt asteroids. Icarus, 170, 324–342. Nesvorný D. and Morbidelli A. (1999) An analytic model of three-body mean motion resonances. Cel. Mech. Dyn. Astron., 71, 243–271. Nesvorný D. and Vokrouhlický D. (2006) New candidates for recent asteroid breakups. Astron. J., 132, 1950–1958. Nesvorný D., Bottke W. F., Dones L., and Levison H. F. (2002a) The recent breakup of an asteroid in the main-belt region. Nature, 417, 720–771. Nesvorný D., Morbidelli, A., Vokrouhlický D., BottkeW. F., and Brož M. (2002b) The Flora family: A case of the dynamically dispersed collisional swarm? Icarus, 157, 155–172. Nesvorný D., Ferraz-Mello S., Holman M., and Morbidelli A. (2002c) Regular and chaotic dynamics in the mean-motion resonances: Implications for the structure and evolution of the asteroid belt. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 379–394. Univ. of Arizona, Tucson. Nesvorný D., Bottke W. F., Levison H. F., and Dones L. (2003) Recent origin of the solar system dust bands. Astrophys. J., 591, 486–497. Nesvorný D., Jedicke R., Whiteley R. J., and Ivezić Ž. (2005) Evidence for asteroid space weathering from the Sloan Digital Sky Survey. Icarus, 173, 132–152. Nesvorný D., Enke B. L., Bottke W. F., Durda D. D., Asphaug E., and Richardson D. C. (2006a) Karin cluster formation by asteroid impact. Icarus, 183, 296–311. Nesvorný D., Bottke W. F., Vokrouhlický D., Morbidelli A., and Jedicke R. (2006b) Asteroid families. Asteroids Comets Meteors, 229, 289-299. Nesvorný D., Vokrouhlický D., and Bottke W.F. (2006c) The breakup of a main-belt asteroid 450 thousand years ago. Science, 312, 1490. Nesvorný D., Roig F., Gladman B., et al. (2008a) Fugitives from the Vesta family. Icarus, 183, 85–95. Nesvorný D., Bottke W. F., Vokrouhlický D., et al. (2008b) Origin of the near-ecliptic circumsolar dust band. Astrophys. J., 679, 143–146. Nesvorný D., Vokrouhlický D., Morbidelli A., and Bottke W. F. (2009) Asteroidal source of L chondrite meteorites. Icarus, 200, 698–701. Novaković B. (2010) Portrait of Theobalda as a young asteroid family. Mon. Not. R. Astron. Soc., 407, 1477–1486. Novaković B., Tsiganis K., and Knežević Z. (2010a) Dynamical portrait of the Lixiaohua asteroid family. Cel. Mech. Dyn. Astron., 107, 35–49. Novaković B., Tsiganis K., and Knežević Z. (2010b) Chaotic transport and chronology of complex asteroid families. Mon. Not. R. Astron. Soc., 402, 1263–1272. Novaković B., Cellino A., and Knežević Z. (2011) Families among high-inclination asteroids. Icarus, 216, 69–81. Novaković B., Dell’Oro A., Cellino A., and Knežević Z. (2012a) Recent collisional jet from a primitive asteroid. Mon. Not. R. Astron. Soc., 425, 338–346. Novaković B., Hsieh H. H., and Cellino A. (2012b) P/2006 VW139: A main-belt comet born in an asteroid collision? Mon. Not. R. Astron. Soc., 424, 1432–1441. Novaković B., Hsieh H. H., Cellino A., Micheli M., and Pedanim M. (2014) Discovery of a young asteroid cluster associated with P/2012 F5 (Gibbs). Icarus, 231, 300–309. Parker A., Ivezić Ž., Jurić M., et al. (2008) The size distributions of asteroid families in the SDSS Moving Object Catalog 4. Icarus, 198, 138–155. Reddy V., Carvano J. M., Lazzaro D., et al. (2011) Mineralogical characterization of Baptistina asteroid family: Implications for K/T impactor source. Icarus, 216, 184–197.

Rozehnal J. and Brož M. (2013) Jovian Trojans: Orbital structures versus the WISE data. AAS/Division for Planetary Sciences Meeting Abstracts, 45, #112.12. Rožek A., Breiter S., and Jopek T. J. (2011) Orbital similarity functions — application to asteroid pairs. Mon. Not. R. Astron. Soc., 412, 987–994. Rubincam D. P. (2000) Radiative spin-up and spin-down of small asteroids. Icarus, 148, 2–11. Roig F., Ribeiro A. O., and Gil-Hutton R. (2008) Taxonomy of asteroid families among the Jupiter Trojans: Comparison between spectroscopic data and the Sloan Digital Sky Survey colors. Astron. Astrophys., 483, 911–931. Southworth R. B. and Hawkins G. S. (1963) Statistics of meteor streams. Smithson. Contrib. Astrophys., 7, 261. Tsiganis K., Knežević Z., and Varvoglis H. (2007) Reconstructing the orbital history of the Veritas family. Icarus, 186, 484–497. Usui F., Kasuga T., Hasegawa S., et al. (2013) Albedo properties of main belt asteroids based on the all-sky survey of the Infrared Astronomical Satellite AKARI. Astrophys. J., 762, 56–70. Vernazza P., Binzel R. P., Thomas C. A., et al. (2008) Compositional differences between meteorites and near-Earth asteroids. Nature, 454, 858–860. Vokrouhlický D. and Nesvorný D. (2008) Pairs of asteroids probably of a common origin. Astron. J., 136, 280–290. Vokrouhlický D. and Nesvorný D. (2009) The common roots of asteroids (6070) Rheinland and (54827) 2001 NQ8. Astron. J., 137, 111–117. Vokrouhlický D. and Nesvorný D. (2011) Half-brothers in the Schulhof family? Astron. J., 142, 26–34. Vokrouhlický D., Brož M., Morbidelli A., et al. (2006a) Yarkovsky footprints in the Eos family. Icarus, 182, 92–117. Vokrouhlický D., Brož M., BottkeW. F., Nesvorný D., and Morbidelli A. (2006b) Yarkovsky/YORP chronology of asteroid families. Icarus, 182, 118–142. Vokrouhlický D., Brož M., BottkeW. F., Nesvorný D., and Morbidelli A. (2006c) The peculiar case of the Agnia asteroid family. Icarus, 183, 349–361. Vokrouhlický D., Durech J., Michalowski T., et al. (2009) Datura family: The 2009 update. Astron. Astrophys., 507, 495–504. Vokrouhlický D., Nesvorný D., Bottke W. F., and Morbidelli A. (2010) Collisionally born family about 87 Sylvia. Astron. J., 139, 2148–2158. Walsh K. J., Delbo M., Bottke W. F., et al. (2013) Introducing the Eulalia and new Polana asteroid families: Re-assessing primitive asteroid families in the inner main belt. Icarus, 225, 283–297. Warner B. D., Harris A. W., Vokrouhlický D., et al. (2009) Analysis of the Hungaria asteroid population. Icarus, 204, 172–182. Weiss B. P. and Elkins-Tanton L. T. (2013) Differentiated planetesimals and the parent bodies of chondrites. Annu. Rev. Earth Planet. Sci., 41, 529–560. Willman M., Jedicke R., Nesvorný D., Moskovitz N., Ivezić Ž., and Fevig R. (2008) Redetermination of the space weathering rate using spectra of Iannini asteroid family members. Icarus, 195, 663–673. Wisdom J. (1982) The origin of the Kirkwood gaps — a mapping for asteroidal motion near the 3/1 commensurability. Astron. J., 87, 577–593. Zappalà V., Cellino A., Farinella P., and Knežević Z. (1990) Asteroid families. I — Identification by hierarchical clustering and reliability assessment. Astron. J., 100, 2030–2046. Zappalà V., Cellino A., Farinella P., and Milani A. (1994) Asteroid families. 2:  Extension to unnumbered multiopposition asteroids. Astron. J., 107, 772–801. Zappalà V., Cellino A., dell’Oro A., and Paolicchi P. (2002) Physical and dynamical properties of asteroid families. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 619–631. Univ. of Arizona, Tucson.

Masiero J. R., DeMeo F. E., Kasuga T., and Parker A. H. (2015) Asteroid family physical properties. In Asteroids IV (P. Michel et al., eds.), pp. 323–340. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch017.

Asteroid Family Physical Properties Joseph R. Masiero

NASA Jet Propulsion Laboratory/California Institute of Technology

Francesca E. DeMeo

Harvard/Smithsonian Center for Astrophysics

Toshihiro Kasuga

Planetary Exploration Research Center, Chiba Institute of Technology

Alex H. Parker

Southwest Research Institute

An asteroid family is typically formed when a larger parent body undergoes a catastrophic collisional disruption, and as such, family members are expected to show physical properties that closely trace the composition and mineralogical evolution of the parent. Recently a number of new datasets have been released that probe the physical properties of a large number of asteroids, many of which are members of identified families. We review these datasets and the composite properties of asteroid families derived from this plethora of new data. We also discuss the limitations of the current data, as well as the open questions in the field.

1. INTRODUCTION Asteroid families provide waypoints along the path of dynamical evolution of the solar system, as well as laboratories for studying the massive impacts that were common during terrestrial planet formation. Catastrophic disruptions shattered these asteroids, leaving swarms of bodies behind that evolved dynamically under gravitational perturbations and the Yarkovsky effect to their present-day locations, both in the main belt and beyond. The forces of the family-forming impact and the gravitational reaccumulation of the collisional products also left imprints on the shapes, sizes, spins, and densities of the resultant family members (see the chapter by Michel et al. in this volume). By studying the physical properties of the collisional remnants, we can probe the composition of the parent asteroids, important source regions of transient populations like the near-Earth objects (NEOs), and the physical processes that asteroids are subjected to on million- and billion-year timescales. In the 13 years since the publication of Asteroids III, research programs and sky surveys have produced physical observations for nearly 2 orders of magnitude more asteroids than were previously available. The majority of these characterized asteroids are members of the main belt, and approximately one-third of all known main-belt asteroids (MBAs) with sizes larger than a few kilometers can be associated with asteroid families. As such, these datasets

represent a windfall of family physical property information, enabling new studies of asteroid family formation and evolution. These data also provide a feedback mechanism for dynamical analyses of families, particularly age-dating techniques that rely on simulating the nongravitational forces that depend on an asteroid’s albedo, diameter, and density. In Asteroids III, Zappalà et al. (2002) and Cellino et al. (2002) reviewed the physical and spectral properties (respectively) of asteroid families known at that time. Zappalà et al. (2002) primarily dealt with asteroid size distributions inferred from a combination of observed absolute H magnitudes and albedo assumptions based on the subset of the family members with well-measured values. Surveys in the subsequent years have expanded the number of measured diameters and albedos by nearly 2 orders of magnitude, allowing for more accurate analysis of these families. Cellino et al. (2002) discussed the spectroscopic properties of the major asteroid families known at that time. The principal leap forward since Asteroids III in the realm of spectroscopy has been the expansion of spectroscopic characterization to near-infrared (NIR) wavelengths. The development of more sensitive instrumentation covering the 1- and 2-m silicate absorption features and new observing campaigns to acquire NIR spectra for a large number of objects have revolutionized studies of asteroid composition and space weathering. By greatly expanding the number of family members with measured physical properties, new investigations of asteroid

323

324   Asteroids IV families can be undertaken. Measurements of colors and albedo allow us to identify outliers in our population lists and search for variations in surface properties of family members that might indicate heterogeneity of the parent-body or weathering processes. Diameter measurements let us build a size frequency distribution and estimate the original parent-body size, both of which are critical to probing the physics of giant impacts. Spectra provide detailed mineralogical constraints of family members, allowing for more sensitive tests of space weathering and parent heterogeneity, albeit for a smaller sample size, while also probing the formation environment and allowing for comparisons to meteorite samples. In this chapter, we highlight the datasets that have been obtained since Asteroids III, which have greatly expanded our ability to understand asteroid families. We discuss their implications for specific families, and tabulate average photometric, albedo, and spectroscopic properties for 109 families identified in the chapter by Nesvorný et al. in this volume. We also discuss the key questions that have been answered since Asteroids III, those that remain open, and the new puzzles that have appeared over the last decade. 2. NEW DATASETS The field of asteroid research has benefited in the last 13 years from a huge influx of data. Many of these large sets of asteroid characterization data (including photometric and thermophysical data) have been ancillary results of surveys primarily designed to investigate astrophysical sources beyond the solar system. Simultaneously, observing programs designed to acquire more time-intensive data products such as asteroid spectra, photometric light curves, or polarimetric phase curves have also blossomed. We review below the main datasets that have advanced family characterization in recent years. 2.1. Optical Colors from the Sloan Digital Sky Survey The Sloan Digital Sky Survey (SDSS) (York et al., 2000) produced one of the first extremely large, homogeneous datasets that contained information about asteroid surface properties at optical wavelengths. These data are archived in the SDSS Moving Object Catalog (http://www.astro. washington.edu/users/ivezic/sdssmoc/sdssmoc.html), which currently contains 471,569 entries of moving objects from survey scans conducted up to March 2007. The catalog entries can be associated with 104,449 unique known moving objects; however, ~250,000 entries do not have corresponding associations in the orbital element catalogs, implying the potential for a significant benefit from future data mining efforts. While the SDSS five-color photometric system (u, g, r, i, z, with central wavelengths of 0.3543 µm, 0.4770 µm, 0.6231 µm, 0.7625 µm, and 0.9134 µm, respectively) was not designed with asteroid taxonomy in mind [unlike previous surveys such as the Eight Color Asteroid Survey (Zellner et al., 1985a)], the sheer size of the dataset coupled with its

extremely well-characterized performance has made SDSS an immensely valuable asset for defining asteroid families and exploring their properties. The near-simultaneous optical color information obtained during the course of the SDSS survey can be used to infer the spectroscopic properties of tens of thousands of asteroids at optical wavelengths. The SDSS, primarily designed to measure the redshifts of a very large sample of galaxies, serendipitously observed many asteroids over the course of its several survey iterations. Under standard survey operations with 53.9-s exposures, its five-color camera was sensitive to stationary sources as faint as r ~ 22.2, with similar performance in u and g and somewhat brighter limits in i and z (21.3 and 20.5, respectively). To enable the accurate determination of photometric redshifts, high-precision internal and absolute calibrations were essential. The care and effort expended on these calibrations carried over into the dataset of moving object photometry, resulting in the largest well-calibrated dataset of multi-band asteroid photometry to date. As of the latest data release, the Moving Object Catalog 4 (MOC4) (Parker et al., 2008) contains asteroid observations from 519 survey observing runs. The automatic flagging and analysis of moving objects required that they be brighter than magnitude r = 21.5. The brightest object in the sample is r ~ 12.91, giving the survey a dynamic range of over 8.5 mag. The large sample size and dynamic range of this survey make it a powerful tool for studying luminosity functions of dynamically — or photometrically — selected subpopulations of the moving objects, of which asteroid families are a natural example. Because of the much smaller sample size of asteroids with u-band observations having photometric errors 10 in the g, r, i, and z bands used to calculate a⋆ and i–z. Family taxonomy is given only for cases in which a majority of family members with taxonomic classes had the same class. If no subclass (e.g., Ch, Sq, Ld) had a majority, but a majority of members were in the same complex, that complex is listed (e.g., C, S, L). For each of these parameters we include the number of objects used to compute the listed value.

Masiero et al.:  Asteroid Family Physical Properties   329

TABLE 1. Physical properties of asteroid families.



⋆



SFD Range Tax ntax (km)

Number Name PDS ID np np nSDSS SFD Slope V NIR

2 3 4 8 10 15 20 24 25 27 31 44 46 81 84 87 89 96 128 137 142 144 145 148 158 163 170 173 221 283 293 298 302 313 322 329 363 369 375 396 410 434 480 490 495 569 589 606 618 623 627 656 668 686 702 709 729 752 778 780 808 832 845 847 909 918 945 1128 1189 1222 1270

Pallas Juno Vesta Flora Hygiea Eunomia Massalia Themis Phocaea Euterpe Euphrosyne Nysa (Polana) Hestia Terpsichore Klio Sylvia Julia Aegle Nemesis Meliboea Polana (Nysa) Vibilia Adeona Gallia Koronis Erigone Maria Ino Eos Emma Brasilia Baptistina Clarissa Chaldaea Phaeo Svea Padua Aeria Ursula Aeolia Chloris Hungaria Hansa Veritas Eulalia (Polana) Misa Croatia Brangane Elfriede Chimaera Charis Beagle Dora Gersuind Alauda Fringilla Watsonia Sulamitis Theobalda Armenia Merxia Karin Naema Agnia Ulla Itha Barcelona Astrid Terentia Tina Datura

801 501 401 402 601 502 404 602 701 410 901 405 503 622 413 603 540 630 504 604 n/a 529 505 802 605 406 506 522 606 607 608 403 407 415 530 416 507 539 631 508 509 003 803 609 n/a 510 638 511 632 414 616 620 512 804 902 623 537 408 617 905 513 610 611 514 903 633 805 515 618 806 411

0.134 ± 0.026 0.262 ± 0.054 0.363 ± 0.088 0.305 ± 0.064 0.070 ± 0.018 0.270 ± 0.059 0.247 ± 0.053 0.068 ± 0.017 0.290 ± 0.066 0.270 ± 0.062 0.059 ± 0.013 0.289 ± 0.074 0.267 ± 0.049 0.050 ± 0.010 0.059 ± 0.014 0.051 ± 0.012 0.225 ± 0.036 0.072 ± 0.013 0.072 ± 0.019 0.060 ± 0.013 0.056 ± 0.012 0.065 ± 0.011 0.060 ± 0.011 0.251 ± 0.059 0.238 ± 0.051 0.051 ± 0.010 0.255 ± 0.061 0.244 ± 0.069 0.163 ± 0.035 0.047 ± 0.011 0.174 ± 0.048 0.179 ± 0.056 0.048 ± 0.010 0.063 ± 0.017 0.059 ± 0.015 0.050 ± 0.009 0.069 ± 0.015 0.180 ± 0.011 0.061 ± 0.014 0.107 ± 0.022 0.084 ± 0.031 0.456 ± 0.217 0.269 ± 0.067 0.066 ± 0.016 0.057 ± 0.012 0.052 ± 0.013 0.054 ± 0.010 0.112 ± 0.028 0.052 ± 0.012 0.054 ± 0.012 0.071 ± 0.010 0.080 ± 0.014 0.056 ± 0.012 0.145 ± 0.037 0.066 ± 0.015 0.050 ± 0.014 0.134 ± 0.019 0.055 ± 0.011 0.062 ± 0.016 0.056 ± 0.013 0.234 ± 0.054 0.178 ± 0.031 0.064 ± 0.012 0.238 ± 0.060 0.048 ± 0.009 0.239 ± 0.056 0.290 ± 0.064 0.045 ± 0.010 0.064 ± 0.012 0.128 ± 0.042 0.288 ± 0.000

49 125 1900 1330 1951 1448 214 2218 715 45 742 1345 28 57 107 121 2 83 347 163 1130 180 874 24 1089 716 1361 90 3509 260 110 581 44 169 99 30 427 22 600 43 171 527 316 697 2008 287 99 44 36 63 39 30 667 106 687 51 51 134 107 28 93 18 155 110 19 28 52 213 13 26 1

0.114 ± 0.047 0.488 ± 0.000 0.465 ± 0.156 0.440 ± 0.082 0.065 ± 0.028 0.374 ± 0.088 ... ± ... 0.074 ± 0.030 0.355 ± 0.203 0.493 ± 0.000 0.082 ± 0.173 0.356 ± 0.059 0.068 ± 0.000 0.053 ± 0.000 0.089 ± 0.031 0.082 ± 0.000 0.339 ± 0.000 0.102 ± 0.000 0.071 ± 0.000 0.050 ± 0.029 0.061 ± 0.006 ... ± ... 0.068 ± 0.078 ... ± ... 0.325 ± 0.059 0.061 ± 0.013 0.370 ± 0.068 ... ± ... 0.180 ± 0.053 0.118 ± 0.113 0.224 ± 0.017 0.390 ± 0.198 ... ± ... 0.083 ± 0.039 0.181 ± 0.000 0.134 ± 0.166 0.067 ± 0.022 0.266 ± 0.000 0.083 ± 0.047 0.115 ± 0.000 0.081 ± 0.095 0.727 ± 1.692 0.377 ± 0.068 0.068 ± 0.011 0.066 ± 0.029 0.064 ± 0.027 0.068 ± 0.000 0.137 ± 0.000 0.063 ± 0.000 0.049 ± 0.000 0.264 ± 0.000 0.070 ± 0.006 0.047 ± 0.017 0.328 ± 0.000 0.071 ± 0.013 0.212 ± 0.788 0.181 ± 0.000 0.048 ± 0.000 0.070 ± 0.000 0.060 ± 0.000 0.347 ± 0.030 0.294 ± 0.000 0.055 ± 0.000 0.389 ± 0.015 ... ± ... 0.353 ± 0.084 0.510 ± 0.000 0.046 ± 0.000 0.058 ± 0.000 0.137 ± 0.000 ... ± ...

10 8 54 142 3 148 0 86 119 1 5 22 1 1 3 1 2 1 1 12 3 0 19 0 67 17 69 0 205 2 4 25 0 11 2 2 5 6 15 1 10 9 9 3 15 3 1 2 1 3 2 5 17 1 26 2 2 1 1 2 3 1 1 3 0 8 1 1 1 1 0

–0.14 ± 0.03 0.08 ± 0.05 0.12 ± 0.05 0.13 ± 0.06 –0.11 ± 0.05 0.13 ± 0.05 0.07 ± 0.05 –0.11 ± 0.04 0.10 ± 0.11 0.11 ± 0.05 –0.08 ± 0.05 0.13 ± 0.06 0.14 ± 0.04 –0.08 ± 0.03 –0.06 ± 0.04 –0.07 ± 0.05 0.05 ± 0.02 0.02 ± 0.05 –0.08 ± 0.06 –0.10 ± 0.08 –0.12 ± 0.10 –0.10 ± 0.04 –0.11 ± 0.08 0.10 ± 0.03 0.09 ± 0.07 –0.08 ± 0.10 0.12 ± 0.05 0.09 ± 0.05 0.05 ± 0.05 –0.07 ± 0.06 –0.04 ± 0.04 0.01 ± 0.09 –0.14 ± 0.04 –0.10 ± 0.05 0.00 ± 0.06 –0.04 ± 0.06 –0.04 ± 0.06 –0.05 ± 0.04 –0.05 ± 0.08 –0.04 ± 0.05 –0.05 ± 0.08 –0.01 ± 0.08 0.10 ± 0.05 –0.07 ± 0.04 –0.12 ± 0.05 –0.07 ± 0.07 –0.05 ± 0.04 0.07 ± 0.04 –0.09 ± 0.05 –0.05 ± 0.03 0.16 ± 0.06 –0.12 ± 0.03 –0.12 ± 0.07 0.09 ± 0.07 –0.10 ± 0.06 –0.03 ± 0.06 0.08 ± 0.04 –0.07 ± 0.07 –0.16 ± 0.03 –0.05 ± 0.01 0.08 ± 0.05 0.03 ± 0.05 –0.10 ± 0.11 0.04 ± 0.05 –0.07 ± 0.02 0.14 ± 0.04 0.09 ± 0.05 –0.07 ± 0.05 –0.01 ± 0.00 0.01 ± 0.00 0.01 ± 0.00

–0.01 ± 0.08 13 –0.03 ± 0.07 87 –0.26 ± 0.10 2148 –0.04 ± 0.07 922 0.01 ± 0.07 606 –0.03 ± 0.06 798 –0.04 ± 0.08 386 0.01 ± 0.06 640 –0.04 ± 0.08 252 –0.04 ± 0.08 42 0.04 ± 0.06 169 –0.03 ± 0.07 1544 –0.03 ± 0.04 22 0.08 ± 0.10 15 0.05 ± 0.08 23 0.09 ± 0.11 20 0.12 ± 0.07 3 0.10 ± 0.08 23 0.03 ± 0.07 109 0.05 ± 0.07 53 0.00 ± 0.08 375 0.04 ± 0.07 35 0.04 ± 0.07 274 –0.06 ± 0.06 15 –0.02 ± 0.08 810 0.05 ± 0.08 201 –0.02 ± 0.07 809 –0.06 ± 0.07 93 0.03 ± 0.07 1692 0.04 ± 0.08 75 0.05 ± 0.07 78 –0.02 ± 0.09 321 0.00 ± 0.06 10 0.06 ± 0.07 34 0.05 ± 0.08 34 0.04 ± 0.05 8 0.05 ± 0.07 135 0.03 ± 0.09 18 0.06 ± 0.09 194 0.04 ± 0.03 10 0.06 ± 0.05 59 0.04 ± 0.10 636 –0.06 ± 0.07 134 0.05 ± 0.08 207 0.01 ± 0.07 531 0.03 ± 0.08 79 0.02 ± 0.09 22 0.09 ± 0.06 20 0.06 ± 0.05 8 0.09 ± 0.10 20 0.04 ± 0.08 59 0.01 ± 0.06 16 0.04 ± 0.07 175 0.08 ± 0.07 36 0.03 ± 0.07 197 0.09 ± 0.08 24 0.07 ± 0.02 12 0.06 ± 0.11 33 0.00 ± 0.05 28 0.03 ± 0.04 4 –0.08 ± 0.08 98 –0.01 ± 0.07 33 0.04 ± 0.06 45 –0.07 ± 0.08 179 0.02 ± 0.06 3 –0.01 ± 0.05 14 –0.11 ± 0.09 21 0.08 ± 0.08 33 0.09 ± 0.00 1 0.03 ± 0.05 3 –0.10 ± 0.00 1

... ± ... –2.427 ± 0.108 –3.417 ± 0.030 –2.692 ± 0.030 –3.883 ± 0.040 –3.091 ± 0.033 –3.544 ± 0.140 –2.313 ± 0.017 –2.663 ± 0.039 ... ± ... –4.687 ± 0.082 –3.083 ± 0.030 ... ± ... –4.371 ± 0.508 –2.478 ± 0.129 –3.339 ± 0.232 ... ± ... –3.252 ± 0.305 –4.320 ± 0.121 –1.513 ± 0.051 –3.177 ± 0.041 –3.137 ± 0.135 –2.854 ± 0.037 ... ± ... –2.451 ± 0.026 –3.215 ± 0.050 –2.637 ± 0.025 –3.141 ± 0.268 –2.222 ± 0.013 –3.442 ± 0.113 –3.462 ± 0.243 –3.254 ± 0.063 ... ± ... –3.058 ± 0.119 –2.852 ± 0.195 ... ± ... –2.588 ± 0.053 ... ± ... –2.677 ± 0.046 ... ± ... –2.814 ± 0.103 ... ± ... –3.378 ± 0.104 –2.744 ± 0.043 –2.687 ± 0.021 –2.508 ± 0.067 –3.383 ± 0.224 ... ± ... ... ± ... –2.586 ± 0.235 ... ± ... ... ± ... –2.610 ± 0.043 –2.653 ± 0.158 –2.707 ± 0.042 ... ± ... ... ± ... –2.417 ± 0.126 –3.097 ± 0.185 ... ± ... –2.662 ± 0.190 ... ± ... –4.274 ± 0.220 –3.055 ± 0.165 ... ± ... ... ± ... ... ± ... –2.567 ± 0.080 ... ± ... ... ± ... ... ± ...

... 2.7–7.3 2.5–11.9 2.8–12.2 6.1–19.3 4.4–17.6 2.0–4.1 7.3–55.6 3.5–14.6 ... 7.3–18.4 2.5–13.0 ... 5.0–7.3 3.3–8.0 7.0–12.4 ... 6.8–11.4 3.8–8.4 8.0–39.4 3.6–12.4 4.5–9.7 5.3–23.2 ... 5.1–32.0 3.3–11.9 3.5–24.8 2.7–4.6 5.6–47.3 6.7–15.3 3.7–6.4 2.5–7.2 ... 3.7–8.6 5.1–10.1 ... 4.5–16.4 ... 7.3–27.2 ... 5.2–14.0 ... 3.4–7.9 5.8–22.6 3.0–18.4 4.0–13.3 5.8–11.1 ... ... 3.8–7.2 ... ... 5.7–21.6 3.8–8.0 9.2–36.7 ... ... 3.8–8.8 6.5–13.3 ... 3.2–6.7 ... 6.0–10.6 3.8–8.0 ... ... ... 3.5–11.1 ... ... ...

B Sq V S C S S C S S Cb ... Xc Cb Ch X Ld T C Ch B Ch Ch Sl S Ch S ... K C X S F C D C X M ... Xe C Xe S Ch C Ch X L C XC X X Ch ... ... X L Ch ... C S S C S X Sl Sq C Ch X S

8 1 49 74 1 30 1 7 39 1 1 0 1 1 1 1 1 1 2 11 3 1 12 1 34 1 23 0 30 1 2 9 1 3 1 1 10 1 0 1 8 14 2 8 13 1 1 1 1 1 1 1 29 0 0 1 2 1 0 1 6 47 1 8 1 4 1 5 1 1 4

330   Asteroids IV TABLE 1. (continued)

⋆



SFD Range Tax ntax (km)

Number Name PDS ID np np nSDSS SFD Slope V NIR

1272 1303 1332 1400 1484 1658 1668 1726 1892 2085 2262 2344 2384 2732 2782 3152 3438 3556 3811 3815 4203 4652 5438 5567 5614 7353 7468 7481 9506 10811 14627 15454 15477 16598 18405 36256 53546 106302

Gefion Luthera Marconia Tirela Postrema Innes Hanna Hoffmeister Lucienne Henan Mitidika Xizang Schulhof Witt Leonidas Jones Inarrados Lixiaohua Karma Konig Brucato Iannini Lorre Durisen Yakovlev Kazuia Anfimov SanMarcello Telramund Lau Emilkowalski 1998 YB3 1999 CG1 1992 YC2 1993 FY12 1999 XT17 2000 BY6 2000 UJ87

516 904 636 612 541 518 533 519 409 542 531 536 525 535 528 538 634 613 534 517 807 520 527 624 625 532 635 626 614 619 523 627 628 524 615 629 526 637

0.267 ± 0.058 0.050 ± 0.009 0.042 ± 0.008 0.239 ± 0.057 0.047 ± 0.010 0.259 ± 0.057 0.052 ± 0.011 0.047 ± 0.010 0.228 ± 0.029 0.227 ± 0.065 0.066 ± 0.014 0.134 ± 0.044 0.280 ± 0.000 0.261 ± 0.053 0.068 ± 0.013 0.054 ± 0.004 0.067 ± 0.015 0.044 ± 0.009 0.054 ± 0.010 0.049 ± 0.011 0.064 ± 0.017 0.309 ± 0.033 0.054 ± 0.002 0.043 ± 0.010 0.046 ± 0.008 0.214 ± 0.025 0.166 ± 0.061 0.194 ± 0.054 0.237 ± 0.063 0.274 ± 0.000 0.149 ± 0.046 0.054 ± 0.006 0.095 ± 0.030 ... ± ... 0.173 ± 0.049 0.203 ± 0.066 0.139 ± 0.000 0.045 ± 0.004

737 125 6 419 30 195 102 609 19 106 279 18 1 124 67 14 24 367 78 135 233 18 2 16 25 13 10 27 46 1 4 11 68 0 15 13 1 12

0.350 ± 0.154 0.078 ± 0.000 0.080 ± 0.000 0.073 ± 0.095 0.051 ± 0.006 0.318 ± 0.149 0.048 ± 0.000 0.052 ± 0.013 ... ± ... 0.165 ± 0.000 0.060 ± 0.013 ... ± ... 0.289 ± 0.000 0.347 ± 0.018 ... ± ... 0.061 ± 0.000 0.069 ± 0.000 0.053 ± 0.011 ... ± ... ... ± ... 0.041 ± 0.009 ... ± ... ... ± ... 0.050 ± 0.000 ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ...

25 1 1 7 3 8 1 4 0 3 10 0 4 3 0 1 1 3 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Although we implicitly assume that the variation in observed properties is a result of statistical uncertainties and that all family members should have the same physical properties, this is not necessarily true. Outlier objects may be statistical flukes, or background contamination, but they may just as easily be interesting pieces of the parent body warranting further study, a determination that cannot be made or captured here. Additionally, a single mean value ignores any size-dependent effects in the data, either real or imposed by detection or sample-selection biases. Only a proper debiasing of each survey accounting for observing geometry, detector sensitivity, and detection efficiency can determine the true value for each parameter. This is particularly important for cases of mismatched sensitivities, such as the SDSS r vs. z magnitudes needed for colors or the NEOWISE W3 flux vs. groundbased HV magnitude needed for albedo determination; only objects seen in both datasets will have a measured value that strongly biases the outcome as a function of apparent brightness. Thus Table 1 is meant as a overarching guide, but caution is mandated for any interpretation of values or trends.

0.10 ± 0.06 0.01 ± 0.04 ... ± ... 0.15 ± 0.09 –0.05 ± 0.05 0.09 ± 0.06 –0.09 ± 0.03 –0.10 ± 0.05 0.09 ± 0.03 0.11 ± 0.06 –0.11 ± 0.06 0.04 ± 0.05 0.08 ± 0.07 0.15 ± 0.07 –0.10 ± 0.07 –0.02 ± 0.00 –0.10 ± 0.03 –0.06 ± 0.05 –0.06 ± 0.08 –0.08 ± 0.02 –0.11 ± 0.05 0.01 ± 0.04 ... ± ... –0.02 ± 0.03 –0.08 ± 0.00 0.06 ± 0.08 0.23 ± 0.03 –0.05 ± 0.04 0.09 ± 0.05 0.26 ± 0.00 0.06 ± 0.00 –0.11 ± 0.03 0.04 ± 0.04 0.10 ± 0.00 –0.04 ± 0.03 0.21 ± 0.07 0.04 ± 0.03 –0.10 ± 0.04

–0.02 ± 0.07 0.10 ± 0.07 ... ± ... 0.08 ± 0.08 0.02 ± 0.06 –0.04 ± 0.07 0.08 ± 0.05 0.03 ± 0.08 0.00 ± 0.09 –0.02 ± 0.09 0.01 ± 0.08 0.08 ± 0.07 –0.05 ± 0.03 0.01 ± 0.08 0.04 ± 0.07 0.04 ± 0.01 0.05 ± 0.05 0.04 ± 0.09 0.03 ± 0.07 0.06 ± 0.06 0.05 ± 0.07 –0.08 ± 0.06 ... ± ... 0.11 ± 0.05 0.07 ± 0.01 –0.03 ± 0.02 –0.14 ± 0.09 0.04 ± 0.06 –0.02 ± 0.09 –0.18 ± 0.00 0.11 ± 0.00 0.04 ± 0.03 0.05 ± 0.06 –0.09 ± 0.00 0.07 ± 0.08 –0.04 ± 0.05 0.06 ± 0.04 0.05 ± 0.04

523 39 0 225 5 163 20 145 10 163 71 12 2 190 22 2 11 95 20 25 45 21 0 4 2 3 13 18 33 1 1 7 25 1 12 6 9 3

–3.262 ± 0.050 –3.955 ± 0.264 ... ± ... –3.454 ± 0.073 ... ± ... –3.385 ± 0.128 –3.502 ± 0.240 –2.856 ± 0.047 ... ± ... –3.667 ± 0.276 –2.832 ± 0.091 ... ± ... ... ± ... –3.114 ± 0.173 –2.142 ± 0.245 ... ± ... ... ± ... –3.499 ± 0.098 –2.659 ± 0.241 –3.032 ± 0.150 –3.604 ± 0.109 ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... ... ± ... –4.768 ± 0.602 ... ± ... ... ± ... ... ± ... ... ± ... ... ± ...

4.0–14.3 7.9–13.0 ... 4.8–14.3 ... 3.1–7.0 3.9–7.2 4.5–17.2 ... 3.4–5.8 4.6–11.4 ... ... 3.8–7.7 5.1–9.4 ... ... 6.8–15.7 3.7–6.7 4.1–9.2 5.3–13.3 ... ... ... ... ... ... ... ... ... ... ... 4.3–6.0 ... ... ... ... ...

S ... L Ld B S ... C S L ... ... ... ... ... T ... ... ... ... ... ... C ... ... L ... ... ... ... ... ... ... Sq ... ... ... ...

32 0 1 10 1 2 0 9 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0

A number of low-albedo families can only be identified when the low-albedo population of the main belt is considered independently. This is due to the bias toward discovery of high-albedo objects by groundbased visible-light surveys. As the population of high-albedo asteroids is probed to smaller sizes (and thus larger numbers), these families will overwhelm traditional HCM techniques, particularly the calculation of the quasi-random level needed to assess the reality of a given family, making low-albedo families harder to identify. Masiero et al. (2013) circumvented this by considering each albedo component separately, and by restricting their sample to objects detected in the thermal infrared, which is albedo-independent (see the chapter by Mainzer et al. in this volume for further discussion). As the sample of known asteroids continues to increase, development of new techniques for the identification of asteroid families from the background population (e.g., Milani et al., 2014) will increase in importance. Below we discuss individual families that merit specific mention based on recent research. We include the Planetary Data System (PDS) ID number from Nesvorný et al. (2012)

Masiero et al.:  Asteroid Family Physical Properties   331

Reflectance

(2) Pallas

(3) Juno

0.26

Tax: B NSDSS = 13 0.5

1.0

1.5

2.0

2.5

0.5

Reflectance

Tax: C NSDSS = 640 0.5

1.0

1.5

2.0

2.5

Reflectance

0.26 0.13

0.5

0.08

Tax: Ch NSDSS = 23 0.5

1.0

1.5

2.0

2.5

Reflectance Reflectance Reflectance Reflectance

1.5

2.0

1.5

2.0

1.0

1.5

2.5

2.5

Tax: Ch NSDSS = 274

0.03 0.5

1.0

1.5

2.0

2.0

2.5

1.0

1.5

2.0

0.5

1.0

2.0

2.5

1.5

2.0

2.5

0.06

Tax: T NSDSS = 23 0.5

1.0

1.5

2.0

2.5

0.08 0.5

1.0

1.5

2.0

2.5

Tax: X NSDSS = 135 0.5

1.0

1.5

2.0

Tax: M NSDSS = 18

0.09

2.5

0.5

0.5

1.0

1.0

1.5

2.0

1.5

2.0

2.5

0.06 0.03

Tax: Ch NSDSS = 207 0.5

1.0

1.5

2.0

0.04

2.5

0.5

1.0

0.5

0.09

1.5

2.0

2.5

2.0

0.5

1.0

1.5

2.0

0.5

(752) Sulamitis

0.06

Tax: Ch NSDSS = 33 0.5

1.0

1.5

2.0

1.5

2.0

0.5

1.0

1.5

2.0

2.0

1.0

1.5

2.0

1.0

1.5

2.0

2.5

0.02

1.0

1.0

1.5

2.0

1.5

2.0

0.5

1.0

1.5

2.0

0.5

1.0

1.5

2.0

1.0

1.0

0.5

0.5

1.0

1.5

2.0

0.27

0.33

0.18

0.22

1.0

0.5

1.0

1.5

2.0

λ (µm)

2.5

1.0

1.5

2.0

2.5

0.5

1.0

1.5

2.0

0.5

λ (µm)

1.5

2.0

2.5

2.5

0.02

2.0

2.5

Tax: Cb NSDSS = 15 0.5

1.0

1.5

2.0

2.5

(144) Vibilia

0.06

0.5

1.0

1.5

2.0

Tax: Ch NSDSS = 35

0.03 2.5

0.5

(173) Ino

1.5

2.0

1.0

1.5

2.0

2.5

(221) Eos 0.24

0.24

1.0

1.5

2.0

0.5

1.5

2.0

2.5

1.5

2.0

1.5

2.0

1.0

1.5

2.0

0.02 2.5

0.5

0.10

0.5

0.5

1.0

1.5

2.0

1.0

1.5

2.0

2.5

0.05

NSDSS = 36 1.0

1.5

2.0

2.5

0.03

Tax: S NSDSS = 33 0.5

1.0

1.5

2.0

2.5

1.5

2.0

λ (µm)

2.5

1.5

2.0

2.5

1.5

2.0

0.5

1.0

1.5

2.0

2.5

1.0

1.5

2.0

1.5

2.0

2.5

NSDSS = 39 0.5

1.0

1.5

2.0

2.5

0.11

Tax: Ld NSDSS = 225 0.5

0.12

NSDSS = 71 0.5

1.0

1.5

2.0

1.0

1.5

2.0

2.5

0.06

2.5

1.0

1.5

2.0

2.5

NSDSS = 12 1.0

1.5

2.0

2.5

1.0

1.5

2.0

λ (µm)

2.5

1.5

2.0

NSDSS = 45 1.0

1.5

2.0

2.5

0.15

1.0

1.5

2.0

λ (µm)

2.5

2.5

1.0

1.5

2.0

2.5

Tax: L NSDSS = 12 0.5

1.0

1.5

2.0

2.5

0.33 0.22

Tax: S NSDSS = 179 0.5

1.0

1.5

2.0

2.5

(1658) Innes

0.11

Tax: Sl NSDSS = 14 0.5

1.0

1.5

2.0

2.5

(1668) Hanna

0.08 0.06

Tax: S NSDSS = 163 0.5

1.0

1.5

2.0

0.04 2.5

NSDSS = 20 0.5

1.0

1.5

2.0

2.5

(2782) Leonidas 0.09 0.06

NSDSS = 190 0.5

1.0

1.5

2.0

2.5

0.03

NSDSS = 22 0.5

1.0

1.5

2.0

2.5

(7468) Anfimov

0.40 0.32 0.24 0.16

NSDSS = 21 0.5

1.0

1.5

2.0

2.5

0.08

NSDSS = 13 0.5

1.0

1.5

2.0

2.5

(53546) 2000 BY6 0.18

0.02

0.5

0.06

(36256) 1999 XT17

0.01

2.0

(918) Itha

0.03

NSDSS = 12

1.5

(729) Watsonia

0.12 2.5

0.30

0.5

0.5 0.24

(4652) Iannini

0.16 0.08

2.5

0.45

0.24

0.5

0.13

(18405) 1993 FY12

NSDSS = 25

2.0

0.26

0.06 0.03

1.0

0.24 0.12

1.0

Tax: XC NSDSS = 20

(2732) Witt

0.09

0.5

0.5

(4203) Brucato

NSDSS = 25

1.5

0.39

0.5

0.5

0.18

(2344) Xizang

0.06

1.0

0.36

0.22

2.5

Tax: S NSDSS = 134

0.04

Tax: X NSDSS = 24

0.48

0.33

2.0

(623) Chimaera

(709) Fringilla

0.22

2.5

1.5

0.06

0.04

0.11

1.0

0.13

0.33

1.0

0.5

(847) Agnia

Tax: C NSDSS = 45 0.5

Tax: C NSDSS = 8

0.26

Tax: C NSDSS = 8 0.5

0.02

2.5

0.08

0.08

NSDSS = 197 0.5

0.02

(618) Elfriede

0.04 2.5

2.0

(480) Hansa

Tax: Xe NSDSS = 636

0.08

(1400) Tirela

0.18

0.04

1.0

1.5

(329) Svea

0.04

0.06

(1303) Luthera

0.08

1.0

0.03

(15477) 1999 CG1

NSDSS = 7 0.5

0.5

1.0

0.39

(845) Naema

0.12

0.04

2.5

(702) Alauda

0.09

0.02

2.0

0.06

0.04 2.5

1.5

1.0

0.22

Tax: L NSDSS = 20

(3815) Konig

NSDSS = 20

1.0

0.5 0.08

(434) Hungaria

Tax: C NSDSS = 59

(2262) Mitidika

2.5

2.5

Tax: D NSDSS = 34

0.04

(606) Brangane

0.04

0.03

2.0

0.06

0.06

0.09

0.5

0.02

1.5

0.06

0.08

2.5

1.0

Tax: K NSDSS = 1692

0.08

(322) Phaeo

Tax: C NSDSS = 34 0.5

2.5

Tax: X NSDSS = 22 0.5

0.08

0.16

NSDSS = 93

0.12

2.5

0.15

(15454) 1998 YB3

2.5

1.0

0.04

0.08

NSDSS = 33

2.0

Tax: B NSDSS = 375

(410) Chloris

0.06

0.04 2.5

1.5

0.10

(832) Karin

0.06

0.11

0.5

0.03

Tax: Xe NSDSS = 10

(3811) Karma

(9506) Telramund

NSDSS = 18

0.5

0.07

Tax: L NSDSS = 163

0.11

NSDSS = 95

1.0

0.08

0.08

(7481) San Marcello

0.09

0.05

2.5

0.06

2.5

0.12

0.06

0.14

Tax: S NSDSS = 523

(3556) Lixiaohua

0.02

1.0

Tax: S NSDSS = 809

(686) Gersuind

Tax: S NSDSS = 98

0.5

2.5

1.5

0.09

(313) Chaldaea

Tax: F NSDSS = 10

(2085) Henan

Tax: S NSDSS = 10

0.11

0.04

2.0

0.02

2.5

Tax: Ch NSDSS = 175

0.13 2.5

0.22

0.06

1.5

2.5

0.21

0.26

0.33

0.06

1.0

2.0

0.06

0.5

0.5

0.04

0.09

0.04

(1272) Gefion

Tax: C NSDSS = 33

1.0

(81) Terpsichore

0.04

0.36

(589) Croatia

Tax: Ch NSDSS = 79

0.5

0.22

0.09

0.5

1.5

0.06

0.5

0.33

2.5

NSDSS = 11

1.0

0.08

0.39

(3438) Inarrados

0.03

0.5

(808) Merxia

2.5

0.5 0.08

(142) Polana (Nysa)

Tax: Ch NSDSS = 53

0.24

Tax: Ch NSDSS = 201

0.06

1.5

2.5

(170) Maria

0.09

1.0

2.5

0.06

0.5

0.16

0.5

2.0

0.36

(569) Misa

(1892) Lucienne

Tax: C NSDSS = 145

2.5

0.24

0.04

0.06

0.5

0.5

(1128) Astrid

2.5

2.0

0.22

(1726) Hoffmeister

0.04

NSDSS = 194

0.04

0.06

0.14

1.5

1.5

0.44

0.11

2.0

0.08

(163) Erigone

(668) Dora

NSDSS = 28

1.0

(137) Meliboea

0.03

0.33

2.5

Tax: Sq NSDSS = 21

0.5 0.09

0.06

(945) Barcelona

0.28

2.5

0.09

0.03

0.42

2.0

0.66

2.5

1.5

Tax: Xc NSDSS = 22

0.13

0.08

(778) Theobalda

0.08

0.04

1.0

1.5

NSDSS = 1544

0.12

0.06

0.04 2.5

0.26

0.10

2.5

Tax: X NSDSS = 16

0.28

(396) Aeolia

0.08

0.08

Tax: X NSDSS = 59

0.06

0.02

1.5

1.0

Tax: S NSDSS = 386

0.12

(46) Hestia

0.15

(656) Beagle

0.12

0.03

1.0

0.5

0.06

0.04

0.12

0.15

1.0

0.04

0.06

Tax: C NSDSS = 531

2.5 0.39

(302) Clarissa

Tax: S NSDSS = 321

0.08

0.06

2.0

0.09

2.5

0.08

0.09

1.5

0.42

0.14

0.06

0.03

(495) Eulalia (Polana)

1.0

0.04

0.09 0.06

0.5

(375) Ursula

0.18

1.0

0.24

Tax: S NSDSS = 798

0.13

(44) Nysa (Polana)

Tax: C NSDSS = 109

0.08

Tax: S NSDSS = 810

0.16 0.08

0.5

0.26

0.06

(369) Aeria

0.27

0.03

Tax: C NSDSS = 606

0.06

(298) Baptistina

Tax: X NSDSS = 78

2.5

(20) Massalia 0.36

0.06

0.5

0.09

0.11

2.0

(128) Nemesis

0.24

0.16

2.5

1.5

0.06

(293) Brasilia

Tax: C NSDSS = 75

1.0

0.22

0.24

0.5

0.5

0.09

0.03

1.5

Tax: Cb NSDSS = 169

0.04

(158) Koronis

Tax: Sl NSDSS = 15

0.12

2.5

0.06 0.04

0.13

1.0

0.06

0.33

0.24

0.5

0.03

(31) Euphrosyne

Tax: S NSDSS = 42

(15) Eunomia 0.39

0.06

Tax: S NSDSS = 922

0.15

(96) Aegle

0.36

0.06

0.30

0.08

(148) Gallia

(627) Charis

Reflectance

1.0

0.26

Tax: X NSDSS = 20 0.5

(490) Veritas

Reflectance

1.0

0.04

0.09

0.03

(10) Hygiea 0.09

(27) Euterpe

0.06

0.06

(363) Padua

Reflectance

0.5

(87) Sylvia

0.08

(283) Emma

Reflectance

2.5

Tax: S NSDSS = 252

(145) Adeona

Reflectance

2.0

0.39

(84) Klio

Reflectance

1.5

0.39

0.12

0.02

1.0

Tax: V NSDSS = 2148

0.18

(25) Phocaea

0.18

0.04

0.36

Tax: Sq NSDSS = 87

0.13

(24) Themis

0.06

(8) Flora 0.45

0.06 0.03

(4) Vesta 0.54

0.39

0.09

0.12

NSDSS = 6 0.5

1.0

1.5

2.0

λ (µm)

2.5

0.06

NSDSS = 9 0.5

1.0

1.5

2.0

2.5

λ (µm)

Fig. 1. Average solar-corrected SDSS colors (points) and sample optical/NIR spectra (from SMASS) for all asteroid families listed in Table  1 with sufficient data. Plots are scaled such that the interpolated reflectance at 0.55  µm equals the average visible geometric albedo (pV) for the family from all infrared surveys. The “N” in the bottom right of each plot indicates the number of SDSS observations used, and taxonomic class is given when available. Note the reflectance scale in each plot is different.

332   Asteroids IV both below and in Table 1 for easier association with other work and with the family dynamical properties given in the chapter by Nesvorný et al. in this volume. 3.2.1. Hungaria. The Hungaria asteroid family (PDS ID 003) occupies a region of space interior to the rest of the main belt and with an orbital inclination above the n6 secular resonance. This region is an island of stability between the major resonances that dominate this area of the solar system, and likely samples a unique region of the protoplanetary disk (Bottke et al., 2012). Warner et al. (2009) analyzed light curves of 129 Hungaria asteroids, finding a significant excess of very slow rotating bodies. They also showed that the binary fraction of this population is ~15%, comparable to the fraction seen in the NEO population. The albedos for Hungaria family members derived from the NEOWISE data by Masiero et al. (2011) have values significantly larger than pV > 0.5; however, this is an artifact of bad absolute magnitude fits for these objects in orbital element databases, which when corrected bring the best-fit albedo values to the range of 0.4 < pV  < 0.5 (B.  Warner, personal communication). Spectroscopic and SDSS color studies of the Hungaria family show the classification to be X-type, which when combined with the very high albedos translates to an E-type classification (Carvano et al., 2001; Assandri and Gil-Hutton, 2008; Warner et al., 2009). Polarimetric observations by Gil-Hutton et al. (2007) of the overall Hungaria region indicate inconsistencies in the polarimetric behavior of asteroids in and around the Hungaria family. 3.2.2. Flora. The Flora family (PDS ID 401) is a large S-type family residing in the inner main belt. The largest remnant, (8) Flora, has an orbit just exterior to the n6 resonance, and only the half of the family at larger semimajor axes is seen today. The n6 resonance is particularly good at implanting asteroids into the NEO population (Bottke et al., 2000), meaning that Flora family members are likely well represented in the NEO population and meteorite collections. Recent spectroscopic observations of Flora family members have been combined with analyses of meteorite samples to link the LL chondrite meteorites to the Flora family (Vernazza et al., 2008; de Leon et al., 2010; Dunn et al., 2013). This provides an important ground-truth analog for interpreting physical properties of S-type objects in the main belt and near-Earth populations. We note that in contrast to previous analyses, Milani et al. (2014) did not identify a family associated with Flora, instead finding that candidate member asteroids merged with the Vesta and Massalia families, or are potentially part of their newly identified Levin family. However, the Vesta family has a distinct i–z color that is not shown by Flora family members (see Table 1), making these populations easily distinguished by their photometric properties. While the Flora and Massalia populations overall have properties that are consistent within uncertainties, the difference between the mean albedos of these two populations suggests they in fact are different populations. 3.2.3. Baptistina. Over the past decade, the Baptistina family (PDS ID 403) has been the focus of a number of investigations, leading to controversy over the physical char-

acteristics of these asteroids. Initial investigations assumed the family had characteristics similar to C-type asteroids (e.g., low albedo) based on spectra of the largest member, (298) Baptistina (Bottke et al., 2007). This was used in numerical simulations to show that Baptistina was a probable source of the K/T impactor. Further spectral investigations of a 16 large family members found compositions more analogous to LL chondrites, ruling out a C-type association (Reddy et al., 2011). However, a major difficulty in studying this family is the significant overlap in orbital element-space with the much larger Flora family [or with the Levin family, according to Milani et al. (2014)], making it difficult to ensure that the spectral studies were probing Baptistina and not Flora. Using albedos to separate these families finds a mean albedo of pV = 0.16, which is not consistent with either C-type or LL-chondrite compositions (Masiero et al., 2013). Recent analysis of the Chelyabinsk meteorite samples showed that shock darkening of chondritic material could produce an albedo consistent with the Baptistina family without altering the composition (Reddy et al., 2014), offering a potential solution to the seemingly contradictory information about this family, but future work will be necessary to confirm this hypothesis. 3.2.4. “Nysa-Polana.” In the years leading up to Asteroids III it had become increasingly clear that Nysa-Polana, interpreted as a single entity, was likely to be a short-lived phenomenon. Cellino et al. (2001) presented a spectroscopic study of 22 asteroids associated with the group, and found that the group was best understood as two compositionally distinct families partly overlapping in orbital-element space, one associated with the F class in the Tholen taxonomy and one with the S class, while (44) Nysa was compositionally distinct and potentially not associated with either family. Masiero et al. (2011) showed that the albedo distribution of the ~3000 asteroids identified as part of the Nysa-Polana complex were strongly bimodal, unlike the majority of families. Although overlapping in semimajor axis-inclination space, the high- and low-albedo components occupy distinct regions of semimajor axis-eccentricity space, supporting the theory that they are two distinct populations coincidentally overlapping as opposed to a single parent body that was composed of two distinct mineralogies. Using albedo as a discriminant, Masiero et al. (2013) were able to uniquely identify two separate families, a low-albedo one associated with (142) Polana, and a highalbedo one associated with (135) Hertha (PDS ID 405), while (44) Nysa no longer linked to either family. In Table 1 we continue to refer to the high-albedo family as “Nysa” despite the evidence to the contrary, for consistency with other literature. Walsh et al. (2013) expanded on this, and used the family albedos to reject objects with S-type physical properties and focus on the low-albedo component of the Nysa-Polana group. Using dynamical constraints, they were able to further subdivide the low-albedo component of this group into two distinct families, which they identify as the Eulalia family and the “new Polana” family. They estimate ages for each of these families of 0.9–1.5 b.y. and >2 b.y.,

Masiero et al.:  Asteroid Family Physical Properties   333

respectively. Conversely, Milani et al. (2014) identify the whole complex as associated with Hertha and split this region into two components by combining dynamics and physical properties, which they identify as the Polana and Burdett families (low and high albedo, respectively). 3.2.5. Vesta. The Vesta asteroid family (PDS ID 401) has historically been one of the most well-studied families, due to its clear association with one of the largest known asteroids, the high albedos and locations in the inner main belt making members favorable for groundbased observations, and association with the howardite-eucrite-diogenite (HED) meteorites leading to the interpretation of (4) Vesta as a differentiated parent body (McCord et al., 1970; Zappala et al., 1990; Binzel and Xu, 1993; Consolmagno and Drake, 1977; Moskovitz et al., 2010; Mayne et al., 2011). With the recent visit of the Dawn spacecraft to (4) Vesta (see the chapter by Russell et al. in this volume), ground-truth data can be compared to remote-sensing observations of family members. Additionally, constraints on the ages of the major impact basins of 1.0 ± 0.2 b.y. for Rheasilvia and 2.1 ± 0.2 b.y. years for Veneneia (Schenk et al., 2012) set strong constraints on the possible age of Vesta family members. Milani et al. (2014) find that the Vesta family splits into two subgroups in their analysis, which they attribute to these two events. The Vesta family has a unique mineralogical composition in the main belt, making it easily distinguishable in color-, albedo-, or spectral-space. In particular, members stand out from all other asteroids in terms of their high albedo, low i–z color, and deep 1-µm and 2-µm absorption bands. This has prompted searches for objects with similar properties at more distant locations in the main belt (e.g., Moskovitz et al., 2008; Duffard and Roig, 2009; Moskovitz et al., 2010; Solontoi et al., 2012). These bodies could only have evolved from the Vesta family via a low-probability series of secular resonances (Carruba et al., 2005; Roig et al., 2008a), and may be indicative of other parent bodies that were differentiated. To date only a few candidate objects from these searches have been confirmed to be V-type, indicating that the collisional remnants of the other differentiated objects that must have formed in the early solar system has likely been dynamically erased. 3.2.6. Eunomia. The Eunomia family (PDS ID 502) is an old, S-type family located in the middle main belt. Spectral evidence presented by Lazzaro et al. (1999) indicates that the Eunomia family may have originated from a partially differentiated parent body. Natheus et al. (2005) and Nathues (2010) investigated the physical properties of the Eunomia largest remnant and 97 smaller family members as a probe of the composition and differentiation history of the original parent body. They found that the largest remnant shows two hemispheres with slightly different compositions that support an interpretation of the impact causing significant crust loss and some mantle loss on a partially differentiated core. Milani et al. (2014) found two subfamilies within Eunomia, which they attribute to separate cratering events. 3.2.7. Eos. The Eos family (PDS ID 606) represents the primary reservoir of K-type asteroids in the main belt,

and can easily be identified by their 3.4-µm albedo (Masiero et al., 2014). This spectral class has been proposed as the asteroidal analog of the CO and CV carbonaceous chondrite meteorites (Bell et al., 1988; Doressoundiram et al., 1998; Clark et al., 2009). This would imply that the Eos family is one of the best-sampled collisional families in our meteorite collection, and would mean that many of these samples do not probe the C-complex asteroids as had frequently been assumed. Mothé-Diniz and Carvano (2005) compared spectra of (221) Eos with meteorite samples and inferred that the Eos parent body likely underwent partial differentiation. MothéDiniz et al. (2008) extended this work to 30 Eos family members and found mineral compositions consistent with forsteritic olivine consistent with a history of differentiation or a composition similar to CK-type meteorites. However, Masiero et al. (2014) instead interpret the surface properties as consistent with shock darkening of silicates (cf. Britt and Pieters, 1994, Reddy et al., 2014). Future work will enable us to resolve the ambiguity in the composition of these objects. The Eos family represents one of the key fronts of advancing our understanding of family formation that has been opened by our wealth of new data. 3.2.8. Themis. The Themis family (PDS ID 602) is one of the largest low-albedo families in the main belt. The majority of Themis family members are classified as C-complex bodies (Mothé-Diniz et al., 2005; Ziffer et al., 2011). Spectral surveys have found variations in the spectral slope among Themis members, ranging from neutral to moderately red (Ziffer et al., 2011; de Leon et al., 2012). As the first asteroid discovered to show cometary activity (133P Elst-Pizzaro) is dynamically associated with Themis, Hsieh and Jewitt (2006) searched 150 other Themis family members for signs of cometary activity, discovering one additional object: (118401) 1999 RE70. The periodic nature of this activity points to volatile sublimation as the probable cause, as opposed to collisions or YORP spinup (see the chapter by Jewitt et al. in this volume), meaning that the Themis family members, and (24) Themis itself, likely harbor subsurface ice. Further, Rivkin and Emery (2010) and Campins et al. (2010) reported evidence of water ice features on the surface of (24) Themis. If this icy material was primordial to the Themis parent and not implanted by a later impact, this would set constraints on where the Themis parent formed relative to the “snow line” in the protosolar nebula. These objects are also likely to be a new reservoir of water, and may have contributed to the volatile content of the early Earth. 3.2.9. Sylvia. The Sylvia family (PDS ID 603) in the Cybele region resides at the outer edge of the main belt [3.27 < a ≤ 3.70 AU (Zellner et al., 1985b)], beyond the 2:1 Jupiter mean-motion resonance. These asteroids, along with the objects in the Hilda and Jupiter Trojan populations, likely have limited contamination by materials from the inner solar system, and represent a pristine view of the materials present near Jupiter at the end of planetary migration. The Nice model proposed that these asteroids are transneptunian

334   Asteroids IV objects (TNOs) that were scattered inward during the chaotic phase of planetary evolution (Levison et al., 2009); however, the Cybeles show different spectral characteristics from the Hildas and Trojans, and thus may represent the material native to this region of the solar system. Kasuga et al. (2012) studied the size- and albedo-distributions of the Sylvia asteroid family to better understand the history of these bodies. They found that the largest Cybeles (D > 80 km) are predominantly C- or P-types, and the best-fit power law to the size distribution is consistent with a catastrophic collision. However, the estimated mass and size of the parent body lead to collisional timescales larger than the age of the solar system, assuming an equilibrium collisional cascade. These are comparable to the timescales for the Hildas, although they find that the Trojan population is consistent with collisional origin. Numerical simulations of the collisional formation and dynamical evolution of the Cybeles will allow for a more detailed study of the history of this population. 3.3. Relationship Between Albedo and Color Almost every major taxonomic class of asteroid is represented in the list of asteroid families. Using the physical property data described above, we can investigate relationships between the averaged physical properties for each family. By nature of the large sample sizes, the SDSS colors and optical albedos are the best-determined parameters for the majority of families. Figure 2 shows the composite a⋆ and i–z colors derived for each family from SDSS compared to the composite optical albedo as determined via thermal radiometry. There is a clear linear correlation between the SDSS a⋆ color and the log of the albedo, although with significant scatter. The i–z color is approximately flat for low and moderate albedos, but decreases noticeably for high-albedo families. It is important to again note that these data are subject to

observational selection and completeness biases, and so these relations should be interpreted with caution. 4. DISCUSSION 4.1. Correlation of Observed Properties with the Primordial Composition of the Main Belt When considering the distributions of colors and albedos, asteroid families fall into one of only a small number of groupings. The Hungaria, Vesta, and Eos families have unique properties that distinguish them from all other families. Similarly, the Watsonia family shows unique polarimetric properties. While the properties of these families can be used to efficiently identify family members and mineral analogs, it is more difficult to relate the mineralogy and history of these families to that of the currently observed main belt as a whole [although they may be good analogs for now-extinct populations (cf. Bottke et al., 2012)]. Conversely, almost all other families fall into either the S-complex or the C-complex, both of which can be further subdivided by spectral taxonomic properties. Given the number of different parent bodies with these compositions, it has been inferred that these two complexes are probes of the pristine material from the protoplanetary disk in this region of the solar system. However, studies of the evolution of the giant planets in the early solar system call into question the specific locations from which these bodies originated (e.g., Gomes et al., 2005). One possible scenario, known as the “Grand Tack” (Walsh et al., 2012), postulates that the protoplanetary core of Jupiter migrated through the planetesimal disk, evacuating the main-belt region of its primordial material and repopulating it with material from both inward and outward in the disk (see the chapter by Morbidelli et al. in this volume). In this case, the two different compositional complexes would represent these implanted objects. Further

0.3

(a)

(b)

0.1

0.2 0.0

a

i–z

0.1

0.0

–0.2

–0.1

–0.2

–0.1

10–1

–0.3

pV

10–1

pV

Fig. 2. Average SDSS a⋆ and i-z colors compared with optical albedos (logarithmically scaled) for asteroid families, as given in Table 1.

Masiero et al.:  Asteroid Family Physical Properties   335

study of the physical properties of asteroid families and the other small-body populations of the solar system will allow us to test this theory. 4.2. Properties of Observed Families Contrasted with the Background Population Using computed a⋆ colors from the SDSS MOC 4, Parker et al. (2008) divided asteroid families into blue and red groups, tracing the C and S taxonomic complexes, respectively. For both groups, they found that family membership as a fraction of total population increased with decreasing brightness from ~20% at HV = 9 to ~50% at HV = 11. For objects with absolute magnitudes of H > 11 the fractions of blue and red asteroids in families diverge, with blue objects in families making up a smaller fraction of the total population while red objects stay at the levels seen at brighter magnitudes; however, it is unclear what contribution the survey biases have to these observed differences. If this difference in behavior is indeed a physical effect, it may indicate a difference in internal structure or collisional processing rates between the two populations. When exploring the taxonomic distribution of asteroids as a function of distance from the Sun, families have been problematic because the large number of homogeneous objects concentrated in small regions of orbital-element space can skew the results. Studies of the overall distributions of physical properties therefore typically use only the largest member of the family, removing the smaller members (e.g., Mothé-Diniz et al., 2003). Alternatively, the distribution could be explored by volume or mass, in which case all family members may be included because their individual volumes or masses contribute to the whole (e.g., DeMeo and Carry, 2013). A comprehensive study of the taxonomic contribution of families to the population of small asteroids has not yet been undertaken; however, disentangling families from the background is critical to correctly interpreting an overall picture of the compositional makeup of the asteroid belt and how the asteroid belt and the bodies within it formed. Distinguishing between families and the background becomes increasingly difficult at smaller sizes where orbital parameters have evolved further due to gravitational and nongravitational forces. Even the background itself is likely composed of many small families forming from small parent bodies (Morbidelli et al., 2003). 4.3. Families as Feeders for the Near-Earth Object Population The Yarkovsky and YORP nongravitational effects play a critical role in repopulating the NEOs with small bodies from the main belt (Bottke et al., 2000). Primordial asteroids with diameters of ~100  m should be efficiently mobilized from their formation locations into a gravitational resonance over the age of the solar system, limiting the contribution of these objects to the currently observed NEO population.

However, family-formation events act as an important source of objects in this size regime, injecting many thousands of small asteroids into the main belt with each impact (Durda et al., 2007). The complete census of family physical properties, combined with better estimates for family ages that can now be made, enable us to trace the history of specific NEAs from their formation in the main belt to their present-day orbits. For the same reasons, recently fallen meteorites are also good candidates for comparisons to asteroid families, but the differences between the surface properties we can observe on asteroids and the atmosphere-selected materials surviving to the ground complicate this picture. 4.4. Families Beyond the Main Belt Although the vast majority of known asteroid families are in the main belt, massive collisions resulting in family-formation events are not unique to this region of the solar system. While the NEA population is dynamically young (Gladman et al., 2000) and thus these objects have a low probability of undergoing collisional breakup, the more-distant reservoirs that date back to the beginning of the solar system are expected to undergo the same collisional processing as the main belt, albeit with lower impact velocities. Searches for young families in both the NEO and Mars Trojan populations have yielded only a single candidate family cluster associated with (5261) Eureka (Schunová et al., 2012; Christou, 2013). Dynamical families have been identified in the Hilda, Jupiter Trojan, and TNO populations. The first two populations are trapped in long-term stable resonant orbits with Jupiter, providing a population that has suffered far less dispersion than the majority of main-belt families. Similarly, the TNO population is cross-cut by a range of Neptune resonances, some of which are similarly stable long term. The Yarkovsky and YORP effects are greatly diminished for all three populations compared to the main belt (especially the TNOs) due to the larger distances from the Sun, further reducing the dispersion of collisional fragments. Grav et al. (2012) present visible and infrared albedos for the Hilda and Schubart asteroid families found in the 3:2 Jupiter mean-motion resonance. Using these albedos, they show the Hilda family is associated with D-type taxonomy, while the Schubart family is associated with C- or P-type taxonomy. The Hilda population in general is dominated by C- and P-type objects at the largest sizes, but transitions to primarily D-class at the smallest sizes measured, which may be indicative of the effect of the Hilda family on the overall population (Grav et al., 2012; DeMeo and Carry, 2014). However, we note that recent family analysis by Milani et al. (2014) showed that the Hilda family was not statistically significant using their methodology, in contrast to previous work. The Jupiter Trojans comprise the L4 and L5 Lagrange point swarms that lead and trail Jupiter (respectively) on its orbit. Multiple families have been identified in each of the swarms (Milani, 1993; Beaugá and Roig, 2001), but there is some debate as to the significance of these families

336   Asteroids IV (cf. Brož and Rozehnal, 2011). Fornasier et al. (2007) combined measured spectra from multiple sources (Fornasier et al., 2004; Dotto et al., 2006) to characterize Trojan family members. In the L5 cloud, members of the Aneas, Anchises, Misenus, Phereclos, Sarpedon, and Panthoos families were found to have spectra with moderate-to-high spectral slopes, with most members being classified as D-type. The background population had a wider range of slopes and taxonomies from P- to D-type (Fornasier et al., 2004). In the L4 cloud members of the Eurybates, 1986  WD and 1986 TS6 families were studied. The 1986  WD and 1986 TS6 family members had featureless spectra and high slopes resulting in a classification for most as D-types, while the few with lower slopes were placed in the C- and P-classes. Eurybates members, however, have markedly different spectra with low to moderate slopes splitting the classifications evenly between the C- or P-classes (Fornasier et al., 2007; De Luise et al., 2010). Roig et al. (2008b) used the SDSS data to investigate asteroid families in the Jupiter Trojan population, and found that the families in the Trojan populations account for the differences in the compositional distributions between the L4 and L5 clouds. In particular, the families in the L4 cloud show an abundance of C- and P-type objects not reflected in the L5 families or the background populations in either cloud. The TNO population covers a much larger volume of space than any of the populations of objects closer to the Sun, but is also estimated to contain over 1000× the mass of the main belt. Collisions resulting in catastrophic disruptions are believed to have occurred at least twice in the TNO population. Pluto’s five [or potentially more (Weaver et al., 2006)] satellites speak to a massive collision, which will be a key area of investigation of the New Horizons flyby of the Pluto system. The dwarf planet Haumea is highly elongated with a very short rotational period (~4 h), is orbited by two small satellites, has a relatively high density, and has a spectrum that is consistent with nearly pure water ice. These properties are thought to be the result of a mantle-shattering collisional event, although the details of this event remain contentious. A group of TNOs with colors substantially bluer than the typical neutral-to-ultrared surfaces of the Kuiper belt, all sharing high inclinations similar to Haumea, has been identified as a collisional family produced by this event (Brown et al., 2007). Because of the orbital velocity regimes in transneptunian space, collisional families are in general unlikely to be identified there through dynamics alone (as they are in the asteroid belt). It was only through the unique composition of the family members (akin to the extremely distinct photometric properties of the Vesta family members) that the Haumea family could be readily identified. This implies that more collisional families may be hiding in the TNO population, but cannot be spotted by orbits alone. Although massive collisions dominated the solar system environment during the epoch of planet building, they also played an important role in shaping all the major populations of small bodies during the subsequent ~4 b.y. Collisional

evolution, although stochastic in nature, was a major determinant in the structure of the solar system we see today (see the chapter by Bottke et al. in this volume). 5. OPEN PROBLEMS AND FUTURE PROSPECTS The effect of space weathering on asteroidal surfaces still remains an important topic for future exploration (see the chapter by Brunetto et al. in this volume for further discussion). The range of studies carried out so far have found a wide dispersion of results, both in terms of the timescale of weathering and the specific effects on various taxonomic classes. Studies to date have relied on the assumption that all asteroids with similar taxonomic types have identical mineralogical compositions, or have been based on a single pair of families known to be compositionally identical but with different ages (i.e., Karin and Koronis). As deeper surveys and dynamical analysis techniques begin to increase the number of identified cases of family-within-a-family, physical studies of these interesting populations will allow better measurements of the specific effects and timing of space-weathering processes. Advances in physical measurements of asteroid families have not uniformly addressed the various parameters needed for a robust scientific investigation. In particular, there has been only a nominal advancement in the measurement of asteroid masses and densities, owing to the difficulty in determining these parameters. Carry (2012) compiled known measurements of asteroid densities into a comprehensive list; however, only a handful of families have more than one member represented, and for most the only measurement is of the largest remnant body. A larger survey of densities including many family members over a range of sizes would enable testing of family formation conditions via reaccretion (cf. the chapter by Michel et al. in this volume), as well as improve family ages derived from numerical simulations of gravitational and Yarkovsky orbital evolution (cf. the chapter by Nesvorný et al. in this volume). This could be accomplished by a more comprehensive search for binaries, or through modeling of gravitational perturbations to asteroid orbits detectable in next-generation astrometric catalogs. One highly anticipated survey will be carried out by the European Space Agency’s (ESA) Gaia mission (Hestroffer et al., 2010), which is expected to provide spectral characterization of all objects down to an apparent magnitude of V = 20, including many asteroid family members (Campins et al., 2012; Delbó et al., 2012; Cellino and Dell’Oro, 2012). This dramatic increase in the number of characterized family members will enable a host of new investigations of the composition and differentiation of family parent bodies. By spectrally probing bodies as small as ~2 km, inhomogeneities in asteroid family composition may begin to be revealed. Another key scientific product will be refined astrometry for all asteroids, which can be searched for gravitational perturbations and used to determine the masses of the largest asteroids (Mignard et al., 2007). This wealth

Masiero et al.:  Asteroid Family Physical Properties   337

of new data will feed into theoretical models and numerical simulations, allowing us to improve the ages determined from orbital evolution simulations (e.g., Masiero et al., 2012; Carruba et al., 2014). The collision events that form families are very rare, and the probability of a massive collision in the next 10, 100, or 1000 years is vanishingly small (see the chapter by Bottke et al. in this volume). However, a new class of active mainbelt objects has recently been identified that may nonetheless provide a window into the collisional environment of the solar system (see the chapter by Jewitt et al. in this volume for further discussion). While some of these objects show repeated activity indicative of a cometary nature complete with subsurface volatiles, others are best explained by impact events. In particular, the observed outburst events of P/2010 A2 (Jewitt et al., 2010) and (596) Scheila (Jewitt et al., 2011) are consistent with impacts by very small (D < 50 m) asteroids. As current and future sky surveys probe to smaller diameters in the main belt, the frequency at which these events will be observed, or even predicted in advance, will increase. Study of these small-scale disruptions offers an important constraint on impact physics in the low-gravity environment of asteroids, and provides test cases for comparing to the small-scale impact experiments that can be performed in Earth-based laboratories. Recently, Reddy et al. (2014) presented evidence that shock darkening may play a role in altering the spectroscopic properties of chondritic materials in the Baptistina and Flora families. If evidence for this effect is seen in other families across a range of compositions, this technique may provide a method for determining the conditions of familyforming impacts in the main belt, and thus provide better constraints on the ages of families. This may also help explain some of the differences observed in space-weathering studies that find albedo changes happen very quickly while spectral changes have long timescales. As new datasets have rapidly increased our ability to characterize asteroid family members, and through this the parent body from which they originated, one glaring question remains at the forefront of the field: Where are the families of differentiated parent bodies that were completely disrupted? Vesta and its family members have given us a excellent example of the composition and resultant albedo, color, and spectral properties of the crust of a differentiated body (see the chapter by Russell et al. in this volume for further discussion). However, searches for objects with similar properties in different regions of the main belt have yielded no significant populations of these basaltic crust and mantle fragments that should be left over from these collisions. On the other hand, data from iron meteorites has indicated that differentiation of protoplanets, if not common, at a minimum happened multiple times (see the chapters by Scheinberg et al. and Scott et al. in this volume for further discussion). While it is possible that these collisions happened at the earliest stages of the solar system’s formation and the evidence (in the form of families) was erased during the epoch of giant planet migration — the foundation

of the “Nice” model (see the chapter by Morbidelli et al. in this volume) — a dynamical explanation of this problem would need to preserve in the main belt the core material that still falls to Earth today. Conversely, if these impacts happened after the last great shakeup of the solar system, a mineralogical explanation for how metallic cores could form without leaving a basaltic “residue” in the main belt is required. The limitations on what could not have happened that are being set by current surveys are just as important as our discoveries of what did happen. The next decade of large surveys, both ground- and spacebased, promises to expand our knowledge of asteroid physical properties by potentially another order of magnitude beyond what is known today. In this data-rich environment, family research will focus not just on individual families and their place in the main belt, but on specific subgroupings within families: on the knots, clumps, and collisional cascade fragments that trace the disruption and evolutionary dynamics that families have undergone. As the sizes of objects probed reach smaller and smaller, we can expect to find more young families like Karin and Iannini that can be directly backward-integrated to a specific time of collision, improving our statistics of collisions in the last 10 m.y. As catalogs increase in size, we can also expect to more frequently have characterization data of objects both before and after they undergo catastrophic disruption. This will enable us to test our impact-physics models on scales not achievable on Earth. Additionally, we will begin to see a time when we routinely use remote sensing data of asteroids to not just associate families but also assess the mineralogy of family members as a probe of the parent body. Asteroid family physical properties, numerical simulations, and evolutionary theory will leapfrog off each other, pushing forward our understanding of the asteroids and of the solar system as a whole. Acknowledgments. J.R.M. was partially supported by a grant from the NASA Planetary Geology and Geophysics Program. F.E.D. was supported by NASA through Hubble Fellowship grant HSTHF-51319.01-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. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by NASA. This publication also makes use of data products from NEOWISE, which is a project of the Jet Propulsion Laboratory/ California Institute of Technology, funded by the Planetary Science Division of NASA. Funding for the creation and distribution of the SDSS archive (http://www.sdss. org/) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, NASA, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the participating institutions. The participating institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy

338   Asteroids IV (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the U.S. Naval Observatory, and the University of Washington. This research is based on observations with AKARI, a Japan Aerospace Exploration Agency (JAXA) project with the participation of ESA. The authors wish to thank B. Bus, B. E. Clark, H. Kaluna, and P. Vernazza for providing proprietary spectra to include in Fig. 1. We also thank the referees, A. Cellino and B. Bus, and editor P. Michel for helpful comments that improved this chapter.

REFERENCES Alí-Lagoa V., de León J., Licandro J., et al. (2013) Physical properties of B-type asteroids from WISE data. Astron. Astrophys., 554, A71. Assandri M. C. and Gil-Hutton R. (2008) Surface composition of Hungaria asteroids from the analysis of the Sloan Digital Sky Survey. Astron. Astrophys., 488, 339. Beaugé C. and Roig F. (2001) A semianalytical model for the motion of the Trojan asteroids: Proper elements and families. Icarus, 153, 391. Bell J. F. (1988) A probable asteroidal parent body for the CO or CV chondrites. Meteoritics, 23, 256. Binzel R. P. and Xu S. (1993) Chips off of asteroid 4 Vesta — Evidence for the parent body of basaltic achondrite meteorites. Science, 260, 186. Bottke W. F., Vokrouhlický D., and Nesvorný D. (2007) An asteroid breakup 160 Myr ago as the probable source of the K/T impactor. Nature, 449, 48. Bottke W. F., Rubincam D. P., and Burns J. A. (2000) Dynamical evolution of main belt meteoroids: Numerical simulations incorporating planetary perturbations and Yarkovsky thermal forces. Icarus, 145, 301. Bottke W. F., Vokrouhlický D., Minton D., et al. (2012) An Archaean heavy bombardment from a destabilized extension of the asteroid belt. Nature, 485, 78. Bowell E., Oszkiewicz D. A., Wasserman L. H., Muinonen K., Penttilä A., and Trilling D. E. (2014) Asteroid spin-axis longitudes from the Lowell Observatory database. Meteoritics & Planet. Sci., 49, 95. Britt D. T. and Pieters C. M. (1991) Black ordinary chondrites: An analysis of abundance and fall frequency. Meteoritics, 26, 279. Britt D. T. and Pieters C. M. (1994) Darkening in black and gas-rich ordinary chondrites: The spectral effect of opaque morphology and distribution. Geochim. Cosmochim. Acta, 58, 3905. Brown M. E., Barkume K. M., Ragozzine D., and Schaller E. L. (2007) A collisional family of icy objects in the Kuiper belt. Nature, 446, 294. Brož M. and Morbidelli A. (2013) The Eos family halo. Icarus, 223, 844. Brož M. and Rozehnal J. (2011) Eurybates — the only asteroid family among Trojans? Mon. Not. R. Astron. Soc., 414, 565. Brož M., Morbidelli A., Bottke W. F., Rozehnal J., Vokrouhlický D., and Nesvorný D. (2013) Constraining the cometary flux through the asteroid belt during the late heavy bombardment. Astron. Astrophys., 551, A117. Burbine T. and Binzel R. P. (2002) Small Main-Belt Asteroid Spectroscopic Survey in the near-infrared. Icarus, 159, 468. Burbine T. H, Gaffey M. J., and Bell J. F. (1992) S-asteroids 387 Aquitania and 980 Anacostia — Possible fragments of the breakup of a spinel-bearing parent body with CO3/CV3 affinities. Meteoritics, 27, 424. Bus S. J. and Binzel R. P. (2002) Phase II of the Small Main-Belt Asteroid Spectroscopic Survey: A feature-based taxonomy. Icarus, 158, 146. Campins H., Hargrove K., Pinilla-Alonso N., et al. (2010) Water ice and organics on the surface of the asteroid 24 Themis. Nature, 464, 1320. Campins H., de León J., Licandro J., et al. (2012) Spectra of asteroid families in support of Gaia. Planet. Space Sci., 73, 95–97. Carruba V. (2013) An analysis of the Hygiea asteroid family orbital region. Mon. Not. R. Astron. Soc., 431, 3557–3569. Carruba V., Michtchenko T. A., Roig F., Ferraz-Mello S., and Nesvorný D. (2005) On the V-type asteroids outside the Vesta family.

I. Interplay of nonlinear secular resonances and the Yarkovsky effect: The cases of 956 Elisa and 809 Lundia. Astron. Astrophys., 441, 819. Carruba V., Domingos R. C., Nesvorný D., Roig F., Huaman M. E., and Souami D. (2013) A multidomain approach to asteroid families’ identification. Mon. Not. R. Astron. Soc., 433, 2075–2096. Carruba V., Aljbaae S., and Souami D. (2014) Peculiar Euphrosyne. Astrophys. J., 792, 46. Carry B. (2012) Density of asteroids. Planet. Space Sci., 73, 98. Carvano J. M., Lazzaro D., Mothé-Diniz T., Angeli C. A., and Florczak M. (2001) Spectroscopic survey of the Hungaria and Phocaea dynamical groups. Icarus, 149, 173. Carvano J. M., Hasselmann P. H., Lazzaro D., and Mothé-Diniz T. (2010) SDSS-based taxonomic classification and orbital distribution of main belt asteroids. Astron. Astrophys., 510, A43. Clark B. E., Ockert-Bell M. E., Cloutis E. A., Nesvorný D., Mothé-Diniz T., and Bus S. J. (2009) Spectroscopy of K-complex asteroids: Parent bodies of carbonaceous meteorites? Icarus, 202, 119. Cellino A. and Dell’Oro A. (2012) The derivation of asteroid physical properties from Gaia observations. Planet. Space Sci., 73, 52. Cellino A., Gil-Hutton R., Tedesco E. F., Di Martino M., and Brunini A. (1999) Polarimetric observations of small observations: Preliminary results. Icarus, 138, 129. Cellino A., Zappala V., Doressoundiram A., et al. (2001) The puzzling case of the Nysa-Polana family. Icarus, 152, 225. Cellino A., Bus S. J., Doressoundiram A., and Lazzaro D (2002) Spectroscopic properties of asteroid families. In Asteroids III (W. F. Bottke Jr. et al., eds.), p. 633. Univ. of Arizona, Tucson. Cellino A., Dell’Oro A., and Tedesco E. F. (2009) Asteroid families: Current situation. Planet. Space Sci., 57, 173. Cellino A., Delbò M., Bendjoya Ph., and Tedesco E. F. (2010) Polarimetric evidence of close similarity between members of the Karin and Koronis dynamical families. Icarus, 209, 556. Cellino A., Bagnulo S., Tanga P., Novaković B., and Delbò M. (2014) A successful search for hidden Barbarians in the Watsonia asteroid family. Mon. Not. R. Astron. Soc., 439, L75-L79. Christou A. A. (2013) Orbital clustering of martian Trojans: An asteroid family in the inner solar system? Icarus, 224, 144. Consolmagno G. J. and Drake M. J. (1977) Composition and evolution of the eucrite parent body — Evidence from rare earth elements. Geochim. Cosmochim. Acta, 41, 1271. Delbó M., Gayon-Markt J., Busso G., et al. (2012) Asteroid spectroscopy with Gaia. Planet. Space Sci., 73, 86. de Leon J., Licandro J., Serra-Ricart M., Pinilla-Alonso N., and Campins H (2010) Observations, compositional, and physical characterization of near-Earth and Mars-crosser asteroids from a spectroscopic survey. Astron. Astrophys., 517, 23. de León J., Pinilla-Alonso N., Campins H., Licandro L., and Marzo G. A. (2012) Near-infrared spectroscopic survey of B-type asteroids: Compositional analysis. Icarus, 218, 196. De Luise F., Dotto E., Fornasier S., Barucci M. A., Pinilla-Alonso N., Perna D., and Marzari F. (2010) A peculiar family of Jupiter Trojans: The Eurybates. Icarus, 209, 586–590. DeMeo F. E. and Carry B. (2013) The taxonomic distribution of asteroids from multi-filter all-sky photometric surveys. Icarus, 226, 723. DeMeo F. E. and Carry B. (2014) Solar system evolution from compositional mapping of the asteroid belt. Nature, 505, 629. de Sanctis M. C., Migliorini A., Luzia Jasmim F., Lazzaro D., et al. (2011) Spectral and mineralogical characterization of inner main-belt V-type asteroids. Astron. Astrophys., 533, A77. Dohnanyi J. S. (1969) Collisional model of asteroids and their debris. J. Geophys. Res., 74, 2531. Doressoundiram A., Barucci M. A., Fulchignoni M., and Florczak M. (1998) Eos family: A spectroscopic study. Icarus, 131, 15. Dotto E., Fornasier S., Barucci M. A., et al. (2006) The surface composition of Jupiter Trojans: Visible and near-infrared survey of dynamical families. Icarus, 183, 420. Duffard R. and Roig F. (2009) Two new V-type asteroids in the outer main belt? Planet. Space Sci., 57, 229. Dunn T. L., Burbine T. H., BottkeW. F., and Clark J. P. (2013) Mineralogies and source regions of near-Earth asteroids. Icarus, 222, 273–282. Durda D. D., Bottke W. F., Nesvorný D., et al. (2007) Size frequency distribution of fragments from SPH/N-body simulations of asteroid

Masiero et al.:  Asteroid Family Physical Properties   339 impacts: Comparison with observed asteroid families. Icarus, 186, 498. Fieber-Beyer S. K., Gaffey M. J., Kelley M. S., Reddy V., Reynolds C. M., and Hicks T. (2011) The Maria asteroid family: Genetic relationships and a plausible source of mesosiderites near the 3:1 Kirkwood gap. Icarus, 213, 524. Fornasier S., Dotto E., Marzari F., et al. (2004) Visible spectroscopic and photometric survey of L5 Trojans: Investigation of dynamical families. Icarus, 172, 221. Fornasier S., Dotto E., Hainaut O., et al. (2007) Visible spectroscopic and photometric survey of Jupiter Trojans: Final results on dynamical families. Icarus, 190, 622. Gaffey M. J., Burbine T. H., Piatek J. L., et al. (1993) Mineralogical variations within the S-type asteroid class. Icarus, 106, 573. Gil-Hutton R., Lazzaro D., and Benavidez P. (2007) Polarimetric observations of Hungaria asteroids. Astron. Astrophys., 468, 1109. Gladman B., Michel P., and Froeschlé C. (2000) The near-Earth object population. Icarus, 146, 176. Gomes R., Levison H. F., Tsiganis K., and Morbidelli A. (2005) Origin of the cataclysmic late heavy bombardment period of the terrestrial planets. Nature, 435, 26. Grav T., Mainzer A. K., Bauer J., et al. (2012) WISE/NEOWISE observations of the Hilda population: Preliminary results. Astrophys. J., 744, 197. Hanuš J., Durech J., Brož M., et al. (2011) A study of asteroid polelatitude distribution based on an extended set of shape models derived by the light curve inversion method. Astron. Astrophys., 530, A134. Hanuš J., Brož M., Durech J., et al. (2013) An anisotropic distribution of spin vectors in asteroid families. Astron. Astrophys., 559, A134. Harris A. W, Muller M., Lisse C. M., and Cheng A. F. (2009) A survey of Karin cluster asteroids with the Spitzer Space Telescope. Icarus, 199, 86. Hestroffer D., Dell’Oro A., Cellino A., and Tanga P. (2010) The Gaia mission and the asteroids. In Dynamics of Small Solar System Bodies and Exoplanets (J. Souchay and R. Dvorak, eds.), pp. 251–340. Lecture Notes in Physics Vol. 790, Springer-Verlag, Berlin. Hsieh H. H. and Jewitt D. J. (2006) A population of comets in the main asteroid belt. Science, 312, 561. Ishihara D., Onaka T., Kataza H., et al. (2010) The AKARI/IRC midinfrared all-sky survey. Astron. Astrophys., 514, 1. Ivezić Ž., Tabachnik S., Rafikov R., et al. (2001) Solar system objects observed in the Solar Digital Sky Survey commissioning data. Astron. J., 122, 2749. Ivezić Ž., Lupton R. H., Jurić M., et al. (2002) Color confirmation of asteroid families. Astron. J., 124, 2943. Jasmim F. L., Lazzaro D., Carvano J. M. F., Mothé-Diniz T., and Hasselmann P. H. (2013) Mineralogical investigation of several Qp asteroids and their relation to the Vesta family. Astron. Astrophys, 552, A85. Jedicke R., Nesvorný D., Whiteley R. J., Ivezić Ž., and Jurić M. (2004) An age-colour relationship for main-belt S-complex asteroids. Nature, 429, 275. Jewitt D., Weaver H., Agarwal J., Mutchler M., and Drahus M. (2010) A recent disruption of the main-belt asteroid P/2010A2. Nature, 467, 817. Jewitt D., Weaver H., Mutchler M., Larson S., and Agarwal J. (2011) Hubble Space Telescope observations of main-belt Comet (596) Scheila. Astrophys. J. Lett., 733, 4. Kasuga T., Usui F., Hasegawa S., et al. (2012) AKARI/AcuA physical studies of the Cybele asteroid family. Astron. J., 143, 141. Kim M.-J., Choi Y.-J., Moon H.-K., et al. (2014) Rotational properties of the Maria asteroid family. Astron. J., 147, 56. Kohout T., Gritsevich M., Grokhovsky V. I., et al. (2014) Mineralogy, reflectance spectra, and physical properties of the Chelyabinsk LL5 chondrite — Insight into shock-induced changes in asteroid regoliths. Icarus, 228, 78. Kryszczyńska A., Colas F., Polińska M., et al. (2012) Do Slivan states exist in the Flora family? I. Photometric survey of the Flora region. Astron. Astrophys., 546, A72. Lazzaro D., Mothé-Diniz T., Carvano J. M., et al. (1999) The Eunomia family: A visible spectroscopic survey. Icarus, 142, 445. Lazzaro D., Angeli C. A., Carvano J. M., Mothé-Diniz T., Duffard R., and Florczak M. (2004) S3OS2: The visible spectroscopic survey of 820 asteroids. Icarus, 172, 179.

Lebofsky L. A. and Spencer J. R. (1989) Radiometry and a thermal modeling of asteroids. In Asteroids II (R. P. Binzel et al., eds.), p. 128. Univ. of Arizona, Tucson. Lebofsky L. A., Sykes M. V., Tedesco E. F., et al. (1986) A refined ‘standard’ thermal model for asteroids based on observations of 1 Ceres and 2 Pallas. Icarus, 68, 239. Levison H. F., Bottke W. F., Gounelle M., Morbidelli A., Nesvorný D., and Tsiganis K. (2009) Contamination of the asteroid belt by primordial trans-Neptunian objects. Nature, 460, 364–366. Licandro J., Hargrove K., Kelley M., et al. (2012) 5–14 µm Spitzer spectra of Themis family asteroids. Astron. Astrophys., 537, A73. Mainzer A. K., Bauer J., Grav T., et al. (2011) Preliminary results from NEOWISE: An enhancement to the Wide-field Infrared Survey Explorer for solar system science. Astrophys. J., 731, 53. Mainzer A. K., Bauer J., Cutri R.M., et al. (2014) Initial performance of the NEOWISE reactivation mission. Astrophys. J., 792, 30. Masiero J. R., Mainzer A. K., Grav T., et al. (2011) Main belt asteroids with WISE/NEOWISE. I. Preliminary albedos and diameters. Astrophys. J., 741, 68. Masiero J. R., Mainzer A. K., Grav T., Bauer J. M., and Jedicke R. (2012) Revising the age for the Baptistina asteroid family using WISE/NEOWISE data. Astrophys. J., 759, 14. Masiero J. R., Mainzer A. K., Bauer J. M., Grav T., Nugent C. R., and Stevenson R. (2013) Asteroid family identification using the hierarchical clustering method and WISE/NEOWISE physical properties. Astrophys. J., 770, 7. Masiero J. R., Grav T., Mainzer A. K., et al. (2014) Main belt asteroids with WISE/NEOWISE: Near-infrared albedos. Astrophys. J., 791, 121. Mayne R. G., Sunshine J. M., McSween H. Y., Bus S. J., and McCoy T. J. (2011) The origin of Vesta’s crust: Insights from spectroscopy of the vestoids. Icarus, 214, 147. McCord T. B., Adams J. B., and Johnson T. V. (1970) Asteroid Vesta: Spectral reflectivity and compositional implications. Science, 168, 1445. Mignard F., Cellino A., Muinonen K., et al. (2007) The Gaia mission: Expected applications to asteroid science. Earth Moon Planets, 101, 97. Milani A. (1993) The Trojan asteroid belt: Proper elements, stability, chaos and families. Cel. Mech. Dyn. Astron., 57, 59. Milani A., Cellino A., Knežević Z., Novaković B., Spoto F., and Paolicchi P. (2014) Asteroid families classification: Exploiting very large datasets. Icarus, 239, 46. Morbidelli A., Nesvorný D., Bottke W. F., Michel P., Vokrouhlický D., and Tanga P. (2003) The shallow magnitude distribution of asteroid families. Icarus, 162, 328. Moskovitz N. A., Jedicke R., Gaidos E.,Willman M., Nesvorný D., Fevig R., and Ivezić Ž. (2008) The distribution of basaltic asteroids in the main belt. Icarus, 198, 77. Moskovitz N. A., Willman M., Burbine T. H., Binzel R. P., and Bus S. J. (2010) A spectroscopic comparison of HED meteorites and V-type asteroids in the inner main belt. Icarus, 208, 773. Mothé-Diniz T. and Carvano J. M. (2005) 221 Eos: A remnant of a partially differentiated parent body? Astron. Astrophys., 442, 727. Mothé-Diniz T. and Nesvorný D. (2008a) Visible spectroscopy of extremely young asteroid families. Astron. Astrophys. Lett., 486, 9. Mothé-Diniz T. and Nesvorný D. (2008b) Tirela: An unusual asteroid family in the outer main belt. Astron. Astrophys., 492, 593. Mothé-Diniz T., Carvano J. M., and Lazzaro D. (2003) Distribution of taxonomic classes in the main belt asteroids. Icarus, 162, 10. Mothé-Diniz T., Roig F., and Carvano J. M. (2005) Reanalysis of asteroid families structure through visible spectroscopy. Icarus, 174, 54. Mothé-Diniz T., Carvano J. M., Bus S. J., Duffard R., and Burbine T. H. (2008) Mineralogical analysis of the Eos family from near-infrared spectra. Icarus, 195, 277. Murakami H., Baba H., Barthel P., et al. (2007) The infrared astronomical mission AKARI. Publ. Astron. Soc. Japan, 59, S369. Nathues A. (2010) Spectral study of the Eunomia asteroid family. Part II: The small bodies. Icarus, 208, 252. Nathues A., Mottola S., Kaasalainen M., and Neukum G. (2005) Spectral study of the Eunomia asteroid family. I. Eunomia. Icarus, 175, 452. Neese C., ed. (2010) Asteroid Taxonomy V6.0. EAR-A-5DDRTAXONOMY-V6.0, NASA Planetary Data System.

340   Asteroids IV Nesvorný D. (2012) Nesvorny HCM Asteroid Families V2.0. EAR-AVARGBDET-5-NESVORNYFAM-V2.0, NASA Planetary Data System. Nesvorný D., Jedicke R., Whiteley R. J., and Ivezić Ž. (2005) Evidence for asteroid space weathering from the Sloan Digital Sky Survey. Icarus, 173, 132. Novaković B., Cellino A., and Knežević Z. (2011) Families among highinclination asteroids. Icarus, 216, 184. Oszkiewicz D. A., Muinonen K., Bowell E., et al. (2011) Online multiparameter phase-curve fitting and application to a large corpus of asteroid photometric data. J. Quant. Spectrosc. Radiat. Transfer, 112, 1919. Oszkiewicz D. A, Bowell E., Wasserman L. H., Muinonen K., Penttilä A., et al. (2012) Asteroid taxonomic signatures from photometric phase curves. Icarus, 219, 283. Parker A., Ivezić Ž., Jurić M., Lupton R., Sekora M. D., and Kowalski A. (2008) The size distributions of asteroid families in the SDSS Moving Object Catalog 4. Icarus, 198, 138. Rayner J. T., Toomey D. W., Onaka P. M., et al. (2003) SpeX: A medium-resolution 0.8–5.5 micron spectrograph and imager for the NASA Infrared Telescope Facility. Publ. Astron. Soc. Pac., 115, 362. Reddy V., Emery J. P., Gaffey M. J., Bottke W. F., Cramer A., and Kelley M. S. (2009) Composition of 298 Baptistina: Implications for the K/T impactor link. Meteoritics & Planet. Sci., 44, 1917. Reddy V., Carvano J. M., Lazzaro D., et al. (2011) Mineralogical characterization of Baptistina asteroid family: Implications for K/T impactor source. Icarus, 216, 184. Reddy V., Sanchez J. A., Bottke W. F., et al. (2014) Chelyabinsk meteorite explains unusual spectral properties of Baptistina asteroid family. Icarus, 237, 116. Rivkin A. S. and Emery J. P. (2010) Detection of ice and organics on an asteroidal surface. Nature, 464, 1322. Roig F., Nesvorný D., Gil-Hutton R., and Lazzaro D. (2008a) V-type asteroids in the middle main belt. Icarus, 194, 125. Roig F., Ribeiro A. O., and Gil-Hutton R. (2008b) Taxonomy of asteroid families among the Jupiter Trojans: Comparison between spectroscopic data and the Sloan Digital Sky Survey colors. Astron. Astrophys., 483, 911. Schenk P., O’Brien D. P., Marchi S., et al. (2012) The geologically recent giant impact basins at Vesta’s south pole. Science, 336, 694. Schunová E., Granvik M., Jedicke R., Gronchi G., Wainscoat R., and Abe S. (2012) Searching for the first near-Earth object family. Icarus, 220, 1050. Slivan S. M., Binzel R. P., Crespo da Silva L. D., et al. (2003) Spin vectors in the Koronis family: Comprehensive results from two independent analyses of 213 rotation lightcurves. Icarus, 162, 285. Slivan S. M., Binzel R. P., Kaasalianen M., et al. (2009) Spin vectors in the Koronis family. II. Additional clustered spins, and one stray. Icarus, 200, 514. Slivan S. M., Binzel R. P., Boroumand S. C., et al. (2008) Rotation rates in the Koronis family, complete to H11.2. Icarus, 195, 226. Solontoi M. R., Hammergren M., Gyuk G., and Puckett A. (2012) AVAST survey 0.4–1.0 µm spectroscopy of igneous asteroids in the inner and middle main belt. Icarus, 220, 577. Sunshine J. M., Bus S. J., McCoy T. J., Burbine T. H., Corrigan C. M., and Binzel R. P. (2004) High-calcium pyroxene as an indicator of igneous differentiation in asteroids and meteorites. Meteoritics & Planet. Sci., 39, 1343. Sunshine J. M., Connolly H. C., McCoy T. J., Bus S. J., and La Croix L. M. (2008) Ancient asteroids enriched in refractory inclusions. Science, 320, 514.

Szabó G. M. and Kiss L. L. (2008) The shape distribution of asteroid families: Evidence for evolution driven by small impacts. Icarus, 196, 135. Thomas C. A., Rivkin A. S., Trilling D. E., Enga M.-T., and Grier J. A. (2011) Space weathering of small Koronis family members. Icarus, 212, 158. Thomas C. A., Trilling D. E., and Rivkin A. S. (2012) Space weathering of small Koronis family members in the SDSS Moving Object Catalog. Icarus, 219, 505. Usui F., Kuroda D., Müller T. G., et al. (2011) Asteroid catalog using Akari: AKARI/IRC Mid-infrared asteroid survey. Publ. Astron. Soc. Japan, 63, 1117. Vernazza P., Birlan M., Rossi A., et al. (2006) Physical characterization of the Karin family. Astron. Astrophys, 460, 945. Vernazza P., Binzel R. P., Thomas C. A., et al. (2008) Compositional differences between meteorites and near-Earth asteroids. Nature, 454, 858. Vernazza P., Binzel R. P., Rossi A., Fulchignoni M., and Birlan M. (2009) Solar wind as the origin of rapid reddening of asteroid surfaces. Nature, 458, 993. Vernazza P., Zanda B., Binzel R. P., et al. (2014) Multiple and fast: The accretion of ordinary chondrite parent bodies. Astrophys. J., 791, 120. Vokrouhlický D., Nesvorný D., and Bottke W. F. (2003) The vector alignments of asteroid spins by thermal torques. Nature, 425, 147. Walsh K. J., Morbidelli A., Raymond S. N., O’Brien D. P., and Mandell A. M. (2012) Populating the asteroid belt from two parent source regions due to the migration of giant planets — “The Grand Tack.” Meteoritics & Planet. Sci., 47, 1941. Walsh K. J., Delbó M., Bottke W. F., Vokrouhlický D., and Lauretta D. S. (2013) Introducing the Eulalia and new Polana asteroid families: Re-assessing primitive asteroid families in the inner main belt. Icarus, 225, 283-297. Warner B. D., Harris A. W., Vokrouhlický D., Nesvorný D., and Bottke W. F. (2009) Analysis of the Hungaria asteroid population. Icarus, 204, 172. Weaver H. A., Stern S. A., Mutchler M. J., et al. (2006) Discovery of two new satellites of Pluto. Nature, 439, 943. Willman M., Jedicke R., Nesvorný D., Moskovitz N., Ivezić Ž., and Fevig R. (2008) Redetermination of the space weathering rate using spectra of Iannini asteroid family members. Icarus, 195, 663. Willman M., Jedicke R., Moskovitz N., Nesvorný D., Vokrouhlický D., and Mothé-Diniz T. (2010) Using the youngest asteroid clusters to constrain the space weathering and gardening rate on S-complex asteroids. Icarus, 208, 758. York D. G., Adelman J., Anderson J. E., et al. (2000) The Sloan Digital Sky Survey: Technical summary. Astron. J., 120, 1579. Zappala V., Cellino A., Farinella P., and Knezevic Z. (1990) Asteroid families. I — Identification by hierarchical clustering and reliability assessment. Astron. J., 100, 2030. Zappalà V., Cellino A., Dell’Oro A., and Paolicchi P. (2002) Physical and dynamical properties of asteroid families. In Asteroids III (W. F. Bottke Jr. et al., eds.), p. 619. Univ. of Arizona, Tucson. Zellner B., Tholen D. J., and Tedesco E. F. (1985a) The eight-color asteroid survey — results for 589 minor planets. Icarus, 61, 355. Zellner B., Thirunagari A., and Bender D. (1985b) The large-scale structure of the asteroid belt. Icarus, 62, 505–511. Ziffer J., Campins H., Licandro J., et al. (2011) Near-infrared spectroscopy of primitive asteroid families. Icarus, 213, 538.

Michel P., Richardson D. C., Durda D. D., Jutzi M., and Asphaug E. (2015) Collisional formation and modeling of asteroid families. In Asteroids IV (P. Michel et al., eds.), pp. 341–354. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch018.

Collisional Formation and Modeling of Asteroid Families Patrick Michel

Lagrange Laboratory, University of Nice-Sophia, CNRS, Côte d’Azur Observatory

Derek C. Richardson University of Maryland

Daniel D. Durda

Southwest Research Institute

Martin Jutzi

University of Bern

Erik Asphaug

Arizona State University

In the last decade, thanks to the development of sophisticated numerical codes, major breakthroughs have been achieved in our understanding of the formation of asteroid families by catastrophic disruption of large parent bodies. In this review, we describe numerical simulations of asteroid collisions that reproduced the main properties of families, accounting for both the fragmentation of an asteroid at the time of impact and the subsequent gravitational interactions of the generated fragments. The simulations demonstrate that the catastrophic disruption of bodies larger than a few hundred meters in diameter leads to the formation of large aggregates due to gravitational reaccumulation of smaller fragments, which helps explain the presence of large members within asteroid families. Thus, for the first time, numerical simulations successfully reproduced the sizes and ejection velocities of members of representative families. Moreover, the simulations provide constraints on the family dynamical histories and on the possible internal structure of family members and their parent bodies.

1. INTRODUCTION Observed asteroid families in the main asteroid belt are each composed of bodies that are thought to originate from the catastrophic disruption of larger parent bodies (e.g., Farinella et al., 1996). Cratering collisions can also lead to families, such as the one associated with asteroid Vesta, but we do not address this origin scenario here as few families have been linked to cratering events and their modeling requires a different approach (for more details, see the chapter by Jutzi et al. in this volume). A few tens of asteroid families have been identified, corresponding to groups of small bodies well-concentrated in proper-orbital-element space (see, e.g., Hirayama, 1918; Arnold, 1969; and the chapter by Nesvorný et al. in this volume) and sharing similar spectral properties (see, e.g., Chapman et al., 1989 and the chapter by Masiero et al. in this volume). Large families contain up to several hundred identified members, while small and compact families have on the order of 10 identified members. Interestingly,

the theory of the collisional origin of asteroid families rested for decades entirely on these similarities in dynamical and spectral properties and not on the detailed understanding of the collisional physics itself. Indeed, laboratory experiments on centimeter-scale targets, analytical scaling rules, or even complete numerical simulations of asteroid collisions were unable to reproduce the physical and dynamical properties of asteroid families (e.g., Ryan and Melosh, 1998). The extrapolation of laboratory experiments to asteroidal scales yielded bodies much too weak to account for both the size distribution and the dynamical properties of family members. In other words, there was no solution to match both the sizes and ejection velocities of family members simultaneously. To produce the large (assumed coherent) fragments seen in real families required an impact energy leading to ejection speeds of individual fragments that were much too small for them to overcome their own gravitational attraction. The parent body would then be merely shattered but not dispersed and therefore no family would be created (Davis et al., 1979).

341

342   Asteroids IV Conversely, matching individual ejection velocities and deriving the necessary fragment distribution resulted in a size distribution in which no big fragment was present, contrary to most real families (e.g., Davis et al., 1985; Chapman et al., 1989). Thus, big sizes implied no fragment dispersion (at the level of the dispersion of family members), and fragment dispersion implied no big fragments (at the level of the sizes of family members). A big caveat in the extrapolation of laboratory results to large asteroid scales is that the role of gravity (of both the targets and their fragments) is not taken into account in a laboratory-scale disruption involving centimeter-sized targets. Thus, the role of gravity in the catastrophic disruption of a large asteroid at the origin of a family remained to be assessed. Indeed, a possible scenario reconciling the sizes and ejection velocities of family members could be that the parent body (up to several hundred kilometers in size) is disrupted into small pieces by the propagation of cracks resulting from a hypervelocity impact but then the small fragments generated this way would typically escape from the parent and, due to their mutual gravitational attraction, reaccumulate elsewhere in groups in order to build up the most massive family members. This idea had been suggested previously by Chapman et al. (1982), and numerical simulations by Benz and Asphaug (1999) had already shown that at least the largest remnant of an asteroid disruption had to be a bound aggregate. However, the formation of a full family by reaccumulation of smaller fragments remained to be demonstrated. In the last decade, the formation of asteroid families was simulated explicitly for the first time accounting for the two phases of a large-scale disruption: the fragmentation phase and the gravitational reaccumulation phase. In these simulations, the two phases are usually computed separately using a hybrid approach. This chapter reviews the major advances achieved since Asteroids III thanks to this new modeling work, and the implications for our understanding of asteroid family formation and properties. 2. SIMULATING A FAMILY-FORMING EVENT Families are thought to form from the disruption of a large asteroid, called the parent body, as a result of the impact of a smaller projectile. Simulating such a process requires accounting for both the propagation of cracks in the parent body, leading to its conversion into separate fragments, and the possible gravitational interactions of these fragments. As explained above, the latter gravitational phase turns out to be crucial for reproducing asteroid family properties. In asteroid disruptions resulting from an hypervelocity impact, the fragmentation and the gravitational reaccumulation phases have very different associated dynamical times. In the fragmentation phase, the timescale for the propagation of the shock wave is determined by the target’s diameter divided by the sound speed of the material (a few to tens of seconds for an asteroid 100  km in diameter). In the second phase, the timescale for gravitational reaccumulation is proportional

to 1 Gρ, where G is the gravitational constant and r is the target bulk density, which corresponds to at least hours for r = 1 to 3 g cm–3. Therefore it is possible to model the collisional event by separating the two phases. A hybrid approach is generally adopted that consists of simulating first the fragmentation phase using an appropriate fragmentation code (called a hydrocode; see the chapter by Jutzi et al. in this volume), and then the gravitational phase, during which the fragments produced by the fragmentation phase can interact under their mutual attraction, using a gravitational N-body code. 2.1. The Fragmentation Phase Several hydrocodes exist and are used in the planetary science community (see the chapters by Asphaug et al. and Jutzi et al. in this volume). In the first studies devoted to direct simulations of asteroid family formation (Michel et al., 2001, 2002, 2003, 2004), a three-dimensional “smoothed-particle hydrodynamics” (SPH) code was used. This code solves in a Lagrangian framework the usual conservation equations (mass, momentum, and energy) in which the stress tensor has a nondiagonal part. The first families modeled in this way (Eunomia, Koronis, and Flora) were of the S taxonomic type. S-type asteroids are expected to be mostly made of ordinary chondrite materials, for which basalt plausibly has similar properties, and therefore the parent bodies of these S-type families were assumed to be nonporous basalt. The Tillotson equation of state for basalt was used (Tillotson, 1962), which is computationally expedient while sophisticated enough to allow its application over a wide range of physical conditions. Plasticity was introduced by modifying the stresses beyond the elastic limit with a von Mises yielding relation (Benz and Asphaug, 1994, 1995). A yielding relation accounting for the dependence of shear stress on pressure, such as Mohr-Coulomb or Drucker Prager, is generally more appropriate for rock material (see the chapter by Jutzi et al. in this volume). It turns out to be important for cratering events for which part of the process is dominated by shearing or when the impacted body is composed of interacting boulders [a so-called “rubble pile” (Davis et al., 1979) or gravitational aggregate (Richardson et al., 2002); see also Jutzi (2015)]. However, it was found that in the case of the disruption of monolithic parent bodies, the details of the strength model (e.g., pressure-dependent vs. pressureindependent yield strength) do not play an important role (Jutzi, 2015). For the lower tensile stresses associated with brittle failure, a fracture model was used, based on the nucleation of incipient flaws whose number density is given by a Weibull distribution (Weibull, 1939; Jaeger and Cook, 1969). Durda et al. (2004) and Nesvorný et al. (2006) used a similar hydrocode to study the formation of satellites from asteroid disruptions and other family-forming events. Leinhardt and Stewart (2009) studied large-scale disruptions and modeled the shock deformation with an Eulerian shock-physics code, CTH (McGlaun et al., 1990), instead of the Lagrangian SPH code used in previous works.

Michel et al.:  Collisional Formation and Modeling of Asteroid Families   343

Recently, the SPH impact code used by Michel et al. (2001, 2002, 2003, 2004) was extended to include a model adapted for microporous materials (Jutzi et al., 2008, 2009) (see also the Jutzi et al. chapter in this volume). The formation of asteroid families formed from a microporous parent body, such as for dark- (carbonaceous) type families, could thus also be investigated (Jutzi et al., 2010; Michel et al., 2011). Another study looked at the case of rubble-pile parent bodies [containing macroporous voids (Benavidez et al., 2012)]. 2.2. The Gravitational Phase Once the fragmentation phase is over and fractures cease to propagate (within the first simulated tens of seconds), the hydrodynamic simulations are stopped and intact fragments are identified. For impact energies typical of asteroid disruptions and for targets with a diameter typically greater than 1 km, it was found that the bodies are totally shattered into fragments of mass equal to the mass resolution of the simulations. In the first simulations performed in this way, the numerical resolution was limited to a few 105 particles and corresponded to minimum boulder diameters of about 1 to 4 km, for a parent body of a few hundred kilometers in diameter. Thanks to increased computer performance, it is now possible to perform simulations with up to several million particles. However, the gain in particle size resolution is not dramatic and simulations are still limited to minimum fragment diameters of a few hundred meters for target diameter of a few hundred kilometers. Reaching fragment diameters down to meters or less is beyond the capabilities of current and probably near-future technologies. Only when the target’s diameter is in the few hundred meters range can this minimum size be reached, but unfortunately, no asteroid family can be identified involving a parent body of such a small size. Once identified in the simulation outcome, the fragments and their corresponding velocity distributions are then fed into a gravitational N-body code, which computes the gravitational evolution of the system from the handoff point to subsequent hours or days of simulated time. Because the number of fragments is up to a few 106, and their gravitational interaction as well as their potential collisions need to be computed over long periods of time (up to several simulated days), a very efficient N-body code is required to compute the dynamics. The most appropriate code to tackle this problem, which is the only one used so far by various groups to simulate the outcome of the gravitational phase of a collision, is the code called pkdgrav [see Richardson et al. (2000) for the first application of this code to solar system problems]. This parallel hierarchical tree code was developed originally for cosmological studies. Essentially, the tree component of the code provides a convenient means of consolidating forces exerted by distant particles, reducing the computational cost, with the tradeoff of introducing a slight force error (on the order of 1%) that does not affect the results appreciably since the dynamics are dominated by dissipative collisions. The parallel component divides the

work evenly among available processors, adjusting the load at each timestep according to the amount of work done in the previous force calculation. The code uses a straightforward second-order leapfrog scheme for the integration and computes gravity moments from tree cells to hexadecapole order. For the purpose of computing the gravitational phase of an asteroid disruption during which the generated fragments can interact and collide with each other, collisions are identified at each step with a fast neighbor-search algorithm in pkdgrav. Once a collision occurs, because the relative speeds are small enough (on the order of meters per second), it is assumed that no further fragmentation takes place between components generated during the fragmentation phase. In fact, the simulations presented by Michel et al. (2001) assumed perfect sticking of colliding fragments and all colliding fragments were forced to merge into a single particle regardless of their relative velocities. This assumption is justified because the initial impact results in an overall expanding cloud of fragments of relatively small individual masses, down to the minimum fragment size imposed by the numerical resolution, and colliding fragments have typical relative speeds that are smaller than their individual escape speeds. Since the fragments in pkdgrav are represented by spheres, when two spherical fragments reacumulate, they are merged into a single spherical particle with the same momentum. The same assumption was used by Durda et al. (2004) and Nesvorný et al. (2006) in their studies of satellite formation and other family-forming events. In a second and subsequent papers, Michel et al. (2002, 2003, 2004) improved their treatment of fragment collisions by using a merging criterion based on relative speed and angular momentum. In this case, fragments are allowed to merge only if their relative speed is smaller than their mutual escape speed and the resulting spin of the merged fragment is smaller than the threshold value for rotational fission (based on a simple prescription of a test particle remaining on the equator of a sphere). Nonmerging collisions are modeled as bounces between hard spheres whose postcollision velocities are determined by the amount of dissipation taking place during the collisions. The latter is computed in these simulations using coefficients of restitution in the normal and tangential directions [see Richardson (1994) for details on this computation]. Note that Durda et al. (2011, 2013) performed bouncing experiments between 1-m granite spheres as well as between centimeter-scale rocky spheres. These experiments gave a value for the normal coefficient of restitution of ≈0.8, although much lower values are found with increasing roughness of contact surfaces. These results are particularly interesting because they are performed in an appropriate size regime (meter-sized bodies). However, bouncing in simulations occur at somewhat higher speeds (up to tens of meters per second) than in those experiments, which may result in a decrease in the coefficient of restitution due to the start of cracking and other energy dissipation processes. Moreover, although in our numerical modeling, perfect spheres are used, it is reasonable to account for actual irregularities of fragments formed during the fragmentation phase to set the value of the coefficient of restitution. Since

344   Asteroids IV the values of these coefficients are poorly constrained, we usually arbitrarily set them equal to 0.5, meaning, for example, the rebound speed is set to half the impact speed. More recently, Richardson et al. (2009) enhanced the collision handling in pkdgrav to preserve shape and spin information of reaccumulated bodies in high-resolution simulations of asteroid family formation. Instead of merging, fragments are able to stick on contact and optionally bounce or subsequently detach, depending on user-selectable parameters that include for the first time several prescriptions for variable material strength/cohesion. As a result, the reaccumulated fragments can take a wide range of shapes and spin states, which can be compared with those observed. This comes with a cost in terms of computation time as several weeks to months are needed for one simulation using a few tens of current processors. This is the reason why this approach has so far only been used for particular cases, such as modeling the formation of the asteroid Itokawa (Michel and Richardson, 2013), and not systematically for familyformation investigations. And finally, we must note that the Soft-Sphere Discrete Element Method (SSDEM) has been introduced in pkdgrav (Schwartz et al., 2012; chapter by Murdoch et al. in this volume), which accounts more realistically for the contact forces between colliding/reaccumulating particles. This method should eventually replace the one developed by Richardson et al. (2009) to investigate the shape of reaccumulated fragments as it avoids arbitrary particle sticking and rather lets the reaccumulated particles evolve naturally toward the resulting equilibrium shape of the aggregate. However, solving for all contact forces between particles over the whole timescale of the gravitational phase, and covering a large enough parameter space (accounting for the uncertainty on the various friction coefficients), remains a computational challenge. Nevertheless, some collisional studies started using the SSDEM implementation in pkdgrav focusing on low-speed impact events. In effect, no fragmentation code was used for the impact phase, which is needed for impacts during which the sound speed of the material is reached. Thus, Ballouz et al. (2014, 2015) used pkdgrav and SSDEM to simulate low-speed impacts between rotating aggregates and investigate the influence of the initial rotation of colliding bodies on the impact outcome and the sensitivity of some friction parameters. The number of particles was small enough (104 at most) that simulations could be performed within a reasonable computation time. In the case of a family formation, the outcome of hydrocode simulations consists in several hundred thousands to millions of particles. Feeding them into the SSDEM version of pkdgrav requires another level of computer performance, although tests are underway. 3. MODELING THE FAMILY PARENT BODIES Different possible internal structures have been considered for the family parent bodies. Monolithic parent bodies composed of one material type with or without microporosity (meaning micropores in the solid rock; for a definition of

microporosity, see the chapter by Jutzi et al. in this volume) have been considered, as well as pre-shattered or rubble-pile parent bodies, with or without microporosity in the solid components. The assumed pre-shattered state could be seen as a natural consequence of the collisional evolution of mainbelt asteroids. Indeed, several studies (see, e.g., Asphaug et al., 2002; Davis et al., 2002; Richardson et al., 2002) have indicated that for any asteroid, collisions at high impact energies leading to a disruption occur with a smaller frequency than collisions at lower impact energies leading to shattering effects only. Thus, in general, a typical asteroid gets battered over time until a major collision eventually disrupts it into smaller dispersed pieces. Consequently, since the formation of an asteroid family corresponds to the ultimate disruptive event of a large object, the internal structure of this body before its disruption may be shattered by all the smaller collisional events that it has suffered over its lifetime in the belt, as suggested by Housen (2009) based on laboratory experiments and extrapolations using scaling laws. This would result in the presence of internal macroscopic damaged zones and/or voids. To model a pre-shattered target, Michel et al. (2003, 2004) devised an algorithm that distributes a given number of internal fragments of arbitrary shape and size within the volume of the parent body. The reason the internal fragments are given arbitrary shapes is that a network of fractures inside a parent body resulting from many uncorrelated small impacts is unlikely to yield spherical internal fragments whose sizes follow a well-defined power law. Then, void spaces are created by randomly removing a given number of particles from the fractured set. Since there are various ways to define a pre-shattered internal structure, Michel et al. (2004) also built a model of a pre-shattered parent body in which large fragments are preferentially distributed near the center and smaller fragments are generated close to the surface. Another model, closer to the definition of a rubble pile, was also built by Michel et al. (2003). In that case, spherical components whose sizes followed a specified power law distribution were distributed at random inside the parent body. Particles not belonging to one of these spherical components were removed to create void space and particles at the interface of two or more spherical components were assigned to fractures. Some simulations were performed using those two additional models and the collisional outcomes did not show any major qualitative difference compared to those obtained from the first pre-shattered model. Benavidez et al. (2012) constructed arbitrary rubble-pile targets by filling the interior of a 100-km-diameter spherical shell with an uneven distribution of solid basalt spheres having diameters between 8 km and 20 km. However, simulations performed so far using such rubble-pile parent bodies used a version of a SPH hydrocode with a strength model that did not allow the proper modeling of friction between the individual components of the rubble pile. As found by Jutzi (2015), the bodies in this case show a fluid-like behavior and are very (somewhat unrealistically) weak. Therefore, in the following, we will only consider the results obtained for

Michel et al.:  Collisional Formation and Modeling of Asteroid Families   345

monolithic and pre-shattered bodies (as defined by Michel et al., 2003, 2004) either with or without microporosity. 4. REPRODUCING WELL-KNOWN FAMILIES For the first time, Michel et al. (2001) simulated entirely and successfully the formation of asteroid families from monolithic basalt-like parent bodies in two extreme regimes of impact energy leading to either a small or a large mass ratio of the largest remnant to the parent body Mlr /M pb. Two well-identified families were used for comparison with simulations: The Eunomia family, with a 284-km-diameter parent body and Mlr /M pb  ≈ 0.67, was used to represent the barely disruptive regime, whereas the Koronis family, with a 119-km-diameter parent body and Mlr/Mpb  ≈ 0.04, represented the highly catastrophic one. Both families are of the S taxonomic type, for which ordinary chondrites are the best meteorite analog, but basalt material is typically used as an analog material in collisional studies. In these simulations, the collisional process was carried out to late times (typically several days), during which the gravitational interactions between the fragments could eventually lead to the formation of self-gravitating aggregates (as a representation of rubble piles) far from the largest remnant. These first simulations assumed perfect sticking of reaccumulated fragments, regardless of relative speed and mass. This treatment was improved by Michel et al. (2002), allowing for the dissipation of kinetic energy in such collisions and applying an energy-based merging criterion, as described previously. This improved treatment did not change the conclusion obtained with the more simplistic method because typical relative speeds between ejected fragments are most often below their mutual escape speed. Therefore, this new set of simulations confirmed the idea that the reaccumulation process is at the origin of large family members. Durda et al. (2007) and Benavidez et al. (2012) made a systematic study of collisional disruption of monolithic and rubble-pile basalt-like 100-km-diameter parent bodies, assuming perfect sticking during reaccumulation, over a large range of impact conditions, and then rescaled their results to compare with real families, showing again that the reaccumulation process is necessary to find any good solution. However, a caution about extending results from the disruption of 100-kmdiameter parent bodies to observed families that originated from parent bodies very different in size from 100 km is in order and was acknowledged by Durda et al. (2007). 4.1. The Size Distribution of Family Members The role of geometric constraints accounting for the finite volume of the parent body in the production of family members was investigated by Tanga et al. (1999) and Campo Bagatin and Petit (2001). By filling the parent body with spherical (Tanga et al., 1999) or irregular (Campo Bagatin and Petit, 2001) pieces, starting from the largest member, they were able to reproduce the size distribution of some asteroid families to an encouraging level of agreement.

However, these models do not incorporate any physics, nor do they take into account fragment reaccumulation, and therefore they do not provide any explanation for how family members are formed nor any prediction for their internal properties. Moreover, ejection velocities are not addressed by this approach. The first full numerical simulations of catastrophic disruption and gravitational reaccumulation by Michel et al. (2001) assumed a monolithic structure of the parent body represented by a sphere with material properties of basalt (no internal porosity was considered). These simulations already reproduced qualitatively the main properties of real family member size distributions. However, when looking into more quantitative details, it was found that the cumulative size distribution of simulated fragments was characterized systematically by a lack of intermediate-sized bodies and a very steep slope for the smaller ones (see an example in Fig. 1). Such characteristics are not always observed in the size distributions of real family members. In fact, for some families, the size distribution looks rather continuous. In their systematic study, Durda et al. (2007), using the same internal structures (monolithic, basalt) but considering 100-km-diameter parent bodies only, found a larger variety of size distributions in terms of power-law slopes and discontinuities, depending on the considered impact conditions. Nevertheless, it is also known that the outcome of a collision is influenced by the initial internal structure of the parent body and that, depending on the initial structure, the fragment size distribution may be more or less continuous. In order to check this, Michel et al. (2003, 2004) modeled parent bodies with an internal structure composed of different zones of voids and fractures, as if they had first been shattered during their collisional history before undergoing a major event leading to their disruption, as explained in section 3. The simulations of the Eunomia and Koronis family formations were redone using pre-shattered parent bodies (Michel et al., 2004), and the results were compared with those obtained using monolithic parent bodies. The best agreement was actually found with pre-shattered parent bodies. In particular, in the case of the Koronis family, an interesting result was obtained from these simulations, which may have important implications concerning the real family history. The size distribution obtained from the disruption of a pre-shattered parent body contains four largest fragments of approximately the same size, as can be seen in Fig. 1. This peculiar characteristic is shared by the real family, and has been a source of debate as it was assumed that a single collisional event cannot produce such a property (see Michel et al., 2004, for a discussion). Moreover, the simulation using a monolithic parent body did not result in such a distribution. It was then demonstrated numerically for the first time, by using a pre-shattered parent body, that these fragments can actually be produced by the original event, and therefore no subsequent mechanism needs to be invoked to form them, which would otherwise require a revision of the entire family history (Marzari et al., 1995). According to these results, which show that even old families

346   Asteroids IV Koronis Family: Cumulative Size Distribution 106

105

106 Actual members

Actual members

Monolithic

Monolithic

Pre-shattered

105

104

Number > D

Number > D

104

103

103

102

102

101

101

100 100

Pre-shattered

101

102

D (km)

100 100

101

102

D (km)

Fig. 1. Cumulative diameter distributions in log-log plots for the fragments of the simulated Koronis families. The plot on the left was obtained with a projectile colliding head-on, whereas an impact with an angle of incidence q equal to 45° gave rise to that on the right. Different symbols are used to distinguish between parent-body models. The plots also show the estimated sizes of the actual members down to the completeness limit (Tanga et al., 1999). Note that the simulations using a preshattered target reproduce the four nearly identical largest members.

may well have originated from pre-shattered parent bodies, it was concluded that most large objects in the present-day asteroid belt may well be pre-shattered or self-gravitating aggregates/rubble piles. Constraints provided by the measured size distribution of family members can eliminate formation scenarios in numerical simulations. An interesting example is the Karin cluster, a small asteroid family identified by Nesvorný et al. (2002) that formed ~5.8 m.y. ago in the outer main belt. The estimated size distribution for this family, when first identified, was fairly smooth and continuous over all sizes. In particular, there was no big gap between the size of the largest member of the family, (832) Karin, and that of the second-largest member, (4507) 1990 FV. Numerical simulations by Michel et al. (2003) indicated that the best match to the continuous size distribution was provided by the breakup of a pre-shattered or rubble-pile parent body. Simulations starting from a monolithic parent body, on the other hand, produced size distributions showing a large gap between the sizes of the largest and next-largest fragments. The finding that the parent body of the Karin cluster needed to be a rubble pile was actually consistent with its history. Specifically, the parent asteroid of the Karin cluster is thought to have been produced by an early disruptive collision that created the much larger Koronis family some 2–3 G.y. ago. According

to the results of Koronis family-formation simulations, the parent asteroid of the Karin cluster should have been formed as a rubble pile from Koronis family debris. However, Nesvorný et al. (2006) later revised the definition of the Karin cluster. In particular, they found that the original second-largest identified member of the family, (4507) 1990 FV, is in fact a background asteroid with no relation whatsoever to the recent breakup at the origin of the Karin cluster. Once this body is removed from the cluster membership, a large gap opens between the size of the largest family member and smaller members, a distribution that is now best reproduced in simulation by starting with a monolithic parent body. This change in implication for the internal structure of the parent body shows the importance of having a reliable estimate of the actual size distribution of family members. However, in the case of the Karin cluster, this change is problematic because the parent body of the Karin cluster is expected to be a rubble pile, if it is an original fragment of the Koronis-forming event. A solution proposed by Nesvorný et al. (2006) is that the Karin cluster parent body was really formed by reaccumulation of smaller fragments during the Koronis family formation, as found in numerical simulations, but then was somehow consolidated into a more coherent body by various possible processes (lithification of regolith filling the interior, etc.). Another pos-

Michel et al.:  Collisional Formation and Modeling of Asteroid Families   347

sibility is that in simulations, we are missing cases in which large intact fragments are created, so that the Karin cluster parent body could really have been a monolithic body. In fact, this systematic absence of large intact fragments in asteroid disruption simulations is often mentioned as a potential issue when discussing, for example, the internal structure of Eros, imaged by the Near Earth Asteroid Rendezvous (NEAR) Shoemaker spacecraft (see section 5.1). A model of fragmentation adapted for microporous bodies (for a definition of microporosity, see the chapter by Jutzi et al. in this volume) has recently been implemented into an SPH hydrocode and tested against experiments on pumice targets (Jutzi et al., 2008, 2009). It then became possible to simulate the formation of asteroid families from a microporous parent body. A microporous structure is assumed to be appropriate for parent bodies of dark taxonomic type or primitive asteroid families. In effect, several pieces of evidence point to the presence of a high degree of porosity in asteroids belonging to the C-complex, such as the low bulk density (≈1.3 g cm–3) estimated for some of them, for instance, the asteroid (253) Mathilde encountered by the NEAR Shoemaker spacecraft (Yeomans et al., 1997), and as inferred from meteorite analysis (Britt et al., 2006). This model adapted for microporous bodies was used to reproduce the formation of the Veritas family, which is classified as a dark-type family whose members have spectral characteristics of low-albedo, primitive bodies, from C to D taxonomic types (Di Martino et al., 1997). This family is located in the outer main belt and is named after its apparent largest constituent, the asteroid (490) Veritas. The family age was estimated by two independent studies to be quite young, around 8 m.y. (Nesvorný et al., 2003; Tsiganis et al., 2007). Therefore, current properties of the family may retain signatures of the catastrophic disruption event that formed it. Michel et al. (2011) investigated the formation of the Veritas family by numerical simulations of catastrophic disruption of a 140-km-diameter parent body, which was considered to be the size of the original family parent body, made of either porous or nonporous material. Pumice material properties were used for the porous body, while basalt material properties were used for the nonporous body. Not one of these simulations was able to produce satisfactorily the estimated size distribution of real family members. Previous studies devoted to either the dynamics or the spectral properties of the Veritas family treated (490) Veritas as a special object that may be disconnected from the family. Simulations of the Veritas family formation were then performed representing the family with all members except Veritas itself. For that case, the parent body was smaller (112 km in diameter), and a remarkable match was found between the simulation outcome, using a porous parent body, and the real family. Both the size distribution and the velocity dispersion of the real reduced family were reproduced, while the disruption of a nonporous parent body did not reproduce the observed properties very well (see Fig. 2). This finding was consistent with the C spectral type of family members, which suggests that the parent body was porous and showed the importance

of modeling the effect of porosity in the fragmentation process. It was then concluded that it is very likely that the asteroid (490) Veritas and probably several other small members do not belong to the family as originally defined, and that the definition of this family should be revised. This example shows how numerical modeling can better constrain the definition of (or the belonging to) an asteroid family, provided that (1) the fragmentation model used to simulate its formation is consistent with the possible material properties of the parent body, and (2) the family is young enough that a direct comparison with the modeling is possible. 4.2. The Ejection Velocity Distribution of Family Members In addition to fragment sizes, numerical simulations also provide the ejection velocities. In general, impact simulations find that smaller fragments tend to have greater ejection speeds than larger ones. However, there is still a wide spread of values for fragments of a given mass, which makes it difficult to define a power-law relationship between fragment masses and speeds, such as the ones often used in collisional evolution models (see, e.g., Davis et al., 2002). Figure 3 shows an example of this relation for a simulation reproducing the Eunomia family as a result of the disruption of a monolithic (basalt-like) parent body impacted at an impact angle of 45°. In the case of real asteroid families, however, the dispersion of their members is characterized through their orbital proper elements, in particular their proper semimajor axis, eccentricity, and inclination. These elements have long been assumed to be essentially constants of motion that remain practically unchanged over astronomically long timescales (e.g., Milani and Knezević, 1994), although some perturbations have been found to be capable of modifying them, as we will explain below. Thus, we do not have direct access to the ejection velocities of family members. Fortunately, ejection velocities can be converted into a dispersion in orbital elements through Gauss’ equations (Zappalà et al., 1996), provided that both the true anomaly and the argument of perihelion of the family parent body at the impact instant are known or assumed. For a given family, the estimated values of the barycenter semimajor axis, eccentricity, and inclination can be used with the Gauss formulae up to first order in eccentricity to compute for each member the distance of its orbital elements da, de, and dI from the barycenter of the family 2  da [(1 + e b cos f 0 )VT + e b sin f 0 VR ] a = b na b 1 − e 2b    1 − e b2  e b + 2 cos f 0 + e b cos 2 f 0  VT + sin f 0 VR    de = 1 + e b cos f 0 na b     2 1 − e b cos(w + f 0 )  VW  dI = na b 1 + e b cos f 0 



(1)

348   Asteroids IV Veritas Family: Cumulative Size Distribution 105

Veritas non-porous PB without Veritas, t = 11.6 d

105

Veritas real members Veritas (porous)

104

104

103

103

Number > D

Number > D

Veritas real members Veritas (non-porous)

102

101

100 100

Veritas porous PB without Veritas, t = 11.6 d

102

101

101

102

D (km)

100 100

101

102

D (km)

Fig. 2. Cumulative size distributions of fragments from the simulations of the disruption of a Veritas monolithic parent body, either nonporous (left) or porous (right). The impact angle is 0° (head-on) and the impact speed is 5 km s–1. The distribution of the real family is also shown for comparison. In this case, the family consists of all members except Veritas itself, which reduces the size of the parent body to 112 km. The simulated time is about 11.6 d after the impact.

where VT, VR, and VW are the components of the ejection velocity in the along-track, radial, and out-of-plane directions, respectively, n is the mean motion, f0 is the true anomaly of the parent body at the instant of the breakup, and w is its argument of perihelion. Since these last two angles are not known, their values must be assumed. Zappalà et al. (1996) showed that the most sensitive angle is f0. Assuming different values of this angle changes the shape of the cluster containing the family members in orbital element space. In other words, it defines whether the breakup generates a family that is spread in semimajor axis, in eccentricity, or in inclination. Thanks to this conversion, it is thus possible to assess the realism of a numerical simulation of a family formation by comparing the dispersion of family members and simulated fragments in the same space. Unfortunately, other mechanisms exist that, depending on the age of the considered family, can obscure the original dispersion of family members. In fact, once a family is created, its members are subjected to various perturbations. In particular, high-order secular resonances, mean-motion resonances even involving multiple planets (Morbidelli and Nesvorný, 1999), and the Yarkovsky thermal effect (Farinella and Vokrouhlický, 1999) have been shown to be capable of altering the proper elements. Therefore, while proper elements have been assumed conventionally to retain the memory of the disruption

outcome conditions, these later studies demonstrated that this is not necessarily true, even for the proper semimajor axis in the case when the asteroid is small enough that Yarkovsky drift is effective (see Bottke et al., 2002; chapter by Vokrouhlický et al. in this volume). Depending on how old the family is, the current proper elements of family members cannot be interpreted as reflecting their starting conditions; rather, they must be seen as a result of such secular processes acting over time, whose effects are to cause a slow diffusion of family members in orbital-element space, starting from a smaller dispersion. The Koronis family is a good example showing these effects. The current distribution of Koronis family members in proper-element space is quite spread and its shape suggests that it has been subjected to the Yarkovsky effect as well as to the effects of nearby secular resonances and mean-motion resonances. Bottke et al. (2001) computed the dynamical evolutions of 210 simulated Koronis family members under the influence of the Yarkovsky effect and dynamical diffusion due to several resonances (namely, the 5:2 and 7:3 mean-motion resonances with Jupiter, a secular resonance that involves the precession rate of the small body’s longitude of perihelion g and the fundamental frequencies of Jupiter g5 and Saturn g6). The test family members were started with a dispersion that is consistent with the ones obtained from impact simulations of Koronis

Michel et al.:  Collisional Formation and Modeling of Asteroid Families   349

ibility to family-formation simulations that reproduce both the size distribution and velocity dispersion of actual members.

Eunomia (Monolithic) 1.00

Projectile: R = 38 km, θ = 45°

Diameter Ratio D/Dpb

5. IMPLICATIONS 5.1. Internal Structure of Asteroids

0.10

0.01

0.10

1.00

Ejection Speed υ (km –1) Fig. 3. Fragment diameter D (normalized to that of the parent body Dpb) vs. ejection speed in a log-log plot obtained from a monolithic Eunomia parent body simulation using a projectile impacting at an angle of incidence q = 45°. Only fragments with size above the resolution limit (i.e., those that underwent at least one reaccumulation event) are shown here. From Michel et al. (2004).

family formation. They were integrated over 700 m.y., which is still shorter than the estimated age of the family (>1 G.y.). However, this evolution showed that the current shape of the family cluster in proper-element space does not represent the original shape from the collisional event but is well explained by its subsequent evolution. Fortunately, if a family is young enough, its dispersion can still be close to the original one resulting from the parent body breakup, and in that case, the comparison between numerical simulations of family formation and actual family dispersion is straightforward. On the other hand, the degree of spreading observed now, together with the knowledge of the degree of dispersion resulting directly from the breakup by numerical simulations, can better constrain the age of the family, once the efficiency of the diffusion processes is well assessed. Nesvorný et al. (2002, 2003) identified several asteroid families with formation ages smaller than 10 m.y. These families represent nearly the direct outcome of disruptive asteroid collisions, because the observed remnants of such recent breakups have apparently suffered limited dynamical and collisional erosion (Bottke et al., 2005). As already described in the previous section, the Karin cluster and the Veritas family belong to this group of young families. Figure  4 shows an example in which the dispersion of the actual Veritas family is compared with that of fragments from an impact simulation of Veritas family formation. The simulated dispersion matches the shape of the ellipses representing the real dispersion. This result is consistent with the expectation that the orbital extent of the family is not produced by post-diffusion processes, which gives some cred-

According to numerical simulations of family formation, all fragments produced by the catastrophic disruption of a large asteroid (typically larger than 1 km in diameter, e.g., in the gravity regime) consist of self-gravitating aggregates, except the smallest ones. If this is correct, then most asteroids that are at least second generation should be rubble piles. We note that Campo Bagatin et al. (2001) ran a number of simulations of main-belt collisional evolution to assess the size range where reaccumulated bodies should be expected to be abundant in the main asteroid belt. They found that this diameter range goes from about 10 to 100 km, but may extend to smaller or larger bodies, depending on the prevailing collisional response parameters, such as the strength of the material, the strength scaling law, the fraction of kinetic energy of the impact transferred to the fragments, and the reaccumulation model. The collisional lifetime of bodies larger than a few tens to hundreds of kilometers in diameter is longer than the age of the solar system, suggesting that most bodies in that size range are likely to be primordial, while smaller bodies are probably collisional fragments (see, e.g., Bottke et al., 2005, and the chapter by Bottke et al. in this volume). The exact size above which a body is more likely to be primordial is somewhat model-dependent. Binzel et al. (1989), from a study of light curves, suggested that this transition occurs at a diameter of ≈125 km. However, as this is a statistical measure, some smaller asteroids may still be primordial and some larger ones may have broken up in the past. In fact, due to the variability in possible interior starting compositions, and variations in the chaotic dynamics of accumulation, the size above which a body is more likely to be primordial is dependent on the specific formation scenario, as well as the compositions, masses, and velocities involved. Thus, some asteroids smaller than 100 km may still be primordial, and some larger ones may have broken up catastrophically in the past. This is especially true if one goes back to the very earliest formation, in the first few million years, when considering hit-and-run collisions (see the chapter by Asphaug et al. in this volume). These may have completely disrupted some of the largest asteroids, as projectiles, when they experienced grazing collisions into larger target embryos. This makes the internal structure of middle-sized asteroids one of the most important aspects of these bodies that can be determined by future space missions and observations, allowing us to test our interpretations based on theoretical collisional studies (see also the chapter by Scheeres et al. in this volume). During the past 4 b.y., catastrophic disruption has been the result of hypervelocity collisions. Bottke et al. (2005) estimate that about 20 asteroid families have formed from the breakup of parent bodies larger than 100 km diameter over

350   Asteroids IV Veritas Family, D > 8 km, ω + f = 180°W, f = 30° Projectile: υimpact = 5 km s–1; Angle of Incidence = 0°; α = 3 AU; i = 0° 0.165

0.065

0.164

0.063

0.163

e

i (rad)

0.061 0.162

0.059 0.161 0.057 0.160

0.055 3.15

3.16

3.17

3.18

3.19

a (AU)

0.159 3.15

3.16

3.17

3.18

3.19

a (AU)

Fig. 4. Distribution of fragments larger than 8 km from a simulation of disruption of a porous monolithic Veritas family parent body excluding Veritas itself as a result of a head-on impact of a projectile at 5 km s–1 with orbital semimajor axis a of 3 AU and inclination I of 0°. The outcome is represented in the ae plane (left) and a-I plane (right). The superimposed ellipse is an equivelocity curve for speed cutoff of 40 m s–1, parent body true anomaly f = 30° and argument of perihelion w = 150°. This curve was defined by Tsiganis et al. (2007) as that closest to representing the dispersion of the real Veritas family in orbital element space. From Michel et al. (2011).

the last 4 b.y. But several hundred asteroids currently exist in the 100-km size range, making it likely that most of these are original bodies. In this regard, asteroid (21) Lutetia, approximately 90 km in diameter, is a scientifically important object of which we have obtained a quick glimpse during Rosetta’s 2010 flyby (see the chapter by Barucci et al. in this volume). The relatively high measured mass (bulk density 3.1 g cm–3) led Weiss et al. (2012) to interpret Lutetia as being a partly differentiated, impact-shattered, but largely intact parent body, covered in a predominately chondritic outer component. Other interpretations are of course possible. Assuming that the transition between primordial and second-generation bodies occurs at diameters ~100 km, what about (433) Eros, whose diameter is much below this threshold and therefore should be a fragment of a larger body? There is still a debate about the internal structure of this asteroid, as the images of its surface can be explained by either a fractured (but solid/strength-dominated) structure or a rubble pile (Asphaug, 2009; chapter by Marchi et al. in this volume). However, if Eros is not a rubble pile, its formation as a fragment of a large asteroid would need a solution that is not yet found in numerical simulations of catastrophic disruptions.

Another point of view could thus be that it is a monolithic body that has been shattered in place (e.g., Housen, 2009; Buczkowski et al., 2008). In this case, major impacts fracture it in place, introducing only modest increases to its porosity. This requires a very low strain rate of expansion, e.g., a small elastic strain at fracture, which may be consistent with size-dependent relationships for brittle failure. So this is probably feasible to form a shattered monolith when a single monolithic body is impacted, but with relatively low energy compared to disruption. But then one must ask, where did the single monolithic body come from to begin with, and why has it not been subsequently fragmented and jumbled by slightly more energetic collisions? The alternative is that the grooves have nothing to do with brittle failure, but are instead planes of granular failure. Thus, so far, the formation of a dispersed cloud of sizable fragments (larger than a few hundreds of meters) systematically requires that the parent body is first fragmented into small pieces, down to the resolution limit of simulations (a few hundreds of meters), and then that gravitational reaccumulation takes place to form larger final remnants. This is probably what happened for (25143) Itokawa, which appears

Michel et al.:  Collisional Formation and Modeling of Asteroid Families   351

to be a rubble pile (Fujiwara et al., 2006). In fact, if the major blocks on Itokawa were intact monolithic, then they would give us a kind of lower size range of intact fragments produced from large impacts. Using the version of pkdgrav with enhanced collision handling to preserve shape and spin information of reaccumulated bodies (Richardson et al., 2009), Michel and Richardson (2013) showed that the process of catastrophic disruption and gravitational reaccumulation can form fragments with shapes similar to that of Itokawa, and can explain the presence of a large amount of boulders on the surface, as observed. Figure 5 shows the outcome of such a simulation. We note that in this kind of modeling, the shapes of the aggregates formed by the reaccumulation process are parameter dependent. In particular, if we change the assumed strength of the aggregates or the bouncing coefficients (see Michel and Richardson, 2013, for a definition of these parameters), the final shape may be different. For instance, a preliminary simulation using a lower strength leads to a final largest aggregate that is more spherical. Because of the lower assumed strength, reaccumulating aggregates break more easily as a result of tidal and rotational forces, and therefore the object produced by this reaccumulation has difficulty keeping its irregular shape and instead becomes more and more rounded. Further studies are required to determine whether this type of outcome has some interesting implications, and to assess the actual sensitivity of the final shapes of reaccumulated objects to the parameters. It may be that we can provide some rough constraints on some of the mechanical properties of asteroids whose shapes are known, based on the parameters required to form them using this model. An extensive set of simulations that will require long runs with current computer power is planned for this purpose. The production of rubble goes up with size, because it gets harder and harder (with increasing gravity) to liberate mass to escape speed than to beat it into small fragments that eventually can reaccumulate. The implication is that if Itokawa is a rubble pile, then Eros should be even more so. Whether this is in fact reality awaits direct seismic or internal-structure exploration (e.g., by radar tomography)

of objects Eros-sized and larger (see also the chapter by Scheeres et al. in this volume). 5.2. Compositions Originally families were only identified on the basis of dynamical considerations. Then, once spectral observations became available, it was found that the vast majority of those families identified by dynamics showed remarkable homogeneous spectral properties (see the chapter by Masiero et al. in this volume). So, homogeneity in terms of spectral properties seems to be the norm. However, when an object satisfies the distance criterion to be associated with a family, it is often considered as an interloper when its spectral properties do not match. Therefore, the identification of family membership also relies on homogeneous spectral properties and whether the homogeneity in spectral properties is a reality, or an assumption is not yet clear. Such homogeneity can only be explained if the family parent body was homogenous itself, so that when fragments reaccumulate during the reaccumulation phase, there’s no mixture of different materials taking place. Alternatively, it may also be that the reaccumulation process does not mix different materials that could be initially present in the parent body or mixes it so well that the outcome still looks homogeneous. Otherwise, if the parent body was heterogeneous in composition and if some mixtures happened, then the resulting family would show a variety of spectral properties within its members. In fact, if reaccumulation is a random process, we expect the particles of a given large fragment to originate from uncorrelated regions within the parent body. In that case, if the parent body was heterogeneous in composition, then the composition of reaccumulated fragments could be a mixture of various material. Conversely, if the initial velocity field imposed by the fragmentation process determines the reaccumulation phase, the particles belonging to the same fragment should originate from well-defined areas inside the parent body. In addition, the position and extent of these regions would provide indications about the mixing occurring as a result of the reaccumulation process.

Fig. 5. Snapshots of the reaccumulation process following the disruption of a 25-km-diameter asteroid. From left to right: first instant at the end of the fragmentation phase when all fragments (white dots) are about 200  m in diameter; the ejection of those fragments a few seconds later; the first reaccumulations that occur because of the slow relative speed between some fragments, showing the formation of a few aggregates represented by different gray levels; the formation of the largest fragment of this disruption by reaccumulation of several aggregates into a single body; and the final largest fragment shown at two different instants: The boulders on its surface and its overall shape are reminiscent of Itokawa. Credit: Michel and Richardson, A&A, 554, L1, 2013, reproduced with permission ©ESO.

352   Asteroids IV Michel et al. (2004) traced back, at least for some of the largest fragments, the original positions within the parent body of the particles that end up forming the aggregates during some family formations. As an example, they traced the particles belonging to the three largest fragments of their simulation of the Koronis family formation back to their original positions inside the parent body. Recall that the Koronis family was formed in a highly catastrophic event, as its largest member is estimated to contain only 4% of the parent body’s mass. In such an event, the reaccumulation process lasts up to several days, much longer than for a barely disruptive event, and gives rise to many gravitational encounters. Therefore, this kind of event may well lose the memory of the initial velocity field. Nevertheless, it was found that particles forming a large reaccumulated fragment originate from well-clustered regions within the parent body. This indicates that reaccumulation is definitely not a random process. Interestingly, the position of the original region depends greatly on the internal properties of the parent body. The largest remnant of the pre-shattered model of the Koronis parent body involves particles that were initially located between the core and the region antipodal to the impact point. Conversely, in the monolithic parent body, those particles were initially much more clustered in the core region, with no particles originating from the antipode. This difference also holds true for the next-largest fragments. Nevertheless, these results indicate that the velocity field arising from the fragmentation phase has a major influence on the reaccumulation process. Particles that eventually belong to a given fragment originate from the same region inside the parent body. However, this location (as well as its extent, which determines the degree of mixing of the fragments) depends also on the parent body’s internal properties in a complex way. Recently Michel et al. (2015) looked at the cases of parent bodies with internal structures that could represent large asteroids formed early in solar system history. Some results are shown in the chapter by Jutzi et al. in this volume. They confirm that most particles in each reaccumulated fragment are sampled from the same original region within the parent body. However, they also found that the extent of the original region varies considerably depending on the internal structure of the parent body and seems to shrink with its solidity. As a conclusion, the spectral homogeneity within a family may represent the material homogeneity of the initial parent body. It may also be due to the way reaccumulation takes place. But in that case, and if the parent body was heterogeneous, although each family member would still be homogeneous, we may expect different spectral properties from one member to another, depending on which original region of the parent body it samples. The fact that most families do not show strong spectral variations between family members, at least in the data from groundbased observations — except if this is imposed by the membership criterion — is consistent with the theory of homogeneity of the family parent body.

6. CONCLUSIONS Our understanding of the collisional physics and our account for gravity in large asteroid disruptions have allowed numerical simulations to successfully reproduce the formation of asteroid families, in agreement with the idea that these families originate from the disruption of a large parent body. Simulation results indicate that asteroid family members are not just the product of the fragmentation of the parent body, leading to intact fragments, but rather the outcome of the subsequent gravitational phase of the event, which allows some of the intact fragments to reaccumulate and form gravitational aggregates, or rubble piles. For all considered cases so far (family parent bodies of diameter typically larger than tens of kilometers), this outcome is systematic for fragments larger than a few hundred meters. Thus, according to simulations, since it is believed that most bodies smaller than 100 km in diameter originate from the disruption of a larger body, then they should be rubble piles or heavily shattered bodies, which is consistent with the low measured bulk densities for some of them and the finding by Campo Bagatin et al. (2001) based on main-belt collisional evolution modeling. Therefore, exploring the origin of asteroid families unexpectedly led to a result that has great implications for the entire asteroid population and its history. Moreover, it was also found that the outcome of a disruption is very sensitive to the original internal structure of the parent body, in particular the kind and amount of internal porosity. Thus, the comparison between simulation outcomes for various kinds of parent-body structures (monolithic, pre-shattered, microporous, rubble pile) and real family properties can help to constrain the internal properties of the parent body of the considered families and in the family identification itself. For instance, it was found that the Veritas family is very well reproduced if the asteroid Veritas itself is excluded from its family, which was already recognized as a possibility before disruption simulations were performed to model the formation of this family. Thanks to the improved sensitivity of observations, allowing us to reach smaller asteroid sizes, and to the tools developed to better define asteroid families, new asteroid families keep being identified, especially small and young ones. The latter, which have not yet been affected by dynamical diffusion or post-collisional processes, are a good test for numerical simulations, which must be able to reproduce them as they are. Such an exercise, which has already been done successfully for some young families (e.g., Veritas, Karin), must keep being performed as a check for our numerical models. In particular, new fragmentation models are continuously being developed, accounting for various possible strength models and fragmentation modes. Once they are validated at small laboratory scales by comparison with impact experiments, they can be used at large scale (with an associated N-body code) to reproduce young family properties, allowing us to increase the range of internal

Michel et al.:  Collisional Formation and Modeling of Asteroid Families   353

structures and fragmentation modes that can be considered for the parent body. This modeling work, calling for different models, is crucial to better constrain the possible internal structure of family parent bodies, to refine the definition of a family, and to understand whether some families are formed from differentiated/heterogeneous parent bodies, despite their apparent (or assumed) homogeneities. Asteroid families are very important tracers of the entire asteroid belt history and as we have already seen, our understanding of them can have profound implications on determination of the physical properties of asteroids in general. More work is also required to check in which context large intact fragments can be produced in numerical simulations of large asteroid disruptions. Although there is no firm conclusion about Eros’ internal structure, the fact that it may be a shattered object only and not a rubble pile raises the issue of the formation of such large fragments in a collision. It may also be that the reaccumulation process is followed by internal processes that may consolidate boulders. Such processes would eventually transform reaccumulated fragments into a coherent body. If this were the case, then reaccumulation would not necessarily imply a rubble-pile structure. Simulations of the reaccumulation phase now include the possibility of accounting for the final possible shapes of reaccumulated fragments. This modeling needs further improvement to increase its realism, but it will be very difficult, if even possible, to achieve the level of complexity needed to model the internal processes that may consolidate boulders. Asteroid internal processes are poorly understood and depend on too many parameters and unknowns. Space missions dedicated to direct measurement of internal structures, and possibly to their response to an impact (e.g., by using a kinetic impactor), are thus crucial to improve our understanding of these important internal properties of asteroids and to check our modeling of the collisional and internal processes. Moreover, sample return missions as well as visits/flybys of members of asteroid families would also provide detailed information on their physical properties and would allow us to check whether groundbased measurements wash out some important data regarding their composition and possible variations among members. Asteroid families and the collisional process, which is at the heart of family formation and evolutionary main-belt history, rely on our efforts to combine complex models and space-/groundbased measurements. Acknowledgments. We are grateful to Clark Chapman and an anonymous reviewer for their comments that greatly helped to improve the chapter. P.M. acknowledges support from the French space agency CNES and the French national program of planetology. D.C.R. acknowledges NASA grant NNX08AM39G and NSF grant AST1009579 (and previous NASA/NSF grants). D.D.D. acknowledges support from the National Science Foundation (Planetary Astronomy Program grants AST0098484, AST0407045, and AST0708517). M.J. is supported by the Ambizione program of the Swiss National Science Foundation.

REFERENCES Arnold J. R. (1969) Asteroid families and jet streams. Astron. J., 74, 1235–1242. Asphaug E. (2009) Growth and evolution of asteroids. Annu. Rev. Earth Planet. Sci., 37, 413–448. Asphaug E., Ryan E. V., and Zuber M. T. (2002) Asteroid interiors. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 463–484. Univ. of Arizona, Tucson. Ballouz R.-L., Richardson D. C., Michel P., and Schwartz S. R. (2014) Rotation-dependent catastrophic disruption of gravitational aggregates. Astrophys. J., 789, 158. Ballouz R. L., Richardson D. C., Michel P., Schwartz S. R., and Yu Y. (2015) Numerical simulations of collisional disruption of rotating gravitational aggregates: Dependence on material properties. Planet. Space Sci., 107, 29–35. Benavidez P., Durda D. D., Enke B. L., et al. (2012) A comparison between rubble-pile and monolithic targets in impact simulations: Application to asteroid satellites and family size distributions. Icarus, 219, 57–76. Benz W. and Asphaug E. (1994) Impact simulations with fracture. I. Method and tests. Icarus, 107, 98–116. Benz W. and Asphaug E. (1995) Simulations of brittle solids using smooth particle hydrodynamics. Comp. Phys. Commun., 87, 253–265. Benz W. and Asphaug E. (1999) Catastrophic disruptions revisited. Icarus, 142, 5–20. Binzel R. P., Farinella P., Zappalà V, and Cellino A. (1989) Asteroid rotation rates-distributions and statistics. In Asteroids II (R. P. Binzel et al., eds.), pp. 416–441. Univ. of Arizona, Tucson. Bottke W. F., Vokrouhlický D., Borz M., Nesvorný D., and Morbidelli A. (2001) Dynamical spreading of asteroid families via the Yarkovsky effect. Science, 294, 1693–1696. Bottke W. F., Vokrouhlický D., Rubincam D. P., and Broz M. (2002) The effect of Yarkovsky thermal forces on the dynamical evolution of asteroids and meteoroids. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 395–408. Univ. of Arizona, Tucson. BottkeW. F., Durda D. D., Nesvorný D., Jedicke R., Morbidelli A., Vokrouhlický D., and Levison H. (2005) The fossilized size distribution of the main asteroid belt. Icarus, 175, 111–140. Britt D.T., Consolmagno G. J., and Merline W. J. (2006) Small body density and porosity: New data, new insights. Lunar Planet. Sci. XXXVII, Abstract #2214. Lunar and Planetary Institute, Houston. Buczkowski D. L., Barnouin-Jha O. S., and Prockter L. M. (2008) 433 Eros lineaments: Global mapping and analysis. Icarus, 193, 39–52. Campo Bagatin A. and Petit J.-M. (2001) Effects of the geometric constraints on the size distributions of debris in asteroidal fragmentation. Icarus, 149, 210–221. Campo Bagatin A., Petit J.-M., and Farinella P. (2001) How many rubble piles are in the asteroid belt? Icarus, 149, 198–209. Chapman C. R., Davis D. R., and Greenberg R. (1982) Apollo asteroids: Relationships to main belt asteroids and meteorites. Meteoritics, 17, 193–194. Chapman C. R., Paolicchi P., Zappalà V., Binzel R. P., and Bell J. F. (1989) Asteroid families: Physical properties and evolution. In Asteroids II (R. P. Binzel et al., eds.), pp. 386–415. Univ. of Arizona, Tucson. Davis D. R., Chapman C. R., Greenberg R., Weidenschilling S. J., and Harris A. W. (1979) Collisional evolution of asteroids — Populations, rotations, and velocities. In Asteroids (T. Gehrels ed.), pp. 528–557. Univ. of Arizona, Tucson. Davis D. R., Chapman C. R., Greenberg R., and Weidenschilling S. J. (1985) Hirayama families: Chips off the old block or collections of rubble piles? Bull. Am. Astron. Soc., 14, 720. Davis D. R., Durda D. D., Marzari F., Campo Bagatin A., and GilHutton R. (2002) Collisional evolutions of small body populations. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 545–558. Univ. of Arizona, Tucson. Di Martino M., Migliorini F., Zappalà V., Manara A., and Barbieri C. (1997) Veritas asteroid family: Remarkable spectral differences inside a primitive parent body. Icarus, 127, 112–120.

354   Asteroids IV Durda D. D., Bottke W. F., Enke B. L., Merline W. J., Asphaug E., Richardson D. C., and Leinhardt Z. M. (2004) The formation of asteroid satellites in large impacts: Results from numerical simulations. Icarus, 170, 243–257. Durda D. D., Bottke W. F., Nesvorný D., Enke B. L., Merline W. J., Asphaug E., and Richardson D. C. (2007) Size frequency distributions of fragments from SPH/N-body simulations of asteroid impacts: Comparison with observed asteroid families. Icarus, 186, 498–516. Durda D. D., Movshovitz N., Richardson D. C., Asphaug E., Morgan A., Rawlings A. R., and Vest C. (2011) Experimental determination of the coefficient of restitution for meter-scale granite spheres. Icarus, 211, 849–855. Durda D. D., Richardson D. C., Asphaug E., and Movshovitz N. (2013) Size dependence of the coefficient of restitution: Small scale experiments and the effects of rotation. Lunar Planet. Sci. XLIV, Abstract #2263. Lunar and Planetary Institute, Houston. Farinella P. and Vokrouhlický D. (1999) Semimajor axis mobility of asteroidal fragments. Science, 283, 1507–1510. Farinella P., Davis D. R., and Marzari F. (1996) Asteroid families, old and young. In Completing the Inventory of the Solar System (T. W. Rettig and J. M. Hahn, eds.), pp. 45–55. ASP Conf. Ser. 107, Astronomical Society of the Pacific, San Francisco. Fujiwara A., Kawaguchi J., Yeomans D. K., et al. (2006) The rubble-pile asteroid Itokawa as observed by Hayabusa. Science, 312, 1330–1334. Hirayama K. (1918) Groups of asteroids probably of common origin. Astron. J., 31, 185–188. Housen K. (2009) Cumulative damage in strength-dominated collisions of rocky asteroids: Rubble piles and brick piles. Planet. Space Sci., 57, 142–153. Jaeger J. C. and Cook N. G. W. (1969) Fundamentals of Rock Mechanics. Chapman and Hall, London. Jutzi M. (2015) SPH calculations of asteroid disruptions: The role of pressure dependent failure models. Planet. Space Sci., 107, 3–9. Jutzi M., Benz W., and Michel P. (2008) Numerical simulations of impacts involving porous bodies. I. Implementing subresolution porosity in a 3D SPH hydrocode. Icarus, 198, 242–255. Jutzi M., Michel P., Hiraoka K., Nakamura A. M., and Benz W. (2009) Numerical simulations of impacts involving porous bodies. II. Confrontation with laboratory experiments. Icarus, 201, 802–813. Jutzi M., Michel P., Benz W., and Richardson D. C. (2010) The formation of the Baptistina family by catastrophic disruption: Porous versus non-porous parent body. Meteoritics & Planet. Sci., 44, 1877–1887. Leinhardt Z. M. and Stewart S. T. (2009) Full numerical simulations of catastrophic small body collisions. Icarus, 199, 542–559. Marzari F., Davis D., and Vanzani V. (1995) Collisional evolution of asteroid families. Icarus, 113, 168–187. McGlaun J. M., Thompson S. L., and Elrick M. G. (1990) CTH: A 3-dimensional shock-wave physics code. Intl. J. Impact Eng., 10, 351–360. Michel P. and Richardson D.C. (2013) Collision and gravitational reaccumulation: Possible formation mechanism of the asteroid Itokawa. Astron. Astrophys., 554, L1–L4. Michel P., Benz W., Tanga P., and Richardson D. C. (2001) Collisions and gravitational reaccumulation: Forming asteroid families and satellites. Science, 294, 1696–1700. Michel P., Benz W., Tanga P., and Richardson D. C. (2002) Formation of asteroid families by catastrophic disruption: Simulations with fragmentation and gravitational reaccumulation. Icarus, 160, 10–23.

Michel P., Benz W., and Richardson D. C. (2003) Fragmented parent bodies as the origin of asteroid families. Nature, 421, 608–611. Michel P., Benz W., and Richardson D. C. (2004) Disruption of preshattered parent bodies. Icarus, 168, 420–432. Michel P., Jutzi M., Richardson D. C., and Benz W. (2011) The asteroid Veritas: An intruder in a family named after it? Icarus, 211, 535–545. Michel P., Jutzi M., Richardson D. C., Goodrich C. A., Hartmann W. K., and O’Brien D. P. (2015) Selective sampling during catastrophic disruption: Mapping the location of reaccumulated fragments in the original parent body. Planet. Space Sci., 107, 24–28. Milani A. and Knezević Z. (1994) Asteroid proper elements and the dynamical structure of the asteroid belt. Icarus, 107, 219–254. Morbidelli A. and Nesvorný D. (1999) Numerous weak resonances drive asteroids toward terrestrial planets orbits. Icarus, 139, 295–308. Nesvorný D., Bottke W. F., Dones L., and Levison H. F. (2002) The recent breakup of an asteroid in the main-belt region. Nature, 417, 720–771. Nesvorný D., Bottke W. F., Levison H. F., and Dones L. (2003) Recent origin of the solar system dust bands. Astrophys. J., 591, 486–497. Nesvorný D., Enke B. L., Bottke W. F., Durda D. D., Asphaug E., and Richardson D. C. (2006) Karin cluster formation by asteroid impact. Icarus, 183, 296–311. Richardson D. C. (1994) Tree code simulations of planetary rings. Mon. Nat. R. Astron. Soc., 269, 493–511. Richardson D. C., Quinn T., Stadel J., and Lake G. (2000) Direct large-scale N-body simulations of planetesimal dynamics. Icarus, 143, 45–59. Richardson D. C., Leinhardt Z. M., Melosh H. J., Bottke W. F. Jr., and Asphaug E. (2002) Gravitational aggregates: Evidence and evolution. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 501–515. Univ. of Arizona, Tucson. Richardson D. C., Michel P., Walsh K. J., and Flynn K. W. (2009) Numerical simulations of asteroids modelled as gravitational aggregates with cohesion. Planet. Space Sci., 57, 183–192. Ryan E. V. and Melosh H. J. (1998) Impact fragmentation: From the laboratory to asteroids. Icarus, 133, 1–24. Schwartz S. R., Richardson D. C., and Michel P. (2012) An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code. Granular Matter, 14(3), 363–380, DOI: 10.1007/s10035-012-0346-z. Tanga P., Cellino A., Michel P., Zappalà V., Paolicchi P., and Dell’Oro A. (1999) On the size distribution of asteroid families: The role of geometry. Icarus, 141, 65–78. Tillotson J. H. (1962) Metallic Equations of State for Hypervelocity Impact. General Atomic Report GA-3216. Tsiganis K., Knezević Z., and Varvoglis H. (2007) Reconstructing the orbital history of the Veritas family. Icarus, 186, 484–497. Weibull W. A. (1939) A statistical theory of the strength of material (transl.). Ingvetensk. Akad. Handl., 151, 5–45. Weiss B. P., Elkins-Tanton L. T., Barucci M. A., et al. (2012) Possible evidence for partial differentiation of asteroid Lutetia from Rosetta. Planet. Space Sci., 66, 137–146. Yeomans D. K. and 12 colleagues (1997) Estimating the mass of asteroid 253 Mathilde from tracking data during the NEAR flyby. Science, 278, 2106–2109. Zappalà V., Cellino A., Dell’Oro A., Migliorini F., and Paolicchi P. (1996) Re-constructing the original ejection velocity fields of asteroid families. Icarus, 124, 156–180.

Margot J.-L., Pravec P., Taylor P., Carry B., and Jacobson S. (2015) Asteroid systems: Binaries, triples, and pairs. In Asteroids IV (P. Michel et al., eds.), pp. 355–374. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch019.

Asteroid Systems: Binaries, Triples, and Pairs Jean-Luc Margot

University of California, Los Angeles

Petr Pravec

Astronomical Institute of the Czech Republic Academy of Sciences

Patrick Taylor

Arecibo Observatory

Benoît Carry

Institut de Mécanique Céleste et de Calcul des Éphémérides

Seth Jacobson

Côte d’Azur Observatory

In the past decade, the number of known binary near-Earth asteroids has more than quadrupled and the number of known large main-belt asteroids with satellites has doubled. Half a dozen triple asteroids have been discovered, and the previously unrecognized populations of asteroid pairs and small main-belt binaries have been identified. The current observational evidence confirms that small (20 km) binaries with small satellites are most likely created during large collisions.

1. INTRODUCTION 1.1. Motivation Multiple-asteroid systems are important because they represent a sizable fraction of the asteroid population and because they enable investigations of a number of properties and processes that are often difficult to probe by other means. The binaries, triples, and pairs inform us about a great variety of asteroid attributes, including physical, mechanical, and thermal properties, composition, interior structure, formation processes, and evolutionary processes. Observations of binaries and triples provide the most powerful way of deriving reliable masses and densities for a large number of objects. The density measurements help us understand the composition and internal structure of minor planets. Binary systems offer opportunities to measure thermal and mechanical properties, which are generally poorly known. The binary and triple systems within near-Earth asteroids (NEAs), main-belt asteroids (MBAs), and transneptunian objects (TNOs) exhibit a variety of formation mechanisms

(Merline et al., 2002c; Noll et al., 2008). As such, they provide an invaluable window on accretional, collisional, tidal, and radiative processes that are critical in planet formation. The distribution and configurations of the multiple-asteroid systems also provide a rich array of constraints on their environment, their formation, and their evolutionary pathways. Observations rely primarily on groundbased telescopes and the Hubble Space Telescope (HST). For an up-to-date list of binaries and triples in the solar system, see Johnston (2014). We describe observational techniques only briefly because this material is available elsewhere (e.g., Merline et al., 2002c). A few emerging techniques will be described in more detail. Likewise, we refer the reader to other texts for an extensive history of the field (e.g., Merline et al., 2002c) and highlight only a few of the developments here. 1.2. History Early search programs for asteroid satellites were unsuccessful, returning negative or dubious results, such that the authors of the Asteroids II review chapter chose the prudent title “Do asteroids have satellites?” (Weidenschilling et al.,

355

356   Asteroids IV 1989). The chapter provides an excellent discussion of the physics of several formation mechanisms that were postulated at the time. The perspective changed with the flyby of (243) Ida by the Galileo spacecraft in 1993 and the discovery of its small satellite Dactyl (Chapman et al., 1995; Belton et al., 1995). Groundbased efforts intensified and resulted in the discovery of a satellite around (45) Eugenia by Merline et al. (1999). Several other discoveries followed in rapid succession. The relatively small sizes of the MBA satellites suggested formation in subcatastrophic or catastrophic collisions (Durda, 1996; Doressoundiram et al., 1997). The discovery of MBA satellites, coupled with analysis of terrestrial doublet craters (Bottke and Melosh, 1996a,b) and anomalous lightcurve observations (Pravec and Hahn, 1997), suggested the existence of binary asteroids in the nearEarth population as well. The unambiguous detection of five NEA binaries by radar cemented this finding and indicated that NEA satellites form by a spin-up and rotational fission process (Margot et al., 2002). Lightcurve observers reached the same conclusion independently (Pravec and Harris, 2007). Both radar and lightcurve observations revealed that, far from being rare, binary asteroids are relatively common (Pravec et al., 1999, 2006; Margot et al., 2002). By the time the Asteroids III review chapter was written, a more decisive title (“Asteroids do have satellites”) had become appropriate (Merline et al., 2002c). This review focuses on the developments that followed the publication of Asteroids III.

objects are substantially affected by the Yarkovsky-O’KeefeRadzievskii-Paddack (YORP) effect during their lifetime. For typical NEAs and MBAs, this dividing line corresponds to a diameter of about 20 km (Jacobson et al., 2014a). We define very small asteroids as those with diameters of 3 km in diameter. It is likely that ~8-km-diameter (1866) Sisyphus has a secondary based on analysis of frequency-only observations obtained on four separate dates in 1985 (S. Ostro, personal communication, 2001). Radar observations can be used to detect asteroid satellites because of the ability to resolve the components of the system both spatially (along the observer’s line of sight) and in terms of frequency (due to Doppler shifts from the rotational and orbital line-of-sight velocities), resulting in

Two- and three-component asteroids that are gravitationally bound will be referred to as binary asteroids (or binaries) and triple asteroids (or triples), respectively. (Triple is favored over the more directly analogous terms trinary and ternary because of long-established usage in astronomy.) Asteroid pairs denote asteroid components that are genetically related but not gravitationally bound. Paired binaries or paired triples are asteroid pairs where the larger asteroid is itself a binary or triple asteroid. The larger component in binaries, triples, and pairs is referred to as the primary component or primary. The smaller component in binaries is referred to as the secondary component or secondary. There has been some confusion in the literature about the meaning of the word “asynchronous.” Here, we adopt the terminology proposed by Margot (2010) and later implemented by Jacobson and Scheeres (2011b) and Fang and Margot (2012c). Binaries with an absence of spin-orbit synchronism are called asynchronous binaries. Binaries with a secondary spin period synchronized to the mutual orbit period are called synchronous binaries. Binaries with both primary and secondary spin periods synchronized to the mutual orbit period are called doubly synchronous binaries. If generalization to systems with more than one satellite is needed, we affix the terms synchronous and asynchronous to the satellites being considered. It is useful to present results for small and large asteroids. We place an approximate dividing line at the size at which

2. OBSERVATIONS Several observational techniques are available for discovering, detecting, and studying binaries, triples, and pairs, each with its strengths and weaknesses. This section describes recent results and illustrates the complementarity of the observational techniques that characterize individual asteroid systems and entire populations. 2.1. Radar Observations of Near-Earth Asteroid Systems

Margot et al.:  Asteroid Systems: Binaries, Triples, and Pairs   357

a measurable separation between the components in two dimensions. Direct detection of a satellite in frequencyonly spectra or radar images typically occurs within one observing session and often within minutes of observation. The bandwidth of the echo of a component scales directly with the diameter and rotation rate. Thus, in a frequencyonly experiment, the signal of the smaller, relatively slowly rotating satellite is condensed to a smaller bandwidth that is superimposed upon the broadband signal of the larger, often rapidly rotating, primary (Fig.  1a). Not all radar-observed binaries present this characteristic spectrum (e.g., where the secondary spins faster than the synchronous rate), but all are readily detected in radar images when the components are also resolved spatially (Fig.  1b). Because the spatial resolution achieved with radar instruments corresponds to an effective angular resolution of better than ~1 milliarcsecond (mas), there is no bias against the detection of satellites orbiting very close to the primary component. Multiple measurements of the range and frequency separations of the components over days of sky motion provide the geometric leverage required to determine the orbit of the secondary around the primary. This can be done for any orbital orientation and yields the total system mass, a property that is difficult to estimate otherwise. Other techniques involve analyzing spacecraft flyby and orbit trajectories (e.g., Yeomans et al., 1999), measuring the Yarkovsky orbital drift in conjunction with thermal properties (e.g., Chesley et al., 2014), or observing the gravitational perturbations resulting from asteroid encounters (e.g., Hilton, 2002). Most binary NEA systems observed to date have a rapidly rotating primary and a smaller secondary on the order of a few tenths the size of the primary (a secondary-to-primary mass ratio of roughly 0.001 to 0.1), whose rotation is synchronized to the mutual orbit period. The majority of primaries rotate in less than 2.8  h, although they range from 2.2593 h for (65803) Didymos (Pravec et al., 2006) to 4.749 h for 1998 QE2 (P. Pravec, personal communication, 2013). The known outlier is the nearly equal-mass binary (69230)  Hermes, whose components both appear to have 13.894-h periods synchronized to their mutual orbit period (Margot et al., 2006). This doubly synchronous configuration is most likely due to rapid tidal evolution (Taylor and Margot, 2011). While the rotations of satellites in NEA binaries tend to be tidally locked to their orbital mean motions with periods typically within a factor of 2 of 24 h (often resulting in the characteristic appearance shown in Fig. 1), about one in four radar-observed multiple-asteroid systems have an asynchronous satellite (Brozović et al., 2011), all of which rotate faster than their orbital rate. Well-studied examples include (35107)  1991  VH (Naidu et al., 2012), (153958)  2002 AM31 (Taylor et al., 2013), (311066) 2004 DC (Taylor et al., 2008), and the outer satellites of both undisputed triple systems (153591) 2001 SN263 (Nolan et al., 2008; Fang et al., 2011; Becker et al., 2015) and (136617) 1994 CC (Brozović et al., 2011; Fang et al., 2011). Of the known asynchronous satellites, all have wide component separations (>7 primary radii), translating to

(a)

–10

–5

0

5

10

Doppler Frequency (Hz)

(b)

Fig. 1. Binary near-Earth asteroid (285263) 1998 QE2 as detected using the Arecibo planetary radar system. (a)  In this frequency-only spectrum showing echo power as a function of Doppler frequency, the narrowband echo of the tidally locked secondary stands out against the broadband echo of the larger, faster-rotating primary. (b) In this radar image, the components are spatially resolved (7.5 m/pixel). The vertical axis represents distance from the observer increasing downward. The horizontal axis is Doppler frequency due to the orbital and rotational motion of the components. Note that if one summed the pixel values in each column of the image, the intensity as a function of Doppler frequency would approximate the spectrum above. The secondary is roughly one-fourth the size of the primary (measured in the vertical dimension), although the Doppler breadth of the primary gives the illusion of a greater size disparity. The shape of the secondary (inset on (b)) is distinctly nonspherical when viewed with finer frequency resolution.

358   Asteroids IV longer-than-typical orbital periods, and/or eccentric orbits (>0.05) that are either remnants of their formation mechanism or products of subsequent dynamical evolution (Fang and Margot, 2012c). The shortest orbital periods detected with radar so far are +0.03 those of Didymos and 2006  GY2 with Porb  = 11.90 −0.02 h and 11.7 ± 0.2 h, respectively (Benner et al., 2010; Brooks, +0.04 2006). For Didymos, the semimajor axis is a = 1.18 −0.02 km, just outside the classical fluid Roche limit of ~1  km for equal-density components. Other systems with satellites orbiting near the Roche limit include 2002  CE 26 and 2001 SN263. The significance of this is unclear, as ~100-m secondaries with a cohesion comparable to comet regolith or sand can likely survive on orbits interior to the Roche limit (Taylor and Margot, 2010, and references therein). Inversion of a series of radar images can provide a threedimensional shape model and complete spin-state description given sufficient signal, resolution, and orientational coverage (Hudson, 1993; Magri et al., 2007). Shape reconstruction of the larger component of (66391)  1999  KW4 (Ostro et al., 2006) demonstrated that the canonical shape of an NEA primary has a characteristic circular equatorial bulge, uniformly sloped sides, and polar flattening akin to a spinning top. Such a shape is shared by the primaries of 2004  DC, 1994 CC, 2001 SN263, and (185851) 2000 DP107 (Naidu et al., 2015), although some primaries have less pronounced equatorial belts, e.g., 2002 CE26 and 1998 QE2. Some single asteroids have a similar shape, e.g., (101955) Bennu (Nolan et al., 2013) and (341843)  2008  EV5 (Busch et al., 2011), but do not have satellites, possibly because one has not yet formed or has been lost in the past. Shape model renditions are shown in the chapter by Benner et al. in this volume. Often the resolution of radar images of the smaller satellites is insufficient for shape inversion, but radar images suggest that the satellites are typically elongated, e.g., 2000 DP107, 1999 KW4, 2001 SN263, 1991 VH, and 1998 QE2. Shapes and volumes obtained from inversion of radar images, combined with the system mass derived from the orbital motion observed in radar images, provide the density of the system (or of the individual components if the mass ratio is measurable from reflex motion). Low densities on the order of 1 g cm–3 (Shepard et al., 2006; Becker et al., 2015) to 2 g cm–3 (Ostro et al., 2006; Brozović et al., 2011) suggest significant internal macroporosity on the order of 50%, implying a rubble-pile internal structure for the components. At such low densities, the rapid rotation of the primary places particles along the equatorial belt in a near-weightless environment. The combination of rapid rotation, shape, and implied porosity and rubble-pile structure has implications for the formation mechanism of small multiple-asteroid systems (section 4). While radar allows for direct, unambiguous detection of asteroid satellites, its range is limited. Because radar requires the transmission and reception of a signal, the strength of the received signal falls as the fourth power of the distance to the target and, thus, is best suited for detecting multiplecomponent systems passing within ~0.2 astronomical units

(AU) of Earth. Satellites in the main asteroid belt simply tend to be too small and too far away to detect with present radar capabilities and require application of different observational techniques. 2.2. Lightcurve Observations of Near-Earth-Asteroid and Small-Main-Belt-Asteroid Systems A photometric lightcurve is a time series of measurements of the total brightness of an asteroid. Detections of binary asteroids by photometric lightcurve observations utilize the fact that the components can obscure or cast a shadow on one another, producing occultations or eclipses, respectively. The attenuations can be used to both reveal and characterize binaries (Fig. 2). The observational, analysis, and modeling techniques were described in Pravec et al. (2006), Scheirich and Pravec (2009), and Scheirich et al. (2015). Early reports (Tedesco, 1979; Cellino et al., 1985) of asteroids suspected to be binaries on the basis of anomalous lightcurves [including (15) Eunomia, (39) Laetitia, (43) Ariadne, (44)  Nysa, (49)  Pales, (61)  Danae, (63) Ausonia, (82) Alkmene, (171)  Ophelia, and (192)  Nausikaa] have remained largely unconfirmed despite extensive follow-up searches. The first serious candidate for detection with this technique was NEA (385186) 1994 AW1 (Pravec and Hahn, 1997), whose binary nature was confirmed by photometric observations in 2008 (Birlan et al., 2010). Since 1997, nearly 100 binaries among NEAs and small MBAs have been detected with the photometric method. The binary asteroid database constructed by Pravec and Harris (2007) (http:// www.asu.cas.cz/~asteroid/binastdata.htm) includes data for 86 MBA and NEA binaries that were securely detected by photometry and for which basic parameters have been derived, such as the primary spin period, the orbital period, and the primary-to-secondary mean diameter ratio. A few tens of additional MBAs and NEAs are suspected to be binaries and await confirmation with more detailed observations in the future. Among the main findings obtained from photometric observations is that binary asteroids are ubiquitous. They have been found among NEAs and Mars-crossers (MCs), as well as throughout the main belt, both among asteroids that have been identified as family members and among asteroids that have not. Pravec et al. (2006) derived the fraction of binaries among NEAs larger than 300  m to be 15  ± 4%. A binary fraction among MBAs has not been derived precisely due to less-well-characterized observational selection effects, but their photometric discovery rate is similar to the discovery rate of binaries among NEAs. Thus, binaries are suspected to be as frequent among MBAs as they are among NEAs. There appears to be an upper limit on the primary diameter for photometrically detected binaries of about 13 km; the largest detected binary is (939)  Isberga with Dp  = 13.4  ± 1.3 km (Carry et al., 2015). A lower size limit on the primary diameter Dp is less clear. The smallest detected binary is 2000 UG11 with Dp = 0.26 ± 0.03 km (Pravec et al., 2006), but smaller binaries are known to exist (section 2.1). Their

Margot et al.:  Asteroid Systems: Binaries, Triples, and Pairs   359 12.4

Relative

12.5 12.6 12.7 12.8

(a)

12.9 12.4

(1338) Duponta

12.5 12.6 12.7

(b)

12.8 12.4

0

0.2

0.4

12.5 12.6 12.7 12.8

(c) 0

0.2

0.4

0.6

0.8

1

0.6 0.8 1 Phase (Epoch 2454184.28, Porb = 17.57 h) 2007-03-06.9 to 22.9 (Modra) 2007-03-18.2 to 25.3 (GMARS) 2007-03-22.2 to 24.2 (Badlands) 2007-03-23.5 (Hunters Hill) 2007-03-23.6 (Leura) 2007-03-24.1 and 26.1 (Carbuncle Hill)

Fig. 2. Lightcurve data of (1338) Duponta, which has a secondary-to-primary diameter ratio of about 0.24. (a) The original data showing both lightcurve components, folded with the orbit period. (b) The orbital lightcurve component, derived after subtraction of the primary lightcurve component, showing the mutual events between components of the binary system. (c) The primary lightcurve component. Figure from Pravec et al. (2012).

absence in lightcurve datasets may be due in part to a bias against detecting small binaries in the initial surveys. Another key finding is that small binary asteroids have, with only two or three exceptions, a near-critical angular momentum content (Fig.  3). As shown by Pravec and Harris (2007), their angular momentum is consistent with formation by fission of critically spinning parent bodies of a cohesionless, rubble pile structure. The exceptions are the semi-wide systems (32039) 2000 JO23 and (4951) Iwamoto, and possibly also (1717) Arlon, with orbital periods of 117 h to 360 h and supercritical total angular momentum content. The orbital poles of main-belt binaries were found to have a highly anisotropic distribution, concentrating within 30° of the poles of the ecliptic (Pravec et al., 2012). The preferential orientations of the orbital poles suggest that their parent bodies or the primaries were tilted by the YORP effect toward the asymptotic spin states near obliquities 0° and 180°, consistent with observations of single asteroids (Hanuš et al., 2011). Another significant finding is that there appears to be a lower limit on the separation between components of binary systems of about a/Dp  = 1.5, corresponding to an orbital period of 11–12  h for typical densities. Lightcurve observations indicate that the orbital period of Didymos is Porb = 11.91 ± 0.02 h (Pravec et al., 2006), consistent with the radar estimate. This suggests an orbit close to the Roche limit for strengthless satellites (but see prior remark about orbits interior to the Roche limit). Photometric observations of a binary system over multiple apparitions can be used to detect a change in the separation

of the components due to the effect on mutual event timing. An extensive set of photometric observations of the synchronous binary (175706) 1996 FG3 obtained during 1996–2013 places an upper limit on the drift of its semimajor axis that is 1 order of magnitude less than estimated on the basis of the BYORP theory (Scheirich et al., 2015). This system may be in an equilibrium between BYORP and tidal torques, as proposed for synchronous binary asteroids by Jacobson and Scheeres (2011a). Some datasets strongly suggest the presence of triple aster‑ oids. In these cases, an additional rotational component that does not belong to the primary or the close eclipsing secondary is present in the lightcurve. This additional rotational component does not disappear during mutual events where the eclipsing close secondary is obscured by or in the shadow of the primary. Pravec et al. (2012) identified three such cases: (1830)  Pogson, (2006)  Polonskaya, and (2577) Litva. The latter has been confirmed by direct imaging observations of the third body (second satellite) on a wide orbit (Merline et al., 2013). Other datasets reveal the existence of paired binaries/ triples. Two such cases have been published:  the pair composed of (3749)  Balam and 2009  BR60 (Vokrouhlický, 2009, and references therein) and the pair composed of (8306) Shoko and 2011 SR158 (Pravec et al., 2013). Balam is a confirmed triple, with a distant satellite detected by direct imaging (Merline et al., 2002a) and a close satellite detected by lightcurve observations (Marchis et al., 2008d). Shoko is a suspected triple as well: Using lightcurve observations, Pravec et al. (2013) detected an eclipsing, synchronous close

360   Asteroids IV 3.5

0.1

1

10

100

0.1

100 3.5

Ds/Dp ≤ 0.5

1

10

100

1000

Ds/Dp > 0.5

1

3

(32039) 2000 J023

A

Spin barrier

L

2.5

2.5

Pp (h)

Normalized Total Angular Momentum Content αL

Ds/Dp > 0.5 3

1

Ds/Dp ≤ 0.5

(4951) Iwamoto (617) Patroclus

3

10

10

B Double, synchronous

3

(1717) Arlon

B 1.5

1.5

100

100

(90) Antiope 1

1

0

L

0.1

1

10

100

1000

Dp (km)

A

0.5

0.1

1

10

100

0.5

0 100

Dp (km)

Fig. 3. Estimated values of the normalized total angular momentum content of binaries vs. primary diameter. The quantity aL is the sum of orbital and spin angular momenta normalized by the angular momentum of an equivalent sphere spinning at the critical disruption spin rate wd = 4πρG 3 where r is the density and G is the gravitational constant. In the Darwin notation, aL = 1 corresponds to J/J′ = 0.4. Group A contains small NEA, MC, and MBA binaries. Group B consists of doubly synchronous small MBAs with nearly equal-sized components. Group L represents large MBAs with small satellites (section 2.5). Two exceptional cases are the doubly synchronous asteroids (90) Antiope and (617) Patroclus (section 2.5). Figure updated from Pravec and Harris (2007).

satellite with Porb = 36.2 h and a third rotational component attributed to an outer satellite. While the population of binary NEAs and small MBAs is composed primarily of synchronous systems, and secondarily of asynchronous systems with low secondary-to-primary size ratios (Ds /Dp < 0.5), doubly synchronous binaries with nearly equal-sized components also exist (Fig. 4). Nine such systems with Ds /Dp > 0.7 and orbital periods between 15 h and 118  h have been reliably identified in the main belt (e.g., Behrend et al., 2006; Kryszczyńska et al., 2009) (see also the Pravec and Harris binary database described above). Another important observation is that, with the exception of doubly synchronous systems, all binaries have unelongated, near-spheroidal primary shapes, as evidenced by their low primary amplitudes not exceeding 0.3 mag (when

Fig. 4. Primary rotation period vs. primary diameter. Groups A, B, and L are defined in the caption of Fig.  3. Three doubly synchronous asteroids with nearly equal-sized components lie isolated in the plot: (69230) Hermes on the left, and (90) Antiope and (617) Patroclus on the right of group B. Note that members of group A cluster near the disruption spin limit for strengthless bodies. Figure from Pravec and Harris (2007).

corrected to zero phase angle). This suggests that their primaries may have shapes similar to the top-like shapes that have been observed for 1999 KW4 (Ostro et al., 2006) and several other binaries by radar. All the properties revealed by photometric observations indicate that binary systems among NEAs and small MBAs were formed from critically spinning cohesionless parent bodies, with YORP as the predominant spin-up mechanism. This finding is consistent with the fact that the observed 0.2–13-km size range of binaries corresponds to the size range where the spin barrier against asteroid rotations faster than about 2.2 h has been observed (e.g., Pravec et al., 2007). Although lightcurve observations provide powerful constraints on binaries, there are limitations. Detection of mutual events requires an edge-on geometry and observations at the time of the events, such that some binaries remain undetected [e.g., (69230) Hermes during its 2003 apparition]. Small satellites also escape detection because their effect on the lightcurve is not measurable (e.g., satellites with Ds /Dp  < 0.17 remain undetected if the minimum detectable relative brightness attenuation is ~0.03  mag). The probability of mutual event detection is larger at smaller semimajor axes (expressed in units of primary radius) and at larger size ratios, resulting in observational biases (e.g., Pravec et al., 2012). Finally, lightcurve observations yield relative, not absolute, measurements of orbital separations. Detection of small or distant secondaries and direct measurement of orbital separation must instead rely on other observational techniques.

Margot et al.:  Asteroid Systems: Binaries, Triples, and Pairs   361

2.3. Lightcurve Observations of Asteroid Pairs Spin Period of Primary Component (h)

Vokrouhlický and Nesvorný (2008) reported evidence for pairs of MBAs with bodies in each pair having nearly identical heliocentric orbits. Because chance associations can be ruled out, the asteroids in each pair must be genetically related. Quantifying the difference in orbital parameters is accomplished with a metric d that corresponds roughly to the relative velocity between the bodies at close encounter. Vokrouhlický and Nesvorný identified 44 asteroid pairs (excluding family members) with a distance between the orbits of their components amounting to d < 10 m s–1. They showed that, when integrated backward in time, the orbits converge at a certain moment in the past with a physical distance much less than the radius of the Hill sphere and with a low relative velocity on the order of 1 m s–1. Pravec and Vokrouhlický (2009) developed a method to identify probable asteroid pairs by selecting candidate pairs with a similar distance criterion, then computing the probability that each candidate pair emerged as a result of a coincidence between two unrelated asteroids. They identified 72 probable asteroid pairs, reproducing most of the 44 previously known pairs. Most of the new candidates were later confirmed to be real pairs using backward integrations of their heliocentric orbits. Vokrouhlický and Nesvorný (2008) proposed a few possible formation mechanisms for the asteroid pairs: collisional disruption, rotational fission, and splitting of unstable asteroid binaries. Pravec et al. (2010) conducted a survey of the rotational properties of asteroid pairs, and they found a strong correlation between the primary rotational periods and the secondary-to-primary mass ratio (Fig. 5). They showed that this correlation fits precisely with the predictions of a model by Scheeres (2007) in which a parent body with zero tensile strength undergoes rotational fission. The model predicts that primaries of low-mass-ratio pairs (q  < 0.05) have not had their spin substantially slowed down in the separation process and should rotate rapidly with frequencies close to the fission spin rate. The observed periods are between 2.4 and 5 h. Primaries of medium mass ratio pairs (q = 0.05 to ~0.2) have had their spin slowed down according to the model because a substantial amount of angular momentum was taken away by the escaped secondary. This trend is observed in the data (Fig. 5). Finally, high-mass-ratio pairs with q > 0.2 should not exist, as the free energy in the protobinary system formed by rotational fission would be negative and the components would be unable to separate. Observations mostly corroborate this prediction: All 32 pairs in the sample of Pravec et al. (2010) were found to have a mass ratio 0.5). Their formation requires an additional supply of angular momentum. Another important finding by Pravec et al. (2010) is that the primaries of asteroid pairs have lightcurve amplitudes that imply shapes with a broad range of elongations; i.e., unlike the primaries of binaries (sec-

1

0

1

2

3

4

5

10

1

10

Up = 3 100

Up = 2 0

1

1

2

∆H

3

0.1

4

0.01

5

100

0.001

Mass Ratio (q) 1

Size Ratio

0.1

Fig. 5. Primary rotation periods vs. mass ratios of asteroid pairs. The mass ratio values were estimated from the differences between the absolute magnitudes of the pair components, DH. Circles are data points with quality code rating Up = 3, meaning a precise period determination. Diamonds are data points with Up = 2, which are somewhat less certain estimates. Error bars are one standard deviation. The data match the predictions (curves) of a model of rotational fission with a few adjustable parameters. In the model, Aini is the binary system’s initial orbit semimajor axis, aL is the normalized total angular momentum of the system (Fig. 3), and ap, bp, cp are the long, intermediate, and short axis of the dynamically equivalent equal mass ellipsoid of the primary. All models shown assume bp /cp = 1.2. The dashed curve shows the best-fit model with aL = 1.0, ap /bp = 1.4 and Aini / bp = 3. Solid curves represent upper and lower limiting cases with aL = 0.7−1.2. Figure updated from Pravec et al. (2010).

tions  2.1 and 2.2), the primaries of asteroid pairs do not tend to be nearly spheroidal. 2.4. Spectral Observations of Asteroid Pairs Colorimetric and spectral observations of about 20 asteroid pairs indicate that members of an asteroid pair generally have similar spectra (Duddy et al., 2012, 2013; Moskovitz, 2012; Polishook et al., 2014a; Wolters et al., 2014). In some pairs, the authors observed subtle spectral differences between the components and attributed them to a larger amount of weathered material on the surface of the primary. In two pairs, they observed somewhat more significant spectral differences. For the pair (17198)–(229056), both Duddy et al. (2013) and

362   Asteroids IV Wolters et al. (2014) found that the primary is redder, i.e., it has a somewhat higher spectral slope than the secondary in the observed spectral range 0.5–0.9  μm. It is unclear why their spectra differ despite a strong dynamical link between the two asteroids. For the pair (19289)–(278067), Wolters et al. (2014) observed a spectral difference similar to that seen in (17198)–(229056), but Duddy et al. (2013) observed very similar spectra. Cross-validation of the methods or additional observations, perhaps rotationally resolved, are needed to resolve the discrepancy. 2.5. Direct Imaging of Main-Belt-Asteroid and Trojan Systems Direct imaging of asteroids can reveal the presence of satellites and, following the long tradition of orbit determination of binary stars and planetary satellites, lead to estimates of orbital parameters (Fig. 6). This observing mode remains challenging because the satellites are generally much smaller and fainter than their respective primaries and because most satellites known to date orbit at angular separations below 1  arcsec. Satellite discoveries have therefore followed the development of adaptive optics (AO), and recent advances have enabled the detection of asteroid satellites that had remained undetected in prior searches. Instruments must have sufficient contrast and resolving power to detect asteroid satellites with direct imaging. For a 50–100-km-diameter asteroid in the main belt orbited by a satellite a few kilometers across, the typical angular separation is generally less than an arcsecond with a contrast of 5–10 mag [computed as 2.5 log(Fp/Fs), where F is the flux and p and s indicate primary and secondary, respectively]. In some situations, direct images can actually resolve the primary. A 50–100-km-diameter asteroid at 2 AU subtends 34–68 mas while the diffraction limit of a 10-m telescope at a typical imaging wavelength of 1.2 μm is about 30 mas. Although the diffraction limit is not reached, it can be approached with high-performance AO instruments in excellent

conditions. With a sequence of disk-resolved images that provide sufficient orientational coverage, it is possible to estimate the three-dimensional shape of the primary. This enables volume and density determinations. Instruments capable of meeting the contrast and resolution requirements include HST and large (10-m-class) groundbased telescopes equipped with AO. Spacecraft encounters provide an opportunity to detect small satellites at small separations because of proximity to the target and the absence of the point-spread-function halo that affects groundbased AO instruments. At the time Asteroids III was published, MBA satellite discoveries included one by spacecraft [(243) Ida], one by HST [(107)  Camilla], and six by groundbased AO instruments. Since then, groundbased AO instruments have been responsible for almost all large MBA satellite discoveries: (121) Hermione (Merline et al., 2002b), (379)  Huenna (Margot, 2003), (130) Elektra (Merline et al., 2003c), a second satellite to (87) Sylvia (Marchis et al., 2005b) and to (45) Eugenia (Marchis et al., 2007), (702) Alauda (Rojo and Margot, 2007), (41)  Daphne (Conrad et al., 2008), two satellites to (216)  Kleopatra (Marchis et al., 2008b) and (93) Minerva (Marchis et al., 2009), and (317) Roxane (Merline et al., 2009). The wide binaries (1509) Esclangona (Merline et al., 2003a) and (4674) Pauling (Merline et al., 2004), which are small asteroids in our classification, have also been identified using AO-fed cameras. HST enabled detections of two additional wide binaries: (22899) 1999 TO14 (Merline et al., 2003b) and (17246) 2000 GL74 (Tamblyn et al., 2004), both of which are small MBAs. No satellites have been discovered around any of the seven asteroids recently visited by spacecraft: (4) Vesta, (21) Lutetia, (2867) Šteins, (4179)  Toutatis, (5535) Annefrank, (25143)  Itokawa, and (132524) APL. The number of known large MBAs with satellites is now 16, which includes the only known large doubly synchronous system, (90) Antiope (Merline et al., 2000; Michałowski et al., 2004; Descamps et al., 2007, 2009). The fraction of large MBAs with satellites is difficult

Fig. 6. Satellite detection by direct imaging with adaptive optics (AO). (a)  Image of asteroid (41) Daphne (Vmag = 10) obtained with a groundbased AO-fed camera (NACO at ESO VLT, 5 s exposure). (b) Same image after subtraction of the flux from the primary, enabling more accurate measurements of the flux and position of the secondary. (c) Orbit determination. The relative positions of the satellite from VLT/ NACO and Keck/NIRC2 images are indicated. Figure adapted from Carry (2009).

Margot et al.:  Asteroid Systems: Binaries, Triples, and Pairs   363

to estimate because of a complex dependence of satellite detectability on primary-to-secondary angular separation and primary-to-secondary flux ratio. However, because several independent programs have surveyed more than 300 large MBAs, it is likely that the abundance of binaries in large MBAs is substantially smaller than the ~16% abundance in NEAs and small MBAs. Properties of large MBA binaries and triples are summarized in Figs. 7 and 8. With the exception of the nearly equal-mass binary (90) Antiope, the known satellites have secondary-to-primary mass ratios between 10−6 and 10−2. All have orbital periods between 1 and 5.5 d, except (379) Huenna, whose orbit has a period of ~88  d and an eccentricity of ~0.2 (Marchis et al., 2008c). Many orbits have near-zero eccentricity (e.g., Marchis et al., 2008a), likely the result of tidal damping, but the inner satellites of triples generally have nonzero eccentricities. These eccentricities may have originated when orbits crossed mean-motion resonances while tidally expanding (e.g., Fang et al., 2012). At first glance, large MBA densities appear to cluster in two groups, between 1 and 2 g cm–3 and above 3 g cm–3. However, interpretations are limited by the possibility of systematic errors, including overestimates of volumes and underestimates of densities (Pravec and Harris, 2007). Because volume uncertainties almost always dominate the error budget for binary asteroid densities (e.g., Merline et al., 2002c; Carry, 2012), it is important to assess the realism of uncertainties associated with volume determinations. Some published density values should be regarded with caution because overconfidence in the fractional uncertainty of volume estimates has led to underestimates of bulk density uncertainties. The platinum standard of an orbiting spacecraft yields densities with ~1% accuracy. The gold standard of radar observations where tens of images with hundreds or thousands of pixels per image are used to reconstruct a detailed three-dimensional shape model yields volumes (and densities) with ~10% accuracy. In contrast, AO images contain at most a few independent resolution cells of the target asteroid. Shape reconstructions based on AO images and/or lightcurve data may not routinely yield volume accuracies at the 10% level, although one analysis reached that level (Carry et al., 2012). In the absence of precise volume information, one might be tempted to infer bulk densities from the theory of fluid equilibrium shapes, but this approach is problematic (Holsapple, 2007; Harris et al., 2009). In the Jupiter Trojan population, one satellite to (624) Hektor has been reported (Marchis et al., 2006b) since the discovery of the first Trojan satellite to (617) Patroclus (Merline et al., 2001). These are the only Trojans confirmed to have satellites in spite of several active search programs. The apparent low abundance of binary Trojans is intriguing and, if confirmed, may provide additional support for the idea that Jupiter Trojans originated in the transneptunian region (Morbidelli et al., 2005; Levison et al., 2009) where they experienced a different collisional environment than in the main belt of asteroids. (624) Hektor has a satellite in a ~3-d orbit that is eccentric (~0.3) and inclined (~50°) with respect

to Hektor’s equator (Marchis et al., 2014). (617) Patroclus is unusual because it has two components of similar size in a relatively tight (~680  km) orbit, with a normalized total angular momentum exceeding that available from fission of a single parent body (Marchis et al., 2006a). In the transneptunian region, 14 and 64 binary systems have been discovered with AO and HST, respectively (Johnston, 2014). The apparent larger abundance of binary TNOs in the cold classical belt may be due to a different dynamical environment and formation mechanism (section 5). Objects in the Trojan and TNO populations are generally too faint for AO observations in natural guide star (NGS) mode, in which the science target is also used to measure the properties of the wavefront and command the deformable mirror. These objects can be observed in appulse when their sky position happens to be within 0.2 and low-mass-ratio q  < 0.2 binary systems evolve differently (Scheeres, 2009a; Jacobson and Scheeres, 2011b). Primarily, positive-energy low-mass-ratio systems will chaotically explore orbital phase space until the majority find a disruption trajectory creating an asteroid pair; this evolutionary route is unavailable to high-mass-ratio systems. The asteroid pair population provides a natural laboratory to test this relationship (Scheeres, 2007; Vokrouhlický and Nesvorný, 2008). Pravec et al. (2010) examined many asteroid pair systems and measured the rotation rate of the primary and the absolute magnitude difference between the pair members. These two quantities should follow a simple relationship related to wq, although many of the ignored details mentioned at the beginning of this section can move asteroids away from this relationship. Indeed, Pravec et al. (2010) discovered that asteroid pairs do follow this

368   Asteroids IV relationship (Fig. 5). Furthermore, they found that the large members of asteroid pairs have a broader range of elongations than the primaries of binary systems, consistent with the findings of Jacobson and Scheeres (2011b) that prolate primaries are less likely to remain in a bound binary system after rotational fission. Thus, there is strong evidence to support the hypothesis that asteroid pairs are the products of rotational fission. Asteroid pairs continue to be a fertile observational land‑ scape. Since dynamical integrations can derive the “birthdate” of such systems, observers can test ideas regarding space-weathering timescales and YORP evolution after fission (Polishook et al., 2014a; Polishook, 2014). Along with binary systems, the surfaces of asteroid pairs may provide clues in the future regarding the violence of the rotational fission process (Polishook et al., 2014b). 4.3. Binary and Triple Systems Jacobson and Scheeres (2011b) showed that after rotational fission there are a number of possible outcomes. Their numerical studies produced the evolutionary flow chart shown in Fig. 11; many of these outcomes were also found by Fang and Margot (2012c). The high- and low-mass-ratio distinction for rotational fission emphasized above plays

YORP Process ~ 105–106 yr

an important role in distinguishing the two evolutionary pathways. Along the high-mass-ratio pathway, both binary members tidally synchronize and then evolve according to the BYORP effect. Along the low-mass-ratio pathway, the binary system is unbound. Since these systems are chaotic, many are disrupted and become asteroid pairs. During this chaotic binary state, the secondary can often go through rotational fission itself, although this rotational fission is torqued by spin-orbit coupling (Fig. 10) rather than the YORP effect. Loss of material from the secondary stabilizes the remaining orbiting components. The lost mass may reaccrete onto the primary, perhaps contributing to the observed equatorial ridges, or may escape from the system. In these cases, the system undergoes another chaotic binary episode with three possible outcomes: a reshaped asteroid, an asteroid pair, or a stable binary. These binaries still possess positive free energy such that they may disrupt if disturbed. In other cases, the system retains three components after secondary fission. While the numerical simulations of Jacobson and Scheeres (2011b) did not yield this latter outcome, it is possible that this pathway explains the existence of stable triple systems. After stabilization of the low-mass-ratio binary system, the secondary synchronizes due to tides (e.g., Goldreich and Sari, 2009), although some satellites may be trapped in a

Tidal Process ~ 104–106 yr

q> ~ 0.2 Chaotic Binary

Contact Binary BYORP Process ~ 105–106 yr

Doubly Synchronous Binary Asteroid Pair

Tidal Process ~ 106–107 yr Chaotic Triple Asteroid

Stable Triple

Dynamic Processes < ~ 1 yr q< ~ 0.2

Chaotic Binary

Dynamic Processes < ~ 1 yr

Reshaped Asteroid

Reshaped Asteroid

Tidal Process ~ 104–106 yr

YORP Process ~ 105–106 yr

BYORP Process ~ 105–106 yr Stable Binary Asteroid Pair

Asteroid Pair

Fig. 11. Flowchart showing the possible evolutionary paths for an asteroid after it undergoes rotational fission. Each arrow is labeled with the dominant process and an estimated timescale for this process. Underlined states are nominally stable for a YORP effect timescale. Figure from Jacobson and Scheeres (2011b).

Margot et al.:  Asteroid Systems: Binaries, Triples, and Pairs   369

chaotic rotation state for durations that exceed the classic spin synchronization timescales (Naidu and Margot, 2015). Then the system evolves according to the BYORP effect and tides. These binary evolutionary processes and their outcomes are discussed in the chapter by Walsh and Jacobson in this volume. As shown in Fig. 11, these evolutionary paths include each of the binary morphologies identified in this chapter and by other teams (Pravec and Harris, 2007; Fang and Margot, 2012c). In particular, the formation of wide asynchronous binaries such as (1509)  Esclangona, (4674) Pauling, (17246) 2000 GL74, and (22899) 1999 TO14 is best explained by a rotational fission mechanism (Polishook et al., 2011) followed by BYORP orbital expansion (Jacobson et al., 2014b). An alternative formation mechanism for triples such as (153591)  2001  SN263 and (136617)  1994  CC is that after creating a stable binary system, the primary undergoes rotational fission a second time. As long as the third component is on a distant enough orbit, then this process may result in a stable triple system (Fang et al., 2011; Fang and Margot, 2012c; Jacobson et al., 2014b). 5. LARGE ASTEROIDS: SYNTHESIS The primaries of most known binary and triple asteroids greater than 20 km have spin periods in the range of 4 h to 7 h (Fig. 7). While these spin rates are not near the disruption spin limit, they are typically faster than the mean spin rates for asteroids of similar sizes. The total angular momentum content, however, is well below that required for rotational fission. The secondary-to-primary mass ratios in these systems range from 10−6 to 10−2. These properties are consistent with satellite formation during large collisions (Fig.  12). Durda et al. (2004) have shown in numerical simulations that impacts of 10- to 30-km-diameter projectiles striking at impact velocities between 3 km s−1 and 7  km  s−1 can produce satellites that match observed properties. Multiple asteroid systems, e.g., (45)  Eugenia (Merline et al., 1999; Marchis et al., 2007) and (87) Sylvia (Margot and Brown, 2001; Marchis et al., 2005a), can also plausibly form through collisions. There is more uncertainty related to the formation of (90) Antiope and (617) Patroclus, which are both too large to be substantially affected by YORP. Hypotheses for the formation of (90) Antiope include primordial fission due to excessive angular momentum (Pravec and Harris, 2007), an improbable low-velocity collision of a large impactor (Weidenschilling et al., 2001), or shrinking of an initially wide binary formed by gravitational collapse (Nesvorný et al., 2010). Gravitational collapse in a gas-rich protoplanetary disk has been invoked to explain the formation of numerous binaries in the transneptunian region. (617)  Patroclus may be a primordial TNO that avoided disruption during emplacement in the Trojan region (Nesvorný et al., 2010). Wide TNO binaries would not be expected to survive this process, but encounter calculations (e.g., Fang and Margot, 2012a) show that tight binaries would.

Fig. 12. Numerical simulations show that binaries can form as a result of large impacts between asteroids. In some scenarios, impact debris can remain gravitationally bound to the target body, forming a satellite (SMATs). This process likely explains the formation of large MBA binaries. In other scenarios, two fragments from the escaping ejecta have sufficiently similar trajectories, such that they become bound to one another (EEBs). Figure from Durda et al. (2004).

6. CONCLUSIONS Studies of binaries, triples, and pairs remain a fertile ground for observing processes that are important in planet formation and for measuring quantities that are difficult to obtain by other means. These include masses and densities as well as thermal, mechanical, and interior properties. Binaries or triples have been found in ~50 NEAs, ~50 small MBAs, ~20 large MBAs, and 2 Trojans. A unifying paradigm based on rotational fission and post-fission dynamics explains the formation of small binaries, triples, and pairs. Because the Sun-powered rotational fission process is unrelenting, and because the production of pairs is a frequent outcome of this process, a substantial fraction of small bodies likely originated in a rotational disruption event. This origin affects the size distribution of asteroids and may explain the presence of single NEAs with equatorial bulges observed with radar. Small satellites of large MBAs are likely formed during large collisions. Advances in instrumentation, observational programs, and analysis techniques hold the promise of exciting findings in the next decade. REFERENCES Bartczak P., Michałowski T., Santana-Ros T., and Dudziński G. (2014) A new non-convex model of the binary asteroid 90 Antiope obtained with the SAGE modelling technique. Mon. Not. R. Astron. Soc., 443, 1802–1809. Becker T. M., Howell E. S., Nolan M. C., Magri C., Pravec P., Taylor P. A., Oey J., Higgins D., Világi J., Kornoš L., Galád A., Gajdoš Š., Gaftonyuk N. M., Krugly Y. N., Molotov I. E., Hicks M. D., Carbognani A., Warner B. D., Vachier F., Marchis F., and Pollock J. T. (2015) Physical modeling of triple near-Earth asteroid (153591) 2001 SN263 from radar and optical light curve observations. Icarus, 248, 499–515.

370   Asteroids IV Behrend R., Bernasconi L., Roy R., Klotz A., Colas F., Antonini P., Aoun R., Augustesen K., Barbotin E., Berger N., Berrouachdi H., Brochard E., Cazenave A., Cavadore C., Coloma J., Cotrez V., Deconihout S., Demeautis C., Dorseuil J., Dubos G., Durkee R., Frappa E., Hormuth F., Itkonen T., Jacques C., Kurtze L., Laffont A., Lavayssière M., Lecacheux J., Leroy A., Manzini F., Masi G., Matter D., Michelsen R., Nomen J., Oksanen A., Pääkkönen P., Peyrot A., Pimentel E., Pray D., Rinner C., Sanchez S., Sonnenberg K., Sposetti S., Starkey D., Stoss R., Teng J.-P., Vignand M., and Waelchli N. (2006) Four new binary minor planets: (854) Frostia, (1089) Tama, (1313) Berna, (4492) Debussy. Astron. Astrophys., 446, 1177–1184. Belton M., Chapman C., Thomas P., Davies M., Greenberg R., Klaasen K., Byrnes D., D’Amario L., Synnott S., Merline W., Petit J.-M., Storrs A., and Zellner B. (1995) The bulk density of asteroid 243 Ida from Dactyl’s orbit. Nature, 374, 785–788. Benner L. A. M., Margot J. L., Nolan M. C., Giorgini J. D., Brozovic M., Scheeres D. J., Magri C., and Ostro S. J. (2010) Radar imaging and a physical model of binary asteroid 65803 Didymos. Bull. Am. Astron. Soc., 42, 1056. Berthier J., Vachier F., Marchis F., Ďurech J., and Carry B. (2014) Physical and dynamical properties of the main belt triple asteroid (87) Sylvia. Icarus, 239, 118–130. Binzel R. P. and van Flandern T. C. (1979) Minor planets — The discovery of minor satellites. Science, 203, 903–905. Birlan M., Vaduvescu O., Tudorica A., Sonka A., Nedelcu A., Galad A., Colas F., Pozo F. N., Barr A. D., Toma R., Comsa I., Rocher P., Lainey V., Vidican D., Asher D., Opriseanu C., Vancea C., Colque J. P., Soto C. P., Rekola R., and Unda-Sanzana E. (2010) More than 160 near Earth asteroids observed in the EURONEAR network. Astron. Astrophys., 511, A40. Birlan M., Nedelcu D. A., Popescu M., Vernazza P., Colas F., and A. Kryszczyńska (2014) Spectroscopy and surface properties of (809) Lundia. Mon. Not. R. Astron. Soc., 437, 176–184. Bottke W. F. and Melosh H. J. (1996a) The formation of asteroid satellites and doublet craters by planetary tidal forces. Nature, 381, 51–53. Bottke W. F. and Melosh H. J. (1996b) Binary asteroids and the formation of doublet craters. Icarus, 124, 372–391. Bottke W. F., Vokrouhlický D., Rubincam D. P., and Brož M. (2002) The effect of Yarkovsky thermal forces on the dynamical evolution of asteroids and meteoroids. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 395–408. Univ. of Arizona, Tucson. Bottke W. F., Vokrouhlický D., Rubincam D. P, and Nesvorný D. (2006) The Yarkovsky and YORP effects: Implications for asteroid dynamics. Annu. Rev. Earth Planet. Sci., 34, 157–191. Braga-Ribas F., Sicardy B., Ortiz J. L., Snodgrass C., Roques F., VieiraMartins R., Camargo J. I. B., Assafin M., Duffard R., Jehin E., Pollock J., Leiva R., Emilio M., Machado D. I., Colazo C., Lellouch E., Skottfelt J., Gillon M., Ligier N., Maquet L., Benedetti- Rossi G., Gomes A. R., Kervella P., Monteiro H., Sfair R., El Moutamid M., Tancredi G., Spagnotto J., Maury A., Morales N., Gil-Hutton R., Roland S., Ceretta A., Gu S.-H., Wang X.-B., Harpsøe K., Rabus M., Manfroid J., Opitom C., Vanzi L., Mehret L., Lorenzini L., Schneiter E. M., Melia R., Lecacheux J., Colas F., Vachier F., Widemann T., Almenares L., Sandness R. G., Char F., Perez V., Lemos P., Martinez N., Jørgensen U. G., Dominik M., Roig F., Reichart D. E., Lacluyze A. P., Haislip J. B., Ivarsen K. M., Moore J. P., Frank N. R., and Lambas D. G. (2014) A ring system detected around the Centaur (10199) Chariklo. Nature, 508, 72–75. Brooks H. E. (2006) Orbits of binary near-Earth asteroids from radar observations. Bull. Am. Astron. Soc., 38, 934. Brozović M., Benner L. A. M., Taylor P. A., Nolan M. C., Howell E. S., Magri C., Scheeres D. J., Giorgini J. D., Pollock J. T., Pravec P., Galád A., Fang J., Margot J. L., Busch M. W., Shepard M. K., Reichart D. E., Ivarsen K. M., Haislip J. B., Lacluyze A. P., Jao J., Slade M. A., Lawrence K. J., and Hicks M. D. (2011) Radar and optical observations and physical modeling of triple near-Earth asteroid (136617) 1994 CC. Icarus, 216, 241–256. Buie M. W., Olkin C. B., Merline W. J., Timerson B., Herald D., Owen W. M., Abramson H. B., Abramson K. J., Breit D. C., Caton D. B., Conard S. J., Croom M. A., Dunford R. W., Dunford J. A., Dunham D. W., Ellington C. K., Liu Y., Maley P. D., Olsen A. M., Royer R., Scheck A. E., Sherrod C., Sherrod L., Swift T. J., Taylor L. W., and Venable R. (2014) Shape and size of Patroclus and Menoetius from a stellar occultation. Bull. Am. Astron. Soc., 46, #506.09. Busch M. W (2009) ALMA and asteroid science. Icarus, 200, 347–349.

Busch M. W., Ostro S. J., Benner L. A. M., Brozovic M., Giorgini J. D., Jao J. S., Scheeres D. J., Magri C., Nolan M. C., Howell E. S., Taylor P. A., Margot J. L., and Brisken W. (2011) Radar observations and the shape of near-Earth asteroid 2008 EV5. Icarus, 212, 649–660. Carry B. (2009) Asteroids physical properties from high angularresolution imaging. Ph.D. thesis, Observatoire de Paris. Carry B. (2012) Density of asteroids. Planet. Space Sci., 73, 98–118. Carry B., Kaasalainen M., Merline W. J., Müller T. G., Jorda L., Drummond J. D., Berthier J., O’Rourke L., Ďurech J., Küppers M., Conrad A., Tamblyn P., Dumas C., Sierks H., and the OSIRIS Team (2012) Shape modeling technique KOALA validated by ESA Rosetta at (21) Lutetia. Planet. Space Sci., 66, 200–212. Carry B., Matter A., Scheirich P., Pravec P., Molnar L., Mottola S., Carbognani A., Jehin E., Marciniak A., Binzel R. P., DeMeo F. E., Birlan M., Delbo M., Barbotin E., Behrend R., Bonnardeau M., Colas F., Farissier P., Fauvaud M., Fauvaud S., Gillier C., Gillon M., Hellmich S., Hirsch R., Leroy A., Manfroid J., Montier J., Morelle E., Richard F., Sobkowiak K., Strajnic J., and Vachier F. (2015) The small binary asteroid (939) Isberga. Icarus, 248, 516–525. Cellino A., Pannunzio R., Zappala V., Farinella P., and Paolicchi P. (1985) Do we observe light curves of binary asteroids? Astron. Astrophys., 144, 355–362. Chapman C. R., Veverka J., Thomas P. C., Klaasen K., Belton M. J. S., Harch A., McEwen A., Johnson T. V., Helfenstein P., Davies M. E., Merline W. J., and Denk T. (1995) Discovery and physical properties of Dactyl a satellite of asteroid 243 Ida. Nature, 374, 783. Chesley S. R., Farnocchia D., Nolan M. C., Vokrouhlický D., Chodas P. W., Milani A., Spoto F., Rozitis B., Benner L. A. M., Bottke W. F., Busch M. W., Emery J. P., Howell E. S., Lauretta D. S., Margot J.-L., and Taylor P. A. (2014) Orbit and bulk density of the OSIRISREx target asteroid (101955) Bennu. Icarus, 235, 5–22. Conrad A. R., Merline W. J., Drummond J. D., Tamblyn P. M., Dumas C., Carry B. X., Campbell R. D., Goodrich R. W., Owen W. M., and Chapman C. R. (2008) S/2008 (41) 1. IAU Circular 8930. Cotto-Figueroa D., Statler T. S., Richardson D. C., and Tanga P. (2013) Killing the YORP cycle: A stochastic and self-limiting YORP effect. Bull. Am. Astron. Soc., 45, #106.09. Ćuk M. (2007) Formation and destruction of small binary asteroids. Astrophys. J. Lett., 659, L57–L60. Ćuk M. and Burns J. A. (2005) Effects of thermal radiation on the dynamics of binary NEAs. Icarus, 176, 418–431. Ćuk M. and Nesvorný D. (2010) Orbital evolution of small binary asteroids. Icarus, 207, 732–743. Delbo M., Ligori S., Matter A., Cellino A., and Berthier J. (2009) First VLTI-MIDI direct determinations of asteroid sizes. Astrophys. J., 694, 1228–1236. Delbo M., Walsh K., Mueller M., Harris A. W., and Howell E. S. (2011) The cool surfaces of binary near-Earth asteroids. Icarus, 212, 138–148. DeMeo F. E., Carry B., Marchis F., Birlan M., Binzel R. P., Bus S. J., Descamps P., Nedelcu A., Busch M., and Bouy H. (2011) A spectral comparison of (379) Huenna and its satellite. Icarus, 212, 677–681. Descamps P., Marchis F., Michalowski T., Vachier F., Colas F., Berthier J., Assafin M., Dunckel P. B., Polinska M., Pych W., Hestroffer D., Miller K. P. M., Vieira-Martins R., Birlan M., Teng-Chuen-Yu J.-P., Peyrot A., Payet B., Dorseuil J., Léonie Y., and Dijoux T. (2007) Figure of the double asteroid 90 Antiope from adaptive optics and lightcurve observations. Icarus, 187, 482–499. Descamps P., Marchis F., Pollock J., Berthier J., Vachier F., Birlan M., Kaasalainen M., Harris A. W., Wong M. H., Romanishin W. J., Cooper E. M., Kettner K. A., Wiggins P., Kryszczynska A., Polinska M., Coliac J.-F., Devyatkin A., Verestchagina I., and Gorshanov D. (2008) New determination of the size and bulk density of the binary asteroid 22 Kalliope from observations of mutual eclipses. Icarus, 196, 578–600. Descamps P., Marchis F., Michalowski T., Berthier J., Pollock J., Wiggins P., Birlan M., Colas F., Vachier F., Fauvaud S., Fauvaud M., Sareyan J.-P., Pilcher F., and Klinglesmith D. A. (2009) A giant crater on 90 Antiope? Icarus, 203, 102–111. Descamps P., Marchis F., Berthier J., Emery J. P., Duchêne G., de Pater I., Wong M. H., Lim L., Hammel H. B., Vachier F., Wiggins P., Teng-Chuen-Yu J.-P., Peyrot A., Pollock J., Assafin M., VieiraMartins R., Camargo J. I. B., Braga-Ribas F., and Macomber B. (2011) Triplicity and physical characteristics of asteroid (216) Kleopatra. Icarus, 211, 1022–1033.

Margot et al.:  Asteroid Systems: Binaries, Triples, and Pairs   371 Doressoundiram A., Paolicchi P., Verlicchi A., and Cellino A. (1997) The formation of binary asteroids as outcomes of catastrophic collisions. Planet. Space Sci., 45, 757–770. Duddy S. R., Lowry S. C., Wolters S. D., Christou A., Weissman P. R, Green S. F., and Rozitis B. (2012) Physical and dynamical characterisation of the unbound asteroid pair 7343-154634. Astron. Astrophys., 539, A36. Duddy S. R., Lowry S. C., Christou A., Wolters S. D., Rozitis B., Green S. F., and Weissman P. R. (2013) Spectroscopic observations of unbound asteroid pairs using the WHT. Mon. Not. R. Astron. Soc., 429, 63–74. Dunham D. W. (1981) Recently-observed planetary occultations. Occultation Newsletter, International Occultation Timing Association (IOTA), 2, 139–143. Durda D. D. (1996) The formation of asteroidal satellites in catastrophic collisions. Icarus, 120, 212–219. Durda D. D.,Bottke W. F., Enke B. L., Merline W. J., Asphaug E., Richardson D. C., and Leinhardt Z. M. (2004) The formation of asteroid satellites in large impacts: Results from numerical simulations. Icarus, 170, 243–257. Emery J. P., Cruikshank D. P., and Van Cleve J. (2006) Thermal emission spectroscopy (5.2–38 µm) of three Trojan asteroids with the Spitzer Space Telescope: Detection of fine-grained silicates. Icarus, 182, 496–512. Fahnestock E. G. and Scheeres D. J. (2008) Simulation and analysis of the dynamics of binary near-Earth asteroid (66391) 1999 KW4. Icarus, 194, 410–435. Fahnestock E. G. and Scheeres D. J. (2009) Binary asteroid orbit expansion due to continued YORP spin-up of the primary and primary surface particle motion. Icarus, 201, 135–152. Fang J. and Margot J. L. (2012a) Binary asteroid encounters with terrestrial planets: Timescales and effects. Astron. J., 143, 25. Fang J. and Margot J. L. (2012b) The role of Kozai cycles in near-Earth binary asteroids. Astron. J., 143, 59. Fang J. and Margot J. L. (2012c) Near-Earth binaries and triples: Origin and evolution of spin-orbital properties. Astron. J., 143, 24. Fang J., Margot J. L., Brozovic M., Nolan M. C., Benner L. A. M., and Taylor P. A. (2011) Orbits of near-Earth asteroid triples 2001 SN263 and 1994 CC: Properties, origin, and evolution. Astron. J., 141, 154. Fang J., Margot J. L., and Rojo P. (2012) Orbits, masses, and evolution of main belt triple (87) Sylvia. Astron. J., 144, 70. Frouard J. and Compère A. (2012) Instability zones for satellites of asteroids: The example of the (87) Sylvia system. Icarus, 220, 149–161. Goldreich P. and Sari R. (2009) Tidal evolution of rubble piles. Astrophys. J., 691, 54–60. Hanuš J., Ďurech J., Brož M., Warner B. D., Pilcher F., Stephens R., Oey J., Bernasconi L., Casulli S., Behrend R., Polishook D., Henych T., Lehký M., Yoshida F., and Ito T. (2011) A study of asteroid pole-latitude distribution based on an extended set of shape models derived by the lightcurve inversion method. Astron. Astrophys., 530, A134. Harris A. W., Fahnestock E. G., and Pravec P. (2009) On the shapes and spins of rubble pile asteroids. Icarus, 199, 310–318. Hilton J. L. (2002) Asteroid masses and densities. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 103–112. Univ. of Arizona, Tucson. Holsapple K. A. (2007) Spin limits of solar system bodies: From the small fast-rotators to 2003 EL61. Icarus, 187(2), 500–509. Hudson R. S. (1993) Three-dimensional reconstruction of asteroids from radar observations. Remote Sensing Rev., 8, 195–203. Jacobson S. A. and Scheeres D. J. (2011a) Long-term stable equilibria for synchronous binary asteroids. Astrophys. J. Lett., 736, L19. Jacobson S. A. and Scheeres D. J. (2011b) Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems. Icarus, 214(1), 161–178. Jacobson S. A., Marzari F., Rossi A., Scheeres D. J., and Davis D. R. (2014a) Effect of rotational disruption on the size-frequency distribution of the main belt asteroid population. Mon. Not. R. Astron. Soc. Lett., 439, L95–L99. Jacobson S. A., Scheeres D. J., and McMahon J. (2014b) Formation of the wide asynchronous binary asteroid population. Astrophys. J., 780, 60. Johnston W. R. (2014) Binary Minor Planets V7.0. EAR-A-COMPIL-5BINMP-V7.0, NASA Planetary Data System. Kryszczyńska A., Colas F., Descamps P., Bartczak P., Polińska M., Kwiatkowski T., Lecacheux J., Hirsch R., Fagas M., Kamiński

K., Michałowski T., and Marciniak A. (2009) New binary asteroid 809 Lundia. I. Photometry and modelling. Astron. Astrophys., 501, 769–776. Laver C., de Pater I., Marchis F., Ádámkovics M., and Wong M. H. (2009) Component-resolved near-infrared spectra of the (22) Kalliope system. Icarus, 204, 574–579. Levison H. F., Bottke W. F., Gounelle M., Morbidelli A., Nesvorný D., and Tsiganis K. (2009) Contamination of the asteroid belt by primordial trans-neptunian objects. Nature, 460, 364–366. Magri C., Ostro S. J., Scheeres D. J., Nolan M. C., Giorgini J. D., Benner L. A. M., and Margot J. L. (2007) Radar observations and a physical model of asteroid 1580 Betulia. Icarus, 186, 152–177. Marchis F., Descamps P., Hestroffer D., and Berthier J. (2005a) Discovery of the triple asteroidal system 87 Sylvia. Nature, 463, 822–824. Marchis F., Descamps P., Hestroffer D., Berthier J., Brown M. E., and Margot J. L. (2005b) Satellites of (87) Sylvia. IAU Circular 8582. Marchis F., Hestroffer D., Descamps P., Berthier J., Bouchez A. H., Campbell R. D., Chin J. C. Y., van Dam M. A., Hartman S. K., Johansson E. M., Lafon R. E., Le Mignant D., de Pater I., Stomski P. J., Summers D. M., Vachier F., Wizinovich P. L., and Wong M. H. (2006a) A low density of 0.8 g cm−3 for the Trojan binary asteroid 617 Patroclus. Nature, 439, 565–567. Marchis F., Wong M. H., Berthier J., Descamps P., Hestroffer D., Vachier F., Le Mignant D., and de Pater I. (2006b) S/2006 (624) 1. IAU Circular 8732. Marchis F., Baek M., Descamps P., Berthier J., Hestroffer D., and Vachier F. (2007) S/2004 (45) 1. IAU Circular 8817. Marchis F., Descamps P., Baek M., Harris A. W., Kaasalainen M., Berthier J., Hestroffer D., and Vachier F. (2008a) Main belt binary asteroidal systems with circular mutual orbits. Icarus, 196, 97–118. Marchis F., Descamps P., Berthier J., and Emery J. P. (2008b) S/2008 (216) 1 and S/2008 (216) 2. IAU Circular 8980. Marchis F., Descamps P., Berthier J., Hestroffer D., Vachier F., Baek M., Harris A. W., and Nesvorný D. (2008c) Main belt binary asteroidal systems with eccentric mutual orbits. Icarus, 195, 295–316. Marchis F., Pollock J., Pravec P., Baek M., Greene J., Hutton L., Descamps P., Reichart D. E., Ivarsen K. M., Crain J. A., Nysewander M. C., Lacluyze A. P., Haislip J. B., and Harvey J. S. (2008d) (3749) Balam. IAU Circular 8928. Marchis F., Macomber B., Berthier J., Vachier F., and Emery J. P. (2009) S/2009 (93) 1 and S/2009 (93) 2. IAU Circular 9069. Marchis F., Lainey V., Descamps P., Berthier J., Van Dam M., de Pater I., Macomber B., Baek M., Le Mignant D., Hammel H. B., Showalter M., and Vachier F. (2010) A dynamical solution of the triple asteroid system (45) Eugenia. Icarus, 210, 635–643. Marchis F., Enriquez J. E., Emery J. P., Berthier J., Descamps P., and Vachier F. (2011) The origin of (90) Antiope from componentresolved near-infrared spectroscopy. Icarus, 213, 252–264. Marchis F., Enriquez J. E., Emery J. P., Mueller M., Baek M., Pollock J., Assafin M., Vieira Martins R., Berthier J., Vachier F., Cruikshank D. P., Lim L. F., Reichart D. E., Ivarsen K. M., Haislip J. B., and LaCluyze A. P. (2012) Multiple asteroid systems: Dimensions and thermal properties from Spitzer Space Telescope and ground-based observations. Icarus, 221, 1130–1161. Marchis F., Durech J., Castillo-Rogez J., Vachier F., Cuk M., Berthier J., Wong M. H., Kalas P., Duchene G., van Dam M. A., Hamanowa H., and Viikinkoski M. (2014) The puzzling mutual orbit of the binary Trojan asteroid (624) Hektor. Astrophys. J. Lett., 783, L37. Margot J. L. (2003) S/2003 (379) 1. IAU Circular 8182. Margot J. L. (2010) Recent observations of binary and multiple systems. In Second Workshop on Binaries in the Solar System, Wasowo, Poland. Margot J. L. and Brown M. E. (2001) Discovery and characterization of binary asteroids 22 Kalliope and 87 Sylvia. Bull. Am. Astron. Soc., 33, 1133. Margot J. L. and Brown M. E. (2003) A low density M-type asteroid in the main belt. Science, 300(5627), 1939–1942. Margot J. L., Nolan M. C., Benner L. A. M., Ostro S. J., Jurgens R. F., Giorgini J. D., Slade M. A., and Campbell D. B. (2002) Binary asteroids in the near-Earth object population. Science, 296, 1445–1448. Margot J. L., Pravec P., Nolan M. C., Howell E. S., Benner L. A. M., Giorgini J. D., Jurgens R. F., Ostro S. J., Slade M. A., Magri C., Taylor P. A., Nicholson P. D., and Campbell D. B. (2006) Hermes as an exceptional case among binary near-Earth asteroids. In IAU General Assembly.

372   Asteroids IV Marzari F., Rossi A., and Scheeres D. J. (2011) Combined effect of YORP and collisions on the rotation rate of small main belt asteroids. Icarus, 214(2), 622–631. McMahon J. and Scheeres D. (2010a) Secular orbit variation due to solar radiation effects: A detailed model for BYORP. Cel. Mech. Dyn. Astron., 106, 261–300. McMahon J. and Scheeres D. (2010b) Detailed prediction for the BYORP effect on binary near-Earth asteroid (66391) 1999 KW4 and implications for the binary population. Icarus, 209, 494–509. Merline W. J., Close L. M., Dumas C., Chapman C. R., Roddier F., Menard F., Slater D. C., Duvert G., Shelton C., and Morgan T. (1999) Discovery of a moon orbiting the asteroid 45 Eugenia. Nature, 401, 565. Merline W. J., Close L. M., Shelton J. C., Dumas C., Menard F., Chapman C. R., and Slater D. C. (2000) Satellites of minor planets. IAU Circular 7503. Merline W. J., Close L. M., Siegler N., Potter D., Chapman C. R., Dumas C., Menard F., Slater D. C., Baker A. C., Edmunds M. G., Mathlin G., Guyon O., and Roth K. (2001) S/2001 (617) 1. IAU Circular 7741. Merline W. J., Close L. M., Siegler N., Dumas C., Chapman C., Rigaut F., Menard F., Owen W. M., and Slater D. C. (2002a) S/2002 (3749) 1. IAU Circular 7827. Merline W. J., Tamblyn P. M., Dumas C., Close L. M., Chapman C. R., Menard F., Owen W. M., Slater D. C., and Pepin J. (2002b) S/2002 (121) 1. IAU Circular 7980. Merline W. J., Weidenschilling S. J., Durda D. D., Margot J. L., Pravec P., and Storrs A. D. (2002c) Asteroids do have satellites. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 289–312. Univ. of Arizona, Tucson. Merline W. J., Close L. M., Tamblyn P. M., Menard F., Chapman C. R., Dumas C., Duvert G., Owen W. M., Slater D. C., and Sterzik M. F. (2003a) S/2003 (1509) 1. IAU Circular 8075. Merline W. J., Tamblyn P. M., Chapman C. R., Nesvorny D., Durda D. D., Dumas C., Storrs A. D., Close L. M., and Menard F. (2003b) S/2003 (22899) 1. IAU Circular 8232. Merline W. J., Tamblyn P. M., Dumas C., Close L. M., Chapman C. R., and Menard F. (2003c) S/2003 (130) 1. IAU Circular 8183. Merline W. J., Tamblyn P. M., Dumas C., Menard F., Close L. M., Chapman C. R., Duvert G., and Ageorges N. (2004) S/2004 (4674) 1. IAU Circular 8297. Merline W. J., Tamblyn P. M., Drummond J. D., Christou J. C., Conrad A. R., Carry B., Chapman C. R., Dumas C., Durda D. D., Owen W. M., and Enke B. L. (2009) S/2009 (317) 1. IAU Circular 9099. Merline W. J., Tamblyn P. M., Warner B. D., Pravec P., Tamblyn J. P., Neyman C., Conrad A. R., Owen W. M., Carry B., Drummond J. D., Chapman C. R., Enke B. L., Grundy W. M., Veillet C., Porter S. B., Arcidiacono C., Christou J. C., Durda D. D., Harris A. W., Weaver H. A., Dumas C., Terrell D., and Maley P. (2013) S/2012 (2577) 1. IAU Circular 9267. Michałowski T., Bartczak P., Velichko F. P., Kryszczyńska A., Kwiatkowski T., Breiter S., Colas F., Fauvaud S., Marciniak A., Michałowski J., Hirsch R., Behrend R., Bernasconi L., Rinner C., and Charbonnel S. (2004) Eclipsing binary asteroid 90 Antiope. Astron. Astrophys., 423, 1159–1168. Morbidelli A., Levison H. F., Tsiganis K., and Gomes R. (2005) Chaotic capture of Jupiter’s Trojan asteroids in the early solar system. Nature, 435, 462–465. Moskovitz N. A. (2012) Colors of dynamically associated asteroid pairs. Icarus, 221(1), 63–71. Mueller M., Marchis F., Emery J. P., Harris A. W., Mottola S., Hestroffer D., Berthier J., and di Martino M. (2010) Eclipsing binary Trojan asteroid Patroclus: Thermal inertia from Spitzer observations. Icarus, 205, 505–515. Naidu S. P. and Margot J. L. (2015) Near-Earth asteroid satellite spins under spin-orbit coupling. Astron. J., 149, 80. Naidu S. P., Margot J. L., Busch M. W., Taylor P. A., Nolan M. C., Howell E. S., Giorgini J. D., Benner L. A. M., Brozovic M., and Magri C. (2012) Dynamics of binary near-Earth asteroid system (35107) 1991 VH. Bull. Am. Astron. Soc., 43, #07.07. Naidu S. P., Margot J. L., Taylor P. A., Nolan M. C., Busch M. W., Benner L. A. M., Brozovic M., Giorgini J. D., Jao J. S., and Magri C. (2015) Radar imaging and characterization of binary near-Earth asteroid (185851) 2000 DP107. Astron. J., 150, 54.

Nesvorný D., Youdin A. N., and Richardson D. C. (2010) Formation of Kuiper belt binaries by gravitational collapse. Astron. J., 140, 785–793. Nolan M. C., Hine A. A., Howell E. S., Benner L. A. M., and Giorgini J. D. (2003) 2003 SS84. IAU Circular 8220. Nolan M. C., Howell E. S., Becker T. M., Magri C., Giorgini J. D., and Margot J. L. (2008) Arecibo radar observations of 2001 SN263: A near-Earth triple asteroid system. Bull. Am. Astron. Soc., 40, 432. Nolan M. C., Magri C., Howell E. S., Benner L. A. M., Giorgini J. D., Hergenrother C. W., Hudson R. S., Lauretta D. S., Margot J. L., Ostro S. J., and Scheeres D. J. (2013) Shape model and surface properties of the OSIRIS-REx target asteroid (101955) Bennu from radar and lightcurve observations. Icarus, 226, 629–640. Noll K. S., Grundy W. M., Chiang E. I., Margot J. L., and Kern S. D. (2008) Binaries in the Kuiper belt. In The Solar System Beyond Neptune (A. Barucci et al., eds.), pp. 345–363. Univ. of Arizona, Tucson. Ostro S. J., Margot J. L., Benner L. A. M., Giorgini J. D., Scheeres D. J., Fahnestock E. G., Broschart S. B., Bellerose J., Nolan M. C., Magri C., Pravec P., Scheirich P., Rose R., Jurgens R. F., De Jong E. M., and Suzuki S. (2006) Radar imaging of binary near-Earth asteroid (66391) 1999 KW4. Science, 314, 1276–1280. Perets H. B. and Naoz S. (2009) Kozai cycles, tidal friction, and the dynamical evolution of binary minor planets. Astrophys. J. Lett., 699, L17–L21. Polishook D. (2014) Spin axes and shape models of asteroid pairs: Fingerprints of YORP and a path to the density of rubble piles. Icarus, 241, 79–96. Polishook D. and Brosch N. (2009) Photometry and spin rate distribution of small-sized main belt asteroids. Icarus, 199, 319–332. Polishook D., Brosch N., and Prialnik D. (2011) Rotation periods of binary asteroids with large separations — Confronting the escaping ejecta binaries model with observations. Icarus, 212, 167–174. Polishook D., Moskovitz N., Binzel R. P., DeMeo F. E., Vokrouhlický D., Žižka J., and Oszkiewicz D. (2014a) Observations of “fresh” and weathered surfaces on asteroid pairs and their implications on the rotational-fission mechanism. Icarus, 233, 9–26. Polishook D., Moskovitz N., DeMeo F. E., and Binzel R. P. (2014b) Rotationally resolved spectroscopy of asteroid pairs: No spectral variation suggests fission is followed by settling of dust. Icarus, 243, 222–235. Pravec P. and Hahn G. (1997) Two-period lightcurve of 1994 AW1: Indication of a binary asteroid? Icarus, 127, 431–440. Pravec P. and Harris A. W. (2000) Fast and slow rotation of asteroids. Icarus, 148, 12–20. Pravec P. and Harris A. W. (2007) Binary asteroid population. 1. Angular momentum content. Icarus, 190, 250–259. Pravec P. and Vokrouhlický D. (2009) Significance analysis of asteroid pairs. Icarus, 204, 580–588. Pravec P., Wolf M., and Šarounová L. (1999) How many binaries are there among the near-Earth asteroids? In Evolution and Source Regions of Asteroids and Comets (J. Svoren et al., eds.), p. 159. IAU Colloq. 173. Pravec P., Scheirich P., Kušnirák P., Šarounová L., Mottola S., Hahn G., Brown P., Esquerdo G., Kaiser N., Krzeminski Z., Pray D. P., Warner B. D., Harris A. W., Nolan M. C., Howell E. S., Benner L. A. M., Margot J. L., Galád A., Holliday W., Hicks M. D., Krugly Y. N., Tholen D., Whiteley R., Marchis F., Degraff D. R., Grauer A., Larson S., Velichko F. P., Cooney W. R., Stephens R., Zhu J., Kirsch K., Dyvig R., Snyder L., Reddy V., Moore S., Gajdoš Š., Világi J., Masi G., Higgins D., Funkhouser G., Knight B., Slivan S., Behrend R., Grenon M., Burki G., Roy R., Demeautis C., Matter D., Waelchli N., Revaz Y., Klotz A., Rieugné M., Thierry P., Cotrez V., Brunetto L., and Kober G. (2006) Photometric survey of binary near-Earth asteroids. Icarus, 181, 63–93. Pravec P., Harris A. W., and Warner B. D. (2007) NEA rotations and binaries. In Near Earth Objects, Our Celestial Neighbors: Opportunity and Risk (A. Milani et al., eds.), pp. 167–176. IAU Symp. 236, Cambridge Univ., Cambridge. Pravec P., Harris A. W., Vokrouhlický D., Warner B. D., Kušnirák P., Hornoch K., Pray D. P., Higgins D., Oey J., Galád A., Gajdoš Š., Kornoš L., Világi J., Husárik M., Krugly Y. N., Shevchenko V.,

Margot et al.:  Asteroid Systems: Binaries, Triples, and Pairs   373 Chiorny V., Gaftonyuk N., Cooney W. R., Gross J., Terrell D., Stephens R. D., Dyvig R., Reddy V., Ries J. G., Colas F., Lecacheux J., Durkee R., Masi G., Koff R. A., and Goncalves R. (2008) Spin rate distribution of small asteroids. Icarus, 197, 497–504. Pravec P., Vokrouhlický D., Polishook D., Scheeres D. J., Harris A. W., Galád A., Vaduvescu O., Pozo F., Barr A., Longa P., Vachier F., Colas F., Pray D. P., Pollock J., Reichart D., Ivarsen K., Haislip J., Lacluyze A., Kušnirák P., Henych T., Marchis F., Macomber B., Jacobson S. A., Krugly Y. N., Sergeev A. V., and Leroy A. (2010) Formation of asteroid pairs by rotational fission. Nature, 466, 1085–1088. Pravec P., Scheirich P., Vokrouhlický D., Harris A. W., Kušnirák P., Hornoch K., Pray D. P., Higgins D., Galád A., Világi J., Gajdoš Š., Kornoš L., Oey J., Husárik M., Cooney W. R., Gross J., Terrell D., Durkee R., Pollock J., Reichart D. E., Ivarsen K., Haislip J., LaCluyze A., Krugly Y. N., Gaftonyuk N., Stephens R. D., Dyvig R., Reddy V., Chiorny V., Vaduvescu O., Longa-Peña P., Tudorica A., Warner B. D., Masi G., Brinsfield J., Gonçalves R., Brown P., Krzeminski Z., Gerashchenko O., Shevchenko V., Molotov I., and Marchis F. (2012) Binary asteroid population. 2. Anisotropic distribution of orbit poles of small, inner main-belt binaries. Icarus, 218, 125–143. Pravec P., Kusnirak P., Hornoch K., Galad A., Krugly Y. N., Chiorny V., Inasaridze R., Kvaratskhelia O., Ayvazian V., Parmonov O., Pollock J., Mottola S., Oey J., Pray D., Zizka J., Vrastil J., Molotov I., Reichart D. E., Ivarsen K. M., Haislip J. B., and LaCluyze A. (2013) (8306) Shoko. IAU Circular 9268. Rojo P. and Margot J. L. (2007) S/2007 (702) 1. Central Bureau Electronic Telegram 1016. Rossi A., Marzari F., and Scheeres D. J. (2009) Computing the effects of YORP on the spin rate distribution of the NEO population. Icarus, 202(1), 95–103. Rozitis B., Maclennan E., and Emery J. P. (2014) Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA. Nature, 512, 174–176. Rubincam D. P. (2000) Radiative spin-up and spindown of small asteroids. Icarus, 148(1), 2–11. Sánchez D. P. and Scheeres D. J. (2011) Simulating asteroid rubble piles with a self-gravitating soft-sphere distinct element method model. Astrophys. J., 727(2), 120. Sánchez D. P. and Scheeres D. J. (2014) The strength of regolith and rubble pile asteroids. Meteoritics & Planet. Sci., 49(5), 788–811. Scheeres D. J. (2002) Stability of binary asteroids. Icarus, 159, 271–283. Scheeres D. J. (2007) Rotational fission of contact binary asteroids. Icarus, 189, 370–385. Scheeres D. J. (2009a) Stability of the planar full 2-body problem. Cel. Mech. Dyn. Astron., 104, 103–128. Scheeres D. J. (2009b) Minimum energy asteroid reconfigurations and catastrophic disruptions. Planet. Space Sci., 57(2), 154–164. Scheeres D. J., Fahnestock E. G., Ostro S. J., Margot J. L., Benner L. A. M., Broschart S. B., Bellerose J., Giorgini J. D., Nolan M. C., Magri C., Pravec P., Scheirich P., Rose R., Jurgens R. F., De Jong E. M., and Suzuki S. (2006) Dynamical configuration of binary nearEarth asteroid (66391) 1999 KW4. Science, 314, 1280–1283. Scheirich P. and Pravec P. (2009) Modeling of lightcurves of binary asteroids. Icarus, 200, 531–547. Scheirich P., Pravec P., Jacobson S. A., Ďurech J., Kušnirák P., Hornoch K., Mottola S., Mommert M., Hellmich S., Pray D., Polishook D., Krugly Y. N., Inasaridze R. Y., Kvaratskhelia O. I., Ayvazian V., Slyusarev I., Pittichová J., Jehin E., Manfroid J., Gillon M., Galád A., Pollock J., Licandro J., Alí-Lagoa V., Brinsfield J., and Molotov I. E. (2015) The binary near-Earth asteroid (175706) 1996 FG3 — An observational constraint on its orbital evolution. Icarus, 245, 56–63. Shepard M. K., Margot J. L., Magri C., Nolan M. C., Schlieder J., Estes B., Bus S. J., Volquardsen E. L., Rivkin A. S., Benner L. A. M., Giorgini J. D., Ostro S. J., and Busch M. W. (2006) Radar and infrared observations of binary near-Earth asteroid 2002 CE26. Icarus, 184, 198–210. Springmann A., Taylor P. A., Howell E. S., Nolan M. C., Benner L. A. M., Brozović M., Giorgini J. D., and Margot J. L. (2014) Radar shape model of binary near-Earth asteroid (285263) 1998 QE2.

Lunar Planet. Sci. Conf. XLV, Abstract #1313. Lunar and Planetary Institute, Houston. Takahashi Y., Busch M. W., and Scheeres D. J. (2013) Spin state and moment of inertia characterization of 4179 Toutatis. Astron. J., 146, 95. Tamblyn P. M., Merline W. J., Chapman C. R., Nesvorny D., Durda D. D., Dumas C., Storrs A. D., Close L. M., and Menard F. (2004) S/2004 (17246) 1. IAU Circular 8293. Tanga P. and Delbo M. (2007) Asteroid occultations today and tomorrow: Toward the GAIA era. Astron. Astrophys., 474, 1015–1022. Taylor P. A. and Margot J. L. (2010) Tidal evolution of close binary asteroid systems. Cel. Mech. Dyn. Astron., 108, 315–338. Taylor P. A. and Margot J. L. (2011) Binary asteroid systems: Tidal end states and estimates of material properties. Icarus, 212, 661–676. Taylor P. A. and Margot J. L. (2014) Tidal end states of binary asteroid systems with a nonspherical component. Icarus, 229, 418–422. Taylor P. A., Margot J. L., Nolan M. C., Benner L. A. M., Ostro S. J., Giorgini J. D., and Magri C. (2008) The shape, mutual orbit, and tidal evolution of binary near-Earth asteroid 2004 DC. In Asteroids, Comets, Meteors Conference, Abstract #8322. Lunar and Planetary Institute, Houston. Taylor P. A., Howell E. S., Nolan M. C., and Thane A. A. (2012a) The shape and spin distributions of near-Earth asteroids observed with the Arecibo radar system. Bull. Am. Astron. Soc., 44, #302.07. Taylor P. A., Nolan M. C., and Howell E. S. (2012b) 5143 Heracles. Central Bureau Electronic Telegram 3176. Taylor P. A., Nolan M. C., Howell E. S., Benner L. A. M., Brozovic M., Giorgini J. D., Margot J. L., Busch M. W., Naidu S. P., Nugent C., Magri C., and Shepard M. K. (2012c) 2004 FG11. Central Bureau Electronic Telegram 3091. Taylor P. A., Howell E. S., Nolan M. C., Springmann A., Brozovic M., Benner L. M., Jao J. S., Giorgini J. D., Margot J., Fang J., Becker T. M., Fernandez Y. R., Vervack R. J., Pravec P., Kusnirak P., Franco L., Ferrero A., Galad A., Pray D. P., Warner B. D., and Hicks M. D. (2013) Physical characterization of binary near-Earth asteroid (153958) 2002 AM31. Bull. Am. Astron. Soc., 45, #208.08. Taylor P. A., Warner B. D., Magri C., Springmann A., Nolan M. C., Howell E. S., Miller K. J., Zambrano-Marin L. F., Richardson J. E., Hannan M., and Pravec P. (2014) The smallest binary asteroid? The discovery of equal-mass binary 1994 CJ1. Bull. Am. Astron. Soc., 46, #409.03. Tedesco E. F. (1979) Binary asteroids — Evidence for their existence from lightcurves. Science, 203, 905–907. Timerson B., Brooks J., Conard S., Dunham D. W., Herald D., Tolea A., and Marchis F. (2013) Occultation evidence for a satellite of the Trojan asteroid (911) Agamemnon. Planet. Space Sci., 87, 78–84. Vokrouhlický D. (2009) (3749) Balam: A very young multiple asteroid system. Astrophys. J. Lett., 706, L37–L40. Vokrouhlický D. and Nesvorný D. (2008) Pairs of asteroids probably of a common origin. Astron. J., 136, 280–290. Walsh K. J., Richardson D. C., and Michel P. (2008) Rotational breakup as the origin of small binary asteroids. Nature, 454, 188–191. Weidenschilling S. J. (1980) Hektor — Nature and origin of a binary asteroid. Icarus, 44, 807–809. Weidenschilling S. J., Paolicchi P., and V. Zappalà (1989) Do asteroids have satellites? In Asteroids II (R. P. Binzel et al., eds.), pp. 643– 660. Univ. of Arizona, Tucson. Weidenschilling S. J., Marzari F., Davis D. R., and Neese C. (2001) Origin of the double asteroid 90 Antiope: A continuing puzzle. Lunar Planet. Sci. XXXII, Abstract #1890. Lunar and Planetary Institute, Houston. Wolters S. D., Weissman P. R., Christou A., Duddy S. R., and Lowry S. C. (2014) Spectral similarity of unbound asteroid pairs. Mon. Not. R. Astron. Soc., 439, 3085–3093. Yeomans D. K., Antreasian P. G., Cheng A., Dunham D. W., Farquhar R. W., Gaskell R. W., Giorgini J. D., Helfrich C. E., Konopliv A. S., McAdams J. V., Miller J. K., Owen W. M. Jr., Thomas P. C., Veverka J., and Williams B. G. (1999) Estimating the mass of asteroid 433 Eros during NEAR spacecraft flyby. Science, 285, 560–561.

Walsh K. J. and Jacobson S. A. (2015) Formation and evolution of binary asteroids. In Asteroids IV (P. Michel et al., eds.), pp. 375–393. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch020.

Formation and Evolution of Binary Asteroids Kevin J. Walsh

Southwest Research Institute

Seth A. Jacobson

Observatoire de la Cote d’Azur and University of Bayreuth

Satellites of asteroids have been discovered in nearly every known small-body population, and a remarkable aspect of the known satellites is the diversity of their properties. They tell a story of vast differences in formation and evolution mechanisms that act as a function of size, distance from the Sun, and the properties of their nebular environment at the beginning of solar system history and their dynamical environment over the next 4.5 G.y. The mere existence of these systems provides a laboratory to study numerous types of physical processes acting on asteroids, and their dynamics provide a valuable probe of their physical properties otherwise possible only with spacecraft. Advances in understanding the formation and evolution of binary systems have been assisted by (1) the growing catalog of known systems, increasing from 33 to ~250 between the Merline et al. (2002) chapter in Asteroids III and now; (2) the detailed study and long-term monitoring of individual systems such as 1999 KW4 and 1996 FG3, (3) the discovery of new binary system morphologies and triple systems, (4) and the discovery of unbound systems that appear to be end-states of binary dynamical evolutionary paths. Specifically for small bodies (diameter smaller than 10 km), these observations and discoveries have motivated theoretical work finding that thermal forces can efficiently drive the rotational disruption of small asteroids. Long-term monitoring has allowed studies to constrain the system’s dynamical evolution by the combination of tides, thermal forces, and rigid-body physics. The outliers and split pairs have pushed the theoretical work to explore a wide range of evolutionary end-states.

1. INTRODUCTION There have been considerable advances in the understanding of the formation and evolution of binary systems since the Asteroids III review by Merline et al. (2002) and a subsequent comprehensive review by Richardson and Walsh (2006). The current properties of this population are detailed in the chapter in this volume by Margot et al., and this review will rely on their analysis in many places as we review work on the formation and dynamics of these systems. While the inventory of known binary systems in all populations has increased, for some populations the understanding of dynamics and formation have advanced only minimally, while in others areas research has moved rapidly. Therefore this chapter will not be evenly weighted between different populations; rather there will be substantial discussion of small asteroids and the Yarkovsky-O’KeefeRadzievskii-Paddack (YORP) effect. The scope of this chapter will be different from that of the Asteroids III chapter by Merline et al. (2002). Thanks to an excellent review of binary systems in the Kuiper belt by Noll et al. (2008) in the Solar System Beyond Neptune book, and the apparent physical, dynamical, and evolutionary differences between binary minor planets in the outer

and inner regions of the solar system, we will exclude the Kuiper belt population from our discussion here. 1.1 The Known Population of Binary Minor Planets The known population of asteroid satellites has increased from 33 to ~244 between the time of the Merline et al. (2002) Asteroids III chapter and now: 49 near-Earth, 19 Mars-crossing, and 93 main-belt asteroids (MBAs) (Pravec and Harris, 2007; Johnston, 2014). As noted in 2002, the binary systems found among near-Earth asteroids (NEAs) have only a subset of the properties of those found among the MBAs. While the orbital and collisional dynamics differ substantially in these two populations, further study has found that the variation and similarities between binary properties is most strongly dependent on size. The known binary systems among NEAs have primary component diameters exclusively less than 10 km. These small systems typically have moderately sized secondaries between 4% and 58% the size of the primary — corresponding to a mass ratio range of 6.4 × 10–5–2.0 × 10–1 assuming equal densities, are on tight orbits with typically 2.5–7.2 primary radii separation, and have a fast-spinning primary with rotation period between 2.2 and 4.5 h — all are below

375

376   Asteroids IV

Separation (a/Rp) Size Ratio (RS/Rp) Rotation Period (h)

twice the critical disruption spin period of 2.3 h for a sphere with a density of 2 g cm–3. The data for these systems is presented in Fig. 1. When lightcurve surveys probed similarsized asteroids in the main belt, they found systems with the same characteristics existing at roughly the same proportion of the population (Warner and Harris, 2007). The known binary systems among MBAs have properties that vary with their size. The small population [D < 15 km; (4492) Debussy is the largest] look similar to the various morphologies found among NEAs, including a few that appear similar to (69230) Hermes, while asteroid satellites around large asteroids [D > 25 km; (243) Ida is the smallest of this group] fall into other categories. These larger asteroid systems have by comparison much smaller satellites on much more distant orbits. While a number of the large asteroids with satellites have rotation periods lower than the average asteroids of these sizes [geometric means and 1s deviations are 7.6 ± 0.4 h vs. 12.2 ± 0.5 h (Warner et al., 2009; Pravec et al., 2012)], their rotation periods are all more than twice the critical disruption spin period of 2.3 h for a sphere with a density of 2 g cm–3, with the exception of (22) Kalliope (Pravec et al., 2012; Johnston, 2014). The techniques used to increase this database of known systems over time are important as they define any biases of our knowledge of each population. Lightcurve techniques, which are important for finding close companions around

10

1 0.8 0.6 0.4 0.2 0 100

200 km 29 km 2 km 0.2 km

10

1

0.6

1

2

3

4

5

Binary Heliocentric Perihelion (AU)

Fig. 1. The known population of binary asteroids. The three panels show (bottom) the component separation in terms of the primary radius, (middle) the size ratio of the two components, and (top) the rotation period of the primary, all plotted as a function of the system’s heliocentric orbit’s pericenter (Johnston, 2014). The size of the symbol indicates the size of the primary body, with the scale being on the left side of the bottom panel.

small asteroids, are strongly biased against finding distant companions. Meanwhile, radar can discover satellites widely separated from their primaries, but is ineffective for observing distant MBAs (Ostro et al., 2002). Direct highresolution imaging is best for finding distant companions of large MBAs (Merline et al., 2002). The size of the known population of small binary asteroid systems has increased substantially owing to the ready availability of small telescopes to survey asteroid light curves and the increased frequency of radar observations. Meanwhile, many large MBAs have been surveyed with groundbased telescopes with far fewer recent discoveries — although new adaptive optics (AO) technologies may uncover previously unseen satellites at previously studied asteroids (Marchis and Vega, 2014). 1.2. The YORP Effect The largest shift in the understanding of binary formation and evolution has come from studies of thermal forces that can affect a single body or a binary system. The reflection and reemission of solar radiation can produce a torque that changes the rotation rate and obliquity of a small body. This effect is referred to as the YORP effect, coined by Rubincam (2000), and evolved out of the work of many researchers on similar topics (Radzievskii, 1952; Paddack, 1969; Paddack and Rhee, 1975; O’Keefe, 1976). We only provide a brief summary here [see Bottke et al. (2006) and the Vokrouhlický et al. chapter in this volume for a detailed discussion of the effect]. The YORP effect has been directly detected for several asteroids through observed rotation-rate changes (Taylor et al., 2007; Lowry et al., 2007; Kaasalainen et al., 2007; Ďurech et al., 2008a,b, 2012). These rotation-rate changes match the predicted magnitude of the effect from theoretical predictions (Rubincam, 2000; Bottke et al., 2002; Vokrouhlický and Čapek, 2002; Čapek and Vokrouhlický, 2004; Rozitis and Green, 2013b). The YORP effect has a straightforward dependence on asteroid size (timescales increase with R2) and distance from the Sun (timescales increase with a2), but a complicated relationship with shape (Nesvorný and Vokrouhlický, 2007; Scheeres, 2007b). This shape dependence is characterized by a YORP coefficient, which measures the asymmetry of the body averaged about a rotation state and a heliocentric orbit. While instantaneous estimates of the YORP coefficient are available from astronomical measurements of the radial accelerations of asteroids, theoretical models of long-term averaged values are stymied by a sensitive dependence on small-scale topography (Statler, 2009; McMahon and Scheeres, 2013a; Cotto-Figueroa et al., 2015) and regolith properties (Rozitis and Green, 2012, 2013a). NEAs and MBAs with diameters below about 20 km are likely to be affected on solar system timescales (Bottke et al., 2006; Jacobson et al., 2014b). Kilometer-sized NEAs can have rotation-rate-doubling timescales shorter than their dynamical lifetime of ~10 m.y. and MBAs shorter than their collision lifetime of ~100 m.y. (Bottke et al., 2006; Jacobson, 2014).

Walsh and Jacobson:  Formation and Evolution of Binary Asteroids   377

2. BINARY SUBPOPULATIONS With over 100 systems spread between NEAs and MBAs, clear subpopulations of binary systems have emerged.

Pravec and Harris (2007) compiled the parameters for the catalog of known binary systems, including a calculation of the total angular momentum of each system. They used this data to create a classification system of the known inner solar system binary systems that is well suited for the topics in this chapter (most of these populations are clear in Figs. 1 and 2), and we update it below: Group L: Large asteroids (diameter: D > 20 km) with relatively very small satellites (secondary to primary diameter ratio: D2/D1 < 0.2). We identify 11 members. Group A: Small asteroids (D < 20 km) with relatively small satellites (0.1 > D2/D1  < 0.6) in tight mutual orbits (semimajor axis, a, less than 9 primary radii, Rp). We identify 88 members. Group B: Small asteroids (D < 20 km) with relatively large satellites (0.7 > D2/D1) in tight mutual orbits (a < 9 Rp). We identify 9 members. Group W: Small asteroids (D < 20 km) with relatively small satellites (0.2 > D2/D1  < 0.7) in wide mutual orbits (a > 9 Rp). We identify 9 members. Three outliers: Two would-be Group L members [(90) Antiope and (617) Patroclus] have the Group B characteristic of similar-sized components but are much larger than the other Group B members (D ~ 87 and 101 km, respectively), and a would-be Group W member [(4951) Iwamoto] has the Group B characteristic of similar-sized components but a much wider mutual orbit (a ~ 17 Rp). Split pairs: These are inferred systems due to dynamical models that very closely link their heliocentric orbits.

Size Ratio (RS/Rp) Primary Rotation (h) Separation (a/Rp)

The distribution of spin rates observed for bodies smaller than 40 km in size show excesses of very fast and slow rotators (Pravec and Harris, 2000; Warner and Harris, 2007), which is matched very well by a spin-distribution model that includes the YORP effect (Pravec et al., 2008; Rossi et al., 2009; Marzari et al., 2011), as suspected in the Asteroids III chapter by Pravec et al. (2002). Note that the very large asteroid lightcurve survey of Masiero et al. (2009) found a more Maxwellian distribution of spin rates among small asteroids, although it is not necessarily incompatible with YORP spin evolution. Among larger bodies, a subset of the Koronis asteroid family was found to have aligned obliquity and clustered spin rates (Slivan, 2002), which is due to the YORP effect driving them into spin-orbit resonances (Vokrouhlický et al., 2003). Among asteroid families, whose spreading is controlled by the Yarkovsky drift of family members, there are clear signatures of the YORP effect changing the obliquity of smaller bodies and in turn changing their Yarkovsky drift rates (Vokrouhlický et al., 2006; Bottke et al., 2006, 2015). Morning and evening thermal differences across regolith blocks torque the asteroid similarly in magnitude to the “normal” YORP effect. Unlike the effect described above, this “tangential” YORP effect does depend on the rotation rate, material properties of the regolith, and size distribution of the blocks (Golubov and Krugly, 2012; Golubov et al., 2014). Furthermore, the tangential YORP effect has a prograde bias unlike the normal YORP effect, which is unbiased. This additional torque may explain the difference between the predicted rotational deceleration of (25143) Itokawa (Scheeres et al., 2007; Ďurech et al., 2008b; Breiter et al., 2009) and the observed acceleration by the Japanese space mission Hayabusa (Lowry et al., 2014; Golubov et al., 2014). Similarly, a preference for spinning up may be necessary to explain the large fraction of observed binary systems, ~15% of small asteroids, which are presumed to be formed from rotational disruption caused by continued YORP spinup (discussed in detail below). As mentioned as early as the Vokrouhlický and Čapek (2002) and Bottke et al. (2002) works on the YORP effect, this effect was a very good candidate to rotationally disrupt rubble-pile asteroids. As the catalog of known systems has grown, and the subpopulations of binary systems became more defined, rotational disruption by the YORP effect emerged as the primary candidate as the dominant formation mechanism. Much of the recent research, and the discussion below, is focused on the step(s) between when the YORP effect starts increasing the angular momentum of an asteroid and when we observe the diverse catalog of systems today. Some subpopulations may emerge directly from YORPinduced rotational disruption, while others seem to demand further evolutionary forces.

10

10

1

0.1 0

2

4

6

8

10

Primary Diameter (km)

Fig. 2. The population of small binary systems, showing their (bottom) size ratio, (middle) primary rotation period, and (top) component separation, all plotted as a function of their primary diameter (Pravec and Harris, 2007; Johnston, 2014). The NEAs are black symbols and MBAs are gray symbols.

378   Asteroids IV Therefore they are not actual binaries, but are rather inferred dynamical end-states. Some pair members are binaries themselves. The principal change in this classification scheme from Pravec and Harris (2007) is the size — splitting “large” and “small” asteroids. Previously, “large” was defined to be asteroids with diameters larger than 90 km, but from more recent binary asteroid observations and YORP theory, a more natural boundary between “large” and “small” is 20 km (Pravec et al., 2012; Jacobson et al., 2014a). The boundaries between the various defining characteristics appear robust in Fig. 1, where adjustments on the order of 10% lead to the creation of no or only a few new outliers. The data in the paragraphs above come from P. Pravec’s binary catalog (Pravec et al., 2012). 2.1. Large Systems: Group L Group L members are distinct in the bottom two panels of Fig.  1, and are defined by having large primaries with D > 20 km (large symbols), and relatively smaller size ratios (D2/D1 < 0.2). These size ratios range from 0.03 to 0.2 with the lowest mean of any group: 0.08 ± 0.06 (1s) (Pravec et al., 2012). They are typically discovered with groundbased high-resolution imaging with (243) Ida a notable exception, whose satellite was discovered by the Galileo space mission (Belton and Carlson, 1994). There are 11 known systems, with the largest being (87) Sylvia (D ~ 256 km) with its satellites Romulus and Remus (Brown et al., 2001; Marchis et al., 2005) and the smallest being (243) Ida (D ~ 32 km) with its satellite Dactyl (Belton and Carlson, 1994). None of the eight asteroids larger than (87) Sylvia have been reported to have satellites, but there are likely many satellites among the asteroids with sizes near that of (243) Ida and up to that of (87) Sylvia since severe biases limit detection in that population. The rotation periods of these large asteroids range from 4.1 to 7.0 h with a geometric mean: 5.6 ± 0.8 (1s h) (Pravec et al., 2012). With the exception of (22) Kalliope, all the Group L members rotate at less than half the critical disruption rate for a spherical body with a density of 2 g cm–3 (2.3-h rotation period). As discussed in Descamps et al. (2011), the lower than typical rotation periods [asteroids of similar sizes have 12.2 ± 0.5-h rotation periods (Warner et al., 2009)] and the elongated shapes of the primaries [e.g., the bean-shape of (87) Sylvia (Marchis et al., 2005)] are suggestive of a violent disruption process, with the reaccumulation of the parent body into high-angular-momentum shape and spin configurations. However, previous numerical models of asteroid disruptions did not retain shape and spin information of the reaccumulated remnants (Durda et al., 2007), except in the case of (25143) Itokawa (Michel and Richardson, 2013), so this has not been explicitly tested. It is important to note that due to an increase of YORP timescales with surface area, YORP cannot play a role for these large systems.

2.2. Small Systems: Groups A, B, and W Systems with small primary bodies (D < 20 km) almost all fit in the subpopulation of Group A, and are found among NEAs, small MBAs and Mars crossers. Members of Group A have diameters between 0.15 and 11 km (Pravec et al., 2012). Their mutual orbits are within 2.7 and 9.0 primary radii (mean statistics: 4.8 ± 1.3 Rp), and the satellites are between 0.09 and 0.58 the size of the primary (mean statistics:  0.3 ± 0.1). Group A members have similar amounts of angular mo‑ mentum relative to their critical values (where critical is enough to break up the combined masses if in a single body). Typically this is due to the rapidly rotating primary with a period between 2.2 and 4.4 h (Margot et al., 2002; Pravec et al., 2006, 2012) — always within a factor of 2 of the critical disruption rate for a spherical body with a density of 2 g cm–3 (2.3-h rotation period). The geometric mean of their rotation periods is 2.9 ± 0.8 (1s) h compared to 7.4 ± 0.3 h for asteroids in the same size range (Pravec et al., 2012; Warner et al., 2009). While the orbit period is never synchronous with the very fast primary rotation (see Figs. 1 and 2), the synchronicity of the satellite rotation with the orbit period divides Group A into two distinct subgroups. Most belong to the synchronous satellite subgroup [~66% (Pravec et al., 2012)], although it is possible that these satellites have chaotic rotation but appear nearly synchronous (Naidu and Margot, 2015). The rest of the asteroids have satellites that are asynchronous, and have rotation periods between the primary rotation period and the orbit period (Pravec et al., 2012). There are very few well-characterized mutual orbits — only seven binary and two triple systems (Fang and Margot, 2012b). Among these, there is a trend between their measured orbital eccentricity and the synchronicity of the satellites’ rotation and orbit periods [see Fig. 1 of Fang and Margot (2012b)], where synchronous satellites are generally less eccentric. This trend is consistent with limits on the eccentricity determined by lightcurve studies (Pravec and Harris, 2007). Some asynchronous satellites on eccentric orbits may be in chaotic rotation as a result of torques on their elongated shapes [e.g., 1991 VH (Naidu and Margot, 2015)]. This could explain the high frequency (~33%) of asynchronous satellites in light of possibly rapid theoretical despinning timescales — around 102–108 yr [the tidal parameters are very uncertain (Goldreich and Sari, 2009; Jacobson and Scheeres, 2011c; Fang and Margot, 2012b)], compared to a ~107-yr dynamical lifetime in the NEA population or a ~108-yr collisional lifetime in the MBA population. The Group B members have nearly equal-sized components (mean D2/D1 is 0.88 ± 0.09; they stand out in the middle panel of Fig. 1). There is a break among the small binary population between Group A and Group B, suggesting an alternate evolutionary route (Scheeres, 2004; Jacobson and Scheeres, 2011a). These systems are in a doubly synchronous state with synchronized rotation and orbital periods (Pravec

Walsh and Jacobson:  Formation and Evolution of Binary Asteroids   379

and Harris, 2007). Orbital periods extend from 13.9 h to 49.1 h, similar to the Group A binaries [11.7 h to 58.6 h (Pravec et al., 2012)]. Nearly all this population is found in the main belt and discovered by lightcurve observations with the exception of the NEA (69230) Hermes. Hermes is decidely smaller [D ~ 0.6 km (Margot et al., personal communication)] than the next smallest confirmed Group B member [(7369) Gavrilin, D ~ 4.6 km (Pravec and Harris, 2007)], but an unconfirmed member of Group B, 1994 CJ1, is even smaller [D < 0.15 km (Taylor et al., 2014)]. The mean size D is 7 ± 3 km, and the largest, (4492) Debussy, is 12.6 km (Pravec et al., 2012). Because these systems are doubly synchronous, there are strong biases against discovery; only mutual events reveal the presence of the satellite. Furthermore, they are not typically separated enough to be detected by high-resolution imaging [the widest is (854) Frostia, with a component separation of only 36.9 km], and too distant and small for radar detection in the main belt. Thus they are possibly significantly underrepresented among known asteroid binaries. Group W binary members have very large separations (between 9 and 116 Rp), and are typically detected by the Hubble Space Telescope or AO observations from groundbased telescope observatories. The existence of some of this group in the main belt defies formation only from planetary encounters (Fang and Margot, 2012a). Like Group A and B members, they are small [mean size D is 4.8 ± 2.3 km (Pravec et al., 2012)], so radiative torques like the YORP effect are important. Like Group A members, they are rapidly rotating [geometric mean primary rotation period 3.3 ± 0.8 hr; Polishook et al., 2011)] and have moderate size ratios [mean size ratio D2/D1 is 0.4 ± 0.2 (Pravec et al., 2012)]. They follow the pattern of the asynchronous subgroup of Group A and all their satellites have rotation periods that are between that of the primary’s rotation and the satellite’s orbital period. The links between Group A and Group W are strong, and Jacobson et al. (2014b) developed an evolutionary pathway from the former to the latter. Previously, Group W members have been suspected to be debris from catastrophic collisions [dubbed escaping ejecta binary systems (EEBs) in Durda et al. (2004)], but further study consistently finds rapidly rotating primaries (Polishook et al., 2011). Many of these systems were discovered and characterized by lightcurve observations, which produce rotation periods as well as some information on shape from the amplitude of the light curve (Pravec and Harris, 2007). The lightcurve amplitude principally constrains two of the axes of the body, the long a and intermediate b axis (for principal axis rotation about its shortest c principal axis). It can constrain the other axis ratio if there are multiple observing geometries. The lightcurve amplitude can be converted to determine the a/b relationship, which roughly describes the shape of the body’s equatorial cross-section. Group A, B, and W members have a/b from 1.01 to 1.35 with an average value of 1.13 ± 0.07 (Pravec et al., 2012) — nearly circular equatorial cross-

sections. Meanwhile, the satellites of Group A, B, and W members have a/b from 1.06 to 2.5 with an average value of 1.44 ± 0.24 (Pravec et al., 2012). Thus satellites represent a much larger variety of equatorial cross-sections. Finally, some primary members of Group A and W have a characteristic spheroidal “top” shape due to a pronounced deviation from a sphere along an equatorial ridge. This radarderived shape was made famous by 1999 KW4 (Ostro et al., 2006), but has been found for many other binary and single asteroids [(29075) 1950 DA (Busch et al., 2007); 2004 DC (Taylor et al., 2008); 2008 EV 5 (Busch et al., 2011); (101955) Bennu (Nolan et al., 2013); (136617)  1994  CC (Brozović et al., 2011); (153591) 2001 SN263 (Becker et al., 2015)]. This ridge preserves a low a/b ratio, i.e., a circular equatorial cross-section, but due to the confluence of rotation and shape, this reduces the gravitational binding energy of material on the ridge (Ostro et al., 2006; Busch et al., 2011; Scheeres, 2015). At high rotation rates, the entire midlatitudes obtain high slopes and therefore disturbed loose material would naturally move toward the potential low at the equator; this material upon reaching the equator may move off the surface entirely and enter into orbit (Ostro et al., 2006; Walsh et al., 2008; Harris et al., 2009). This discovery has driven studies of asteroid reshaping focusing on the granular and cohesive properties of the surface material and possible secondary fragmentation and infall of orbital material (Ostro et al., 2006; Walsh et al., 2008; Harris et al., 2009; Holsapple, 2010; Jacobson and Scheeres, 2011a; Scheeres, 2015). 2.3. Triples The first discovered triple in the main belt was (87) Sylvia, with two small satellites orbiting its beanshaped primary body (Marchis et al., 2005). More triples have since been found, with (45) Eugenia (Marchis et al., 2007), (93) Minerva (Marchis et al., 2009), and (216) Kleopatra joining the list (Marchis et al., 2008). As discussed below, this is believed to be a natural outcome of formation via asteroid collisions. There are also a few confirmed and suspected small asteroid triple systems: (136617) 1994 CC, (153591) 2001 SN263, 2002  CE26, (3749) Balam, and (8306) Shoko (Brozović et al., 2009; Nolan et al., 2008; Shepard et al., 2006; Marchis et al., 2008; Pravec et al., 2013). All have rapidly rotating primaries (2001 SN263 is the lowest at 3.425 h) and low size ratios between the smaller two members and the primary (Balam has the largest measured satellite at 46.6% its size). For the two triple systems with known primary shapes [(136617) 1994 CC, (153591) 2001 SN263], both have the typical “top” shape described above (Brozović et al., 2011; Becker et al., 2009). Both Balam and Shoko are also members of split pairs, and the other members are 2009 BR60 and 2011 SR158, respectively (Vokrouhlický, 2009; Pravec et al., 2013). As explained in the next subsection, split pairs have a dynamical

380   Asteroids IV age that is interpreted as the rotational fission formation age. Since it is unlikely that the split pair member could have formed without significantly affecting the triple system, it is possible that all components were created at the same time from a single rotational fission event (Jacobson and Scheeres, 2011b). 2.4. Outliers Large double asteroids such as the MBA (90) Antiope and Trojan (617) Patroclus appear unique in the inner solar system. These are too large, with diameters greater than 100 km, to have gained angular momentum from thermal effects, and collision simulations do not typically create such systems (Durda et al., 2004). They have very large angular momentum content, owing to the similar-sized components (Pravec and Harris, 2007; Descamps et al., 2007; Michałowski et al., 2004). Antiope is notable as it is among the largest fragments in an asteroid family, owing to the exceptional size of Themis and its family. Meanwhile, Patroclus is a Trojan, and solar system formation models suggest that many or all of them may have been implanted from the primordial Kuiper belt region (Morbidelli et al., 2005; Nesvorný et al., 2013). Thus this system may share a common origin with the systems found in the Kuiper belt (see Noll et al., 2008; Nesvorný et al., 2010). The other outlier, (4951) Iwamoto, has a much wider mutual orbit than other Group B members, but this may be explained by orbit expansion due to the BYORP effect as discussed below (Ćuk, 2007; Jacobson and Scheeres, 2011b). 2.5. Split Pairs An important discovery related to the dynamics of binary systems is the existence of individual asteroids that are not bound to each other but instead show convincing signs of being split pairs (Vokrouhlický and Nesvorný, 2008, 2009; Pravec and Vokrouhlický, 2009; Pravec et al., 2010). These were found using dynamical studies similar to those that search for families of asteroids, but here pairs were found to be closely linked dynamically. Follow-up observations have found convincing links in both size and rotation of the pairs (Pravec et al., 2010) as well as photometric appearance (Moskovitz, 2012; Duddy et al., 2012). Their sizes and rotation make a very strong case that the smaller member of the pair was ejected during a rotational fission event, with the signature of this in the slow rotation of the larger object as a function of the size of the smaller object. The latter work finds similar photometric colors for the pairs, supporting the dynamical links between them. The dynamical models suggest that some of these pairs separated less than just ~17 k.y. ago, and hence the photometric colors have not had time to evolve significantly due to space weathering or other effects (Vokrouhlický and Nesvorný, 2009; Vokrouhlický et al., 2011).

3. FORMATION While the community and the literature largely agree on the collisional origin of the satellites of large asteroids (Group L), there is continued work on the details of how the small systems (Groups A, B, W) form and evolve. An important part of understanding the formation of the small systems concerns both the properties and variety of outliers and the possible complicated evolutionary paths for satellites or building blocks of satellites once in orbit around a rubble-pile asteroid. 3.1. Large Systems: Collision Collisions were proposed as a potentially important formation mechanism even before the discovery of Ida’s moon Dactyl in 1993. Most works focused on ejecta from a collision becoming mutually bound, becoming bound around the largest remnant, or rotational fission due to a highly oblique or glancing impact (Weidenschilling et al., 1989; Merline et al., 2002; Richardson and Walsh, 2006). Both Weidenschilling et al. (1989) and Merline et al. (2002) found that complete disruption is a far more likely outcome than collisionally induced rotational fission, and there are no observed systems that can be clearly attributed to this latter process. The study of the other collisional mechanisms first focused on cratering events on the asteroid Ida, numerically tracking the evolution of ejected debris in order to form its small satellite Dactyl (Durda, 1996; Doressoundiram et al., 1997). Studies of asteroid impacts gained a numerical boost by combining smoothed particle hydrodynamics models of asteroid fragmentation with N-body models of their gravitational reaccumulation (Michel et al., 2001, 2002, 2003, 2004; Durda et al., 2004, 2007). These models were more capable of modeling the physics of catastrophic collisions and maintaining high-resolution models of the fragments’ long-term gravitational interactions and reaccumulation. They found that the formation of satellites is a natural outcome in an asteroid disruption. Durda et al. (2004) further explored the different types of systems formed during a collision. This large suite of 161 impact simulations studied 100-km basalt targets being impacted by objects of various sizes hitting at a range of velocities and angles. In their suite of collision and reaccumulation simulations they observed, and named, the two previously proposed types of systems: escaping ejecta binary systems (EEBs) and smashed target satellites (SMATS). The SMATs generally featured small satellite(s) orbiting the reaccumulated target body. The known satellites around large (D > 10 km) MBAs share similar properties: extreme size ratio between primary and secondary and large orbital separation (where the orbital separations are too large to be explained by tides; see section 4.2). They predicted a formation rate that should roughly produce the observed number of satellites detected around very large asteroids (D > 140 km), accounting for their production due to colli-

Walsh and Jacobson:  Formation and Evolution of Binary Asteroids   381

sions, satellites destroyed by collisions, and the very early clearing of the asteroid belt. Meanwhile, they proposed that some small main-belt systems featuring two small components of roughly similar size on distant orbits are possibly EEBs. Their examples were (3749) Balam and (1509) Esclangona, and while at the time both were interesting candidates, (3749) Balam has been discovered to have a third component and a split pair and (1509) Esclangona has been found to have a very rapid rotation period similar to that found among many of the binary systems formed by the YORP effect (Warner et al., 2010). The best remaining candidates are (317) Roxane because of its slow primary rotation [8.2 h (Harris et al., 1992; Polishook et al., 2011; Jacobson et al., 2014b)] and (1717) Arlon because of its slow primary rotation [5.1 h (Cooney et al., 2006)] and high size ratio [>0.22 (Cooney et al., 2006; Jacobson et al., 2014b)]. The lack of EEBs in the known catalog is curious, as the simulations of Durda et al. (2004) formed hundreds of systems immediately after a collision, although the stability of these binaries was not thoroughly examined. This is an important avenue for future work, especially given the importance of spin-orbit coupling for binaries after rotational fission (Jacobson and Scheeres, 2011a). Tens of asteroid families are known (see the chapter by Nesvorný et al. in this volume) and there is evidence for even very recent impacts throughout the solar system (Nesvorný et al., 2002; Vokrouhlický and Nesvorný, 2009). However, small and wide binary systems are difficult to find, and small components are more susceptible to collisional grinding (see the chapter by Bottke et al. in this volume), which may explain the lack of discoveries of this type of system. Meanwhile, the known systems need substantial characterization (rotation periods, etc.) to try to distinguish between possible EEBs and end-states of YORP/ BYORP evolution processes (see below). All the numerical work to understand formation of satellites during collisions have found triple and multiple systems in their simulations. Durda et al. (2004) reported temporary multiple systems, and Leinhardt and Richardson’s (2005) reanalysis of a single simulation found 10% triples and 3% quadruple systems that lasted the length of the simulations (days). While triples have now been found among some large systems, longer-term dynamical simulations of their formation and evolution following large impacts would be needed to quantify the match between observations and models. Catastrophic impact modeling has generally relied on very similar collision scenarios (impact speeds and angles, etc.) to model both the formation of satellites and asteroid families (Michel et al., 2001, 2003; Durda et al., 2004, 2007). While asteroid families are strictly correlated with collisions, it does not mean that the presence of a family demands satellites, as not every collision forms satellites, and small satellites themselves are susceptible to collisional evolution/destruction on timescales shorter than the age of many observed asteroid families (Durda et al., 2004).

3.2. Small Systems: Rotational Disruption Even before the discovery of small binary systems, the doublet craters found on the terrestrial planets (Melosh and Stansberry, 1991; Bottke and Melosh, 1996) and crater chains on the Moon (see Richardson et al., 1998) suggested that there were mechanisms to disrupt small asteroids. The demonstration provided by Comet Shoemaker-Levy 9 and its tidal disruption at Jupiter further instigated models of “rubblepile” interiors and their tidal disruptions while encountering planetary bodies (Asphaug and Benz, 1996; Richardson et al., 1998). Bottke and Melosh (1996) suggested that searches for asteroid satellites “place emphasis on kilometer-sized Earth-crossing asteroids with short-rotation periods,” and lightcurve surveys found many interesting targets in this sample. Observations of multi-frequency light curves and possible eclipse/occultation events became common, and gave very strong indications of possible satellites (Pravec and Hahn, 1997; Pravec et al., 1998, 2000; Mottola and Lahulla, 2000). The radar imaging of NEA 2000 DP107 confirmed that the lightcurve observations were detecting actual satellites (Margot et al., 2002). Combining all possible detections, Margot et al. (2002) suggested that up to 16% of the population were binaries and that rotational disruption was a primary culprit (Pravec et al., 1999; Margot et al., 2002; Pravec and Harris, 2007). Rubble-pile asteroids encountering Earth were studied with a granular dynamics code by Richardson et al. (1998) and again by Walsh and Richardson (2006). While both groups found that binaries are at least initially formed following some disruptive tidal event, Walsh and Richardson (2006) found that the primary bodies were typically elongated, the secondaries were on very eccentric orbits, and the primary rotated with a period around 3.5–6 h, rather than the nearcritical 2–4-h periods. Walsh and Richardson (2008) took the resulting simulation outcomes and built a Monte Carlo model including the expected time between planetary encounters, expected encounter outcomes, nominal tidal evolution of orbits and primary spin, and observed asteroid shape and spin characteristics. They found that the produced systems are not expected to survive very long, owing to the large semimajor axes and high eccentricities. These works, and the discovery of small binary systems in the main belt (Warner and Harris, 2007) where there is no planetary body to tidally disrupt an asteroid, strongly suggested that tidal disruption is not a primary mechanism. Tidal disruption of NEAs could still account for a small subset of the population, although it is not clear if the elongated primaries and eccentric secondaries could survive long enough to be observed (Walsh and Richardson, 2008). A more ubiquitous method for rotational disruption of small asteroids is the YORP effect. Rubincam (2000) proposed that the YORP effect could spin centimeter-sized objects so fast that they would eventually burst. Vokrouhlický and Čapek (2002) pointed out that this effect will likely drive asteroids to 0°/180° obliquity end-states and then in many cases of

382   Asteroids IV continued spinup could drive them to “rotational fission.” YORP was connected directly with binary formation in Asteroids III (Bottke et al., 2002), where it was proposed as a possible means for forming small binary asteroids and inducing reshaping. Ostro et al. (2006) observed NEA 1999 KW4 with radar and produced an incredibly detailed shape model of the primary, while Scheeres et al. (2006) analyzed the dynamics of the system (see Fahnestock and Scheeres, 2008). This system was similar to previously discovered NEA systems — it featured a rapidly rotating primary (essentially at critical rotation rate) and a small secondary on a close orbit just beyond its Roche limit. However, owing to the exceptional resolution of these radar observations, the derived shape model was found to have a bulging equatorial ridge (see Fig. 3). As part of the dynamical analysis of the system, Scheeres et al. (2006) hypothesized that the system disrupted and shed mass due to tidal torques from a planetary flyby or the YORP effect. The primary would have evolved to build the ridge and reach the very rapid rotation rate due to the infall of material that was not accreted/incorporated in the satellite. Starting with the Scheeres et al. (2006) work on the state of the 1999 KW4 system, and their suggestion that the equatorial ridge could have been formed by the infall of material, this started one of two tracks of thought about the ridge and its formation that were followed up in a number of works (Scheeres, 2007b; Jacobson and Scheeres, 2011a). These works posited that the mass loss was a more singular catastrophic event — a fission event — and that later processing of this lost mass accounts for the equatorial ridge and other widely observed system properties. At the other end of the discussion, Walsh et al. (2008) modeled YORP-spinup of rubble piles made of thousands of constituent particles and

Fig. 3. The radar-derived shape model of 1999 KW4. The shading indicates local gravitational slopes, with the majority being near 30–40 and the lighter and darker shades at the equator and poles near zero (Ostro et al., 2006; Scheeres et al., 2006).

posited that the equatorial ridge was caused by reshaping of the primary rubble-pile asteroid as a result of spinup and consequent mass loss. In this model the satellite was slowly built in orbit by repeated mass-shedding events. These models in some ways were working from opposite ends of a spectrum of model resolution and techniques. The Scheeres (2007b) work focused on the rigid body dynamics of separated contact binaries, and Jacobson and Scheeres (2011a) extended this to consider what might happen if the ejected fragment itself was allowed to fragment once in orbit, which is critical to prevent rapid ejection of the fragment, and also whether the infall of some of the material could explain the ubiquitous top-shape primaries. Meanwhile, Walsh et al. (2008, 2012) started with model asteroids constructed of thousands of individual solid spherical particles interacting through their gravity and through mutual collisions. While the gravity and collisions of the particles are efficiently modeled throughout the simulations, the timescales for spinup were necessarily shortened for computational reasons and the structure of the body consisted of different, but very simple, size distributions of spherical particles. A valuable test of these different ideas may occur when NASA’s Origins Spectral Interpretation Resource Identification and Security-Regolith Explorer (OSIRIS-REx) space mission reaches asteroid (101955) Bennu, which shows signs of having an equatorial ridge (Nolan et al., 2013; Lauretta et al., 2014). All scenarios suffer confusion from new studies of the sensitivity of the YORP effect to very small changes in an asteroid’s shape. Model asteroids were generated, inclusive of small features such as boulders and small craters, and when YORP evolutions were calculated it was found that very small changes on the surface of a small body can dramatically change its YORP behavior (Statler, 2009; CottoFigueroa et al., 2015). The changes could be so dramatic that nearly any reshaping of a body during its YORP spinup could essentially result in a completely different YORP state. Essentially each shape change, no matter the scale, results in a coin-flip outcome to determine if the body continues spinning up or reverses and spins down. The population of asteroids with secondaries is ~15% (Pravec and Harris, 2007), and so the rotational disruption mechanism appears to be quite efficient. If each movement on the surface of an asteroid results in a coin-flip to determine spinup or spindown, then seemingly bodies would never spin up enough to rotationally disrupt. This perplexing issue may demand some underlying tendency for small bodies to “spin up” by the YORP effect. It is possible that the YORP effect could actually induce preferential spinup for even a symmetrically shaped asteroid, following the “tangential YORP effect,” which may play a big role in understanding these issues (Golubov and Krugly, 2012; Golubov et al., 2014). 3.3. Split Pairs The rotational fission hypothesis states that at a critical spin rate an asteroid’s components enter into orbit about

Walsh and Jacobson:  Formation and Evolution of Binary Asteroids   383

each other from a state of resting on each other (Jacobson and Scheeres, 2011a). The spin energy of the asteroid at this critical spin and any released binding energy is the free energy available to disrupt the asteroid system. Therefore, there is a direct energy and angular momentum relationship between the spin states of the newly formed components and the mutual orbit. From these considerations and some simple assumptions, this theory predicts a relationship between the sizes of the two components and the rotation rate of the larger component. Observations of split pairs directly confirm this theoretical prediction (Pravec et al., 2010). This is powerful evidence that the rotational fission hypothesis is correct for split pairs. Further observations of split pairs confirm that each member is a good spectroscopic match to the other (Moskovitz, 2012; Duddy et al., 2012; Polishook et al., 2014a). Interesting observations that there is no significant longitudinal spectroscopic variations and that the spin axes between members are identical are interesting twists that future theory must account for (Polishook et al., 2014a,b). 4. Evolution of Binary Systems There are a number of different binary evolution mechanisms. Classical solid body tides are long studied and binary asteroids provide useful test cases. Meanwhile, thermal effects can affect a single body in the system or the pair of bodies. A single body having its spin state changed by a thermal effect can possibly reshape due to its angular momentum increase. Binaries on near-Earth orbits can encounter the terrestrial planets, which can destabilize or otherwise alter a system’s mutual orbit, while also distorting or disrupting either component. Finally, an impact can destroy a satellite, remove it from a system, or simply perturb its orbit. The small number of known large systems are unaffected by many of these evolutionary mechanisms: Their satellites are typically too distant for tides and their sizes too large for thermal effects, and there are no planets in the main belt to perturb them. Meanwhile, the known small systems may be affected by multiple effects simultaneously in ways that are difficult to disentangle. Therefore, the primary set of data used to understand evolutionary effects are the large number of small systems — Groups A, B, and W. The majority of all systems (Group A) look quite similar — they have rapidly rotating primaries, their secondaries just beyond the nominal Roche limit at ~2.5 a/Rp (where a is the semimajor axis and Rp is the primary radius), and they are between 9% and 58% the size of the primary (typically less than 2–3% of the primary mass). The outliers are a minority, but they and the split pairs point to important evolutionary end-states of the small systems. 4.1. Binary YORP The theory of binary YORP (BYORP) is a direct extension of the Yarkovsky and YORP effects; instead of modifying the spin state of an asteroid, the BYORP effect modifies the mutual orbit of a double asteroid system in a spin-orbit

resonance, typically the synchronous 1:1 spin-orbit resonance (Ćuk and Burns, 2005). Similar to YORP, the back-reaction force from the photon causes a torque, but here the lever arm connects the center of mass of the binary system to the emitting surface element. The back-reaction torques the satellite about this mass center, changing the mutual orbit. Unlike the YORP effect, the relative position and orientation of the emitting surface element can change the mutual orbit’s semimajor axis a with respect to the center of mass of the binary system (unlike a rigidly rotating asteroid in the case of the YORP effect), so only binary members that occupy a spin-orbit resonance have nonzero cumulative BYORP effects; the torques on all binary members outside of spin-orbit resonances cancel out over time. Ćuk and Burns (2005) recognized that this effect could be significant for small asteroids found throughout the binary asteroid population. Most discovered binaries in the nearEarth and main-belt populations have small (radius < 10 km) secondaries, which are tidally locked in a synchronous spinorbit resonance (Richardson and Walsh, 2006; Pravec et al., 2006). From these characteristics and shape estimates, simple estimates scaled from the YORP effect concluded that the BYORP effect is able to significantly modify an orbit in as little as ~105 yr (Ćuk and Burns, 2005; Ćuk, 2007; Goldreich and Sari, 2009). Secular averaging theory has agreed with these short timescale estimates (McMahon and Scheeres, 2010b,a; Steinberg and Sari, 2011). Assuming the smaller secondary is synchronously rotating and expanding the solution to only first order in eccentricity, the secular evolution of the mutual orbit’s semimajor axis a, measured in primary radii Rp, and eccentricity e are (equations (93) and (94) from McMahon and Scheeres, 2010a, with redefined variables) 3/ 2 1+ q da 3H  Bs a = 2 1/ 3 dt 2πrw d R p q



(1a)

3H B a1/ 2 e 1 + q de e da =−  s =− 2 1/ 3 4a dt dt 8πrw d R p q



(1b)

where q is the mass ratio between the secondary and the primary, r is the density of both asteroids assumed to be the same since they are likely to be of common origin, wd = 4πrG 3 is the critical rotational disruption rate for a sphere of density r, G is the gravitational constant, H⊙ = F a 2 1 − e2 is a heliocentric orbit factor, F⊙ is the solar radiation constant, and a⊙ and e⊙ are the heliocentric semimajor axis and eccentricity of the binary asteroid system. Finally, Bs is the BYORP coefficient of the secondary. As defined here, Bs does not depend on the size of the secondary, only its shape relative to its orientation (see McMahon and Scheeres, 2010a). The BYORP coefficient can be positive corresponding to outward expansion of the mutual orbit or negative corresponding to inward shrinking. (66391) 1999 KW4 has the only existing detailed secondary shape model (Ostro et al., 2006), and it has an

(

)

384   Asteroids IV estimated magnitude of |Bs| ~ 0.04 (McMahon and Scheeres, 2010a, 2012b). Estimates of Bs from other asteroid shape models and Gaussian ellipsoids suggest that the BYORP coefficients are typically |B s| < 0.05 (McMahon and Scheeres, 2012a). Scaling the (66391) 1999 KW4 estimate to other binary asteroid systems, Pravec and Scheirich (2010) calculated mutual orbit evolution predictions for seven observable binaries: (7088) Ishtar, (65803) Didymos, (66063) 1998 RO1, (88710) 2001 SL9, (137170) 1999 HF1, (175706) 1996 FG3, and (185851) 2000 DP107. First results regarding (175706) 1996 FG3 have been reported in Scheirich et al. (2015) and are discussed below. Close observations of these candidates over the next few years will test the nascent BYORP theories. As noticed initially by Ćuk and Burns (2005), outward BYORP expansion of the mutual orbit damps the eccentricity. This potentially provides a disruption pathway for binary asteroids. Their orbit can expand until the semimajor axis reaches their Hill radii since outward expansion is a runaway process. If so, then these binaries would become unbound by three-body interactions with the Sun and create asteroid pairs. Unlike most observed asteroid pairs, these would not follow the rotation-size ratio relationship set by immediate disruption after rotational fission (Scheeres, 2004; Pravec et al., 2010). No such pairs have yet been identified; however, the expected ratio between pairs formed from fission to those formed from BYORP expansion is high (Jacobson and Scheeres, 2011a). BYORP expansion of the orbit of the secondary will only continue if the rotation of the secondary remains synchronous with its orbital period. However, a numerical experiment by Ćuk and Nesvorný (2010) found that the eccentricity may actually increase. Eccentricity growth induces chaotic rotation that is then halted by the BYORP effect, and if the orientation of the secondary is reversed, then the mutual orbit will contract. Ćuk and Nesvorný (2010) rule out the role of the evection resonance for responsibility of this eccentricity increase and attributes it to spin-orbit coupling. This disagrees with evolution resulting from the force decomposition and averaged equations (Ćuk and Burns, 2005; Goldreich and Sari, 2009; McMahon and Scheeres, 2010b; Steinberg and Sari, 2011). Future work directly comparing long-term evolution of a Ćuk and Nesvorný (2010)-type model and the secular evolution equations is needed to determine resolutely the consequences of outward BYORP evolution on eccentricity. Using the secular evolution equations and including mutual tides, Jacobson et al. (2014b) found that outward expansion can be interrupted by an adiabatic invariance between the mutual semimajor axis and libration state of the secondary. As the mutual orbit expands, a small libration can grow until the rotation of the secondary desynchronizes and begins to circulate. This has been proposed as the mechanism by which to explain the small known population of wide binary asteroid systems that are found among NEAs and in the main belt, as this process can leave secondaries stranded so far from the primary to make tidal synchronization timescales very long (Jacobson et al., 2014b). As observations continue

to be made of wide and possibly expanding binaries such as (185851) 2000 DP107, the theories regarding expansion due to the BYORP effect will continue to be tested. The BYORP effect can also shrink orbits and simultaneously increase eccentricity (Ćuk and Burns, 2005; Goldreich and Sari, 2009; McMahon and Scheeres, 2010b; Steinberg and Sari, 2011). This will be discussed after describing tides, which are important when considering very tight binary asteroid systems. 4.2. Tides The evolutionary consequences of mutual body tides have been considered for the evolution of asteroids since the discovery of the first asteroid satellite, Dactyl, about (243) Ida (Petit et al., 1997; Hurford and Greenberg, 2000). These body tides are the result of the asteroid’s mass distribution chasing an ever-changing equilibrium figure determined by the asteroid’s spin state and the gravitational potentials of both binary members. Since the relaxation toward this figure is dissipative, energy is lost in the form of heat and removed from the rotation state of the asteroid. The difference in potential between the delayed figure and the theoretical equilibrium figure is referred to as the tidal bulge. This tidal bulge torques the mutual orbit, ensuring conservation of angular momentum within the asteroid system. Unlike lunar tides on Earth, where most of the energy is dissipated at the ocean-seabed interface and in the deep ocean itself (Taylor, 1920; Jeffreys, 1921; Egbert and Ray, 2000), the mutual tides between asteroids do not dissipate energy along an interface or in a fluid layer but rather throughout the solid body. However, new results indicate that tidal dissipation in rubble piles may be much higher (Scheirich et al., 2015) than previously expected (Goldreich and Sari, 2009), so where and how tidal energy is dissipated must be examined much more thoroughly in the future. Under most proposed formation circumstances and observed in nearly all small systems, except for those with synchronous rotations, asteroids rotate at rates greater than their mutual orbit mean motion (Pravec et al., 2006). In this case, the tidal bulge lags behind the line connecting the mass centers of the binary members, and the binary’s primary is rotationally decelerated. In this case, the mutual orbit expands, similar to the Earth-Moon system. Alternatively, the tidal bulge precedes the line connecting the two asteroids, and the binary’s primary is rotationally accelerated. In this case, the mutual orbit shrinks, similar to the Mars-Phobos system. No observed binary asteroids currently occupy this state. A third tidal state also exists: Librational tides can oscillate through tidally locked binary members. This tide is responsible for removing libration from synchronous satellites. The tidal bulge oscillates from the trailing to leading hemisphere as the secondary librates, so the torque on the orbit cancels out and the orbit does not evolve. Formally deriving an explicit set of equations to describe these torques has been a focus of research for over a century (Darwin, 1879). Historically, most theoretical descriptions

Walsh and Jacobson:  Formation and Evolution of Binary Asteroids   385

of tides have fallen into two camps, split by their assumptions regarding the relationship between the tidal bulge and the line connecting the mass centers of the two asteroids: (1) Some assume a constant lag angle (Goldreich, 1963; Kaula, 1964; MacDonald, 1964; Goldreich and Soter, 1966; Taylor and Margot, 2010), and (2) some assume a constant lag time (Singer, 1968; Mignard, 1979, 1980; Hut, 1980, 1981). Neither relationship is expected to accurately reflect potential asteroid rheology (Efroimsky and Williams, 2009; Greenberg, 2009; Goldreich and Sari, 2009; Jacobson and Scheeres, 2011c; Ferraz-Mello, 2013). Although the constant lag angle is believed to better represent circulating tides through solid bodies, Greenberg (2009) describes its shortcomings in vivid starkness. For the sake of this review, we will consider using the theory only for nearly circular orbits and will be careful to state when we feel that this theory may not be adequate. If systems have a nonnegligible eccentricity, the tidal despinning calculated by the first-order theory will be a lower bound, but the effects on the orbital evolution, particularly the eccentricity, are more difficult to determine. For instance, the theories in Goldreich (1963) and Hut (1981) give different predictions regarding the orbital evolution of asynchronous asteroids depending on orbital parameters. Constant lag angle tidal theory assumes that the tidal bulge raised by an orbiting companion lags the line connecting the bodies’ centers by a constant angle e, which is related to a tidal dissipation number Q via Q = 1/2e. The tidal dissipation number quantifies the amount of energy dissipated each tidal frequency cycle over the maximum energy stored in the tidal distortion [for further discussion, see Goldreich and Soter (1966), Greenberg (2009), and Efroimsky and Williams (2009)]. This theory is appropriate for determining the tidal torque on a circulating body, but as the body approaches synchronization and when the body is librating, this theory likely overestimates the actual tidal torque. The circulating tidal torque on a spherical asteroid with radius R from a perturbing binary member with a mass ratio of q is



ΓC =

2πk 2 w d2rR 5 q 2  w − n   | w − n |  Qa 6

(2)

where the semimajor axis a is measured in asteroid radii R, (w–n/|w–n|) indicates the direction of the torque given the spin rate of the asteroid w and the mean motion of the mutual orbit n, and k2 is the second-order Love number of the asteroid. The potential Love number k quantifies the additional gravitational potential produced by the tidal bulge over the perturbing potential. In other words, it captures how much the tidal bulge responds to the deforming potential. We are currently considering only the lowest-order relevant surface harmonic, namely the second [for further discussion of the perturbing potential and its expansion, see Ferraz-Mello et al. (2008)]. A perfectly rigid asteroid would have a tidal Love number of 0, whereas a inviscid fluid would have a Love number of 3/2 according to its definition (Goldreich and Sari, 2009).

This tidal torque is most applicable to the primary, which is often rapidly rotating compared to the mean motion of the mutual orbit (Pravec et al., 2006; Richardson and Walsh, 2006). In the most common case, the secondary is tidally locked and so does not contribute to the evolution of the semimajor axis of the mutual orbit. Given the torque above, the semimajor axis a, measured in primary radii Rp, and the primary spin rate wp evolution are (Goldreich and Sari, 2009)



da 3k 2, p w d q 1 + q = dt Q p a11/ 2 dw p



dt

=−

(3a)

15k 2, p w d2 q 2 4Q p a 6

(3b)

where k2,p and Qp are the tidal Love and dissipation numbers for the primary [for higher-order expansions, see Taylor and Margot (2010)]. The ratio of tidal despinning timescales for the primary and secondary are



k 2, p Qs 2 ts = q t p k 2 ,s Q p

(4)

where k2,s and Qs are the tidal Love and dissipation numbers for the secondary. Since the mass ratio is often on the order of q ~ 0.01–0.1, it is immediately clear that the secondary tidally locks first. It is possible that the ratio of tidal parameters could counteract this; however, both the tidal parameters derived from a modified continuum tidal theory (Goldreich and Sari, 2009) and the observed parameters from a hypothetical tidal-BYORP equilibrium (Jacobson and Scheeres, 2011c) are consistent with faster tidal synchronization of the secondary, ts/tp ∝ q3/2 and ts/tp ∝ q5/2, respectively. When the mass ratio is nearly equal, tides drive both bodies to synchronization in nearly the same timescale (Jacobson and Scheeres, 2011a). From this configuration, where both members are tidally locked, the BYORP effect can expand or shrink the mutual orbit to great affect. Acting independently on each body, in addition to the YORP effect acting on each component, BYORP can effectively transfer angular momentum to the orbit (Taylor and Margot, 2014). This could lead to rapid separation (Jacobson and Scheeres, 2011a), inward drift leading to unstable configurations (Bellerose and Scheeres, 2008; Scheeres, 2009; Taylor and Margot, 2014), or gentle collisions and contact binaries (Scheeres, 2007a; Jacobson and Scheeres, 2011a). Although circulating tides drive the secondary to synchronous rotation, the secondary still has significant tidal dissipation occurring within it due to librational tides. The circulating theory is inappropriate for libration since according to this theory the tidal bulge instantaneously moves across the body. Mignard (1979) developed an alternative approach that assumes that the phase lag is proportional to the frequency of the tidal forcing. Here l0 is the characteristic spin rate at which the body transitions from a circulation torque to the

386   Asteroids IV libration torque or vice versa [where l0 is related to tidal lag time Dt by 2Q|l0|Dt = 1 (Mignard, 1979)]. In the tidal torque, l0 takes the place of |w–n| in the denominator of equation (2). The libration torque is not only appropriate when the system is librating, but also when the system is circulating slowly compared to l0. However, this torque becomes inappropriate as the body begins to circulate quickly since the tidal bulge could wrap about the body. These two theories are actually one and the same if l = w –n when w –n > l0 and if l = l0 when w –n ≤ l0, in which case l replaces l0 in equation (2). This approximate tidal torque can handle both libration and circulation for nearly circular and non-inclined systems (Jacobson and Scheeres, 2011a). 4.3. BYORP Effect and Tides The leading hypothesized formation mechanism for Group A binary asteroids is by rotational disruption, which is observed to produce a rapidly rotating primary and a secondary that is quickly tidally locked — the secondary is even predicted to begin rotating more slowly (Scheeres, 2007a; Walsh et al., 2008; Jacobson and Scheeres, 2011a). When considering this configuration for nearly circular orbits, circulating tides on the primary and librational tides on the secondary contribute to the change in eccentricity of the mutual orbit. Since the libration of the secondary and the mutual eccentricity are coupled (McMahon and Scheeres, 2013b), the librational tides on the secondary are often broken into direct librational and radial components (Murray and Dermott, 2000). The sum effect of all these tides on the mutual eccentricity is that the eccentricity is always being damped due to the dominance of the librational tides on the secondary, for a wide range of tidal parameters considered (Goldreich and Sari, 2009; Jacobson and Scheeres, 2011c). In the singly synchronous configuration — rapidly rotating primary and tidally locked secondary — the mutual orbit of a small binary asteroid can evolve according to both the BYORP effect and tides. While tides in synchronous binary asteroids systems act only to expand the semimajor axis and decrease eccentricity, the BYORP effect can expand or shrink the semimajor axis depending on the shape and orientation of the secondary. In the case of BYORP effect driven expansion, both processes are growing the semimajor axis and both are reducing the eccentricity. As discussed above, this process can lead to disruption at the Hill radius or desynchronization of the secondary, which can strand the mutual orbit at a wide semimajor axis. Alternatively, the BYORP effect and tides can act in opposite directions. These effects drive the semimajor axis to an equilibrium location  2πk 2, p w d2rR 2p q 4 / 3  a =  Bs H  Q p  

1/ 7

*



(5)

This semimajor axis location depends directly on the tidal parameters and the BYORP coefficient. If this location is dis-

tant, then secondaries could be rapidly lost (Ćuk and Burns, 2005; Ćuk, 2007; Goldreich and Sari, 2009; McMahon and Scheeres, 2010a), and the binary formation rate would have to be significant to account for the observed ~15% fraction (Ćuk, 2007). Alternatively, the proposed equilibrium of tides and BYORP prevents this rapid destruction of systems and no longer requires binary formation rates to match potentially very fast BYORP disruption rates (Jacobson et al., 2014c). A prediction for occupying this equilibrium is that the semimajor axis should not be changing significantly. While measured changes in the semimajor axis or orbital period require precision that is currently unobtainable, a change in the semimajor axis does lead to a quadratic drift in the mean anomaly (McMahon and Scheeres, 2010a), which can be measured very precisely through the timing of mutual events in photometric light curves. A large survey has been undertaken to examine whether these drifts occur (Scheirich and Pravec, 2009). The first results from this survey find no drift in mean anomaly for NEA binary (175706) 1996 FG3 (Scheirich et al., 2015), which may point to this equilibrium. If the singly synchronous binary population occupies this equilibrium, then we are able to learn about the internal properties of asteroids only from remote sensing measurements (Jacobson and Scheeres, 2011c); however, the tidal and BYORP coefficients are degenerate Bs Q p

k 2, p

=

2πw d2rR 2p q 4 / 3 H a 7

(6)

This parameter relationship is shown in Fig. 4 along with a fit to the data: BsQp/k2,p = 6 × 103 (Rp/1 km). As discussed above, estimates for the BYORP coefficient are around Bs ~ 0.01 (Ćuk and Burns, 2005; Goldreich and Sari, 2009; McMahon and Scheeres, 2010a, 2012a). From the data, the tidal parameters then follow: Q/k2 = 6 × 105 (Rp/1 km), very different than the Q/k2  > 107 (1 km/Rp) predicted from a modification of the continuum theory for rubble-pile asteroids (Goldreich and Sari, 2009). Taylor and Margot (2011) predict tidal properties by assuming a tidal evolutionary path from twice the primary radius to the current orbital separation in under a certain timescale. For (175706) 1996 FG3, they estimate that Q/k2 ≈ 2.7 × 107 in order to migrate from 2 to 3.6 primary radii in 10 m.y. Using the new estimate of the tidal parameters from Scheirich et al. (2015), Q/k ≈ 2.4 × 105 and this same tidal migration (assuming no influence from the BYORP effect) could take place in 5.6 × 104 yr. This much higher rate of tidal dissipation or much larger tidal Love number can only be consistent with a tidal rheology very different than that for terrestrial planets and moons. Furthermore, the equations that convert the tidal Love number to a rigidity or elastic modulus, often denoted μ, assume a continuum model that may not apply for this rubble-pile tidal rheology. So far, the discussed tidal theory assumes that all the rotation axes are aligned and that the mutual orbit is nearly circular. If this is not the case, then the tidal bulge can have a

Walsh and Jacobson:  Formation and Evolution of Binary Asteroids   387

BSQp/k2,p

105 104 1000 100 10 1

0.2

0.5

1.0

2.0

5.0

Primary Radius, Rp (km) Fig. 4. BQ/kp were calculated directly from observed quantities according to equation (6) for each known synchronous binary, and plotted as a function of primary radius Rp along with 1s uncertainties. The large circle in the center highlights the binary (175706) 1996 FG3. All the data is from http://www. asu.cas.cz/asteroid/binastdata.htm, maintained by P. Pravec according to Pravec et al. (2006). The solid line is a fitted model to the data: BsQp/k2,p = 6 × 103 Rp. The dashed lines indicate the range of predicted scatter in the model due to the BYORP coefficient (possibly 10× stronger or 100× weaker). Reproduced with some updated binary parameters from Jacobson and Scheeres (2011c).

significant effect on the mutual orbit and rotation state of the asteroid. The differences between the different tidal theories become more extreme, and they differ by more than a matter of magnitudes, but also of direction. This is an ongoing area of active research, with new tidal theories being developed to eventually accurately describe asteroid lithologies (Goldreich and Sari, 2009; Efroimsky and Williams, 2009). A separate tidal effect relies on “tidal saltation,” or the physical lofting of material off the surface of the primary. The very rapid, near critical, rotation of the primary permits the very small perturbations of the secondary to loft debris off the primary’s equator (Fahnestock and Scheeres, 2009; Harris et al., 2009), and during flight angular momentum is transfered from the debris to the orbit of the secondary. This expands the orbit of the secondary at rates that could potentially compete with tidal foces. Given the direct physical alteration of the primary by the repeated lofting and landing of particles on the equator, this theory provides an interesting observational test for future observations of equatorial ridges on NEAs. 4.4. Asteroid Reshaping If the asteroids were simply fluids, then they would follow permissible shape and spin configurations that have been studied by many, including Newton, Maclaurin, Jacobi, Poincaré, Roche, and Chandresekhar. Observations of asteroids clearly show that they are not fluids, and their distribution of shape and spin configurations agree (Pravec et al., 2002). Observations also suggest that they are not simply monolithic rocks. Rather, the population of small asteroids (D < 10 km) are thought to be primarily gravitational aggregates consisting

of small bodies held together almost strictly by their selfgravity. Numerous observations and models contribute to this line of thought, including not only their spin and shape distributions, but also observations of crater chains on the Moon, the breakup of Comet Shoemaker-Levy  9, the very large observed impact crater on the large primitive asteroid (253) Mathilde, and, of course, the striking images of the small asteroid (25143) Itokawa. These arguments were last summarized in Asteroids III by Richardson et al. (2002), and the chapter by Scheeres et al. in this volume reviews our general knowledge of asteroid interiors. Efforts to understand asteroid shape and spin configurations borrow cohesionless elastic-plastic yield criteria from soil mechanics (Holsapple, 2001, 2004; Sharma, 2009). These formulations calculate envelopes of allowable spin and shape configurations as a function of the material properties — typically relying on an angle of friction as the critical parameter. Neither cohesion nor tensile strength is required to explain the shapes and spins of nearly all large (D > 200 m) observed asteroids (Holsapple, 2001, 2004), although the spins and shapes do not rule out any material strength either. What about cohesion? Multiple recalculations of allowable spin rates as a function of cohesive forces find that even very small amounts of cohesion can dramatically change the allowable spin rates for a body. Even amounts as low as 100 Pa allow for kilometer-sized asteroids to rotate much faster than the observed 2.3–4-h limit (Holsapple, 2007; Sánchez and Scheeres, 2014). Only a single body is observed to be larger than 200 m and rotate faster than 2.3–4 h (Warner et al., 2009). Rozitis et al. (2014) combined measurements of Yarkovsky drift and thermal properties to estimate the density of a kilometer-sized NEA, 1950 DA. Measurements of this asteroid’s spin rate find that it is rotating faster than what simply gravity and friction would allow, and thus it must have nonzero cohesive strength to prevent disruption. As pointed out by Holsapple (2007), very small amounts of cohesive strength are needed to allow bodies to rotate faster than the classical spin limits. Hirabayashi et al. (2014) estimated between 40 and 210 Pa for the cohesive strength of mainbelt comet P/2013 R3, and Rozitis et al. (2014) estimated only 64+−12 20 Pa of cohesive strength of (29075) 1950 DA. This amount of cohesion is in line with the predictions for cohesion produced by fine grain “bonding” larger constituent pieces of an asteroid (Scheeres et al., 2010; Sánchez and Scheeres, 2014), and would be similar to what is found in weak lunar regolith (see the chapter by Scheeres et al. in this volume). The exciting radar-produced shape model of 1999 KW4 showed that the asteroid shape held more information than could be contained in a simple triaxial ellipsoid model (Ostro et al., 2006). The equatorial bulge seen in those radar shape models became ubiquitous among primaries of other rapidly rotating asteroids (see the chapter by Margot et al. in this volume). A simple rigid ellipsoid that increases its angular momentum will drive surface material toward its equator, and this happens before the material would simply become

388   Asteroids IV unbound (Guibout and Scheeres, 2003). This suggests that shape change would precede mass loss if there is loose material available. Basic granular flow models can estimate what shapes the body might actually take. As the spin rate increases, the effective slope angle on the surface changes owing to the increased centrifugal force, and as slopes become higher on certain regions of the surface they can surpass critical values (angle of repose or angle of friction) and fail. After failing, material will flow “down” to the potential lows near the equator, settling in at lower slopes. This model found a surprisingly good match for the equatorial ridge shape of 1999 KW4, using an angle of failure of 37° (Harris et al., 2009). The failure causes very regular slopes through midlattitudes on nearly circular bodies, a trait clearly observed in the shape of 1999 KW4 (Harris et al., 2009; Sánchez and Scheeres, 2014; Scheeres, 2015). Discrete particle approaches to modeling rubble-pile interior structure and evolution rely on N-body billiard-ball-style granular mechanics. Many of the first models of rubble-pile dynamics, tidal disruption, and spin/shape configurations relied on hard spherical particles that never overlap or interpenetrate (Richardson et al., 1998, 2005). While these “hard-sphere” incarnations of the models did not directly account for friction forces, Richardson et al. (2005) showed that standard hexagonal closest packing configurations of the spheres produce enough shear strength so that modeled bodies can maintain spin and shape configurations within ~40° angle-of-friction-allowable envelopes produced by Holsapple (2001). While different and more simplistic than the “soft-sphere” representations used to model rubble-pile asteroids (Sánchez and Scheeres, 2011, 2012; Schwartz et al., 2012), the modeled aggregates can hold shape and spin configurations similar to those observed on actual asteroids (see Fig. 10 of Walsh et al., 2012). Further detail can be found in the chapter by Murdoch et al. in this volume. When a rubble-pile asteroid is slowly spun up by the YORP effect, it can eventually be pushed to mass loss (Rubincam, 2000; Vokrouhlický and Čapek, 2002; Bottke et al., 2002). If the asteroid is made of only a very few constituent pieces than they will reconfigure and eventually separate (Scheeres, 2007b). What happens to those two components is a complicated dynamical dance that involves angular momentum transfer due to nonspherical shapes (Scheeres, 2007b; Jacobson and Scheeres, 2011a). When the asteroid is made of thousands of particles, different evolutions are found for different particle surface interactions. The “hard-sphere” models include dissipation of energy during collisions, but have to rely on structural packing (crystalline) to provide shear strength rather than surface friction (Walsh et al., 2008, 2012). These models found that model asteroids can maintain oblate shapes at critical rotation rates, which leads to equatorial mass-shedding. While it was hypothesized that this could lead to in-orbit growth of the satellite (Ćuk, 2007; Walsh et al., 2008), it is clear from the dynamics of such close orbits (Scheeres, 2009; Jacobson and Scheeres, 2011a) that to avoid almost immediate ejection

from the system, many particles would have to be shed at the same time in order to collide, circularize, and stabilize their orbits beyond the Roche limit. Sánchez and Scheeres (2011, 2012) utilized “soft-sphere” granular models, which allow for more complex surface interactions, including various friction forces and interparticle cohesion. These works explore a wider range of parameters and find a large variety of outcomes, including “fission” events of bodies splitting into nearly equal parts. There is still a strong dependence on the angle of friction for the outcome, with some of the observed oblate-shaped and critically rotating outcomes observed. Observed mass-loss events have been associated with YORP-induced rotational fission (Jewitt et al., 2013, 2014, 2015; Sheppard and Trujillo, 2015). The rotation period of (62412) 2000 SY178 is only 3.33 h (Sheppard and Trujillo, 2015). Minor components outside of the dust are difficult to observe, and the shape of the primary is impossible to deduce. Future observations are necessary to determine whether the dust is associated only with surface failure or satellite formation in these cases. 4.5. Kozai and Planetary Encounters Most secondaries in NEA systems are too close to their primary to experience excursions in eccentricity or inclination due to the Kozai effect (Fang and Margot, 2012c). For more distant NEA systems, such 1998 ST27 at a ~16 Rpri, the Kozai effect could play a role of disrupting systems or driving them to collision and possibly creating contact binaries (Fang and Margot, 2012c). Binary systems in the main belt do not encounter planets, but those on near-Earth orbits can have encounters with terrestrial planets close enough to alter or disrupt their systems (Farinella, 1992; Farinella and Chauvineau, 1993; Walsh and Richardson, 2008; Fang and Margot, 2012a). The timescales for encounters close enough to disrupt or disturb a system depend on its heliocentric orbit (how frequently it approaches a planet), and also depend strongly on the system’s properties — primarily the separation of the primary and secondary. Disruption of a typical system with a = 4 Rpri, where a is semimajor axis and Rpri is the primary’s radius, becomes significant (50% of encounters randomized over phasings) at encounters of 3 R⊕, which occur on average every 2 m.y. for NEAs (Walsh and Richardson, 2008). Planetary flybys may also stymie other evolutionary effects, such as BYORP, by either torquing the secondary and breaking its synchronous rotation, or by exciting its orbital eccentricity (Fang and Margot, 2012a). Eccentricity of 0.2 can be excited for a similar a = 4 Rpri system at only 8 R⊕, which happen every ~1 m.y. on average for NEAs (Walsh and Richardson, 2008; Fang and Margot, 2012a). 5. The Future The advances made in the last decades have been driven by the increased database of known binary systems and the

Walsh and Jacobson:  Formation and Evolution of Binary Asteroids   389

mounting evidence and measurements of thermal effects acting widely in the solar system. Naturally, many questions remain, and we are optimistic that the trajectory of current studies is well aligned to answer many of the outstanding questions. We roughly outline the expected progress, discoveries, and events that we think will be the focus of an Asteroids V chapter on this topic in a decade. 1. More observations from a variety of sources will help to expand the catalog of rare and outlier populations. Largescale surveys should provide a flood of data and continue to increase the size of our catalog [e.g., Gaia and the Large Synoptic Survey Telescope (LSST)]. While observations from small telescopes, including significant contributions from amateurs, have been the basis of many lightcurve discoveries of small systems, some of the high-cadence allsky-survey telescopes may begin to eclipse the production of the network of small telescopes. 2. The nondetection of BYORP at 1996 FG3 is curious and possibly revealing (Scheirich et al., 2015). While there is a proposed theory to explain why and how the effect may be balanced by tides (Jacobson and Scheeres, 2011a), and other nontidal effects may be similarly important (Fahnestock and Scheeres, 2009; Harris et al., 2009), a nondetection is not a detection, and the community awaits a measurement of this interesting thermal effect. A system with a more distant companion, or perhaps one of the triple systems, may allow for a detection in an environment where tides are small and BYORP is strong (Pravec and Scheirich, 2010). The BYORP effect may be a fundamental and dominating mechanism that is widely shaping the observed population of small binary asteroids — so observing it in action will be a great step forward. 3. There are spacecraft visits planned to asteroids with “top shapes.” The KW4 shape (or top shape) that is becoming ubiquitous in shape models of the primaries of binary systems was a revealing discovery in this field. Hopefully careful mapping and geologic studies of these systems will reveal how small asteroids become that particular shape. In turn, knowing how the ridge formed might help researchers answer the many remaining questions about the formation and evolution of the satellites that are so often found around these top-shaped bodies. The currently planned space missions from NASA and the Japan Aerospace Exploration Agency (JAXA), OSIRIS-REx and Hayabusa-2 respectively, are each currently seeking to visit primitive NEAs, and each target appears to show some signs of an equatorial ridge (Nolan et al., 2013; Lauretta et al., 2014). It is hoped that the mission surveys of the asteroid surface will elucidate the reshaping histories of these bodies by showing signs of material flow patterns, variations in ages of different surface features, and material differences in different geologic units. Acknowledgments. K.J.W. was partially supported by the NASA Planetary Geology and Geophysics Program under grant NNX13AM82G. S.A.J. was supported by the European Research Council Advanced Grant ACCRETE (contract number 290568).

REFERENCES Asphaug E. and Benz W. (1996) Size, density, and structure of Comet Shoemaker-Levy 9 inferred from the physics of tidal breakup. Icarus, 121(2), 225–248. Becker T. M., Nolan M., Howell E. S., and Magri C. (2009) Physical modeling of triple near-Earth asteroid (153591) 2001 SN263. Bull. Am. Astron. Soc., 41, 190. Becker T. M., Howell E. S., Nolan M. C., Magri C., Pravec P., Taylor P. A., Oey J., Higgins D., Vilagi J., Kornos L., Galad A., Gajdos S., Gaftonyuk N. M., Krugly Y. N., Molotov I. E., Hicks M. D., Carbognani A., Warner B. D., Vachier F., Marchis F., and Pollock J. (2015) Physical modeling of triple near-Earth asteroid (153591) 2001 SN263 from radar and optical light curve observations. Icarus, 248, 499–515. Bellerose J. and Scheeres D. J. (2008) Energy and stability in the full two body problem. Cel. Mech. Dyn. Astron., 100(1), 63–91. Belton M. and Carlson R. (1994) 1993 (243) 1. IAU Circular 5948, 2. Bottke W. F. and Melosh H. J. (1996) Formation of asteroid satellites and doublet craters by planetary tidal forces. Nature, 381(6), 51–53. Bottke W. F., Vokrouhlický D., Rubincam D. P., and Brož, M. (2002) The effect of Yarkovsky thermal forces on the dynamical evolution of asteroids and meteoroids. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 395–408. Univ. of Arizona, Tucson. Bottke W. F., Vokrouhlický D., Rubincam D. P., and Nesvorný D. (2006) The Yarkovsky and YORP effects: Implications for asteroid dynamics. Annu. Rev. Earth Planet. Sci., 34, 157–191. Bottke W. F., Vokrouhlický D.,Walsh K. J., Delbo M., Michel P., Lauretta D. S., Campins H., Connolly H. C., Scheeres D. J., and Chelsey S. R. (2015) In search of the source of asteroid (101955) Bennu: Applications of the stochastic YORP model. Icarus, 247, 191–217. Breiter S., Bartczak P., Czekaj M., Oczujda B., and Vokrouhlický D. (2009) The YORP effect on 25143 Itokawa. Astron. Astrophys., 507(2), 1073–1081. Brown M. E., Margot J.-L., Keck W. M. I., de Pater I., and Roe H. (2001) S/2001 (87) 1. IAU Circular 7588, 1. Brozovic M., Benner L. A. M., Nolan M. C., Howell E. S., Magri C., Giorgini J. D., Taylor P. A., Margot J.-L., Busch M. W., Shepard M. K., Carter L. M., Jao J. S., Van Brimmer J., Franck C. R., Silva M. A., Kodis M. A., Kelley D. T., Slade M. A., Bramson A., Lawrence K. J., Pollock J. T., Pravec P., Reichart D. E., Ivarsen K. M., Haislip J. B., Nysewander M. C., and Lacluyze A. P. (2009) (136617) 1994 CC. IAU Circular 9053, 2. Brozović M., Benner L. A. M., Taylor P. A., Nolan M. C., Howell E. S., Magri C., Scheeres D. J., Giorgini J. D., Pollock J., Pravec P., Galad A., Fang J., Margot J.-L., Busch M. W., Shepard M. K., Reichart D. E., Ivarsen K. M., Haislip J. B., Lacluyze A. P., Jao J. S., Slade M. A., Lawrence K. J., and Hicks M. D. (2011) Radar and optical observations and physical modeling of triple near-Earth asteroid (136617) 1994 CC. Icarus, 216(1), 241–256. Busch M. W., Giorgini J. D., Ostro S. J., Benner L. A. M., Jurgens R. F., Rose R., Hicks M. D., Pravec P., Kusnirák P., Ireland M. J., Scheeres D. J., Broschart S. B., Magri C., Nolan M. C., Hine A. A., and Margot J.-L. (2007) Physical modeling of near-Earth asteroid (29075) 1950 DA. Icarus, 190(2), 608–621. Busch M. W., Ostro S. J., Benner L. A. M., Brozović M., Giorgini J. D., Jao J. S., Scheeres D. J., Magri C., Nolan M. C., Howell E. S., Taylor P. A., Margot J.-L., and Brisken W. (2011) Radar observations and the shape of near-Earth asteroid 2008 EV5. Icarus, 212(2), 649–660. Čapek D. and Vokrouhlický D. (2004) The YORP effect with finite thermal conductivity. Icarus, 172(2), 526–536. Cooney W. R. Jr., Gross J., Terrell D., Stephens R. D., Pravec P., Kusnirák P., Durkee R., and Galad A. (2006) (1717) Arlon. Central Bureau Electronic Telegram, 369, 1. Cotto-Figueroa D., Statler T. S., Richardson D. C., and Tanga P. (2015) Coupled spin and shape evolution of small rubble-pile asteroids: Self-limitation of the YORP effect. Astrophys. J., 803(1), 25. Ćuk M. (2007) Formation and destruction of small binary asteroids. Astrophys. J. Lett., 659(1), L57–L60. Ćuk M. and Burns J. A. (2005) Effects of thermal radiation on the dynamics of binary NEAs. Icarus, 176(2), 418–431. Ćuk M. and Nesvorný D. (2010) Orbital evolution of small binary asteroids. Icarus, 207(2), 732–743.

390   Asteroids IV Darwin G. H. (1879) A tidal theory of the evolution of satellites. The Observatory, 3, 79–84. Descamps P., Marchis F., Michalowski T., Vachier F., Colas F., Berthier J., Assafin M., Dunckel P. B., Polinska M., Pych W., Hestroffer D., Miller K. P. M., Vieira Martins R., Birlan M., Teng-Chuen-Yu J. P., Peyrot A., Payet B., Dorseuil J., Léonie Y., and Dijoux T. (2007) Figure of the double asteroid 90 Antiope from adaptive optics and lightcurve observations. Icarus, 187(2), 482–499. Descamps P., Marchis F., Berthier J., Emery J. P., Duchêne G., de Pater I., Wong M. H., Lim L., Hammel H. B., Vachier F., Wiggins P., Teng-Chuen-Yu J.-P., Peyrot A., Pollock J., Assafin M., VieiraMartins R., Camargo J. I. B., Braga-Ribas F., and Macomber B. (2011) Triplicity and physical characteristics of asteroid (216) Kleopatra. Icarus, 211, 1022–1033. Doressoundiram A., Paolicchi P., Verlicchi A., and Cellino A. (1997) The formation of binary asteroids as outcomes of catastrophic collisions. Planet. Space Sci., 45, 757–770. Duddy S. R., Lowry S. C., Wolters S. D., Christou A., Weissman P. R., Green S. F., and Rozitis B. (2012) Physical and dynamical characterisation of the unbound asteroid pair 7343-154634. Astron. Astrophys., 539, A36. Durda D. D. (1996) The formation of asteroidal satellites in catastrophic collisions. Icarus, 120(1), 212–219. Durda D. D., Bottke W. F., Enke B. L., Merline W. J., Asphaug E., Richardson D. C., and Leinhardt Z. M. (2004) The formation of asteroid satellites in large impacts: Results from numerical simulations. Icarus, 170(1), 243–257. Durda D. D., Bottke W. F., Nesvorný D., Enke B. L., Merline W. J., Asphaug E., and Richardson D. C. (2007) Size-frequency distributions of fragments from SPH/ N-body simulations of asteroid impacts: Comparison with observed asteroid families. Icarus, 186(2), 498–516. Ďurech J., Vokrouhlický D., Kaasalainen M., Higgins D., Krugly Y. N., Gaftonyuk N. M., Shevchenko V. S., Chiorny V. G., Hamanowa H., Hamanowa H., Reddy V., and Dyvig R. R. (2008a) Detection of the YORP effect in asteroid (1620) Geographos. Astron. Astrophys., 489(2), L25–L28. Ďurech J., Vokrouhlický D., Kaasalainen M., Weissman P. R., Lowry S. C., Beshore E., Higgins D., Krugly Y. N., Shevchenko V. S., Gaftonyuk N. M., Choi Y.-J., Kowalski R. A., Larson S.,Warner B. D., Marshalkina A. L., Ibrahimov M. A., Molotov I. E., Michałowski T., and Kitazato K. (2008b) New photometric observations of asteroids (1862) Apollo and (25143) Itokawa — an analysis of YORP effect. Astron. Astrophys., 488(1), 345–350. Ďurech J., Vokrouhlický D., Baransky A. R., Breiter S., Burkhonov O. A., Cooney W. R. Jr., Fuller V., Gaftonyuk N. M., Gross J., Inasaridze R. Y., Kaasalainen M., Krugly Y. N., Kvaratshelia O. I., Litvinenko E. A., Macomber B., Marchis F., Molotov I. E., Oey J., Polishook D., Pollock J., Pravec P., Sárneczky K., Shevchenko V. S., Slyusarev I., Stephens R. D., Szabó G., Terrell D., Vachier F., Vanderplate Z., Viikinkoski M., and Warner B. D. (2012) Analysis of the rotation period of asteroids (1865) Cerberus, (2100) RaShalom, and (3103) Eger — search for the YORP effect. Astron. Astrophys., 547, 10. Efroimsky M. and Williams J. G. (2009) Tidal torques: A critical review of some techniques. Cel. Mech. Dyn. Astron., 104(3), 257–289. Egbert G. D. and Ray R. D. (2000) Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature, 405(6), 775–778. Fahnestock E. G. and Scheeres D. J. (2008) Simulation and analysis of the dynamics of binary near-Earth asteroid (66391) 1999 KW4. Icarus, 194, 410. Fahnestock E. G. and Scheeres D. J. (2009) Binary asteroid orbit expansion due to continued YORP spin-up of the primary and primary surface particle motion. Icarus, 201(1), 135–152. Fang J. and Margot J.-L. (2012a) Binary asteroid encounters with terrestrial planets: Timescales and effects. Astron. J., 143(1), 25. Fang J. and Margot J.-L. (2012b) Near-Earth binaries and triples: Origin and evolution of spin-orbital properties. Astron. J., 143(1), 24. Fang J. and Margot J.-L. (2012c) The role of Kozai cycles in near-Earth binary asteroids. Astron. J., 143(3), 59. Farinella P. (1992) Evolution of Earth-crossing binary asteroids due to gravitational encounters with the Earth. Icarus, 96, 284. Farinella P. and Chauvineau B. (1993) On the evolution of binary Earthapproaching asteriods. Astron. Astrophys., 279, 251–259.

Ferraz-Mello S. (2013) Tidal synchronization of close-in satellites and exoplanets. A rheophysical approach. Cel. Mech. Dyn. Astron., 116(2), 109–140. Ferraz-Mello S., Rodríguez A., and Hussmann H. (2008) Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited. Cel. Mech. Dyn. Astron., 101(1), 171–201. Goldreich P. (1963) On the eccentricity of satellite orbits in the solar system. Mon. Not. R. Astron. Soc., 126, 257. Goldreich P. and Sari R. (2009) Tidal evolution of rubble piles. Astrophys. J., 691(1), 54–60. Goldreich P. and Soter S. (1966) Q in the solar system. Icarus, 5, 375–389. Golubov O. and Krugly Y. N. (2012) Tangential component of the YORP effect. Astrophys. J. Lett., 752(1), L11. Golubov O., Scheeres D. J., and Krugly Y. N. (2014) A threedimensional model of tangential YORP. Astrophys. J., 794(1), 22. Greenberg R. (2009) Frequency dependence of tidal q. Astrophys. J. Lett., 698(1), L42–L45. Guibout V. and Scheeres D. J. (2003) Stability of surface motion on a rotating ellipsoid. Cel. Mech. Dyn. Astron., 87(3), 263–290. Harris A. W., Young J. W., Dockweiler T., Gibson J., Poutanen M., and Bowell E. (1992) Asteroid lightcurve observations from 1981. Icarus, 95(1), 115–147. Harris A. W., Fahnestock E. G., and Pravec P. (2009) On the shapes and spins of “rubble pile” asteroids. Icarus, 199(2), 310–318. Hirabayashi M., Scheeres D. J., Sánchez D. P., and Gabriel T. (2014) Constraints on the physical properties of main belt comet P/2013 R3 from its breakup event. Astrophys. J. Lett., 789(1), L12. Holsapple K. A. (2001) Equilibrium configurations of solid cohesionless bodies. Icarus, 154(2), 432–448. Holsapple K. A. (2004) Equilibrium figures of spinning bodies with selfgravity. Icarus, 172(1), 272–303. Holsapple K. A. (2007) Spin limits of solar system bodies: From the small fast-rotators to 2003 EL61. Icarus, 187(2), 500–509. Holsapple K. A. (2010) On YORP-induced spin deformations of asteroids. Icarus, 205(2), 430–442. Hurford T. A. and Greenberg R. (2000) Tidal evolution by elongated primaries: Implications for the Ida/Dactyl system. Geophys. Res. Lett., 27(1), 1595–1598. Hut P. (1980) Stability of tidal equilibrium. Astron. Astrophys., 92, 167–170. Hut P. (1981) Tidal evolution in close binary systems. Astron. Astrophys., 99, 126–140. Jacobson S. A. (2014) Small asteroid system evolution. In Complex Planetary Systems (Z. Knežević and A. Lemaitre, eds.), pp. 108–117. Proc. IAU Vol. 9, Symposium S310. Jacobson S. A. and Scheeres D. J. (2011a) Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems. Icarus, 214(1), 161–178. Jacobson S. A. and Scheeres D. J. (2011b) Evolution of small near-Earth asteroid binaries. EPSC-DPS Joint Meeting 2011, 647. Jacobson S. A. and Scheeres D. J. (2011c) Long-term stable equilibria for synchronous binary asteroids. Astrophys. J. Lett., 736(1), L19. Jacobson S. A., Marzari F., Rossi A., Scheeres D. J., and Davis D. R. (2014a) Effect of rotational disruption on the size-frequency distribution of the main belt asteroid population. Mon. Not. R. Astron. Soc. Lett., 439, L95–L99. Jacobson S. A., Scheeres D. J., and McMahon J.W. (2014b) Formation of the wide asynchronous binary asteroid population. Astrophys. J., 780(1), 60. Jacobson S. A., Scheeres D. J., Rossi A., and Marzari F. (2014c) The effects of rotational fission on the main belt asteroid population. Lunar Planet. Sci. XLV, Abstract #2363. Lunar and Planetary Institute, Houston. Jeffreys H. (1921) Tidal friction in shallow seas. Philos. Trans. R. Soc. Ser. A, 221, 239–264. Jewitt D., Ishiguro M., and Agarwal J. (2013) Large particles in active asteroid P/2010 A2. Astrophys. J. Lett., 764(1), L5. Jewitt D., Agarwal J., Li J.-Y., Weaver H., Mutchler M., and Larson S. (2014) Disintegrating asteroid P/2013 R3. Astrophys. J. Lett., 784(1), L8. Jewitt D., Agarwal J., Peixinho N., Weaver H., Mutchler M., Hui M.-T., Li J.-Y., and Larson S. (2015) A new active asteroid 313P/Gibbs. Astron. J., 149(2), 81.

Walsh and Jacobson:  Formation and Evolution of Binary Asteroids   391 Johnston W. R. (2014) Binary Minor Planets V7.0. EAR-A-COMPIL-5BINMP-V7.0, NASA Planetary Data System. Kaasalainen M., Ďurech J., Warner B. D., Krugly Y. N., and Gaftonyuk N. M. (2007) Acceleration of the rotation of asteroid 1862 Apollo by radiation torques. Nature, 446(7), 420–422. Kaula W. M. (1964) Tidal dissipation by solid friction and the resulting orbital evolution. Rev. Geophys. Space Phys., 2, 661–685. Lauretta D. S., Bartels A. E., Barucci M. A., Bierhaus E. B., Binzel R. P., Bottke W. F., Campins H., Chesley S. R., Clark B. C., Clark B. E., Cloutis E. A., Connolly H. C., Crombie M. K., Delbo M., Dworkin J. P., Emery J. P., Glavin D. P., Hamilton V. E., Hergenrother C. W., Johnson C. L., Keller L. P., Michel P., Nolan M. C., Sandford S. A., Scheeres D. J., Simon A. A., Sutter B. M., Vokrouhlický D., and Walsh K. J. (2014) The OSIRIS-REx target asteroid (101955) Bennu: Constraints on its physical, geological, and dynamical nature from astronomical observations. Meteoritics & Planet. Sci., 50(4), 834–849. Leinhardt Z. M. and Richardson D. C. (2005) A fast method for finding bound systems in numerical simulations: Results from the formation of asteroid binaries. Icarus, 176(2), 432–439. Lowry S. C., Fitzsimmons A., Pravec P., Vokrouhlický D., Boehnhardt H., Taylor P. A., Margot J.-L., Galad A., Irwin M., Irwin J., and Kusnirák P. (2007) Direct detection of the asteroidal YORP effect. Science, 316(5), 272–274. Lowry S. C., Weissman P. R., Duddy S. R., Rozitis B., Fitzsimmons A., Green S. F., Hicks M. D., Snodgrass C., Wolters S. D., Chesley S. R., Pittichová J., and van Oers P. (2014) The internal structure of asteroid (25143) Itokawa as revealed by detection of YORP spin-up. Astron. Astrophys., 562, A48. MacDonald G. J. F. (1964) Tidal friction. Rev. Geophys. Space Phys., 2, 467–541. Marchis F. and Vega D. (2014) The potential of GPI extreme AO system to image and characterize exoplanets and asteroids. In AAS/Division for Planetary Sciences Meeting Abstracts, 46, #201.07. Marchis F., Descamps P., Hestroffer D., and Berthier J. (2005) Discovery of the triple asteroidal system 87 Sylvia. Nature, 436(7), 822–824. Marchis F., Baek M., Descamps P., Berthier J., Hestroffer D., and Vachier F. (2007) S/2004 (45) 1. IAU Circular 8817, 1. Marchis F., Pollock J., Pravec P., Baek M., Greene J., Hutton L., Descamps P., Reichart D. E., Ivarsen K. M., Crain J. A., Nysewander M. C., Lacluyze A. P., Haislip J. B., and Harvey J. S. (2008) (3749) Balam. Central Bureau Electronic Telegram, 1297, 1. Marchis F., Descamps P., Berthier J., Colas F., Melbourne J., Stockton A. N., Fassnacht C. D., and Dupuy T. J. (2009) Occultations of the (93) Minerva system. Central Bureau Electronic Telegram, 1986, 1. Margot J.-L., Nolan M. C., Benner L. A. M., Ostro S. J., Jurgens R. F., Giorgini J. D., Slade M. A., and Campbell D. B. (2002) Binary asteroids in the near-Earth object population. Science, 296(5), 1445–1448. Marzari F., Rossi A., and Scheeres D. J. (2011) Combined effect of YORP and collisions on the rotation rate of small main belt asteroids. Icarus, 214(2), 622–631. Masiero J. R., Jedicke R., Ďurech J., Gwyn S., Denneau L., and Larsen J. (2009) The Thousand Asteroid Light Curve Survey. Icarus, 204(1), 145–171. McMahon J. W. and Scheeres D. J. (2010a) Detailed prediction for the BYORP effect on binary near-Earth asteroid (66391) 1999 KW4 and implications for the binary population. Icarus, 209(2), 494–509. McMahon J.W. and Scheeres D. J. (2010b) Secular orbit variation due to solar radiation effects: A detailed model for BYORP. Cel. Mech. Dyn. Astron., 106(3), 261–300. McMahon J. W. and Scheeres D. J. (2012a) Binary-YORP coefficients for known asteroid shapes. AAS/Division for Planetary Sciences Meeting Abstracts, 44, #105.08. McMahon J. W. and Scheeres D. J. (2012b) Effect of small scale surface topology on near-Earth asteroid YORP and bYORP coefficients. AAS/Division of Dynamical Astronomy Meeting, 43, #7.04. McMahon J. W. and Scheeres D. J. (2013a) A statistical analysis of YORP coefficients. AAS/Division for Planetary Sciences Meeting Abstracts, 45, #112.17. McMahon J. W. and Scheeres D. J. (2013b) Dynamic limits on planar libration-orbit coupling around an oblate primary. Cel. Mech. Dyn. Astron., 115, 365–396. Melosh H. J. and Stansberry J. A. (1991) Doublet craters and the tidal disruption of binary asteroids. Icarus, 94, 171–179.

Merline W. J., Weidenschilling S. J., Durda D. D., Margot J.-L., Pravec P., and Storrs A. D. (2002) Asteroids do have satellites. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 289–312. Univ. of Arizona, Tucson. Michałowski T., Bartczak P., Velichko F. P., Kryszczýnska A., Kwiatkowski T., Breiter S., Colas F., Fauvaud S., Marciniak A., Michałowski J., Hirsch R., Behrend R., Bernasconi L., Rinner C., and Charbonnel S. (2004) Eclipsing binary asteroid 90 Antiope. Astron. Astrophys., 423, 1159–1168. Michel P. and Richardson D. C. (2013) Collision and gravitational reaccumulation: Possible formation mechanism of the asteroid Itokawa. Astron. Astrophys., 554, L1. Michel P., Benz W., Tanga P., and Richardson D. C. (2001) Collisions and gravitational reaccumulation: Forming asteroid families and satellites. Science, 294(5), 1696–1700. Michel P., Tanga P., Benz W., and Richardson D. C. (2002) Formation of asteroid families by catastrophic disruption: Simulations with fragmentation and gravitational reaccumulation. Icarus, 160(1), 10–23. Michel P., Benz W., and Richardson D. C. (2003) Disruption of fragmented parent bodies as the origin of asteroid families. Nature, 421(6923), 608–611. Michel P., Benz W., and Richardson D. C. (2004) Catastrophic disruption of pre-shattered parent bodies. Icarus, 168(2), 420–432. Mignard F. (1979) The evolution of the lunar orbit revisited. I. Moon Planets, 20, 301–315. Mignard F. (1980) The evolution of the lunar orbit revisited. II. Moon Planets, 23, 185–201. Morbidelli A., Levison H. F., Tsiganis K., and Gomes R. S. (2005) Chaotic capture of Jupiter’s Trojan asteroids in the early solar system. Nature, 435(7041), 462–465. Moskovitz N. A. (2012) Colors of dynamically associated asteroid pairs. Icarus, 221(1), 63–71. Mottola S. and Lahulla F. (2000) Mutual eclipse events in asteroidal binary system 1996 FG3: Observations and a numerical model. Icarus, 146(2), 556–567. Murray C. D. and Dermott S. F. (2000) Solar System Dynamics. Cambridge Univ., Cambridge. Naidu S. P. and Margot J.-L. (2015) Near-Earth asteroid satellite spins under spin-orbit coupling. Astron. J., 149(2), 80. Nesvorný D. and Vokrouhlický D. (2007) Analytic theory of the YORP effect for near-spherical objects. Astron. J., 134(5), 1750. Nesvorný D., Bottke W. F., Dones L., and Levison H. F. (2002) The recent breakup of an asteroid in the main-belt region. Nature, 417(6), 720–771. Nesvorný D., Youdin A. N., and Richardson D. C. (2010) Formation of Kuiper belt binaries by gravitational collapse. Astron. J., 140(3), 785–793. Nesvorný D., Vokrouhlický D., and Morbidelli A. (2013) Capture of Trojans by jumping Jupiter. Astrophys. J., 768(1), 45. Nolan M. C., Howell E. S., Benner L. A. M., Ostro S. J., Giorgini J. D., Busch M. W., Carter L. M., Anderson R. F., Magri C., Campbell D. B., Margot J.-L., Vervack R. J. Jr., and Shepard M. K. (2008) (153591) 2001 SN26. IAU Circular 8921. Nolan M. C., Magri C., Howell E. S., Benner L. A. M., Giorgini J. D., Hergenrother C. W., Hudson R. S., Lauretta D. S., Margot J.-L., Ostro S. J., and Scheeres D. J. (2013) Shape model and surface properties of the OSIRIS-REx target asteroid (101955) Bennu from radar and lightcurve observations. Icarus, 226(1), 629–640. Noll K. S., Grundy W. M., Chiang E. I., Margot J.-L., and Kern S. D. (2008) Binaries in the Kuiper belt. In The Solar System Beyond Neptune (M. A. Barucci et al., eds.), pp. 345–363. Univ. of Arizona, Tucson. O’Keefe J. A. (1976) Tektites and Their Origin. Elsevier, Amsterdam. Ostro S. J., Hudson R. S., Benner L. A. M., Giorgini J. D., Magri C., Margot J.-L., and Nolan M. C. (2002) Asteroid radar astronomy. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 151–168. Univ. of Arizona, Tucson. Ostro S. J., Margot J.-L., Benner L. A. M., Giorgini J. D., Scheeres D. J., Fahnestock E. G., Broschart S. B., Bellerose J., Nolan M. C., Magri C., Pravec P., Scheirich P., Rose R., Jurgens R. F., De Jong E. M., and Suzuki S. (2006) Radar imaging of binary near-Earth asteroid (66391) 1999 KW4. Science, 314(5), 1276–1280. Paddack S. J. (1969) Rotational bursting of small celestial bodies: Effects of radiation pressure. J. Geophys. Res., 74, 4379–4381.

392   Asteroids IV Paddack S. J. and Rhee J. W. (1975) Rotational bursting of interplanetary dust particles. Geophys. Res. Lett., 2, 365–367. Petit J.-M., Durda D. D., Greenberg R., Hurford T. A., and Geissler P. E. (1997) The long-term dynamics of Dactyl’s orbit. Icarus, 130(1), 177–197. Polishook D., Brosch N., and Prialnik D. (2011) Rotation periods of binary asteroids with large separations — Confronting the escaping ejecta binaries model with observations. Icarus, 212(1), 167–174. Polishook D., Moskovitz N. A., Binzel R. P., Demeo F. E., Vokrouhlický D., Žižka J., and Oszkiewicz D. A. (2014a) Observations of “fresh” and weathered surfaces on asteroid pairs and their implications on the rotational-fission mechanism. Icarus, 233, 9–26. Polishook D., Moskovitz N. A., DeMeo F., and Binzel R. P. (2014b) Rotationally resolved spectroscopy of asteroid pairs: No spectral variation suggests fission is followed by settling of dust. Icarus, 243, 222–235. Pravec P. and Hahn G. (1997) Two-period lightcurve of 1994 AW1: Indication of a binary asteroid? Icarus, 127(2), 431–440. Pravec P. and Harris A. W. (2000) Fast and slow rotation of asteroids. Icarus, 148(1), 12–20. Pravec P. and Harris A. W. (2007) Binary asteroid population. 1. Angular momentum content. Icarus, 190(1), 250–259. Pravec P. and Scheirich P. (2010) Binary system candidates for detection of BYORP. Bull. Am. Astron. Soc., 42, 1055. Pravec P. and Vokrouhlický D. (2009) Significance analysis of asteroid pairs. Icarus, 204(2), 580–588. Pravec P., Wolf M., and Šarounová L. (1998) Occultation/eclipse events in binary asteroid 1991 VH. Icarus, 133(1), 79–88. Pravec P., Wolf M., and Šarounová L. (1999) How many binaries are there among the near-Earth asteroids? In Evolution and Source Regions of Asteroids and Comets (J. Svoren et al., eds.), p. 159. IAU Colloq. 173, Univ. of Rochester. Pravec P., Šarounová L., Rabinowitz D. L., Hicks M. D., Wolf M., Krugly Y. N., Velichko F. P., Shevchenko V. G., Chiorny V. G., Gaftonyuk N. M., and Genevier G. (2000) Two-period lightcurves of 1996 FG3, 1998 PG, and (5407) 1992 AX: One probable and two possible binary asteroids. Icarus, 146(1), 190–203. Pravec P., Harris A. W., and Michalowski T. (2002) Asteroid rotations. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 113–122. Univ. of Arizona, Tucson. Pravec P., Scheirich P., Kusnirák P., Šarounová L., Mottola S., Hahn G., Brown P., Esquerdo G., Kaiser N., Krzeminski Z., Pray D. P.,Warner B. D., Harris A. W., Nolan M. C., Howell E. S., Benner L. A. M., Margot J.-L., Galad A., Holliday W., Hicks M. D., Krugly Y. N., Tholen D. J., Whiteley R. J., Marchis F., Degraff D. R., Grauer A., Larson S., Velichko F. P., Cooney W. R. Jr., Stephens R. D., Zhu J., Kirsch K., Dyvig R., Snyder L., Reddy V., Moore S., Gajdos S., Vilagi J., Masi G., Higgins D., Funkhouser G., Knight B., Slivan S. M., Behrend R., Grenon M., Burki G., Roy R., Demeautis C., Matter D., Waelchli N., Revaz Y., Klotz A., Rieugné M., Thierry P., Cotrez V., Brunetto L., and Kober G. (2006) Photometric survey of binary near-Earth asteroids. Icarus, 181(1), 63–93. Pravec P., Harris A. W., Vokrouhlický D., Warner B. D., Kusnirák P., Hornoch K., Pray D. P., Higgins D., Oey J., Galad A., Gajdos S., Kornoš L., Vilagi J., Husarik M., Krugly Y. N., Shevchenko V. S., Chiorny V., Gaftonyuk N. M., Cooney W. R. Jr., Gross J., Terrell D., Stephens R. D., Dyvig R., Reddy V., Ries J. G., Colas F., Lecacheux J., Durkee R., Masi G., Koff R. A., and Goncalves R. (2008) Spin rate distribution of small asteroids. Icarus, 197(2), 497–504. Pravec P., Vokrouhlický D., Polishook D., Scheeres D. J., Harris A. W., Galad A., Vaduvescu O., Pozo F., Barr A., Longa P., Vachier F., Colas F., Pray D. P., Pollock J., Reichart D. E., Ivarsen K. M., Haislip J. B., Lacluyze A. P., Kusnirák P., Henych T., Marchis F., Macomber B., Jacobson S. A., Krugly Y. N., Sergeev A. V., and Leroy A. (2010) Formation of asteroid pairs by rotational fission. Nature, 466(7), 1085–1088. Pravec P., Scheirich P., Vokrouhlický D., Harris A. W., Kusnirák P., Hornoch K., Pray D. P., Higgins D., Galad A., Vilagi J., Gajdos S., Kornoš L., Oey J., Husarik M., Cooney W. R. Jr., Gross J., Terrell D., Durkee R., Pollock J., Reichart D. E., Ivarsen K. M., Haislip J. B., Lacluyze A. P., Krugly Y. N., Gaftonyuk N. M., Stephens R. D., Dyvig R., Reddy V., Chiorny V., Vaduvescu O., Longa-Peña P., Tudorica A.,Warner B. D., Masi G., Brinsfield J., Goncalves R., Brown P., Krzeminski Z., Gerashchenko O., Shevchenko V. S., Molotov I. E., and Marchis F. (2012) Binary asteroid population.

2. Anisotropic distribution of orbit poles of small, inner main-belt binaries. Icarus, 218(1), 125–143. Pravec P., Kusnirák P., Hornoch K., Galad A., Krugly Y. N., Chiorny V., Inasaridz R. Y., Kvaratskhelia O., Ayvazian V., Parmonov O., Pollock J., Mottola S., Oey J., Pray D., Zizka J., Vraštil J., Molotov I. E., Reichart D. E., Ivarsen K. M., Haislip J. B., and Lacluyze A. P. (2013) (8306) Shoko. IAU Circular 9268, 1. Radzievskii V. V. (1952) A mechanism for the disintegration of asteroids and meteorites. Astron. Zh., 29, 162–170. Richardson D. C. and Walsh K. J. (2006) Binary minor planets. Annu. Rev. Earth Planet. Sci., 34, 47–81. Richardson D. C., BottkeW. F., and Love S. G. (1998) Tidal distortion and disruption of Earth-crossing asteroids. Icarus, 134(1), 47–76. Richardson D. C., Leinhardt Z. M., Melosh H. J., Bottke W. F., and Asphaug E. (2002) Gravitational aggregates: Evidence and evolution. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 501–515. Univ. of Arizona, Tucson. Richardson D. C., Elankumaran P., and Sanderson R. E. (2005) Numerical experiments with rubble piles: Equilibrium shapes and spins. Icarus, 173(2), 349–361. Rossi A., Marzari F., and Scheeres D. J. (2009) Computing the effects of YORP on the spin rate distribution of the NEO population. Icarus, 202(1), 95–103. Rozitis B. and Green S. F. (2012) The influence of rough surface thermal-infrared beaming on the Yarkovsky and YORP effects. Mon. Not. R. Astron. Soc., 423(1), 367–388. Rozitis B. and Green S. F. (2013a) The influence of global self-heating on the Yarkovsky and YORP effects. Mon. Not. R. Astron. Soc., 433(1), 603–621. Rozitis B. and Green S. F. (2013b) The strength and detectability of the YORP effect in near-Earth asteroids: A statistical approach. Mon. Not. R. Astron. Soc., 430(2), 1376–1389. Rozitis B., MacLennan E., and Emery J. P. (2014) Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA. Nature, 512(7), 174–176. Rubincam D. P. (2000) Radiative spin-up and spin-down of small asteroids. Icarus, 148(1), 2–11. Sánchez D. P. and Scheeres D. J. (2011) Simulating asteroid rubble piles with a self-gravitating soft-sphere distinct element method model. Astrophys. J., 727(2), 120. Sánchez D. P. and Scheeres D. J. (2012) DEM simulation of rotationinduced reshaping and disruption of rubble-pile asteroids. Icarus, 218(2), 876–894. Sánchez D. P. and Scheeres D. J. (2014) The strength of regolith and rubble pile asteroids. Meteoritics & Planet. Sci., 49(5), 788–811. Scheeres D. J. (2004) Bounds on rotation periods of disrupted binaries in the full 2-body problem. Cel. Mech. Dyn. Astron., 89(2), 127–140. Scheeres D. J. (2007a) Rotational fission of contact binary asteroids. Icarus, 189, 370. Scheeres D. J. (2007b) The dynamical evolution of uniformly rotating asteroids subject to YORP. Icarus, 188(2), 430–450. Scheeres D. J. (2009) Stability of the planar full 2-body problem. Cel. Mech. Dyn. Astron., 104(1), 103–128. Scheeres D. J. (2015) Landslides and mass shedding on spinning spheroidal asteroids. Icarus, 247, 1–17. Scheeres D. J., Fahnestock E. G., Ostro S. J., Margot J.-L., Benner L. A. M., Broschart S. B., Bellerose J., Giorgini J. D., Nolan M. C., Magri C., Pravec P., Scheirich P., Rose R., Jurgens R. F., De Jong E. M., and Suzuki S. (2006) Dynamical configuration of binary nearEarth asteroid (66391) 1999 KW4. Science, 314(5), 1280–1283. Scheeres D. J., Abe M., Yoshikawa M., Nakamura R., Gaskell R. W., and Abell P. A. (2007) The effect of YORP on Itokawa. Icarus, 188, 425. Scheeres D. J., Hartzell C. M., Sánchez D. P., and Swift M. (2010) Scaling forces to asteroid surfaces: The role of cohesion. Icarus, 210(2), 968–984. Scheirich P. and Pravec P. (2009) Modeling of lightcurves of binary asteroids. Icarus, 200(2), 531–547. Scheirich P., Pravec P., Jacobson S. A., Ďurech J., Kusnirák P., Hornoch K., Mottola S., Mommert M., Hellmich S., Pray D., Polishook D., Krugly Y. N., Inasaridze R. Y., Kvaratshelia O. I., Ayvazian V., Slyusarev I., Pittichová J., Jehin E., Manfroid J., Gillon M., Galad A., Pollock J., Licandro J., Alí-Lagoa V., Brinsfield J., and Molotov I. E. (2015) The binary near-Earth asteroid (175706) 1996 FG3 — An observational constraint on its orbital evolution. Icarus, 245, 56–63.

Walsh and Jacobson:  Formation and Evolution of Binary Asteroids   393 Schwartz S. R., Richardson D. C., and Michel P. (2012) An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code. Granular Matter, 14(3), 363–380. Sharma I. (2009) The equilibrium of rubble-pile satellites: The Darwin and Roche ellipsoids for gravitationally held granular aggregates. Icarus, 200(2), 636–654. Shepard M. K., Margot J.-L., Magri C., Nolan M. C., Schlieder J., Estes B., Bus S. J., Volquardsen E. L., Rivkin A. S., Benner L. A. M., Giorgini J. D., Ostro S. J., and Busch M. W. (2006) Radar and infrared observations of binary near-Earth asteroid 2002 CE26. Icarus, 184(1), 198–210. Sheppard S. S. and Trujillo C. (2015) Discovery and characteristics of the rapidly rotating active asteroid (62412) 2000 SY178 in the main belt. Astron. J., 149(2), 44. Singer S. F. (1968) The origin of the Moon and geophysical consequences. Geophys. J. R. Astron. Soc., 15(1–2), 205–226. Slivan S. M. (2002) Spin vector alignment of Koronis family asteroids. Nature, 419(6), 49–51. Statler T. S. (2009) Extreme sensitivity of the YORP effect to smallscale topography. Icarus, 202(2), 502–513. Steinberg E. and Sari R. (2011) Binary YORP effect and evolution of binary asteroids. Astron. J., 141(2), 55. Taylor G. I. (1920) Tidal friction in the Irish Sea. Philos. Trans. R. Soc. Ser. A, 220, 1–33. Taylor P. A. and Margot J.-L. (2010) Tidal evolution of close binary asteroid systems. Cel. Mech. Dyn. Astron., 108(4), 315–338. Taylor P. A. and Margot J.-L. (2011) Binary asteroid systems: Tidal end states and estimates of material properties. Icarus, 212(2), 661–676. Taylor P. A. and Margot J.-L. (2014) Tidal end states of binary asteroid systems with a nonspherical component. Icarus, 229, 418–422. Taylor P. A., Margot J.-L., Vokrouhlický D., Scheeres D. J., Pravec P., Lowry S. C., Fitzsimmons A., Nolan M. C., Ostro S. J., Benner L. A. M., Giorgini J. D., and Magri C. (2007) Spin rate of asteroid (54509) 2000 PH5 increasing due to the YORP effect. Science, 316(5), 274–277. Taylor P. A., Margot J.-L., Nolan M. C., Benner L. A. M., Ostro S. J., Giorgini J. D., and Magri C. (2008) The shape, mutual orbit, and tidal evolution of binary near-Earth asteroid 2004 DC. In Asteroids, Comets, Meteors 2008, Abstract #8322. Lunar and Planetary Institute, Houston. Taylor P. A., Warner B. D., Magri C., Springmann A., Nolan M. C., Howell E. S., Miller K. J., Zambrano-Marin L. F., Richardson J. E., Hannan M., and Pravec P. (2014) The smallest binary asteroid? The discovery of equal-mass binary 1994 CJ1. AAS/Division for Planetary Sciences Meeting Abstracts, 46, #409.03.

Vokrouhlický D. (2009) (3749) Balam: A very young multiple asteroid system. Astrophys. J. Lett., 706(1), L37–L40. Vokrouhlický D. and Čapek D. (2002) YORP-induced long-term evolution of the spin state of small asteroids and meteoroids: Rubincam’s approximation. Icarus, 159(2), 449–467. Vokrouhlický D. and Nesvorný D. (2008) Pairs of asteroids probably of a common origin. Astron. J., 136(1), 280–290. Vokrouhlický D. and Nesvorný D. (2009) The common roots of asteroids (6070) Rheinland and (54827) 2001 NQ8. Astron. J., 137(1), 111–117. Vokrouhlický D., Nesvorný D., and Bottke W. F. (2003) The vector alignments of asteroid spins by thermal torques. Nature, 425(6), 147–151. Vokrouhlický D., Brož M., Bottke W. F., Nesvorný D., and Morbidelli A. (2006) Yarkovsky/YORP chronology of asteroid families. Icarus, 182(1), 118–142. Vokrouhlický D., Ďurech J., Polishook D., Krugly Y. N., Gaftonyuk N. N., Burkhonov O. A., Ehgamberdiev S. A., Karimov R., Molotov I. E., Pravec P., Hornoch K., Kusnirák P., Oey J., Galad A., and Žižka J. (2011) Spin vector and shape of (6070) Rheinland and their implications. Astron. J., 142(5), 159. Walsh K. J. and Richardson D. C. (2006) Binary near-Earth asteroid formation: Rubble pile model of tidal disruptions. Icarus, 180, 201. Walsh K. J. and Richardson D. C. (2008) A steady-state model of NEA binaries formed by tidal disruption of gravitational aggregates. Icarus, 193, 553. Walsh K. J., Richardson D. C., and Michel P. (2008) Rotational breakup as the origin of small binary asteroids. Nature, 454(7), 188–191. Walsh K. J., Richardson D. C., and Michel P. (2012) Spin-up of rubblepile asteroids: Disruption, satellite formation, and equilibrium shapes. Icarus, 220(2), 514–529. Warner B. D. and Harris A. W. (2007) Lightcurve studies of small asteroids. Bull. Am. Astron. Soc., 39, 432. Warner B. D., Harris A.W., and Pravec P. (2009) The asteroid lightcurve database. Icarus, 202(1), 134–146. Warner B. D., Pravec P., Kusnirák P., Hornoch K., Harris A. W., Stephens R. D., Casulli S., Cooney, W. R. Jr., Gross J., Terrell D., Durkee R., Gajdos S., Galad A., Kornos L., Toth J., Vilagi J., Husarik M., Marchis F., Reiss A. E., Polishook D., Roy R., Behrend R., Pollock J., Reichart D., Ivarsen K. M., Haislip J., Lacluyze A. P., Nysewander M. C., Pray D. P., and Vachier F. (2010) A trio of Hungaria binary asteroids. Minor Planet Bull., 37, 70–73. Weidenschilling S. J., Paolicchi P., and Zappalá V. (1989) Do asteroids have satellites? In Asteroids II (R. P. Binzel et al., eds.), pp. 643– 658. Univ. of Arizona, Tucson.

Yoshikawa M., Kawaguchi J., and Fujiwara A. (2015) Hayabusa sample return mission. In Asteroids IV (P. Michel et al., eds.), pp. 397–418. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch021.

Hayabusa Sample Return Mission Makoto Yoshikawa, Junichiro Kawaguchi, and Akira Fujiwara Japan Aerospace Exploration Agency

Akira Tsuchiyama Kyoto University

Hayabusa was the first asteroid sample return mission. It was launched in May 2003, and arrived at the target asteroid (25143) Itokawa in September 2005. The mission enabled us to see close up a very tiny asteroid in detail for the first time. Hayabusa observed Itokawa with its scientific instruments, and attempted to collect surface material. The mission experienced several serious problems, but successfully returned to Earth in June 2010. After retrieving the capsule, we found thousands of small grains that had been captured from the asteroid. We studied Itokawa in detail with both the remote sensing data and the returned samples, which revealed a great deal of new information to shed light on its origin. In this chapter, we review the Hayabusa mission and summarize the scientific results.

2. HAYABUSA MISSION DESCRIPTION AND FLIGHT RESULTS

1. INTRODUCTION Hayabusa, the world’s first asteroid sample return mission, was built and launched by the Institute of Space and Astronautical Science (ISAS), which was later merged with the Japan Aerospace Exploration Agency (JAXA). The project code name was MUSES-C, and after launch in May 2003 was given the name “Hayabusa,” which literally translates to “falcon.” Hayabusa arrived at its target asteroid in September 2005, and returned to Earth in June 2010. The main purpose of the mission was to demonstrate the key technologies required for future planetary missions. Hayabusa made a roundtrip flight to a celestial object outside of Earth’s gravity sphere. The voyage, however, entailed many hardships, most of which were not anticipated before launch, but Hayabusa successfully returned surface material from the asteroid. Hayabusa was also the first spacecraft to explore a subkilometer-sized asteroid. The target asteroid was the S-type near-Earth asteroid (25143) Itokawa, about 500 m in length. Hayabusa revealed the strange nature of Itokawa by observing it with its remote sensing instruments in 2005. Although the amount of sample from Itokawa was quite small, the analyses of the returned samples have been continued worldwide after the capsule returned to Earth in 2010, and much new information has been gained from this sample analysis. In this chapter, we first explain the mission description as originally conceived and provide a flight summary, including what anomalies occurred and how the project team coped with those anomalies during the flight. The science results are then summarized in section 3 for remote sensing observations and in section 4 for sample analyses.

2.1. Mission Objectives The Hayabusa project was primarily a technology demonstration for future sample-return attempts from primitive bodies such as comets and asteroids (Kawaguchi, 1986, 2003; Kawaguchi et al., 2002). The spacecraft lifted off on May 9, 2003, onboard an M-V vehicle from Uchinoura, Japan. It performed an Earth swingby the following May. The mission plan adopted by Hayabusa was a little different from that taken by such missions as Rosetta, whose efforts were concentrated on the in situ analysis of the surface material of a comet. Instead of delivering the analysis equipment, the Hayabusa project intended to return a small amount of the surface sample to Earth, where large state-of-the-art facilities are available for detailed analysis. According to the original scenario, the spacecraft was to jettison a small reentry capsule in June 2007, when it would have returned back to Earth. The flight period scheduled was approximately four years. However, as this chapter describes later, due to unexpected incidents, the flight was extended and it actually returned home on June 13, 2010, resulting in a flight duration of seven years. Hayabusa carried five key technology objectives to be demonstrated: (1) interplanetary cruise via ion engines as primary propulsion, (2)  autonomous navigation and guidance using optical measurements, (3) sample collection from the asteroid surface under microgravity, (4) direct reentry for sample recovery from interplanetary orbit, and (5) combination of

397

398   Asteroids IV low thrust and gravity assist. In addition to these, Hayabusa also carried other new technologies, such as a bi-propellant small thrust reaction control system (20N), X-band up/down communication, complete Consultative Committee for Space Data Systems (CCSDS) packet telemetry, duty guaranteed heater control electronics, wheel unloading via ion engines, pseudo-noise (PN) code ranging, lithium ion rechargeable battery, multi-junction solar cell, etc. The development of Hayabusa was proposed to the government in 1995, and the project began in 1996. The original target asteroid was the near-Earth asteroid (4660)  Nereus and the backup target was another near-Earth asteroid, (10302) 1989 ML. However, when the spacecraft development started, the project faced mass capability issues and Nereus was replaced by 1989  ML as the primary target body. In 2000, a launch mishap occurred as the result of a launcher propulsion element flaw. As a result, the launch of MUSES-C was shifted half a year and the target asteroid was again switched to a different object, the near-Earth asteroid (25143) 1998 SF36, which was renamed Itokawa after Hayabusa’s launch. It should be noted that there were only a very few objects for which sampling and return opportunities were possible. While there were a great number of known asteroids, the number of those for which a low-energy mission scenario could be employed was approximately 10 to 20. In contrast to Nereus and 1989  ML, the new mission target was found to be accessible only via an Earth gravity assist due to the low thrust propulsion of the spacecraft. This technique is what is known as the Electric Delta-V Earth Gravity Assist (EDVEGA) strategy, and was first devised by the ISAS of JAXA. It is the most efficient way of accelerating a spacecraft from Earth when electric or low-thrust propulsion is used. The Hayabusa spacecraft was the first demonstration of the EDVEGA technology (Kawaguchi et al., 2004). The first year after launch was devoted to acceleration in the vicinity of Earth. The EDVEGA phase was followed by the transfer phase, which took approximately one year, and the spacecraft arrived at asteroid Itokawa in the summer of 2005 (Fig.  1). The spacecraft’s return was originally planned to occur in June 2007, and the mission should have been completed in four years. However, as a result of numerous difficulties, the flight was extended to seven years and it finally returned in June 2010. 2.2. The Hayabusa Spacecraft System 2.2.1. Configuration. Hayabusa was a small probe whose dimensions were 1.0 m × 1.6 m × 1.1 m, with a total weight (wet mass) of 510  kg, including 70  kg of chemical fuel for the reaction control system (RCS) and 60 kg of Xe propellant for the ion engines. The relatively large solar array generated 2.6 kW of electric power at Earth. The top and bottom views of the Hayabusa spacecraft are shown in Fig.  2. It was a three-axis stabilized spacecraft with a fixed high-gain antenna (HGA) and solar array panel (SAP). Most of the instruments were on the bottom of the spacecraft so they could be pointed to the asteroid surface when the spacecraft descended and

touched down on the surface. The ion engine thruster apertures were located on a side panel (+X panel), while the reentry capsule and star tracker were on the –X panel. The ion engine system adopted consisted of four thruster heads located on a two-axis gimbal plate so that the thrust could always penetrate the center of gravity and the attitude could eliminate the disturbance torque. On both ±X panels there were medium-gain antennas (MGA) that enabled the spacecraft to communicate with ground stations while the ion engines were turned on, and the HGA was not pointed to Earth. There was a sample collection horn that extended down from the –Z panel. The –X panel was the surface that was not supposed to be illuminated by the Sun, while the +X panel could be exposed to the Sun to a certain extent. The HGA was basically the same as that on the ISAS Mars Exploration spacecraft Nozomi, and its diameter was 1.6 m. The communication system adopted X-band for both up and down links. During the EDVEGA phase, since the distance from the Sun decreased below 1 AU, the HGA was painted white for thermal control. There was a Sun angle sensor and a low-gain antenna (LGA) at the top of the HGA. 2.2.2. Special ion engines adopted. The special characteristics of the ion engines onboard Hayabusa were (1) the use of microwave discharge to generate plasma and (2) the use of a carbon-carbon (CC) composite for the grids. Since there were no electrodes in the system, the life of the thruster was greatly extended to 18,000 hours. 2.2.3. Autonomous descent and touchdown. When the spacecraft made its initial approach to the surface of Itokawa, it jettisoned a target marker that served as an artificial landmark, illuminated by a flash lamp onboard the spacecraft once every second so that the optical navigation camera (ONC) could detect the marker by subtracting two images, 2.0

1.5

Hayabusa Earth (25143) Itokawa Asteroid arrival Sept. 12 2005

Earth

1.0 (25143) Itokawa

Hayabusa

0.5

0.0

–0.5

–1.0

–1.5 –1.5

Launch May 9, 2003 Earth swingby May 19, 2004 –1.0

–0.5

0.0

0.5

1.0

1.5

2.0

Fig. 1. Orbit of Hayabusa from launch to asteroid arrival. The EDVEGA phase was from launch to Earth swingby, and the transfer phase was from Earth swingby to asteroid arrival.

Yoshikawa et al.:  Hayabusa Sample Return Mission   399

one that was illuminated by a lamp and the other that was not illuminated. The primary purpose of the target marker was to enable the spacecraft to autonomously identify lateral velocity. As is often the case with soft landing, the horizontal velocity detection and control is always key, while the vertical navigation and control is less difficult. The spacecraft then stopped RCS firings and touchdown was performed in a free-fall manner in order to avoid surface contamination. 2.2.4. Sample collection device. The sample collection was designed to be performed in a very unique manner, and depended upon the motion of fragments when a projectile impacts a surface in a vacuum in microgravity. The mission designers decided to avoid the problems of anchoring and drilling. Instead, the Hayabusa mission adopted ejecta collection via a projectile shot, which can cope with a variety of surface conditions, even sand, and collect sufficient samples for detailed analysis in a rapid manner. In the adopted sampling technique, the ejected fragments are guided through a funnel-like device, the sampler horn. The device was deployed immediately after the spacecraft was in orbit. The length of the horn was ~1 m, sufficient to prevent the tip of the SAP from hitting the asteroid’s surface. The design called for the ejected sample to reach the canister, which would be pushed into the reentry capsule for recovery. The expected collected sample amount was approximately less than 1 g. The main advantage of sample return is that a very small sample is adequate. Low-Gain Antenna Sun Sensor

High-Gain Antenna

Solar Array Panel

Ion Thruster Bi-Propellant Thruster

Reentry Capsule

Star Tracker

Sampler

Middle-Gain Antenna

ONC-T

LIDAR MINERVA

Near-Infrared Spectrometer Fan Beam Sensor

Laser Range Finder

ONC-W X-Ray Fluorescence Spectrometer

Target Marker

Fig. 2. Diagram of the Hayabusa spacecraft and its instruments.

2.2.5. Sample recovery capsule and its operation. When the spacecraft returned to Earth, since the trajectory’s incoming asymptote would point to the southern hemisphere so that the reentry flight path angle remained shallow, the reentry point needed to be in the southern hemisphere. Otherwise, the reentry would become steep and the heat flux experienced would become too high for successful recovery. As a result, the recovery location was situated in the Woomera Prohibited Area in Southern Australia. The diameter of the capsule was 400  mm and weighed about 20  kg. The reentry capsule consisted of the thermal protection shield, structure, sample container, and sequencer, including the beacon transmitter. The heat shield shells consisted of forward and aft shells that were designed to be separated from the instrument section when the parachute deployed. The development of the heat shield was one of the most critical issues in the Hayabusa project. ISAS built an arc-heating test facility and also performed heating experiments at the NASA Ames Research Center in collaboration with NASA. 2.3. Summary of Incidents and Difficulties The spacecraft was launched in May 2003. From the beginning, the flight was not easy and experienced many unfortunate events. The spacecraft experienced the largest solar flare that had ever happened, consequently resulting in degradation of a solar cell, eventual loss of two out of the three reaction wheels, a fuel gas eruption and consequent loss of attitude, loss of communication with the ground for seven weeks, loss of the lithium ion battery during loss of attitude, loss of the onboard chemical engines, the gradual loss of ion engines and loss of three out of the four neutralizers, and failure of the sample collector. The most significant critical events occurred when the spacecraft got lost after the completion of the second touchdown to the surface of asteroid Itokawa at the end of 2005, and when the spacecraft’s ion engine shut down due to the end of life associated with the neutralizer six months prior to the return to Earth. 2.3.1. Proximity operation and descent and touchdown sampling. After the spacecraft arrived at the home position located 20  km above the asteroid’s surface, the spacecraft conducted a mapping and imaging operation for more than a month. The spacecraft utilized asteroid gravity along with RCS firings to move up and down and side to side. Shape modeling of the asteroid was done during this period. The spacecraft then performed practice descent maneuvers to practice and confirm the touchdown scenario. During this period the spacecraft released a surface robot, the Micro/ Nano Experimental Robot Vehicle Asteroid (MINERVA), aiming it at the asteroid’s surface. However, due to the very subtle but inaccurate ground-control operation, MINERVA was not accurately released, and it was traveling away from the asteroid. Thus the MINERVA operation largely failed, but the relay capability was successful and a photo of the solar paddle of Hayabusa taken by MINERVA was relayed back to the ground.

400   Asteroids IV A sophisticated autonomous maneuver was successfully performed when Hayabusa performed its first touchdown attempt on November  20, 2005. At the first touchdown, after releasing a target marker, the spacecraft detected the marker and everything seemed ready for shooting a projectile. However, the spacecraft-carried obstruction detection sensor detected a reflection from some small particles, probably aloft above the surface, and the sample collection shot was not directed. The spacecraft bounced a few times and it settled down on the surface near the polar region waiting for commands from the ground for almost 30 minutes. The spacecraft lifted off when the emergency lift command was sent from the ground. The second touchdown was attempted on November 25, 2005. During this attempt, a new target marker was not deployed because of the possibility that the spacecraft could detect two target markers at the same time, resulting in confusion. The guidance accuracy was well developed and the expected landing accuracy was sufficiently high. The spacecraft clearly photographed the target marker placed one week before when the spacecraft made its first touchdown (Fig.  3). The spacecraft touched down as planned and the projectile shot was directed from the inboard computer, and the sampling was thought at first to have been performed perfectly. However, it was revealed later that the shooting pyro control circuit was turned to safe mode and the projectile was not fired. Fortunately, the recovered capsule carried back many particles that must have been caught by static electricity when the spacecraft descended to the surface two times. 2.3.2. Leak of reaction control system fuel. When the spacecraft made a successful landing on the surface and lifted off from there on November  25, 2005, firing RCS thrusters on the top panel to decelerate the ascent speed, one of the thrusters began leaking fuel. This caused the

Fig. 3. Hayabusa’s shadow on the surface during the second touchdown. The white dot in the circle is the target maker released during the first touchdown.

spacecraft to be placed in safe-hold mode. All the hydrazine leaked out, and the RCS became unusable for the remainder of the mission. Another large gas eruption made the spacecraft tumble, and beginning in December 2005, radio communication was lost for seven weeks. 2.3.3. Resumption of communication and restoration. The tumbling precluded solar power and the spacecraft power was turned completely off. The onboard battery probably maintained the system for approximately 40 minutes, but it was probably dead after that. The project team developed a rescue operation plan to wake up the spacecraft. Fortunately, the spacecraft was designed to settle into a single spin motion around the maximum moment of inertia, the Z-axis. Once the gas eruption stopped, the attitude settled into a single spin whose rotation axis was fixed to a particular direction with respect to the background sky. There was a chance for the spacecraft to acquire solar power together with the omni-antenna aperture open toward Earth. The probability of this was calculated to be up to 60–70% during the following year. The project team devised the operation so that the command could be heard at any high spin rate, at any attitude, regardless of any antenna profile gaps. The ground team continued to monitor the spacecraft, hoping to receive any signal. The miracle occurred at the end of January 2006, when a carrier signal was finally received by JAXA’s deep space antenna. The spacecraft was rotating in the opposite spin direction because of the gas eruption torque. The spin rate was high, and the radio signal was intermittent. 2.3.4. Recovery operation. The project team began recovery operations immediately. The biggest challenge was how to reorient the spacecraft attitude to Earth with the lowered spin motion. The operation started by initial Sun acquisition using the coarse Sun sensor. Ion engines were used to decelerate the spin motion by exhausting Xe gas with no electric acceleration. It took five months to properly correct the spacecraft attitude. There was the constant threat of loss of solar power, since the spacecraft spin direction was frozen in the inertial frame and the Sun direction shifts 90° over three months. The operation also had severe time constraints, and thus the project team gave up on the goal of the spacecraft returning in 2007. Instead, the project team amended the flight sequence, and decided to have it return in 2010. 2.3.5. Auto-Sun tracking with no fuel. While the spacecraft was restored and telemetry was again being received, the biggest anticipated obstacle was how to perform the attitude control to make sure the spacecraft was appropriately pointed toward the Sun while at the same time making sure that the apertures of its ion engines are properly pointed to the intended direction with no fuel. Hayabusa was equipped with ion engines independent of RCS and carried an additional propulsion system, even though the thrust was very weak and was never really intended for impulsive maneuvers. With the gimbaled table on which ion engines were mounted, the angular momentum of the spacecraft was managed in the Y- and Z-axes. Since the ion engine thrust was along the X-axis, no propulsion torque was available

Yoshikawa et al.:  Hayabusa Sample Return Mission   401

around that axis, and therefore the project team came up with another new strategy. It used solar radiation torque to maintain the spacecraft spin direction, keeping it automatically pointed toward the Sun like an arrow in the wind. 2.3.6. Ion engine end of life and cross-connection of engines. The spacecraft’s ion engine drive performed successfully from 2007 to till 2009. However, the engines reached the end of their life in November 2009, when all four engines became inoperable due to the death of the neutralizers. Among the four engines, three neutralizers were broken and it was therefore not possible to extract electrons from them. However, there was a single intact neutralizer left, Neutralizer A. Engine A had remained undriven since launch, since a problem was discovered in its radio frequency cable, and the ion source A did not work well and had been left unused. Engine A was still not usable, but the decision was made to use its neutralizer combined with ion sources B, C, and D, even though the engines were not designed to function in such a cross-connection configuration. Thus the project team found that they could successfully drive engine  B with neutralizer A, which allowed was a miraculous restoration of the propulsion system. 2.3.7. Guidance via ion engines. The consecutive ion engine cruise lasted until the end of March 2010. The reentry required accurate trajectory corrections. These were applied in five segments, from April to June 2010, with the goal of reentry on June 13, 2010. The trajectory correction maneuvers (TCMs) actually took 250 h 46 min 40 s just for 13.54 m s–1 DV. There was a stringent attitude constraint in Hayabusa. The ion engine heads were aligned to the X-axis only, while the power source solar array panels were fixed to the Z-axis. Orbital control via ion engines only was a big challenge. 2.3.8. Capsule reentry and recovery. The project team had performed the successive TCMs via ion engine operation. The final maneuver, TCM 4, was performed to accurately target the touchdown point within the recovery area where the ground staff was deployed to locate the capsule landing point via radio signal. The anticipated accuracy was within several kilometers. On June 13, 2010, Hayabusa returned to Earth, and a small reentry capsule containing the asteroid sample separated from the spacecraft three hours prior to its own reentry. Hayabusa plunged into the atmosphere over the Australian desert (Fig. 4). The deployment of the parachute was designed to be triggered by not only a given time, but also by the peak acceleration detected onboard, whichever occurred first. The primary capsule detection system consisted of three sets of double UHF antenna arrays that precisely identified the signal direction. The combination of the signal confirmed the possible landing area within 5–10 km, and a helicopter was used to find the sample return container. The capsule was discovered within 30 minutes of reentry, about 500 m from the presumed location. The recovered capsule was placed inside a special container filled with nitrogen and shipped to Japan for sample removal (Kawaguchi, 2010a,b; Kawaguchi et al., 2011).

Fig. 4. Hayabusa’s reentry into Earth’s atmosphere.

2.3.9. Remarks. The Hayabusa mission presented a huge challenge that had never before been achieved. For seven years the Hayabusa mission was plagued with incidents and mishaps, but the mission team and engineers maintained their spirit and commitment to bringing the spacecraft safely home. 3. RESULTS OBTAINED BY IN SITU OBSERVATION 3.1. Global Properties of (25143) Itokawa Itokawa measures 535 × 294 × 209 m, and has a mean diameter of 320  m, a spin period of 12.1  h, a density of 1.9  g  cm–3, and revolves with retrograde rotation. More detailed information is given by Fujiwara et al. (2006). The mean diameter is in good agreement with the value obtained by groundbased mid-infrared (Sekiguchi et al., 2003) and radar observations (Ostro et al., 2004, 2005; see the chapter by Benner et al. in this volume). The pre-arrival results from groundbased observations of the rotation period and spin direction (retrograde rotation, perpendicularity of the spin axis to the ecliptic), along with its spectral type (Binzel et al., 2001; Dermawan et al., 2002; Kaasalainen et al., 2003; Ohba et al., 2003; Ostro et al., 2004, 2005; Lowry et al., 2005; see the chapter by Li et al. in this volume), were confirmed by the more detailed data obtained by Hayabusa. There is no apparent short-term precession of the spin pole, which shows that enough time has passed for the asteroid to be dynamically relaxed after the last large impact event. No satellites were found by the Asteroid Multi-band Imaging Camera (AMICA) (also called ONC-T, one of the optical navigation cameras) images (Fuse et al., 2008), which is consistent with past optical and radar observations and not inconsistent with the suggestion of the existence of meteoroids related with Itokawa from groundbased observations (Ohtsuka et al., 2011), although none were directly observed by the spacecraft. The mass of the asteroid was estimated from Hayabusa tracking and navigation. Using lidar (light radar) data (Abe et al., 2006b; Mukai et al., 2007), as well as navigation data, and considering the effects of attitude maneuvers, the mass was determined to be 3.51 × 1010 kg. Coupled with the volume of Itokawa, estimated from the three-dimensional

402   Asteroids IV shape models (Demura et al., 2006), the bulk density of Itokawa is estimated to be 1.9 g cm–3. Itokawa has a bifurcated shape like a floating sea otter (Figs. 5, 6, and 7). The smaller part is called the “head” and the larger part is called the “body.” In the attitude of Fig. 6, south is up and north is down due to retrograde rotation. The overall shape of both parts is not angular like the asteroid (951) Gaspra (Veverka et al., 1994), but rather rounded and there is no global lineament as seen on (433) Eros (Cheng et al., 2007). The size of the ellipsoid fitted to the body is 490 × 310 × 260 m, and that to the head is 230 × 200 × 180 m, respectively (Demura et al., 2006). The appearance of the surface is different from any other asteroids so far observed by spacecraft, including (243) Ida, (253) Mathilde, and Eros, whose surfaces are globally covered with a thick regolith layer and many craters (Chapman, 2002), as seen even in images of Eros taken with scales comparable with Itokawa. The surface of Itokawa is divided into two distinct types of terrain: rough terrain, consisting of numerous boulders, and smooth terrain, which shows the existence of a smoother regolith layer (see the chapter by Murdoch et al. in this volume). Rough terrain (see close-up view in Fig. 8) makes up ~80% of the surface (Saito et al., 2006). The smooth terrain is distributed into two distinct regions: “MUSES-C,”

named for the wide region extending around the “breast” on the “body,” where the spacecraft landed for sampling, and “Sagamihara,” around the north-polar region near the “back” of the body. Close-up viewing of the MUSES-C Regio (Fig.  9) shows that the smooth terrain is composed of centimeter- to millimeter-scale fragmental debris and pebbles (Yano et al., 2006). Most grains in the MUSES-C Regio are larger than those observed in the close-up view of Eros’ surface, and there is a strong depletion of fine grains on Itokawa compared with Eros. The boundaries between the rough and smooth terrains are relatively sharp, but a gradient of boulder number density and some evidence of movement of the surface material are evident (Miyamoto et al., 2007). 3.2. Boulders Most boulders are found in the rough terrain, while in the smooth terrain boulders appear buried by regolith. The average number density of boulders larger than 5  m is 103 km–2 (Michikami et al., 2008), which is slightly larger than that on the surface of Eros (Thomas et al., 2001). A black boulder is found at the top of the head, where the gravitational potential is the highest (Fig. 7), and which was assigned as the prime meridian (longitude 0°) (Fujiwara et al., 2006). This boulder measures ~6 m and has unusually low brightness, resulting in a striking contrast with its surroundings. Three other smaller similar boulders were also found (Hirata and Ishiguro, 2011). The largest boulder, named Yoshinodai, is about 50 × 30 × 20 m in size (Saito et al., 2006) and is located near the “right foot” of the “body” (Fig. 6). There are several boulders with sizes larger than a few tens of meters on the western side (longitude 0°–180°W) while large boulders are less abun-

Fig. 5. Eastern side of Itokawa. The bottom is north. The spacecraft landed on the smooth terrain near MUSES-C.

Fig. 6. Western side of Itokawa. On this side, large boulders are more abundant than on the eastern side. Yoshinodai is the largest boulder.

Fig. 7. “Back head” of Itokawa viewed from top. A large depression at the “neck” is Yosinobu. On the top of the “head” a black boulder is evident (inside the square). Scale bar is 10 m.

Yoshikawa et al.:  Hayabusa Sample Return Mission   403

dant on the eastern side. There are several large pinnacles at the neck region on the western side (Fig. 6), believed to have resulted from landside from the higher gravitational potential of the “head” to the lower potential region of the “neck” to “breast” region. An experimental relationship exists between the size of a crater and the maximum size of the excavated fragment (Gault et al., 1963), which was confirmed observationally for the main-belt asteroid Ida and other asteroids (Lee et al., 1996). These are also consistent with boulders around the Shoemaker crater on Eros (Thomas et al., 2001). Following these empirical relationships, the size of the crater that would have produced the largest boulder, Yoshinodai, and some others actually exceeds the size of the largest crater candidates found on Itokawa. Hence these boulders are the likely relics formed in some cataclysmic event related to the formation of Itokawa’s current configuration. The cumulative size distribution of boulders obtained by Michikami et al. (2008) is shown in Fig. 10. The slope index of the distribution is –3.1 ± 0.1, which is comparable with the value of –3.2 for the 15 –80-m boulder size range on Eros (Thomas et al., 2001). It should be noted that the index changes slightly depending on the measurement method, and in Michikami et al.’s (2008) work the size is defined as that measured horizontally. If the largest size is measured instead of horizontal size, the index is –2.8 (Saito et al., 2006). This is because larger boulders have longer or spall-like shapes, which suggests that those fragments are produced by impacts. Actually, this is consistent with the shape of many fragments observed on Itokawa’s surface (as shown in Fig. 8), which are very similar to those observed in some laboratory impact experiments (Nakamura et al., 2008a; Michikami et al., 2008). Morphological features

Fig. 9. Close-up view of MUSES-C Regio.

1000

Cumulative Number of Boulders per km2

Fig. 8. Close-up view of rough terrain on Itokawa. Irregular plate-like fragments are characteristic of impact spalls.

100

10

1

5

6

7

8

9 10

20

30

Boulder Size (m) Fig. 10. Boulder size distribution on Itokawa (Michikami et al., 2008). Size is defined as the mean horizontal dimension of a boulder. The broken line is a fitted regression line. The power-law index is –3.1 ± 0.1.

of Itokawa boulders are also discussed by Noguchi et al. (2010). Mazrouei et al. (2014) performed a more detailed study of the size distribution of boulders greater than 6 m and showed that the slope index is –3.5, which is significantly steeper than the slope obtained by Michikami et al. (2008). A latitudinal variation of the block population also exists on the body, which may suggest that the asteroid is a composite of two different bodies (i.e., a binary asteroid).

404   Asteroids IV

3.3. Craters Many crater-like depressions are found on Itokawa, but most of them have a shape that does not make them as easily identified as craters as those found on the surface of other asteroids. Hirata et al. (2009) listed 38 crater candidates on Itokawa’s surface (see the chapter by Marchi et al. in this volume): five candidates — Yoshinobu (Fig. 7), Arcoona, LINEAR, Uchinoura (Fig. 5), and Ohsumi (Fig. 6) — have diameters larger than 100 m, and the others are smaller than 100  m. Generally, most of the crater-like depressions are shallower than craters observed on the surface of other planetary bodies and asteroids. Large craters have flat or convex floors affected by the pre-impact local surface curvature as shown in laboratory impact experiments (Fujiwara, et al., 1993), and a typical example of this type is Arcoona, which has a circular structure about 150 m in diameter extending around the bottom of the “body” (longitude of ~180°). Many small craters are found on the smooth terrains on Itokawa, and those are also shallow. The depth/diameter ratio for the crater candidates is around 0.1 for diameters larger than 50  m, and has lower values for diameters less than 50 m (Hirata et al., 2009). For comparison, the same ratio is 0.14 for fresh craters on Gaspra (Carr et al., 1994), 0.15 for fresh craters on Ida (Sullivan et al., 1996), and 0.13 for Eros (Barnouin-Jha et al., 2001; Robinson et al., 2002). The low value of the ratio for small craters on Itokawa could be due to some granular processes, such as seismic shaking and granular convection (Güttler et al., 2014; Yamada and Katsuragi, 2014; Matsuura et al., 2014). The observed density of the crater candidates on Itokawa is close to the empirical saturation level at the largest diameter, and declines with decreasing diameter (Fig.  11). This decreasing trend is also seen for crater diameters less than 100 m for Eros (Chapman et al., 2002). The lack of small craters on Itokawa may be attributed in part to elimination of craters due to seismic shaking and as well as the inefficiency of creating craters due to the effect of armoring by boulders (Miyamoto et al., 2007; Barnouin-Jha et al., 2008), as demonstrated by laboratory experiments (Güttler et al., 2012). Michel et al. (2009) studied cratering and crater erasure processes and provided an age estimate for Itokawa. They find that the time necessary to accumulate Itokawa’s craters was at least ~75 m.y., and perhaps as long as 1 G.y.,

1

Itokawa Model Crater Population (Bottke Impacting Population, Strength-A) Empirical Saturation

0.1

R

The boulder density does not show a correlation with the crater density. The boulders exist regardless of the position of the craters. The total estimated volume of boulders is 8.2  × 104  m–3, and the ratio of boulder volume to crater volume is ~25% (Michikami et al., 2008). This value is higher than that obtained so far for other small bodies. For example, on Eros the ratio is less than 1% (Thomas et al., 2001), and on the Moon it is ~5% (Cintala et al., 1982). Considering that Itokawa is very small and has a very low escape velocity (on the order of 10 cm s–1), boulders currently observed on Itokawa could not have been produced from the recent craters.

0.01 0.001 0.0001 1e-05 1

Model crater population Observed craters (Class 1–4) 10

100

1000

Crater Diameter (m) Fig. 11. R-plot diagram (differential crater size-frequency distribution divided by D–3, where D is the crater’s diameter) of Itokawa’s crater population (Michel et al., 2009). The observed data [including all crater candidates classified as class 1–4 by Hirata et al. (2009)] and one of the model fits (solid line) by Michel et al. (2009) are shown. The impacting population of Bottke et al. (2005) is assumed in the model to accumulate craters on Itkokawa’s surface over time and impact scaling laws (labeled Strength A) by Nolan et al. (1996) are used in this example to convert projectile size to crater size. The exposure times represented are 25, 75, and 150 m.y. (gray dots are placed to help discriminate between the different curves). The best fit occurs after about 75 m.y. However, given the small number statistics for the few largest craters, any exposure time in the range 25–150 m.y. is actually plausible. Note that the model predicts significantly more craters smaller than 10 m in diameter than are actually observed, which suggests that some processes may be efficient at erasing craters smaller than this size (see Michel et al., 2009, for details).

and suggest that the pronounced deficiency of small craters (D), as a function of asteroid diameter D, from Morbidelli et al. (2009). These coagulation models started with either (a) kilometer-sized planetesimals or (b) an initial size distribution following the current, observed size distribution of asteroids between 100 and 1000 km in diameter. The gray line shows the current size distribution of asteroids larger than 100 km in diameter. The model with small planetesimals overproduces asteroids smaller than 100 km in diameter (the upper dashed line represents the current size distribution of small asteroids while the lower dashed lines indicates a tighter constraint on the size distribution directly after accretion of the main belt). Starting with large asteroids gives a natural bump in the size distribution at 100 km in diameter, as the smaller asteroids are created in impacts between the larger primordial counterparts.

Weidenschilling (2011) managed to reproduce the elbow at D ~ 100 km in the asteroid belt from collisional coagulation simulations starting from objects 50–200 m in radius. Because of the small size of these objects, collisional damping and gas drag keep the disk very dynamically cold (i.e., with a small velocity dispersion among the objects). Hence, in the simulations of Weidenschilling (2011), the elbow at D ~ 100 km is produced by a transition from dispersiondominated runaway growth to a regime dominated by Keplerian shear, before the formation of large planetary embryos. However, any external dynamical stirring of the population,

478   Asteroids IV for instance due to gas turbulence in the disk, would break this process. Moreover, these simulations are based on the assumption that any collision that does not lead to fragmentation results in a merger, but 100-m-scale objects have very weak gravity and the actual capability of bodies so small to remain bound to each other is questionable. Finally, we stress that the formation of 100-m-scale bodies is an open issue, in view of the bouncing barrier and meter-sized barrier discussed in section 4. 3.2. Snowline Problems Among the various meteorite types that we know, carbonaceous meteorites (or at least some of them like CI and CM) contain today a considerable amount (5–10%) of water by mass. Evidence for water alteration is widespread, and it is possible that the original ice content of these bodies was higher, close to the 50% value expected from unfractionated solar abundances. Instead, ordinary chondrites contain 10× local enhancement of the usually assumed 1% cosmic solids-to-gas ratio within some few 104 km of the mid-plane) could match the required rate of planetesimal formation and the characteristic mass mode around 100–200-km diameter. Cuzzi et al. (2010) gave a number of caveats regarding the built-in assumptions of this model; one caveat regarding scale-dependence of the concentration process has been found to be important enough to change the predictions of the scenario quantitatively (see below). Subsequently, Cuzzi and Hogan (2012) resolved a discrepancy in a key timescale between Cuzzi et al. (2010) and Chambers (2010), which makes planetesimal formation 1000× faster than in Cuzzi et al. (2010) [and correspondingly slower than in Chambers (2010)]. 5.2. New Insights into Turbulent Concentration The primary issues are whether it is always Kolmogorov friction time particles that are most effectively concentrated, and whether the physics of their concentration are scaleinvariant. Hogan and Cuzzi (2007) argued by analogy with the observed scale-invariance of turbulent dissipation, which is dominated by Kolmogorov-time vortex tubes (little tornados in turbulence) that the concentration of Kolmogorovfriction-time particles would also be scale-invariant (see also Cuzzi and Hogan, 2012). They developed a so-called cascade model by which to extend the low-Re results to nebula conditions. The primary accretion scenarios of Cuzzi et al. (2010) and Chambers (2010) used this cascade model to generate density-vorticity probability density functions (PDFs) as

a function of nebula scale. Pan et al. (2011) ran simulations at higher Re than Hogan and Cuzzi (2007) and found that the clump density PDFs dropped faster than would be predicted by the scale-invariant cascade. They suggested that the physics of particle concentration might indeed be scale-dependent, and that planetesimal formation rates obtained using the Hogan and Cuzzi (2007) cascade might be significantly overestimated. Ongoing work supports this concern about scale dependence. Cuzzi et al. (2014) have analyzed much higher Re simulations (Bec et al., 2010) and found that the cascade measures, called “multiplier distributions,” that determine how strongly particles get clustered at each spatial scale do depend on scale at least over the largest decade or so of length scale; i.e., the scale-invariant inertial range for particle concentration and dissipation does not become established at the largest scale, causing little concentration to occur until roughly an order of magnitude smaller scale. Because the cascade process is multiplicative, this slow start means that fewer dense zones are to be found at any given scale size than previously thought. New, scale-dependent cascades can now be implemented to predict planetesimal IMFs using the approach of Cuzzi et al. (2010, 2014). The quantitative implications are not clear as yet, but particles with friction times significantly longer than those of single chondrules are most strongly clustered at length scales most relevant to direct planetesimal formation (see also Bec et al., 2007). Meanwhile, turbulent concentration of small particles may play a critical and as yet unmodeled (in astrophysics) role in formation of aggregates by collisions and sticking (see, e.g., Shaw, 2003; Pan et al., 2011) (section 4). Some combination of these effects probably contributes to observed chondrule size distributions, some (but not all) of which appear broader than previously thought (Fisher et al., 2014; Friedrich et al., 2015; Ebel et al., 2015). 6. PRESSURE BUMPS AND STREAMING INSTABILITY The turbulent concentration mechanism described in the previous section operates on the smallest scales of the turbulent flow (although the vortical structures that expel particles can be very elongated). The dynamical timescales on such small-length scales are much shorter than the local orbital timescale of the protoplanetary disk. In contrast, the largest scales of the turbulent flow are dominated by the Coriolis force, and this allows for the emergence of largescale geostrophic structures (high-pressure regions in perfect balance between the outward-directed pressure gradient force and the inward-directed Coriolis force). Whipple (1972) found that particles are trapped by the zonal flow surrounding large-scale pressure bumps. Pressure bumps [in a way azimuthally extended analogs to the vortices envisioned in Barge and Sommeria (1995)] can arise through an inverse cascade of magnetic energy (Johansen et al., 2009a; Simon et al., 2012; Dittrich et al., 2013) in tur-

Johansen et al.:  New Paradigms for Asteroid Formation   483

bulence driven by the magnetorotational instability (Balbus and Hawley, 1991). Pressure bumps concentrate primarily large (0.1–10 m) particles that couple to the gas on an orbital timescale (Johansen et al., 2006), reaching densities at least 100× the gas density, which leads to the formation of 1000-km-scale planetesimals (Johansen et al., 2007, 2011). The magnetorotational instability is nevertheless no longer favored as the main driver of angular momentum transport in the asteroid-formation region of the solar protoplanetary disk, since the ionization degree is believed to be too low for coupling the gas to the magnetic field (see review by Turner et al., 2014). The magnetorotational instability can still drive turbulence (with a in the interval from 10–3 to 10–2) in the mid-plane close to the star (within approximately 1 AU where the ionization is thermal) and far away from the star (beyond 20 AU where ionizing cosmic rays and X-rays penetrate to the mid-plane). Accretion through the “dead zone,” situated between these regions of active turbulence, can occur in ionized surface layers far above the mid-plane (Oishi et al., 2007), from disk winds (Bai and Stone, 2013) and by purely hydrodynamical instabilities in the vertical shear of the gas (Nelson et al., 2013) or radial convection arising from the subcritical baroclinic instability (Klahr and Bodenheimer, 2003; Lesur and Papaloizou, 2010). The mid-plane is believed to be stirred to a mild degree by these hydrodynamical instabilities or by perturbations from the active layers several scale-heights above the mid-plane, driving effective turbulent diffusivities in the interval from 10–5 to 10–3 in the mid-plane. The inner and outer edges of this “dead zone,” where the turbulent viscosity transitions abruptly, are also possible sites of pressure bumps and large-scale Rossby vortices that feed off the pressure bumps (Lyra et al., 2008, 2009). 6.1. Streaming Instability The low degree of turbulent stirring in the asteroidformation region also facilitates the action of the streaming instability, a mechanism where particles take an active role in the concentration process (Youdin and Goodman, 2005; Youdin and Johansen, 2007; Johansen and Youdin, 2007). The instability arises from the speed difference between gas and solid particles. The gas is slightly pressure-supported in the direction pointing away from the star, due to the higher temperature and density close to the star, which mimics a reduced gravity on the gas. The result is that the gas orbital speed is approximately 50 m s–1 slower than the Keplerian speed at any given distance from the star. Solid particles are not affected by the global pressure gradient — they would move at the Keplerian speed in the absence of drag forces, but drift radially due to the friction from the slower-moving gas. The friction exerted from the particles back onto the gas leads to an instability whereby a small overdensity of particles accelerates the gas and diminishes the difference from the Keplerian speed. The speed increase in turn reduces the local headwind on the dust. This slows down the radial drift of particles locally, which leads to a runaway process

where isolated particles drift into the convergence zone and the density increases exponentially with time. This picture is a bit simplified, as Youdin and Goodman (2005) and Jacquet et al. (2011) showed that the streaming instability operates only in the presence of rotation, i.e., the instability relies on the presence of Coriolis forces. This explains why the instability occurs on relatively large scales of the protoplanetary disk where Coriolis forces are important, typically a fraction of an astronomical unit, and operates most efficiently on large particles with frictional coupling times around one-tenth of the orbital timescale (typically decimeter sizes at the location of the asteroid belt). 6.2 Computer Simulations of the Streaming Instability Computer simulations that follow the evolution of the streaming instability into its nonlinear regime show the emergence of axisymmetric filaments with typical separations of 0.2× the gas scale-height (Yang and Johansen, 2014) and local particle densities reaching several thousand times the gas density (Bai and Stone, 2010; Johansen et al., 2012). These high densities trigger the formation of large planetesimals (100–1000 km in diameter) by gravitational fragmentation of the filaments (Johansen et al., 2007), although planetesimal sizes decrease to approximately 100 km for a particle column density comparable to that of the solar protoplanetary disk (Johansen et al., 2012). An important question concerning planetesimal formation through the streaming instability is whether the process can operate for particles as small as chondrules in the asteroid belt. In Fig. 3, we show numerical experiments from Carrera et al. (2015) on the streaming instability in particles with sizes down to a fraction of a millimeter. The streaming instability requires a threshold particle mass loading Z = Sp/Sg, where Sp and Sg are the particle and gas column densities, to trigger the formation of overdense filaments (Johansen et al., 2009b; Bai and Stone, 2010). The simulations in Fig. 3 start at Z = Z0 = 0.01, but the particle mass-loading is continuously increased by removing the gas on a timescale of 30 orbital periods. This was done to identify how the critical value of Z depends on the particle size. The result is that overdense filaments form already at Z  = 0.015 for centimeter-sized particles, while large chondrules of millimeter sizes require Z = 0.04 to trigger filament formation. Chondrules smaller than millimeters do not form filaments even at Z = 0.08. A lowered gas column density may thus be required to trigger concentration of chondrule-sized particles by the streaming instability. It is possible that the solar protoplanetary disk had a lower gas density than what is inferred from the current mass of rock and ice in the planets (which multiplied by 100 gives the MMSN), if the planet-forming regions of the nebula were fed by pebbles drifting in from larger orbital distances (Birnstiel et al., 2012). In this picture the growing planetesimals and planets are fed by drifting pebbles, so that the current mass of the planets was achieved by the integrated capture efficiency of the drifting solids; this

484   Asteroids IV τf = 0.001

τf = 0.003

τf = 0.01

τf = 0.03

0.08

0.04

150

100

0.02

50

0.01

–0.1

0

0.1 –0.1

0

0.1 –0.1

0

0.1 –0.1

0

0.1

Solid Concentration (Z)

Simulation Time (t/2πΩ–1) for ∆ = 0.05

200

5e–3

Fig. 3. Space-time plots of particle concentration by streaming instabilities, from Carrera et al. (2015), with the x-axis indicating the radial distance from the center of the simulation box and the y-axis the time (on the left) and the dust-to-gas ratio (on the right). The four columns show particle sizes 0.8 mm (tf = 0.001W–1), 2.4 mm (tf = 0.003W–1), 8 mm (tf = 0.01W–1), and 2.4 cm (tf = 0.03W–1). Simulations start with a mean dust-to-gas ratio of Z = 0.01, but gas is removed on a timescale of 30 orbits (1 orbit = 2pW–1), increasing the dust-to-gas ratio accordingly . While centimeter-sized particles concentrate in overdense filaments already at a modest increase in dust-to-gas ratio to Z = 0.015, smaller particles require consecutively increasing gas removal to trigger clumping.

allows for gas column densities lower than in the MMSN to be consistent with the current masses of planets in the solar system. The gas will also be removed by accretion and photoevaporation (Alexander and Armitage, 2006). The high mass-loading in the gas could be obtained through pileup by radial drift and release of refractory grains near the iceline (Sirono, 2011). Turbulence as weak as a ~ 10–7 is necessary to allow the sedimentation of chondrules (with St ~ 10–3) into a thin midplane layer with scale-height Hp = 0.01Hg and rp ≈ rg (see equation (2)), the latter being a necessary density criterion for activating particle pileup by streaming instabilities. Very low levels of a are consistent with protoplanetary disk models where angular momentum is transported by disk winds and the mid-plane remains laminar (Bai and Stone, 2013), except for mild stirring by Kelvin-Helmholtz (Youdin and Shu, 2002) and streaming instabilities (Bai and Stone, 2010). Weak turbulence also facilitates the formation of decimeter-sized chondrule aggregates (Ormel et al., 2008), which would concentrate much more readily in the gas. Stirring by hydrodynamical instabilities in the mid-plane, such as the vertical shear instability (Nelson et al., 2013), would preclude significant sedimentation of chondrule-sized particles and affect the streaming instability, as well as the formation of chondrule aggregates, negatively. An alternative possibility is that the first asteroid seeds in fact did not form from

chondrules (or chondrule aggregates), but rather from larger icy particles that would have been present in the asteroidformation region in stages of the protoplanetary disk where the iceline was much closer to the star (Martin and Livio, 2012; Ros and Johansen, 2013). Chondrules could have been incorporated by later chondrule accretion (see section 7). 7. LAYERED ACCRETION The turbulent concentration model and the streaming instability, reviewed in the previous sections, are the leading contenders for primary accretion of chondrules into chondrites. However, neither of the two are completely successful in explaining the dominance of chondrules in chondrites: The turbulent concentration models may not be able to concentrate sufficient amounts for gravitational collapse, while the streaming instability relies on the formation of chondrule aggregates and/or gas depletion and pileup of solid material from the outer parts of the protoplanetary disk. In the layered accretion model the chondrules are instead accreted onto the growing asteroids over millions of years after the formation of the first asteroid seeds — those first seeds forming by direct coagulation from a population of 100-msized planetesimals as envisioned in Weidenschilling (2011) or by one or more of the particle concentration mechanisms described in the previous sections.

Johansen et al.:  New Paradigms for Asteroid Formation   485

7.1. Chondrule Accretion Chondrules are perfectly sized for drag-force-assisted accretion onto young asteroids. The ubiquity of chondrules inside chondrites, and their large age spread (Connelly et al., 2012), indicates that planetesimals formed and orbited within a sea of chondrules. Chondrules would have been swept past these young asteroids with the sub-Keplerian gas. The gas is slightly pressure-supported in the radial direction and hence moves slower than the Keplerian speed by the positive amount Dv (Weidenschilling, 1977b; Nakagawa et al., 1986). The Bondi radius RB = GM/(Dv)2 marks the impact parameter for gravitational scattering of a chondrule by an asteroid of mass M, with 2



RB  R   Dv  = 0.87   50 km   53 m s −1  R

−2

  r·  −3   3.5 g cm 

(4)

Here we have normalized by Dv = 53 m s–1, the nominal value in the MMSN model of Hayashi (1981), and used the chondrule density r· = 3.5 g cm–3 as a reference value. Chondrules with friction time comparable to the Bondi timescale tB = RB/Dv are accreted by the asteroid (Johansen and Lacerda, 2010; Ormel and Klahr, 2010; Lambrechts and Johansen, 2012). The accretion radius Racc can be calculated numerically as a function of asteroid size and chondrule size by integrating the trajectory of a chondrule moving with the sub-Keplerian gas flow past the asteroid. The accretion radius peaks at Racc ≈ RB for tf/tB in the range from 0.5 to 10 (Lambrechts and Johansen, 2012). Accretion at the full Bondi radius happens for particle sizes 3

 R   Dv  a = [ 0.008, 0.16 ] mm   50 km   53 m s −1 



r   ×   2.5 AU 

−3

 ∑g  ∑

MMSN

 

−3

(5)

An asteroid of radius 50 km thus “prefers” to accrete chondrules of sizes smaller than 0.1 mm, corresponding to the smallest chondrules found in chondrites. At 100 km in radius, the preferred chondrule size is closer to 0.2 mm, a 200-kmradius body prefers millimeter-sized chondrules, and larger bodies can only grow efficiently if they can accrete chondrules of several millimeters or centimeters in diameter. Carbonaceous chondrites accreted significant amounts of CAIs and matrix together with their chondrules; Rubin (2011) suggested that matrix was accreted in the form of centimeter-sized porous aggregates with aerodynamical friction time comparable to chondrules and CAIs. Aerodynamical accretion of chondrules could explain the narrow range of chondrule sizes found in the various classes of meteorites. The model predicts that asteroids accrete increasingly larger chondrules as they grow. This prediction

may be at odds with the little variation in chondrule sizes found within chondrite classes [70% of EH3 and CO3 chondrules have apparent diameters within a factor of 2 of the mean apparent diameters in the group, according to Rubin (2000)]. The least-metamorphosed LL chondrites nevertheless do seem to host on the average larger chondrules (Nelson and Rubin, 2002). More metamorphosed LL chondrites actually show a lack of small chondrules; this could be due to the fact that the smallest chondrules disappeared from the strongly heated central regions of the parent body. 7.2 Chondrule Accretion Rates The accretion rate of chondrules (and other macroscopic particles) is  = pf 2 R 2 r Dv M B B p



(6)



Here fB parameterizes the actual accretion radius relative to the Bondi radius and rp is the chondrule density. Accretion of chondrules is a runaway process, since M ∝ RB2  ∝ M2 if the optimal chondrule size is present (so that fB = 1 in equation (6)). The characteristic growth timescale is

t exp =



M  R  = 1.66 m.y.    50 km  M r   ×   2.5 AU 

2.75

 ∑g  ∑

−3

MMSN

 

Dv     53 m s −1  −1

3

  r·  −3   3.5 g cm 

(7)

−1



We assumed here that the chondrules have sedimented to a thin mid-plane layer of thickness 1% relative to the gas scale-height. The strong dependence of the accretion rate on the planetesimal mass will drive a steep differential size distribution of a population of planetesimals accreting chondrules. This is illustrated in Fig. 4, where asteroid seeds with initial sizes from 10 to 50 km in radius have been exposed to chondrule accretion over 5 m.y. The value of the turbulent viscosity is a = 2 × 10–6. The resulting differential size distribution (which manifests itself after around 3 m.y. of chondrule accretion) shows a bump at 70 km in radius, a steep decline toward 200 km in radius, and finally a slower decline toward larger asteroids. The shallower decline is caused by the lack of centimeter-sized particles needed to drive the continued runaway accretion of large asteroids (this can be seen as a drop in fB in equation (6)). All the features in the size distribution in Fig. 4 are in good agreement with features of the observed size distribution of asteroids that are not explained well in coagulation models (Morbidelli et al., 2009). Layered accretion of chondrules can readily explain the large age spread of individual chondrules inside chondrites (Connelly et al., 2012), as well as the remnant magnetization of the Allende meteorite (Elkins-Tanton et al., 2011), imposed on the accreted chondrules from the internal dynamo in the

486   Asteroids IV

Nominal model (t = 5.0 m.y.) Initial size distribution Asteroid belt (×3931) Embryos

106

dN/dR (km–1)

104 (1) Ceres

Moon Mars

102

100

10–2 10

100

1000

R (km) Fig. 4. The size distribution of asteroids and planetary embryos after accreting chondrules with sizes from 0.1 to 1.6 mm in diameter for 5 m.y. The original asteroid sizes had sizes between 10 and 50 km in radius (light gray line), here envisioned to form by the streaming instability in a population of decimeter-sized icy particles. The resulting size distribution of asteroids is in good agreement with the bump at 70 km in radius, the steep size distribution from 70 km to 200 km, and the shallower size distribution of larger asteroids whose chondrule accretion is slowed down by friction within their very large Bondi radius. Figure based on Johansen et al. (2015).

parent body’s molten core. Efficient chondrule accretion requires, as does the streaming instability discussed in the previous section, sedimentation of chondrules to a thin midplane layer. The turbulent viscosity of a = 2 × 10–6 in Fig. 4 is nevertheless significantly larger than the a ~ 10–7 needed to sediment chondrules to a thin mid-plane layer of thickness 1% of the gas scale height; indeed the timescale to grow to the current asteroid population is 3 m.y. in the simulation shown in Fig. 4, about twice as long as in equation (7), but in good agreement with the ages of the youngest chondrules. 8. OPEN QUESTIONS The formation of asteroids is a complex problem that will only be solved through a collective effort from astronomers, planetary scientists, and cosmochemists. Although many details of asteroid formation are still not understood, we hope to have convinced the reader that new insights have been achieved in many areas in the past years. Here we highlight 10 areas of open questions in which we believe that major progress will be made in the next decade: 1. Short-lived radionuclides. What is the origin of the short-lived radioactive elements that melted the differentiated parent bodies? Was 26Al heterogeneous in the solar protoplanetary disk? How did the young solar system

become polluted in 26Al without receiving large amounts of 60Fe, an element that is copiously produced in supernovae? 2. Maintaining free-floating chondrules and CAIs. How is it possible to preserve chondrules and CAIs for millions of years in the disk before storing them in a chondritic body, without mixing them too much to erase chondrule classes and chondrule-matrix complementarity? What are we missing that makes this issue so paradoxical? 3. Chondrules vs. matrix. Why do carbonaceous chon­ drites contain large amounts of matrix while ordinary chon­ drites contain very little matrix? Did the matrix enter the chondrites as (potentially icy) “matrix lumps” or on finegrained rims attached to chondrules and other macroscopic particles? 4. Initial asteroid sizes. What is the origin of the steep differential size distribution of asteroids beyond the knee at 100 km? Did asteroids form small as in the coagulation picture, medium-sized as in the layered accretion model, or large as in some turbulent concentration models? Why do Kuiper belt objects, which formed under very different conditions in temperature and density, display a similar size distribution as asteroids? 5. The origin of asteroid classes. How is the radial gradient of asteroid composition produced and retained in the presence of considerable preaccretionary turbulent mixing and postaccretionary dynamical mixing? Is asteroid formation a continuous process that happens throughout the lifetime of the protoplanetary disk? What do the different chondrite groups mean in terms of formation location and time? 6.  Dry and wet chondrites.  Why do we have dry chondrites (enstatite, ordinary)? If chondrites form at 2–4 m.y. after CAIs, then the snowline should have been well inside the inner edge of the asteroid belt. Are there overlooked heating sources that could keep the iceline at 3 AU throughout the lifetime of the protoplanetary disk? Or did the asteroid classes form at totally different places only to be transported to their current orbits later? 7. Internal structure of asteroids. Does the chondrite and asteroid family evidence suggest that the primary asteroids — before internal heating — are homogeneous, roughly 100-km-diameter bodies composed of a physically, chemically, and isotopically homogeneous mix of chondrulesized components? Or is internal heterogeneity, as may be the case for the Allende parent body, prevalent? 8. Turbulent concentration of chondrules. Under what nebula conditions can vortex tubes over a range of nebula scales concentrate enough chondrules into volumes that are gravitationally bound, at a high enough rate to produce the primordial asteroids and meteorite parent bodies directly? What other roles could turbulent concentration play in planetesimal formation given that the optimally concentrated particle is chondrule-sized under nominal values of the turbulent viscosity? 9. Streaming instability with chondrules. Will the conditions for streaming instabilities to concentrate chondrulesized particles, i.e., gas depletion and/or particle pileup, be fulfilled in the protoplanetary disk? How does an overdense

Johansen et al.:  New Paradigms for Asteroid Formation   487

filament of chondrule-sized particles collapse under selfgravity given the strong support by gas pressure? 10. Layered accretion. What is the origin of the apparent scarcity of heterogeneous asteroid families, given that asteroids orbiting within an ocean of chondrules should accrete these prodigiously? What is the thermal evolution of early-formed asteroid seeds that continue to accrete chondrules over millions of years? Acknowledgments. A.J. was supported by the Swedish Research Council (grant 2010-3710), the European Research Council under ERC Starting Grant agreement 278675-PEBBLE2PLANET, and the Knut and Alice Wallenberg Foundation. He would like to thank B. Weiss for stimulating discussions on layered accretion. E.J. wishes to remember his colleague and friend G. Barlet (1985– 2014), who as a short-lived radionuclide theorist and chondrule/ refractory inclusion specialist would certainly have contributed to the new paradigms discussed herein, true to his attachment to interdisciplinary interactions, but left us far too early. J.C. thanks C. Ormel for a careful reading, and E. Scott, A. Rubin, N. Kita, and G. Wasserburg for helpful comments and references. We would like to thank A. Rubin and an additional anonymous referee for insightful referee reports.

REFERENCES Alexander C. M. O. and Ebel D. S. (2012) Questions, questions: Can the contradictions between the petrologic, isotopic, thermodynamic, and astrophysical constraints on chondrule formation be resolved? Meteoritics & Planet. Sci., 47, 1157. Alexander C. M. O., Grossman J. N., Ebel D. S., et al. (2008) The formation conditions of chondrules and chondrites. Science, 320, 1617. Alexander R. D. and Armitage P. J. (2006) The stellar mass-accretion rate relation in T Tauri stars and brown dwarfs. Astrophys. J. Lett., 639, L83. Arnould M., Paulus G., and Meynet G. (1997) Short-lived radionuclide production by non-exploding Wolf-Rayet stars. Astron. Astrophys., 321, 452. Bai X.-N. and Stone J. M. (2010) Dynamics of solids in the midplane of protoplanetary disks: Implications for planetesimal formation. Astrophys. J., 722, 1437. Bai X.-N. and Stone J. M. (2013) Wind-driven accretion in protoplanetary disks. I. Suppression of the magnetorotational instability and launching of the magnetocentrifugal wind. Astrophys. J., 769, 76. Balbus S. A. and Hawley J. F. (1991) A powerful local shear instability in weakly magnetized disks. I — Linear analysis. II — Nonlinear evolution. Astrophys. J., 376, 214. Barge P. and Sommeria J. (1995) Did planet formation begin inside persistent gaseous vortices? Astron. Astrophys., 295, L1. Bec J., Biferale L., Cencini M., et al. (2007) Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett., 98(8), Article ID 084502. Bec J., Biferale L., Cencini M., et al. (2010) Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech., 646, 527. Beckwith S. V. W., Henning T., and Nakagawa Y. (2000) Dust properties and assembly of large particles in protoplanetary disks. In Protostars and Planets IV (V. Mannings et al., eds.), p. 533. Univ. of Arizona, Tucson. Beitz E., Güttler C., Blum J., et al. (2011) Low-velocity collisions of centimeter-sized dust aggregates. Astrophys. J., 736, 34. Birnstiel T., Dullemond C. P., and Brauer F. (2010) Gas- and dust evolution in protoplanetary disks. Astron. Astrophys., 513, A79. Birnstiel T., Ormel C. W., and Dullemond C. P. (2011) Dust size distributions in coagulation/fragmentation equilibrium: Numerical solutions and analytical fits. Astron. Astrophys., 525, A11. Birnstiel T., Klahr H., and Ercolano B. (2012) A simple model for the evolution of the dust population in protoplanetary disks. Astron. Astrophys., 539, A148.

Bitsch B., Morbidelli A., Lega E., et al. (2014) Stellar irradiated discs and implications on migration of embedded planets. III. Viscosity transitions. Astron. Astrophys., 570, A75. Bitsch B., Johansen A., Lambrechts L., and Morbidelli A. (2015) The structure of protoplanetary discs around evolving young stars. Astron. Astrophys., 575, A28. Bland P. A., Howard L. E., Prior D. J., et al. (2011) Earliest rock fabric formed in the solar system preserved in a chondrule rim. Nature Geosci., 4, 244. Blum J. and Wurm G. (2008) The growth mechanisms of macroscopic bodies in protoplanetary disks. Annu. Rev. Astron. Astrophys., 46, 21. Boss A. P. (1996) A concise guide to chondrule formation models. In Chondrules and the Protoplanetary Disk (R. H. Hewins et al., eds.) pp. 257–263. Cambridge Univ., Cambridge. Boss A. P. and Keiser S. A. (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. Bottke W. F., Durda D. D., Nesvorný D., et al. (2005) The fossilized size distribution of the main asteroid belt. Icarus, 175, 111. Bottke W. F., Vokrouhlický D., Minton D., et al. (2012) An Archaean heavy bombardment from a destabilized extension of the asteroid belt. Nature, 485, 78. Brauer F., Dullemond C. P., and Henning T. (2008) Coagulation, fragmentation and radial motion of solid particles in protoplanetary disks. Astron. Astrophys., 480, 859. Brearley A. J. (1993) Matrix and fine-grained rims in the unequilibrated CO3 chondrite, ALHA77307 — Origins and evidence for diverse, primitive nebular dust components. Geochim. Cosmochim. Acta, 57, 1521. Brearley A. J. (1996) Nature of matrix in unequilibrated chondrites and its possible relationship to chondrules. In Chondrules and the Protoplanetary Disk (by R. H. Hewins et al., eds.), pp. 137–151. Cambridge Univ., Cambridge. Brearley A. J. (2003) Nebular versus parent-body processing. In Treatise on Geochemistry, Vol. 1: Meteorites, Comets and Planets (A. M. Davis, ed.), p. 247. Elsevier, Amsterdam. Brearley A. and Jones A. (1998) Chondritic meteorites. In Planetary Materials (J. J. Papike, ed.), pp. 3-1 to 3-398. Mineralogical Society of America, Chantilly, Virginia. Burbine T. H., McCoy T. J., Meibom A., et al. (2002) Meteoritic parent bodies: Their number and identification. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 653–667. Univ. of Arizona, Tucson. Cameron A. G. W. and Truran J. W. (1977) The supernova trigger for formation of the solar system. Icarus, 30, 447. Carrera D., Johansen A., and Davies M. B. (2015) Formation of asteroids from mm-sized chondrules. Astron. Astrophys., 579, A43. Chambers J. E. (2010) Planetesimal formation by turbulent concentration. Icarus, 208, 505. Chaussidon M. and Barrat J.-A. (2009) 60Fe in eucrite NWA 4523: Evidences for secondary redistribution of Ni and for secondary apparent high 60Fe/56Fe ratios in troilite. Lunar Planet. Sci. XL, Abstract #1752. Lunar and Planetary Institute, Houston. Chen J. H., Papanastassiou D. A., Telus M., et al. (2013) Fe-Ni isotopic systematics in UOC QUE 97008 and Semarkona chondrules. Lunar Planet. Sci. XLIV, Abstract #2649. Lunar and Planetary Institute, Houston. Chevalier R. A. (1999) Supernova remnants in molecular clouds. Astrophys. J., 511, 798. Chevalier R. A. (2000) Young circumstellar disks near evolved massive stars and supernovae. Astrophys. J. Lett., 538, L151. Chiang E. and Youdin A. N. (2010) Forming planetesimals in solar and extrasolar nebulae. Annu. Rev. Earth Planet. Sci., 38, 493. Ciesla F. J., Lauretta D. S., and Hood L. L. (2004) The frequency of compound chondrules and implications for chondrule formation. Meteoritics & Planet. Sci., 39, 531. Clayton R. N., Mayeda T. K., Olsen E. J., et al. (1991) Oxygen isotope studies of ordinary chondrites. Geochim. Cosmochim. Acta, 55, 2317. Connolly H. C. Jr. and Desch S. J. (2004) On the origin of the “kleine Kugelchen” called chondrules. Chem. Erde–Geochem., 64, 95. Connelly J. N., Bizzarro M., Krot A. N., et al. (2012) The absolute chronology and thermal processing of solids in the solar protoplanetary disk. Science, 338, 651. Cuzzi J. N. (2004) Blowing in the wind: III. Accretion of dust rims by chondrule-sized particles in a turbulent protoplanetary nebula. Icarus, 168, 484.

488   Asteroids IV Cuzzi J. N. and Alexander C. M. O. (2006) Chondrule formation in particle-rich nebular regions at least hundreds of kilometers across. Nature, 441, 483. Cuzzi J. N. and Hogan R. C. (2003) Blowing in the wind. I. Velocities of chondrule-sized particles in a turbulent protoplanetary nebula. Icarus, 164, 127. Cuzzi J. N. and Hogan R. C. (2012) Primary accretion by turbulent concentration: The rate of planetesimal formation and the role of vortex tubes. Lunar Planet. Sci. XLIII, Abstract #2536. Lunar and Planetary Institute, Houston. Cuzzi J. N. and Weidenschilling S. J. (2006) Particle-gas dynamics and primary accretion. In Meteorites and the Early Solar System II (D. S. Lauretta and H. Y. McSween Jr., eds.), pp. 353–381. Univ. of Arizona, Tucson. Cuzzi J. N., Dobrovolskis A. R., and Hogan R. C. (1996) Turbulence, chondrules, and planetesimals. In Chondrules and the Protoplanetary Disk (R. H. Hewins et al., eds.), pp. 35–43. Cambridge Univ., Cambridge. Cuzzi J. N., Hogan R. C., Paque J. M., et al. (2001) Size-selective concentration of chondrules and other small particles in protoplanetary nebula turbulence. Astrophys. J., 546, 496. Cuzzi J. N., Ciesla F. J., Petaev M. I., et al. (2005) Nebula evolution of thermally processed solids: Reconciling models and meteorites. In Chondrites and the Protoplanetary Disk (A. N. Krot et al., eds.), p. 732. ASP Conf. Series 341, Astronomical Society of the Pacific, San Francisco. Cuzzi J. N., Hogan R. C., and Shariff K. (2008) Toward planetesimals: Dense chondrule clumps in the protoplanetary nebula. Astrophys. J., 687, 1432. Cuzzi J. N., Hogan R. C., and Bottke W. F. (2010) Towards initial mass functions for asteroids and Kuiper Belt Objects. Icarus, 208, 518. Cuzzi J. N., Hartlep T., Weston B., et al. (2014) Turbulent concentration of mm-size particles in the protoplanetary nebula: Scale-dependent multiplier functions. Lunar Planet. Sci. XLIV, Abstract #2764. Lunar and Planetary Institute, Houston. Dauphas N. and Chaussidon M. (2011) A perspective from extinct radionuclides on a young stellar object: The Sun and its accretion disk. Annu. Rev. Earth Planet. Sci., 39, 351. Deharveng L., Schuller F., Anderson L. D., et al. (2010) A gallery of bubbles. The nature of the bubbles observed by Spitzer and what ATLASGAL tells us about the surrounding neutral material. Astron. Astrophys., 523, A6. Desch S. J., Morris M. A., Connolly H. C., et al. (2012) The importance of experiments: Constraints on chondrule formation models. Meteoritics & Planet. Sci., 47, 1139. Dittrich K., Klahr H., and Johansen A. (2013) Gravoturbulent planetesimal formation: The positive effect of long-lived zonal flows. Astrophys. J., 763, 117. Dodd R. T. (1976) Accretion of the ordinary chondrites. Earth Planet. Sci. Lett., 30, 281. Dominik C. and Tielens A. G. G. M. (1997) The physics of dust coagulation and the structure of dust aggregates in space. Astrophys. J., 480, 647. Dominik C., Blum J., Cuzzi J. N., et al. (2007) Growth of dust as the initial step toward planet formation. In Protostars and Planets V (B. Reipurth et al., eds.), pp. 783–800. Univ. of Arizona, Tucson. Doyle P. M., Krot A. N., Nagashima K., et al. (2014) Manganesechromium ages of aqueous alteration of unequilibrated ordinary chondrites. Lunar Planet. Sci. XLIV, Abstract #1726. Lunar and Planetary Institute, Houston. Drążkowska J., Windmark F., and Dullemond C. P. (2013) Planetesimal formation via sweep-up growth at the inner edge of dead zones. Astron. Astrophys., 556, A37. Eaton J. K. and Fessler J. R. (1994) Preferential concentration of particles by turbulence. Intl. J. Multiphase Flow, Suppl., 20, 169–209. Ebel D., Brunner C., Leftwich K., Erb I., Lu M., Konrad K., Rodriguez H., Friedrich J., and Weisberg M. (2015) Abundance, composition and size of inclusions and matrix in CV and CO chondrites. Geochim. Cosmochim. Acta, in press. Elkins-Tanton L. T., Weiss B. P., and Zuber M. T. (2011) Chondrites as samples of differentiated planetesimals. Earth Planet. Sci. Lett., 305, 1. Eugster O., Herzog G. F., Marti K., et al. (2006) Irradiation records, cosmic-ray exposure ages, and transfer times of meteorites. In Meteorites and the Early Solar System II (D. S. Lauretta and H. Y. McSween Jr., eds.), pp. 829–851. Univ. of Arizona, Tucson.

Fisher K. R., Tait A. W., Simon J. I., et al. (2014) Contrasting size distributions of chondrules and inclusions in Allende CV3. Lunar Planet. Sci. XLIV, Abstract #2711. Lunar and Planetary Institute, Houston. Fraser W. C., Brown M. E., Morbidelli A., et al. (2014) The absolute magnitude distribution of Kuiper belt objects. Astrophys. J., 782, 100. Fressin F., Torres G., Charbonneau D., et al. (2013) The false positive rate of Kepler and the occurrence of planets. Astrophys. J., 766, 81. Friedrich J. M., Weisberg M. K., Ebel D. S., Biltz A. E., Corbett B. M., Iotzov I. V., Khan W. S., and Wolman M. D. (2015) Chondrule size and related physical properties: A compilation and evaluation of current data across all meteorite groups. Chem. Erde, in press, DOI: 10.1016/j.chemer.2014.08.003. Fu R. R. and Elkins-Tanton L. T. (2014) The fate of magmas in planetesimals and the retention of primitive chondritic crusts. Earth Planet. Sci. Lett., 390, 128. Fujiya W., Sugiura N., Sano Y., et al. (2013) Mn-Cr ages of dolomites in CI chondrites and the Tagish Lake ungrouped carbonaceous chondrite. Earth Planet. Sci. Lett., 362, 130. Gaidos E., Krot A. N., Williams J. P., et al. (2009) 26Al and the formation of the solar system from a molecular cloud contaminated by Wolf-Rayet winds. Astrophys. J., 696, 1854. Gail H.-P., Trieloff M., Breuer D., et al. (2014) Early thermal evolution of planetesimals and its impact on processing and dating of meteoritic material. In Protostars and Planets VI (H. Beuther et al., eds.), pp. 571–593. Univ. of Arizona, Tucson. Gal-Yam A., Arcavi I., Ofek E. O., et al. (2014) AWolf-Rayet-like progenitor of SN 2013cu from spectral observations of a stellar wind. Nature, 509, 471. Garaud P., Meru F., Galvagni M., et al. (2013) From dust to planetesimals: An improved model for collisional growth in protoplanetary disks. Astrophys. J., 764, 146. Gounelle M. (2014) Aluminium-26 in the early solar system: A probability estimate. Lunar Planet. Sci. XLIV, Abstract #2113. Lunar and Planetary Institute, Houston. Gounelle M. and Meibom A. (2008) The origin of short-lived radionuclides and the astrophysical environment of solar system formation. Astrophys. J., 680, 781. Gounelle M. and Meynet G. (2012) Solar system genealogy revealed by extinct short-lived radionuclides in meteorites. Astron. Astrophys., 545, A4. Gounelle M., Shu F. H., Shang H., et al. (2006) The irradiation origin of beryllium radioisotopes and other short-lived radionuclides. Astrophys. J., 640, 1163. Gounelle M., Meibom A., Hennebelle P., et al. (2009) Supernova propagation and cloud enrichment: A new model for the origin of 60Fe in the early solar system. Astrophys. J. Lett., 694, L1. Gounelle M., Chaussidon M., and Rollion-Bard C. (2013) Variable and extreme irradiation conditions in the early solar system inferred from the initial abundance of 10Be in Isheyevo CAIs. Astrophys. J. Lett., 763, L33. Grimm R. E. and McSween H. Y. (1993) Heliocentric zoning of the asteroid belt by aluminum-26 heating. Science, 259, 653. Guan Y., Huss G. R., Leshin L. A., et al. (2006) Oxygen isotope and 26Al-26Mg systematics of aluminum-rich chondrules from unequilibrated enstatite chondrites. Meteoritics & Planet. Sci., 41, 33. Güttler C., Blum J., Zsom A., et al. (2010) The outcome of protoplanetary dust growth: Pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments. Astron. Astrophys., 513, A56. Hartmann L., Calvet N., Gullbring E., et al. (1998) Accretion and the evolution of T Tauri disks. Astrophys. J., 495, 385. Hayashi C. (1981) Structure of the solar nebula, growth and decay of magnetic fields and effects of magnetic and turbulent viscosities on the nebula. Progr. Theor. Phys. Suppl., 70, 35. Henke S., Gail H.-P., Trieloff M., et al. (2013) Thermal evolution model for the H chondrite asteroid-instantaneous formation versus protracted accretion. Icarus, 226, 212. Hester J. J., Desch S. J., Healy K. R., et al. (2004) The cradle of the solar system. Science, 304, 1116. Hewins R. H., Connolly H. C., Lofgren G. E., et al. (2005) Experimental constraints on chondrule formation. In Chondrites and the Protoplanetary Disk (A. N. Krot et al, eds.), pp. 286–316. ASP Conf. Series 341, Astronomical Society of the Pacific, San Francisco.

Johansen et al.:  New Paradigms for Asteroid Formation   489 Hezel D. C. and Palme H. (2010) The chemical relationship between chondrules and matrix and the chondrule matrix complementarity. Earth Planet. Sci. Lett., 294, 85. Hezel D. C., Russell S. S., Ross A. J., et al. (2008) Modal abundances of CAIs: Implications for bulk chondrite element abundances and fractionations. Meteoritics & Planet. Sci., 43, 1879. Hogan R. C. and Cuzzi J. N. (2007) Cascade model for particle concentration and enstrophy in fully developed turbulence with mass-loading feedback. Phys. Rev. E, 75(5), Article ID 056305. Huss G. R., Rubin A. E., and Grossman J. N. (2006) Thermal metamorphism in chondrites. In Meteorites and the Early Solar System II (D. S. Lauretta and H. Y. McSween Jr., eds.), pp. 567–586. Univ. of Arizona, Tucson. Huss G. R., Meyer B. S., Srinivasan G., et al. (2009) Stellar sources of the short-lived radionuclides in the early solar system. Geochim. Cosmochim. Acta, 73, 4922. Ida S., Guillot T., and Morbidelli A. (2008) Accretion and destruction of planetesimals in turbulent disks. Astrophys. J., 686, 1292. Jacobsen B., Yin Q.-z., Moynier F., et al. (2008) 26Al-26Mg and 207Pb206Pb systematics of Allende CAIs: Canonical solar initial 26Al/27Al ratio reinstated. Earth Planet. Sci. Lett., 272, 353. Jacquet E. (2014a) The quasi-universality of chondrule size as a constraint for chondrule formation models. Icarus, 232, 176. Jacquet E. (2014b) Transport of solids in protoplanetary disks: Comparing meteorites and astrophysical models. Compt. Rend. Geosci., 346, 3. Jacquet E., Balbus S., and Latter H. (2011) On linear dust-gas streaming instabilities in protoplanetary discs. Mon. Not. R. Astron. Soc., 415, 3591. Jacquet E., Alard O., and Gounelle M. (2012a) Chondrule trace element geochemistry at the mineral scale. Meteoritics & Planet. Sci., 47, 1695. Jacquet E., Gounelle M., and Fromang S. (2012b) On the aerodynamic redistribution of chondrite components in protoplanetary disks. Icarus, 220, 162. Jarosewich E. (1990) Chemical analyses of meteorites — A compilation of stony and iron meteorite analyses. Meteoritics, 25, 323. Johansen A. and Lacerda P. (2010) Prograde rotation of protoplanets by accretion of pebbles in a gaseous environment. Mon. Not. R. Astron. Soc., 404, 475. Johansen A. and Youdin A. (2007) Protoplanetary disk turbulence driven by the streaming instability: Nonlinear saturation and particle concentration. Astrophys. J., 662, 627. Johansen A., Klahr H., and Henning T. (2006) Gravoturbulent formation of planetesimals. Astrophys. J., 636, 1121. Johansen A., Oishi J. S., Mac Low M.-M., et al. (2007) Rapid planetesimal formation in turbulent circumstellar disks. Nature, 448, 1022. Johansen A., Brauer F., Dullemond C., et al. (2008) A coagulation fragmentation model for the turbulent growth and destruction of preplanetesimals. Astron. Astrophys., 486, 597. Johansen A., Youdin A., and Klahr H. (2009a) Zonal flows and longlived axisymmetric pressure bumps in magnetorotational turbulence. Astrophys. J., 697, 1269. Johansen A., Youdin A., and Mac Low M.-M. (2009b) Particle clumping and planetesimal formation depend strongly on metallicity. Astrophys. J. Lett., 704, L75. Johansen A., Klahr H., and Henning T. (2011) High-resolution simulations of planetesimal formation in turbulent protoplanetary discs. Astron. Astrophys., 529, A62. Johansen A., Youdin A. N., and Lithwick Y. (2012) Adding particle collisions to the formation of asteroids and Kuiper belt objects via streaming instabilities. Astron. Astrophys., 537, A125. Johansen A., Blum J., Tanaka H., et al. (2014) The multifaceted planetesimal formation process. In Protostars and Planets V (B. Reipurth et al., eds.), pp. 547–570. Univ. of Arizona, Tucson. Johansen A., Mac Low M.-M., Lacerda P., and Bizzarro M. (2015) Growth of asteroids, planetary embryos, and Kuiper belt objects by chondrule accretion. Sci. Adv., 1(3), 1500109. Jones R. H. (2012) Petrographic constraints on the diversity of chondrule reservoirs in the protoplanetary disk. Meteoritics & Planet. Sci., 47, 1176. Kastner J. H. and Myers P. C. (1994) An observational estimate of the probability of encounters between mass-losing evolved stars and molecular clouds. Astrophys. J., 421, 605. Kato M. T., Fujimoto M., and Ida S. (2012) Planetesimal formation at the boundary between steady super/sub-Keplerian flow created by

inhomogeneous growth of magnetorotational instability. Astrophys. J., 747, 11. Keil K., Stoeffler D., Love S. G., et al. (1997) Constraints on the role of impact heating and melting in asteroids. Meteoritics & Planet. Sci., 32, 349. Kita N. T. and Ushikubo T. (2012) Evolution of protoplanetary disk inferred from 26Al chronology of individual chondrules. Meteoritics & Planet. Sci., 47, 1108. Kita N. T., Yin Q.-Z., MacPherson G. J., et al. (2013) 26Al-26Mg isotope systematics of the first solids in the early solar system. Meteoritics & Planet. Sci., 48, 1383. Klahr H. H. and Bodenheimer P. (2003) Turbulence in accretion disks: Vorticity generation and angular momentum transport via the global baroclinic instability. Astrophys. J., 582, 869. Kretke K. A. and Lin D. N. C. (2007) Grain retention and formation of planetesimals near the snow line in MRI-driven turbulent protoplanetary disks. Astrophys. J. Lett., 664, L55. Krot A., Petaev M., Russell S. S., et al. (2004) Amoeboid olivine aggregates and related objects in carbonaceous chondrites: Records of nebular and asteroid processes. Chem. Erde–Geochem., 64, 185. Krot A. N., Amelin Y., Bland P., et al. (2009) Origin and chronology of chondritic components: A review. Geochim. Cosmochim. Acta, 73, 4963. Kruijer T. S., Sprung P., Kleine T., et al. (2012) Hf-W chronometry of core formation in planetesimals inferred from weakly irradiated iron meteorites. Geochim. Cosmochim. Acta, 99, 287. Kuebler K. E., McSween H. Y., Carlson W. D., et al. (1999) Sizes and masses of chondrules and metal-troilite grains in ordinary chondrites: Possible implications for nebular sorting. Icarus, 141, 96. Lambrechts M. and Johansen A. (2012) Rapid growth of gas-giant cores by pebble accretion. Astron. Astrophys., 544, A32. Lambrechts M., Johansen A., and Morbidelli A. (2014) Separating gas-giant and ice-giant planets by halting pebble accretion. Astron. Astrophys., 572, A35. Larsen K. K., Trinquier A., Paton C., et al. (2011) Evidence for magnesium isotope heterogeneity in the solar protoplanetary disk. Astrophys. J. Lett., 735, L37. Laughlin G., Steinacker A., and Adams F. C. (2004) Type I planetary migration with MHD turbulence. Astrophys. J., 608, 489. Lauretta D. S., Nagahara H., and Alexander C. M. O. (2006) Petrology and origin of ferromagnesian silicate chondrules. In Meteorites and the Early Solar System II (D. S. Lauretta and H. Y. McSween, Jr., eds.), pp. 431–459. Univ. of Arizona, Tucson. Lee T. (1978) A local proton irradiation model for isotopic anomalies in the solar system. Astrophys. J., 224, 217. Lee T., Papanastassiou D. A., and Wasserburg G. J. (1976) Demonstration of Mg-26 excess in Allende and evidence for Al-26. Geophys. Res. Lett., 3, 41. Lee T., Shu F. H., Shang H., et al. (1998) Protostellar cosmic rays and extinct radioactivities in meteorites. Astrophys. J., 506, 898. Lesur G. and Papaloizou J. C. B. (2010) The subcritical baroclinic instability in local accretion disc models. Astron. Astrophys., 513, A60. Libourel G. and Krot A. N. (2007) Evidence for the presence of planetesimal material among the precursors of magnesian chondrules of nebular origin. Earth Planet. Sci. Lett., 254, 1. Liu M.-C., Chaussidon M., Göpel C., et al. (2012) A heterogeneous solar nebula as sampled by CM hibonite grains. Earth Planet. Sci. Lett., 327, 75. Looney L. W., Tobin J. J., and Fields B. D. (2006) Radioactive probes of the supernova-contaminated solar nebula: Evidence that the Sun was born in a cluster. Astrophys. J., 652, 1755. Lugaro M., Doherty C. L., Karakas A. I., et al. (2012) Short-lived radioactivity in the early solar system: The super-AGB star hypothesis. Meteoritics & Planet. Sci., 47, 1998. Lyra W., Johansen A., Klahr H., et al. (2008) Embryos grown in the dead zone. Assembling the first protoplanetary cores in low mass self-gravitating circumstellar disks of gas and solids. Astron. Astrophys., 491, L41. Lyra W., Johansen A., Zsom A., et al. (2009) Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks. Astron. Astrophys., 497, 869. MacPherson G. J. (2005) Calcium-aluminum-rich inclusions in chondritic meteorites. In Treatise on Geochemistry, Vol. 1: Meteorites, Comets and Planets (A. M. Davis, ed.), pp. 201–246. Elsevier, Amsterdam.

490   Asteroids IV MacPherson G. J., Hashimoto A., and Grossman L. (1985) Accretionary rims on inclusions in the Allende meteorite. Geochim. Cosmochim. Acta, 49, 2267. MacPherson G. J., Davis A. M., and Zinner E. K. (2014) Distribution of 26Al in the early solar system: A 2014 reappraisal. Lunar Planet. Sci. XLIV, Abstract #2134. Lunar and Planetary Institute, Houston. Makide K., Nagashima K., Krot A. N., et al. (2013) Heterogeneous distribution of 26Al at the birth of the solar system: Evidence from corundum-bearing refractory inclusions in carbonaceous chondrites. Geochim. Cosmochim. Acta, 110, 190. Martin R. G. and Livio M. (2012) On the evolution of the snow line in protoplanetary discs. Mon. Not. R. Astron. Soc., 425, L6. Martin R. G. and Livio M. (2013) On the evolution of the snow line in protoplanetary discs — II. Analytic approximations. Mon. Not. R. Astron. Soc., 434, 633. Metzler K. (2012) Ultrarapid chondrite formation by hot chondrule accretion? Evidence from unequilibrated ordinary chondrites. Meteoritics & Planet. Sci., 47, 2193. Metzler K., Bischoff A., and Stoeffler D. (1992) Accretionary dust mantles in CM chondrites — Evidence for solar nebula processes. Geochim. Cosmochim. Acta, 56, 2873. Mizuno H., Markiewicz W. J., and Voelk H. J. (1988) Grain growth in turbulent protoplanetary accretion disks. Astron. Astrophys., 195, 183. Monnereau M., Toplis M. J., Baratoux D., et al. (2013) Thermal history of the H-chondrite parent body: Implications for metamorphic grade and accretionary time-scales. Geochim. Cosmochim. Acta, 119, 302. Morbidelli A., Chambers J., Lunine J. I., et al. (2000) Source regions and time scales for the delivery of water to Earth. Meteoritics & Planet. Sci., 35, 1309. Morbidelli A., Bottke W. F., Nesvorný D., et al. (2009) Asteroids were born big. Icarus, 204, 558. Morfill G. E., Durisen R. H., and Turner G. W. (1998) NOTE: An accretion rim constraint on chondrule formation theories. Icarus, 134, 180. Mostefaoui S., Lugmair G. W., and Hoppe P. (2005) 60Fe: A heat source for planetary differentiation from a nearby supernova explosion. Astrophys. J., 625, 271. Mothé-Diniz T. and Nesvorný D. (2008) Visible spectroscopy of extremely young asteroid families. Astron. Astrophys., 486, L9. Mothé-Diniz T., Roig F., and Carvano J. M. (2005) Reanalysis of asteroid families structure through visible spectroscopy. Icarus, 174, 54. Mothé-Diniz T., Carvano J. M., Bus S. J., et al. (2008) Mineralogical analysis of the Eos family from near-infrared spectra. Icarus, 195, 277. Nakagawa Y., Sekiya M., and Hayashi C. (1986) Settling and growth of dust particles in a laminar phase of a low-mass solar nebula. Icarus, 67, 375. Nelson R. P. and Gressel O. (2010) On the dynamics of planetesimals embedded in turbulent protoplanetary discs. Mon. Not. R. Astron. Soc., 409, 639. Nelson R. P. and Papaloizou J. C. B. (2004) The interaction of giant planets with a disc with MHD turbulence — IV. Migration rates of embedded protoplanets. Mon. Not. R. Astron. Soc., 350, 849. Nelson V. E. and Rubin A. E. (2002) Size-frequency distributions of chondrules and chondrule fragments in LL3 chondrites: Implications for parent-body fragmentation of chondrules. Meteoritics & Planet. Sci., 37, 1361. Nelson R. P., Gressel O., and Umurhan O. M. (2013) Linear and nonlinear evolution of the vertical shear instability in accretion discs. Mon. Not. R. Astron. Soc., 435, 2610. O’Brien D. P., Walsh K. J., Morbidelli A., et al. (2014) Water delivery and giant impacts in the “Grand Tack” scenario. Icarus, 239, 74. Oishi J. S., Mac Low M.-M., and Menou K. (2007) Turbulent torques on protoplanets in a dead zone. Astrophys. J., 670, 805. Okuzumi S., Tanaka H., Kobayashi H., et al. (2012) Rapid coagulation of porous dust aggregates outside the snow line: A pathway to successful icy planetesimal formation. Astrophys. J., 752, 106. Ormel C. W. and Cuzzi J. N. (2007) Closed-form expressions for particle relative velocities induced by turbulence. Astron. Astrophys., 466, 413. Ormel C. W. and Klahr H. H. (2010) The effect of gas drag on the growth of protoplanets. Analytical expressions for the accretion of small bodies in laminar disks. Astron. Astrophys., 520, A43. Ormel C. W. and Okuzumi S. (2013) The fate of planetesimals in turbulent disks with dead zones. II. Limits on the viability of runaway accretion. Astrophys. J., 771, 44.

Ormel C. W., Cuzzi J. N., and Tielens A. G. G. M. (2008) Co-accretion of chondrules and dust in the solar nebula. Astrophys. J., 679, 1588. Ouellette N., Desch S. J., and Hester J. J. (2007) Interaction of supernova ejecta with nearby protoplanetary disks. Astrophys. J., 662, 1268. Palme H. and Jones A. (2005) Solar system abundances of the elements. In Treatise on Geochemistry, Vol. 1: Meteorites, Comets and Planets (A. M. Davis, ed.), pp. 41–60. Elsevier, Amsterdam. Pan M. and Sari R. (2005) Shaping the Kuiper belt size distribution by shattering large but strengthless bodies. Icarus, 173, 342. Pan L., Padoan P., Scalo J., et al. (2011) Turbulent clustering of protoplanetary dust and planetesimal formation. Astrophys. J., 740, 6. Pan L., Desch S. J., Scannapieco E., et al. (2012) Mixing of clumpy supernova ejecta into molecular clouds. Astrophys. J., 756, 102. Quitté G., Halliday A. N., Meyer B. S., et al. (2007) Correlated iron 60, nickel 62, and zirconium 96 in refractory inclusions and the origin of the solar system. Astrophys. J., 655, 678. Quitté G., Latkoczy C., Schönbächler M., et al. (2011) 60Fe-60Ni systematics in the eucrite parent body: A case study of Bouvante and Juvinas. Geochim. Cosmochim. Acta, 75, 7698. Raymond S. N., Quinn T., and Lunine J. I. (2004) Making other Earths: Dynamical simulations of terrestrial planet formation and water delivery. Icarus, 168, 1. Ros K. and Johansen A. (2013) Ice condensation as a planet formation mechanism. Astron. Astrophys., 552, A137. Rubin A. E. (2000) Petrologic, geochemical and experimental constraints on models of chondrule formation. Earth Sci. Rev., 50, 3. Rubin A. E. (2005) Relationships among intrinsic properties of ordinary chondrites: Oxidation state, bulk chemistry, oxygen isotopic composition, petrologic type, and chondrule size. Geochim. Cosmochim. Acta, 69, 4907. Rubin A. E. (2011) Origin of the differences in refractorylithophileelement abundances among chondrite groups. Icarus, 213, 547. Rubin A. E. and Brearley A. J. (1996) A critical evaluation of the evidence for hot accretion. Icarus, 124, 86. Schneider D. M., Akridge D. G., and Sears D. W. G. (1998) Size distribution of metal grains and chondrules in enstatite chondrites. Meteoritics & Planet. Sci., Suppl., 33, 136. Schräpler R., Blum J., Seizinger A., et al. (2012) The physics of protoplanetesimal dust agglomerates. VII. The low-velocity collision behavior of large dust agglomerates. Astrophys. J., 758, 35. Scott E. R. D. and Krot A. N. (2003) Chondrites and their components. In Treatise on Geochemistry, Vol. 1: Meteorites, Comets and Planets (A. M. Davis, ed.), p. 143. Elsevier, Amsterdam. Scott E. R. D. and Rajan R. S. (1981) Metallic minerals, thermal histories and parent bodies of some xenolithic, ordinary chondrite meteorites. Geochim. Cosmochim. Acta, 45, 53. Scott E. R. D., Rubin A. E., Taylor G. J., et al. (1984) Matrix material in type 3 chondrites — Occurrence, heterogeneity and relationship with chondrules. Geochim. Cosmochim. Acta, 48, 1741. Scott E. R. D., Krot T. V., Goldstein J. I., et al. (2014) Thermal and impact history of the H chondrite parent asteroid during metamorphism: Constraints from metallic Fe-Ni. Geochim. Cosmochim. Acta, 136, 13. Sekiya M. (1983) Gravitational instabilities in a dust-gas layer and formation of planetesimals in the solar nebula. Progr. Theor. Phys. Suppl., 69, 1116. Setoh M., Hiraoka K., Nakamura A. M., et al. (2007) Collisional disruption of porous sintered glass beads at low impact velocities. Adv. Space Res., 40, 252. Shaw R. (2003) Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech., 35, 183–227. Shukolyukov A. and Lugmair G. W. (1993) Live iron-60 in the early solar system. Science, 259, 1138. Simon J. B., Beckwith K., and Armitage P. J. (2012) Emergent mesoscale phenomena in magnetized accretion disc turbulence. Mon. Not. R. Astron. Soc., 422, 2685. Sirono S.-i. (2011) Planetesimal formation induced by sintering. Astrophys. J. Lett., 733, L41. Sonett C. P. and Colburn D. S. (1968) Electrical heating of meteorite parent bodies and planets by dynamo induction from a pre-main sequence T Tauri “solar wind.” Nature, 219, 924. Squires K. D. and Eaton J. K. (1990) Particle response and turbulence modification in isotropic turbulence. Phys. Fluids, 2, 1191. Squires K. D. and Eaton J. K. (1991) Preferential concentration of particles by turbulence. Phys. Fluids, 3, 1169.

Johansen et al.:  New Paradigms for Asteroid Formation   491 Stewart S. T. and Leinhardt Z. M. (2009) Velocity-dependent catastrophic disruption criteria for planetesimals. Astrophys. J. Lett., 691, L133. Tachibana S. and Huss G. R. (2003) The initial abundance of 60Fe in the solar system. Astrophys. J. Lett., 588, L41. Tachibana S., Huss G. R., Kita N. T., et al. (2006) 60Fe in chondrites: Debris from a nearby supernova in the early solar system? Astrophys. J. Lett., 639, L87. Tang H. and Dauphas N. (2012) Abundance, distribution, and origin of 60Fe in the solar protoplanetary disk. Earth Planet. Sci. Lett., 359, 248. Tang X. and Chevalier R. A. (2014) Gamma-ray emission from supernova remnant interactions with molecular clumps. Astrophys. J. Lett., 784, L35. Tatischeff V., Duprat J., and de Séréville N. (2010) A runaway WolfRayet star as the origin of 26Al in the early solar system. Astrophys. J. Lett., 714, L26. Taylor G. J., Maggiore P., Scott E. R. D., et al. (1987) Original structures, and fragmentation and reassembly histories of asteroids ‑ Evidence from meteorites. Icarus, 69, 1. Telus M., Huss G. R., Ogliore R. C., et al. (2012) Recalculation of data for short-lived radionuclide systems using less-biased ratio estimation. Meteoritics & Planet. Sci., 47, 2013. Testi L., Birnstiel T., Ricci L., et al. (2014) Dust evolution in protoplanetary disks. In Protostars and Planets VI (H. Beuther et al., eds.), pp. 339–362. Univ. of Arizona, Tucson. Trieloff M., Jessberger E. K., Herrwerth I., et al. (2003) Structure and thermal history of the H-chondrite parent asteroid revealed by thermochronometry. Nature, 422, 502. Trinquier A., Elliott T., Ulfbeck D., et al. (2009) Origin of nucleosynthetic isotope heterogeneity in the solar protoplanetary disk. Science, 324, 374. Turner N. J., Fromang S., Gammie C., et al. (2014) Transport and accretion in planet-forming disks. In Protostars and Planets VI (H. Beuther et al., eds.), pp. 411–432. Univ. of Arizona, Tucson. Urey H. C. (1955) The cosmic abundances of potassium, uranium, and thorium and the heat balances of the Earth, the Moon, and Mars. Proc. Natl. Acad. Sci., 41, 127. Vasileiadis A., Nordlund Å., and Bizzarro M. (2013) Abundance of 26Al and 60Fe in evolving giant molecular clouds. Astrophys. J. Lett., 769, L8. Vernazza P., Zanda B., Binzel R. P. et al. (2014) Multiple and fast: The accretion of ordinary chondrite parent bodies. Astrophys. J., 791, 120. Villeneuve J., Chaussidon M., and Libourel G. (2012) Lack of relationship between aluminum-26 ages of chondrules and their mineralogical and chemical compositions. Compt. Rend. Geosci., 344, 423. Voelk H. J., Jones F. C., Morfill G. E., et al. (1980) Collisions between grains in a turbulent gas. Astron. Astrophys., 85, 316. Wada K., Tanaka H., Suyama T., et al. (2009) Collisional growth conditions for dust aggregates. Astrophys. J., 702, 1490. Wada K., Tanaka H., Okuzumi S., et al. (2013) Growth efficiency of dust aggregates through collisions with high mass ratios. Astron. Astrophys., 559, A62. Walsh K. J., Morbidelli A., Raymond S. N., et al. (2011) A low mass for Mars from Jupiter’s early gas-driven migration. Nature, 475, 206. Wang L.-P. and Maxey M. R. (1993) Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech., 256, 27. Wasserburg G. J.,Wimpenny J., and Yin Q.-Z. (2012) Mg isotopic heterogeneity, Al-Mg isochrons, and canonical 26Al/27Al in the early solar system. Meteoritics & Planet. Sci., 47, 1980. Wasson J. T., Isa J., and Rubin A. E. (2013) Compositional and petrographic similarities of CV and CK chondrites: A single group with variations in textures and volatile concentrations attributable to impact heating, crushing and oxidation. Geochim. Cosmochim. Acta, 108, 45. Weidenschilling S. J. (1977a) Aerodynamics of solid bodies in the solar nebula. Mon. Not. R. Astron. Soc., 180, 57.

Weidenschilling S. J. (1977b) Aerodynamics of solid bodies in the solar nebula. Mon. Not. R. Astron. Soc., 180, 57. Weidenschilling S. J. (2011) Initial sizes of planetesimals and accretion of the asteroids. Icarus, 214, 671. Weidling R., Güttler C., and Blum J. (2012) Free collisions in a microgravity many-particle experiment. I. Dust aggregate sticking at low velocities. Icarus, 218, 688. Weisberg M. K., McCoy T. J., and Krot A. N. (2006) Systematics and evaluation of meteorite classification. In Meteorites and the Early Solar System II (D. S. Lauretta and H. Y. McSween, Jr., eds.), pp. 19–52. Univ. of Arizona, Tucson. Weiss B. P. and Elkins-Tanton L. T. (2013) Differentiated planetesimals and the parent bodies of chondrites. Annu. Rev. Earth Planet. Sci., 41, 529. Weiss B. P., Gattacceca J., and Stanley S. et al. (2010) Paleomagnetic records of meteorites and early planetesimal differentiation. Space Sci. Rev., 152, 341. Whattam S. A., Hewins R. H., Cohen B. A., et al. (2008) Granoblastic olivine aggregates in magnesian chondrules: Planetesimal fragments or thermally annealed solar nebula condensates? Earth Planet. Sci. Lett., 269, 200. Whipple F. L. (1972) On certain aerodynamic processes for asteroids and comets. In From Plasma to Planet (A. Elvius, ed.), p. 211. Wiley, New York. Williams J. P. and Gaidos E. (2007) On the likelihood of supernova enrichment of protoplanetary disks. Astrophys. J. Lett., 663, L33. Windmark F., Birnstiel T., Güttler C., et al. (2012a) Planetesimal formation by sweep-up: How the bouncing barrier can be beneficial to growth. Astron. Astrophys., 540, A73. Windmark F., Birnstiel T., Ormel C. W., et al. (2012b) Breaking through: The effects of a velocity distribution on barriers to dust growth. Astron. Astrophys., 544, L16. Wood J. A. (2005) The chondrite types and their origins. In Chondrites and the Protoplanetary Disk (A. N. Krot et al, eds.), p. 953. ASP Conf. Series 341, Astronomical Society of the Pacific, San Francisco. Woosley S. E. and Heger A. (2007) Nucleosynthesis and remnants in massive stars of solar metallicity. Phys. Rept., 442, 269. Wurm G., Paraskov G., and Krauss O. (2005) Growth of planetesimals by impacts at ~25 m/s. Icarus, 178, 253. Xie J.-W., Payne M. J., Thébault P., et al. (2010) From dust to planetesimal: The snowball phase? Astrophys. J., 724, 1153. Yang C.-C. and Johansen A. (2014) On the feeding zone of planetesimal formation by the streaming instability. Astrophys. J., 792, 86. Yang C.-C., Mac Low M.-M., and Menou K. (2012) Planetesimal and protoplanet dynamics in a turbulent protoplanetary disk: Ideal stratified disks. Astrophys. J., 748, 79. Youdin A. N. and Goodman J. (2005) Streaming instabilities in protoplanetary disks. Astrophys. J., 620, 459. Youdin A. and Johansen A. (2007) Protoplanetary disk turbulence driven by the streaming instability: Linear evolution and numerical methods. Astrophys. J., 662, 613. Youdin A. N. and Shu F. H. (2002) Planetesimal formation by gravitational instability. Astrophys. J., 580, 494. Young E. D. (2014) Inheritance of solar short- and long-lived radionuclides from molecular clouds and the unexceptional nature of the solar system. Earth Planet. Sci. Lett., 392, 16. Zanda B., Humayun M., and Hewins R. H. (2012) Chemical composition of matrix and chondrules in carbonaceous chondrites: Implications for disk transport. Lunar Planet. Sci. XLIII, Abstract #2413. Lunar and Planetary Institute, Houston. Zinner E. and Göpel C. (2002) Aluminum-26 in H4 chondrites: Implications for its production and its usefulness as a fine-scale chronometer for early solar system events. Meteoritics & Planet. Sci., 37, 1001. Zsom A., Ormel C. W., Güttler C., et al. (2010) The outcome of protoplanetary dust growth: Pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier. Astron. Astrophys., 513, A57.

Morbidelli A., Walsh K. J., O’Brien D. P., Minton D. A., and Bottke W. F. (2015) The dynamical evolution of the asteroid belt. In Asteroids IV (P. Michel et al., eds.), pp. 493–507. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch026.

The Dynamical Evolution of the Asteroid Belt Alessandro Morbidelli

Lagrange Laboratory, Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS

Kevin J. Walsh

Southwest Research Institute

David P. O’Brien

Planetary Science Institute

David A. Minton Purdue University

William F. Bottke

Southwest Research Institute

The asteroid belt is the remnant of the original planetesimal population in the inner solar system. However, the asteroids currently have orbits with all possible values of eccentricities and inclinations compatible with long-term dynamical stability, whereas the initial planetesimal orbits should have been quasicircular and almost coplanar. The total mass now contained in the asteroid population is a small fraction of that existing primordially. Also, asteroids with different chemical/mineralogical properties are not ranked in an orderly manner with mean heliocentric distance (orbital semimajor axis) as one might expect from the existence of a radial gradient of the temperature in the protoplanetary disk, but they are partially mixed. These properties show that the asteroid belt has been severely sculpted by one or a series of processes during its lifetime. This paper reviews the processes that have been proposed so far, discussing the properties that they explain and the problems with which they are confronted. Emphasis is paid to the interplay between the dynamical and the collisional evolution of the asteroid population, which allows the use of the size distribution or crater densities observed in the asteroid belt to constrain the dynamical models. We divide the asteroid belt evolution into three phases. The first phase started during the lifetime of the gaseous protoplanetary disk, when the giant planets formed and presumably experienced large-scale migrations, and continued after the removal of the gas, during the buildup of the terrestrial planets. The second phase occurred after the removal of the gaseous protoplanetary disk, and it became particularly lively for the asteroid belt when the giant planets suddenly changed their orbits as a result of a mutual dynamical instability and the interaction with the transneptunian planetesimal disk. The third phase covers the aftermath of the giant-planet instability through the present day.

1. INTRODUCTION The asteroid belt helps us in reconstructing the origin and the evolution of the solar system, probably better than the planets themselves. This is because the asteroid belt provides several key constraints that can be used to effectively guide the development, calibration, and validation of evolutionary models. Compared to other small-body populations, such as the Kuiper belt or Oort cloud, the constraints provided by the asteroid belt are probably more stringent, due to the fact that the number and the properties of the asteroids are better known, thanks to groundbased observations, space missions, and meteorite analysis.

The structure of this review chapter is therefore as follows. We start by reviewing in section 2 what the most important observational constraints on the asteroid belt are and what they suggest. Then, in section 3, we will review the main models proposed, from the oldest to the most recent, and from the earliest to the latest evolutionary phases they address. In section 4, we will discuss several implications for asteroid science from our current preferred view of the dynamical evolution of the asteroid belt. The dynamical evolution of the asteroid belt has already been the object of a review chapter by Petit et al. (2002) in the Asteroids III book. This review therefore has an important overlap with that chapter. Nevertheless, both our

493

494   Asteroids IV

2. OBSERVATIONAL CONSTRAINTS ON THE PRIMORDIAL EVOLUTION OF THE ASTEROID BELT The observational constraints most useful for reconstructing the formation and evolution of the asteroid belt are those related to large asteroids (larger than ~50–100 km in diameter). In fact, it has been argued that these asteroids are the most likely to be “pristine” in the sense that they were not generated in large numbers in collisional breakup events of larger parent bodies (Bottke et al., 2005a; see also the chapter by Bottke et al. in this volume), nor have they been affected by gas drag and other nongravitational forces (e.g., the Yarkovsky effect; see the chapter by Vokrouhlický et al. in this volume). Moreover, there is an emerging view that the first planetesimals were big, with a preferred diameter in the range mentioned above (Morbidelli et al., 2009; see also the chapter by Johansen et al. in this volume). Thus, throughout this chapter we will limit our discussion to the properties of large asteroids and refer to smaller asteroids only when explicitly mentioned. A key major characteristic of the asteroid belt population is the orbital excitation, i.e., the fact that the eccentricities and inclinations of many asteroidal orbits are quite large (e.g, Petit et al., 2002). The median proper inclination of D > 100 km asteroids is 11° and the median proper eccentricity is 0.145. More importantly, the values of eccentricities and inclinations of the largest asteroids are considerably dispersed, with the former ranging between 0 and 0.30, while the latter ranges between 0° and 33° (see Fig. 1). It has been shown that asteroids of modest inclinations (i < 20°) fill the entire orbital space available for long-term dynamical stability, although some stable regions are more densely populated than others (Minton and Malhotra, 2009, 2011). The reader should be aware that, whatever the preferred formation mechanism (see the chapter by Johansen et al. in this volume), planetesimals are expected to have formed on circular and coplanar orbits. Thus, one or more dynamical excitation mechanism(s) within the primordial asteroid belt were needed to stir up eccentricities and inclinations to randomly dispersed values. Asteroid eccentricities and inclinations do not show a strong dependence on semimajor axis (Fig. 1). A second fundamental characteristic of the asteroid belt is the partial mixing of taxonomic classes. Asteroids can be

grouped into many taxonomic classes on the basis of their visual and infrared spectroscopic signatures (Tholen, 1984; Bus and Binzel, 2002; DeMeo et al., 2009). As shown first by Gradie and Tedesco (1982) for the largest asteroids, the inner belt is dominated by S-complex asteroids, many of which are probably related to the meteorites known as ordinary chondrites (Binzel et al., 1996; see also the chapter by Vernazza et al. in this volume). The central belt (2.5–3.2 AU) is dominated by C-complex asteroids, probably related to carbonaceous chondrites (Burbine et al., 2002; see also the chapters by DeMeo et al. and Rivkin et al. in this volume). The Cybeles asteroids (3.2–3.7 AU), the Hilda asteroids (in the 3:2 mean-motion resonance with Jupiter), and the Jupiter Trojan asteroids (in the 1:1 resonance with Jupiter) are dominated by P- and D-type asteroids (see the chapter by Emery et al. in this volume). The C2 ungrouped meteorite “Tagish Lake” has been proposed to be a fragment of a D-type asteroid (Hiroi et al., 2001). This stratification of the main belt makes intuitive sense in terms of a general view that protoplanetary disks should have temperatures decreasing with increasing distance from the central star. In fact, ordinary chondrites are less abundant in organics and water than carbonaceous chondrites and therefore are more likely to have formed in a warmer part of the disk. The small water content in ordinary chondrites, well below the solar proportion, suggests that these bodies accreted closer to the Sun than the snowline. The fact that some water is nevertheless present is not in contradiction with this statement. A small amount of water could have been accreted by collisions with primitive bodies scattered or drifting into the inner part of the disk. At the opposite extreme, the CI meteorites show no chemical fractionation relative to the solar composition, except H, C, N, O, and all noble gases, suggesting that they formed in a region of 0.4

Proper eccentricity Proper sin i

0.3

e/sin i

observational knowledge of the asteroid belt and our theoretical understanding of solar system evolution have improved significantly since the early 2000s, providing an emerging view of a very dynamic early solar system, in which various episodes of planet migration played a fundamental role in sculpting the small-body reservoirs and displacing planetesimals far from their original birthplaces. Thus this chapter will present in greater details models proposed after 2002, focusing on their implications for asteroid science. Moreover, when reviewing models already presented in Petit et al., we will refer to numerical simulations of these models made after the publication of the Petit et al. chapter.

0.2

0.1

0

Inner a < 2.5 AU

Middle 2.5 < a < 2.8 AU

Outer a > 2.8 AU

Fig. 1. The points show mean proper eccentricity (circles) and mean proper inclination (squares) for the D > 100 km asteroids, divided into three bins of semimajor axis. The error bars show the 1s standard deviation. There is little systematic difference in excitation across the main belt. The slightly increase of inclination from the inner to the outer belt is due to the effect of the g = g6 secular resonance (see section 3), which most strongly affects high-inclination asteroids in the inner belt.

Morbidelli et al.:  The Dynamical Evolution of the Asteroid Belt   495

the disk where the temperature was low enough to allow the condensation of most elements. As shown in Fig. 2, however, asteroids of different taxonomic types are partially mixed in orbital semimajor axis, which smears the trend relating physical properties to heliocentric distance. The mixing of taxonomic type should not be interpreted as the existence of asteroids of intermediate physical properties between those of adjacent types; instead, it is due to the coexistence of asteroids of different types with various relative proportions at each value of semimajor axis. Some mixing could come from the fact that the thermal and chemical compositional properties of the disk probably changed over time. However, given that no systematic differences in accretion ages is observed among the main group of chondrites (Villeneuve et al., 2009), it is more likely that some mechanism, possibly the same that excited the orbital eccentricities and inclinations, also changed somewhat in a random fashion the original semimajor axes of the bodies, causing the observed partial mixing. The asteroid belt contains overall very little mass. From the direct determination of the masses of the largest asteroids and an estimate of the total mass of the ring of bodies, which cannot be individually “weighted,” based on the collective gravitational perturbations exerted on Mars, Krasinsky et al. (2002), Kuchynka and Folkner (2013), and Somenzi et al. (2010) concluded that the total mass contained in the asteroid belt is ~4.5 × 10–4 Earth masses (M⊕). This value is very low compared to that estimated to have originally existed in the primordial asteroid belt region by interpolating the mass densities required to form the terrestrial planets and the core of Jupiter at both ends of the belt (Weidenschilling, 1977), which is on the order of 1 M⊕ (within a factor of a few). Thus, the mass in the asteroid belt has potentially been depleted by 3 orders of magnitude compared to these expectations. 1

Relative Abundance

D 0.8

3. MODELS OF PRIMORDIAL EVOLUTION OF THE ASTEROID BELT 3.1. Early Models

S P

0.6 C 0.4

0.2

0

We can glean insights into how the primordial belt lost its mass by investigating what we know about its collisional evolution. The collisional history of asteroids is the subject of the chapter by Bottke et al. in this volume, but we report the highlights here that are needed for this discussion. In brief, using a number of constraints, Bottke et al. (2005a) concluded that the integrated collisional activity of the asteroid belt is equivalent to the one that would be produced at the current collisional rate over 8–10 G.y. This result has several implications. First, it strongly suggests that the 3-orders-of-magnitude mass depletion could not come purely from collisional erosion; such intense comminution would violate numerous constraints. Second, it argues that the mass depletion of the asteroid belt occurred very early. This is because once the eccentricities and inclinations are excited to values comparable to the current ones, for a given body every million years spent in an asteroid belt 1000× more populated brings a number of collisions equivalent to that suffered in 1 G.y. within the current population. For this reason, the third implication is that the dynamical excitation and the mass-depletion event almost certainly coincided. This argues that the real dynamical excitation event was stronger than suggested by the current distribution of asteroid eccentricities. One way to reconcile a massive asteroid belt with this scenario is to assume that more than 99% of the asteroids had their orbits so excited that they left the asteroid belt forever (hence the mass depletion). This would make the eccentricities (and to a lesser extent the inclinations) we see today to be those defined by the lucky survivors, namely the bodies whose orbits were excited the least. Using these constraints, we discuss in the next section the various models that have been proposed for the primordial sculpting of the asteroid belt.

2

3

4

5

Semimajor Axis (AU) Fig. 2. The relative distribution of large asteroids (D > 50 km) of different taxonomic types as originally observed by Gradie and Tedesco (1982). Further works by Mothé-Diniz et al. (2003), Carvano et al. (2010), and DeMeo and Carry (2014) demonstrate that the level of mixing increases for smaller asteroid sizes.

The first attempts to explain the primordial dynamical excitation of the asteroid belt were made by Heppenheimer (1980) and Ward (1981), who proposed that secular resonances swept through the asteroid belt region during the dissipation of gas in the protoplanetary disk. Secular resonances occur when the precession rate of the orbit of an asteroid is equal to one of the fundamental frequencies of precession of the orbits of the planets. There are two angles that characterize the orientation of an orbit in space, the longitude of perihelion (v) and the longitude of the ascending node (W), each of which can precess at different rates depending on the gravitational effects of the other planets and nebular gas (if present). The resonances that occur when the precession rates of the longitudes of perihelion of an asteroid (denoted by g) and of a planet are equal to each other excite the asteroid’s eccentricity. Similarly, the resonances occurring when the precession rates of the longitudes of node of an asteroid (denoted by s) and of a planet are equal to each other

496   Asteroids IV excite the asteroid’s inclination. In the case of asteroids in the main belt, the planets’ precession frequencies that most influence their dynamics are those associated with the orbits of Jupiter and Saturn. These are called g5 and g6 for the longitude of perihelion precession (the former dominating in the precession of the perihelion of Jupiter, the latter in that of Saturn), and s6 for the longitude of the node precession (both the nodes of Jupiter and Saturn precess at the same rate, if measured relative to the invariable plane, defined as the plane orthogonal to their total angular momentum vector). The dissipation of gas from the protoplanetary disk changes the gravitational potentials that the asteroids and planets feel, and hence changes the precession rates of their orbits. Given that the planets and asteroids are at different locations, they will be affected somewhat differently by this change of gravitational potential and consequently their precession rates will not change proportionally. It is therefore possible that secular resonances sweep through the asteroid belt as the gas dissipates. This means that every asteroid, whatever its location in the belt, first has orbital precession rates slower than the g5, g6 frequencies of Jupiter and Saturn when there is a lot of gas in the disk, then enters resonance (g = g5 or g = g6) when some appropriate fraction of the gas has been removed, and eventually is no longer in resonance (its orbital precession frequency being faster than those of the giant planets, i.e., g > g6) after all the gas has disappeared. The same occurs for the asteroid’s nodal frequency s relative to the planetary frequency s6. This sweeping of perihelion and nodal secular resonances has the potential to excite the orbital eccentricities and inclinations of all asteroids. This mechanism of asteroid excitation due to disk dissipation has been revisited with numerical simulations in Lemaitre and Dubru (1991), Lecar and Franklin (1997), Nagasawa et al. (2000, 2001, 2002), Petit et al. (2002), and finally by O’Brien et al. (2007). Nagasawa et al. (2000) found that of all the scenarios for gas depletion they studied (uniform depletion, inside-out, and outside-in), inside-out depletion of the nebula was most effective at exciting eccentricities and inclinations of asteroids throughout the main belt. However, they (unrealistically) assumed that the nebula coincided with the ecliptic plane. Protoplanetary disks can be warped, but they are typically aligned with the orbit of the locally dominant planet (Mouillet et al., 1997). Thus, there is no reason that the gaseous disk in the asteroid belt region was aligned with the current orbital plane of Earth (which was not yet formed). Almost certainly it was aligned with the orbits of the giant planets. Taking the invariable plane (the plane orthogonal to the total angular momentum of the solar system) as a proxy of the original orbital plane of Jupiter and Saturn, Nagasawa et al. (2001, 2002) found that the excitation of inclinations would be greatly diminished. Furthermore, since nebular gas in the inside-out depletion scenario would be removed from the asteroid belt region before the resonances swept through it, there would be no gas drag effect to help deplete material from the main-belt region. The work of O’Brien et al. (2007) accounted for the fact that the giant planets should have had orbits significantly

less inclined and eccentric than their current values when they were still embedded in the disk of gas, because of the strong damping that gas exerts on planets (Cresswell et al., 2008; Kley and Nelson, 2012). They concluded that secular resonance sweeping is effective at exciting eccentricities and inclinations to their current values only if gas is removed from the inside-out and very slowly, on a timescale of ~20 m.y. This gas-removal mode is very different from our current understanding of the photoevaporation process (Alexander et al., 2014), and inconsistent with observations suggesting that disks around solar-type stars have lifetimes of only 1–10 m.y., with an average of ~3 m.y. (e.g., Strom et al., 1993; Zuckerman et al., 1995; Kenyon and Hartmann, 1995; Haisch et al., 2001). Earlier studies found that the final eccentricities of the asteroids are quite randomized because two perihelion secular resonances sweep the entire asteroid belt in sequence: first the resonance g = g5, then the resonance g = g6. The first resonance excites the eccentricities of the asteroids from zero to approximately the same value, but the second resonance, sweeping an already excited belt, can increase or decrease the eccentricity depending on the position of the perihelion of each asteroid at the time of the encounter with the resonance (Ward et al., 1976; Minton and Malhotra, 2011). O’Brien et al. (2007) found that when Jupiter and Saturn were on orbits initially closer together, as predicted by the Nice model (e.g., Tsiganis et al., 2005), the resonance with frequency g6 would only sweep part of the outer belt, leading to less randomization of eccentricities in the inner belt. All studies in which the mid-plane of the protoplanetary disk of gas coincides with the invariable plane of the solar system find that the final inclinations tend to have comparable values. This is because there is only one dominant frequency (s6) in the precession of the nodes of Jupiter and Saturn and hence there is only one nodal secular resonance and no randomization of the final inclinations of the asteroids. Clearly, this is in contrast with the observations. For all these problems, the model of secular resonance sweeping during gas removal is no longer considered to be able to alone explain the excitation and depletion of the primordial asteroid belt. An alternative model for the dynamical excitation of the asteroid belt was proposed by Ip (1987). In this model, putative planetary embryos are scattered out of the Jupiter region and cross the asteroid belt for some timescale before being ultimately dynamically ejected from the solar system. If the embryos are massive enough, their repeated crossing of the asteroid belt can excite and randomize the eccentricities and inclinations of the asteroids, through close encounters and secular effects. That scenario has been revisited by Petit et al. (1999), who found that, whatever the mass of the putative embryos, the resulting excitation in the asteroid belt ought to be very unbalanced. Excitation would be much stronger in the outer belt than in the inner belt (because the embryos come from Jupiter’s region) and it would be much stronger in eccentricity than in inclination. By contrast, the main asteroid belt shows no such trend (see Fig. 1). So, again, this model has since been abandoned. If massive embryos have been

Morbidelli et al.:  The Dynamical Evolution of the Asteroid Belt   497

scattered from Jupiter’s zone, they must have crossed the asteroid belt very briefly so that their limited effects could be completely overprinted by other processes, such as those discussed below. 3.2. Wetherill’s Model The first comprehensive model of asteroid belt sculpting, which linked the evolution of the asteroid belt with the process of terrestrial planet formation, was that proposed by Wetherill (1992) and later simulated in a number of subsequent papers (e.g., Chambers and Wetherill, 1998; Petit et al., 2001, 2002; O’Brien et al., 2006, 2007). In this model, at the time gas was removed from the system, the protoplanetary disk interior to Jupiter consisted of a bimodal population of planetesimals and planetary embryos, the latter with masses comparable to those of the Moon or Mars. Numerical simulations show that, under the effect of the mutual perturbations among the embryos and the resonant perturbations from Jupiter, embryos are generally cleared from the asteroid belt region, whereas embryos collide with each other and build terrestrial planets inside 2 AU. While they are still crossing the asteroid belt, the embryos also excite and eject most of the original resident planetesimals. Only a minority of the planetesimals (and often no embryos) remain in the belt at the end of the terrestrial planet formation process, which explains the mass depletion of the current asteroid population. The eccentricities and inclinations of the surviving asteroids are excited and randomized, and the remaining asteroids have generally been scattered somewhat relative to their original semimajor axes. A series of simulation snapshots demonstrating this process is shown in Fig. 3. Whereas earlier simulations assumed that Jupiter and Saturn were originally on their current orbits, O’Brien et al. (2006, 2007) performed simulations with Jupiter and Saturn on the low-inclination, nearly circular orbits predicted in the Nice model. The resulting asteroids from a set of simulations with these initial conditions are shown in Fig. 4. Overall, the range of values compare well with those observed for the real asteroids, although the final inclination distribution is skewed toward large inclinations. The reason for this is that it is easier to excite a low-inclination asteroid to large eccentricity and remove it from the belt than it is for a high-inclination asteroid, because the encounter velocities with the embryos are slower and more effective in deflecting the low-inclination asteroid’s orbit. Also, with the giant planets on nearly circular orbits, it takes longer to clear embryos from the asteroid belt, allowing more time to excite asteroids to large inclinations. As noted earlier, the surviving asteroids have their orbital semimajor axes displaced from their original values, as a result of the embryos’ gravitational scattering. O’Brien et al. (2007) found that the typical change in semimajor axis is on the order of 0.5 AU (comparable to earlier simulations), with a tail extending to 1–2 AU, and the semimajor axis can be either decreased or increased. This process can explain the partial mixing of taxonomic types. As shown in Fig. 2, the distribution of the S-type and C-type asteroids

has a Gaussian-like shape, with a characteristic width of ~0.5 AU. Thus, if one postulates that all S-type asteroids originated from the vicinity of 2 AU and all C-type asteroids originated in the vicinity of 3 AU,Wetherill’s model explains the current distribution. 3.3. The Grand Tack Model A more recent, alternative model to Wetherill’s is the socalled Grand Tack scenario, proposed in Walsh et al. (2011). Initially the Grand Tack scenario had not been developed to explain the asteroid belt, but to answer two questions left open by Wetherill’s model: Why is Mars so small relative to Earth? Why is Jupiter so far from the Sun despite planets having a tendency to migrate inward in protoplanetary disks? Nevertheless, this scenario has profound implications for the asteroid belt, as we discuss below. The Grand Tack scenario is built on results from hydrodynamics simulations finding that Jupiter migrates toward the Sun if it is alone in the gas disk, while it migrates outward if paired with Saturn (Masset and Snellgrove, 2001; Morbidelli and Crida, 2007; Pierens and Nelson, 2008; Pierens and Raymond, 2011; D’Angelo and Marzari, 2012). Thus, the scenario postulates that Jupiter formed first. As long as the planet was basically alone, Saturn being too small to influence its dynamics, Jupiter migrated inward from its initial position (poorly constrained but estimated at ~3.5 AU) down to 1.5 AU. Then, when Saturn reached a mass close to its current one and an orbit close to that of Jupiter, Jupiter reversed migration direction (i.e., it “tacked,” hence the name of the model) and the pair of planets started to move outward. This outward migration continued until the final removal of gas in the disk, which the model assumes happened when Jupiter reached a distance of ~5.5 AU. The migration of the cores of giant planets is still not fully understood (see Kley and Nelson, 2012, for a review). Thus, the Grand Tack model comes in two “flavors.” In one, Saturn, while growing, migrates inward with Jupiter. In another, Saturn is stranded at a no-migration orbital radius until its mass exceeds 50 M⊕ (Bitsch et al., 2014), then it starts migrating inward and it catches Jupiter in resonance because it migrates faster. Both versions exist with and without Uranus and Neptune. All these variants are described in Walsh et al. (2011); the results are very similar in all these cases, which shows the robustness of the model, at least within the range of tested possibilities. The scheme presented in Fig. 5 has been developed in the framework of the first “flavor.” Assuming that Jupiter formed at the snowline (a usual assumption to justify the large mass of its core and its fast formation), the planetesimals that formed inside its initial orbit should have been mostly dry. It is therefore reasonable to associate these planetesimals (whose distribution is sketched as a dashed area in Fig. 5) with the S-type asteroids and other even dryer bodies (enstatite-type, Earth precursors, etc.). During its inward migration, Jupiter penetrates into the disk of these planetesimals. In doing so, most planetesimals (and planetary embryos) are captured in mean-motion resonances

498   Asteroids IV 1

0.6

0.4

0.4

0.2

0.2

1

0

1

2

3

0

4

1

3 m.y.

0.8

0.6

0.4

0.4

0.2

0.2 0

1

2

3

0

4

1

2

3

4

1

2

3

4

2

3

4

10 m.y.

0

1

1 30 m.y.

0.8

0.6

0.4

0.4

0.2

0.2 0

100 m.y.

0.8

0.6

0

0

0.8

0.6

0

1 m.y.

0.8

0.6

0

Eccentricity

1

0 m.y.

0.8

1

2

3

0

4

0

1

Semimajor Axis (AU) Fig. 3. Snapshots of the evolution of the solar system and of the asteroid belt in a simulation of Wetherill’s model performed in O’Brien et al. (2006) and assuming Jupiter and Saturn on initial quasicircular orbits. Each panel depicts the eccentricity vs. semimajor axis distribution of the particles in the system at different times, labeled on top. Planetesimals are represented with gray dots and planetary embryos by black circles, whose size is proportional to the cubic root of their mass. The solid lines show the approximate boundaries of the current main belt. 0.5

(a)

30

0.3 0.2

25 20 15 10

0.1 0

(b)

35

Inclination

Eccentricity

0.4

40

Proper Elements of Real MB Asteroids Asteroids in Simulations

5 2

2.5

3

3.5

Semimajor Axis (AU)

4

0

2

2.5

3

3.5

4

Semimajor Axis (AU)

Fig. 4. The final eccentricities and inclinations of asteroids in Wetherill ’s (1992) model (black dots), according to the simulations presented in O’Brien et al. (2007). For comparison, the observed distribution of large asteroids is depicted with gray dots.

with Jupiter and are pushed inward, increasing the mass density of the inner part of the disk. However, some 10% of the planetesimals are kicked outward by an encounter with Jupiter, reaching orbits located beyond Saturn that collectively have an orbital (a,e) distribution typical of a scattered disk (i.e., with mean eccentricity increasing with semimajor axis). In semimajor axis range, this scattered disk overlaps with the inner part of the disk of primitive bodies (whose distribution is sketched as a dotted area in Fig. 5) that are initially on circular orbits beyond the orbit of Saturn. These bodies, being formed beyond the snowline, should be rich

in water ice and other volatile elements, and therefore it is again reasonable to associate them with C-type asteroids. After reaching ~1.5 AU [this value is constrained by the requirement to form a small Mars and a big Earth (Walsh et al., 2011; Jacobson et al., 2014; Jacobson and Morbidelli, 2014)], Jupiter reverses its migration direction and begins its outward migration phase, during which the giant planets encounter the scattered S-type disk, and then also the primitive C-type disk. Some of the bodies in both populations are scattered inward, reach the asteroid-belt region, and are implanted there as Jupiter moves out of it.

Morbidelli et al.:  The Dynamical Evolution of the Asteroid Belt   499

The final orbits of the planetesimals, at the end of the outward migration phase, are shown in Fig. 6. A larger dot size is used to highlight the planetesimals trapped in the asteroid belt region and distinguish them from those in the inner solar system or at eccentricities too large to be in the asteroid belt. Notice that the asteroid belt is not empty, although it has been strongly depleted (by a factor of several hundred relative to its initial population). This result is not trivial. One could have expected that Jupiter migrating through the asteroid belt twice (first inward then outward) would have completely removed the asteroid population, invalidating the Grand Tack scenario. The eccentricities and the inclinations of the particles in the asteroid belt are excited and randomized. The S-type particles (black) are found predominantly in the inner part of the belt and the C-type particles (gray) in the outer part, but there is a wide overlapping region where both are present. This is qualitatively consistent with what is observed. As discussed above, the Grand Tack scenario solves open problems in Wetherill’s model. The small mass of Mars is explained as a result of the disk of the remaining solid material being truncated at ~1 AU (Hansen, 2009; Walsh et al., 2011). Fischer and Ciesla (2014) reported that they could obtain a small-mass Mars in a few percent of simulations conducted in the framework of Wetherill’s model. However, the rest of the planetary system in these simulations does not resemble

C-type

red

tte

S

20 10 0

Eccentricity

a Sc

es

p -ty

30

Inclination

S-type

the real terrestrial planet system (Jacobson and Walsh, 2015). For instance, another massive planet is formed in the Mars region or beyond. The outward migration of Jupiter explains why the giant planets in our solar system are so far from the Sun, whereas most giant planets found so far around other stars are located at 1–2 AU. For all these reasons, one can consider the Grand Tack model more as an improvement of Wetherill’s model than an alternative, because it is built in the same spirit of linking the asteroid belt sculpting to the evolution of the rest of the solar system (terrestrial planet formation and giant-planet migration, the latter of which was still unknown during Wetherill’s time). It is nevertheless interesting to compare the Grand Tack model and Wetherill’s model on the basis of the final asteroid belts that they produce. Comparing Fig. 6 with Fig. 4, it is apparent that the Grand Tack model provides a better inclination distribution, more uniform than Wetherill’s, but it produces a worse eccentricity distribution, which is now more skewed toward the upper eccentricity boundary of the asteroid belt. As we will see in section 3.5, however, the eccentricity distribution can be remodeled somewhat during a later evolutionary phase of the solar system. This is also partially true for the inclination distribution. So, for what concerns the eccentricity and inclination distributions, one might declare a tie in the competition between the two models.

0.8 0.6 0.4 0.2 0

2

4

6

8

Semimajor Axis (AU) Semimajor Axis Fig. 5. A scheme showing the Grand Tack evolution of Jupiter and Saturn and its effects on the asteroid belt. The three panels show three evolutionary states in temporal sequence. First, the planets migrate inward, then, when Saturn reaches its current mass, they move outward. The dashed and dotted areas schematize the (a,e) distributions of S-type and C-type asteroids respectively. The dashed and dotted arrows in the lower panel illustrate the injection of scattered S-type and C-type asteroids into the asteroid belt during the final phase of outward migration of the planets.

Fig. 6. Final semimajor axis, eccentricity, and inclination distribution of bodies surviving the inward and outward migration of Jupiter and Saturn. The black particles were originally placed inside the initial orbit of Jupiter and the gray particles outside the initial orbit of Saturn. The particles finally trapped in the asteroid belt are depicted with larger symbols than the others. The dashed curve in the lower panel shows the approximate boundaries of the asteroid belt inward of the 2:1 resonance with Jupiter. This final distribution was achieved in the simulations of Walsh et al. (2011) accounting only for Jupiter and Saturn (i.e., not including Uranus and Neptune) moving together in the 2:3 resonance, as shown in Fig. 5.

500   Asteroids IV The Grand Tack model makes it conceptually easier to understand the significant differences between S-type and C-type asteroids and their respective presumed daughter populations: the ordinary and carbonaceous chondrites. In fact, in the Grand Tack model these two populations are sourced from clearly distinct reservoirs on either side of the snowline. Instead, in Wetherill’s model these bodies would have formed just at the two ends of the asteroid belt, so less than 1 AU apart. Despite such a vast difference in predicted formation locations for these two populations, the debate is open. Some authors (e.g., Alexander et al., 2012) think that bodies formed in the giant-planet region would be much more similar to comets than to asteroids, while others (Gounelle et al., 2008) argue that there is a continuum between C-type asteroids and comets and a clear cleavage of physical properties between ordinary and carbonaceous chondrites. We review the available cosmochemical constraints and their uncertain compatibility with the model in section 3.4. A clear distinction between the Grand Tack model and Wetherill’s model is that the former provides a faster and more drastic depletion of the asteroid belt. This point is illustrated in Fig. 7, which shows the fraction of the initial asteroid population that is in the main-belt region at any time. The Grand Tack scenario depletes the asteroid belt down to 0.3%, and does so basically in 0.1 m.y. Assuming that the final asteroid belt consisted of one current asteroid belt mass in S-type asteroids and three current asteroid belt masses in C-type asteroids (the reason for 4× more total mass in the asteroid belt will be clarified in section 3.6), this implies that the asteroid belt at t = 0 should have contained 0.6 M⊕ in planetesimals (the rest in embryos). Also, a calculation of

Fraction Remaining in Main Belt

1 Wetherill

0.1

0.01

10–3 10–3

Grand Tack

0.01

0.1

1

10

100

Time (m.y.) Fig. 7. The depletion of the asteroid belt in Wetherill’s model (black) and Grand Tack model (gray). In the Grand Tack model notice the bump between 0.1 and 0.6 m.y. due to the implantation of primitive objects into the main belt. Overall, the depletion of the asteroid belt is faster and stronger in the Grand Tack model.

the collision probability of the asteroids as a function of time (both among each other and with the planetesimals outside the asteroid belt) shows that the integrated collisional activity suffered by the surviving asteroids during the first 200 m.y. would not exceed the equivalent of 4 G.y. in the current population. Thus, assuming that the exceeding factor of 4 in the asteroid population is lost within the next 500 m.y. (see sections 3.5 and 3.6), the integrated collisional activity of asteroids throughout the entire solar system age would probably remain within the 10-G.y. constraint described in section 2. In contrast, Wetherill’s model depletes the asteroid belt on a timescale of 100 m.y. Also, about 2–3% of the initial population remains in the belt at the end. Thus, to be consistent with constraints on the current population and its integrated collisional activity, the initial mass in planetesimals in the asteroid-belt region should have been no larger than 200× the current asteroid-belt mass, or less than one Mars mass (Bottke et al., 2005b). 3.4. Are Cosmochemical Constraints Consistent with the Grand Tack Model? The Grand Tack model predicts that C-type asteroids have been implanted into the asteroid belt from the giantplanet region. Is this supported or refuted by cosmochemical evidence? Although there is a spread in values, the D/H ratios of carbonaceous chondrites (with the exception of CR chondrites) are a good match to Earth’s water (Alexander et al., 2012). Oort cloud comets are usually considered to have formed in the giant-planet region (e.g., Dones et al., 2004). The D/H ratio was measured for the water from seven Oort cloud comets (see Bockelée-Morvan et al., 2012, and references within). All but one [Comet 153P/Ikeya-Zhang (Biver et al., 2006)] have water D/H ratios about twice as high as chondritic. This prompted Yang et al. (2013) to develop a model where the D/H ratio of ice in the giant-planet region is high. However, Brasser et al. (2007) showed that cometsized bodies could not be scattered from the giant-planet region into the Oort cloud in the presence of gas drag (i.e., when the giant planets formed), and Brasser and Morbidelli (2013) demonstrated that the Oort cloud population is consistent with an origin from the primordial transneptunian disk at a later time. The recent measurement (Altwegg et al., 2014) of a high D/H ratio for the ice of Comet 67P/ Churyumov-Gerasimenko, which comes from the Kuiper belt, supports this conclusion by showing that there is no systematic difference between Oort cloud comets and Kuiper belt comets. Care should therefore be taken in using Oort cloud comets as indicators of the D/H ratio in the giantplanet region. Conflicting indications on the local D/H ratio come from the analysis of Saturn’s moons. Enceladus’ D/H ratio is roughly twice Earth’s (Waite et al., 2009), but Titan’s D/H ratio is Earth-like (Coustenis et al., 2008; Abbas et al., 2010; Nixon et al., 2012). Alexander et al. (2012) also noticed a correlation between D/H and C/H in meteorites and interpreted it as evidence

Morbidelli et al.:  The Dynamical Evolution of the Asteroid Belt   501

for an isotopic exchange between pristine ice and organic matter within the parent bodies of carbonaceous chondrites. From this consideration, they argued that the original water reservoir of carbonaceous asteroids had a D/H ratio lower than Titan, Enceladus, or any comet, again making asteroids distinct from bodies formed in the giant-planet region and beyond. However, a reservoir of pristine ice has never been observed; the fact that Earth’s water and other volatiles are in chondritic proportion (Marty, 2012; however, see Halliday, 2013) means that carbonaceous chondrites — wherever they formed — reached their current D/H ratios very quickly, before delivering volatiles to Earth. It is also possible that the D/H ratio measured for comets and satellites might have been the result of a similar rapid exchange between a pristine ice and the organic matter. Another isotopic constraint comes from the nitrogen isotope ratio. Comets seem to have a rather uniform 15N/14N ratio (Rousselot et al., 2014). Even the comets with a chondritic D/H ratio [e.g., Comet Hartley 2 (Hartogh et al., 2011)] have a nonchondritic 15N/14N ratio (Meech et al., 2011). The 15N/14N ratio, however, is only measured in HCN or NH2, never in molecular nitrogen (N2). Titan has a cometary 15N/14N ratio as well [in this case measured in N (Niemann 2 et al., 2010)]. Here, again, a few caveats are in order. First, it is difficult to relate the composition of a satellite, born from a circumplanetary disk with its own thermal and chemical evolution, to the composition of bodies born at the same solar distance but on heliocentric orbits. Second, it is unclear whether any comets for which isotope ratios have been measured originate from the giant-planet region, as opposed to the transneptunian disk (Brasser and Morbidelli, 2013). We also point out that hot spots with large 15N/14N ratios are found in primitive meteorites (Busemann et al., 2006). Arguments in favor of an isotopic similarity between carbonaceous chondrites and comets come from the analysis of micrometeorites. Most micrometeorites (particles of ~100 µm collected in the Antarctic ice) have chondritic isotopic ratios for H, C, N, and O [with the exception of ultracarbonaceous micrometeorites, which have a large D/H ratio, comparable to that in the organics of some chondrites, but which constitute only a minority of the micrometeorite population (Duprat et al., 2010)]. Yet according to the best available model of the dust distribution in the inner solar system (Nesvorný et al., 2010), which is compelling given that it fits the zodiacal light observations almost perfectly, most of the dust accreted by Earth should be cometary, even when the entry velocity bias is taken into account. Similarly, from orbital considerations, Gounelle et al. (2006) concluded that the CI meteorite Orgueil is a piece of a comet. Compelling evidence for a continuum between chondrites and comets also comes from the examination of Comet Wild 2 particles returned to Earth by the Stardust mission (e.g., Zolensky et al., 2006, 2008; Ishii et al., 2008; Nakamura et al., 2008). These considerations suggest that if one looks at their rocky components, comets and carbonaceous asteroids are very similar from a compositional and isotopic point of view, if not in fact indistinguishable.

Finally, it has been argued that if the parent bodies of carbonaceous chondrites had accreted among the giant planets, they would have contained ~50% water by mass. Instead, the limited hydrous alteration in carbonaceous meteorites suggests that only about 10% of the original mass was in water (A. N. Krot, personal communication, 2014; but see Alexander et al., 2010). However, a body’s original water content cannot easily be estimated from its aqueous alteration. Even if alteration is complete, there is a finite amount of water that the clays can hold in their structures. Thus, the carbonaceous parent bodies may have been more water-rich than their alteration seems to imply. In fact, the discoveries of main-belt comets releasing dust at each perihelion passage (Hsieh and Jewitt, 2006), of water ice on asteroids Themis (Campins et al., 2010; Rivkin and Emery, 2010) and Cybele (Licandro et al., 2011; Hargrove et al., 2012), and of vapor plumes on Ceres (Kuppers et al., 2014) show that C-type asteroids are more rich in water than their meteorite counterpart seems to suggest, supporting the idea that they might have formed near or beyond the snowline. Meteorites may simply represent rocky fragments of bodies that were far wetter/icier. Clearly, the debate on whether carbonaceous asteroids really come from the giant-planet region as predicted by the Grand Tack model is wide open. More data are needed from a broader population of comets. The investigation of main-belt comets, both remote and in situ, and the Dawn mission at Ceres will be key to elucidating the real ice content of carbonaceous asteroids and their relationship with classic “comets.” 3.5. The Nice Model: A Second Phase of Excitation and Depletion for the Asteroid Belt Figure 7 seems to suggest that after ~100 m.y. the asteroid belt had basically reached its final state. However, at this time the orbits of the giant planets were probably still not the current ones. In fact, the giant planets are expected to have emerged from the gas-disk phase in a compact and resonant configuration as a result of their migration in the gas-dominated disk. This is true not only in the Grand Tack model, but in any model where Jupiter is refrained from migrating inside ~5 AU by whatever mechanism (Morbidelli et al., 2007). The transition of the giant planets from this early configuration to the current configuration is expected to have happened via an orbital instability, driven by the interaction of the planets with a massive disk of planetesimals located from a few astronomical units beyond the original orbit of Neptune to about 30 AU (Morbidelli et al., 2007; Batygin and Brown, 2010; Levison et al., 2011; Nesvorný, 2011; Batygin et al., 2012; Nesvorný and Morbidelli, 2012; see also a precursor work by Thommes et al., 1999). In essence, the planetesimals disturbed the orbits of the giant planets and, as soon as two planets fell off resonance, the entire system became unstable. In the simulations, the instability can occur early (e.g., Morbidelli et al., 2007) or late (Levison et al., 2011), depending on the location of the inner edge of the transneptunian disk.

502   Asteroids IV Constraints suggest that in the real solar system the instability occurred relatively late, probably around 4.1 G.y. ago (namely 450 m.y. after gas removal). These constraints come primarily from the Moon. Dating lunar impact basins is difficult, because it is not clear which samples are related to which basin (e.g., Norman and Nemchin, 2014). Nevertheless, it is clear that several impact basins, probably a dozen, formed in the 4.1–3.8-Ga period (see Fassett and Minton, 2013, for a review). Numerical tests demonstrate that these late basins (even just Imbrium and Orientale, whose young ages are undisputed) are unlikely to have been produced by a declining population of planetesimals, left over from the terrestrial planet accretion process, because of their short dynamical and collisional lifetimes (Bottke et al., 2007). There is also a surge in lunar rock impact ages ~4 G.y. ago, which contrasts with a paucity of impact ages between 4.4 and 4.2 Ga (Cohen et al., 2005). This is difficult to explain if the bombardment had been caused by a population of leftover planetesimals slowly declining over time. The situation is very similar for the bombardment of asteroids, with meteorites showing a surge in impact ages at 4.1 Ga and a paucity of ages between 4.2 and 4.4 Ga (Marchi et al., 2013). Meteorites also show many impact ages near 4.5 Ga, demonstrating that the apparent lack of events in the 4.2–4.4-Ga interval is not due to clock resetting processes. All these constraints strongly suggest the appearance of a new generation of projectiles in the inner solar system about 4.1 G.y. ago, which argues that either a very big asteroid broke up at that time (Cuk, 2012) (but such a breakup is very unlikely from collision probability arguments and we do not see any remnant asteroid family supporting this hypothesis), or that the dynamical instability of the giant planets occurred at that time, partially destabilizing small-body reservoirs that had remained stable until then. Other constraints pointing to the late instability of the giant planets come from the outer solar system. If the planets had become unstable at the disappearance of the gas in the disk, presumably the Sun would still have been in a stellar cluster and consequently the Oort cloud would have formed more tightly bound to the Sun than it is thought to be from the orbital distribution of long-period comets (Brasser et al., 2008, 2012). Also, the impact basins on Iapetus (a satellite of Saturn) have topographies that have relaxed by 25% or less, which argues that they formed in a very viscous lithosphere; according to models of the thermal evolution of the satellite, these basins can not have formed earlier than 200 m.y. after the beginning of the solar system (Robuchon et al., 2011). For all these reasons, it is appropriate to discuss the consequences of the giant-planet instability on the asteroid belt, after the events described by the Grand Tack or Wetherill’s models. In fact, it is important to realize that the model of giant-planet instability (often called the Nice model) is not an alternative to the models described before on the early evolution of the asteroid belt; instead it is a model of the subsequent evolution. The phase of giant-planet instability is very chaotic and therefore a variety of orbital evolutions are possible. Neverthe-

less, the planetary evolutions can be grouped in two categories. In the first category, Saturn, Uranus, and Neptune have close encounters with each other, but none of them have encounters with Jupiter. Saturn typically scatters either Uranus or Neptune outward and thus it recoils inward. As a result, Uranus and Neptune acquire large eccentricity orbits that cross the transneptunian disk. The dispersal of the planetesimal disk damps the eccentricities of the planets by dynamical friction and drives the planets’ divergent migration in semimajor axis (Tsiganis et al., 2005). Thus, the planets achieve stable orbits that are well separated from each other. The orbital separation between Jupiter and Saturn first decreases, when Saturn recoils, and then increases due to planetesimal-driven migration. The timescale for the latter is typically ~10 m.y. The slow separation between the two major planets of the solar system drives a slow migration of secular resonances across the asteroid belt (Minton and Malhotra, 2009, 2011) and the terrestrial planet region (Brasser et al., 2009). The problem is that the resulting orbital distribution in the asteroid belt is very uneven, as shown in Fig. 8a, with most asteroids surviving at large inclination (Morbidelli et al., 2010), and the orbits of the terrestrial planets become too excited (Brasser et al., 2009; Agnor and Lin, 2012). In the second category of evolutions, Saturn scatters an ice giant planet (Uranus, Neptune, or a putative fifth planet) inward, thus recoiling outward, and then Jupiter scatters the ice giant outward, thus recoiling inward. The interaction with the planetesimals eventually damps and stabilizes the orbits of the planets. In this evolution, dubbed “jumping-Jupiter,” the orbital separation between Jupiter and Saturn initially jumps, when Saturn recoils outward and Jupiter inward; then there is a final smooth phase of separation, due to planetesimal-driven migration. In the jump, the secular resonances can jump across the asteroid belt (Morbidelli et al., 2010) and across the terrestrial planet region (Brasser et al., 2009) without disrupting their orbital structure (see Fig. 8b). The jumping-Jupiter evolution also explains the capture of the irregular satellites of Jupiter with an orbital distribution similar to those of the irregular satellites of the other giant planets (Nesvorný et al., 2007, 2014). It can also explain the capture of Jupiter’s Trojans in uneven proportions around the L4 and L5 Lagrangian points (Nesvorný et al., 2013; see also the chapter by Emery et al. in this volume). So far, no other model is capable of achieving these results. For all these reasons, simulated solar system evolutions these days are required to show a jumping-Jupiter evolution to be declared successful (Nesvorný and Morbidelli, 2012). Although it avoids secular resonances sweeping across the asteroid belt, a jumping-Jupiter evolution is not without consequences for the asteroids. The sudden change in the eccentricity of Jupiter (from an initial basically circular orbit, like that observed in hydrodynamical simulations of the four giant planets evolving in the gaseous protoplanetary disk, to one with current eccentricity) changes the forced eccentricity felt by the asteroids in their secular evolution. Consequently, the proper eccentricities of the asteroids are changed. Depending on the value of the longitude of

Morbidelli et al.:  The Dynamical Evolution of the Asteroid Belt   503

perihelion when the forced eccentricity changes, the proper eccentricity of an asteroid can decrease or increase. Roughly, 50% of the asteroids are kicked to larger eccentricities and therefore are removed from the asteroid belt. The remaining 50% of the asteroids have their eccentricities reduced. This can potentially reconcile the eccentricity distribution of asteroids at the end of the Grand Tack evolution (see Fig. 6) with the current distribution. Indeed, Minton and Malhotra (2011) showed that the current eccentricity distribution can be achieved starting from a primordial distribution peaked at e ~ 0.3, similar to that produced by the Grand Tack evolution of Jupiter (Fig. 6). They obtained this result using secular resonance sweeping, but the basic result should hold also for a sudden enhancement of Jupiter’s eccentricity. Nevertheless, specific numerical simulations have never been done to demonstrate that the eccentricity distribution of asteroids at the end of the Grand Tack model can be transformed into the current distribution via the jumping-Jupiter evolution [at

40

(a)

35

3:1

2:1

ν16

30

Inclination (°)

5:2

25 20

ν6

15 10 5 0

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

Azimuth (AU) 40

(b)

35

3:1

2:1

ν16

30

Inclination (°)

5:2

25 20

ν6

15 10 5 0

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

Azimuth (AU) Fig. 8. A comparison between the final (a,i) distribution of asteroids if (a) Jupiter and Saturn migrate slowly away from each other or (b) jump due to them scattering an ice giant planet. In the first case the orbital distribution is inconsistent with that observed, while in the second case it is. From Morbidelli et al. (2010).

the time of this writing, this work is ongoing and seems to give positive results (Deienno and Gomes, personal communication)]. The jump in Jupiter’s inclination due to its encounter(s) with another planet should also have partially reshuffled the asteroid inclination distribution, possibly reconciling the final distribution in Wetherill’s model (see Fig. 4) with the current one. However, the effects on the inclination during Jupiter’s jump seem less pronounced than those on the eccentricity (Morbidelli et al., 2010). The current inner edge of the asteroid belt is marked by the presence of the secular resonance between the precession frequency of the perihelion of an asteroid and the g6 planetary frequency. The resonance makes unstable all objects inside 2.1 AU at low to moderate inclinations, which truncates the belt at its current edge. But before the impulsive separation between the inner orbits of Jupiter and Saturn, this resonance was much weaker (because the g6 mode was less excited in the planetary system, the giant-planet orbits being more circular) and located away from the asteroid belt. Thus, in principle the asteroid belt might have extended closer to Mars before the giant-planet-instability event. Bottke et al. (2012) showed that the destabilization of this extended belt — or “E belt” — could have dominated the formation of impact basins on the Moon, producing 12–15 basins over a 400-m.y. interval. Given the age of the Orientale basin (usually estimated at 3.7–3.8 Ga), this implies that the giant-planet instability and the destabilization of the E belt happened 4.1–4.2 G.y. ago and was responsible for the production of the last dozen lunar basins, known as the Nectarian and post-Nectarian basins. Earlier basins and craters would have to have come from other sources, such as the planetesimals leftover from the terrestrial planet-formation process. The existence of two populations of projectiles, namely the leftover planetesimals dominating the bombardment at early times and the E-belt asteroids dominating the impact rate at a later epoch, should have produced a sawtooth-shaped bombardment history of the Moon (Morbidelli et al., 2012). The E belt should also have caused a long, slowly decaying tail of Chicxulub-sized impacts on Earth, possibly continuing until ~2 G.y. ago. Evidence for this long tail in the time-distribution of impacts is provided by the existence of terrestrial impact spherule beds, which are globally distributed ejecta layers created by the formation of Chicxulub-sized or larger craters (Johnson and Melosh, 2012): 10, 4, and 1 of these beds have been found on well-preserved, non-metamorphosed terrains between 3.23 and 3.47 Ga, 2.49 and 2.63 Ga, and 1.7 and 2.1 Ga, respectively (Simonson and Glass, 2004; Bottke et al., 2012). Moreover, the escape to high-eccentricity orbits of bodies from the main-belt and E-belt regions produced a spike in the impact velocities on main-belt asteroids at the time of the giant-planet instability. Thus, although the impact frequency on asteroids decreased with the depletion of 50% of the main-belt population and 100% of the E-belt population, the production of impact melt on asteroids increased during this event because melt production is very sensitive to impact velocities (Marchi et al., 2013). For this reason, the impact ages of meteorites show a spike at 4.1 Ga like

504   Asteroids IV the lunar rocks, although for the latter this is due to a surge in the impact rate. A final consequence of the giant-planet instability on the asteroid belt is the capture into its outer region of planetesimals from the transneptunian disk (Levison et al., 2009). Because Jupiter Trojans are captured in the same event, these last captured asteroids should have had the same source as the Trojans and therefore they should be mostly taxonomic D- and P-types. The probability of capture in the asteroid belt is nevertheless small, so it is unlikely that an object as big as Ceres was trapped from the transneptunian region in this event. 3.6. After the Giant-Planet Instability After the giant-planet instability the orbits of all planets, giants and terrestrial, are similar to the current ones (within the range of semimajor axis, eccentricity, and inclination oscillation provided by the current dynamical evolution). Thus, the asteroid belt has finished evolving substantially under the effect of external events such as giant-planet migration or instability. The asteroid belt thus entered into the current era of evolution. Asteroids became depleted at the locations of unstable resonances (mean-motion and secular) on time‑ scales that varied from resonance to resonance. In this way, the asteroid belt acquired its current final orbital structure. In this process, it is likely that another ~50% of the asteroids were removed from the belt, most of them during the first 100 m.y. after the giant-planet instability (Minton and Malhotra, 2010). Combining this 50% with the 50% loss during the instability itself is the reason that we require that the primordial depletion event (Wetherill’s model or Grand Tack) left a population of asteroids in the belt that was about 4× the current one. With the depletion of unstable resonances, the asteroid belt would have become an extraordinarily boring place from a dynamical point of view. Fortunately, collisional breakup events keep refreshing the asteroid population, generating dynamical families very rich in small objects, while nongravitational forces, mostly the Yarkovsky effect (Bottke et al., 2006), cause small asteroids to drift in semimajor axis, eventually supplying new bodies to the unstable resonances. This combination of collisional activity and nongravitational forces allow the main asteroid belt to resupply and sustain in a quasi-steady state the intrinsically unstable population of near Earth objects. But this is the subject of another chapter. 4. CONCLUSIONS AND IMPLICATIONS In this chapter, we have reviewed our current understanding of the evolution of the asteroid belt, from a massive and dynamically quiet disk of planetesimals to its current state, which is so complex and rich from the points of view of both its dynamical and physical structures.

According to this understanding, the asteroid population mainly evolved in two steps. There was an early event of strong dynamical excitation and asteroid removal, which left about 4× the current asteroid population on orbits with a wide range of eccentricities and inclinations. This event may have been due to the self-stirring of a population of planetary embryos resident in the asteroid belt (Wetherill, 1992), or to the migration of Jupiter through the asteroid belt [the Grand Tack scenario (Walsh et al., 2011)]. The second step occurred later, possibly as late as 4.1 G.y. ago or ~400 m.y. after the removal of gas from the protoplanetary disk. At that time, the asteroid belt underwent a second dynamical excitation and depletion when the giant planets became temporarily unstable and their orbits evolved from an initial resonant and compact configuration to the current configuration. During this second event, the asteroid belt lost about 50% of its members. After this second event, the asteroid belt structure settled down with the progressive depletion at unstable resonances with the giant and terrestrial planets. Another 50% of the asteroid population was lost in this process, mostly during the subsequent 100 m.y. If the first evolutionary step was due to the Grand Tack migration of Jupiter, we expect that S-type asteroids formed more or less in situ (2–3-AU region); the C-type asteroids formed in the giant-planet region (roughly 3–15 AU), and the P- and D-type asteroids formed beyond the initial location of Neptune (roughly 15–30 AU). The hot population of the Kuiper belt, the scattered disk, and the Oort cloud would also derive from the same transneptunian disk (Levison et al., 2008; Brasser and Morbidelli, 2013). There is a growing consensus that the cold Kuiper belt (42–45 AU) is primordial and born in situ (Petit et al., 2011; Parker et al., 2011; Batygin et al., 2011; Fraser et al., 2014). Thus, the cold Kuiper belt objects should not have any correspondent in the asteroid belt. If instead the first step was due to the self-stirring of resident embryos as inWetherill’s model, we expect that S-type asteroids formed in the inner part of the belt, C-type asteroids in the outer part, and no asteroids sample the planetesimal population in the giant-planet region. The origin of P- and D-type asteroids would be the same as above. Thus, deciding which of these two models is preferable requires a better understanding of the nature of C-type asteroids and their water content, the similarities and differences between them and comets, and among comets themselves. This may not be an easy task. The population of main-belt comets (asteroids showing cometary activity such as 133P/Elst-Pizarro or 238P/Read) and their relationship with the parent bodies of carbonaceous chondrites is key in this respect. If it turns out that main-belt comets are consistent with carbonaceous chondrites in terms of isotope composition (mostly for H, N, and O), then this will argue that carbonaceous chondrites are just the rocky counterpart of bodies much richer in water/ice than meteorites themselves. This would imply that C-type asteroids formed beyond the snowline, thus presumably in the vicinity of the giant planets. If instead the main-belt comets

Morbidelli et al.:  The Dynamical Evolution of the Asteroid Belt   505

are not related to carbonaceous chondrites, but are more similar to comets from their isotope composition (it should be noted that even though Comet Hartley 2 has a chondritic water D/H ratio, it has a nonchondritic 14N/15N ratio), then this would argue for their injection in the belt from the cometary disk and would suggest that the parent bodies of carbonaceous chondrites are not so water-rich, and therefore formed somewhat closer to the Sun than the snowline. Whatever the preferred scenario for the first depletion and excitation of the asteroid belt, it is clear that the asteroid population must have suffered in the first hundreds of millions of years as much collisional evolution as over the last 4 G.y. However, all asteroid families formed during the early times are not identifiable today because the dynamical excitation events dispersed them (and possibly depleted them) too severely. The presence of metallic asteroids not associated with a family of objects of basaltic or dunitic nature, as well as the existence of rogue basaltic asteroids such as 1459 Magnya, should therefore not come as a surprise. The only families that are preserved are those that formed after the last giant-planet-instability event and have not been made unrecognizable by subsequent collisional evolution and Yarkovsky drift; thus they are either relatively young or large. In this chapter, we have also examined several other asteroid excitation and depletion scenarios, most of which have serious difficulties in reconciling their predicted outcomes with observations. We have done this not just for historical completeness, but also to illustrate the critical constraints on putative alternative scenarios of solar system evolution. For instance, numerous studies on the possible in situ formation of extrasolar super-Earths close to their host stars assume a large pileup of drifting material of various sizes, from grains to small-mass embryos, in the inner part of the protoplanetary disks (Hansen, 2014; Chatterjee and Tan, 2014; Boley et al., 2014). By analogy, these models could be used to suggest that the outer edge of the planetesimal disk at 1 AU, required to form a small Mars, was due to the same phenomenon rather than to the Grand Tack migration of Jupiter. However, from what we reported in this chapter, we think that the asteroid belt rules out this possibility. In fact, the inward migration of small planetesimals (due to gas drag) and large embryos (due to disk tides) could explain the pileup of solid mass inside 1 AU and the mass deficit of the asteroid belt, but not the asteroids’ orbital distribution (Izidoro et al., 2015). In the absence of the Grand Tack migration of Jupiter, we showed in section 3 that the only mechanism that could give the belt an orbital structure similar to that observed is Wetherill’s model of mutual scattering of resident embryos. But if this was the case, then the mass distribution could not be concentrated within 1 AU because a massive population of embryos is required in the main-belt region. Thus, at the current state of knowledge (which may change in the future), only the Grand Tack scenario seems able to explain the required mass concentration to make a small Mars.

In summary, the asteroid belt remains the population of choice to test old, current, and future models of solar system evolution. Acknowledgments. A.M. was supported by the European Research Council (ERC) Advanced Grant ACCRETE (contract number 290568).

REFERENCES Abbas M. M. and 11 colleagues (2010) D/H ratio of Titan from observations of the Cassini/Composite Infrared Spectrometer. Astrophys. J., 708, 342–353. Agnor C. B. and Lin D. N. C. (2012) On the migration of Jupiter and Saturn: Constraints from linear models of secular resonant coupling with the terrestrial planets. Astrophys. J., 745, 143. Alexander C. M. O’D., Newsome S. D., Fogel M. L., Nittler L. R., Busemann H., and Cody G. D. (2010) Deuterium enrichments in chondritic macromolecular material — Implications for the origin and evolution of organics, water and asteroids. Geochim. Cosmochim. Acta, 74, 4417–4437. Alexander, C. M. O’D., Bowden R., Fogel M. L., Howard K. T., Herd C. D. K., and Nittler L. R. (2012) The provenances of asteroids, and their contributions to the volatile inventories of the terrestrial planets. Science, 337, 721–723. Alexander R., Pascucci I., Andrews S., Armitage P., and Cieza L. (2014) The dispersal of protoplanetary disks. In Protostars and Planets VI (H. Beuther et al., eds.), pp. 475–496. Univ. of Arizona, Tucson. Altwegg K. and 32 colleagues (2014) 67P/Churyumov-Gerasimenko, a Jupiter family comet with a high D/H ratio. Science, 347(6220), DOI: 10.1126/science.1261952. Batygin K. and Brown M. E. (2010) Early dynamical evolution of the solar system: Pinning down the initial conditions of the Nice model. Astrophys. J., 716, 1323–1331. Batygin K., Brown M. E., and Fraser W. C. (2011) Retention of a primordial cold classical Kuiper belt in an instability-driven model of solar system formation. Astrophys. J., 738, 13. Batygin K., Brown M. E., and Betts H. (2012) Instability-driven dynamical evolution model of a primordially five-planet outer solar system. Astrophys. J. Lett., 744, L3. Binzel R. P., Bus S. J., Burbine T. H., and Sunshine J. M. (1996) Spectral properties of near-Earth asteroids: Evidence for sources of ordinary chondrite meteorites. Science, 273, 946–948. Bitsch B., Morbidelli A., Lega E., and Crida A. (2014) Stellar irradiated discs and implications on migration of embedded planets. II. Accreting-discs. Astron. Astrophys., 564, AA135. Biver N., Bockelée-Morvan D., Crovisier J., Lis D. C., Moreno R., Colom P., Henry F., Herpin F., Paubert G., and Womack M. (2006) Radio wavelength molecular observations of comets C/1999 T1 (McNaught-Hartley), C/2001 A2 (LINEAR), C/2000 WM1 (LINEAR) and 153P/Ikeya-Zhang. Astron. Astrophys., 449, 1255–1270. Bockelée-Morvan D. and 21 colleagues (2012) Herschel measurements of the D/H and 16O/18O ratios in water in the Oort-cloud comet C/2009 P1 (Garradd). Astron. Astrophys., 544, LL15. Boley A. C., Morris M. A., and Ford E. B. (2014) Overcoming the meter barrier and the formation of systems with tightly packed inner planets (STIPs). Astrophys. J. Lett., 792, L27. Bottke W. F., Durda D. D., Nesvorný D., Jedicke R., Morbidelli A., Vokrouhlický D., and Levison H. (2005a) The fossilized size distribution of the main asteroid belt. Icarus, 175, 111–140. Bottke W. F., Durda D. D., Nesvorný D., Jedicke R., Morbidelli A., Vokrouhlický D., and Levison H. F. (2005b) Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion. Icarus, 179, 63–94. Bottke W. F. Jr., Vokrouhlický D., Rubincam D. P., and Nesvorný D. (2006) The Yarkovsky and YORP effects: Implications for asteroid dynamics. Annu. Rev. Earth Planet. Sci., 34, 157–191. Bottke W. F., Levison H. F., Nesvorný D., and Dones L. (2007) Can planetesimals left over from terrestrial planet formation produce the lunar late heavy bombardment? Icarus, 190, 203–223.

506   Asteroids IV Bottke W. F., Vokrouhlický D., Minton D., Nesvorný D., Morbidelli A., Brasser R., Simonson B., and Levison H. F. (2012) An Archaean heavy bombardment from a destabilized extension of the asteroid belt. Nature, 485, 78–81. Brasser R. and Morbidelli A. (2013) Oort cloud and Scattered Disc formation during a late dynamical instability in the Solar System. Icarus, 225, 40–49. Brasser R., Duncan M. J., and Levison H. F. (2007) Embedded star clusters and the formation of the Oort cloud. II. The effect of the primordial solar nebula. Icarus, 191, 413–433. Brasser R., Duncan M. J., and Levison H. F. (2008) Embedded star clusters and the formation of the Oort cloud. III. Evolution of the inner cloud during the galactic phase. Icarus, 196, 274–284. Brasser R., Morbidelli A., Gomes R., Tsiganis K., and Levison H. F. (2009) Constructing the secular architecture of the solar system II: The terrestrial planets. Astron. Astrophys., 507, 1053–1065. Brasser R., Duncan M. J., Levison H. F., Schwamb M. E., and Brown M. E. (2012) Reassessing the formation of the inner Oort cloud in an embedded star cluster. Icarus, 217, 1–19. Burbine T. H., McCoy T. J., Meibom A., Gladman B., and Keil K. (2002) Meteoritic parent bodies: Their number and identification. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 653–667. Univ. of Arizona, Tucson. Bus S. J. and Binzel R. P. (2002) Phase II of the Small Main-Belt Asteroid Spectroscopic Survey. A feature-based taxonomy. Icarus, 158, 146–177. Busemann H., Young A. F., Alexander C. M. O’D., Hoppe P., Mukhopadhyay S., and Nittler L. R. (2006) Interstellar chemistry recorded in organic matter from primitive meteorites. Science, 312, 727–730. Campins H., Hargrove K., Pinilla-Alonso N., Howell E. S., Kelley M. S., Licandro J., Mothé-Diniz T., Fernández Y., and Ziffer J. (2010) Water ice and organics on the surface of the asteroid 24 Themis. Nature, 464, 1320–1321. Carvano J. M., Hasselmann P. H., Lazzaro D., and Mothé-Diniz T. (2010) SDSS-based taxonomic classification and orbital distribution of main belt asteroids. Astron. Astrophys., 510, A43. Chambers J. E. andWetherill G. W. (1998) Making the terrestrial planets: N-body integrations of planetary embryos in three dimensions. Icarus, 136, 304–327. Chatterjee S. and Tan J. C. (2014) Inside-out planet formation. Astrophys. J., 780, 53. Cohen B. A., Swindle T. D., and Kring D. A. (2005) Geochemistry and 40Ar-39Ar geochronology of impact-melt clasts in feldspathic lunar meteorites: Implications for lunar bombardment history. Meteoritics & Planet. Sci., 40, 755. Coustenis A. and 10 colleagues (2008) Detection of C2HD and the D/H ratio on Titan. Icarus, 197, 539–548. Cresswell P. and Nelson R. P. (2008) Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc. Astron. Astrophys., 482, 677–690. Ćuk M. (2012) Chronology and sources of lunar impact bombardment. Icarus, 218, 69–79. D’Angelo G. and Marzari F. (2012) Outward migration of Jupiter and Saturn in evolved gaseous disks. Astrophys. J., 757, 50. DeMeo F. E. and Carry B. (2014) Solar system evolution from compositional mapping of the asteroid belt. Nature, 505, 629–634. DeMeo F. E., Binzel R. P., Slivan S. M., and Bus S. J. (2009) An extension of the Bus asteroid taxonomy into the near-infrared. Icarus, 202, 160–180. Dones L., Weissman P. R., Levison H. F., and Duncan M. J. (2004) Oort cloud formation and dynamics. In Comets II (M. C. Festou et al., eds.,) pp. 153–174. Univ. of Arizona, Tucson. Duprat J., Dobrica E., Engrand C., Aleon J., Marrocchi Y., Mostefaoui S., Meibom A., Leroux H., Rouzaud J. N., Gounelle M., and Robert F. (2010) Extreme deuterium excesses in ultracarbonaceous micrometeorites from central Antarctic, snow. Science, 1126, 742–745. Fassett C. I. and Minton D. A. (2013) Impact bombardment of the terrestrial planets and the early history of the solar system. Nature Geosci., 6, 520–524. Fischer R. A. and Ciesla F. J. (2014) Dynamics of the terrestrial planets from a large number of N-body simulations. Earth Planet. Sci. Lett., 392, 28–38. Fraser W. C., Brown M. E., Morbidelli A., Parker A., and Batygin K. (2014) The absolute magnitude distribution of Kuiper belt objects. Astrophys. J., 782, 100.

Gounelle M., Spurný P., and Bland P. A. (2006) The orbit and atmospheric trajectory of the Orgueil meteorite from historical records. Meteoritics & Planet. Sci., 41, 135–150. Gounelle M., Morbidelli A., Bland P. A., Spurný P., Young E. D., and Sephton M. (2008) Meteorites from the outer solar system? In The Solar System Beyond Neptune (M. A. Barucci et al., eds.), pp. 525– 541. Univ. of Arizona, Tucson. Gradie J. and Tedesco E. (1982) Compositional structure of the asteroid belt. Science, 216, 1405–1407. Haisch K. E. Jr., Lada E. A., and Lada C. J. (2001) Disk frequencies and lifetimes in young clusters. Astrophys. J. Lett., 553, L153– L156. Halliday A. N. (2013) The origins of volatiles in the terrestrial planets. Geochim. Cosmochim. Acta, 105, 146–171. Hansen B. M. S. (2009) Formation of the terrestrial planets from a narrow annulus. Astrophys. J., 703, 1131–1140. Hansen B. M. S. (2014) The circulation of dust in protoplanetary discs and the initial conditions of planet formation. Mon. Not. R. Astron. Soc., 440, 3545–3556. Hargrove K. D., Kelley M. S., Campins H., Licandro J., and Emery J. (2012) Asteroids (65) Cybele, (107) Camilla and (121) Hermione: Infrared spectral diversity among the Cybeles. Icarus, 221, 453–455. Hartogh P. and 12 colleagues (2011) Ocean-like water in the Jupiterfamily comet 103P/Hartley 2. Nature, 478, 218–220. Heppenheimer T. A. (1980) Secular resonances and the origin of eccentricities of Mars and the asteroids. Icarus, 41, 76–88. Hiroi T., Zolensky M. E., and Pieters C. M. (2001) The Tagish Lake meteorite: A possible sample from a D-type asteroid. Science, 293, 2234–2236. Hsieh H. H. and Jewitt D. (2006) A population of comets in the main asteroid belt. Science, 312, 561–563. Ip W.-H. (1987) Gravitational stirring of the asteroid belt by Jupiter zone bodies. Beitr. Geophys., 96, 44–51. Ishii H. A., Bradley J. P., Dai Z. R., Chi M., Kearsley A. T., Burchell M. J., Browning N. D., and Molster F. (2008) Comparison of Comet 81P/ Wild 2 dust with interplanetary dust from comets. Science, 319, 447. Izidoro A., Raymond S. N., Morbidelli A., and Winter D. C. (2015) Terrestrial planet formation constrained by Mars and the structure of the asteroid belt. Mon. Nat. R. Astron. Soc., in press. Jacobson S. A. and Morbidelli A. (2014) Lunar and terrestrial planet formation in the Grand Tack scenario. Philos. Trans. R. Soc. London Ser. A, 372, 174. Jacobson S. A. and Walsh K. J. (2015) The Earth and terrestrial planet formation. In The Early Earth (J. Badro and M. Walter, eds.), in press. Wiley, New York. Jacobson S. A., Morbidelli A., Raymond S. N., O’Brien D. P., Walsh K. J., and Rubie D. C. (2014) Highly siderophile elements in Earth’s mantle as a clock for the Moon-forming impact. Nature, 508, 84–87. Johnson B. C. and Melosh H. J. (2012) Impact spherules as a record of an ancient heavy bombardment of Earth. Nature, 485, 75–77. Kenyon S. J. and Hartmann L. (1995) Pre-main-sequence evolution in the Taurus-Auriga molecular cloud. Astrophys. J. Suppl., 101, 11. Kley W. and Nelson R. P. (2012) Planet-disk interaction and orbital evolution. Annu. Rev. Astron. Astrophys., 50, 211–249. Krasinsky G. A., Pitjeva E. V., Vasilyev M. V., and Yagudina E. I. (2002) Hidden mass in the asteroid belt. Icarus, 158, 98–105. Kuchynka P. and Folkner W. M. (2013) A new approach to determining asteroid masses from planetary range measurements. Icarus, 222, 243–253. Küppers M., and 12 colleagues (2014) Localized sources of water vapour on the dwarf planet (1) Ceres. Nature, 505, 525–527. Lecar M. and Franklin F. (1997) The solar nebula, secular resonances, gas drag, and the asteroid belt. Icarus, 129, 134–146. Lemaitre A. and Dubru P. (1991) Secular resonances in the primitive solar nebula. Cel. Mech. Dyn. Astron., 52, 57–78. Levison H. F., Morbidelli A., Van Laerhoven C., Gomes R., and Tsiganis K. (2008) Origin of the structure of the Kuiper belt during a dynamical instability in the orbits of Uranus and Neptune. Icarus, 196, 258–273. Levison H. F., Bottke W. F., Gounelle M., Morbidelli A., Nesvorný D., and Tsiganis K. (2009) Contamination of the asteroid belt by primordial trans-neptunian objects. Nature, 460, 364–366. Levison H. F., Morbidelli A., Tsiganis K., Nesvorný D., and Gomes R. (2011) Late orbital instabilities in the outer planets induced by inter‑ action with a self-gravitating planetesimal disk. Astron. J., 142, 152. Licandro J., Campins H., Kelley M., Hargrove K., Pinilla-Alonso N., Cruikshank D., Rivkin A. S., and Emery J. (2011) (65) Cybele:

Morbidelli et al.:  The Dynamical Evolution of the Asteroid Belt   507 Detection of small silicate grains, water-ice, and organics. Astron. Astrophys., 525, A34. Marchi S. and 10 colleagues (2013) High-velocity collisions from the lunar cataclysm recorded in asteroidal meteorites. Nature Geosci., 6, 303–307. Marty B. (2012) The origins and concentrations of water, carbon, nitrogen and noble gases on Earth. Earth Planet. Sci. Lett., 313, 56–66. Masset F. and Snellgrove M. (2001) Reversing type II migration: Resonance trapping of a lighter giant protoplanet. Mon. Not. R. Astron. Soc., 320, L55–L59. Meech K. J. and 196 colleagues (2011) EPOXI: Comet 103P/Hartley 2 observations from a worldwide campaign. Astrophys. J. Lett., 734, L1. Minton D. A. and Malhotra R. (2009) A record of planet migration in the main asteroid belt. Nature, 457, 1109–1111. Minton D. A. and Malhotra R. (2010) Dynamical erosion of the asteroid belt and implications for large impacts in the inner solar system. Icarus, 207, 744–757. Minton D. A. and Malhotra R. (2011) Secular resonance sweeping of the main asteroid belt during planet migration. Astrophys. J., 732, 53. Morbidelli A. and Crida A. (2007) The dynamics of Jupiter and Saturn in the gaseous protoplanetary disk. Icarus, 191, 158–171. Morbidelli A., Tsiganis K., Crida A., Levison H. F., and Gomes R. (2007) Dynamics of the giant planets of the solar system in the gaseous protoplanetary disk and their relationship to the current orbital architecture. Astron. J., 134, 1790–1798. Morbidelli A., Bottke W. F., Nesvorný D., and Levison H. F. (2009) Asteroids were born big. Icarus, 204, 558–573. Morbidelli A., Brasser R., Gomes R., Levison H. F., and Tsiganis K. (2010) Evidence from the asteroid belt for a violent past evolution of Jupiter’s orbit. Astron. J., 140, 1391–1401. Morbidelli A., Marchi S., Bottke W. F., and Kring D. A. (2012) A sawtooth-like timeline for the first billion years of lunar bombardment. Earth Planet. Sci. Lett., 355, 144–151. Mothé-Diniz T., Carvano J. M. á., and Lazzaro D. (2003) Distribution of taxonomic classes in the main belt of asteroids. Icarus, 162, 10–21. Mouillet D., Larwood J. D., Papaloizou J. C. B., and Lagrange A. M. (1997) A planet on an inclined orbit as an explanation of the warp in the Beta Pictoris disc. Mon. Not. R. Astron. Soc., 292, 896. Nagasawa M., Tanaka H., and Ida S. (2000) Orbital evolution of asteroids during depletion of the solar nebula. Astron. J., 119, 1480–1497. Nagasawa M., Ida S., and Tanaka H. (2001) Origin of high orbital eccentricity and inclination of asteroids. Earth Planets Space, 53, 1085–1091. Nagasawa M., Ida S., and Tanaka H. (2002) Excitation of orbital inclinations of asteroids during depletion of a protoplanetary disk: Dependence on the disk configuration. Icarus, 159, 322–327. Nakamura T. and 11 colleagues (2008) Chondrule-like objects in shortperiod Comet 81P/Wild 2. Science, 321, 1664. Nesvorný D. (2011) Young solar system’s fifth giant planet? Astrophys. J. Lett., 742, L22. Nesvorný D. and Morbidelli A. (2012) Statistical study of the early solar system’s instability with four, five, and six giant planets. Astron. J., 144, 117. Nesvorný D., Vokrouhlický D., and Morbidelli A. (2007) Capture of irregular satellites during planetary encounters. Astron. J., 133, 1962–1976. Nesvorný D., Jenniskens P., Levison H. F., Bottke W. F., Vokrouhlický D., and Gounelle M. (2010) Cometary origin of the zodiacal cloud and carbonaceous micrometeorites. Implications for hot debris disks. Astrophys. J., 713, 816–836. Nesvorný D., Vokrouhlický D., and Morbidelli A. (2013) Capture of Trojans by jumping Jupiter. Astrophys. J., 768, 45. Nesvorný D., Vokrouhlický D., and Deienno R. (2014) Capture of irregular satellites at Jupiter. Astrophys. J., 784, 22. Niemann H. B., Atreya S. K., Demick J. E., Gautier D., Haberman J. A., Harpold D. N., Kasprzak W. T., Lunine J. I., Owen T. C., and Raulin F. (2010) Composition of Titan’s lower atmosphere and simple surface volatiles as measured by the Cassini-Huygens probe gas chromatograph mass spectrometer experiment. J. Geophys. Res.– Planets, 115, E1(2006). Nixon C. A. and 12 colleagues (2012) Isotopic ratios in titan’s methane: Measurements and modeling. Astrophys. J., 749, 159. Norman M. D. and Nemchin A. A. (2014) A 4.2 billion year old impact basin on the Moon: U-Pb dating of zirconolite and apatite in lunar melt rock 67955. Earth Planet. Sci. Lett., 388, 398–398.

O’Brien D. P., Morbidelli A., and Levison H. F. (2006) Terrestrial planet formation with strong dynamical friction. Icarus, 184, 39–58. O’Brien D. P., Morbidelli A., and Bottke W. F. (2007) The primordial excitation and clearing of the asteroid belt — Revisited. Icarus, 191, 434–452. Parker A. H., Kavelaars J. J., Petit J.-M., Jones L., Gladman B., and Parker J. (2011) Characterization of seven ultra-wide trans-neptunian binaries. Astrophys. J., 743, 1. Petit J., Morbidelli A., and Valsecchi G. B. (1999) Large scattered planetesimals and the excitation of the small body belts. Icarus, 141, 367–387. Petit J., Morbidelli A., and Chambers J. (2001) The primordial excitation and clearing of the asteroid belt. Icarus, 153, 338–347. Petit J., Chambers J., Franklin F., and Nagasawa M. (2002) Primordial excitation and depletion of the main belt. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 711–738. Univ. of Arizona, Tucson. Petit J.-M. and 16 colleagues (2011) The Canada-France Ecliptic Plane Survey — Full data release: The orbital structure of the Kuiper belt. Astron. J., 142, 131. Pierens A. and Nelson R. P. (2008) Constraints on resonant-trapping for two planets embedded in a protoplanetary disc. Astron. Astrophys., 482, 333–340. Pierens A. and Raymond S. N. (2011) Two phase, inward-then-outward migration of Jupiter and Saturn in the gaseous solar nebula. Astron. Astrophys., 533, A131. Rivkin A. S. and Emery J. P. (2010) Detection of ice and organics on an asteroidal surface. Nature, 464, 1322–1323. Robuchon G., Nimmo F., Roberts J., and Kirchoff M. (2011) Impact basin relaxation at Iapetus. Icarus, 214, 82–90. Rousselot P. and 11 colleagues (2014) Toward a unique nitrogen isotopic ratio in cometary ices. Astrophys. J. Lett., 780, L17. Simonson B. M. and Glass B. B. (2004) Spherule layers — records of Ancient Impacts. Annu. Rev. Earth Planet. Sci., 32, 329–361. Somenzi L., Fienga A., Laskar J., and Kuchynka P. (2010) Determination of asteroid masses from their close encounters with Mars. Planet. Space Sci., 58, 858–863. Strom S. E., Edwards S., and Skrutskie M. F. (1993) Evolutionary time scales for circumstellar disks associated with intermediate- and solartype stars. In Protostars and Planets III (E. H. Levy and J. I. Lunine, eds.), pp. 837–866. Univ. of Arizona, Tucson. Tholen D. J. (1984) Asteroid taxonomy from cluster analysis of photometry. Ph.D. thesis, Univ. of Arizona, Tucson. Thommes E. W., Duncan M. J., and Levison H. F. (1999) The formation of Uranus and Neptune in the Jupiter-Saturn region of the solar system. Nature, 402, 635–638. Tsiganis K., Gomes R., Morbidelli A., and Levison H. F. (2005) Origin of the orbital architecture of the giant planets of the solar system. Nature, 435, 459–461. Villeneuve J., Chaussidon M., and Libourel G. (2009) Homogeneous distribution of 26Al in the solar system from the Mg isotopic composition of chondrules. Science, 325, 985. Waite J. H. Jr. and 15 colleagues (2009) Liquid water on Enceladus from observations of ammonia and 40Ar in the plume. Nature, 460, 487–490. Walsh K. J., Morbidelli A., Raymond S. N., O’Brien D. P., and Mandell A. M. (2011) A low mass for Mars from Jupiter’s early gas-driven migration. Nature, 475, 206–209. Ward W. R. (1981) Solar nebula dispersal and the stability of the planetary system. I — Scanning secular resonance theory. Icarus, 47, 234–264. Ward W. R., Colombo G., and Franklin F. A. (1976) Secular resonance, solar spin down, and the orbit of Mercury. Icarus, 28, 441–452. Weidenschilling S. J. (1977) The distribution of mass in the planetary system and solar nebula. Astrophys. Space Sci., 51, 153–158. Wetherill G. W. (1992) An alternative model for the formation of the asteroids. Icarus, 100, 307–325. Yang L., Ciesla F. J., and Alexander C. M. O’D. (2013) The D/H ratio of water in the solar nebula during its formation and evolution. Icarus, 226, 256–267. Zolensky M. E. and 74 colleagues (2006) Mineralogy and petrology of Comet 81P/Wild 2 nucleus samples. Science, 314, 1735. Zolensky M. and 30 colleagues (2008) Comparing Wild 2 particles to chondrites and IDPs. Meteoritics & Planet. Sci., 43, 261–272. Zuckerman B., Forveille T., and Kastner J. H. (1995) Inhibition of giantplanet formation by rapid gas depletion around young stars. Nature, 373, 494–496.

Vokrouhlický D., Bottke W. F., Chesley S. R., Scheeres D. J., and Statler T. S. (2015) The Yarkovsky and YORP effects. In Asteroids IV (P. Michel et al., eds.), pp. 509–531. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch027.

The Yarkovsky and YORP Effects David Vokrouhlický Charles University, Prague

William F. Bottke

Southwest Research Institute

Steven R. Chesley

Jet Propulsion Laboratory/California Institute of Technology

Daniel J. Scheeres University of Colorado

Thomas S. Statler

Ohio University and University of Maryland

The Yarkovsky effect describes a small but significant force that affects the orbital motion of meteoroids and asteroids smaller than 30-40 km in diameter. It is caused by sunlight; when these bodies heat up in the Sun, they eventually reradiate the energy away in the thermal waveband, which in turn creates a tiny thrust. This recoil acceleration is much weaker than solar and planetary gravitational forces, but it can produce measurable orbital changes over decades and substantial orbital effects over millions to billions of years. The same physical phenomenon also creates a thermal torque that, complemented by a torque produced by scattered sunlight, can modify the rotation rates and obliquities of small bodies as well. This rotational variant has been coined the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect. During the past decade or so, the Yarkovsky and YORP effects have been used to explore and potentially resolve a number of unsolved mysteries in planetary science dealing with small bodies. Here we review the main results to date, and preview the goals for future work.

1. INTRODUCTION Interesting problems in science usually have a long and complex history. It is rare, though, that they have a prehistory or perhaps even mythology. Yet, until recently this was the case for the Yarkovsky effect. Ivan O. Yarkovsky, a Russian civil engineer born in a family of Polish descent, noted in a privately published pamphlet (Yarkovsky, 1901; Beekman, 2006) that heating a prograde-rotating planet should produce a transverse acceleration in its motion and thus help to counterbalance the assumed drag from the then-popular ether hypothesis. While this context of Yarkovsky’s work was mistaken and he was only roughly able to estimate the magnitude of the effect, he succeeded in planting the seed of an idea that a century later blossomed into a full-fledged theory of how the orbits of small objects revolving about the Sun are modified by the absorption and reemission of solar energy. It is mainly Ernst J. Öpik who is to be credited for keeping Yarkovsky’s work alive and introducing it to western literature, long after the original pamphlet had been lost

(Öpik, 1951). Curiously, at about the same time, similar ideas also started to appear in Russian regular scientific literature through the works of Vladimir V. Radzievskii and his collaborators (Radzievskii, 1952). While Radzievskii was also the first to consider the effects of systematic photon thrust on a body’s rotation, his concept was based on a variable albedo coefficient across the surface (Radzievskii, 1954). However, there is no strong evidence of large enough albedo variations over surfaces of asteroids or meteoroids. Stephen J. Paddack and John O’Keefe pushed the idea forward by realizing that irregular shape, and thermal radiation rather than just reflected sunlight, will more efficiently change the meteoroid’s spin rate. Thence, the Yarkovsky-O’KeefeRadzievskii-Paddack (YORP) effect was born as an alter ego of the Yarkovsky effect little more than half a century after Yarkovsky’s work (see Paddack (1969), Paddack and Rhee (1975), and Rubincam (2000) for a summation of the history and coining of the terminology). Radzievskii’s school also briefly touched upon a concept of a radiation-induced acceleration of synchronous planetary satellites (Vinogradova

509

510   Asteroids IV and Radzievskii, 1965), an idea that reappeared much later in a slightly different form as a binary YORP (BYORP) effect (Ćuk and Burns, 2005). The three decades from the 1950s to the 1970s resulted in today’s understanding of Yarkovsky and YORP effects. The works that led to a major resurgence in these studies, however, occurred in the second half of the 1990s through the work of David P. Rubincam and Paolo Farinella. Interestingly, both were studying thermal perturbations of artificial satellite motion. With that expertise, they realized a direct link between the orbital effects acting on the artificial satellites such as the Laser Geodynamics Satellites (LAGEOS) and the orbital effects on small meteoroids (e.g., Afonso et al., 1995; Rubincam, 1995, 1998; Farinella et al., 1998). From there, a momentum was gained and a wealth of new results appeared, with applications extending to dynamics of small asteroids and their populations (e.g., Bottke et al., 2002a, 2006). Studies of the Yarkovsky effect were soon followed by those of the YORP effect (Rubincam, 2000). Today, both effects belong to a core culture in planetary sciences, as well as beyond (e.g., http://www.youtube. com/ watch?v=kzlgxqXtxYs), and have become an important part of the agenda of space missions (e.g., Lauretta et al., 2015). Especially after the spectacular discovery of the “once lost” Yarkovsky pamphlet in Russian archives by Dutch amateur astronomer George Beekman (see Beekman, 2006), it seems timely to review the current knowledge of the Yarkovsky and YORP effects. This effort could start with a translation, and perhaps a commented edition, of the Yarkovsky work (presently available in its original form as an Appendix to Miroslav Brož’s thesis, http://sirrah. troja.mff.cuni.cz/˜mira/ mp/phdth). We look forward to future historians editing the more than a century long story of the Yarkovsky and YORP effects, with all the known and possibly hidden roots, into a consolidated picture. Leaving historical issues to their own time, we now turn to current scientific issues related to the Yarkovsky and YORP effects. There are several good technical reviews already existing in the literature (e.g., Bottke et al., 2002a, 2006). While not always possible, we try to avoid discussing the same topics as presented in these previous texts. For instance, we do not review the elementary concepts of the Yarkovsky and YORP effects, assuming the reader is familiar with them. Rather, we try to focus on new results and ideas that emerged during the past decade and that will lead to research efforts in the next several years. 2. THEORY OF THE YARKOVSKY AND YORP EFFECTS We start with the simplest analytical models of the Yarkovsky and YORP effects (section 2.1). This is because they provide useful insights, such as scalings with several key parameters, and their results are correct to leading order. They also allow us to understand why modeling of the YORP effect is inevitably more complicated than modeling of the Yarkovsky effect. And yet, the quality of the Yarkovsky

and YORP effects detections, as well as other applications, have reached a level that requires more accurate models to be used. The first steps toward these new models have been taken recently and these are briefly reviewed in section 2.2. 2.1. Classical Models 2.1.1. The Yarkovsky effect. Absorbed and directly re‑ flected sunlight does not tend to produce long-term dynamical effects as far as orbital motion is concerned (e.g., Vokrouhlický and Milani, 2000; Žižka and Vokrouhlický, 2011). The Yarkovsky effect thus fundamentally depends on emitted thermal radiation and requires a body to have a nonzero thermal inertia. Any meaningful evaluation of the Yarkovsky effect, therefore, requires a thermophysical model of that body. Fortunately, an evaluation of the Yarkovsky effect imposes a minimum of requirements on the shape of the body; even a simple spherical model provides us with a fair approximation of how the body will orbitally evolve. While the Yarkovsky effect results in variations to all the orbital elements, what is distinct from most other perturbations is the secular effect in the semimajor axis a, and therefore we only discuss this contribution. Assuming (1) a linearization of the surface boundary condition, (2) a rotation about a spin axis fixed in the inertial space (at least on a timescale comparable with the revolution about the Sun), and (3) a circular orbit about the Sun, one easily finds that the total, orbit-averaged change in a is composed of two contributions (e.g., Rubincam, 1995, 1998; Farinella et al., 1998; Vokrouhlický, 1998a, 1999), the diurnal effect



8 aF  da  W ( R w , Θw ) cos g =  dt diurnal 9 n

(1)

and the seasonal effect



4 aF  da  W ( R n , Θ n ) sin 2 g =   dt seasonal 9 n



(2)

Here, F = pR2F/(mc), where R is the radius of the body, F the solar radiation flux at the orbital distance a from the Sun, m the mass of the body, c the light velocity, n the orbital mean motion, and a = 1-A, with A denoting the Bond albedo (e.g., Vokrouhlický and Bottke, 2001). The F factor is characteristic to any physical effect related to sunlight absorbed or scattered by the surface of the body. Since m ∝ R3, one obtains a typical scaling F ∝ 1/R. More importantly, the diurnal and seasonal components of the Yarkovsky effect have a different dependence on the spin axis obliquity g: (1) the diurnal part is ∝ cos g, and consequently can make a positive or negative change in the semimajor axis, being maximum at 0° and 180° obliquity values; and (2) the seasonal part is ∝ sin2  g, and consequently always results in a decrease in semimajor axis, being

Vokrouhlický et al.:  The Yarkovsky and YORP Effects   511

maximum at 90° obliquity. Their magnitude is proportional to the function



W (R n , Θn ) = -

k1 ( R n )Θ n

1 + 2k 2 ( R n )Θ n + k 3 ( R n )Θ 2n

(3)

determined by the thermal parameters of the body and a frequency n. The latter is equal either to the rotation frequency w for the diurnal component, or the orbital mean motion n for the seasonal component. The thermal parameters required by the model are (1) the surface thermal conductivity K, (2) the surface heat capacity C, and (3) the surface density r. These parameters, together with the frequency n, do not appear in equation (3) individually. Rather, in the process of solving the heat diffusion problem and determination of the orbital perturbations, they combine in two relevant parameters. First, they provide a scale length ln = K (ρCν), which indicates a characteristic penetration depth of temperature changes assuming the surface irradiation is periodic with the frequency n. The nondimensional radius of the body Rn in equation  (3) is defined by Rn = R/ln. Second, the surface thermal inertia G = K ρC enters the nondimensional thermal parameter Θn in equation (3) using a definition Θn = G ν/ 3 ), with e the thermal emissivity of the surface, s the (esT« Stefan-Boltzmann constant, and T« the subsolar temperature 4  = aF). When the characteristic size R of the body (esT« is much larger than ℓn (a large-body limit), a situation met in the typical applications so far, the three k coefficients in equation (3) are simply equal to 12 [Rubincam (1995); see Vokrouhlický (1998a) for their behavior for an arbitrary value of Rn]. Hence, for large bodies the W factors do not depend on the size R and read W ≃ W(Θn)  = – 0.5  Θn / (1  + Θn  + 0.5  Θn2). Consequently, the Yarkovsky effect is maximum when Θn  ≃ 1; for small or large values of Θn the effect vanishes. In this case, the semimajor axis secular change da/dt due to the Yarkovsky effect scales as ∝ 1/R with the characteristic radius R. For small asteroids, either in near-Earth space or in the main belt, Θw is typically on the order of unity (see also the chapter by Delbò et al. in this volume), while Θn is much smaller, which implies that the diurnal Yarkovsky component usually dominates the seasonal component. A handful of models were subsequently developed to probe the role of each of the simplifying assumptions mentioned above using analytical, semianalytical, or fully numerical methods. These include (1) an inhomogeneity of the thermal parameters (e.g., Vokrouhlický and Brož, 1999), (2) a coupling of the diurnal and seasonal components of the Yarkovsky effect (e.g., Vokrouhlický, 1999; Sekiya and Shimoda, 2013, 2014), (3) effects of a nonspherical shape for simple (e.g., Vokrouhlický, 1998b) or general geometries (including nonconvex shapes and the role of small-scale surface features; section 2.2), (4) a nonlinearity of the surface boundary condition of the thermal model (e.g., Sekiya and Shimoda, 2013, 2014), (5) the role of very high orbital eccentricity (e.g., Spitale and Greenberg, 2001, 2002; Sekiya

and Shimoda, 2014); (6) a nonprincipal-axis rotation state (e.g., Vokrouhlický et al., 2005a), or (7) the Yarkovsky effect for binary asteroids (e.g., Vokrouhlický et al., 2005b). Each of them was found to modify results from the zero approximation model by as much as several tens of percent without modifying the fundamental dependence of the Yarkovsky effect on obliquity, size, or thermal parameters [except perhaps for the special case of very high eccentricity orbits, where the sign of the Yarkovsky effect may be changed (see Spitale and Greenberg, 2001)]. 2.1.2. The YORP effect. The YORP effect, the rotational counterpart of the Yarkovsky effect, broadly denotes the torque arising from interaction with the impinging solar radiation. As in the orbital effect, the absorbed sunlight does not result in secular effects (e.g. Breiter et al., 2007; Nesvorný and Vokrouhlický, 2008b; Rubincam and Paddack, 2010). Both directly scattered sunlight in the optical band and the recoil due to thermally reprocessed radiation, however, produce dynamical effects that accumulate over long timescales. In principle, one would need to treat the two components of the YORP effect independently, since the bidirectional characteristics of the scattered and thermally emitted radiation are not the same and would produce different torques. Additionally, the thermal component has a time lag due to the finite value of the surface thermal inertia and its bidirectional function should formally depend on the time history of the particular surface element. While these issues are at the forefront of current research (section 2.2), we start with a zero-order approximation initially introduced by Rubincam (2000): (1) the surface thermal inertia is neglected, such that thermal radiation is reemitted with no time lag; and (2)  the reflected and thermally radiated components are simply assumed to be Lambertian (isotropic). This approximation avoids precise thermal modeling and the results are relatively insensitive to the body’s surface albedo value. At face value, this looks simple, but layers of complexity unfold with the geometrical description of the surface. This is because the YORP effect vanishes for simple shape models [such as ellipsoids of rotation (Breiter et al., 2007)] and stems from the irregular shape of the body (see Paddack, 1969). Obviously, its quantitative description involves a near infinity of degrees of freedom if middle- to small-scale irregularities are included. This may actually be the case for real asteroids because these irregularities may present a large collective cross-section and thus could dominate the overall strength of the YORP effect. This is now recognized as a major obstacle to our ability to model the YORP effect (section 2.2). The importance of fine details of geometry, somewhat unnoticed earlier, were unraveled by the first analytical and semianalytical models of the YORP effect. There were two approaches developed in parallel. Scheeres (2007) and Scheeres and Mirrahimi (2008) used the polyhedral shape description as a starting point for their study, while Nesvorný and Vokrouhlický (2007, 2008a) and Breiter and Michałska (2008) used shape modeling described by a series expansion in spherical harmonics. To keep things simple,

512   Asteroids IV these initial models assumed principal axis rotation and disregarded mutual shadowing of the surface facets. Both models predicted, after averaging the results over the rotation and revolution cycles, a long-term change of the rotational rate w and obliquity g (the precession rate effect is usually much smaller than the corresponding gravitational effect due to the Sun), which could be expressed as

and



dw L = dt C

∑A P

dg L = dt Cw

n 2n

( cos g )

∑B P

1 n 2n

n ≥1

(4)

n ≥1

( cos g )

(5)

Here, L = 2 FR3/(3c) with C being the moment of inertia corresponding to the rotation axis (shortest axis of the inertia tensor), P2n(cos  g) are the Legendre polynomials of even 1 (cos  g) are the corresponding associated degrees, and P2n Legendre functions. The particular characteristics of the even-degree Legendre polynomials and Legendre functions on the order of 1 in equations (4) and (5) under prograde to retrograde reflection g ↔ p-g indicate the behavior of dw/dt and dg/dt: (1) the rotation-rate change is symmetric, while (2) the obliquity change is antisymmetric under this transformation. Earlier numerical studies (e.g., Rubincam, 2000; Vokrouhlický and Čapek, 2002; Čapek and Vokrouhlický, 2004) had suggested that the net effect of YORP on rotation-rate often vanishes near g ~ 55° and g ~ 125°. This feature was finally understood using equation (4) because these obliquity values correspond to the roots of the second-degree Legendre polynomial. The previous works that numerically treated smoothed surfaces thus mostly described situations when the first term in the series played a dominant role. When the effects of the surface finite thermal inertia are heuristically added to these models, one finds that only the coefficients Bn change (e.g., Nesvorný and Vokrouhlický, 2007, 2008a; Breiter and Michałska, 2008). This confirms an earlier numerical evidence of Čapek and Vokrouhlický (2004). Since C ∝ R5, equations (4) and (5) imply that both rotation rate and obliquity effects scale with the characteristic radius as ∝ 1/R2. This is an important difference with respect to the “more shallow” size dependence of the Yarkovsky effect, and it implies that YORP’s ability to change the rotation state increases very rapidly moving to smaller objects. Additionally, we understand well that for very small bodies the Yarkovsky effect becomes eventually nil. When the characteristic radius R becomes comparable to the penetration depth lw of the diurnal thermal wave the efficient heat conduction across the volume of the body makes temperature differences on the surface very small. However, Breiter et al. (2010a) suggested that in the same limit the YORP strength becomes ∝ 1/R, still increasing for small objects. Additionally, their result was only concerned with the thermal component of the YORP effect, while the part

related to the direct sunlight scattering in optical waveband continues to scale with ∝ 1/R2. Thus, the fate of the rotation of small meteoroids is still unknown at present. The principal difference in complexity of the YORP effect results in equations (4) and (5), as compared to simple estimates in equations (1) and (2) for the Yarkovsky effect, is their infinite series nature. The nondimensional coefficients An and Bn in equations (4) and (5) are determined by the shape of the body, either analytically or semianalytically (e.g., Nesvorný and Vokrouhlický, 2007, 2008a; Scheeres and Mirrahimi, 2008; Breiter and Michałska, 2008; Kaasalainen and Nortunen, 2013). Interestingly, analytical methods help us to understand the torque component that changes the spin rate and the components that change the axis orientation couple, at leading order, to different attributes of the surface. The spin torque couples to chirality — the difference between eastward and westward facing slopes — while the other components couple merely to asphericity. Mathematically, this concerns the symmetric and antisymmetric terms in the Fourier expansion of the topography. If mutual shadowing of the surface facets is to be taken into account, one may use the semianalytic approach mentioned by Breiter et al. (2011) (see also Scheeres and Mirrahimi, 2008). Depending on details of the shape, the series in equations (4) and (5) may either converge quickly, with the first few terms dominating the overall behavior, or may slowly converge, with high-degree terms continuing to contribute (e.g., Nesvorný and Vokrouhlický, 2007, 2008a; Kaasalainen and Nortunen, 2013). While this behavior had been noticed in analytical model‑ ing, a detailed numerical study of YORP sensitivity on astronomically motivated, small-scale surface features such as craters and/or boulders was performed by Statler (2009). This also allowed Statler to suggest a new direction to YORP studies. He noted that the sensitivity of YORP on such small-scale features may affect its variability on short enough timescales to significantly modify the long-term evolution of the rotation rate, with the evolution changing from a smooth flow toward asymptotic state to a random walk (section 2.2). The quadrupole (2n = 2), being the highest multipole participating in the series expansion in equations (4) and (5), is related to the assumption of coincidence between the reference frame origin and the geometric center of the body (i.e., its center of mass for homogeneous density distribution). If instead the rotation axis is displaced from this point, additional terms in the series become activated and the coefficients (An;Bn) become modified, and thus the predicted YORP torque will change (e.g., Nesvorný and Vokrouhlický, 2007, 2008a). This theoretical possibility has found an interesting geophysics interpretation for (25143) Itokawa’s anomalously small YORP value by Scheeres and Gaskell (2008) [see section 3.2, Breiter et al. (2009), and eventually Lowry et al. (2014)]. 2.2. Frontiers in Modeling Efforts 2.2.1. Resolved and unresolved surface irregularities. While the models discussed above suffice to describe broad-

Vokrouhlický et al.:  The Yarkovsky and YORP Effects   513

scale features of the Yarkovsky and YORP effects, there are important aspects that are intrinsically nonlinear. Current models need to explicitly treat these nonlinearities in order to capture the physical essence of radiation recoil mechanisms and to provide precise predictions. Here we discuss some recent efforts along these lines. The simplest of such nonlinear effects is shadowing of some parts of the surface by other parts, which can occur on surfaces that are not convex. By blocking the Sun, shadowing lowers the incident flux, and increases the temperature contrast, compared to the clear-horizon case. Computationally, shadowing requires testing whether the sunward-pointing ray from each surface element intersects another surface element (e.g., Vokrouhlický and Čapek, 2002). This “who blocks whom” problem is of O (N2) complexity (where N is the number of surface elements); but there are strategies for storing an initial O (N2) calculation so that all subsequent calculations are only O (N) (e.g., Statler, 2009). Closely related to shadowing are the processes of selfheating (e.g., Rozitis and Green, 2013); these can be split conceptually into self-illumination, in which a surface element absorbs reflected solar flux from other parts of the surface, and self-irradiation, where it absorbs reradiated thermal infrared. Self-heating has the tendency to reduce the temperature contrast, by illuminating regions in shadow. Computing these effects requires prescriptions for the angular distribution of reflected and reradiated power from an arbitrary surface element, as well as the solution to the “who sees whom” problem — similar to the “who blocks whom” problem from shadowing. But since energy is traded between pairs of surface elements, self-heating, unlike shadowing, is unavoidably O (N2) if full accuracy is required. As mentioned in section 2.1, a periodic driving at a frequency n introduces a length scale, the thermal skin depth ln. Asteroid surfaces are driven quasiperiodically, with the fundamental modes at the diurnal and seasonal frequencies. For typical materials, ln is on the order of meters for the seasonal cycle and millimeters to centimeters for the diurnal cycle. If the surface’s radius of curvature s satisfies the condition s ? ln, one can consider surface elements to be independent (facilitating parallelization) and solve the heat conduction problem as a function of the depth only. The radiated flux then depends on the material parameters only through the thermal inertia G. Most models that treat conduction explicitly do so in such one-dimensional approximation. Standard finite-difference methods are typically used to find a solution over a rotation or around a full orbit; but numerical convergence can be slow [although acceleration schemes were also considered (Breiter et al., 2010b)]. Whether the condition s ? ln is truly satisfied depends on the scale on which topography is resolved. A surface boulder can give an object a locally small radius of curvature and three-dimensional effects may become important. Full threedimensional conduction is computationally expensive (e.g., Golubov et al., 2014; Ševeček et al., 2015), but the potential consequences are significant. In this case, a general finiteelement method is used to solve the heat diffusion problem.

Surface roughness concerns the effects of unresolved texture on reflection, absorption, and reradiation. Parametric models for a rough-surface reflectance are well developed [e.g., see Hapke (1993), and references therein; and see Breiter and Vokrouhlický (2011) for an application to the YORP effect], although the functional forms and parameter values are matters of current research. Models for the thermal emission are at present purely numerical. In the most complete implementation (Rozitis and Green, 2012, 2013), a high-resolution model of a crater field is embedded inside a coarse-resolution model of a full object. The primary effects of roughness in this model are to enhance the directionality (“beaming”) of the radiated intensity (relative to Lambertian emission), and to direct the radiated momentum slightly away from the surface normal, toward the Sun. Roughness models for emission and for reflection are not automatically mutually consistent, and the emission models employ the one-dimensional approximation for heat conduction despite the likelihood that s may not be much larger than lw at the roughness scale. Finally, nonlinear dynamical coupling affects both spin evolution and the orbital drift modulated by the spin state. Yarkovsky evolution models have generally incorporated heuristic prescriptions based on the YORP cycle (e.g., Rubincam, 2000; Vokrouhlický and Čapek, 2002), with possibly important effects of spin-induced material motion or reshaping included only in rudimentary ways. These processes may be modeled with particle-based discrete-element numerical codes (e.g., Richardson et al., 2005; Schwartz et al., 2012) and seminumerical granular dynamics in predefined potential fields (e.g., Scheeres, 2015). Simulated rubble piles artificially fed with angular momentum are seen to reshape and shed mass (e.g., Walsh et al., 2008; Scheeres, 2015). Linking a particle code with a thermophysical YORP model would then allow the coupled spin and shape evolution to be followed self-consistently. Statler (2009) argued that topographic sensitivity would make rubble piles, or any objects with loose regolith, susceptible to possibly large changes in torque triggered by small, centrifugally driven changes in shape. Repeated interruptions of the YORP cycle might then render the overall spin evolution stochastic and significantly extend the timescale of the YORP cycles (self-limitation property of YORP). Cotto-Figueroa et al. (2015) have tested this prediction by simulating self-consistently the coupled spin and shape evolution (toggling between configurations in a limit cycle), and stagnating behaviors that result in YORP self-limitation. Bottke et al. (2015) implemented a heuristic form of such stochastic YORP in a Yarkovsky drift model to find an agreement with the structure of the Eulalia asteroid family. Accurate Yarkovsky measurements allow constraining mass and bulk density (section 4.1), but rely on precise models, with an important component due to the surface features discussed above. Rozitis and Green (2012) show that surface roughness can increase the Yarkovsky force by tens of percent, owing mainly to the beaming. Including the seasonal effect caused by the deeper-penetrating thermal wave can

514   Asteroids IV have a comparable influence. Self-heating, in contrast, has a minimal influence on Yarkovsky forces (e.g., Rozitis and Green, 2013). On the other hand, the same works indicate that the YORP effect is in general dampened by beaming because it equalizes torques on opposite sides of the body. Golubov and Krugly (2012) highlight another small-scale aspect of the YORP effect: an asymmetric heat conduction across surface features for which s < lw. A rock conducts heat from its sunlit east side to its shadowed west side in the morning, and from its west side back to its east side in the afternoon. Owing to nighttime cooling, the morning temperature gradient is steeper, and hence more heat is conducted to, and radiated from, the west side, resulting in an eastward recoil. Clearly, if the collective cross section of such surface features is large, details of conduction across them may have significant consequences. Ideally, the situation calls for a complete three-dimensional heat transfer model (e.g., Golubov et al., 2014; Ševeček et al., 2015). Importantly, these studies indicate an overall tendency for YORP to spin objects up. However, a better understanding of small-scale surface effects is essential to understand YORP’s long-term dynamics. 2.2.2. Time domain issues (tumbling). A particular prob‑ lem in the modeling of the thermal effects occurs for tumbling bodies. This is because solving the heat diffusion in the body also involves the time domain. While the spatial dimensions are naturally bound, the time coordinate in general is not. However, both analytical and numerical methods involve finite time domains: The analytical approaches use a development in the Fourier series, while the effective numerical methods use iterations that require one to identify configurations at some moments in time. For bodies rotating about the principal axis of the inertia tensor, thus having a fixed direction in the inertial space, it is usually easy to modify the rotation period within its uncertainty limits such that it represents an integer fraction of the orbital period. The orbital period is then the fundamental time interval for the solution. This picture becomes more complicated for tumbling objects whose rotation is not characterized by a single time period. Rather, it is fully described with two periods, the proper rotation period and precession period, which may not be commensurable. This situation has been numerically studied by Vokrouhlický et al. (2005a) in the case of (4179) Toutatis, and more recently in the case of (99942) Apophis by Vokrouhlický et al. (2015). Both studies suggest the tumbling may not necessarily “shut down the Yarkovsky effect,” at least in the large-bodies regime. Rather, it has been found that the Yarkovsky acceleration for these tumbling objects is well represented by a simple estimate valid for bodies rotating about the shortest axis of the inertia tensor in a direction of the rotational angular momentum and with the fundamental period of tumbling, generally the precession period. 2.2.3. More than one body (binarity). Another particular case is the Yarkovsky effect for binaries (see Vokrouhlický et al., 2005b). Unless the satellite has nearly the same size as the primary component, the rule of thumb is that the heliocentric

motion of the system’s center of mass is affected primarily by the Yarkovsky acceleration of the primary component, while the motion of the satellite feels the Yarkovsky acceleration of the satellite itself. Nevertheless, a secular change in the orbit of the satellite is actually caused by an interplay of the thermal effects and the shadow geometry in the system dubbed the Yarkovsky-Schach effect [and introduced years ago in space geodesy (Rubincam, 1982)]. However, it turns out that the BYORP effect, discussed in section 2.3, is more important and dominates the orbital evolution of the satellite. 2.3. Binary YORP The binary YORP (BYORP) effect was first proposed in a paper by Ćuk and Burns (2005). They noted that an asymmetrically shaped synchronous secondary asteroid in a binary system should be subject to a net force differential that acts on average in a direction tangent to the orbit. Thus, as the secondary orbits about the primary body and maintains synchronicity, this would lead to either an acceleration or deceleration of the secondary, which would cause the mutual orbit of the system to spiral out or in, respectively. This seminal paper presented a basic conceptual model for the BYORP effect and provided a broad survey of many of the possible implications and observable outcomes of this effect. It also numerically studied the evolution of randomly shaped secondary bodies over a year to establish the physical validity of their model. It is key to note that a necessary condition for the BYORP effect is that at least one of the bodies be synchronous with the orbit, and it can be shut off if both bodies are nonsynchronous. Ćuk and Burns concluded that the BYORP effect should be quite strong and lead binary asteroids to either spiral in toward each other or cause them to escape in relatively short periods of time. This was further expanded in a second paper by Ćuk (2007) that outlined significant implications for the rate of creation and destruction of binary asteroid systems in both the near-Earth asteroid (NEA) and main-belt population, leading to the initial estimate of binary asteroid lifetimes due to BYORP on the order of only 100 k.y. McMahon and Scheeres (2010a,b) then developed a detailed analytical model of the BYORP effect that utilized the existing shape model of the (66391) 1999 KW4 binary asteroid satellite (Ostro et al., 2006). In their approach the solar radiation force was mapped into the secondary-fixed frame and expanded as a Fourier series, following a similar approach to the YORP model development of Scheeres (2007). This enables any given shape model to be expressed with a series of coefficients that can be directly computed, and allows for time averaging. Using this approach they showed that the primary outcome of the BYORP effect could be reduced to a single parameter — the so-called “BYORP coefficient,” B  — uniquely computed from a given shape model. Henceforth, if the secondary is in a near-circular orbit, the entire BYORP effect results in simple evolutionary equations for semimajor axis a and eccentricity e(=1) of the binary orbit



da FB a 3/ 2 = dt ch′ m 2 m



de FB ea 3/ 2 =dt 4ch′ m 2 m

(6)



(7)



where again F is the solar radiation flux at the heliocentric distance aʹ (equal to the semimajor axis of the heliocentric orbit), hʹ  = 1 − e ′ 2 with eʹ being the eccentricity of the heliocentric orbit, c the light velocity, m2 the mass of the secondary, and m = G(m1 + m2) the gravitational parameter of the binary system. If the orbit is expansive (B > 0), the eccentricity will be stabilized, and vice-versa (see Ćuk and Burns, 2005). In the case where the binary orbit is highly elliptic, the evolutionary equations become much more complex, and require additional Fourier coefficients to be included into the secular equations, as discussed in detail in McMahon and Scheeres (2010a). The BYORP coefficient B is computed as a function of the shape of the body and the obliquity of the binary’s orbit relative to the heliocentric orbit of the system. Assume a model for the instantaneous solar radiation force acting on the secondary has been formulated by some means, denoted as FSRP (M,Mʹ), where M and Mʹ are the mean anomalies of the binary mutual orbit and heliocentric orbit, respectively. Then the computation of the BYORP coefficient requires double averaging of the radiation force over the binary and heliocentric revolution cycles, and projection in the direction of binary orbital motion (denoted here in abstract as ^t )



B = t ⋅

1 ( 2p )

2

2p

2p

0

0

∫ ∫

FSRP dM dM ′ P(rs )



(8)

where P(rs) = (F/c) (aʹ/rs)2 is the solar radiation pressure acting on the unit surface area of the body at the heliocentric distance rs. The normalization by P implies that units of the BYORP coefficient are measured in area; thus B can be further normalized by dividing it by the effective radius squared of the secondary body. The BYORP coefficient is a function of several physical quantities such as albedo, surface topography, and potentially thermophysical effects. However, the strongest variation of the BYORP coefficient is seen to vary with the binary obliquity with respect to the heliocentric orbit (Fig. 1). If the synchronous body is rotated by 180° relative to the orbit, then the sign of the BYORP coefficient will be uniformly reversed. Due to this, when a body initially enters into a synchronous state it is supposed that the probability of it being either positive or negative is 50%. A more recent analysis of the BYORP effect was published by Steinberg and Sari (2011), who found a positive correlation between the strength of the BYORP and YORP effects for bodies, and provided predictions related to the BYORP-driven evolution of the obliquity of a binary asteroid. In addition, they probed the possible effects of thermophysical models on the evolution of a binary system.

Normalized BYORP Coefficient

Vokrouhlický et al.:  The Yarkovsky and YORP Effects   515

0.02

(66391) 1999 KW4

0.01

0

–0.01 0

30

60

90

120

150

180

Obliquity (°) Fig. 1. BYORP coefficient B, normalized by the square of the effective radius, computed for the secondary of the (66391) 1999 KW4 binary asteroid system, as a function of the binary orbital obliquity (abscissa).

The above discussions focus on the effect of BYORP in isolation, and not in conjunction with other evolutionary effects. However, recent work has found that the BYORP effect can mix with other evolutionary effects in surprising ways that require additional verification and study. These are primarily discussed later in section 5.3, where the long-term evolution of binary systems subject to BYORP is briefly considered. However, one of these combined effects has significant implications and is discussed here. In particular, Jacobson and Scheeres (2011b) proposed the existence of an equilibrium between the BYORP effect and tides. For this equilibrium to exist, the BYORP coefficient must be negative, leading to a contractive system, and the primary asteroid must be spinning faster than the orbit rate. This creates a tidal dissipation torque that acts to expand the secondary orbit. Based on current theories of energy dissipation within rubble-pile asteroids (e.g., Goldreich and Sari, 2009), Jacobson and Scheeres (2011b) noted that all singly-synchronous rubble-pile binary asteroids with a negative BYORP coefficient for the secondary should approach a stable equilibrium that balances these two effects. This is significant, as it provides a mechanism for the persistent effect of BYORP to become stalled, leaving binary asteroids that should remain stable over long time spans. This, in turn, means that rapid formation of binary asteroids is not needed to explain the current population. 3. DIRECT DETECTIONS Accurate observations have now allowed direct detections of both the Yarkovsky and YORP effects. This is an important validation of their underlying concepts, but also it motivates further development of the theory. These direct detections have two aspects of usefulness or application. First, the Yarkovsky effect is being currently implemented as a routine part of the orbit determination of small NEAs whose orbits are accurately constrained in the forefront software packages.

Additionally, the Yarkovsky effect is already known to be an essential part of the Earth impact hazard computations in selected cases (section 4.2 and the chapter by Farnocchia et al. in this volume). Second, many applications of the Yarkovsky and YORP effects involve statistical studies of small-body populations in the solar system rather than a detailed description of the dynamics of individual objects. Aside from a general validation, the known detections help in setting parameter intervals that could be used in these statistical studies. 3.1. Yarkovsky Effect The possibility of detecting the Yarkovsky effect as a measurable orbital deviation was first proposed by Vokrouhlický et al. (2000). The idea is at first astounding given that the transverse thermal recoil force on a half-kilometer NEA should be at most 0.1 N, causing an acceleration of only ~1 pm s–2. And yet such small perturbations can lead to tens of kilometers of orbital deviation for 0.5-km NEAs after only a decade. In principle, such a deviation is readily detectable during an Earth close approach, either by optical or radar observations, but the key challenge is that the precision of the position prediction must be significantly smaller than the Yarkovsky deviation that is to be measured. In practical terms, this means that detection of the Yarkovsky effect acting on a typical 0.5-km NEA requires at least three radar ranging apparitions spread over a decade, or several decades of optical astrometry in the absence of radar ranging. Of course, smaller objects could in principle reveal the Yarkovsky effect much more quickly, but the problem for small objects is that it is more difficult to build up suitable astrometric datasets. Because of this, only a few objects with diameters D < 100 m have direct detections of the Yarkovsky effect. It should be pointed out that observations do not allow measurement of the secular change in the orbital semimajor axis directly. Rather, they reveal an associated displacement in the asteroid position along the orbit, an effect that progresses ∝ t2 in a given time t (see Vokrouhlický et al., 2000). This is similar to the way the YORP effect is observed as discussed in section 3.2. As predicted by Vokrouhlický et al. (2000), (6489) Golevka was the first asteroid with an unambiguous detection of the signature of the Yarkovsky effect in its orbit (Chesley et al., 2003). In this case the detection was possible only due to the availability of three well-separated radar ranging apparitions, in 1991, 1995, and 2003. The first two radar apparitions constrain the semimajor axis, affording a precise position prediction in 2003, while the 2003 radar ranging revealed a deviation from a ballistic trajectory. Figure 2 depicts the predicted 2003 delay-Doppler observations with their uncertainty along with the associated uncertainties. The predictions were well separated with >90% confidence, and the actual asteroid position fell close to the Yarkovsky prediction. The second reported detection of the Yarkovsky effect was for (152563) 1992 BF, which was also the first detection that did not rely on radar astrometry (Vokrouhlický et

Range Rate Offset (mm s–1)

516   Asteroids IV

With Yarko

6

Arecibo

4

2

0 Pure gravity –2 –10

0

10

20

30

Range Offset (km) Fig. 2. Orbital solution of near-Earth asteroid (6489) Golevka from astrometric data before May  2003 projected into the plane of radar observables: (1) range at the abscissa, and (2)  range-rate on the ordinate. The origin referred to the center of the nominal solution that only includes gravitational perturbations. The gray ellipse labeled “pure gravity” represents a 90% confidence level in the orbital solution due to uncertainties in astrometric observations as well as small body and planetary masses. The center of the gray ellipse labeled “with Yarko” is the predicted solution with the nominal Yarkovsky forces included (taken from Vokrouhlický et al., 2000); note the range offset of ~15 km and the range rate offset of ~5  mm  s–1. The actual Arecibo observations from May  24, 26, and 27, 2003, are shown by the black symbol (the measurement uncertainty in range is too small to be noted in this scale). The observations fall perfectly in the uncertainty region of the orbital solution containing the Yarkovsky forces. Adapted from Chesley et al. (2003).

al., 2008). This 0.5-km asteroid had a 13-yr optical arc (1992–2005) and four archival positions over two nights dating to 1953. These so-called precovery observations could not be fit to a purely gravitational orbit, but including the Yarkovsky effect in the orbit fitting enabled the observations to fit well and allowed a da/dt estimate with the signal-tonoise ratio SNR ≃ 15 (Fig. 3). In these cases, where the detection relies heavily on isolated and archival data, caution is warranted to avoid the possibility that mismeasurement or astrometric time tag errors are corrupting the result. As depicted in Fig. 3, the 1953 position offsets could not be attributed to timing errors, and the trail positions were remeasured with modern catalogs. In subsequent studies a progressively increasing number of Yarkovsky detections have been announced (Chesley et al., 2008; Nugent et al., 2012a; Farnocchia et al., 2013b). The most precise Yarkovsky measurement is that of (101955) Bennu, the target of the OSIRIS-REx asteroid sample return mission, which has a 0.5% precision Yarkovsky detection, by far the finest precision reported to date. At the extremes, asteroid 2009 BD is the smallest object (D ~ 4 m) with a verified Yarkovsky detection, which was achieved

Vokrouhlický et al.:  The Yarkovsky and YORP Effects   517

extrapolated

January 10, 1953

extrapolated January 12, 1953

(a)

(b)

DEC Offset (arcsec)

20

10

0

10

5

0

RA Offset (arcsec)

10

5

0

–5

RA Offset (arcsec)

Fig. 3. Measured and predicted positions of (152563) 1992 BF on (a) January 10 and (b) January 12, 1953. The dark gray solid line is the asteroid trail appearing on Palomar plates on the two nights. Coordinate origin, right ascension at the abscissa, and declination at the ordinate are arbitrarily set to the end of the respective trail. The leftmost dashed trail labeled “extrapolated” represent pure extrapolation of the modern orbit without the thermal forces included. The mismatch in right ascension slightly improves if the 1953 data are included in the orbital solution as shown by the middle dashed trail. Still, the solution is more than 3s away from the measured trail. Only when the thermal accelerations are included in the orbital solution do the predicted orbital positions match the observations: Stars show fitted position at the beginning and the end of the trail. Adapted from Vokrouhlický et al. (2008).

because of its Earth-like orbit and the 2-yr arc of observations that the orbit enabled (Mommert et al., 2014). On the large end, there are two detections of 2- to 3-km-diameter asteroids, namely (2100) Ra-Shalom and (4179) Toutatis (Nugent et al., 2012a; Farnocchia et al., 2013b), which are both exceptionally well observed, having four and five radar apparitions, respectively. To initially test for a signal from the Yarkovsky effect in the astrometric data of a given object, one can fit the orbit with a transverse nongravitational acceleration aT = A2/r2, with A2 being an estimated parameter, in addition to the orbital elements. This simple model yields a mean semimajor axis drift rate proportional to A2, thus capturing the salient orbital deviation due to the Yarkovsky effect. The approach of using a one-parameter (A2) Yarkovsky model is particularly convenient because it completely bypasses the thermophysical processes that are otherwise fundamental to the Yarkovsky effect. Instead, by focusing only on the level of perturbation visible in the orbit, one is able to discern the Yarkovsky effect in the absence of any knowledge of physical properties. And yet, as we shall see in section 4.1,

the detection of a Yarkovsky drift can be used to estimate or infer a number of the physical and dynamical characteristics of the body. Obviously, in the case of bodies with particular interest, one can use a detailed thermophysical model of the Yarkovsky acceleration for the orbit determination in a subsequent analysis. A population-wise, head-on approach to Yarkovsky detection thus starts with the list of asteroids with relatively secure orbits, e.g., at least 100 d of observational arc, among the NEAs. For each considered object the statistical significance of the Yarkovsky effect is obtained from the estimated value of A2 and its a posteriori uncertainty sA2 according to SNR = |A2|/sA2, where SNR > 3 is generally considered to be a significant detection. Another parameter that is helpful in interpreting the results for a given object is the ratio between the estimated value of A2 and the expected value for extreme obliquity and the known or inferred asteroid size, which we call A2max. The value of A2max can be obtained by, for instance, a simple diameter scaling from the Bennu result (Farnocchia et al., 2013b; Chesley et al., 2014). The ratio S = A2/A2max = SNR/SNRmax provides an indication of how the estimated value of A2 compares to what could be theoretically expected. A value of S ? 1 indicates that the transverse nongravitational acceleration may be too strong to be related to the Yarkovsky effect. This could imply that the body has a far smaller density or size than assumed, or that nongravitational accelerations other than Yarkovsky are at play. A large value of S could also imply a spurious A2 estimate due to corrupt astrometry in the orbital fit. On the other hand, S = 1 would suggest the possibility of higher density, size, or surface thermal inertia than assumed, but is often more readily explained by mid-range obliquity, which tends to null the diurnal component of the Yarkovsky drift. Figure 4 depicts the distribution of NEAs in the SNR and SNRmax space that we divide into four regions: • We consider cases with SNR > 3 and S < 1.5 to be valid detections because the estimated value is no more than 50% larger than expected, perhaps as a result of unusually low density or a size far smaller than assumed. Table 1 lists the 36 objects with valid Yarkovsky detections given currently available astrometry. • Spurious detections are those with SNR > 3 and S > 1.5. Many of these are due to astrometric errors in isolated observation sets, such as precoveries, and can be moved to the left in Fig. 4 by deweighting the questionable data. We find 56 cases in this category, but only 12 with SNR > 4. There are two spurious cases with SNR > 10 and S ≳ 10 that cannot be due to astrometric errors and are yet unlikely to be attributed to the Yarkovsky effect. • There are a number of objects with relatively low values for sA2 and yet the orbit does not reveal an SNR > 3 detection (denoted as weak signal zone on Fig. 4). Specifically, these cases have SNRmax > 3 and SNR < 3, with S < 2/3. These cases are potentially interesting because they generally

518   Asteroids IV

Weak signal

3.2. YORP Effect

Valid detections

100

SNRmax

10

1

0.1 Spurious detections 0.1

1

10

100

SNR Fig. 4. SNR = A2/sA2, with A2 being the parameter of an empirical transverse acceleration and sA2 its formal uncertainty, for reliable orbits of NEAs at the abscissa. The ordinate shows SNRmax, the maximum expected value of SNR for the body (from an estimate of its size and given an extremal obliquity, optimizing the Yarkovsky effect). Various classes of solutions, organized into four sectors by the straight lines, are discussed in the text. Situation as of December 2014.

indicate a mid-range obliquity and, despite the lack of significance in the A2 estimate, useful bounds can be still placed on the Yarkovsky mobility of the object. We find 35 such cases in the current NEA catalog, six of which have S < 0.05 (Table 2). In fact, this class warrants further dedicated analysis, similar to the search of new detections. • The vast majority of NEAs are currently uninteresting due to SNR < 3 and SNRmax < 3, meaning that no detection was found nor was one reasonably expected. It is worth noting that objects with nonprincipal-axis rotation states can reveal the Yarkovsky effect (e.g., Vokrouhlický et al., 2005a); (4179) Toutatis is a large, slowly tumbling asteroid (e.g., Hudson and Ostro, 1995) with Yarkovsky SNR ≃ 8 (and S ≃ 1) due to an extensive set of radar ranging data. Also, the much smaller asteroid (99942) Apophis, which has been reported to have a measurable polar precession (Pravec et al., 2014), presently has a solid Yarkovsky signal with SNR ≃ 1.8 (and S < 1), although not high enough to be listed in Table 1, but still significant in light of the abundant radar astrometry available for Apophis (Vokrouhlický et al., 2015). Similarly, binary asteroid systems may also reveal Yarkovsky drift in their heliocentric orbits (e.g., Vokrouhlický et al., 2005b), although none presently appears in Table 1. We note that (363599) 2004 FG11 has a satellite (Taylor et al., 2012) and currently has a Yarkovsky SNR ≃ 2.8 (and S ≃ 1).

Analyses of small-asteroid populations indicate clear traits of their evolution due to the YORP effect, both in rotation rate and obliquity (sections 4.5, 5.1, and 5.2). Accurate observations of individual objects, however, do not presently permit detection of the secular change in obliquity and reveal only the secular effect in rotation rate. Even that is a challenging task, because the YORP torque has a weak effect on kilometer-sized asteroids at roughly 1 AU heliocentric distance. Similar to the case of the Yarkovsky effect, the YORP detection is enabled via accurate measurement of a phase ϕ associated with the rotation rate. This is because when the rotation frequency w changes linearly with time, w(t) = w0 + (dw/dt) t (adopting the simplest possible assumption, since dw/dt may have its own time variability), the related phase ϕ grows quadratically in time, ϕ(t) = ϕ0 + 1 w0 t + 2 (dw /dt) t2. Additionally, other perturbations (such as an unresolved weak tumbling) do not produce an aliasing signal that would disqualify YORP detection. So the determination of the YORP-induced change in the rotation rate dw/dt may basically alias with the rotation rate frequency w0 itself in the dw /dt = 0 model. This is because small variations in w0 propagate linearly in time in the rotation phase. The YORP detection stems from the ability to discern this linear trend due to the w0 optimization and the quadratic signal due to a nonzero dw/dt value. In an ideal situation of observations sufficiently densely and evenly distributed over a given time interval T, one avoids the w0 and dw/dt correlation setting time origin at the center of the interval. At the interval limits the YORP effect manifests via phase change ≃ 18 (dw /dt)T2. Therefore, a useful approximate rule is that the YORP effect is detected when this value is larger than the phase uncertainty δϕ in the observations. Assuming optimistically δϕ  ≃ 5° and T about a decade, the limiting detectable dw /dt value is ≃5 × 10-8 rad d–2. Obviously, detection favors a longer time-base T if accuracy of the early observations permits. In practice, the late 1960s or early 1970s was the time during which photoelectric photometry was introduced and allowed sufficiently reliable light curve observations. This sets a maximum T of about 40 yr today for bright-enough objects [e.g., (1620) Geographos (Ďurech et al., 2008a); see, for completeness, an interesting YORP study for asteroid (433) Eros by Ďurech (2005)]. We should also mention that w and ϕ above denote sidereal rotation rate and phase, respectively. Hence to convert asteroid photometry to ϕ one needs to know the orientation of its spin axis in the inertial space and the shape model. Their solution may increase the realistic uncertainty in dw/dt if compared to the simple estimate discussed above. Figure 5 shows an example of detected quadratic advance in sidereal rotation phase ϕ in the case of the small coorbital asteroid (54509) YORP (see Lowry et al., 2007; Taylor et al., 2007). The expected YORP value of rotation-rate change matched the observed value, thus allowing interpretion of the signal as a YORP effect detection, although an accurate comparison is prohibited by lack of knowledge of

Vokrouhlický et al.:  The Yarkovsky and YORP Effects   519

TABLE 1. List of the Yarkovsky effect detections as of December 2014. Object

r H D da/dt SNR (AU) (mag) (m) (×10–4 AU m.y.–1)

(101955) Bennu (2340) Hathor (152563) 1992 BF 2009 BD 2005 ES70 (4179) Toutatis (2062) Aten 1999 MN (6489) Golevka (1862) Apollo 2006 CT (3908) Nyx 2000 PN8 (162004) 1991 VE (10302) 1989 ML (2100) Ra-Shalom (29075) 1950 DA (85953) 1999 FK21 (363505) 2003 UC20 2004 KH17 (66400) 1999 LT7 1995 CR (4034) Vishnu (85774) 1998 UT18 1994 XL1 (3361) Orpheus (377097) 2002 WQ4 (138852) 2000 WN10 (399308) 1999 GD (4581) Asclepius 2007 TF68 1999 FA (2063) Bacchus (350462) 1998 KG3 (256004) 2006 UP (37655) Illapa

1.10 0.75 0.87 1.01 0.70 1.96 0.95 0.50 2.01 1.22 1.07 1.71 1.22 0.67 1.26 0.75 1.46 0.53 0.74 0.62 0.70 0.45 0.95 1.33 0.57 1.14 1.63 0.97 1.07 0.96 1.36 1.07 1.01 1.15 1.51 0.97



20.6 20.2 19.7 28.2 23.7 15.1 17.1 21.4 19.1 16.3 22.3 17.3 22.1 18.1 19.4 16.1 17.1 18.0 18.2 21.9 19.4 21.7 18.3 19.1 20.8 19.0 19.5 20.1 20.8 20.7 22.7 20.6 17.2 22.2 23.0 17.8



493 210 510 4 61 2800 1300 175 280 1400 119 1000 130 827 248 2240 1300 590 765 197 411 100 420 900 231 348 422 328 180 242 100 300 1200 125 85 950

–18.95 ± 0.10 –17.38 ± 0.70 –11.82 ± 0.56 –489 ± 35 –68.9 ± 7.9 –3.75 ± 0.45 –6.60 ± 0.80 54.6 ± 6.8 –4.52 ± 0.60 –1.58 ± 0.24 –47.6 ± 7.7 9.6 ± 1.7 49.3 ± 8.7 19.2 ± 3.6 38.7 ± 7.5 –5.8 ± 1.2 –2.70 ± 0.57 –11.0 ± 2.4 –4.5 ± 1.0 –42.0 ± 9.8 –35.0 ± 8.3 –314 ± 76 –31.8 ± 8.0 –2.45 ± 0.63 –37.6 ± 9.8 6.2 ± 1.7 –9.6 ± 2.6 17.7 ± 4.9 47 ± 13 –19.7 ± 5.7 –60 ± 18 –43 ± 13 –6.6 ± 2.0 –25.2 ± 7.9 –67 ± 21 –10.3 ± 3.5

S

194.6 24.9 21.0 13.9 8.7 8.4 8.3 8.1 7.5 6.5 6.2 5.8 5.7 5.3 5.2 4.7 4.7 4.5 4.5 4.3 4.2 4.2 4.0 3.9 3.8 3.8 3.7 3.6 3.5 3.5 3.4 3.3 3.2 3.2 3.1 3.0

1.0 0.3 0.6 0.2 0.3 1.1 0.9 0.5 0.1 0.2 0.6 1.1 0.7 0.9 1.1 1.0 0.6 0.3 0.3 0.6 0.9 0.8 1.2 0.2 0.5 0.2 0.4 0.6 0.9 0.4 0.7 1.4 0.8 0.4 0.7 0.5



Data Arc

Nrad

1999–2013 1976–2014 1953–2011 2009–2011 2005–2013 1934–2014 1955–2014 1999–2014 1991–2011 1930–2014 1991–2014 1980–2014 2000–2014 1954–2014 1989–2012 1975–2013 1950–2014 1971–2014 1954–2014 2004–2013 1987–2014 1995–2014 1986–2014 1989–2014 1994–2011 1982–2014 1950–2014 2000–2014 1993–2014 1989–2014 2002–2012 1978–2008 1977–2014 1998–2013 2002–2014 1994–2013

3 1 0 0 0 5 4 0 3 2 1 2 0 0 0 4 2 0 1 1 0 0 1 3 0 0 0 0 0 1 0 0 2 0 0 2

Reliable detections with SNR larger than 3 are listed: r = a 1 − e 2 is the solar flux-weighted mean heliocentric distance, H is the absolute magnitude, D is the diameter derived from the literature when available [and obtained here from the European Asteroid Research Node (EARN) Near-Earth Asteroids Database, http://earn.dlr.de/nea] or from absolute magnitude with 15.4% albedo, the da/dt and formal uncertainty sda/dt are derived from the orbital fit (via A2 and sA2 values as described in Farnocchia et al., 2013b). SNR = (da/dt)/sda/dt is the quality of the semimajor axis drift determination, and S = SNR/SNRmax, where SNRmax is the maximum estimated SNR for the Yarkovsky effect. Data arc indicates the time interval over which the astrometric information is available, and Nrad denotes the number of radar apparitions in the fit.

TABLE 2. List of the most notable Yarkovsky effect nondetections as of December 2014.



Object

r H D 1/S (AU) (mag) (m)

(3757) (247517) (5797) (152742) (1221) (225312)

1.65 0.62 1.71 0.62 1.74 1.19

Anagolay 2002 QY6 Bivoj 1998 XE12 Amor 1996 XB27



19.1 19.6 18.8 18.9 17.4 21.7



390 270 500 413 1100 85

86.8 56.9 53.6 39.7 31.0 20.1

Data Arc

1982–2014 2002–2014 1953–2014 1995–2014 1932–2012 1996–2014

Notable nondetections of the Yarkovsky effect with 1/S > 10 are listed. Columns as in Table 1.

Nrad

1 0 0 0 0 0

Additional Sidereal Phase ∆φ (°)

520   Asteroids IV

(54509) YORP

2005

180 2004

90

2003

2001

2002

0 0

500

1000

1500

Days Since July 27, 2001 Fig. 5. Advance of the sidereal rotation phase Δϕ (ordinate in degrees) vs. time (in days) for the small Earth-coorbital asteroid (54509) YORP. Symbols are measurements with their estimated uncertainty, as follow from assembling the radar observations at different apparitions. The gray line is a quadratic 1 progression Δϕ = 2 (dw/dt)t2, with dw/dt = 350 × 10–8 rad d–2. Time origin set arbitrarily to July 27, 2001, corresponding to the first measurement. Adapted from Taylor et al. (2007).

the full shape of this body (due to repeated similar viewing geometry from Earth). A complete list of the YORP detections, as of September 2014, is given in Table 3. To appreciate their accuracy, we note that they correspond to a tiny change in sidereal rotation period by a few milliseconds per year: 1.25 ms y–1 for (54509) YORP to a maximum value of 45 ms y–1 for (25143) Itokawa. While not numerous at the moment, we expect the list will more than double during the next decade. There are presently two asteroids, (1620) Geographos and (1862) Apollo, for which both Yarkovsky and YORP effects have been detected. These cases are of special value, provided a sufficiently accurate physical model of the body is available (see Rozitis et al., 2013; Rozitis and Green, 2014). (25143) Itokawa holds a special place among the asteroids for which the YORP effect has been detected. Not

only was this the first asteroid for which YORP detection was predicted (Vokrouhlický et al., 2004), but the shape of this body is known very accurately thanks to the visit of the Hayabusa spacecraft. This has led researchers to push the attempts for an accurate YORP prediction to an extreme level (e.g., Scheeres et al., 2007; Breiter et al., 2009; Lowry et al., 2014), realizing that the results depend in this case very sensitively on the small-scale irregularities of the shape (see Statler, 2009, for a general concept). However, in spite of an uncertainty in the YORP prediction, the most detailed computation consistently predicted deceleration of the rotation rate by YORP, as opposed to the detected value (Table 3). A solution to this conundrum has been suggested by Scheeres et al. (2007), who proposed that the difference in density between the “head” and “body” of this asteroid may significantly shift the center of mass. This effect introduces an extra torque component that could overrun the YORP torque, canonically computed for homogeneous bodies, and make the predicted deceleration become acceleration of the rotation rate. Lowry et al. (2014) adopted this solution, predicting that the two parts of Itokawa have a very different densities of ≃1.75 g cm–3 and ≃2.85 g cm–3. Nevertheless, the situation may be even more complicated: Golubov and Krugly (2012) have shown that transverse heat communication across boulder-scale features on the surface of asteroids may cause a systematic trend toward acceleration of the rotation rate. Indeed, in the most complete works so far, Golubov et al. (2014) and Ševeček et al. (2015) show that the detected acceleration of Itokawa’s rotation rate may be in large part due to detailed modeling of the effects described by Golubov and Krugly (2012) without invoking a large density difference in the asteroid. The complicated case of Itokawa thus keeps motivating detailed modeling efforts of the YORP effect. Luckily, not all asteroidal shapes show such an extreme sensitivity on the small-scale surface features (e.g., Kaasalainen and Nortunen, 2013), thus allowing an easier comparison between the detected and predicted YORP signals. On a more general level, we note that in spite of rotation periods ranging from a fraction of an hour to more than 12 h, all five asteroids for which the YORP effect was detected reveal acceleration of the rotation rate. It is not yet known

TABLE 3. List of the YORP effect detections as of September 2014. Object

dw/dt (×10–8 rad/d2)

( 54509) YORP 350 ± 35 (25143) Itokawa 3.5 ± 0.4 (1620) Geographos 1.2 ± 0.2 (1862) Apollo 5.5 ± 1.2 (3103) Eger 1.4 ± 0.6 (1865) Cerberus 120°, after accounting for reasonable variations in other unknowns. If the spin state of the body is known, generally from some combination of radar imaging and optical light curves, we have a much clearer insight into the nature of the body because cos  γ is removed as an unknown and the thermal parameter Θw is better constrained. Indeed, in such cases we are left with a simple relationship between ρD and the

522   Asteroids IV thermal inertia G. But the diameter D can be measured directly by radar, or inferred from taxonomic type or measured albedo, or can just be derived from an assumed distribution of asteroid albedo, allowing the constraint to be cast in terms of the bulk density ρ and thermal inertia G. The gray region of Fig. 6 depicts this type of constraint for the case of (101955) Bennu. The peak in r seen in Fig. 6 is associated with Θw  ≃ 1, where the Yarkovsky effect obtains its maximum effectiveness. This characteristic peak in the ρ vs. G relationship often allows strict upper bounds on ρ (e.g., Chesley et al., 2003). We note that the degeneracy between ρ and G could in principle be broken by an independent estimate of ρ that would allow a direct estimate of G, albeit with the possibility of two solutions. While this approach has so far not been possible, we anticipate it here as a natural outcome of the first detection of the Yarkovsky effect on a well-observed binary system. Another approach to breaking the correlation between ρ and G makes use of measurable solar radiation pressure deviations on the orbit, which yields an area-to-mass ratio. With a size estimate, an independent mass estimate can lead to a double solution for the thermal inertia of the body (e.g., Mommert et al., 2014). The alternative approach has been applied successfully in a few special cases to date. Specifically, observations of an asteroid’s thermal emissions can afford independent constraints on the thermal inertia, breaking the degeneracy between ρ and G, allowing a direct estimate of the asteroid’s bulk density. Perhaps the most striking example here is the

1400

Bulk Density (kg m–3)

(101955) Bennu 1300

1200

1100

Rough Smooth

1000 100

100

100

100

100

100

Thermal Inertia (J m–1 s–1/2 k–1) Fig. 6. Bulk density ρ solution for (101955)  Bennu from detected value of the Yarkovsky orbital effect as a function of the surface thermal inertia G. The dashed line corresponds to the da/dt  = const. solution for a smooth-surface model, taking into account a detailed shape model and a nonlinear boundary condition. The solid line accounts for 50% smallscale roughness in each of the surface facets of the shape model, while the gray zone takes into account the estimated ~17% uncertainty in the roughness value. The nonlinearity of the da/dt isoline in the ρ vs. G plane follows from equations (1) and (3). Adapted from Chesley et al. (2014).

case of (101955) Bennu, which has a well-constrained shape, spin state, and thermal inertia. When these are linked with the high precision da/dt estimate (Table 1), the result is a bulk density of 1260 ± 70 kg m–3 (Fig. 6), where the formal precision is better than 6% (Chesley et al., 2014). Other similar cases include (1862) Apollo, (1620) Geographos, and (29075) 1950 DA (respectively, Rozitis et al., 2013, 2014; Rozitis and Green, 2014). In each of these cases the authors combine da/dt, radar imaging, and thermal measurements to derive the bulk density of the asteroid. In the best cases of Yarkovky detection, where we also have a shape model, spin state, and thermophysical characterization, one can infer the local gravity of the body. This can be of profound engineering interest for the asteroid targets of space missions, e.g., (101955) Bennu. The mission design challenges for the OSIRIS-REx mission are significantly eased due to the Yarkovsky constraint on Bennu’s mass and bulk density. Another such case is (29075) 1950 DA, which is not a space mission target, and yet the estimates of local surface gravity derived from Yarkovsky have profound implications. Rozitis et al. (2014) found that their thermal measurements, when combined with the Yarkovsky drift reported for 1950 DA by Farnocchia and Chesley (2014), required a low asteroid mass. The estimated mass was so low, in fact, that it implied that the equatorial surface material on 1950 DA is in tension due to centrifugal forces. And yet the estimated thermal inertia was low enough that it required a loose, fine-grained regolith on the surface. This seeming contradiction is most readily resolved by the action of cohesive forces due to van der Waals attraction between regolith grains, and represents the first confirmation of such forces acting on an asteroid, which had already been anticipated by Scheeres et al. (2010). And so, through a curious interdisciplinary pathway, the measurement of the Yarkovsky drift on 1950 DA reveals the nature of minute attractive forces at work in the asteroid’s regolith. Population implications — The discussion above treats Yarkovsky detections in a case-by-case manner, deriving additional information for the specific asteroid at hand. However, the wealth of Yarkovsky detections listed in Table 1 allows an insight into the NEA population as a whole. Of particular interest is the distribution of obliquities implied by the tabulated detections, of which 28 out of 36 detections reveal da/dt < 0 and thus about 78% of the sample requires retrograde rotation (see also Fig. 9). This excess of retrograde rotators represents an independent confirmation of a result first reported by La Spina et al. (2004). The mechanism for an excess of retrograde rotators in the NEA population is a result of the Yarkovsky driven transport mechanism (e.g., Morbidelli and Vokrouhlický, 2003). The location of the n6 resonance at the inner edge of the main belt implies that main-belt asteroids entering the inner solar system through this pathway must have da/dt < 0 and thus retrograde rotation. Direct rotators will tend to drift away from the resonance. Asteroids entering the inner solar system through other resonance pathways, principally the 3:1 mean-motion resonance with Jupiter, may drift either in or out into the resonance, and so will have parity between retrograde

Vokrouhlický et al.:  The Yarkovsky and YORP Effects   523

and direct rotators. Farnocchia et al. (2013b) analyze this retrograde prevalence, including selection effects among the Yarkovsky detections, and find that it is fully consistent with the Yarkovsky-driven transport, and point out that this can be used to derive a distribution of the obliquities of NEAs. 4.2. Impact Hazard Assessment Most reported potential impacts are associated with newly discovered objects for which the uncertainty at the threatening Earth encounter is dominated by the uncertainties in the available astrometric observations. However, as the astrometric dataset grows, the fidelity of the force model used to propagate the asteroid from discovery to potential impact becomes more and more important. For a few asteroids with extraordinarily precise orbits, the Yarkovsky effect is a crucial aspect of an analysis of the risk posed by potential impacts on Earth. When the Yarkovsky effect is directly revealed by the astrometric data, the analysis approach is straightforward, as is the case for (101955) Bennu and (29075) 1950 DA (e.g., Milani et al., 2009; Chesley et al., 2014; Farnocchia and Chesley, 2014). However, there are some cases in which the astrometry provides little or no constraint on the Yarkovsky effect, and yet Yarkovsky drift is a major contributor to uncertainties at a potentially threatening Earth encounter. In these situations we are forced to assume distributions on albedo, obliquity, thermal inertia, etc., and from these we can derive a distribution of A2 or da/dt. A Monte Carlo approach with these distributions allows us to better represent uncertainties at the threatening Earth encounter, and thereby compute more realistic impact probabilities. This technique has been necessary for (99942) Apophis and has been applied by Farnocchia et al. (2013a) before Vokrouhlický et al. (2015) made use of rotation-state determination of this asteroid. See the chapter by Farnocchia et al. in this volume) for a more complete discussion of Yarkovsky-driven impact hazard analyses. 4.3. Meteorite Transport Issues The Yarkovsky effect, with its ability to secularly change the semimajor axes of meteoroids (precursors of meteorites, which are believed to be fragments of larger asteroids located in the main belt between the orbits of Mars and Jupiter), was originally proposed to be the main element driving meteorites to Earth (see Öpik, 1951; Peterson, 1976). However, direct transport from the main belt, say as a small body slowly spiraling inward toward the Sun by the Yarkovsky effect, required very long timescales and unrealistic values of the thermal parameters and/or rotation rates for meter-sized bodies. Moreover, a.m./p.m. fall statistics and measured preatmospheric trajectories in rare cases (like the Příbram meteorite) indicated many meteorites had orbits with the semimajor axis still close to the main-belt values. The problem was overcome in the late 1970s and early 1980s by advances in our understanding of asteroid dynamics. Numerous works have shown that the transport routes

that connect main-belt objects to planet-crossing orbits are in fact secular and mean-motion resonances with giant planets, such as the n6 secular resonance at the lower border of the main asteroid belt and/or the 3:1 mean-motion resonance with Jupiter. Putting this information together with the Yarkovsky effect, Vokrouhlický and Farinella (2000) were able to construct a model in which meteoroids or their immediate precursor objects are collisionally born in the inner and/or central parts of the main belt, from where they are transported to the resonances by the Yarkovsky effect. En route, some of the precursors may fragment, which can produce new swarms of daughter meteoroids that eventually reach the escape routes to planet-crossing orbits. With this model, Vokrouhlický and Farinella could explain the distribution of the cosmic-ray exposure ages of stony meteorites as a combination of several timescales: (1) the time it takes for a meteoroid to collisionally break, (2) the time it takes a meteoroid to travel to a resonance, (3) the time it takes for that resonance to deliver the meteoroid to an Earth-crossing orbit, and (4) the time it takes the meteoroid on a planetcrossing orbit to hit Earth. While successful to the first order, this model certainly contains a number of assumptions and potentially weak elements, especially in the light of subsequent rapid development of the YORP effect theory, that warrant further work. For instance, one of the difficulties in refining the meteorite delivery models is the uncertainty in identification of the ultimate parent asteroid (or asteroids) for a given meteorite class (e.g., see the chapter by Vernazza et al. in this volume). Thus, among the ordinary chondrites we have a reasonable guess that LL-chondrites originate from the Flora region [or the asteroid (8) Flora itself] and the L-chondrites originate from disruption of the Gefion family. There were numerous guesses for the H-chondrite source region [such as the asteroid (6) Hebe], but none of them has been unambiguously confirmed. The model presented by Nesvorný et al. (2009), while more educated in the choice of the L-chondrite source region than the previous work of Vokrouhlický and Farinella (2000), requires immediate parent bodies of these meteorites, 5–50 m in size, to reach the powerful 3:1 mean-motion resonance with Jupiter. This means they should have migrated by the Yarkovsky effect some 0.25–0.3 AU from their source location in less than 0.5 b.y. While this is not a problem in a scenario where the bodies rotate about the body-fixed axis whose direction is preserved in the inertial space, it is not clear if this holds when the bodies would start to tumble or their axes started to evolve rapidly due to the YORP effect. Clearly, more work is needed to understand the Yarkovsky effect in the small-size limit for bodies whose spin axis may undergo fast evolution. 4.4. Orbital Convergence in Asteroid Families and Pairs Over the past decade the Yarkovsky and YORP effects have helped to significantly boost our knowledge of the asteroid families (e.g., see the chapter by Nesvorný et al. in

524   Asteroids IV this volume). This is because they represent a unique timedependent process in modeling their structure, thus allowing us to constrain their ages for the first time. The most accurate results are obtained for young-enough families (ages 10 m.y., say) do not permit application of the fine age-determination methods described in section 4.4. This is because orbits in the main asteroid belt are affected by deterministic chaos over long timescales. Hence it is not possible to reliably reconstruct past values of the orbital secular angles, with the proper values of semimajor axis aP, eccentricity eP, and inclination iP being the only well-defined parameters at hand. Still, these proper elements are constructed using approximate dynamical models, spanning time intervals quite shorter than the typical ages of large asteroid families. While the deterministic chaos is still in action over long timescales and produces a

slow diffusion of the proper eP and iP values, the Yarkovsky effect is the principal phenomenon that changes the proper aP values of multi-kilometer-sized asteroids. Bottke et al. (2001), studying an anomalous structure of the Koronis family, presented the first clear example of the Yarkovsky effect sculpting a large-scale shape of an asteroid family in aP and eP. It also approximately constrained its age to ~2.5–3 b.y. [see also Vokrouhlický et al. (2010) for a similar study of the Sylvia family]. A novel method suitable for age determination of families a few hundred million years old has been presented by Vokrouhlický et al. (2006a). It stems from the observation that small asteroids in some families are pushed toward extreme values of the semimajor axis and, if plotted in the aP vs. H (absolute magnitude) diagram, they acquire an “eared” structure (Fig. 7). Since this peculiar structure is not compatible with a direct emplacement by any reasonable ejection field, Vokrouhlický et al. (2006a) argued it must result from a long-term dynamical evolution of the family. In particular, postulating that the initial dispersal in aP of the family members was actually small, they showed that Yarkovsky drift itself accounted for most of the family’s extension in semimajor axis. Assisted by the YORP effect, which over a YORP-cycle timescale tilts obliquities toward extreme values, the Yarkovsky effect (dominated by its diurnal component) is maximized, and pushes small family members toward the extreme values in aP. If properly modeled, this method allows us to approximately constrain the interval of time needed since the family-forming event to reach the observed extension (Fig. 7). Several applications of this method can be found in Vokrouhlický et al. (2006a,b,c), Bottke et al. (2007), Carruba (2009), or Carruba and Morbidelli (2011). Recently Bottke et al. (2015) noticed that the classical setting of this method does not permit a satisfactory solution for the low-albedo, inner-belt Eulalia family. Their proposed modification requires an extended time spent by small asteroids in the extreme obliquity state, which in turn requires a simultaneous slowdown in the evolution of their rotation rates by the YORP effect. In fact, this may be readily obtained by postulating that the YORP strength changes on a timescale shorter than the YORP cycle, an assumption that may follow from the extreme sensitivity of the YORP effect to asteroid shape [the self-limitation effect discussed in section 2.1; see also Cotto-Figueroa et al. (2015)]. It is not clear, however, why this phenomenon should manifest itself primarily in this particular family, or whether it generally concerns all families ~1 b.y. old. The model of Vokrouhlický et al. inherently contains a prediction that the small members in the “eared” families have preferred obliquity values (such that prograde-rotating objects occupy regions in the family with largest a values, and vice versa). Interestingly, recent works of Hanuš et al. (2013b) and Kryszczyńska (2013) confirm this trend in the cases of several families, and more detailed studies are underway. A peculiar situation arises for families embedded in the first-order mean-motion resonances with Jupiter. In these cases, the resonant lock prohibits large changes in the

Vokrouhlický et al.:  The Yarkovsky and YORP Effects   525 18

2

3

3

2

60

1

1

3

1

Incremental Number

Absolute Magnitude

16

14

12

10 2.32

40

2

20

(a) 2.34

2.36

2.38

2.4

2.42

Semimajor Axis (AU)

(b) 0

0

0.01

0.02

0.03

0.04

Displacement from Center (AU)

Fig. 7. (a)  The Erigone family members projected on the plane of the proper semimajor axis aP and the absolute magnitude H; 432 numbered family members, including (163) Erigone (star), are shown as black symbols. The gray lines show 0.2 H = log(|aP–a0|/C), with a0 = 2.3705 AU and three different values of the C parameter labeled 1, 2, and 3. (b) Fixing the H level (16 mag in our case) results in a one-to-one link between the C value and a displacement from the center a0, shown here at the abscissa. The symbols represent the Erigone family using a statistical distribution in the C-bins (assuming a symmetry C → – C in this case); uncertainty is simply N , where N is the number of asteroids in the bin. A numerical model (dark gray line) seeks to match the distribution by adjusting several free parameters such as the family age and initial dispersal of fragments from the largest fragment. The gray arrows point to the corresponding C = const. lines on (a). Adapted from Vokrouhlický et al. (2006a), with the family update as of April 2014.

semimajor axis, but the Yarkovsky effect manifests itself by a secular increase or decrease of the eccentricity. Modeling of this evolution allowed Brož and Vokrouhlický (2008) and Brož et al. (2011) to estimate the age of the Schubart and Hilda families located in the 3:2 mean-motion resonance with Jupiter. 5. APPLICATIONS OF THE YORP AND BINARY YORP EFFECTS 5.1. Distribution of Rotation Rate and Obliquity for Small Asteroids As explained in section 2.1, a secular change in rotation rate and obliquity are the two main dynamical implications of the YORP effect. Therefore, it is has been natural to seek traits of these trends among the populations of small asteroids. Luckily, the amount of data and their quality have significantly increased over the last decade and allowed such analyses. 5.1.1. Rotation-rate distribution. The distribution of rotation frequencies of large asteroids in the main belt matches a Maxwellian function quite well with a mean rotation period of ~8–12 h, depending on the size of the bin used. However, data for asteroids smaller than ~20 km show significant deviations from this law, with many asteroids either having very slow or very fast rotation rates. Note that similar data are also available for NEAs, but the main-belt sample is more

suitable because its interpretation is not complicated by possible effects of planetary close approaches. After eliminating known or suspected binary systems, solitary kilometer-sized asteroids in the main asteroid belt were shown to have a roughly uniform distribution of rotation frequencies (Pravec et al., 2008) (Fig. 8). The only statistically significant deviation was an excess of slow rotators (periods less than a day or so). Note that the sample described by Pravec et al. (2008) is superior to other existing datasets so far in elimination of all possible survey biases [which may prevent recognition of slow rotators (P. Pravec, personal communication)]. These results are well explained with a simple model of a relaxed YORP evolution. In this view asteroid spin rates are driven by the YORP effect toward extreme (large or small) values on a characteristic (YORP) timescale dependent on the size. Asteroids evolving toward a state of rapid rotation shed mass and thus put a brake on their rotation rate, while those who slow their rotation too much enter into a tumbling phase. They may later emerge from this state naturally, with a new spin vector, or may gain rotation angular momentum by subcatastrophic impacts. After a few cycles the spin rates settle to an approximately uniform distribution and the memory of its initial value is erased. In fact, the observations similar to those shown in Fig. 8 may help to quantitatively calibrate the processes that allow bodies to reemerge from the slow-rotating state. Statler et al. (2013) presented a first attempt to obtain unbiased rotation properties of very small NEAs. They found

526   Asteroids IV

Number of Asteroids

Number of Asteroids

100 80 60 Model

40

93 pole solutions for MBAs 15

10

5

0

20

(a)

0

0

2

4

6

8

10

Spin Rate (cycles/day) Fig. 8. Spin rate distribution of 462 small main-belt and Mars-crossing asteroids (sizes in the 3–15-km range, with a median value of 6.5 km). The distribution is flat with only two features: (1)  an excess of slow rotators with periods longer than 1  d (the first bin), and (2)  a linear decrease on the 8–10 cycles d–1 interval. The latter is simply due to rotational fission limit dependence on the actual shape of the body, while the former holds information how the spin reemerges from the slow-rotation limit. Results from a simple model of a YORP-relaxed population of objects is shown in black (model). Adapted from Pravec et al. (2008), with an update from P. Pravec as of April 2014.

an anomalously large fraction of very fast rotating bodies in the 90°), because the prograde-rotating asteroids are perturbed by secular spin-orbit resonances (e.g., Vokrouhlický et al., 2006d). As a result, there is more mixing among the obliquities 50  km as defined by Farinellla and Davis (1992)] and calculated Pi and Vimp between all possible pairs of asteroids, assuming fixed values of semimajor axis, eccentricity, and inclination (a, e, i). A common approximation made here is that the orbits can be integrated over uniform distributions of longitudes of apsides and nodes because secular precession randomizes their orbit orientations over ~104-yr timescales. After all possible orbital intersection positions for each projectile-target pair were evaluated and weighted, they found that main-belt objects striking one another have Pi ~ 2.9 × 10–18 km–2 yr–1 and Vimp  ~ 5.3  km  s–1. These values are fairly reasonable given what we know about the main-belt population today, and comparable values can be found in many works (e.g., Farinella and Davis, 1992; Vedder, 1998; dell’Oro and Paolicchi, 1998; Manley et al., 1998). Estimates for different portions of the main-belt population striking one another have been reported as well (e.g., Levison et al., 2009; Cibulkova et al., 2014). To model collisional evolution in the primordial asteroid belt requires that certain assumptions be made about the excitation of asteroid belt bodies at that time. For example, the process that caused the main-belt population to become dynamically excited (see the chapter by Morbidelli et al. in this volume) should have also driven many primordial mainbelt asteroids onto planet-crossing orbits. While their orbits

704   Asteroids IV were short lived, their higher eccentricity and inclinations would have allowed them to strafe the surviving main belt asteroids at Vimp > 10 km s–1 for tens of millions of years (e.g., Bottke et al., 2005b; Davidson et al., 2013; Marchi et al., 2013). Moreover, if the primordial main belt once had considerably more mass, as discussed in section 1, these departed bodies could be responsible for a considerable amount of collisional evolution in the main belt. A related issue is that the primordial main belt has likely been struck by sizable but transient populations on planetcrossing orbits, such as leftover planetesimals (Bottke et al., 2006, 2007), ejecta from giant impacts in the terrestrial planet region (Bottke et al., 2015b), comet-like planetesimals dispersed from the primordial disk during giant planet migration (Brož et al., 2013), and Jupiter–Saturn-zone planetesimals pushed into the inner solar system via giant planet migration and/or evolution (Walsh et al., 2011; Turrini et al., 2011, 2012). Most of these dramatic events are thought to take place during the first 500 m.y. of solar system history. The nature and evolution of these populations is uncertain, such that dynamical models are needed to set limits on what they were plausibly like (see the chapter by Morbidelli et al. in this volume). Under certain conditions, they could also account for abundant collisional grinding in the main belt. In all cases, dynamical models are needed to allow the computation of Pi and Vimp between the impacting bodies and the main-belt targets. From there, it is a matter of estimating the initial sizes of the populations, how fast they disperse, and how the populations undergo collisional evolution among themselves.

while large asteroids are considered part of the “gravity scaling” regime, where fragmentation is controlled by the self-gravity of the target (see section  4.1). Laboratory experiments and hydrocode modeling work discussed in the references above suggest the transition between the regimes occurs in the range 100 < D < 200 m (Fig. 1). Testing what impacts do to undamaged targets with basaltlike physical properties, Benz and Asphaug (1999) found that the mass of the largest remnant MLR after a collision can be fitted as a function of Q/QD* , where the kinetic energy of the projectile per unit mass of the target is denoted by Q





(

)

D target

  Q  1 M LR =  −0.35  − 1 +  M T *  QD  2  



(4)

for Q > QD* , where MT is the target mass. Whenever MLR in equation  (3) turns out to be negative, one can assume that the target has been pulverized, such that all its mass is lost below some minimal mass threshold. A missing aspect of this discussion is that asteroids have a wide range of physical properties and therefore may disrupt very differently than the idealized bodies used in numerical hydrocode runs. We refer the reader to the chapters in this



(2)

where Vimp is the impact velocity. We assume here that the target and projectile have the same bulk density, although that is by no means assured. Small asteroids are considered part of the “strength-scaling” regime, where the fragmentation of the target body is governed by its tensile strength,

Specific Energy QD (erg g–1)

1012

A second key issue to modeling asteroid collisional evolution concerns the disruption scaling law. This is commonly referred to as the critical impact specific energy QD* , the energy per unit target mass delivered by the projectile required for catastrophic disruption of the target (i.e., such that one-half the mass of the target body escapes). A considerable amount has been written about the value of QD* (e.g., reviews in Holsapple et al., 2002; Asphaug et al., 2002; Davis et al., 2002; see also Leinhardt and Stewart, 2009; 2012), and the latest on the computation of this value can be found in the chapters in this volume by Jutzi et al. and Michel et al. For these reasons, we only briefly review the main issues here. Using QD* , the diameter of a projectile ddisrupt capable of disrupting a target asteroid (Dtarget) can be estimated as 1/ 3

(3)

for Q < QD* , and

2.2. Asteroid Disruption Scaling Laws

2 d disrupt = 2Q D* Vimp

 1 Q  1 M LR =  −  − 1 +  M T *  2   2  Q D

Bottke et al. (2005a) Benz and Asphaug (1999)

1011 1010 109 108 107 106

10–2

100

102

104

106

108

Target Radius R (cm) Fig. 1. The critical impact specific energy QD* defined by Benz and Asphaug (1999). This function is the energy per unit target mass delivered by the projectile that is required for catastrophic disruption of the target, such that one-half the mass of the target body escapes. The dashed line is the function derived by Bottke et al. (2005a) for their modeling results. Both functions pass through the normalization point (QD* , D) set to (1.5 × 107 erg g−1, 8 cm), which was determined using laboratory impact experiments (e.g., Durda et al., 1998).

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   705

volume by Jutzi et al. and Michel et al., who discuss recent advances made in this area. Here we point out that all collisional models must, by necessity, make approximations to deal with complicated systems. This has led many modelers to assume that all asteroids (e.g., monoliths, rubble piles, etc.) follow the exact same QD* functions for disruption. While this approach may be more accurate than one might expect (see results in the chapters in this volume by Jutzi et al. and Michel et al.), future collision evolution models will need to consider how specific asteroid types react to impacts. In addition, the influence of asteroid spin on QD* has not been investigated so far in the hypervelocity impact regime, and it is likely that a spinning asteroid responds differently to an impact than a nonspinning one, as found in low-speed impacts between self-gravitating aggregates (e.g., Ballouz et al., 2014). In practice, this will mean sorting all asteroids into broad categories that can be treated by individual QD* functions. One possible way to divide them up would be by spectral signatures, such as the S-, C-, and X-complexes (see the chapter by DeMeo et al. in this volume). Within the complexes, bodies might share similar albedos (see chapters by Mainzer et al. and Masiero et al.), bulk densities and porosities (see chapter by Scheeres et al.), compositions, and so on. Differences between categories could then be dealt with in a logical fashion. For example, we know that C-complex bodies often have lower bulk densities and higher porosities than S-complex bodies, and studies of primitive carbonaceous chondrites suggest many are structurally weaker and have different grain structures as well (e.g., Britt et al., 2002). Whether this affects their QD* function will then need to be determined by laboratory impact experiments and numerical hydrocode simulations of asteroid collisions. There will also be the issue of how to treat the exceptional cases (e.g., the X-complex include a wide range of asteroid types, internal structures, compositions, and bulk densities). The hope is that this kind of work will eventually lead us to an understanding of the SFDs of different asteroid com‑ plexes and how they have changed over time. By getting the details right, it may be possible to ask more interesting questions about how the main belt reached its current state. Even the assumption that all asteroids should be placed into the S- or C-complexes, where their physical properties would be treated differently, would be an advance over current model assumptions. 2.3. Asteroid Fragmentation One of the most difficult issues to deal with in any collisional evolution model is the treatment of the fragment SFD created when two bodies slam into one another. Given the wide range of parameters that could be involved in any collision, such as impact velocity, projectile and target sizes, impact angle, projectile and target properties, etc., it is a somewhat quixotic task to try to generate a “one size fits all” recipe capable of reproducing the outcomes of all meaningful cratering and catastrophic disruption events that could have ever taken place in the asteroid belt.

Comprehensive experimental work has been carried out over the last several decades on this subject. Studies based on hypervelocity laboratory impacts have provided threshold specific energies for shattering (QS*) among a wide range of materials, and scaling theories including strain-rate and gravity-scaling effects allow one to extrapolate those results to multi-kilometer-sized asteroids (Holsapple et al., 2002; chapter by Michel et al. in this volume). They show that QS* and QD* coincide in the strength regime, but QS* < QD* in the gravity regime and the minimum energy to disperse a given target can be expressed as the sum of the energy needed to shatter the body and the energy required to disperse the fragments. In this way, once the comparison between the impact specific energy and the value of QS* is made, it is possible to determine whether the impact will be a cratering or a disruption event. In both cases the size distribution of the new fragments can potentially be calculated (e.g., Petit and Farinella, 1993). The critical quantity that discriminates cratering from shattering is the mass fraction between the largest fragment (MLR) and the target (MT), which is given by f LF

 Q*  M = LF = 0.5  S  MT  E 2

1.24

(5)

In the case of a barely shattering impact event, fLF  = 0.5. Using QS* instead of QD* has the advantage of allowing one to calculate how many fragments are reaccumulated by the self-gravity of the non-escaping fragments (Campo Bagatin et al., 1994b). One must also consider that many D < 100-km asteroids are likely to be second-generation gravitational aggregates. Campo Bagatin et al. (2001) tracked this aspect of collisional evolution, and found that the amount of reaccumulated mass for each object was enough that it could affect both the target body’s QD* function as well as the fragment SFD created in an impact. Note that the lower size limit on gravitational aggregates is unknown; some meter-sized bodies may possibly be held together by cohesive forces (see the chapter by Scheeres et al. in this volume). Ultimately, little is known about the mass distribution of the fragments —aggregates themselves or single coherent components — coming out of a disrupting impact on a gravitational aggregate, although insights into this can potentially be gleaned from numerical hydrocode experiments of collisions on rubble-pile asteroids (Benavidez et al., 2012; see the chapter by Michel et al. in this volume). Gravitational aggregates may also be produced by multiple subcatastrophic collisions, which may lead to the same result as a single shattering collision, provided their total energy is equivalent to the energy of the shattering event (Housen, 2009). This could mean some second-generation asteroids are gravitational aggregates with limited macroporosity, due to the fact that fragments did not get enough kinetic energy to be jumbled and reshuffled. How these results feed into the creation of new fragment SFDs are uncertain. Improvements in this area, along the lines of an

706   Asteroids IV updated Campo Bagatin et al. (2001) model, could help to better characterize collisional evolution in the main belt. These issues influence the internal structure of asteroids. This may explain why mass and volume measurements of asteroids indicate a wide range of internal macroporosities for S- and C-complex asteroids (see the chapter by Scheeres et al. in this volume). Unfortunately, porosity is only a partial indicator of internal structure, as it is largely independent of the sizes of components. Porosity also hides the absolute sizes of components and their distribution. A porous gravitational aggregate might have a substantial microporosity (e.g., individual constituents with a fairy-castle structure) and/or a sizable macroporosity (e.g., large fragments and empty space near the contact points covered by regolith). The fact that many main-belt asteroids may have unusual internal structures makes it imperative that we obtain more ground truth on how real asteroids are affected by collisions. Beyond this, it is important to recognize that our asteroid belt has been subject to an enormous number of stochastic events, and information about the fragments produced by ancient collisions has been lost by subsequent collisional and dynamical processes. This means the initial conditions for ancient family-forming events or even large cratering events (see the chapters by Asphaug et al. and Nesvorný et al. in this volume) may never be precisely known (see the chapters by Jutzi et al. and Michel et al.). A good example of this is the impact event that created the 400-km Veneneia basin on (4) Vesta; the basin has been partially buried/destroyed by the nearby Rheasilvia basin-formation event (Schenk et al., 2012; see the chapter by Russell et al.). Given these limitations, realistic modelers do the best they can with what they have. This means choosing parameters and formalism that are reasonable within the bounds of what is known and testing their results against the available constraints. The interpretation of even good matches, though, must always be met with some skepticism and wariness. Moreover, a careful modeler must also run simulations over numerous trials in an attempt to characterize how outcomes may have been affected by chance events (e.g., the disruption of an large asteroid at a strategic time or place may allow a model run to match constraints, yet this kind of event may not have happened in our asteroid belt). To this end, modern collisional-evolution models have folded into their codes outcomes of numerical smoothed particle hydrocode (SPH) simulations that account for at least some of the parameters described above. For example, Morbidelli et al. (2009) constructed an algorithm that reproduced the fragment size distribution of the SPH results determined by Durda et al. (2004, 2007), who conducted a large number of collision simulations of projectiles of various masses and velocities striking 100-km-diameter asteroids. They found that most catastrophic collisions produce fragment SFDs that have a continuous, steep power-law size distribution starting from a single large fragment that is well separated in size from that of the largest remnant of the target. The mass of the largest fragment and the slope of the power-law SFD in each of the experiments from Durda et al.

(2007) was described as a function of the ratio Q/QD* that characterized each experiment

M LF

2  Q    −   Q  4Q* = 8 × 10−3  exp  D   ( M (i) + M ( j) ) *  Q D 

(6)

for the mass of the largest fragment and



 Q  q = −10 + 7    Q D* 

0.4

exp

−

Q 7 Q D*

(7)

for the slope of the cumulative power-law size distribution of the fragments. These equations represent empirical fits to the numerical hydrocode data. Note that comparable functions were created by Cibulková et al. (2014) from the rubble-pile impact simulation results of Benavidez et al. (2012). These equations were incorporated into their collisional-evolution models. For fragment SFDs with very steep slopes, equations (5) and (6) can easily exceed the mass of the projectile and target, which is nonphysical. To avoid this problem, it is assumed that the fragment SFDs bend to shallower slopes at small sizes, although the precise diameter where this takes place is unknown; it is beyond the resolution limit of existing numerical hydrocode impact simulations. It can be shown that the derived fragment SFDs from these simulations reproduce many attributes of observed asteroid families (Durda et al., 2007). With that said, however, collisional outcomes and fragment SFDs are strongly affected by the target’s gravitational forces; this means the impact outcomes onto 400-km targets differ from those of 100-km targets in terms of Q/QD* (P.  Benavidez, personal communication). The same is probably true for smaller targets as well. Major advances in this area will therefore come from those modelers who employ fragment SFDs appropriate for their target sizes. A final interesting issue here is that analytical and numerical results suggest the final equilibrium main-belt SFD is often found to be relatively insensitive to the details of the fragmentation law (e.g., Davis et al., 2002; O’Brien and Greenberg, 2003, 2005; Bottke et al., 2005a,b; Morbidelli et al., 2009). This statement is mainly based on experience, and it needs to be better quantified by modeling work. We suggest that while the fragmentation laws used are important, many are unlikely to dramatically change the equilibrium results. On the other hand, the choice of fragment SFD for given breakups will be important for investigating asteroid families and transient perturbations to the main-belt SFD. 2.4. Dynamical Depletion of Main-Belt Asteroids by the Yarkovsky Effect As described in the chapter in this volume by Vokrouh‑ lický et al., D < 30-km asteroids in the main belt slowly drift inward toward or outward away from the Sun in semimajor

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   707

1012

Cumulative Number

axis by Yarkovsky thermal forces. This allows some of them to reach resonances with the planets that drive them onto planet-crossing orbits, thereby allowing them to escape the main-belt region altogether. Additional mobility is provided by encounters with big asteroids like (1) Ceres and (4) Vesta, although the net effect of this mechanism is fairly modest (e.g., Carruba et al., 2003, 2013). The Yarkovsky effect, working in concert with resonances, can therefore be considered a “sink” for small main-belt asteroids. Their depletion should feed back into the collisional evolution of the main belt itself (i.e., fewer smaller bodies means fewer cratering and disruption events among larger bodies). It also means that the near-Earth asteroid (NEA) population could be considered an short-lived component of the main-belt population. This allows the NEA SFD to constrain collisional and dynamical evolution within the main belt, provided the modeler understands the translation between the main belt and NEA SFDs (e.g., Morbidelli and Vokrouhlický, 2003). The challenging part of this is to quantify the nature of small-body populations lost over time via the Yarkovsky effect and resonances. Consider the following: • Every major main-belt resonance has a different character in its ability to produce long-lived nearEarth objects (NEOs) (e.g., Gladman et al., 1997; Bottke et al., 2006). • The flux of asteroids reaching dynamical resonances may change over time as a consequence of asteroid family-forming events. Large asteroid families can produce enormous numbers of fragments, while smaller ones that disrupt in strategic locations next to key “escape hatches” may also influence the planetcrossing population for some interval (Nesvorný et al., 2002). • The dynamical evolution of D < 1-km asteroids is poorly constrained because these bodies are below the observational detection limit of most surveys (e.g., Jedicke et al., 2002; see also the chapter by Jedicke et al. in this volume). Moreover, these bodies are also the most susceptible to YORP thermal torques, which can strongly affect their drift direction and evolution (see next section). So far, no one has yet attempted to model all these factors and include them into an algorithm suitable for insertion into a collisional evolution code. It is a necessary but daunting task to do this correctly, given the current state of our knowledge of how the Yarkovsky/YORP effects modify the orbits, sizes, and shapes of small asteroids. Instead, the best that has been done to date has been to generate loss rates for the asteroid belt that produce a steadystate population of NEOs (Bottke et al., 2005a; O’Brien and Greenberg, 2005; Cibulková et al., 2014) (Fig. 2). This approximation can provide interesting insights; for example, not including the Yarkovsky/resonance “sink” for small bodies may have a substantial affect on the collisional evolution of the main belt, with more projectiles left behind that can disrupt large main-belt asteroids (Cibulková et al., 2014).

NEOs from Harris et al., this volume Rabinowitz et al., 2000 (NEAT) Rabinowitz et al., 2000 (Spacewatch) Brown et al., 2013 (Bolide events) Brown et al., 2013 (Infrasound events) Upper limit for Tunguska-like events

Model Main Belt

1010 108 St

ok

106

es

et

104

al

.(

20

03

) Model NEOs

Debiased Main Belt

102 100 0.001

0.010

0.100

1.000

10.000

100.000 1000.000

Diameter D (km) Fig. 2.  The estimated present-day main belt and NEO populations according to Bottke et al. (2005b) model runs (solid lines). For reference, we plot our results against an estimate of the NEA population made by Stokes et al. (2003), who assumed the D < 1-km size distribution was a power-law extension of the D > 1-km size distribution, and a population discussed in the chapter by Harris et al. in this volume. Our model main-belt population provides a good match to the observed main belt (solid black dots). Most diameter D < 100-km bodies are fragments (or fragments of fragments) derived from a limited number of D > 100-km breakups (Bottke et al., 2005a). Our NEA model population is compared to estimates derived from telescopic surveys (Rabinowitz et al., 2000), as well as satellite and infrasound detections of bolide detonations in Earth’s atmosphere (Brown et al., 2013). For reference, we also include an upper limit estimate of 50-m NEAs based on the airblast explosion that occurred over Tunguska, Siberia, in 1908. A mismatch between the NEA model and data is seen near D ~ 0.1 km.

2.5. Asteroid Disruption by YORP Torques The Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect is a thermal torque that, complemented by a torque produced by scattered sunlight, can modify the spin vectors of small asteroids (see the chapter by Vokrouhlický et al. in this volume). As an asteroid’s obliquity evolves, its orientation can strongly affect a body’s drift rate across the main belt, and therefore how quickly it reaches a resonance that can take it out of the main belt. YORP can also spin asteroids up or down. If the body has substantial unconsolidated material, or is a rubble pile, it must reconfigure itself to adjust to its new rotational angular momentum budget. In certain cases, this can cause the body to shed mass, potentially creating a satellite or an asteroid pair. Many of the latest aspects of the YORP effect are discussed in the chapters by Vokrouhlický et al. and Walsh and Jacobson in this volume. YORP spinup may be so efficient at causing small asteroids to shed mass that this mechanism may dominate the production and elimination of bodies for D  < 1  km. This prospect is exciting, and we believe warrants continued

708   Asteroids IV investigation using a wide range of models in the future. Indeed, recent main-belt modeling work that included collisional disruption and YORP mass-shedding mechanisms show the latter could explain the shape of the main belt SFD for subkilometer- and kilometer-sized bodies (Marzari et al., 2011; Jacobson et al., 2014; see also Penco et al., 2004). The goal of main-belt collisional models is to include all the major processes that affect mass loss from small bodies — collisions, Yarkovsky-driven removal of bodies, and YORP-driven mass shedding — in a self-consistent manner. So far, the models of Bottke et al. (2005a,b) and Cibulková et al. (2014) include the first two, while the models of Marzari et al. (2011) and Jacobson et al. (2014) include the first and third. Future models will have to include all these effects in the most accurate way possible, with their relative contributions sorted out using constraints. While this sounds straightforward, in practice the modeler must deal with numerous uncertainties, as well as all the feedbacks they produce. As an example, consider the mismatch between the model and observed SFDs seen in Fig. 2. While a better fit is possible, and it should be a byproduct of the processes above, which one of them, if any, should dominate? One could argue that varying the Yarkovsky depletion rates of asteroids from the main belt should solve the problem. Unpublished test runs performed by Bottke et al. (2005a,b) have shown that the shape of the main-belt SFD for subkilometer-sized bodies can be reproduced by assuming more asteroids escape over time than previously predicted. The central problem here is that the loss rates of subkilometer-sized bodies from the main belt are highly uncertain, with the coupling between Yarkovsky drift and the frequency/nature of so-called YORP-cycles only modestly well understood at this time (e.g., Bottke et al., 2015a). Alternatively, the mismatch might be readily fixed by including YORP-driven mass shedding, as suggested by Marzari et al. (2011) and Jacobson et al. (2014). We find this highly plausible, yet there is also much we do not yet understand when it comes to the details of YORP-driven mass shedding (see the chapter by Vokrouhlický et al. in this volume). Consider that careful explorations of the YORP effect show there is a preference for asteroidal spinup vs. spindown (e.g., Rozitis and Green, 2012; Golubov and Krugly, 2012; Golubov et al., 2014; see also the chapter by Vokrouhlický et al.). With this said, however, spindown must also exist in order to explain the relatively flat spin frequency distribution of small asteroids as well as why numerous very slow rotators exist (e.g., Bottke et al., 2015a). There is also important work that shows that YORP torques are affected by small topographic changes on an asteroid. For example, Statler (2009) used numerical simulations to demonstrate that minor changes in an asteroid’s shape, such as the formation of a small crater or even the movement of a boulder from one place to another, could modify the YORP torques enough to change the magnitude and sign of the spin rate. These changes produce a random walk in an asteroid’s spin rate,

and has been coined the “stochastic YORP” effect. While more work is needed, stochastic YORP may prevent some small asteroids from undergoing mass shedding as often as predicted (Cotto-Figueroa, 2013; Cotto-Figueroa et al., 2015; Bottke et al., 2015a). This may explain why some small asteroids have shapes that suggest they have largely avoided substantial mass-shedding events. Conversely, certain bodies may return again and again to spinup-driven mass shedding, which may rapidly turn them into top-like shapes (see the chapter by Walsh and Jacobson in this volume). Probing the asteroidal shape dichotomy using numerical modeling work is an intriguing project for the future. In the end, all these Yarkovsky and YORP-related issues will need to be better explored and quantified if we are to formulate superior main-belt-evolution models in the future. 2.6. Additional Processes Some processes that affect planetesimal and planet formation have yet to be implemented into main-belt collisional evolution models. Key examples include (1) the implications of hit-and-run collisions, defined as the disruption and escape of portions of large projectiles striking still larger bodies (see the chapters by Scott et al. and Asphaug et al. in this volume); (2) planetesimal collisional evolution taking place side by side with accretion onto protoplanets/planetary embryos with all the appropriate dynamics and fragmentation events modeled correctly (e.g., Levison et al., 2015a,b); (3) the effects of collisions on the dynamical evolution of an asteroid or planetesimal; and (4)  the bombardment of main-belt asteroids by planetesimals forming and evolving within the terrestrial planet and gas giant regions (e.g., see the chapters by Morbidelli et al. and Scott et al. in this volume). Some of these processes are difficult to include in a model until their effects have been evaluated, although they are almost certainly important for particular issues [e.g., hit-and-run collisions may explain the exposed core-like nature of (16) Psyche and (212) Kleopatra; see the chapters by Asphaug et al. and Scott et al. in this volume]. For other processes, their importance is still unclear because planetformation models are incomplete and/or are lacking in key constraints (e.g., how much net collisional evolution is produced on indigenous main-belt asteroids via planetesimals from the terrestrial planet region?). We believe an exploration of processes (1)–(4) discussed above and their inclusion in future models will greatly improve the state of the art. 3. CONSTRAINTS ON COLLISIONALEVOLUTION MODELS Given the large number of “knobs” that exist in collisional-evolution models, and the fact that these codes may provide the user with non-unique solutions, it is imperative to test results against as many constraints as possible. Given the breadth of predictions for such codes, this means accounting for how individual asteroids, asteroid families, and different asteroid populations have taken on their current

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   709

status. With sufficient constraints, bad parameter choices can be eliminated from contention. On the other hand, it is important that one recognizes that our understanding of main-belt evolution is still limited, and the inclusion of faulty constraints into a code can also produce inaccurate results and poor predictions. Accordingly, most constraints should be treated with some caution, with the modeler and interpreter cognizant that both data and interpretation can and often do change with time. With these caveats, we present a list of many of the constraints that should be considered when modeling the collisional evolution of the main belt. 3.1. Wavy Main-Belt Size-Frequency Distribution One of the primary constraints for collisional-evolution models comes from the main-belt SFD. Improved estimates since the review chapter of Jedicke et al. (2002) were provided by pencil-beam studies of the main-belt population (Gladman et al., 2009), the addition of asteroids colors from the Sloan Digital Sky Survey (SDSS) (e.g., Parker et al., 2008), and new infrared data of many main-belt asteroids (see the chapters by Mainzer et al. and Masiero et al. in this volume). The inclusion of all these datasets into a single debiased SFD, however, has yet to be attempted, and it is beyond the scope of this chapter. For basic purposes, one can derive an approximate mainbelt SFD using the absolute magnitude H distribution provided by Jedicke et al. (2002), who combined results from the Sloan Digital Sky Survey (SDSS) for H > 12 (Ivezić et al., 2001) with the set of known main-belt asteroids with H < 12. To transform the H distribution into a size distribution, one can use the relationship between asteroid diameter D, absolute magnitude H, and visual geometric albedo pv provided by Fowler and Chillemi (1992)



1329 pv

10− H / 5

Asteroid families provide another powerful way to constrain asteroid collisional models. As discussed in the chapter by Nesvorný et al. in this volume, these remnants of cratering and catastrophic disruption events are identified in the main belt by their clustered values of proper semimajor axes ɑp, eccentricities ep, and inclinations ip. The problem with using them to test our model runs is that estimates of ancient family ages can be imprecise and small families can also be eliminated over time by collisional and dynamical processes. For this reason, the best starting constraints come from families where the parent body was large enough that their fragments could not be erased over 4 G.y. of evolution. We assume families formed prior to 4  G.y. ago were erased by sweeping/jumping resonances produced by late giant planet migration (see the chapter by Morbidelli et al. in this volume). Using results discussed in Durda et al. (2007) (see also Cibulková et al., 2014), there are approximately 20 observed families created by catastrophic disruptions of parent bodies with sizes DPB > 100 km, where the ratio of the largest fragment’s mass to the parent body mass is MLR/ MPB < 0.5 (Fig. 3). It is also useful to use the distribution of family parent body sizes to compare model to data. In one case, Bottke et al. (2005a,b) used results later published in Durda et al. (2007) to argue that the number of families formed over the last 3.5  G.y. from catastrophic breakups of parent bodies whose sizes were within incremental logarithmic-separated bins centered on diameters D = 123.5, 155.5, 195.7, 246.4, 310.2, and 390.5 km were 5, 5, 5, 1, 1, 1, respectively. New family identifications discussed in the chapter by Nesvorný et al. in this volume can be used to update these values. Ideally, a good collisional model must account for all types of collisions, even relatively small cratering events. For the purpose of comparison with observations, one has to carefully select synthetic events that would still be observable. Even

(8)

A model main-belt SFD was made by Bottke et al. (2005a), who set pv to 0.092 in order to match the observed asteroids described cited in Farinella and Davis (1992). This population is shown in Fig.  2. Overall, the observed and debiased main-belt SFD is wavy, with “bumps” near D ~ 3 km and one near D ~ 100 km. The reason for these bumps will be discussed in section 4. For more precise constraints, and more model variables, one can treat different regions of the main belt separately. For example, Cibulková et al. (2014) divided the main-belt population into six distinct components: inner, middle, pristine, outer, Cybele, and high-inclination regions. This allowed them to track how each different regional SFD evolved in response to various collisional and dynamical processes. The observed SFDs in each region, however, have yet to be debiased, which means they must be treated as lower limits for modeling constraints.

103

Nfamilies with DPB > D

D=

3.2. Asteroid Families

All observed families Catastrophic disruptions Broz et al. (2013)

100

10

1 10

100

1000

D (km) Fig. 3. A production function [i.e., the cumulative number N(>D) of families with parent-body size DPB larger than D] for all observed families (gray) and families corresponding to catastrophic disruptions (black), i.e., with largest remnant/ parent body mass ratio lower than 0.5. Adapted from Brož et al. (2013) and updated according to the chapter by Nesvorný et al. in this volume. The families were assumed to form prior to 4 G.y. ago (see Fig. 4).

710   Asteroids IV though this number (Nfam ~ 20) appears well defined above, it is difficult to assess its uncertainty for the following reasons: • Determining the size of the parent of an asteroid family depends on the observed fragment distribution, which has experienced collisional and dynamical evolution, and the nature of the precise breakup involved, which may be uncertain. The existence of interlopers within the family can also be hard to exclude. • There are overlapping families that are difficult to separate unambiguously [e.g., several families exist in the Nysa/Polana region (M. Dykhuis, personal communication)]. • The method used for the parent body size determination in Durda et al. (2007) may exhibit some systematic issues since it involves a number of assumptions. Taken together, the uncertainty of Nfam is at least the order of a few, if not more. The distribution of the dynamical ages and sizes of families, as derived using the methods discussed in the chapter by Nesvorný et al. in this volume, may also provide another metric to estimate family completeness. For example, Fig. 4 shows estimates of the ages of cratering and catastrophic disruption events for families derived from different parent body sizes (Brož et al., 2013). We caution the reader that discerning these values for heavily evolved ancient families is problematic, and large uncertainties exist. We therefore use Fig. 4 as a guide to glean insights into interesting possibilities, not as the last word on this topic. We focus here on asteroid families with parent body diameters DPB  > 100  km; they are presumably more difficult to eliminate by collisional and dynamical processes. For families formed over the last 2  G.y., we find several with 100 < DPB < 200 km and few with DPB > 200 km. The opposite is found for families older than 2 G.y.; only a few 100  < DPB  < 200-km families exist, while several DPB  > 200 km are found.

Young

500

Old 10

DPB (km)

400

24

221

300

87

200

137

375

158

100 0

15

3

0

0.5

1

1.5

2

709

170

2.5

3

3.5

107 121

4

Age (Ga) Fig. 4. The relationship between dynamical ages of families and the sizes of their parent bodies. Black labels, shown as x’s and numbers, correspond to catastrophic disruptions, while cratering events, shown as crosses and numbers, are labeled in gray. Some of the families are denoted by the designation of the largest member. Adapted from Brož et al. (2013) and updated according to the chapter by Nesvorný et al. in this volume.

The difference between the two sets warrants additional study, but statistics of small numbers prevents us from saying they are highly unusual. The probability that two DPB > 200-km families formed in the last 2 G.y. out of the seven identified with ages 2  G.y.) families produced by the catastrophic disruptions of DPB > 100-km bodies. The most intriguing issue here is that there are no identified DPB < 100-km families that are >2 G.y. old. This hints at the possibility that some 100  < DPB  < 200-km families older than 2 G.y. are so evolved that they escaped detection. If true, one could argue that something interesting was going on that was producing DPB > 100-km families in the billion years or so after the completion of the major dynamical depletion events >4 G.y. (see section 1 and the chapter by Morbidelli et al. in this volume.). Along these lines, one way to account for the unusual distribution of families in Fig.  4 is to assume that some small families are actually remnants, or “ghosts,” of much larger older families. A possible example might be the cluster of asteroids near asteroid (918) Itha (Brož et al., 2013). It exhibits a very shallow SFD, which could be a possible outcome of comminution and dynamical evolution by the size-dependent Yarkovsky effect. An excellent place to look for ghost families would be the narrow portion of the main belt with semimajor axis ɑ between 2.835 and 2.955 AU. This pristine zone, which is bounded by the 5:2 and 7:3 mean-motion resonances with Jupiter, has a limited background population of small asteroids. We postulate it could resemble what the primordial main belt looked like prior to the creation of many big families. An independent calibration of collisional models might also be based on very young families, namely younger (and larger) than some carefully estimated upper limit for which the respective sample is complete. Indeed, there are many examples of young families with well-determined ages: Veritas (8.3 ± 0.5) m.y. (Nesvorný et al., 2003), Karin (5.8 ± 0.2) m.y. (Nesvorný and Bottke, 2004), Lorre (1.9 ± 0.3) m.y. (Novaković et al., 2012), P/2012 F5 (Gibbs) (1.5 ± 0.1) m.y. (Novaković et al., 2014), etc. A collisional model then would have to reproduce the number of these events in the last =10 m.y. or so of the simulation. 3.3. Impact Basins on (4) Vesta (4) Vesta is one of the most unique asteroids in the main belt. Not only is it among the largest asteroids, with a diameter of 525 km, but it is also has a largely intact basaltic crust that was put in place shortly after it differentiated some 2–3 m.y. after CAIs (see the chapter by Russell et al. in this volume). Decades of groundbased observations, combined with in situ observations of Vesta by the Dawn spacecraft, have shown that the spectral signatures found in Vesta’s crust are a good match to the howardite, eucrite, and diogenite

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   711

(HED) meteorite classes (see the chapter by Russell et al.). We do not consider the impact record on Vesta prior to the formation of this crust, although Vesta’s abundance of highly siderophile elements may eventually allow us to infer what happened during this ancient period (e.g., Dale et al., 2012). Vesta also has two enormous basins that dominate its southern hemisphere: Rheasilvia, a 505-km-diameter crater with an estimated crater retention age of 1 G.y., and Venenia, a 395-km-diameter crater with a crater retention age of >2 G.y. (Marchi et al., 2012). Rheasilvia, being younger, overlaps with and has largely obscured Veneneia (Schenk et al., 2012; Jaumann et al., 2012). The formation of each basin is also thought to have produced a set of fracture-like troughs, or graben, near Vesta’s equator (Buczkowski et al., 2012). Studies of each trough group show they form planes that are orthogonal to the basin centers. Recent simulations of the formation of the Veneneia and Rhealsilvia basins using numerical hydrocodes suggest they were created by the impact of 60–70-km-diameter projectiles hitting Vesta near 5  km  s–1 (Jutzi et al., 2013; see the chapters by Asphaug et al. and Jutzi et al. in this volume). These same events likely produced the majority of the observed Vesta family, a spread out swarm of D < 10-km asteroids in the inner main belt with inclinations and spectral properties similar to Vesta itself (see the chapter by Scott et al. in this volume). Vesta shows no obvious signs that basins similar in size to Rheasilvia or Veneneia were ever erased or buried after its basaltic crust was emplaced; nothing notable is detected in Vesta’s topography, and there are no unaccounted sets of troughs that could be linked with a missing or erased basin. This means Vesta is probably complete in Rheasilvia- or Veneneia-sized basins. This constrains both the size of many primordial populations as well as how long they could have lasted on Vesta-crossing orbits (e.g., main-belt asteroids, leftover planetesimals from terrestrial and giant planet formation, the putative late heavy bombardment (LHB) population, Jupiter-family comets, etc.). As a working example, consider that if we use the mainbelt asteroid population described in Bottke et al. (1994), where there are 682 main-belt asteroids with D  > 50  km, we find that the probability that Vesta has 0, 1, 2, or 3+ Rheasilvia/Veneneia formation events over the last 4  G.y. is 50%, 35%, 12%, and 3%, respectively. If Rheasilvia and Veneneia are actually both 35-km asteroids (Asphaug et al., 1997), only increases the probabilities above by a factor of 2 or so. These calculations become even more interesting if we assume the main-belt population was larger in its early history, and/or that it was hit by objects from outside the main

belt (see the chapter by Morbidelli et al. in this volume). Bottke et al. (2005a) argued the main belt experienced the equivalent of ~7.5–9.5  G.y. of collisional evolution over the last 4.56 G.y. (i.e., roughly translated as the number of impacts Vesta would get if it resided in the current main-belt population for this time; see section 4). For simplicity, we round this value to 10 G.y., which makes the probability of getting 0, 1, 2, or 3+ basins at any time in Vesta’s history 17%, 30%, 27%, and 20%, respectively. This would place the Rheasilvia/Veneneia combination near the center of the probability distribution. If Rheasilvia/Veneneia formed 10 km) that were not in asteroid families produced by catastrophic disruption events: (22) Kalliope, (45) Eugenia, (87) Sylvia, and (762) Pulcova. Additions since that time to the SMATS record could include (216) Kleopatra and (283) Emma, whose primaries have diameters that are nearly 140  km. The secondary

Cumulative Number of Lunar Craters

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   713

Copernican + Eratosthenian

10–5

Copernican

10–6

10–7

10

100

Diameter (km) Fig. 6. Lunar craters in the Copernican and Copernican and Eratosthenian eras as defined by Wilhelms et al. (1978) and McEwen et al. (1997). The absolute ages of these craters are often considered 50–100-km bodies may still have spins that were largely put in place by the planetesimal accretion process. A review of the spin rate literature for the largest asteroids can be found in Bottke et al. (2005a). For smaller bodies, the spin rates and obliquities of D < 30–40-km asteroids are likely dominated by the effects of YORP thermal torques (e.g., Pravec et al., 2002; see the chapter by Vokrouhlický et al. in this volume). Given this, an unambiguous signal of collisions affecting spin vectors in the main belt may be limited to bodies whose evolutionary context is well understood. The interested reader can consider the spin-evolution models of Farinella et al. (1992) and Marzari et al. (2011) for their views on this topic. They should also examine results from the numerical hydrocode simulations of Love and Ahrens (1997), who argued that small erosive collisions have a minimal effect on an object’s spin, while catastrophic disruption events essentially destroy all “memory” of the target body’s initial spin. The collisional signal we are looking for, therefore, may be limited to specific remnants of certain family-forming events. An alternative way to obtain a model constraint may be found in the spin vectors of asteroids in the Koronis asteroid family. The Koronis family is thought to be one of the asteroid belt’s most ancient families, with an estimate age of 2–3 G.y. (see the chapter by Nesvorný et al. in this volume). After years of painstaking observations of Koronis family members, including 21 of the 25 brightest Koronis family members, Slivan et al. (2003, 2009), Slivan (2002), and Slivan and Molnar (2012) reported that nearly all of the observed 15–40-km-diameter Koronis family members with prograde spins have clustered spin periods between 7.5 and 9.5  h and spin obliquities between 39° and 56°. Those with retrograde spins have obliquities larger than nearly 140° with periods either 13 h. Vokrouhlický et al. (2003) demonstrated that all these spin states were a byproduct of YORP thermal torques. The prograde cluster was created by an interaction between YORP torques and spin orbit resonances, and are now called “Slivan states.”

The predicted timescales for these objects to reach these spin states is several billions of years. During that time, collisions did not strongly affect their spin periods or their obliquities; if they had, we would see at least a few bodies with random spin vector values. Limits on this come from (243) Ida, a member of the prograde cluster with dimensions of 53.6 × 24.0 × 15.2 km; it was apparently unaffected by the formation of two ~10-km-diameter craters formed on its surface. Statistically, we would expect catastrophic disruptions to be more rare than smaller, less-energetic impact events that can modify an asteroid’s spin state. In the ancient Koronis family, however, the spin vectors of many large objects show no evidence that collisions have affected them. This presents a key challenge to collisional models that assume disruption events among 20–40-km bodies are relatively common; can this outcome be reconciled with the spin states of Koronis family members? A similar argument could potentially be developed regarding the anisotropic obliquities found among D < 30-km asteroids residing in the background main-belt population (e.g., Hanus et al., 2013). 3.7. Additional Constraints The constraints discussed above are far from complete, and many other datasets could be brought to bear in a collisional model. For space reasons, we do not include a discussion of (1) the cosmic-ray-exposure ages of stony meteorites (e.g., Eugster, 2003); (2) the orbital distribution of fireballs (e.g., Morbidelli and Gladman, 1998); (3)  the population of V-type asteroids across the main belt (see the chapter by Scott et al. in this volume); (4) the crater records found on Mercury, Venus, Earth, and Mars (e.g., Ivanov et al., 2002); (5) all asteroid families not discussed here (see the chapter by Nesvorný et al. in this volume); and (6) the shock degassing ages of meteorites (e.g., Marchi et al., 2013). In fact, the subject of collisional evolution in the main belt is rich enough that data from numerous Asteroids IV chapters could probably be employed as well. 4. INSIGHTS FROM MODELING RESULTS Existing collisional modeling work has provided us with insights into the nature of planetesimal formation, asteroid fragmentation and evolution, planet-formation processes, and the bombardment history of the inner solar system. Here we summarize some of those findings. 4.1. The Relationship Between the Main-Belt Size-Frequency Distribution and Asteroid Disruption Scaling Laws The bump in the main-belt SFD near D ~ 2–3 km (Fig. 2) is a byproduct of collisional evolution (Campo Bagatin et al., 1994; see Davis et al., 2002), and is driven by a change in the QD* function near D  ~ 0.2  km. To trace its origin, we start with the classic work of Dohnanyi (1969) (later

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   715

expanded by Williams and Wetherill, 1994, and Tanaka et al., 1996), who analytically modeled collisions among a SFD of self-similar bodies and found the steady-state SFD should follow a differential power law with an exponent of –3.5. Dohnanyi assumed that the strength per unit mass of the colliding bodies is independent of size. In reality, though, for bodies smaller than ~0.2 km in diameter, material properties cause strength to decrease with increasing size, while for larger bodies, self-gravity makes it more difficult to shatter a body and disperse its fragments, leading to an increase in strength with increasing size (e.g., Asphaug et al., 2002; Holsapple et al., 2002; Davis et al., 2002). This provides us with the classic QD* function discussed above. The dependence of the power-law index of the size distribution on these parameters was explored analytically by O’Brien and Greenberg (2003), and we repeat the main results here. First consider the steady-state of a colliding population of bodies whose strength is described by a single power law. The population is described by the power law

dN = BD − p dD

(9)

where dN is the incremental number of bodies in the interval (D, D + dD). While B should technically be negative as there are more small bodies than large bodies, it is defined to be positive here to avoid the physically unrealistic result of having negative numbers of bodies in a given size interval. p is the power-law index of the population. Equation  (9) would plot as a line with a slope of –p on a log-log plot. O’Brien and Greenberg (2003) considered the case where the impact strength QD* is given by a power law

Q D* = Qo Ds

(10)

where Q0 is a normalization constant and s is the slope of equation (10) on a log-log plot. They find that, in collisional equilibrium, the power-law index p in equation (9) is given by



p=

7+s 3 2+s 3



(11)

For s = 0, which corresponds to size-independent strength QD* , this gives the classical Dohnanyi steady-state solution of p = 3.5. For the more realistic case where QD* decreases with increasing size for small bodies and increases for larger bodies once gravity becomes important (as schematically shown in Fig.  1), O’Brien and Greenberg (2003) show that the strength- and gravity-scaled portions of the size distribution have power-law indices ps and pg that are only dependent on the slope of QD* in the strength and gravityscaled regimes ss and sg, respectively. The power-law index of the size distribution in the strength-scaled regime ps has no dependence on the slope sg of QD* in the gravity-scaled regime, and vice versa; ps is found by using ss, and pg is found by using sg. Because ss is usually negative and sg is usually positive, equation (11) yields ps > 3.5 and pg < 3.5. While the general slope of the size distribution in the gravity regime is unaffected by QD* in the strength regime,

the transition in slope of the size distribution will lead to waves that propagate through the size distribution in the gravity regime. In the derivation of pg, it is implicitly assumed that all asteroids were disrupted by projectiles whose numbers were described by the same power law. However, for those targets just larger than the transition diameter Dt between the strength- and gravity-scaled regimes (i.e., near the small end of the gravity-scaled regime), projectiles are mostly smaller than Dt, and hence are governed by the strength-scaled size distribution. As these projectiles will be stronger and hence more numerous than would be expected by assuming that all bodies are gravity-scaled, they will lead to a depletion of bodies of diameter Dt. This underabundance of bodies of diameter Dt (a “valley”) leads to an overabundance of bodies that impactors of diameter Dt are capable of destroying (a “peak”), which in turn leads to another “valley” and so on. This results in a wave that propagates through the large-body size distribution, as can be seen in Fig. 2. The average power-law index pg of the population in the gravity-scaled regime will not be significantly changed by the initiation of this wave; the wave oscillates about a power law of slope pg. Analytical expressions for the amplitude of the waves, as well as the approximate positions of the “peaks” and “valleys” in the size distribution, are derived in O’Brien and Greenberg (2003). The waves will not continue on to larger bodies if they have long collisonal lifetimes. The origin of the bump for D > 100-km bodies is discussed in the next section. Finally, we note that removing all small bodies instantaneously from the population (i.e., creating a small body cutoff) can also launch a wave into the size-frequency distribution (Campo-Bagatin et al., 1994; Penco et al., 2004). The effect is minimized, however, if removal is more gradual. This was demonstrated by both O’Brien (2009), who found the depletion expected from Yarkovsky removal is too small to significantly perturb the main-belt size distribution (section 2.4), and by Durda et al. (1997), who found the same result when they modeled the expected dust distribution created by the main belt collisions and Poynting-Robertson drag. 4.2. Large Asteroids as Byproducts of Planetesimal Formation One of the most difficult issues to deal with concerning main-belt evolution is estimating the initial SFD created by planetesimal formation mechanisms. Given the current uncertainties surrounding planet formation, a enormous range of starting SFDs are theoretically plausible. This has caused many groups to winnow these possibilities down using collisional models. For example, Bottke et al. (2005a,b) tested a wide range of initial SFDs and QD* functions to determine which combinations work the best at reproducing the observational constraints discussed in section  3. They found that Q*D functions similar to those derived in numerical SPH experiments of asteroid breakup events (Benz and Asphaug, 1999)

716   Asteroids IV tended to work the best (Fig.  1), although this made their D > 100-km asteroids very difficult to disrupt. Accordingly, they inferred that the shape of the main-belt SFD for D > 100-km asteroids was probably close to its primordial shape (Fig. 2). Interestingly, this prediction is consistent with several pioneering papers from the 1950s and 1960s (Kuiper et al., 1958; Anders, 1965; Hartmann and Hartmann, 1968). Next, they tested initial main-belt SFDs where the incremental power law slope of –4.5 between 100  < D  < 200 km had been extended to D < 100-km bodies (Fig. 7). This eliminated the observed bump near D ~ 100 km. They found bodies in this size range were so difficult to disrupt that initial SFDs with these shapes could not reproduce constraints. They argued from this that the bump near 100  km in the main-belt SFD is primordial and that D  < 100-km bodies probably had a shallow power law slope. Accordingly, this would indicate the planetesimal-formation process favors the creation of bodies near 100 km (or larger), with smaller bodies increasingly fragments produced by the disruption of large asteroids. These results may act as a guide for those studying planetesimal-formation processes (e.g., Morbidelli et al., 2009; see the chapter by Johansen et al. in this volume). 4.3. Collisional Evolution of the Primordial Main Belt To understand the history of the main belt, it is important to quantify how much collisional evolution has taken place there over its history. This means choosing a starting SFD and then evaluating what it takes to reach its present-day

106 Debiased Main Belt DX = 120 km DX = 110 km DX = 100 km

Incremental Number

105 104 103 102 101 100

1

10

100

1000

Diameter (km) Fig. 7. The debiased main-belt size-frequency distribution as defined in the main text (solid line). The dashed curves show possible initial shapes of the primordial main belt SFD (Bottke et al., 2005a). They found a best fit in their runs for an elbow near DX ~ 110–120 km. It is likely that the primordial population was larger than the SFDs shown here, with most of the mass eliminated by dynamical processes.

state. The problem is there are many different ways to get from start to finish, and the available constraints may be insufficient to tell us which pathways are favored. In order to glean insights into this, one can adopt a sim‑ plistic but useful metric that can help us evaluate what different evolutionary paths might do. First, let us assume that the main belt is roughly self-contained in terms of collisions, such that we can largely ignore impacts from external sources like escaped main-belt asteroids, leftover planetesimals, comets, etc. Second, we assume the intrinsic collision probabilities and impact velocities of main-belt asteroids hitting one another have remained unchanged over its history. Third, we assume the main belt’s SFD has been close to its current shape throughout its history, although it may have been larger in the past. We define this size to be a factor fMB, the ratio of the main belt’s SFD during some past interval of time defined as DT over the present-day main-belt SFD. Together, these values allow us to estimate the degree of collisional evolution experienced by the main belt in terms of the time exposed to different population sizes. This metric allows to play with evolution scenarios. The simplest example is the nominal case where the current main-belt SFD (fMB  = 1) undergoes collisional evolution over its lifetime (DT = 4.56 G.y.). The two values multiplied together yield 4.56  G.y. of collisional grinding. In a more complicated example, we assume a dynamically excited primordial main belt had f  = 300 for 3  m.y. (0.003  G.y.). At that point, most of the population was lost via escaping embryos or a migrating Jupiter, which reduced it to fMB ~ 5 for ~0.5 G.y. Then, at ~4 G.y., 80% of the bodies were lost via sweeping resonances driven by late giant planet migration, which left the surviving population close to its current state (f = 1) for the next ~4 G.y. Taking all of the multiples, one can say that collectively the survivors experienced (0.9 + 2.5 + 4) = 7.4 G.y. of collisional evolution. This pseudo-time tells us that this main belt roughly experienced the collisional evolution equivalent of a fMB = 1 main belt going through 7.4 G.y. of comminution. Using a collisional model that took advantage of these concepts, as well as the constraints above, Bottke et al. (2005a) found median pseudo-times of 7.5–9.5  G.y. for their best-fit runs, with error bars of a few million years on each end of this range. An example of one of their runs is shown in Fig. 8. Their interpretation was that the main-belt SFD obtained its wavy shape by going through an early time interval where the main-belt survivors were exposed to many more projectiles than are observed today, with most of those bodies due lost to dynamical processes. Thus, the wavy main-belt SFD could be considered a “fossil” produced in part by early collisional evolution in the primordial main belt. This pseudo-time range above can be used to explore dynamical-evolution scenarios, particularly those that create abundant main-belt populations. For example, using our simple metric, one could replace the middle component, which roughly corresponds to the the “Jumping Jupiter” version of the Nice model (Morbidelli et al., 2010; Marchi et al., 2013; see also Nesvorný, 2011; Nesvorný and Morbidelli, 2012),

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   717

with the original Nice model, where fMB ~ 20 for ~0.5 G.y. (Gomes et al., 2005). This change yields (0.9  + 10  + 4)  = 14.9  G.y., a pseudo-time outside the favored range. While it cannot be ruled out statistically, it does suggest that collisional evolution needs to be explored in greater depth here. Another interesting property of Fig.  8 is that once it achieves the shape of the current main belt’s SFD, it tends to keep that shape for an extended time. This would explain why the main-belt SFD could remain in a near-steady-state condition for billions of years. While it would be constantly changing and losing bodies by collisional, dynamical, and

Time = 0 G.y.

Time = 0.5 G.y.

106 Current Main Belt

104 102 Start Pop. (IP at D =

120 km)

Incremental Number

100 Time = 2.5 G.y.

Time = 8.0 G.y.

Time = 15.5 G.y.

Time = 37.2 G.y.

106

104 102 100

106

104 102 100 0.1

1.0

10.0

100.0

0.1

1.0

10.0

100.0

Diameter D (km) Fig. 8. Six snapshots from a representative run where Bottke et al. (2005a) tracked the collisional evolution of the main-belt size distribution for a pseudo-time of 50 G.y. This run uses a starting population with Dx = 120 km. The bump near D  ~ 120 km is a leftover from accretion, while the bump at smaller sizes is driven by the transition at D ~ 0.2  km between strength and gravity scaling regimes in QD* . The model main belt achieves the same approximate shape as the observed population at tpseudo  = 9.25  G.y. (not shown). The model closely adheres to the observed population for many gigayears after this time. Eventually, comminution eliminates enough D > 200-km bodies that the model diverges from the observed population.

YORP spinup processes, it would also be steadily replenished by new large breakup events. This means the vast majority of disruption events produce too few fragments to push the main-belt SFD out of equilibrium for very long. This result also explains why the nonsaturated crater populations on Gaspra, Vesta (i.e., the Marcia and Rheasilvia terrains), and the Moon appear to have been hit by a projectile population with a similarly shaped SFD for an extended period (see section 3.4). 4.4. Processes Affecting Small Asteroids A comparison between the model predictions of Bottke et al. (2005b) and the observed NEO population discussed in the chapter in this volume by Harris et al. (Fig.  2) is intriguing for a different reason (see also O’Brien and Greenberg, 2005). The model does a reasonable job of fitting the observed data for small and larger NEOs, but there is a distinct mismatch near D ~ 0.1 km. The same kind of discrepancy is found between the model main belt and small craters on Vesta at the same approximate location when the craters are scaled back to projectiles (see chapter by Marchi et al. in this volume) (Fig. 5). This difference suggests the model may be missing something (see section 2.5): 1. YORP spinup torques produce such efficient mass shedding as asteroids sizes approach D ~ 0.1 km that they can influence the shape of the main-belt SFD (Marzari et al., 2011; Jacobson et al., 2014). This same mechanism, however, would need to shut off for D < 0.1 km. The reason why YORP mass shedding approaches termination is unknown, but we can think of several possibilities: (i) the physical nature and/or internal structure of small asteroids may be different from large asteroids, with smaller bodies less likely to be rubble-piles; (ii) small asteroids may be more susceptible to being held together by non-gravitational cohesive forces; or (iii) the thermal properties of the small asteroids are different than those of large asteroids and/or small asteroids become isothermal enough that the YORP mass shedding is less pronounced. 2. The Yarkovsky effect is more efficient at delivering small main belt asteroids to resonances than predicted by Bottke et al. (2005b). As more D ~ 0.1 km objects are evacuated from the main-belt population, a steady-state deficit of small bodies may be created in of both the main belt and NEO populations near this size. The reason for this increased delivery efficiency may be related to the YORP shut down discussed above. If YORP becomes less efficient, bodies may become less likely to experience YORP cycles that can cause them to random walk in semimajor axis. In turn, this would enhance their escape rate out of the main belt. These possibilities illustrate the importance of understanding all the physical processes that affect small bodies in the inner solar system; they feed back in interesting ways, and they may ultimately affect how we interpret the ages of surfaces on both asteroids and the terrestrial planets. We look forward to seeing this investigated in the future.

718   Asteroids IV 4.5. Monolithic vs. Rubble-Pile Structures

quickly destroyed on a ~100-m.y. timescale. This is consistent with the main belt staying close to an equilibrium state. Finally, even at the current limit of observational completeness (3 to 6  km, depending on the main belt zone), the frequency of collisions becomes comparable to the dynamical removal of bodies by the Yarkovsky effect and major mean-motion resonances (Bottke et al., 2005a,b) or rotational disruption induced by the YORP effect (Jacobsen et al., 2014). Regarding the former effect, removal rates used by Bottke et al. (2005b) or those in Cibulková et al. (2014) seem to be compatible with observations, namely the observed SFDs of main-belt asteroids and NEAs. The same may also be true for the latter process, although this will need to be examined in greater detail with the implications of Statler (2009) included. At this time, it is not clear which process dominates.

Recent collisional modeling work by Cibulková et al. (2014) has also taken a more sophisticated look at the evolution of six different main-belt regions (Fig. 9): inner, middle, “pristine,” outer, Cybele zone, and high inclination. Their goal was to fit the SFDs and asteroid families formed in all these zones. The observed SFDs in these regions were computed from the available WISE satellite data (Masiero et al., 2011; see the chapter by Mainzer et al. in this volume). They also assumed the bodies were either monolithic asteroids or rubble piles, with the fragment SFDs derived from Durda et al. (2007) and Benavidez et al. (2012), respectively. Their model also allows for dynamical depletion due to the Yarkovsky effect. Cibulková et al. (2014) found a number of intriguing results. First, treating all asteroids as weak rubble piles as defined by Benavidez et al. (2012) led to SFDs that are too shallow below D  < 10  km, as well as a factor of 2 more large families produced than are observed. This does not necessarily mean that asteroids are not rubble piles; an alternative would be that their disruption law is close to that derived for monolithic objects. New models of how porous rubble-pile asteroids break up suggest this may be the most likely answer (see the chapter by Jutzi et al. in this volume). Second, Cibulková et al. (2014) also found that individual breakups are unlikely to change the SFDs of the regions they investigated because small fragments, while numerous, were

Number of Asteroids (N (>D)

104

10

10 100 10 1

1

10

100

1000

Diameter D (km) Outer Belt

106

Observed Initial Evolved

105 104 103

10 100

3

10 1

1

10

100

Diameter D (km) Cybele Zone

106

Observed Initial Evolved

105 104 103

10

104

1000

103 100 10 1

104

10

10

1

Diameter D (km)

10

100

Diameter D (km)

1000

1000

103

1

1

100

Observed Initial Evolved

105

10 1000

10

High-Inclination Region

106

100

100

1

Diameter D (km)

100

10

Observed Initial Evolved

5

100

1

Pristine Zone

106

Observed Initial Evolved

5

104

3

Number of Asteroids (N (>D)

10

Middle Belt

106

Observed Initial Evolved

5

One of the most perplexing issues involving meteorite delivery concerns the fact that we currently have many tens of thousands of meteorites in worldwide collections, yet this population could represent as few as ~100 different asteroid parent bodies: ~27 chondritic, ~2 primitive achondritic, ~6 differentiated achondritic, ~4 stony-iron, ~10 iron groups, and ~50 ungrouped irons (e.g., Burbine et al., 2002). If we remove the stony-iron, iron, and differentiated meteorites,

Number of Asteroids (N (>D)

Inner Belt

106

4.6. Connections Between Asteroid Families and Meteorites

1

1

10

100

1000

Diameter D (km)

Fig. 9. Observed size-frequency distributions (gray lines) for six parts of the main belt compared to simulated initial (dashed) and final SFDs (black), after 4  G.y. of collisional evolution. This particular simulation shows the best-fit model out of more than 200,000 models started with various initial conditions. We assumed the scaling law of Benz and Asphaug (1999) and a monolithic structure of bodies. The largest differences can be seen for the inner and outer belt; they can be attributed to a dynamical removal of small bodies (D < 0.1 km) caused by the Yarkovsky effect, which then cannot serve as projectiles for larger bodies (=1 km). Note that it is not easy to improve these results (e.g., by increasing the normalization of the outer belt; this would feed back and affect the other subpopulations). Figure adapted from Cibulková et al. (2014).

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   719

this number is reduced to as few as ~30 parent bodies. This large difference in numbers is even more puzzling given current meteorite delivery scenarios, where nearly any small main-belt fragment can potentially reach a resonance capable of taking it into the terrestrial planet region via the Yarkovsky effect (see the chapter by Vokrouhlický et al. in this volume). Presumably, this would suggest that our meteorite collections should have samples from thousands upon thousands of distinct parent bodies. An important missing component here is information on how collisional evolution has shaped meteorite delivery in the asteroid belt. Using the models discussed above, it is useful to apply what we have learned to the issue of stony meteoroid production, evolution, and delivery to Earth. First, one can consider what happens when a body undergoes a cratering or catastrophic disruption event. A fragment SFD is created ranging from meteoroid-sized bodies all the way to multi-kilometer-sized asteroids (or more). Subsequent collisions onto bodies in the SFD act as a source for new meteoroids that are genetically the same as those created in the previous generation. This collisional cascade guarantees that some meteoroids from this family, representing a single parent body, will be provided to the main-belt population, resonances, and possibly to Earth for an extended interval. At the same time, dynamical processes and collisions onto the newly created meteoroids act as a sink to eliminate them from the main belt. An example of this process is shown in Fig. 10. It shows what happens when fragment SFDs produced by D  = 30km and 100-km parent bodies are placed in the main belt

D = 30-km Parent Body

1012

D = 100-km Parent Body

1010

ol

Ev d

ve

108

m

Fa

l tia

.6

lF ily

0.100

y.)

y.)

G.

G.

.5

(1

6

) .y.

. (4

5G

am

(1.

ily m 0.010

itia

) .y.

ly

Fa

100 0.001

In

G

mi

d

102

Currrent Main Belt

(4

Currrent Main Belt

Fa

lve 104

ily

Ini

106

o Ev

Incremental Number

~3.1 G.y. ago. For fragments derived from the 30-km body, the initial meteoroid population (i.e., the population of meter-sized bodies) drops by a factor of 100 and 105 within 130 m.y. and within 3.1 G.y., respectively. Thus, meteoroid production by D  < 30-km parent bodies decays away so quickly that breakup events of this size from billions of years ago are unlikely to deliver meaningful numbers of meteoroids to Earth today. For the 100-km parent body, the decay rate is significantly slower, with the meteoroid population only dropping by a factor of 100 over 2–3 G.y. This suggests that many meteoroids reaching Earth today could come from prominent asteroid families with sizable SFDs, even if those families were created billions of years ago. Bottke et al. (2005c) used these ideas to estimate how many stony meteorite classes should be in our collection. They did this by computing the meteoroid decay rates taken from different parent body sizes (Fig.  11) and combining them with the estimated production rates of asteroid families over the last ~4 G.y. This calculation made many simplifying assumptions: (1) meteoroids from all parts of the main belt have an equal chance of reaching Earth, (2) all D > 30-km asteroids disrupted over the last several billion years have the capability of producing a distinct class of meteorites, and (3)  once a family’s meteoroid production rate drops by a factor of 100, an arbitrary choice, it was unlikely to produce enough terrestrial meteorites to be noticed in our collection. They found that asteroid families produced by the breakup of D > 100-km bodies have such slow meteoroid decay rates that most should be providing some meteoroids today, regardless of their disruption time over the last 3 G.y. Among the

1.000 10.000 100.000 0.001

0.010

0.100

1.000 10.000 100.000

Diameter D (km) Fig. 10. The collisional and dynamical evolution of two asteroid families with simple fragment SFDs produced by the disruption of D = 30- and 100-km parent bodies (Bottke et al., 2005c). Both were inserted into the collision evolution model at 1.5 G.y. after solar system formation. The meteoroid population is represented by the number of bodies in the D ~ 0.001-km size bin. The solid lines show the families at present (4.6 G.y.). The smaller family has decayed significantly more than the larger family. Note the shallow slope of the D = 100-km family for 0.7 < D < 5 km. This shape mimics that of the background main-belt population over the same size range.

720   Asteroids IV

4.7. Cometary Impacts on Main-Belt Asteroids During the Late Heavy Bombardment

Meteoroid Fraction Left in Main Belt

An interesting quandary comes from the predicted bombardment of comets on main-belt asteroids during the Nice model (see the chapter by Morbidelli et al. in this volume). Ac-

100 10

D = 98 km D = 77 km D = 61 km D = 49 km D = 39 km D = 31 km

–1

10–2 10–3 10–4 10

–5

10–6

0

500

1000

1500

2000

2500

3000

Time from Family-Forming Event (m.y.) Fig. 11. Decay rates of meteoroid populations from asteroid families with simple power-law fragment SFD produced from parent bodies between 30 < D < 100 km. All families were inserted in the collisional model at 3.1 G.y. ago. The meteoroid population in the smallest families decrease by a factor of 100 over a few 0.1  G.y. while the largest take several gigayears to decay by the same factor.

cording to Brož et al. (2013), a massive 25 M⊕ disk of trans‑ neptunian comets might contain 1012 D  > 1-km comets. Using numerical simulations of Vokrouhlický et al. (2008), they estimated the collision probabilities and impact velocities for a comet hitting main-belt asteroids to be Pi  ~6  × 10–18 km–2 yr–1 and Vimp ~ 10 km s–1. Coupled with models describing the loss of asteroids during resonance sweeping (Minton and Malhotra, 2010), they estimated that the LHB could potentially disrupt more than 100 parent bodies with DPB  > 100  km, depending on the assumptions made (Fig. 12). These values would violate many of the constraints provided in section 3, and they present an intriguing challenge to the main tenets of the Nice model. One option here would be to reject the Nice model altogether, although this would also mean giving up the successes it has had in explaining various solar system attributes (see the chapter by Morbidelli et al. in this volume). The other possibility is that there are aspects of the Nice model or our collision models that need revision. For example, the disk of transneptunian comets may have different initial conditions and/or evolution properties than have been previously assumed, such that the collision probabilities between comets and asteroids are lower than expected (D. Nesvorný, personal communication). It is also possible that numerous transneptunian comets disrupt when they enter the inner solar system (e.g., Levison et al., 2001), with possible mechanisms being volatile pressure buildup, amorphous/ crystalline phase transitions, spinup by jets, etc. Brož et al. (2013) examined this possibility by arbitrarily assuming that all comets disrupt at perihelion distance, qcrit < 1.5 AU. On average, this led to the correct number of catastrophic disruptions for DPB = 200–400-km bodies, but it still proProduction Function Nfamilies with DPB > D

smaller parent bodies (30  < D  < 100  km), they found that, on average, the interval between disruption events across the main belt was short enough that many have disrupted over the last billion years or so, enough to provide some meteoroids as well. They did not examine large cratering events, such as the Rheasilvia formation event on Vesta, but presumably they would factor into this as well, with the biggest events acting like the disruption of a sizable parent body. Overall, they found that stony meteorites were plausibly coming from ~45 different parent bodies. This value is fairly close to the actual value of ~30 parent bodies. A few reasons that the model estimate may be on the high side include (1) some disruption events must occur within existing families, so no unique meteorite class would be created; (2) some outer main-belt meteoroids may have great difficulty reaching Earth because they only have access to resonances that are orders of magnitude less efficient at delivering meteoroids to Earth than inner-main-belt resonances (Gladman et al., 1997; Bottke et al., 2006); and (3) we have not factored in the different fragment SFD actual families can have. We conclude that most stony meteorites are byproducts of a collisional cascade, with some coming from asteroid families produced by the breakup of D > 100-km bodies over the last several billion years and the remainder coming from smaller, more recent breakup events among D  < 100-km asteroids that occurred over recent times (i.e., =1 G.y.).

104

Synthetic families with DLF > 10 km and LF/PB < 0.5 Observed families without craterings

103

100

10

1 10

100

1000

Diameter (km)

Fig. 12. The outcomes of the bombardment of the main asteroid belt by transneptunian comets, as modeled by Brož et al. (2013). The plot shows the family production functions [i.e., the cumulative number Nfam(>D) of families with parent-body size DPB larger than D] and a comparison to the observed one. Here we show 100 individual simulations (differing only by random-seed values) using different grayscale colors.

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   721

duced a factor of 2–3 more disruptions for DPB = 100-km bodies than observed. It is possible that this excess could be removed by subsequent collisional and dynamical evolution. All these values assume, of course, that collisions between low-density porous comets and asteroids are understood, when in reality no hydrocode simulations have ever been run using this set up. Finally, it could be that the main belt can accommodate more early collisions than predicted here. The constraints we have on the early era are extremely limited. All these topics remain exciting areas for future research. 5. CONCLUSIONS Considerable progress has been made over the last several decades in interpreting how the main belt reached its current state by collisional and dynamical evolution, but there is still much work to do. At this time, no model has yet included all the important processes affecting asteroid evolution. Even after this accomplished, these models will still have to be successfully tested against all the known constraints, including new ones that are discussed in other chapters. Still, it is fair to say that many existing models have done a good job of matching the constraints discussed in section 3, and their predictions have made it possible to glean insights into how the main-belt population reached its current state (see section 4). We expect that major advances will also come from the inclusion of new and better constraints that can help modelers rule out solutions. A few of the entries on our wish list for new data, beyond advances in the fields of planetesimal and planet formation, include (1) increased information on the main-belt population for D  < 1-km bodies (e.g., albedos, colors, spectroscopy, sizes, etc.); (2)  a substantiated chronology for lunar and terrestrial crater populations, with crater SFD information verified for a wide range of surface ages; (3) a thorough examination of the main belt for ghost families; (4)  more information on small asteroids that enable better predictions of Yarkovsky drift rates and YORP torques for D < 1-km asteroids; (5) additional nonsaturated crater SFDs from asteroid surfaces; (6) more discoveries of very young families, enough that we convince ourselves we have a complete set for a given time period. In regard to modeling work, the next major steps forward will probably come from next-generation codes that can track how asteroid populations move across the main belt via Yarkovsky/YORP forces while also undergoing comminution and YORP-driven mass shedding. This would allow the collisional cascade in the main belt to be treated as accurately as possible, from disruption all the way to the fragments reaching resonances. Additional information on asteroid collisions at all sizes from numerical hydrocode simulations would be extremely useful, as would laboratory and numerical experiments completed on a wide range of asteroid compositions and internal structures. This would allow new codes to accurately account for the varying QD* functions and fragment SFDs that asteroid families of different composition might have.

Finally, it is imperative that collisional models employ the best estimates of how the main-belt and external small-body populations have dynamically evolved with time. The history of our solar system is etched into the main-belt population in enumerable ways, and the only way to read these markings and tell the story of our home is to unite models of collisional and dynamical evolution from the formation of the first solids all the way to the present day. Acknowledgments. We thank reviewers E. Asphaug and F. Marzari for their helpful and constructive comments. Research funds for W.F.B. and S.M. were provided by NASA’s Solar System Evolution Research Virtual Institute (SSERVI) as part of the Institute for the Science of Exploration Targets (ISET) at the Southwest Research Institute (NASA grant no. NNA14AB03A). The work of M.B. was supported by the Czech Grant Agency (grant no. P209-12-01308S).

REFERENCES Anders E. (1965) Fragmentation history of asteroids. Icarus, 4, 399–408. Asphaug E. (1997) Impact origin of the Vesta family. Meteoritics & Planet. Sci., 32, 965–980. Asphaug E., Ryan E. V., and Zuber M. T. (2002) Asteriod interiors. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 463–484. Univ. of Arizona, Tucson. Ballouz R.-L., Richardson D. C., Michel P., and Schwartz S. R. (2014) Rotation-dependent catastrophic disruption of gravitational aggregates. Astrophys. J., 789, 158. Benavidez P. G., Durda D. D., Enke B. L., Bottke W. F., Nesvorný D., Richardson D. C., Asphaug E., and Merline W. J. (2012) A comparison between rubble-pile and monolithic targets in impact simulations: Application to asteroid satellites and family size distributions. Icarus, 219, 57–76. Benz W. and Asphaug E. (1999) Catastrophic disruptions revisited. Icarus, 142, 5–20. Bottke W. F. and Chapman C. R. (2006) Determining the main belt size distribution using asteroid crater records and crater saturation models. Lunar Planet. Sci. XXXVII, Abstract #1349. Lunar and Planetary Institute, Houston. Bottke W. F., Nolan M. C., Greenberg R., and Kolvoord R. A. (1994) Velocity distributions among colliding asteroids. Icarus, 107, 255–268. Bottke W. F., Durda D. D., Nesvorný D., Jedicke R., Morbidelli A., Vokrouhlický D., and Levison H. (2005a) The fossilized size distribution of the main asteroid belt. Icarus, 175, 111–140. Bottke W. F., Durda D. D., Nesvorný D., Jedicke R.,Morbidelli A., Vokrouhlický D., and Levison H. F. (2005b) Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion. Icarus, 179, 63–94. Bottke W. F., Durda D. D., Nesvorný D., Jedicke R., Morbidelli A., Vokrouhlický D., and Levison H. F. (2005c) The origin and evolution of stony meteorites. In Dynamics of Populations of Planetary Systems (Z. Knežević and A. Milani, eds.), pp. 357–374. Cambridge Univ., Cambridge. Bottke W. F., Nesvorný D., Grimm R. E., Morbidelli A., and O’Brien D. P. (2006) Iron meteorites as remnants of planetesimals formed in the terrestrial planet region. Nature, 439, 821–824. Bottke W. F., Levison H. F., Nesvorný D., and Dones L. (2007) Can planetesimals left over from terrestrial planet formation produce the lunar late heavy bombardment? Icarus, 190, 203–223. Bottke W. F., Vokrouhlický D., Minton D., Nesvorný D., Morbidelli A., Brasser R., Simonson B., and Levison H. F. (2012) An Archaean heavy bombardment from a destabilized extension of the asteroid belt. Nature, 485, 78–81. Bottke W. F. et al. (2015a) In search of the source of asteroid (101955) Bennu: Applications of the stochastic YORP model. Icarus, 247, 191–271. Bottke W. F., Vokrouhlický D., Marchi S., Swindle T., Scott E. R. D., Weirich J., and Levison H. (2015b) Dating the Moon-forming impact event with asteroidal meteorites. Science, 348, 321–323.

722   Asteroids IV Brasser R., Morbidelli A., Gomes R., Tsiganis K., and Levison H. F. (2009) Constructing the secular architecture of the solar system II: The terrestrial planets. Astron. Astrophys., 507, 1053–1065. Britt D. T., Yeomans D., Housen K., and Consolmagno G. (2002) Asteroid density, porosity, and structure. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 485–500. Univ. of Arizona, Tucson. Brown P. G., et al. (2013) A 500-kiloton airburst over Chelyabinsk and an enhanced hazard from small impactors. Nature, 503, 238–241. Brož M., Morbidelli A., Bottke W. F., Rozehnal J., Vokrouhlický D., and Nesvorný D. (2013) Constraining the cometary flux through the asteroid belt during the late heavy bombardment. Astron. Astrophys., 551, A117. Buczkowski D. L. et al. (2012) Large-scale troughs on Vesta: A signature of planetary tectonics. Geophys. Res. Lett., 39, L18205. Burbine T. H., McCoy T. J., Meibom A., Gladman B., and Keil K. (2002) Meteoritic parent bodies: Their number and identification. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 653–667. Univ. of Arizona, Tucson. Carruba V., Burns J. A., Bottke W., and Nesvorný D. (2003) Orbital evolution of the Gefion and Adeona asteroid families: Close encounters with massive asteroids and the Yarkovsky effect. Icarus, 162, 308–327. Carruba V., Huaman M., Domingos R. C., and Roig F. (2013) Chaotic diffusion caused by close encounters with several massive asteroids. II. The regions of (10) Hygiea, (2) Pallas, and (31) Euphrosyne. Astron. Astrophys., 550, A85. Campo Bagatin A., Cellino A., Davis D. R., Farinella P., and Paolicchi P. (1994) Wavy size distributions for collisional systems with a small-size cutoff. Planet. Space Sci., 42, 1079–1092. Campo Bagatin A., Petit J.-M., and Farinella P. (2001) How many rubble piles are in the asteroid belt? Icarus, 149, 198–209. Cibulková H., Brož M., and Benavidez P. G. (2014) A six-part collisional model of the main asteroid belt. Icarus, 241, 358–372. Cotto-Figueroa D. (2013) Radiation recoil effects on the dynamical evolution of asteroids. Ph.D. thesis, Ohio University, Athens, Ohio. Cotto-Figueroa D., Statler T. S., Richardson D. C., and Tanga P. (2015) Coupled spin and shape evolution of small rubble-pile asteroids: Self-limitation of the YORP effect. Astrophys. J., 803, 25. Chambers J. E. and Wetherill G. W. (1998) Making the terrestrial planets: N-body integrations of planetary embryos in three dimensions. Icarus, 136, 304–327. Chambers J. E. and Wetherill G. W. (2001) Planets in the asteroid belt. Meteoritics & Planet. Sci., 36, 381–399. Dale C. W., Burton K. W., Greenwood R. C., Gannoun A., Wade J., Wood B. J., and Pearson D. G. (2012) Late accretion on the earliest planetesimals revealed by the highly siderophile elements. Science, 336, 72–75. Davison T. M., O’Brien D. P., Ciesla F. J., and Collins G. S. (2013) The early impact histories of meteorite parent bodies. Meteoritics & Planet. Sci., 48, 1894–1918. Davis D. R., Chapman C. R., Greenberg R., Weidenschilling S. J., and Harris A. W. (1979) Collisional evolution of asteroids — populations, rotations, and velocities. In Asteroids (T. Gehrels, ed.), pp. 528–557. Univ. of Arizona, Tucson. Davis D. R., Chapman C. R., Weidenschilling S. J., and Greenberg R. (1985) Collisional history of asteroids: Evidence from Vesta and the Hirayama families. Icarus, 63, 30–53. Davis D. R., Weidenschilling S. J., Farinella P., Paolicchi P., and Binzel R. P. (1989) Asteroid collisional history — effects on sizes and spins. In Asteroids II (R. P. Binzel et al., eds.), pp. 805–826. Univ. of Arizona, Tucson. Davis D. R., Durda D. D., Marzari F., Campo Bagatin A., and GilHutton R. (2002) Collisional evolution of small body populations. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 545–558. Univ. of Arizona, Tucson. Dell’Oro A. and Paolicchi P. (1998) Statistical properties of encounters among asteroids: A new, general purpose, formalism. Icarus, 136, 328–339. Dohnanyi J. W. (1969) Collisional models of asteroids and their debris. J. Geophys. Res., 74, 2531–2554. Durda D. D. and Dermott S. F. (1997) The collisional evolution of the asteroid belt and its contribution to the zodiacal cloud. Icarus, 130, 140–164.

Durda D. D., Greenberg R., and Jedicke R. (1998) Collisional models and scaling laws: A new interpretation of the shape of the main-belt asteroid size distribution. Icarus, 135, 431–440. Durda D. D., Bottke W. F., Enke B. L., Merline W. J., Asphaug E., Richardson D. C., and Leinhardt Z. M. (2004) The formation of asteroid satellites in large impacts: Results from numerical simulations. Icarus, 170, 243–257. Durda D. D. et al. (2007) Size-frequency distributions of fragments from SPH/N-body simulations of asteroid impacts: Comparison with observed asteroid families. Icarus, 186, 498–516. Eugster O. (2003) Cosmic-ray exposure ages of meteorites and lunar rocks and their significance. Chem. Erde, 63, 3–30. Farinella P. and Davis D. R. (1992) Collision rates and impact velocities in the main asteroid belt. Icarus, 97, 111–123. Farinella P., Davis D. R., Paolicchi P., Cellino A., and Zappala V. (1992) Asteroid collisional evolution — an integrated model for the evolution of asteroid rotation rates. Astron. Astrophys., 253, 604–614. Fowler J. W. and Chillemi J. R. (1992) IRAS asteroid data processing. In The IRAS Minor Planet Survey (E. F. Tedesco, ed.), pp. 17–43. Tech. Report PL-TR-92-2049, Phillips Laboratory, Hanscom Air Force Base, Massachusetts. Golubov O. and Krugly Y. N. (2012) Tangential component of the YORP effect. Astrophys. J. Lett., 752, L11. Golubov O., Scheeres D. J., and Krugly Y. N. (2014) A three dimensional model of tangential YORP. Astrophys. J., 794, 22. Gomes R., Levison H. F., Tsiganis K., and Morbidelli A. (2005) Origin of the cataclysmic late heavy bombardment period of the terrestrial planets. Nature, 435, 466–469. Gladman B. J., Migliorini F.,Morbidelli A., Zappala V., Michel P., Cellino A., Froeschle C., Levison H. F., Bailey M., and Duncan M. (1997) Dynamical lifetimes of objects injected into asteroid belt resonances. Science, 277, 197–201. Gladman B. J. et al. (2009) On the asteroid belt’s orbital and size distribution. Icarus, 202, 104–118. Hanuš J. et al. (2013) Asteroids’ physical models from combined dense and sparse photometry and scaling of the YORP effect by the observed obliquity distribution. Astron. Astrophys., 551, A67. Hartmann W. K. and Hartmann A. C. (1968) Asteroid collisions and evolution of asteroidal mass distribution and meteoritic flux. Icarus, 8, 361–381. Hiesinger H., van der Bogert C. H., Pasckert J. H., Funcke L., Giacomini L., Ostrach L. R., and Robinson M. S. (2012) How old are young lunar craters? J. Geophys. Res.–Planets, 117, E00H10. Holsapple K., Giblin I., Housen K., Nakamura A., and Ryan E. (2002) Asteroid impacts: Laboratory experiments and scaling laws. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 443–462. Univ. of Arizona, Tucson. Housen K. (2009) Cumulative damage in strength-dominated collisions of rocky asteroids: Rubble piles and brick piles. Planet. Space Sci., 57, 142–153. Ivezić Ž. et al. (2001) Solar system objects observed in the Sloan digital sky survey commissioning data. Astron. J., 122, 2749–2784. Ivanov B. A., Neukum G., Bottke W. F., and Hartmann W. K. (2002) The comparison of size-frequency distributions of impact craters and asteroids and the planetary cratering rate. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 90–101. Univ. of Arizona, Tucson. Jacobson S. A., Marzari F., Rossi A., Scheeres D. J., and Davis D. R. (2014) Effect of rotational disruption on the size frequency distribution of the main belt asteroid population. Mon. Not. R. Astron. Soc., 439, L95–L99. Jaumann R. et al. (2012) Vesta’s shape and morphology. Science, 336, 687–690. Jedicke R., Larsen J., and Spahr T. (2002) Observational selection effects in asteroid surveys. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 71–88. Univ. of Arizona, Tucscon. Jutzi M., Asphaug E., Gillet P., Barrat J.-A., and Benz W. (2013) The structure of the asteroid 4 Vesta as revealed by models of planetscale collisions. Nature, 494, 207–210. Kirchoff M. R., Chapman C. R., Marchi S., Curtis K. M., Enke B., and Bottke W. F. (2013) Ages of large lunar impact craters and implications for bombardment during the Moon’s middle age. Icarus, 225, 325–341.

Bottke W. F. et al.:  The Collisional Evolution of the Main Asteroid Belt   723 Krasinsky G. A., Pitjeva E. V., Vasilyev M. V., and Yagudina E. I. (2002) Hidden mass in the asteroid belt. Icarus, 158, 98–105. Kuchynka P. and Folkner W. M. (2013) A new approach to determining asteroid masses from planetary range measurements. Icarus, 222, 243–253. Kuiper G. P., Fugita Y. F., Gehrels T., Groeneveld I., Kent J., van Biesbroeck G., and van Houten C. J. (1958) Survey of asteroids. Astrophys. J. Suppl., 3, 289. Leinhardt Z. M. and Stewart S. T. (2009) Full numerical simulations of catastrophic small body collisions. Icarus, 199, 542–559. Leinhardt Z. M. and Stewart S. T. (2012) Collisions between gravity dominated bodies. I. Outcome regimes and scaling laws. Astrophys. J., 745, 79. Levison H. F., Dones L., Chapman C. R., Stern S. A., Duncan M. J., and Zahnle K. (2001) Could the lunar “late heavy bombardment”’ have been triggered by the formation of Uranus and Neptune? Icarus, 151, 286–306. Levison H. F., Bottke W. F., Gounelle M., Morbidelli A., Nesvorný D., and Tsiganis K. (2009) Contamination of the asteroid belt by primordial trans-Neptunian objects. Nature, 460, 364–366. Levison H. F., Kretke K. A., Walsh K., and Bottke W. F. (2015a) Growing the terrestrial planets from the slow accumulation of sub-meter-size objects. Proc. Natl. Acad. Sci., in press. Levison H. F., Kretke K. A., and Duncan M. J. (2015b) Growing the gas giant planets from the slow accumulation of centimeter- to metersize objects. Nature, 524, 322–324. Love S. G. and Ahrens T. J. (1997) Origin of asteroid rotation rates in catastrophic impacts. Nature, 386, 154–156. Manley S. P., Migliorini F., and Bailey M. E. (1998) An algorithm for determining collision probabilities between small solar system bodies. Astronomy Astrophys. Suppl., 133, 437–444. Marchi S., Mottola S., Cremonese G., Massironi M., and Martellato E. (2009) A new chronology for the Moon and Mercury. Astron. J., 137, 4936–4948. Marchi S. et al. (2012) The violent collisional history of asteroid 4 Vesta. Science, 336, 690–693. Marchi S. et al. (2013) High-velocity collisions from the lunar cataclysm recorded in asteroidal meteorites. Nature Geosci., 6, 303–307. Marchi S. et al. (2014) Small crater populations on Vesta. Planet. Space Sci., 103, 96–103. Marzari F., Rossi A., and Scheeres D. J. (2011) Combined effect of YORP and collisions on the rotation rate of small main belt asteroids. Icarus, 214, 622–631. Masiero J. et al. (2011) Main belt asteroids with WISE/NEOWISE I: Preliminary albedos and diameters. Astrophys. J., 741, 68. McEwen A. S., Moore J. M., and Shoemaker E. M. (1997) The phanerozoic impact cratering rate: Evidence from the far side of the Moon. J. Geophys. Res., 102, 9231–9242. Melosh H. J. (1989) Impact Cratering: A Geologic Process. Oxford Univ., New York. 253 pp. Merline W. J.,Weidenschilling S. J., Durda D. D., Margot J. L., Pravec P., and Storrs A. D. (2002) Asteroids do have satellites. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 289–312. Univ. of Arizona, Tucson. Minton D. A. and Malhotra R. (2009) A record of planet migration in the main asteroid belt. Nature, 457, 1109–1111. Minton D. A. and Malhotra R. (2010) Dynamical erosion of the asteroid belt and implications for large impacts in the inner solar system. Icarus, 207, 744–757. Minton D. A. and Malhotra R. (2011) Secular resonance sweeping of the main asteroid belt during planet migration. Astrophys. J., 732, 53. Morbidelli A. and Gladman B. (1998) Orbital and temporal distributions of meteorites originating in the asteroid belt. Meteoritics & Planet. Sci., 33, 999–1016. Morbidelli A. and Vokrouhlický D. (2003) The Yarkovsky-driven origin of near-Earth asteroids. Icarus, 163, 120–134. Morbidelli A., Bottke W. F., Nesvorný D., and Levison H. F. (2009) Asteroids were born big. Icarus, 204, 558–573. Morbidelli A., Brasser R., Gomes R., Levison H. F., and Tsiganis K. (2010) Evidence from the asteroid belt for a violent past evolution of Jupiter’s orbit. Astron. J., 140, 1391–1401. Morbidelli A., Marchi S., Bottke W. F., and Kring D. A. (2012) A sawtooth-like timeline for the first billion years of lunar bombardment. Earth Planet. Sci. Lett., 355, 144–151.

Nesvorný D. (2011) Young solar system’s fifth giant planet? Astrophys. J. Lett., 742, L22. Nesvorný D. and Bottke W. F. (2004) Detection of the Yarkovsky effect for main-belt asteroids. Icarus, 170, 324–342. Nesvorný D. and Morbidelli A. (2012) Statistical study of the early solar system’s instability with four, five, and six giant planets. Astron. J., 144, 117. Nesvorný D., Morbidelli A., Vokrouhlický D., Bottke W. F., and Brož M. (2002) The Flora family: A case of the dynamically dispersed collisional swarm? Icarus, 157, 155–172. Nesvorný D., Bottke W. F., Levison H., and Dones L. (2003) Recent origin of the solar system dust bands. Astrophys. J., 591, 486–497. Nesvorný D., Roig F., Gladman B., Lazzaro D., Carruba V., and Mothé-Diniz T. (2008) Fugitives from the Vesta family. Icarus, 193, 85–95. Novaković B., Dell’Oro A., Cellino A., and Knežević Z. (2012) Recent collisional jet from a primitive asteroid. Mon. Not. R. Astron. Soc., 425, 338–346. Novaković B., Hsieh H. H., Cellino A., Micheli M., and Pedani M. (2014) Discovery of a young asteroid cluster associated with P/2012 F5 (Gibbs). Icarus, 231, 300–309. O’Brien D. P. (2009) The Yarkovsky effect is not responsible for small crater depletion on Eros and Itokawa. Icarus, 203, 112–118. O’Brien D. P. and Greenberg R. (2003) Steady-state size distributions for collisional populations: Analytical solution with size dependent strength. Icarus, 164, 334–345. O’Brien D. P. and Greenberg R. (2005) The collisional and dynamical evolution of the main-belt and NEA size distributions. Icarus, 178, 179–212. O’Brien D. P., Morbidelli A., and Levison H. F. (2006) Terrestrial planet formation with strong dynamical friction. Icarus, 184, 39–58. O’Brien D. P., Morbidelli A., and Bottke W. F. (2007) The primordial excitation and clearing of the asteroid belt — revisited. Icarus, 191, 43–452. Öpik E. J. (1951) Collision probability with the planets and the distribution of planetary matter. Proc. R. Irish Acad., 54, 165–199. Parker A., Ivezić Ž., Jurić M., Lupton R., Sekora M. D., and Kowalski A. (2008) The size distributions of asteroid families in the SDSS Moving Object Catalog 4. Icarus, 198, 138–155. Penco U., Dell’Oro A., Paolicchi P., Campo Bagatin A., La Spina A., and Cellino A. (2004) Yarkovsky depletion and asteroid collisional evolution. Planet. Space Sci., 52, 1087–1091. Petit J. M. and Farinella P. (1993) Modelling the outcomes of highvelocity impacts between small solar system bodies. Cel. Mech. Dyn. Astron., 57, 1–28. Petit J., Chambers J., Franklin F., and Nagasawa M. (2002). Primordial excitation and depletion of the main belt. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 711–738. Univ. of Arizona, Tucson. Pravec P., Harris A. W., and Michalowski T. (2002). Asteroid rotations. In Asteroids III (W. F. Bottke Jr. et al., eds.), pp. 113–122. Univ. of Arizona, Tucson. Rabinowitz D. L., Helin E., Lawrence K., and Pravdo S. (2000) A reduced estimate of the number of kilometre-sized near-Earth asteroids. Nature, 403, 165–166. Robbins S. J. (2014) New crater calibrations for the lunar craterage chronology. Earth Planet. Sci. Lett., 403, 188–198. Rozitis B. and Green S. F. (2012) The influence of rough surface thermal-infrared beaming on the Yarkovsky and YORP effects. Mon. Not. R. Astron. Soc., 423, 367–388. Ryder G., Bogard D., and Garrison D. (1991) Probable age of Autolycus and calibration of lunar stratigraphy. Geology, 19, 143–146. Schenk P. et al. (2012) The geologically recent giant impact basins at Vesta’s south pole. Science, 336, 694–697. Slivan S. M. (2002) Spin vector alignment of Koronis family asteroids. Nature, 419, 49–51. Slivan S. M. and Molnar L. A. (2012) Spin vectors in the Koronis family: III. (832) Karin. Icarus, 220, 1097–1103. Slivan S. M., Binzel R. P., Crespo da Silva L. D., Kaasalainen M., Lyndaker M. M., and Krčo M. (2003) Spin vectors in the Koronis family: Comprehensive results from two independent analyses of 213 rotation light curves. Icarus, 162, 285–307.

724   Asteroids IV Slivan S. M., Binzel R. P., Kaasalainen M., Hock A. N., Klesman A. J., Eckelman L. J., and Stephens R. D. (2009) Spin vectors in the Koronis family. II. Additional clustered spins, and one stray. Icarus, 200, 514–530. Statler T. S. (2009) Extreme sensitivity of the YORP effect to smallscale topography. Icarus, 202, 502–513. Stöffler D. and Ryder G. (2001) Stratigraphy and isotope ages of lunar geologic units: Chronological standard for the inner solar system. Space Sci. Rev., 96, 9–54. Stokes G. H., Yeomans D. K., Bottke W. F., Chesley S. R., Evans J. B., Gold R. E., Harris A. W., Jewitt D., Kelso T. S., McMillan R. S., Spahr T. B., and Worden S. P. (2003) Report of the NearEarth Object Science Definition Team: A Study to Determine the Feasibility of Extending the Search for Near-Earth Objects to Smaller Limiting Diameters. NASA OSS-Solar System Exploration Division, Washington, DC. Somenzi L., Fienga A., Laskar J., and Kuchynka P. (2010) Determination of asteroid masses from their close encounters with Mars. Planet. Space Sci., 58, 858–863. Tanaka H., Inaba S., and Nakazawa K. (1996) Steady-state size distribution for the self-similar collision cascade. Icarus, 123, 450–455. Turrini D., Magni G., and Coradini A. (2011) Probing the history of solar system through the cratering records on Vesta and Ceres. Mon. Not. R. Astron. Soc., 413, 2439–2466. Turrini D., Coradini A., and Magni G. (2012) Jovian early bombardment: Planetesimal erosion in the inner asteroid belt. Astrophys. J., 750, 8.

Vedder J. D. (1998) Main belt asteroid collision probabilities and impact velocities. Icarus, 131, 283–290. Vokrouhlický D., Nesvorný D., and Bottke W. F. (2003) The vector alignments of asteroid spins by thermal torques. Nature, 425, 147–151. Vokrouhlický D., Nesvorný D., and Levison H. F. (2008) Irregular satellite capture by exchange reactions. Astron. J., 136, 1463–1476. Walsh K. J., Morbidelli A., Raymond S. N., O’Brien D. P., and Mandell A. M. (2011). A low mass for Mars from Jupiter’s early gas-driven migration. Nature, 475, 206–209. Weidenschilling S. J. (1977) The distribution of mass in the planetary system and solar nebula. Astrophys. Space Sci., 51, 153–158. Wetherill G. W. (1967) Collisions in the asteroid belt. J. Geophys. Res., 72, 2429–2444. Wilhelms D. E. (1987) The Geologic History of the Moon. U.S. Geol. Surv. Prof. Paper 1348, 302 pp. Available online at http://ser.sese. asu.edu/GHM/. Wilhelms D. E., Oberbeck V. R., and Aggarwal H. R. (1978) Sizefrequency distributions of primary and secondary lunar impact craters. Lunar Planet. Sci. IX, pp. 1256–1258. Lunar and Planetary Institute, Houston. Williams D. R. and Wetherill G. W. (1994) Size distribution of collisionally evolved asteroidal populations — analytical solution for self-similar collision cascades. Icarus, 107, 117–125.

Marchi S., Chapman C. R., Barnouin O. S., Richardson J. E., and Vincent J.-B. (2015) Cratering on asteroids. In Asteroids IV (P. Michel et al., eds.), pp. 725–744. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch037.

Cratering on Asteroids Simone Marchi and Clark R. Chapman Southwest Research Institute

Olivier S. Barnouin

The Johns Hopkins University Applied Physics Laboratory

James E. Richardson Arecibo Observatory

Jean-Baptiste Vincent

Max-Planck Institute for Solar System Research

Impact craters are a ubiquitous feature of asteroid surfaces. On a local scale, small craters puncture the surface in a way similar to that observed on terrestrial planets and the Moon. At the opposite extreme, larger craters often approach the physical size of asteroids, thus globally affecting their shapes and surface properties. Crater measurements are a powerful means of investigation. Crater spatial and size distributions inform us of fundamental processes, such as asteroid collisional history. A paucity of craters, sometimes observed, may be diagnostic of mechanisms of erasure that are unique on low-gravity asteroids. Byproducts of impacts, such as ridges, troughs, and blocks, inform us of the bulk structure. In this chapter we review the major properties of crater populations on asteroids visited by spacecraft. In doing so we provide key examples to illustrate how craters affect the overall shape and can be used to constrain asteroid surface ages, bulk properties, and impact-driven surface evolution.

1. INTRODUCTION Until the space age, craters had only been observed on a single astronomical body, the Moon. It was only with the analysis of the first lunar samples, however, that it finally became clear that the vast majority of lunar craters (and a recognizable minority of terrestrial craters) were caused by cosmic impacts and were not generally of volcanic or other endogenic origin (e.g., Wilhelms, 1993). Three decades later, when the Galileo spacecraft flew past (951)  Gaspra, then a few years later past (243) Ida, craters were found on asteroids. During the subsequent two decades, spacecraft flybys and dedicated orbital missions have recorded crater populations on many additional asteroids. While hypervelocity impact by asteroids and comets or by their debris will produce impact craters on any solar system body with a solid surface, there is a fundamental difference between craters on small bodies and those on larger planets and satellites: Instead of cratering on semi-infinite surfaces, asteroidal cratering occurs on smaller bodies generally with minimal gravity. So the ejecta from an impact explosion travel far and often escape into independent orbits around the Sun, becoming individual small asteroids.

Collisional fragmentation and cratering are major evolutionary processes for asteroids since the earliest epochs of solar system history and learning about the visible record of surficial cratering can provide vital clues about their evolution and interactions with the space environment. Cratered terrains provide snapshots of collisions that occurred eons ago, and in turn, inform us about the origin of the impactor populations that have shaped the surfaces of all but the most geologically active bodies. Moreover, craters excavate deep to reveal underlying layers, perhaps differing from surface materials, while some of the escaped material can eventually land on Earth as meteorites. The fundamental observable property of a crater is its size, and the fundamental property of a population of craters concerns the ratio of the number of small craters to large craters, i.e., the size-frequency distribution (SFD). As with crater populations on larger planets and satellites, there are additional factors that interfere with a direct inference of the projectile population from the observed crater SFD. These include saturation of craters (the maximum number of craters that can be accommodated on a given surface), formation of secondary craters (craters made by impact of ejecta rather than from the primary cosmic projectile impacts), as well

725

726   Asteroids IV as often size-dependent processes that erase craters or alter their morphology (downslope mass wasting, pit-formation by volatile release, etc). Crater SFDs are also affected by the properties of the target material (e.g., hard rock, rubbly megaregolith, icy or volatile-rich material); these can vary not only spatially across the target body’s surface but also in the vertical dimension, so that scaling of impactor size to crater size may actually vary across the surface and with impactor size. Furthermore, energetic collisions may drastically alter the bulk properties of asteroids and scramble their surfaces by producing surface features such as troughs, ridges, and grooves. All these issues may initially manifest themselves as prob‑ lems due to our limited knowledge of asteroid properties, but, if one regards them as potentially decipherable challenges, they may eventually enable crater studies to reveal many properties of asteroid interiors, surfaces, and geological processes. In this chapter, we attempt to summarize the most up-todate understanding of asteroidal cratering processes, emphasizing presentation and interpretation of the more recent spacecraft data [e.g., from (4) Vesta, (21) Lutetia, and (25143) Itokawa], while also updating interpretations of earlier results from Gaspra, Ida, (253)  Mathilde, (433)  Eros, and some smaller targets of opportunity. 2. CRATER STATISTICS The identification of impact craters is a challenging process. One may think that craters should resemble nice, sharp bowls, but observations of craters on terrestrial bodies and asteroids readily show that this is naive. In reality, cratered landscapes evolve over time under various forces, such as cratering itself, mass wasting, and other endogenic geological processes, which especially hamper our ability to identify old, degraded craters. Furthermore, there is no unanimously accepted standard procedure to map craters, and researchers need to rely on their own bag of tricks. For instance, when a group of experienced mappers were given the same image from which to count craters, it was found that the results could differ by a factor of 2 (Robbins et al., 2014). In this section we introduce the topic of crater statistics, and crater SFDs, which are a primary diagnostic tool for understanding cratering. Furthermore, we discuss how crater SFDs can reveal important processes that modify or alter the production population of craters — i.e., the crater SFD per unit time that results from the mainly asteroidal projectile population — and are a powerful tool to infer relative and absolute ages of various terrains along with aspects of their bulk mechanical properties. 2.1. Crater Size-Frequency Distributions In this section we review crater SFDs of asteroids visited by spacecraft. As mentioned above, the identification of impact craters can be cumbersome, particularly when they are degraded and heavily modified by post-formation

processes. In addition, oddly shaped asteroids often show large facets that sometimes are interpreted to be the result of impact sculpting or to be a consequence of their rubble-pile structure. Here we take the approach of showing selected examples from the various asteroids to illustrate key processes, rather then presenting a global compilation of every measured crater SFD. In doing so we opt to show crater SFDs from selected references along with some newly measured crater SFDs, and remind readers that there are additional, and sometimes different, counts in the published literature (e.g., Schmedemann et al., 2014). An important and often neglected factor that makes cratering on asteroids different from cratering of terrestrial body surfaces is the fact that the physical sizes of visited asteroids vary by more than 3 orders of magnitude. As a result, craters form and evolve under very different conditions. Here we start our discussion with the largest bodies and continue with smaller asteroids. 2.1.1. Large asteroids. Vesta is the largest asteroid so far visited by a spacecraft (see the chapter by Russell et al. in this volume). The NASA Dawn mission orbited Vesta for more than one year, gathering images of 98% of the surface. The large surface and coverage makes Vesta the best example so far to study cratering on a large asteroid. In addition, Vesta formed within a few million years after the first solar system solids (e.g., McSween and Huss, 2010), implying that its surface has been subject to extensive cratering throughout nearly all of solar system evolution. As anticipated, the surface of Vesta exhibits an extremely diverse set of crater populations. The significant population of craters (~10–15) larger than 50 km, including a few old degraded structures, witnesses the heavy collisional history, recorded primarily in the northern hemisphere (Marchi et al., 2012a). The southern hemisphere, on the contrary, has been obliterated by the two largest impact structures, the ~400-km Veneneia and ~500km Rheasilvia basins. As a result, the overall spatial distribution of craters is rather heterogeneous and shows a marked north-south asymmetry. This is easily seen in the global crater distribution, and in the resulting global average crater density (Fig. 1). The formation of Veneneia and Rheasilvia had major effects on the whole surface, as manifested by the extensive troughs and voluminous ejecta blanketing (Schenk et al., 2012; Buczkowski et al., 2012; Yingst et al., 2014). Mapping of these and other geological features led to the development of a well-defined time-stratigraphic system (Williams et al., 2014). In this system, the youngest epoch — Marcian — begins with the time of formation of the freshest of the large craters, the ~70-km Marcia. The second youngest epoch — Rheasilvian — begins with the formation of the Rheasilvia basin. The relative youthfulness of Marcian and Rheasilvian terrains offers a unique opportunity among asteroids to study the least-processed populations of craters produced by asteroidal bombardment (Marchi et al., 2014) and also reveals the small main-belt asteroid SFDs. Figure  2a shows the crater SFDs of selected Marcian and Rheasilvian terrains. The crater SFDs of older vestan terrains are not easily interpretable because they exhibit odd shapes (for details,

Marchi et al.:  Cratering on Asteroids   727 300

0

60

(b)

120

60

60

30

30

240

300

0

60

120

60

60

30

30

0

0

0

0

–30

–30

–30

–30

–60

–60

–60

–60

240

300

0

60

120

240

300

Longitude

0

60

70

Crater density

240

Latitude

Latitude

(a)

0

120

Longitude

Cumulative Number of Craters (km–2)

Fig. 1.  Vesta’s global crater catalog. (a) The map shows a cylindrical projection of all mapped craters larger than 4 km in diameter (more than 2500 are shown on the map) overlaid on a digital terrain model. The two lines encompassing the south pole are the projections of best-fit circles to Rheasilvia and Veneneia basins. (b)  Crater areal density (in units of number of craters per 104 km2). The map is produced averaging craters over a radius of 80 km. Due to limited imaging coverage at high northern latitudes, the map is not reliable for latitudes above ~75°N.

101

(a) 10% of geometric saturation

100

101

10–1

10–2

10–2

10–3

10–3

10–5

Vesta (Marcia) Vesta (Rheasilvia fl.) Vesta (Rheasilvia ej.) Vesta (HCT) 0.1

1

10–4 10–5 10

Crater Diameter (km)

10% of geometric saturation

100

10–1

10–4

(b)

102

(c) 10% of geometric saturation

101 100 10–1 10–2

Gaspra Lutetia (Achaia) Vesta (Marcia) Mathilde Ida 0.1

1

10–3 10–4 10

Crater Diameter (km)

0.001

Itokawa Vesta (Marcia) Vesta (Rheasilvia ej.) Šteins 0.01

0.1

1

10

Crater Diameter (km)

Fig. 2. Selected crater SFDs of various asteroids. The data are shown in the form of cumulative numbers of craters per unit area as a function of crater diameter. The thick black lines indicate the level of empirical saturation corresponding to 10% of geometric saturation (Gault, 1970; Melosh, 1989, p. 192) (see section 2.2). (a) Crater SFDs of representative terrains within the Marcian and Rheasilvian units on Vesta. Marcia crater SFD is obtained from high-resolution counts within the rim of Marcia crater (from Marchi et al., 2014). The SFDs for craters on the floor of Rheasilvia basin and on its proximal ejecta blanket update those presented by Marchi et al. (2014). (b) A comparative view of crater SFDs of Lutetia [Achaia region, from Marchi et al. (2012b)], Ida (Chapman et al., 1996a), Gaspra (Chapman et al., 1996b), Mathilde (Chapman et al., 1999), and the Vesta heavily cratered terrain (HCT) [count updated from Marchi et al. (2012a)]. For a better comparison with (a), Marcia crater SFD is plotted here again. (c) Crater SFDs of Itokawa (Hirata et al., 2009), and Šteins (Marchi et al., 2010). For a comparison with crater counts shown in (a) and (b), the crater SFDs of Marcia and Rheasilvia are also shown.

see Yingst et al., 2014), and also differ from the arguably more pristine Marcian and Rheasilvian crater SFDs. It is probable that the formation of large basins such as Rheasilvia and Veneneia (and possibly also older ones) altered crater populations on older terrains (see section  2.2). Here we present data from just a relatively small region where the highest crater density has been observed, the so-called heavily cratered terrain (HCT) (Fig. 2b). The plot also indicates a curve corresponding to empirical crater saturation, i.e.,

approximately the highest crater density that can be accumulated on a given surface (Hartmann, 1984) (see also section 2.2). Therefore, Vesta HCT seems to be close to or has reached the empirical saturation level. Interestingly, asteroid Lutetia provides some similarities with Vesta. First, given its large size (~100 km), it may be a primordial object (i.e., not a fragment of some still larger body) according to models of collisional evolution of the main belt (Morbidelli et al., 2009). Furthermore, its surface

728   Asteroids IV shows significant features that were used to map and develop a time-stratigraphic system (Thomas et al., 2012; Massironi et al., 2012). However, the relatively small size and partial surface imaged (40%) did not permit detailed investigations of most of the surface. An exception is the relatively flat, coherent unit, called Achaia (Fig.  2b), which has a crater SFD showing a peculiar kink at crater sizes between ~5 and 8 km (Marchi et al., 2012b; see the chapter by Barucci et al. in this volume). Craters larger than ~8 km are close to the Vesta HCT and saturation, while craters smaller than ~5 km are significantly depleted. The latter has been interpreted as due to resurfacing or a variation of the mechanical properties with depth (see the chapter by Barucci et al.). The smooth appearances of Achaia and Vesta HCT  — suggesting the presence of significant regolith — resemble the surface of asteroid Ida, although on a very different size scale. The Ida crater SFD is also close to the saturation curve, over the size range from ~0.2 to 10 km. A similar conclusion applies to asteroid Mathilde for craters smaller than ~10 km, while for craters larger than ~10 km the crater density is well above the empirical saturation curve. A comparative plot of their crater SFDs is given in Fig. 2b. In conclusion, except for large craters on Mathilde, heavily cratered surfaces of mid- to large-sized asteroids seem to cluster in proximity to the empirical saturation density. In between the two extremes of low crater density represented by Marcian and Rheasilvian terrains on Vesta and the most heavily cratered terrains, we find a range of other terrains. Examples are the asteroid Gaspra (excluding the large facets of uncertain origin), or the Achaia region on Lutetia for craters smaller than 5 km. All these distributions (except for the kinked Achaia crater SFD) share relatively similar slopes, if one considers the statistical uncertainties associated with the measurements. 2.1.2. Small asteroids. Smaller asteroids, however, do not fit the above picture. Consider for instance the wellstudied case of Itokawa (a similar discussion about Eros can be found in section  2.2.4). The crater SFD at sizes larger than ~0.02 km has a characteristic slope somewhat shallower than the slopes observed on other asteroids (see Fig.  2c). Unexpectedly, however, the crater SFD has a considerably shallower slope at smaller sizes (