Planetary Systems Now 9781800613133, 9781800613140, 9781800613157

Table of contents :
Contents
Preface
About the Editors
Acknowledgments
Chapter 1 The Compositional Dimension of Planet Formation
1. Introduction
1.1. Planet formation: Basic concepts
1.2. Chemistry in planet formation: Basic concepts
2. The Initial Chemical Budget of Planet Formation
2.1. Protoplanetary disks
2.2. The host stars and their composition
2.3. Meteorites, comets and extrasolar materials
3. Compositional Structure of Protoplanetary Disks
3.1. Metallicities of refractory materials, organics and ices
3.2. Modeling the compositional structure of gas and solids
3.3. Effects of dust evolution and planetesimal formation
4. Compositional Signatures of Planet Formation
4.1. The limits of the C/O ratio
4.2. Expanding the inventory of elemental ratios
5. Future Outlooks and Concluding Remarks
6. Q&A
References
Chapter 2 The Mercurial Sun at the Heart of Our Solar System
1. Introduction
2. A Nonmagnetic Sun
3. Magnetic Sun
4. The Sun, Stars and Life on Earth
5. A Closer Look
5.1. Stars like the Sun
5.2. Stars of solar mass through time
5.3. Flares and CMEs
6. Conclusions
7. Q&A
References
Appendix: The Sun’s Magnetic Engine
Chapter 3 Twenty-Five Years of Exoplanet Discoveries: The Exoplanet Hosts
1. The Relevance of the Properties of the Planet Hosts
2. Characteristics of the Confirmed Stellar Hosts up to October 2021
2.1. Radial velocity hosts
2.2. Transit hosts
2.3. Direct imaging hosts
2.4. Microlensing hosts
2.5. The sky distribution of the planet hosts
3. Links between the Properties of the Host Stars and Their Planets
3.1. Occurrence rates per star type
3.1.1. Examples from RV surveys
3.1.2. Examples from transit surveys
3.1.3. Examples from direct imaging surveys
3.1.4. Examples from microlensing surveys
3.2. Correlations with metallicity
3.2.1. Giant planet — metallicity correlation
3.2.2. Planet distance/period — metallicity trend
3.3. Correlations with stellar mass
3.4. Chemical signatures of planet formation
4. Conclusions
5. Q&A
References
Chapter 4 Exploration of the Atmospheres of the Terrestrial Planets
1. Introduction: Comparative Planetology
2. Generalities on Planetary Atmospheres
2.1. Equilibrium temperature and greenhouse effect
2.2. Thermal escape to space
3. Observation Techniques
4. Terrestrial Planets
4.1. Mercury
4.2. Venus
4.3. Earth
4.4. Mars
5. Q&A
References
Chapter 5 Atmospheres and Climates of Telluric Planets of the Solar System (and a Bit of Giant Planets and Exoplanets)
1. A Diversity of Planetary Atmospheres
1.1. Earth
1.2. Mars
1.3. Venus
1.4. Titan
2. The Vertical Structure of Planetary Atmospheres
2.1. Basic energy balance
2.2. Two-beam model
2.3. Two-beam equations
2.4. Radiative temperature profile
2.5. Greenhouse effect
2.6. Discontinuity surface-atmosphere
2.7. Atmospheric vertical structure
2.8. Word of caution
3. Atmospheric Circulations
3.1. Impact of temperature gradients
3.1.1. Scale heights
3.1.2. Thermally direct circulations
3.1.3. Hadley cells and other thermally direct circulations
3.1.4. Hadley cells’ impact on heat transport and clouds
3.1.5. Hadley cells on Mars and the Earth
3.2. Impact of planetary rotation
3.2.1. Atmospheric dynamics in rotating planets
3.2.2. Hadley cells in rotating planets
3.2.3. Super-rotation and non-axisymmetric circulations
4. Concluding Remarks
5. Q&A
References
Chapter 6 Habitability and Atmospheric Biosignatures in an Exoplanetary Context
1. Introduction
2. Habitability
2.1. Definition
2.2. Historical context
2.3. Factors affecting habitability
2.4. Evolution of habitability: Venus-Earth-Mars compared
2.5. Evolution of habitability: Case study Earth
2.6. Habitability classes
2.7. Habitable zones
2.8. Exoplanets in the habitable zone
2.9. Examples of potentially habitable worlds
2.9.1. Proxima Centauri-b
2.9.2. K2-18b
2.9.3. LHS-1140b
2.10. Observing planetary habitability
3. Biosignatures and Life
3.1. Defining life
3.2. Biosignature methods
3.3. Atmospheric biosignatures: Photochemical effects
3.4. Atmospheric biosignatures: Transmission spectroscopy
3.5. False positives and negatives
3.6. The ideal atmospheric biosignature and reporting protocols
4. Summary
5. Q&A
References
Chapter 7 The Nature of Gas Giant Planets
1. Introduction
2. Modeling Planetary Interiors
2.1. Mass and radius
2.2. Polytropic models
3. Interior Models
3.1. The EoS of hydrogen, helium and heavies
3.1.1. Hydrogen
3.1.2. Hydrogen–Helium
3.1.3. Heavy elements
3.1.4. Empirical EoS
4. Jupiter
5. Saturn
6. Composition-Agnostic Models
7. Winds on Jupiter and Saturn
8. Love Numbers
9. Summary and Outlook
10. Q&A
References
Chapter 8 The Ice Giants Uranus and Neptune: Current Data and Future Exploration
1. Uranus and Neptune Planetary Systems
1.1. Formation and interior
1.2. Satellites and rings
1.3. Magnetospheres
2. Atmospheres
2.1. Thermal structure
2.2. The visible clouds
2.3. Winds
3. The Deep Weather Layer
4. The Future: New Observatories and Future Missions to the Icy Giants
4.1. James Webb Space Telescope
4.2. Ground-based large telescopes in the optical
4.3. Ground-based observatories in the mm and radio
4.4. Missions to Uranus and/or Neptune
5. Q&A
Acknowledgments
References
Chapter 9 Cloud Formation in Exoplanetary Atmospheres
1. Introduction
2. A Basic Concept for Cloud Formation
3. A Timescale Analysis
4. Cloud Formation Modeling
4.1. Modeling the formation of condensation seeds
4.2. Modeling the bulk growth of cloud particles
5. The Resulting Cloud Structure, the Prerequisites for Extrasolar Weather Forecast
6. Moving Forward
7. Final Thoughts
8. Q&A
Acknowledgments
References
Chapter 10 Planetary Astrophysics of Small Bodies
1. Introduction
2. The Comets
2.1. Destruction of the comets
3. Asteroids
3.1. Spectral and compositional gradients
3.2. Active asteroids
3.2.1. Impact
3.2.2. Rotational instability
3.2.3. Thermal destruction
3.2.4. Sublimation
4. Kuiper Belt
4.1. Planetary migration and late-heavy bombardment
4.2. Unseen planet
4.3. Giant planet Trojans
5. Q&A
References
Chapter 11 Physical Properties of Solar System Minor Bodies: Remote Observations vs. Modeling
1. Introduction
2. Observables and Physical Properties
2.1. Variations with time
2.2. Variations over long-time periods
2.3. Variations with solar phase angle
2.4. Variations with wavelength
2.4.1. Non-independent variables
3. Concluding Remarks
4. Q&A
Acknowledgments
References
Chapter 12 Surface Composition of the Trans-Neptunian Objects: Where are the Ices in the Solar System?
1. Small Bodies, a Treasure Trove for the Understanding of Solar Systems
2. Trans-Neptunian Bodies, Frozen Time Capsules
3. Surface Composition of TNOs
3.1. Icy dwarf planets
3.2. Surface composition of mid-size and small TNOs
4. The Future is Here: The James Webb Space Telescope
4.1. How will JWST study the ingredients of TNOs?
4.1.1. Water ice
4.1.2. Complex organics
4.1.3. Amorphous silicates
4.1.4. Methanol ice
4.1.5. Methane and light-hydrocarbons
4.1.6. Minor components
5. Extending the Study of the Surface Composition by Means of Spitzer/NIRCAM Observations
6. Summary
7. Q&A
Acknowledgments
References
Chapter 13 Interstellar Planetesimals
1. An Astounding Yet Expected Discovery
2. Interstellar Planetesimals are a Byproduct of Planet Formation and Evolution
2.1. Debris disks provide observational evidence that planetesimal formation is common and that the planetesimal belts are depleted with time
2.2. The unbinding of exo-Oort cloud objects enrich the interstellar medium with planetesimals
3. Size Distribution of Interstellar Planetesimals
4. Number Density of Interstellar Planetesimals
4.1. Number density inferred from 1I/’Oumumua’s detection
4.2. Expected contribution from the ejection of planetesimals from protoplanetary disks
4.3. Expected contribution from the release of planetesimals from exo-Oort clouds
4.4. Proposed solutions for the discrepancy between the inferred and expected number density of interstellar planetesimals
4.4.1. 1I/’Oumuamua could have originated in a young nearby system
4.4.2. 1I/’Oumuamua could be the result of a formation/fragmentation process with a narrow size distribution
5. An Unexpected Trajectory Leading to Unconventional Ideas About Origin
5.1. Cosmic dust bunnies and primordial planet building blocks
6. 2I/Borisov: A Planetesimal Ejected from the Cold Outer Edge of a Distant Planetary System
7. Interstellar Planetesimals are Potential Seeds for Planet Formation and Life
7.1. Planetesimal can be transferred between young planetary systems
7.2. Interstellar planetesimals can act as condensation nuclei for planet formation
8. Future Prospects
9. Q&A
References
Chapter 14 Planetesimal/Debris Disks
1. What are Debris Disks?
2. Basic Properties and Observables
2.1. Debris disk formation
3. Collisional Evolution
3.1. The outliers
4. Resolved Observations
4.1. Scattered light observations
4.2. Thermal emission at mm wavelengths
4.2.1. Radius distribution
4.2.2. Widths
4.2.3. Radial structures
4.2.4. Vertical structures
5. Circumstellar Gas
5.1. Absorption lines
5.2. Emission lines
5.3. Evolution of exocometary gas
5.4. Implications
6. Acknowledgments
7. Q&A
References
Index

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Published by World Scientific Publishing Europe Ltd. 57 Shelton Street, Covent Garden, London WC2H 9HE Head office: 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601

Library of Congress Cataloging-in-Publication Data Names: Lara, Luisa M., editor. | Jewitt, D. (David), editor. Title: Planetary systems now / edited by Luisa M. Lara, Instituto de Astrofísica de Andalucía-CSIC, Granada, Spain, David Jewitt, University of California, Los Angeles, USA. Description: New Jersey : World Scientific, [2023] | Includes bibliographical references and index. Identifiers: LCCN 2022028855 | ISBN 9781800613133 (hardcover) | ISBN 9781800613140 (ebook) | ISBN 9781800613157 (ebook other) Subjects: LCSH: Planetary systems. | Planetary theory. Classification: LCC QB361 .P53 2023 | DDC 523.2--dc23/eng/20220617 LC record available at https://lccn.loc.gov/2022028855

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

Copyright © 2023 by World Scientific Publishing Europe Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/Q0388#t=suppl Desk Editors: Jayanthi Muthuswamy/Adam Binnie/Shi Ying Koe Typeset by Stallion Press Email: [email protected] Printed in Singapore

c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 fmatter

Preface

This book is the outgrowth of an online school titled Planets, Exoplanets and their Systems in a Broad and Multidisciplinary Context, organized by Luisa M Lara, and held between January 18 and February 1, 2021. The intent behind the school was to provide a broad and up-to-date perspective on our rapidly evolving knowledge of planetary systems. Solar system studies give us knowledge more detailed than we will ever possess from exoplanets, while exoplanets provide a broader context for understanding planetary science than could ever be obtained from the solar system alone. The school was intended to be of value to students, postdoctoral researchers and others broadly interested in planetary science; no prior knowledge of planetary science was assumed. There were 28 lecturers and 355 registered participants in the school. Lectures were recorded and each was accompanied by a scheduled Question and Answer session, held live with the lecturer. Topics included the formation and evolution of the solar system, the formation and structure of terrestrial, gas and ice giant planets, physics of comets and asteroids, atmospheres of solar system planets and exoplanets, the expanding debris disk and exoplanet populations and even interstellar planetesimals. A majority of the lecturers agreed to write-up their presentations for this book, for which we are extremely grateful. In two cases where this was not possible, Ravit Helled and Christiane Helling kindly agreed to write in order to maintain continuity of the material. v

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Preface

The format of the book mirrors the format of the school. The chapter authors have endeavored to present the most current data, from recent and ongoing space missions that include Maven (Mars), Juno (Jupiter), Cassini–Huygens (Saturn), Rosetta (Comet 67P), New Horizons (Pluto), Osiris-Rex (Asteroid Bennu), Hayabusa 2 (Asteroid Ryugu) and KEPLER and TESS (exoplanets), as well as new measurements from the largest ground and space-based telescopes. Current formation and evolutionary models are also fully described. The Question and Answer sessions were often illuminating; we have included abbreviated versions following each chapter. Luisa M Lara and David Jewitt 2022 February Scan the QR code to access the videos related to this book, https://www.youtube.com/ playlist?list=PL9qXSx4XY6gHmf4bh8mBcYlsG B6CthPDy.

c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 fmatter

About the Editors

Luisa M Lara is a planetary scientist at the Instituto de Astrof´ısica de Andaluc´ıa-CSIC in Granada, Spain, devoting her career to the study of the planets and minor bodies of the Solar System. This study is undertaken from a theoretical and observational point of view, as well as getting involved in the design and development of space missions and their scientific instruments. She has received ESA certificates for outstanding contributions to the Cassini–Huygens (NASA-ESA-ASI), Rosetta (ESA) and Bepi Colombo (ESA/JAXA) missions. She has served in the Solar System and Exploration Working Group and in the Space Science Advisory Committee of ESA. She is currently the only Spanish woman full member of the International Academy of Astronautics. Her most noteworthy works in planetary science are related to Titan’s atmosphere and to the nature of cometary surfaces thanks to the data provided by the Rosetta s/c (ESA). Currently, Luisa M Lara is Professor at the Consejo Superior de Investigaciones Cientificas, committed to delivering several instruments for the exploration of a dynamically new comet with the Comet Interceptor ESA/JAXA mission, and an IR spectrometer to study Venus’s atmosphere. She is also leading a group of researchers to ensure the scientific return of these missions.

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About the Editors

David Jewitt is an observational astronomer interested in the small bodies of the solar system. Using mostly simple techniques, he aims to discover the nature of these bodies and from them to better understand the formation of the Solar System. He was awarded the Shaw Prize in Astronomy and the Kavli Prize in Astrophysics for his discovery and exploration of the Kuiper belt. Recently, he has unveiled a new population of active asteroids in the main belt and, separately, investigated the first two interstellar interlopers. Jewitt is currently Distinguished Professor of Astronomy at the University of California in Los Angeles, where he teaches two large classes in planetary science and oceanography.

c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 fmatter

Acknowledgments

Organizing a virtual school with lecturers and participants from all over the world proved to be both a lot of hard work and a fantastic endeavor. From start to finish, my home institution (Instituto de Astrof´ısica de Andaluc´ıa, IAA), the Consejo Superior de Investigaciones Cient´ıficas (CSIC) and my colleagues provided invaluable support and in many ways made the school possible. Thank you all. Nothing would exist without the lecturers and the participants. I especially want to mention my profound gratitude to the lecturers who kindly accepted to join this venture. They were enthusiastic about the idea from the very first moment I proposed it to them. One of the lecturers had the excellent idea of transforming the material from the school into a book, Planetary Systems Now, of which he is now the co-editor. Thanks Dave. Extra thanks go to all those who agreed to contribute the chapters of this book, and who did so in a timely way. Lastly, the school would not have been a success without the overwhelming curiosity and enthusiasm of the participants. They are the roots of the book, and the future of planetary science. I dedicate this book to you all. Luisa M Lara

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c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 fmatter

Contents

Preface

v

About the Editors

vii

Acknowledgments

ix

Chapter 1

The Compositional Dimension of Planet Formation

1

Diego Turrini Chapter 2

The Mercurial Sun at the Heart of Our Solar System

49

Philip G. Judge Chapter 3

Twenty-Five Years of Exoplanet Discoveries: The Exoplanet Hosts

71

B´ arbara Rojas-Ayala Chapter 4

Exploration of the Atmospheres of the Terrestrial Planets Ann C. Vandaele

xi

97

Contents

xii

Chapter 5

Atmospheres and Climates of Telluric Planets of the Solar System (and a Bit of Giant Planets and Exoplanets)

135

Aymeric Spiga Chapter 6

Habitability and Atmospheric Biosignatures in an Exoplanetary Context

155

John Lee Grenfell Chapter 7

The Nature of Gas Giant Planets

181

Ravit Helled, Naor Movshovitz and Nadine Nettelmann Chapter 8

The Ice Giants Uranus and Neptune: Current Data and Future Exploration

211

Ricardo Hueso Chapter 9

Cloud Formation in Exoplanetary Atmospheres

235

Christiane Helling Chapter 10 Planetary Astrophysics of Small Bodies

259

David Jewitt Chapter 11 Physical Properties of Solar System Minor Bodies: Remote Observations vs. Modeling

285

Daniela Lazzaro Chapter 12 Surface Composition of the TransNeptunian Objects: Where are the Ices in the Solar System?

305

Noem´ı Pinilla-Alonso, M´ ario de Pr´ a and Ana Carolina Souza-Feliciano Chapter 13 Interstellar Planetesimals

333

Amaya Moro-Mart´ın Chapter 14 Planetesimal/Debris Disks

381

Sebastian Marino Index

409

c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 0001

Chapter 1

The Compositional Dimension of Planet Formation

Diego Turrini INAF — Osservatorio Astrofisico di Torino, Via Osservatorio, Pino Torinese, Italy INAF — Istituto di Astrofisica e Planetologia Spaziali, Via Fosso del Cavaliere, Rome, Italy [email protected]

The great diversity of the thousands of planets known to date is proof of the multitude of ways in which formation and evolution processes can shape the life of planetary systems. Multiple formation and evolution paths, however, can result in the same planetary architecture. Because of this, unveiling the individual histories of planetary systems and their planets can prove a challenging task. The chemical composition of planets provides us with a guiding light for navigating this challenge, but to understand the information it carries we need to properly link it to the chemical composition and characteristics of the environments in which the planets formed. To achieve this goal it is necessary to combine the information and perspectives provided by a growing number of different fields of study, spanning the whole lifecycle of stars and their planetary systems. The aim of this chapter is to provide the unifying perspective needed to understand and connect such diverse information, and illustrate the process through which we can decode the message contained into the composition of planetary bodies.

1

D. Turrini

2

1.

Introduction

After centuries where the Solar System was the only planetary system known to humanity and the template on which we shaped our understanding of planet formation, the past quarter of a century saw our view of planets in our galaxy completely revolutionized. A particularly unexpected finding is that the architectures of the thousands of exoplanetary systems known to date span over more than six orders of magnitude in distance from their host stars, going from planets closer to their stars than Mercury is to the Sun and whose equilibrium temperatures exceed a thousand K, to planets embedded in the cold outer regions of their native protoplanetary disks at hundreds of astronomical units. The spatial extension of the planet-forming region hinted by this great diversity of orbital architectures goes well beyond what was suggested by the architecture of the Solar System alone, and implies an also great diversity of formation environments in the natal protoplanetary disks. This, in turn, is expected to result in a large variety of compositional natures of the formed planets, as already hinted by the first exoplanetary population studies (see, e.g., Refs. 1–4). A growing body of literature is investigating what kind of constraints such varied compositions of the planetary bodies can provide on their formation environments and their interplay with the planet formation process (e.g., Refs. 5–10 and references therein, and Refs. 11–17). Understanding the connection between planet formation and planetary composition requires an interdisciplinary point of view encompassing an expanding number of disciplines: from the characterization of stars to the study of the circumstellar disks and the interstellar medium from which they were born, and from the investigation of meteorites and comets in the Solar System to the study of extrasolar materials contaminating the atmospheres of young forming stars as well as of white dwarfs at the end of their evolution. Since discussing each of these fields of study in detail is impossible within the scope of this chapter, the referenced bibliography includes recent reviews on each of these topics for in-depth discussions. While this chapter aims to provide an updated view of how the planet formation process and the environments in protoplanetary disks shape the composition of planets, the rapid pace at which the underlying fields of study are expanding continuously brings new

The Compositional Dimension of Planet Formation

3

results in the picture. As such, the main goal of this chapter is to provide the unifying view linking the different pieces of information each of these fields of study provides, and to illustrate the process through which they can be connected to investigate the compositional dimension of planet formation. Before starting our journey, the following Sections 1.1 and 1.2 will introduce most of the basic concepts that will accompany us throughout the rest of the chapter. 1.1.

Planet formation: Basic concepts

The planet and star formation processes are strongly connected, as planets are born in the circumstellar disks surrounding young forming stars. The circumstellar disks share the same bulk elemental composition of their central stars, as they are both composed by the gas and dust inherited from the parent molecular cloud. Planets are born from the dust and gas of circumstellar disks through two main pathways, one involving the gravitational collapse of the disk gas and the other involving the growth and conversion of the dust into larger and larger objects. The first pathway, indicated by the orange lines in Fig. 1, involves the collapse of parcels of disk gas under their own self-gravity: this process requires cold and massive disks to be triggered, is more effective in forming planets at large distances (50 AU) from the central star where the temperatures are lower and results in massive planets with masses comparable to or greater than that of Jupiter.7,18,19 The second pathway, indicated by the black lines in Fig. 1, involves the gradual growth of dust into larger and larger bodies.7,18,19 Collisions among dust grains will result in their sticking and growth due to electromagnetic forces producing pebbles up to about a few cm in size, after which collisions become erosive and can result either in mass conservation or mass loss.20,21 Dust and pebbles of different sizes will be affected at different levels by their interaction with the disk gas22 (see Section 3.3 for further details), resulting in their differential motion and favoring their concentration and clustering. Clusters of dust and pebbles can become gravitationally bound and collapse under their own self-gravity, forming bodies with sizes ranging from tens to thousands of kilometers called planetesimals20,21,23 on timescales of the order of 105 –106 years (see Refs. 24–26 for the meteoritic constraints on the timescale of this process).

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D. Turrini

Fig. 1. Schematic representation of the formation paths that, starting from the gas and dust in circumstellar disks (the bottom left corner of the diagram), create the different kinds of planets currently observed. Orange and black arrows indicate the paths linked to the formation process, i.e., disk instability and solid/core accretion plus gas capture, respectively, while blue arrows indicate the paths shaped by atmospheric evolution (e.g., atmospheric escape, atmospheric erosion, outgassing). Planets are divided into three broad categories: high-density planets (mainly composed by Si, Mg, Fe, C, O), gas-rich planets (for which H and He represent a significant fraction of their mass) and transitional planets (encompassing the transition between the largest high-density planets and the smallest gas-rich planets). Adapted from Ref. 7.

During the lifetime of circumstellar disks, planetesimals will then grow due to both mutual low velocity collisions and the accretion of pebbles to give rise to larger bodies with masses of the order of ∼0.01–0.1 Earth masses, the planetary embryos27,28 (see Refs. 29 and 30 for the constraints from the Solar System on the timescale of this process). The planetary embryos will also grow due to the accretion of pebbles (while still embedded in the circumstellar disk) and mutual collisions (predominantly after the disk dispersal) until they give rise to larger solid bodies with masses spanning between those of the terrestrial planets in the Solar System and those of the super-Earth planets observed around other stars.7,27 The timescale on which this process completes can vary between a few 106 to several 107 years (see Refs. 27, 29, and 30 for the

The Compositional Dimension of Planet Formation

5

constraints from the Solar System on the timescale of this process) so it can significantly exceed the lifetime of circumstellar disks, which is of the order of a few 106 years.31,32 Planetary bodies succeeding in growing to masses of the order of ∼10 Earth masses before the dispersal of their protoplanetary disk will be able to capture significant masses of gas from the disk in the form of expanded atmospheres.7,18,19,27 Based on their composition being linked to that of the protoplanetary disk, these atmospheres are called primary atmospheres to differentiate them from the secondary atmospheres produced by volcanism and outgassing processes during the geophysical evolution of planets.7 If the mass of captured gas becomes comparable to that of the planetary body to which it is gravitationally bound, the expanded atmosphere will begin to collapse, triggering a runaway process that will allow the solid planet to grow by one to two orders of magnitude in mass and become the core of a giant planet,7,18,19 as illustrated by the horizontal branch of the planet formation sequence (black lines) preceding the disk dispersal in Fig. 1. Differently from the formation pathway shaped by disk instability (orange lines in Fig. 1), the core instability pathway for forming giant planets favors orbital regions closer to the central star (50 AU)7,18,19 due to their higher densities of solids (see Section 2.1). While the first pathway will result in massive giant planets, planets forming through the second pathway will not necessarily become giant planets. The growth process from dust to planetary objects can stop at any stage, resulting in a continuum of planetary masses spanning across the whole spectrum sampled by the terrestrial planets in the Solar System and the super-Earths observed around other stars as illustrated in Fig. 1. Composition-wise, it is important to emphasize that this process of growth is not confined to the local materials initially surrounding the seeds of the forming planets.7,33 As we will discuss in more detail in Section 3.3, dust and pebbles drift radially across the circumstellar disk due to their interaction with the disk gas. Likewise, during their growth the various planetary bodies will interact with the gas in the disk and will migrate radially,34,35 crossing different compositional regions of the disk (see Fig. 2). When most of the initial mass of dust in the disk is converted into a limited number of large planetary bodies, their mutual

6

D. Turrini

Fig. 2. Schematic representation of the dynamical pathways that can deliver planets from their formation regions across the extension of the natal protoplanetary disk to the orbital regions closest to the star. While embedded in their native protoplanetary disks, planets can experience early disk-driven migration due to their interactions with the surrounding gas. Dynamical chaos and planet–planet scattering events can later affect the architecture of planetary systems and cause their planets to experience late migration. Adapted from Ref. 7.

gravitational interactions will cause them to be scattered (either inward or outward) from their original orbit5,7,34 and will allow for planetary bodies initially distant from each other to collide and compositionally mix (see Fig. 2 and Ref. 5). As a result, the orbital location where we observe a planet can in most cases bear little to no significance for identifying its formation region and constrain its past dynamical evolution.5 The density of planets can provide us insight on the abundances of refractory and volatile elements in their elemental budgets and, as such, put constraints on their formation regions or accretion histories, though this information is often uncertain and degenerate.1,7,36 In order to further advance our understanding of planet formation, we therefore need to decode the information enclosed in the composition of planetary bodies.5–8 To properly interpret the compositional signatures left by the planet formation process, in turn, we need to characterize the environment in which planets form.10

The Compositional Dimension of Planet Formation

1.2.

7

Chemistry in planet formation: Basic concepts

The next step before starting the journey into the compositional dimension of planet formation is to clarify the sometimes confusing overlap between the nomenclature and classification schemes adopted in the two main disciplines contributing to our understanding of the subject, astrochemistry and cosmochemistry. The guiding principle at the basis of both classification schemes, however, is always the comparison of the relative volatility of different elements. To first order, elements can be divided into two broad categories: refractory and volatile elements. This broad division, adopted in astrochemical studies of protoplanetary disks, is based on the condensation behavior with temperature of the elements. Refractory elements condense at higher temperatures than volatile elements and they are in solid form across most of the extension of protoplanetary disks. In the following, we will refer to solids mainly composed of refractory elements as refractory materials, grouping both rocks and metals in this general category. Volatile elements remain in gas form down to lower temperatures so, opposite to refractory elements, they are present as gas across vast regions of protoplanetary disks. Volatile elements condense as ices. Throughout the chapter, we will generally follow this very broad classification unless otherwise specified. The transition between refractory and volatile elements can be placed roughly around 300 K.37,38 As we will see in Section 2.3, the meteoritic record in the Solar System37,39–41 shows us that at this temperature all elements except hydrogen (H), the noble gases and the volatile elements carbon (C), oxygen (O) and nitrogen (N) are in condensed form as rocks and metals. Molecules composed by volatile elements can be differentiated between volatile molecules (e.g., H2 O, NH3 , CO2 ) and ultra-volatile molecules (e.g., CH4 , CO, N2 ) with the transition roughly occurring around 30 K.37,38 The noble gases can condense as ices at temperatures lower than 30 K, the condensation of Ne requiring temperatures of about 9 K to occur.38 The noble gases Ar, Kr and Xe can also be effectively trapped into H2 O ice as clathrates 38 at comparatively higher temperatures if the abundance of water ice is large enough. As we will further discuss in Section 2.3, the volatile elements O and C actually behave both as refractory and volatile elements.

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O is distributed in comparable quantities between refractory materials (rocks are mainly composed of Fe, Si and Mg oxides38 ) and ices (H2 O, CO, CO2 ).39–41 C is present in limited quantities in refractory materials39–41 but is the major building block of organics, which in turn can be divided into refractory organics and volatile organics.9,10,15,33,42–46 The third volatile element, N, is that characterized by the highest volatility and only a minor fraction condenses with refractory materials and organics.9,12,37,39–41,46,47 The categorization discussed until now adopts the perspective of the field of study of astrochemistry. The source of confusion mentioned at the beginning arises from the fact that the second field of study dealing with the chemistry of planetary systems, cosmochemistry, uses a similar terminology to indicate somewhat different classes of elements. The starting point of cosmochemical studies are the samples of planetary materials, so there is a strong focus on the composition of solids in protoplanetary disks. Astrochemical studies instead have their starting point in the astronomical observations of molecular clouds and protoplanetary disks, therefore putting a larger emphasis on the volatile elements. Within the cosmochemical classification, the elements astrochemically classified as volatile elements are defined as both highly volatile and atmophile elements,38,39 since their high volatility makes them the major component of planetary atmospheres. The astrochemical category of refractory elements, instead, is split into four different classes. The cosmochemical class of refractory elements groups those elements condensing at temperatures higher than 1,360 K (further subdivisions based on the condensation temperature and the chemical behavior exist and are discussed in Refs. 37 and 38 but are beyond the scope of this chapter), with Ca, Al and Ti being the most abundant refractory elements. The next group includes elements condensing between 1,360 and 1,290 K and contains Fe, Si and Mg: these are among the most abundant cosmic elements and, together with O, the major components of rocks, which is why this group is called major or common elements.37,38 In order of decreasing condensation temperatures we then encounter the moderately volatile elements, which condense at temperatures above 700 K and include P, F, Cl, Na and K, and the volatile elements, which include S and condense at temperatures between 700 and 300 K.37,38 The condensation temperature of S as

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FeS (troilite) at about 700 K is what marks the transition between moderately volatile and volatile elements.37,38 Before proceeding, it is important to point out that condensation is a gradual process where the balance between the condensed and gaseous phases varies over a range of temperature values (at constant pressure).6,38 This, in turn, implies that the condensation fronts (also called snowlines) are transition regions that can extend over multiple AU rather than sharp boundaries. When only one condensation temperature is reported for a element or molecule, its value implicitly refers to the condensation of 50% of its total mass.37–39 Finally, it is also important to point out that the concept of snowline is not always as well defined as one would expect: in chemically active protoplanetary disks, molecules can be characterized by wavy condensation patterns and actually have multiple snowlines.48,49

2.

The Initial Chemical Budget of Planet Formation

The first step to understand planetary composition and the information it carries on planet formation lies in characterizing the initial elemental budget contained in the protoplanetary disks from which planets are born. In the case of young planets still embedded in the native protoplanetary disks, it is in principle possible to directly access this record by probing the composition of the dust and gas of the disks themselves. The original protoplanetary disks of the more than 3,500 exoplanetary systems currently known as well as that of the Solar System, however, have long dispersed. Nevertheless, records of their composition are still provided by their stars and by the composition of their planetary bodies. Combining the information on the stellar composition and that of the planetary bodies can allow to reconstruct the initial chemical budget and structure of the original protoplanetary disks. 2.1.

Protoplanetary disks

Protoplanetary disks are flat, extended structures surrounding young forming stars and composed by the gas and dust inherited from the parent molecular cloud. Supported by their rotation against the

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stellar gravity and irradiated by their central star, protoplanetary disks are characterized by pressure, density and temperature gradients along the radial direction from the host star and the vertical direction from their midplanes. These gradients affect the local thermochemical equilibrium and result in the existence of different compositional regions across their extensions. Here, we will focus on describing the physical and thermal structures of disks, to pave the road for discussing their compositional structure in Section 3. In their vertical direction, protoplanetary disks are characterized by three main chemical layers10 : the photon-dominated layer, the warm molecular layer and the cold midplane. The photon-dominated layer is the outermost vertical layer: here the disk gas interacts with the stellar and interstellar radiation, is mostly in atomic form due to the photo-dissociation of molecules and its chemistry is regulated by photo-processes.10 The warm molecular layer is the intermediate vertical layer: it is shielded from the photo-dissociative radiation and its gas is rich in molecular species produced through ion–neutral and neutral–neutral reactions.10 The cold midplane is the layer most directly involved in planet formation, it is the innermost layer and as such is shielded from the direct stellar radiation by the other layers.10 Due to the aerodynamical drag exerted by the gas, the dust originally mixed with the gas throughout the whole vertical extension of the disk settles in this layer, resulting in the highest density of solids.50 As a consequence, the chemistry in the midplane is mainly controlled by the condensation of the chemical species on the surface of the dust grains and by grain-surface reactions.9,10 In the following, we will focus our attention on the disk midplane, though it is important to bear in mind that the warm molecular layer is expected to play a role in the accretion of the gaseous envelope of giant planets.9 On the disk midplane, with the exception of the innermost region (generally of the order of 1 AU51 ), the temperature gradient in the radial direction depends on the distance from the host star as Tm = T0 (r/r0 )−β ,

(1)

where T0 is the normalization temperature at the reference distance r0 , and the exponent β is generally found to be close to 0.5. Generally, in studies of the Solar System the reference distance is 1 AU while in observational studies of circumstellar disks the reference distance

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is much larger and depends on the spatial resolution of the observations: e.g., Ref. 52 adopts a reference distance of 100 AU for the circumstellar disk surrounding the star HD 163296. A classical parametrization of the temperature profile of the original circumsolar disk, also called the solar nebula, adopts a normalization temperature T0 = 280 K at r0 = 1 AU with β = 0.5 based on the observation of the distribution of refractory and volatile elements in the present Solar System.53 Such parametrization, still widely used in present-day studies, adopts a midplane temperature profile warmer than those observationally estimated for circumstellar disks. As a comparison, the circumstellar disks around HD 163296, AS 209 and TW Hya are characterized by normalization temperatures at 1 AU of 240, 150 and 130 K, respectively.52,54–56 The β values of these disks are instead close to that adopted for the solar nebula, being 0.5–0.6 for HD 163296 and AS 209, and 0.47 for TW Hya.52,54–56 Adopting as case study the midplane thermal profile of HD 163296 and the condensation temperatures of the abundant volatile molecules listed in Table 1, we can have a first dive into the compositional structure in the disk midplane. With the reference temperature T0 = 240 K at 1 AU, all elements belonging to the astrochemical refractory family will be condensed in solid form already at about 0.6 AU (300 K, see Section 1.2). Moving away from the star we first encounter the snowline of H2 O, the most refractory/least volatile molecule formed by the volatile elements, at about 3 AU.

Table 1. Molecule H2 O CH3 OH NH3 CO2 CO N2

Snowlines of volatile molecules.

50% TC (K)

50% RC (AU)

References

140 102.5 80 65 30 26

3 6.5 9 13.7 64 85

57 57 57 57 12, 58 12, 58

Notes: Snowlines of the most abundant volatile molecules for the disk temperature profile of HD 163296, where the condensation distance RC is determined by the orbital distance where the disk temperature matches the condensation temperature TC at which 50% of the volatile molecule condenses as ice.

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The next snowline we encounter is that of the volatile organic molecule CH3 OH at 6.5 AU, followed by those of the ices NH3 at 9 AU and CO2 at 13.7 AU (see Table 1), i.e., from two to four times more distant from the star than the snowline of H2 O. To encounter the snowlines of the highly volatile molecules CO and N2 we need to go five to six times more distant than the snowline of CO2 , reaching 64 and 85 AU, respectively (see Table 1). The most abundant elements H and He, as well as the noble gas Ne (see Sections 1.2 and 2.2), never condense in circumstellar disks and always remain in gas form. As this illustrative example showcases, the different volatility of the elements and of their carriers (rocks, organics, ices) results in compositional gradients across the midplane of circumstellar disks: as we will see in Section 3, the farther we move from the star, the colder the local regions of the disk are, and the more volatile elements and molecules will condense adding to the mass fraction of solids. The colder the circumstellar disk, the closer the snowlines will be to the star: for a temperature profile similar to that of AS 209, the snowlines of H2 O and N2 would be at ≈1.2 and 33 AU, respectively, i.e., 2.5 times closer to the host star. To understand how abundant the different solid components are across the circumstellar disk, the information provided by the temperature profile needs to be combined with the one on the mass distribution provided by gas surface density profile. Based on observational data,52,59,60 the surface density profile of circumstellar disks can be expressed as   (2) Σgas (r) = Σc (r/rc )−γ exp − (r/rc )2−γ , where rc is the characteristic radius of the circumstellar disk, Σc the surface density at the characteristic radius and the exponent γ has been observational constrained in the range 0.8–1.52,59,60 Also in the case of the gas surface density profile, a number of present-day studies still adopt the classical parametrization derived in the case of the solar nebula53,61 : Σ = Σc (r/rc )−γ ,

(3)

where rc is generally 1 AU, Σc is about 2-3 × 103 g cm−2 (see Refs. 23, 53 and 61) and, more importantly, γ = 1.5.23,53,61 As illustrated

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Fig. 3. Comparison between the gas surface density profiles of circumstellar disks with the same total mass of 0.05 M using different parametrizations: the thick solid curve represents the surface density profile obtained from Eq. (2) with γ = 0.8, the thin solid line the surface density profile obtained from Eq. (3) with γ = 0.8, and the dot-dashed line is the classical solar nebula profile from Eq. (3) and γ = 1.5.53,61

in Fig. 3, the classical solar nebula profile is much steeper than those derived from astronomical observations of circumstellar disks. As a consequence of the more rapid fall of its gas surface density, the classical solar nebula profile is characterized by a higher concentration of the disk mass in the regions closer to the star. The dust density profile, i.e., the initial distribution of solids, is generally obtained from the gas surface density profile by adopting a dust-to-gas ratio ξ(r) across the extension of the protoplanetary disk: Σdust (r) = ξ(r) · Σgas (r),

(4)

where a constant value ξ(r) = 0.01 derived from observation of the interstellar medium62 is generally assumed.10 As we will see in Section 3, even at the beginning of the life of protoplanetary disks, ξ(r) is not constant throughout the disk but depends on the local mass fraction of condensed solids. Nevertheless, this approximation is reasonably accurate to estimate the global dust/solid mass in protoplanetary disks (see also Section 2.2).

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Equation (4) highlights how there is a direct proportionality between the gas and dust surface density profiles. Since the classical solar nebula is characterized by a higher concentration of gas in the regions closer to the star (see Fig. 3) and since these regions are also the hotter ones (see Eq. (1)) where fewer elements are condensed, the classical solar nebula profile is characterized by a larger abundance of refractory dust and a lower abundance of ice-rich dust compared to observationally-constrained circumstellar disks. This translates in the classical solar nebula being a comparatively less favorable environment for the formation of volatile-rich planetary bodies with respect to more realistic circumstellar disks. 2.2.

The host stars and their composition

The composition of stars is characterized by observationally measuring the abundances of the elements in their photospheres. Stellar abundances are expressed in what is known as the astrochemical abundance scale,39,63 where the abundances of the different elements are expressed in logarithmic scale in comparison to hydrogen, the most cosmically abundant element. The astrophysical abundance scale is a comparative scale that adopts as reference the abundance [H] of 1012 H atoms, meaning that the abundance of H is by definition 12 dex (log10 [H]). The relative concentration [X/H] of any given elements with respect to H is then expressed as [X/H] = 10X−H : in the case of oxygen, using the values from Table 2, [O/H] = 108.73−12 = 10−3.27 = 5.37 × 10−4 . A subtle yet important point to make is that, as mentioned above, the stellar abundances we can observationally characterize are the photospheric abundances of stars. These abundances are related to, but are not the same as, the abundances of the circumstellar disks that surrounded the stars while they were forming. During the life of a star, elements heavier than hydrogen are affected by sinking and over time they get slowly depleted from the stellar photosphere: in the case of the Sun, this effect is estimated to be of the order of 10%, i.e., 0.04–0.05 dex.39,63 Correcting for this effect allows to derive the abundances of circumstellar disks from those measured in stellar photospheres. Table 2 shows the protosolar abundances and the associated [X/H] relative abundances of the twenty most abundant elements, obtained through the previous procedure from recent estimates of the solar

The Compositional Dimension of Planet Formation Table 2. Element H He O C Ne N Mg Si Fe S Al Ar Ca Na Ni Cr Cl Mn P K

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Protosolar abundances of the elements.

Protosolar abundance

Mass fraction

[X/H]

12.00 10.98 8.73 8.47 7.97 7.87 7.63 7.55 7.51 7.16 6.47 6.44 6.36 6.25 6.24 5.66 5.54 5.46 5.45 5.08

7.15E-01 2.71E-01 6.09E-03 2.51E-03 1.34E-03 7.36E-04 7.35E-04 7.07E-04 1.28E-03 3.29E-04 5.65E-05 7.80E-05 6.51E-05 2.90E-05 7.23E-05 1.69E-05 8.72E-06 1.12E-05 6.19E-06 3.33E-06

1.00E+00 9.55E-02 5.37E-04 2.95E-04 9.33E-05 7.41E-05 4.27E-05 3.55E-05 3.24E-05 1.45E-05 2.95E-06 2.75E-06 2.29E-06 1.78E-06 1.74E-06 4.57E-07 3.47E-07 2.88E-07 2.82E-07 1.20E-07

Notes: Protosolar abundances of the twenty most abundant elements, their mass fractions in the protosolar mixture and their concentrations with respect to H. Values from Refs. 63–65.

photospheric abundances.63–65 Table 2 also shows the mass fraction of each element in the protosolar mixture. Mass fractions are obtained by multiplying the abundance of each element by its atomic weight and dividing the result by the sum of the same product over all elements in the stellar mixture. The information provided by the mass fractions is used to characterize the stellar composition by means of the three parameters X, Y and Z. X is the mass fraction of hydrogen, Y is the mass fraction of helium, and Z is the sum of the mass fractions of all remaining elements, also called the metallicity.39,63 From Table 2 we can see that in the protosolar mixture, H accounts for 71.5% (X = 0.715) of the total mass, He accounts for 27.1% (Y = 0.271) and the metallicity, i.e., all other elements, accounts for only 1.4% (Z = 0.014). For comparison, in the solar photospheric mixture X = 0.738, Y = 0.249 and Z = 0.013.63–65

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The value of the metallicity Z is an important parameter for planet formation as it represents the upper limit to the solid mass fraction that can be reached in circumstellar disks if all elements except for H and He condense. At the beginning of the life of protoplanetary disks the solid mass fraction Zsolids (r) matches the dust-to-gas ξ(r), so in the following we will use the two terms interchangeably. As different elements condense at different temperatures the solid mass fraction Zsolids (r) will always be lower than the metallicity Z (see Sections 1.2 and 2.1). This will affect the amount of solid material available to form terrestrial planets and the cores of giant planets as discussed in Sections 1.1 and 3. The case of neon is illustrative of this point: Ne represents about 10% of the metallicity Z in the protosolar mixture (see Table 2) and condenses as ice at about 9 K. It is doubtful that the temperature in circumstellar disks can reach such low values, as even in the case of the cold disk AS 209 discussed in Section 2.1 such temperature would be reached only at about 280 AU. As a consequence, the dust-to-gas ratio in circumstellar disks matching the protosolar composition will reach at most 1.28% or 0.0128. Note that this argument applies to the initial dust-to-gas ratio of circumstellar disks (see Section 2.1): as introduced in Section 1.1 and further discussed in Section 3, during the lifetime of disks the interplay between dust drift and dust growth will cause the differential migration between gas and dust and between dust grains of different sizes, resulting in locally higher or lower dust-to-gas ratios (see Section 3 and Ref. 52 for an illustrative example). As we will see in Section 3, the information supplied by the relative abundances [X/H] and the mass fractions of the different elements can be combined with that on the gas surface density and temperature profiles to build the gas and dust abundance profiles in circumstellar disks. Before proceeding, however, it is important to emphasize that, while the general considerations discussed in this section are valid for all stars and circumstellar disks, the protosolar composition cannot be used to universally characterize the nowdispersed circumstellar disks around other stars. Depending on their formation environment and their formation age with respect to the formation of the Milky Way, stars will possess different overall metallicities as well as different abundance ratios between their elements.10 As a result of the galactic chemical

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evolution, stars that formed earlier than the Sun will be generally characterized by lower metallicity values than the Sun, while younger stars will possess higher metallicity values. The spread in metallicity values for the currently known planet-hosting stars is of the order of 0.5 dex or a factor of 3.5 (see Ref. 10 and references therein). As the metallicity, also the ratios between their different elements, e.g., the carbon-to-oxygen ratio C/O and the magnesium-to-silicon ratio Mg/Si, will vary from star to star: expected variations are of the order of 0.3–0.4 dex or between a factor of 2 to 2.5 (see Ref. 10 and references therein). These differences in the initial elemental budget will translate in different chemical evolution histories of their disks and in different elemental partitioning between gas and solids across their extension. This, in turn, will translate into different compositions of the formed planets. 2.3.

Meteorites, comets and extrasolar materials

Alongside the stellar composition another important source of information on the elemental setup and the condensation processes of now-dispersed protoplanetary disks is supplied by the characterization of planetary materials, one of the most important of them being the meteorites. Meteorites are fragments of ancient planetary bodies that provide us a direct window into the processes that were occurring at the time planets were forming within the circumsolar disk. As a first classification, we can divide meteorites into two main categories24–26 : chondrites and achondrites. Chondrites are meteorites composed of materials that underwent no or limited modifications due to thermal or shock processes, their composition having been preserved mostly unaltered over the life of the Solar System (but see Refs. 40 and 41 for a discussion of the differences between the various classes of chondrites). Achondrites are instead fragments of planetary bodies that underwent more marked or complete thermal processing and, as such, their composition has been significantly altered by the geophysical evolution of their parent bodies. The most extreme examples of such alterations are provided by the metallic achondrites and the stony achondrites, fragments of the cores and the surfaces, respectively, of planetary bodies that underwent geophysical differentiation like the Earth. This means that both these classes of meteorites lack part of the initial elemental budget

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of their parent bodies, e.g., the metals in the case of the stony achondrites. While achondrites can provide us important clues on the timescales and the sizes of the planetary bodies that were forming in the solar nebula,24–26 for the purpose of understanding the initial elemental budget and condensation process of said planetary bodies our attention will focus on chondrites. Chondrites are divided into multiple classes,40,41 of which the CI chondrites are of particular importance. The elemental composition of CI chondrites is the one that most closely matches the solar composition except for the highly volatile elements C, O, N, H and the noble gasesa (see Table 3 and Fig. 4). All other classes of chondritic meteorites show decreased abundances of O and a trend of comparative enrichment/depletion in more refractory/volatile elements with respect to CI meteorites,40,41 suggesting they formed at higher temperatures based on the condensation sequence of refractory elements (see Section 1.2 and Refs. 40 and 41 for a discussion). These trends are broadly consistent with similar trends observed in the presence of carbonaceous and volatile elements in asteroids across the asteroid belt.66 Meteoritic abundances are generally expressed in the cosmochemical abundance scale39–41 : this scale works like the astrophysical abundance scale (see Section 2.2) in being a comparative abundance scale, the difference being that the reference abundance is provided by 106 atoms of Si (6 dex) instead of 1012 atoms of H.39–41 The two scales can be compared by equaling the abundance of Si atoms and scaling the abundances of all elements in the cosmochemical scale by the ratio between the abundance of Si in the astrophysical scale and 106 atoms of Si. Comparing the abundances of H in Tables 2 and 3 immediately highlights the reason for such change in the reference element. The abundance of H atoms per atom of Si is almost four orders of magnitude lower in meteorites than in a protosolar mixture, as only a minimal fraction of the total budget of H in circumstellar disks is sequestered by refractory materials or, more generally, by solids. As discussed in Section 1.2 and shown in Table 2, Si is a refractory element that is both abundant and condenses at high temperatures,

a The element Cl is notably underrepresented in CI meteorites with respect to the Sun, see Refs. 39–41 for discussion.

The Compositional Dimension of Planet Formation Table 3. Element H He O C Ne N Mg Si Fe S Al Ar Ca Na Ni Cr Cl Mn P K

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Meteoritic abundances of the elements.

Meteoritic abundance

Mass fraction

[X/H]

Meteoritic/solar abundance ratio

8.26 1.33 8.44 7.43 −1.08 6.30 7.57 7.55 7.49 7.19 6.47 −0.46 6.33 6.31 6.24 5.68 5.27 5.52 5.47 5.12

1.94E-02 9.06E-09 4.66E-01 3.42E-02 1.78E-10 2.96E-03 9.56E-02 1.05E-01 1.83E-01 5.26E-02 8.43E-03 1.47E-09 9.07E-03 4.97E-03 1.08E-02 2.63E-03 6.99E-04 1.93E-03 9.68E-04 5.46E-04

1.82E-04 2.14E-11 2.75E-04 2.69E-05 8.32E-14 2.00E-06 3.72E-05 3.55E-05 3.09E-05 1.55E-05 2.95E-06 3.47E-13 2.14E-06 2.04E-06 1.74E-06 4.79E-07 1.86E-07 3.31E-07 2.95E-07 1.32E-07

1.82E-04 2.24E-10 5.12E-01 9.12E-02 8.92E-10 2.70E-02 8.71E-01 1.00E+00 9.54E-01 1.07E+00 1.00E+00 1.26E-07 9.34E-01 1.15E+00 1.00E+00 1.05E+00 5.36E-01 1.15E+00 1.05E+00 1.10E+00

Note: Abundances in CI meteorites of the twenty most abundant elements expressed in the astrophysical abundance scale, their mass fraction in the chondritic mixture, and their concentration with respect to 1012 atoms of H. Values derived by scaling the values from Ref. 39 to the updated Si protosolar abundance.63–65

making it a convenient reference for measuring abundances in solids. The comparison between meteoritic and protosolar values in Table 3 and Fig. 4 provides several pieces of information. First, the abundances of all refractory elements in meteorites match the protosolar ones within 15% or 0.06 dex, the limit to the accuracy in the determination of meteoritic and stellar abundances (see Refs. 39–41 for a detailed discussion of the topic). This match is illustrated in Fig. 4 and indicates that, within the limits of the accuracy of the measures, in CI meteorites all elements belonging to the astrochemical refractory class are condensed in the same proportions as they were present in the solar nebula, which in turn indicates their complete condensation in the orbital region where

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Fig. 4. Comparison between the protosolar elemental abundances (Table 2, Refs. 63–65) and those of CI meteorites (Table 3, Ref. 39) for the twenty cosmically most abundant elements.

the parent body of CI chondrites formed. Because of this match, meteoritic and Solar System studies use the term chondritic composition to indicate planetary materials where the relative abundances of the refractory elements are in the same proportions as in the protosolar composition. As highlighted in Table 3 and Fig. 4, a body with chondritic composition does not possess protosolar abundances of the volatile elements H, C, O, N and the noble gases, which are all underrepresented in meteorites. Noble gases are present only in traces, with abundances in CI meteorites ten orders of magnitude lower than in the solar nebula. H, as mentioned before, is four orders of magnitude less abundant than in the solar nebula. The depletion of the elements O, C and N in meteorites is a function of their relative volatility: O, the comparatively more refractory of the three, is present in CI meteorites with about half the protosolar abundance, meaning that there is only half the total O budget available to form ices at lower temperatures. C and N are increasingly more volatile and are, respectively, present in CI meteorites with abundances that are about 9% and 3% their protosolar abundances. Cometary data,9,46,67 circumstellar disks,9,68 and the interstellar medium41,47,48,69 jointly allow us to investigate the fate of the C,

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O and N not accounted for by meteorites. Before proceeding, an important point to keep in mind is that in general these sources of data do not provide absolute abundances but relative ones: the abundances of the different molecules are measured as relative abundances with respect to water, the most abundant volatile molecule. As a result, in order to convert these relative abundances to absolute ones the information on the abundance of water is required. This, in turn, makes it necessary to know the abundance of O available to form ices, i.e., not already sequestered in molecules involving refractory elements as illustrated by CI meteorites. The information provided by the interstellar medium41,47,48,69 suggests that about 50–60% of O available in volatile form should be in the form of H2 O. Since CI meteorites reveal that about half the total budget of O is sequestered in refractory form before the snowline of H2 O in a protosolar mixture, the O incorporated into H2 O should amount to about 25–30% of the total protosolar O. When we scale by the abundance of H2 O, cometary data46,67 reveals that about 1/3 of the protosolar budget of C is present in comets as ices, mainly CO and CO2 as discussed in Section 1.2. While recent comparative observations support such a scenario of chemical inheritance of the volatile species in protoplanetary disks from the interstellar medium,9,10,70,71 it should be emphasized that also scenarios of chemical reset, where the volatile elements would recombine under different conditions of pressure and temperature with respect to the interstellar medium, are possible (see Refs. 9 and 48 for recent discussions). When the abundance of C in ices is added to the C already present in CI meteorites, refractories and ices cumulatively account for about 40% of the total budget of C. Recent observations of comet 67P Churyumov–Gerasimenko by the ESA mission Rosetta revealed that cometary dust is significantly richer in C than CI chondrites: specifically, the C/Si = 6 and C/H≈1 ratios measured in cometary dust suggest that about 60% of protosolar C is present in comets as organic material.46,72,73 Such a high abundance of organic material in cometary dust means that organics represent, alongside rocks, metals and ices, one of the main solid phases within circumstellar disks. The investigation of prestellar and protostellar environments also confirms the rich chemistry of organic compounds (see Refs. 9 and 10 and references therein).

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We can quantify the implications of such high abundance of organic material directly from the values reported in Table 3: C accounts for 2.5 ×10−3 of the total mass in the protosolar mixture or, equivalently, about 18% of the total mass of its Z elements (2.5 ×10−3 /1.4 ×10−2 ). If 60% of carbon is sequestered in organic compounds, this implies that organics represent about 10% of the total budget of Z elements that can condense as solids in circumstellar disks (see also Ref. 43 for similar considerations for the interstellar medium). This rough estimate does not account for the contributions of O, N and H to the mass fraction of organics in disks,42 yet cometary data suggests their mass contribution to be limited.46 Another information we can derive from cometary data and the interstellar medium is linked to N: as discussed before, only a minimal fraction (∼3%) of the protosolar budget of N is present in meteorites. Cometary ices appear to account for a commensurable fraction of N, likely no more than 10% of its protosolar budget, mainly in the form of NH3 ice. The investigation of the prestellar environments in molecular clouds shows how the majority of N is present as N2 in protoplanetary disks, which condenses as ice at extremely low temperatures (see Sections 1.2 and 2.1) and therefore remains in gas form across most of the disk extension.9,68 Recently, the atmospheres of young A-type stars still surrounded by their protoplanetary disks74 and the depletion patterns of elements in the gas of the disks75 have been used to probe the composition of extrasolar solid materials, revealing that the condensation behavior of elements around other stars follows the same general picture described by meteorites and comets in the Solar System. In particular, observations of S abundances in extrasolar materials in protoplanetary disks suggest that about 80–90% of S is locked in refractory form,74 in agreement with the estimated S abundance in cometary ices (10–20% of the protosolar budget, depending on the abundance of water on which the abundances of the different ices are scaled15,67 ) and with the uncertainty on the determination of the abundance of S in meteorites. Another source of information on extrasolar planetary materials comes from stars at the end of their life, specifically from the atmospheric contamination of white dwarf stars by the accretion of planetary bodies.76 The study of polluted white dwarf stars reveals that the composition of the planetary bodies they accreted is overall

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consistent, in terms of abundances of both refractory elements and O, with the composition of meteorites and comets in the Solar System,76,77 confirming how a large fraction of O is bounded with refractory elements and incorporated into rocky material as shown in the case of meteorites in Table 3.

3.

Compositional Structure of Protoplanetary Disks

By combining the information provided by the stellar composition, planetary materials and the thermal structure of protoplanetary disks as discussed in Sections 2.1–2.3 with the information on the condensation temperatures of the different molecules and materials discussed in Section 1.2, it becomes possible to quantitatively characterize the compositional structure of the planet-forming environments in protoplanetary disks. 3.1.

Metallicities of refractory materials, organics and ices

As discussed in Section 2.3 and illustrated in Fig. 4, the comparison of the elemental abundances in the protosolar mixture and CI meteorites shows that, with a 15% accuracy,39 all elements except for C, H, O, N and the noble gases are sequestered into solids before the snowline of H2 O. The sum of their mass fractions in the protosolar mixture reveals that refractory elements condensing in a CI chondritic mixture have Zref = 6.6 × 10−3 , i.e., about 47% of the protosolar Zproto = 1.41 × 10−2 . The comparison between the protosolar and chondritic mixtures highlights how, due to its high reactivity, O behaves both as a refractory and as a volatile element.38,40 By subtraction of Zref from Zproto , we can see that volatile elements account for 53% of Zproto , i.e., Zvol = 7.5×10−3 . About 18% of Zvol , however, is due to Ne that, as discussed in Sections 1.2, 2.1 and 2.2, likely does not condense in the environment of protoplanetary disks.38 This means that the mass fraction of volatile elements that can condense in protoplanetary disks and contribute to the building blocks of planetary bodies amounts to Zvol,cond = 6.2 × 10−3 . From these values it follows that the mass fraction of condensed material is globally lower than the Z value of the host star, e.g., lower than

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1.4% in the solar nebula, and the metallicity of the gas will globally remain higher than zero, i.e., we generally should not expect to have complete condensation of all Z elements in protoplanetary disks. Another observation we can derive from the comparison of Zref and Zvol is that, at full condensation of all Z elements (except Ne), their mass contributions to the planetary building blocks are about equal. As we discussed above, however, Zvol,cond is generally lower than Zvol , meaning that the mass of planetary building blocks is generally dominated by refractory materials as rocks and metals. Furthermore, as discussed in Section 2.3, about 60% of C appears locked by organics in protoplanetary disks, meaning that Zorg = 1.5 × 10−3 . By subtracting Zorg from Zvol,cond we finally obtain Zice = 4.7×10−3 , i.e., the total mass fraction of condensable ices. The abundance of organics discussed here has been constrained considering only the contribution of C and using observational data from the Solar System. It should be noted, however, that values about twice as high of Zorg were considered in previous studies of the interstellar medium.43 The process of quantifying and balancing the mass contributions described here can be repeated for the different ices composing Zice and the different refractory materials composing Zref to derive the growth of the solid mass fraction in protoplanetary disks when crossing each condensation temperature or snowline,8,15,43,69 as shown in Fig. 5 and illustrated in the following example. 3.2.

Modeling the compositional structure of gas and solids

The following illustrative example is derived from the protoplanetary disk model adopted in Ref. 15 and assumes ≈32% of total O locked in water ([H2 O/H] = 1.7 × 10−4 ), ≈6% of O locked in CO ([CO/H] = 3.4 × 10−5 ), ≈13% of O locked in CO2 ([CO2 /H] = 3.4 × 10−5 ), ≈60% of C locked in organics ([Organics/H] = 1.8 × 10−4 ), ≈3.5% of C locked in CH4 ([CH4 /H] = 1.0 × 10−5 ) based on the combined information from cometary data, the interstellar medium and astrochemical models.48 In terms of N, this model assumes that about 33% of all N not sequestered by refractory materials is in the form of NH3 and the rest in the form of N2 following the astrochemical models by Ref. 48. Note that this partition of N between NH3 and N2 contains much

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Fig. 5. Example of the compositional and solid mass fraction gradients in protoplanetary disks based on the disk model from Ref. 15 and discussed in Sections 3.1 and 3.2.

more NH3 than suggested by the interstellar medium,9,12,13 yet in the framework of this illustrative example this is not critical. The disk model adopted by Ref. 15 is characterized by the same temperature profile as the classical solar nebula, T = T0 (r/r0 )−β where T0 = 280 K and β = 0.5, meaning this disk is warm by the standard of protoplanetary disks (see Section 2.1). In such a warm disk, the ultravolatile molecules CO and N2 never condense and remain in gas form. In the inner and hotter regions of the disk, only refractory elements are condensed as rocks and metals (see Fig. 5). It is worth reminding that, as discussed in Section 1.2 and highlighted in the discussion on chondritic meteorites in Section 2.3, also refractory elements have their own condensation sequence.37,38,40,41 The bulk of the mass of refractory elements, however, is accounted by Fe, Si, Mg and S.39 The most volatile of them, S, condenses at about 700 K (i.e., between 0.1 and 0.2 AU for the adopted temperature profile) and by 1 AU the disk is cold enough for all refractory elements to condense. As a consequence, we can assume that in the inner and hotter regions of the disk Zsolids = Zref = 6.6 × 10−3 and the composition of solids is chondritic as a reasonable approximation. Studies focusing on the

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disk regions within 1 AU, however, need to resolve the condensation sequence of refractory elements. Moving outward, the first snowline we encounter is that of H2 O. As mentioned above, in this model water has an abundance relative to H of 1.7 × 10−4 , with a molecular weight of 18 atomic mass units. Given that in this relative abundance scale the abundance of H is 1 by definition and the atomic weight of His 1, we can compute the  mass fraction of H2 O with respect to H as 18 · 1.7 × 10−4 / (1 · 1) = 3.1 × 10−3 . As the disk gas is not composed only by H but includes also He and the Z elements, to obtain the mass fraction of water with respect to the total mass of the gas, we need to multiply the value just computed by the mass fraction of H in the protosolar mixture, i.e., 0.715 (see Table 2). This gives us the mass fraction of water ice, which is 0.715 · 3.1 × 10−3 = 2.2 × 10−3 . At the crossing of the H2 O snowline, therefore, Zsolids grows to 8.8 × 10−3 . Solid bodies and dust formed beyond the H2 O snowline will be composed of rocks, metals and water ice, as shown by Fig. 5. The following snowline is the one of organics,33,45 which in the model used in this example are assumed to be composed of C only. As the atomic weight of C is 12 and the abundance of organics with respect to H has been set to 1.8 × 10−4, the mass fraction  of organics with respect to the disk gas is 0.715 · 1.8 × 10−4 · 12 / (1 · 1) = 1.5 × 10−3 . The process is repeated at each subsequent snowline to obtain the values reported in Table 4, building the compositional structure shown in Table 4. Example of condensation sequence and Z mass fractions of solids and gas in the solar nebula. Material Rocks + Metals H2 O Org. C NH3 CO2 CH4 Protosolar

Snowlinea

Z solids

Z gas

0.15 AU 2.5 AU 5.0 AU 9.5 AU 10.5 AU 105 AU

6.6 × 10−3 8.8 × 10−3 1.03 × 10−2 1.07 × 10−2 1.18 × 10−2 1.19 × 10−2

7.5 × 10−3 5.3 × 10−3 3.8 × 10−3 3.4 × 10−3 2.3 × 10−3 2.2 × 10−3 1.41 × 10−2

Note: a The snowline of rocks and metals is arbitrarily located just outside the orbital distance where the disk temperature drops below the condensation temperature of S (see main text).

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Fig. 5. The metallicity of the gas Zgas in each compositional region is obtained subtracting Zsolids from Zproto . 3.3.

Effects of dust evolution and planetesimal formation

At the beginning of the life of protoplanetary disks the only solids populating them are dust grains. As a consequence, the solid mass fractions Zsolids reported in Table 4 and shown in Fig. 5 will correspond to the dust-to-gas ratios in the different compositional regions of the disk. The dust surface density profile Σdust can then be derived from the gas surface density profile Σgas as: Σdust (r) = Zsolids (r) · Σgas (r)

  = Zsolids (r) · Σc (r/rc )−γ exp − (r/rc )2−γ ,

(5)

where, as discussed in Section 2.1, rc is the characteristic radius of the disk and Σc the gas surface density at the characteristic radius. The initial dust density distribution described by Eq. (5) matches the distribution of solids in protoplanetary disks only at the very beginning of their life. As introduced in Section 1.1, dust orbits the central star on keplerian orbits while the gas is partially supported by the pressure gradient within the protoplanetary disk22 and, as a result, it orbits with sub-keplerian velocity. This differential orbital motion between gas and dust, with the latter moving faster than the former, results in the dust experiencing an aerodynamic drag. Small dust grains (roughly micron-to-mm sized) will experience the strongest drag effect and will quickly dynamically thermalize, become comoving with the gas. Larger grains (roughly mm-to-cm sized) will experience the headwind of the gas and will lose angular momentum, starting to radially drift inward with respect to the gas. As introduced in Section 1.1, the size-dependent nature of the drag process results in the differential motion between dust grains of different sizes. This differential motion plays an important role in enhancing both the dust growth and the planetesimal formation processes (see Refs. 20 and 21 for detailed discussions). From the perspective of the dust-to-gas ratio, this means that the distribution of the dust with respect to the gas will not necessarily remain as described by Eqs. (4) and (5), with

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several important implications for the compositional structure of the protoplanetary disk. First, the dust distribution of protoplanetary disks will evolve over time as the dust drifts inward toward the inner regions while the outer regions become dust-depleted.50,78,79 This process is observationally confirmed by the comparison of the radial extensions of gas and dust in protoplanetary disks, which reveals how the dust is two to four times more compact than the gas.52,80,81 Since the dust is expected to grow and, due to the size-dependent nature of gas drag, slow down22 and pile up in the inner regions of disks, this process will globally result in enhanced mass fractions of solids (i.e., the solid metallicity Zsolids ) up to the outer radius of the dust distribution.15,82 Because of the differential motion of dust grains with different sizes, however, this enhancement will not necessarily be homogeneous across the disk (see Ref. 52 for an illustrative example). Second, the drifting dust will deliver both refractory and volatile elements inward with respect to the different snowlines at which they condense as refractory materials, organics and ices. As a consequence, part of the condensed mass will be released back to the gas phase, increasing its metallicity Zgas . It should be emphasized how this enrichment will differ across the extension of the disk, as it will selectively concern only the sublimating element: as an example, inside the CO snowline Zgas will be enhanced due to the release of C and O in the gas, while inside the N2 snowline the enhancement will be due to N only. While the composition of solids throughout the disk will remain the same over time, that of gas will evolve. Planets accreting gas while crossing the metallicity-enhanced regions will possess higher metallicity values and will be selectively enriched in specific elements with respect to planets accreting gas not influenced by this process.11,13,16,17 It should be noted that the metallicity enhancement process caused by the dust drift and evaporation can be countered by the thermal evolution of disks, which will radiatively cool down during their lifetimes and experience an inward drift of their snowlines.49,83 As the enriched regions are crossed by the migrating snowlines, the sublimated elements will condense once again on the grains and revert the metallicity of the gas Zgas to its original state. The extent to which the two processes cancel out will depend on the balance between the dust and snowline timescales of inward drift.

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It is important to emphasize, however, that the above-mentioned processes are relevant only as long as most of the mass of solids throughout protoplanetary disks is in the form of dust grains. Since the dust is concentrated and converted into planetesimals during its drifting motion across the gas,20,21,27 over time more and more solid mass will be converted into planetesimals, decreasing the solid mass fraction accounted for by dust. As planetesimals are characterized by less favorable surface-to-volume ratios with respect to dust, when crossing a snowline only a minimal fraction of their mass will be directly affected by the higher temperature and sublimate or provide a site for the cooled volatiles to condense on.10,15 Planetesimal formation, therefore, will act to lower the efficiency of the gas enrichment process as well as the effects of the drifting snowlines described above. Once again, the net effect on the disk will depend on the balance between the timescales of the processes described above and that of the conversion of the dust into planetesimals. The latter process is expected to occur over a timescale of 1 Myr or less based on the most recent theoretical frameworks,20,21,27 a timescale consistent with that suggested by observational data in the Solar System and protoplanetary disks. Specifically, the planetesimal formation timescales derived from radiometric dating of meteorites24–26 are of the order of a few 105 years for the first generations of planetesimals to appear. In parallel, the observations of protoplanetary disks consistently show that disks older than about 1 Myr have dust masses too low to explain the formation of the large number of multi-planet systems we know to date,84 suggesting the conversion of large amounts of dust into planetesimals. Overall, these observational constraints suggest the possibility that the compositional structure of protoplanetary disks can stop evolving within the first 1 Myr, i.e., as soon as most of the initial mass of dust is converted into planetesimals.10,15

4.

Compositional Signatures of Planet Formation

The template protoplanetary disk we built as our working example in Fig. 5 illustrates how the solids and, by subtraction from the stellar composition, the gas at different distances from the star will be characterized by different compositions and elemental budgets: a

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body formed at 8 AU will include in its composition chondritic rocks and metals, water and organics, and will be richer in C and O with respect to a body formed at 2 AU, which will include only the O and C present in chondritic material (see Table 3). These differences can be expressed in terms of the abundance ratios among the different elements, among which O and C were the first used to characterize the composition of solids and gas in protoplanetary disks.69 Since then, a rich literature focusing on the study of the C/O abundance ratio in protoplanetary disks and exoplanets has developed (see Refs. 6 and 8–10 for recent reviews on the subject). The basic idea is illustrated in Fig. 6, where the upper plot reproduces the original figure from Ref. 69 while the bottom one performs the same computation for the template disk of Fig. 5. As the upper plot of Fig. 6 illustrates, at the crossing of the snowlines of their various molecules the abundance ratio between C and O will vary in both gas and solids. As an example, when crossing the H2 O snowline solids will be enriched in O, while gas will be depleted. As the H2 O snowline does not affect C, the C/O ratio of solids will decrease (constant C, increased O) while that of gas will increase (constant C, decreased O). At the crossing of the CO snowline, the most volatile carrier of C and O, the C/O ratio of solids will match the stellar one (assumed by Ref. 69 to be equal to the solar one of 0.55) as all C and O will be in solid form. Before the CO snowline, the C/O ratio of the gas will be 1 as CO molecules contain equal quantities of the two elements (see Fig. 6, upper plot). As a result of the higher relative volatility of C with respect to O, the C/O ratio of solids will be substellar (O condenses in solids earlier than C) while that of the gas will be superstellar. In principle, therefore, one can use the C/O ratio of a planetary body to constrain its formation region: gas-dominated giant planets should be characterized by superstellar C/O ratios. Because of the monotonic trend of the C/O ratio of the gas, the greater the C/O ratio of the giant planet, the farther away from the star it should have formed (see Fig. 6, upper plot). Terrestrial planets and super-Earths should be instead characterized by substellar C/O ratio unless they formed beyond the CO snowline. While the basic idea is sound, the interpretation of the C/O ratio is not necessarily as straightforward as it appears.

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Fig. 6. Illustrative examples of the C/O ratios of gas and solids across protoplanetary disks. The top panel shows the original distribution of C and O considered by Ref. 69 when discussing the use of the planetary C/O ratio as a window into the formation and migration histories of planets. The bottom panel shows the updated C/O ratios of gas and solids derived by Ref. 15 and accounting for the joint information provided by Solar System, interstellar medium and polluted white dwarfs. Note that the bottom plot is based on a warmer disk, which is why it does not include the CO snowline.

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The limits of the C/O ratio

For the interpretation of the C/O ratio to be unequivocal, the compositional structure of protoplanetary disks should satisfy the following two implicit conditions: (a) the compositional signatures created by the different snowlines should not be degenerate (i.e., multiple regions should not produce the same signatures) and (b) the differences in the C/O ratios of gas and solids across the different compositional regions should be large enough to be measurable. As the bottom panel of Fig. 6 illustrates, these two conditions are not necessarily satisfied in disks. Furthermore, planetary bodies would need to satisfy two additional conditions: (c) they should only accrete local material while forming, where by local material we refer to material from the same compositional region of the disk, and (d) they should migrate only after they reached almost their final mass. When we compute the C/O ratio of the gas and solids in the template protoplanetary disk from Fig. 5, accounting for the compositional information provided by all astrophysical sources discussed in Section 3, we can see that there is no monotonic trend in the C/O ratio of the gas, which instead oscillates around a value of 1 (see Fig. 6, bottom panel; also in this case the stellar C/O ratio is assumed to match the solar one). When looking at the solids we can see that, as soon as organics and water are added to their composition, their C/O ratio jumps to an almost stellar value (see Fig. 6, bottom panel). Since the snowlines of organics and water are the closest to the star,45 the C/O ratio of solids across most of the extension of the protoplanetary disk will be indistinguishable from the stellar one. Even in protoplanetary disks satisfying the conditions (a) and (b) discussed above, however, the information encoded in the C/O ratio is not necessarily unequivocal to interpret due to the process of planetary migration. As introduced in Section 1.1, planetary bodies embedded in protoplanetary disks will migrate due to their interactions with the gas. Planetesimals will experience an inward drift due to the aerodynamic drag of the gas whose intensity will vary with the size of the planetesimals.22 Small planetesimals can diffuse inward with respect to their original compositional region and be accreted by other planetary bodies along their path or by terrestrial planets during their final assembly long after the dispersal of the

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disk,27 altering their C/O ratio with respect to that of the orbital region where they formed. Large terrestrial planets formed while still embedded in the circumstellar disk will experience what is known as Type I migration34,35 and are expected to migrate over significant orbital fractions of the disk extension.28,85 Even in disks characterized by limited or no inward diffusion of the planetesimals, therefore, growing planets with masses encompassing the range of super-Earths will cross different compositional regions before reaching their final orbital location and can accrete solid material that can alter their C/O value and mask their original formation region. As an example, when we consider the disk depicted in the upper plot of Fig. 6, we can see that a super-Earth planet accreting half of its mass beyond the CO snowline and the other half between the CO2 and CO snowlines can end up with a C/O ratio resembling that characteristic of planets formed within the H2 O snowline (see Fig. 6 and Refs. 5 and 7). In principle, such ambiguity can be addressed by combining the information provided by the C/O ratio with the one arising from the planetary density, as a body formed beyond the CO2 snowline will be richer in ices than a body formed within the H2 O snowline. As the near-identical densities the asteroid Ceres and the dwarf planet Pluto reveal, however, the information supplied by density can be degenerate (see Ref. 7 for a discussion). The situation is similar for giant planets, which will experience both Type I migration during the growth of their core and Type II migration during the runaway accretion of their massive gaseous envelopes.18,28,34,35,86 During the runaway gas accretion phase, giant planets can accrete large masses of planetesimals or undergo giant impacts with other planetary bodies, acquiring in the process markedly supersolar metallicities15,87,88 consistent with those estimated for extrasolar giant planets1 and observed in the giant planets of the Solar System.89 Extracting details on the migration history of giant planets from their metallicity, however, is not straightforward, as the correlation between the extent of the migration and the metallicity is degenerate with respect to the migration rate.87 As a result, a rapid migration over a shorter distance can produce the same metallicity of a slower migration occurring over a longer distance.87 When

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the metallicity is decomposed into the abundances of the different elements and the C/O ratio is computed, moreover, its values can possess a limited diagnostic power, particularly for giant planets that experienced extensive migration, and only allow to discriminate low-metallicity, gas-dominated giant planets from high-metallicity, solid-enriched giant planets10,15 without providing information on the migration and formation histories (see Fig. 7). 4.2.

Expanding the inventory of elemental ratios

Following the increasing number of elements and molecules that are being identified and whose abundances are starting to be estimated in exoplanetary atmospheres,2–4,90 recent studies started exploring the information delivered by elemental ratios involving other elements than C and O. The initial focus of these studies has been on the elements N (see Refs. 12–15) and S (see Ref. 15), cosmically abundant elements at the opposite ends of the volatility spectrum. As discussed in Sections 1.2, 2.3 and 3.2, N is a highly volatile element whose bulk mass remains in gas phase for most of the extension of protoplanetary disks. S is instead a refractory element whose bulk mass condenses in solid form quite close to the star. Figure 7 shows a comparison of the elemental ratios C/O, N/O, C/N and S/N computed for a set of giant planets starting their formation at orbital distances compatible with the observations of young planets embedded into protoplanetary disks52,91–95 and migrating to become hot Jupiters.15 The top plot of Fig. 7 shows the elemental ratios of the giant planets when they accrete both planetesimals and gas during their migration. From left to right, the migration scenarios are associated to final planetary metallicity values going from the stellar one to eight times that of the star. The bottom plot shows the elemental ratios of giant planets accreting only gas and characterized by a sub-stellar metallicity. The compositional structure of the protoplanetary disk is similar to that discussed in Section 3.2 but assumes a more realistic 9:2 partition between N2 and NH3 .15 As can be immediately seen, the C/O ratio in both plots shows a flat profile with almost no sensitivity to how far the giant planets start their migration and to their actual metallicity. On the contrary, thanks to the higher contrast in volatility of N with respect to C and O, the C/N and N/O ratios show monotonic trends that deviate

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Fig. 7. Elemental ratios of giant planets migrating from different starting positions to become hot Jupiters while accreting both gas and planetesimals (top plot) or only gas (bottom plot) (data from the simulations of Ref. 15). The elemental ratios are normalized to the relevant stellar values, so a ratio of 1 means that the two elements are in the same proportion as in in the star.

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the more from the stellar values the farther away the giant planets start their migration. Since solids are richer in C and O than in N (see Section 3.2 for a discussion), the C/N ratio grows and the N/O ratio decreases with migration for giant planets where planetesimals contribute the most to the metallicity.10,15 For giant planets dominated by gas accretion the C/N ratio decreases while the N/O ratio increases with the extent of migration.10,15 It should be noted that the planetary elemental ratios in Fig. 7 are normalized to the relevant stellar elemental ratios.b This normalization allows to plot the different ratios on a common scale and highlights how, in this normalized scale, solid-enriched giant planets will possess C/N* > C/O* > N/O*.10,15 Giant planets dominated by gas accretion will instead be characterized by N/O* > C/O > C/N*.10,15 The S/N elemental ratio follows a monotonic trend similar to that of C/N (see Fig. 7), but the more refractory nature of S with respect to C allows to extract additional information from the comparison of the two ratios. Specifically, S/N* will be greater than C/N* when the metallicity is mainly due to the accretion of solids, as solids will contain more S than C (see Section 3.2). When the accretion of gas significantly contributes to the planetary metallicity, the C/N* ratio will be greater than the S/N* ratio due to the higher volatility of C (see Fig. 7). Therefore, the comparison of the normalized S/N* and C/N* ratios can allow to discriminate giant planets that accreted gas whose metallicity was enhanced by the drift and evaporation of ice-rich dust and pebbles across their respective snowlines (see Section 3.3) from those that were not affected by this process.10,15 Finally, because of the high contrast in volatility between S and N, the S/N ratio is directly proportional to the contribution of planetesimals and solids to the planetary metallicity and, as such, can be used as a proxy for the latter.10,15 Before concluding, it is worth noting that the properties discussed for the S/N ratio are not exclusive of S but are common to all refractory elements. This fact, combined with b As discussed in Section 2.2 (see also Ref. 10 and references therein), the various planet-hosting stars do not necessarily have elemental abundances matching the solar ones. As a consequence, the abundance ratios can provide meaningful information only when compared to those of the host star, not with the values characteristic of the Sun.

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the use of normalized ratios, can simplify the comparison between planets orbiting different stars since different ratios (e.g., Ca/N*, Ti/N*, Na/N*, Si/N*, Fe/N*) can be used to derive the same information, meaning that the choice of the specific elemental ratio to be adopted can be tuned to the observational data available on the planets and their stars. In conclusion, by normalizing the elemental ratios of giant planets to those of their stars and by comparing the behaviors of ratios of elements characterized by different volatility, it is possible to more robustly constrain the orbital migration and to determine the main source of the planetary metallicity, gas or solids, even without accurated knowledge of the planetary mass and radius (and, consequently, of the metallicity itself) or of the full planetary elemental budget.

5.

Future Outlooks and Concluding Remarks

The number of topics we touched upon during this brief dive into the compositional dimension of planet formation highlights how many different yet complementary pieces of information concur in producing our understanding of the composition of planets and how it comes to be. Rather than reviewing the most up-to-date observational data and theoretical models, the focus of our discussion has been on the process through which these different pieces of information can be connected and integrated into a unified picture. This approach was motivated by two reasons. The first one is that, as mentioned at the beginning of this chapter, discussing in detail each of these interconnected topics would be impossible in the framework of this single chapter. The second one is that all discussed topics are evolving at an extremely rapid pace thanks to the increasingly detailed data provided by existing observational facilities both on ground and in space. The incoming launch of the James Webb Space Telescope96,97 and, in a few years, that of the ESA space mission Ariel7,98,99 promise an unprecedented level of detail in the characterization of exoplanets. In parallel, in the incoming decade the Square Kilometre Array (SKA) promises as large a revolution in the compositional study of protoplanetary disks100–102 as that currently taking place thanks to the Atacama Large Millimeter/submillimeter Array (ALMA).

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While it is difficult, if not impossible, to anticipate the challenges that the new observational data and discoveries will pose in the coming years, this chapter aims at providing the readers with the conceptual tools needed to confront them. I hope that the readers will find these conceptual tools both useful and effective in supporting their efforts to investigate the relationship between the composition of planetary bodies and that of their formation environment. 6.

Q&A

Fernando Tinaut-Ruano: Is there a measurement of how much chondrite material is accreted in the Earth? Diego Turrini: There are estimates for Earth and the terrestrial planets of, typically, a few percent, and even tiny Vesta seems to have accreted a few percent of chondrite material. This material is thought to have been added after planet formation, differentiation and surface cooling as a “late veneer”. The physical argument for this is that differentiation should have been quite efficient at taking the densest elements down into the core, so heavy elements in the crust were presumably added after differentiation. The late veneer is also suspected to have brought the Earth’s water. Rene Duffard: Could water have been part of the original material of the Earth, not accreted later as a veneer? Diego Turrini: Yes. We don’t have a direct constraint on the original water and, after all, the Earth is rather dry (maybe 0.04% of the total mass) as far as we can tell from the surface abundances, so it wouldn’t need to be very wet in the beginning to supply the water we have. Water might have been delivered in another way, or in addition to the late veneer. But we think the Earth formed hot enough that water might not have been easily captured in the original material, so the late veneer origin of water is popular. It’s hard to generalize to extrasolar systems, because we often see planets at much colder locations where water would have been more easily captured in the original material, and the need for a late veneer is reduced. Julia Maia: We always hear that CAIs are the oldest things in the solar system, but one of your plots shows that some chondrules can be older than CAIs. How do you explain that?

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Diego Turrini: The plot is not up-to-date (2007) and older CAIs were discovered after this plot was made. The age determinations are always being updated and improved, but the main point is that the oldest CAIs predate everything else, typically by a million years. But it could change. Luisa M Lara: How much do the timescales for planetesimal formation matter in the models? Diego Turrini: Possibly quite a lot. For example, in a disk that is cooling, the first-formed bodies would be ice poor, but if the temperature drops a lot, then later generations could form from cold material and be ice rich. The problem is that the cooling and dynamical timescales are both short, and are not very well constrained by observations. It means that we need to worry not just about position in the disk, but also about the time of formation. This is a frontier area of research. References [1] D. P. Thorngren et al., The mass-metallicity relation for giant planets, ApJ. 831(1), 64 (Nov., 2016). DOI: 10.3847/0004-637X/831/1/64. [2] A. Tsiaras et al., A population study of gaseous exoplanets, AJ. 155(4), 156 (Apr., 2018). DOI: 10.3847/1538-3881/aaaf75. [3] A. Pinhas et al., H2 O abundances and cloud properties in ten hot giant exoplanets, MNRAS. 482(2), 1485–1498 (Jan., 2019). DOI: 10. 1093/mnras/sty2544. [4] L. Welbanks et al., Mass-Metallicity trends in transiting exoplanets from atmospheric abundances of H2 O, Na, and K, ApJL. 887(1), L20 (Dec., 2019). DOI: 10.3847/2041-8213/ab5a89. [5] D. Turrini, R. P. Nelson, and M. Barbieri. The role of planetary formation and evolution in shaping the composition of exoplanetary atmospheres, Exp. Astron. 40(2–3), 501–522 (Dec., 2015). DOI: 10. 1007/s10686-014-9401-6. [6] N. Madhusudhan et al., Exoplanetary atmospheres—chemistry, formation conditions, and habitability, SSR. 205(1–4), 285–348 (Dec., 2016). DOI: 10.1007/s11214-016-0254-3. [7] D. Turrini et al., The contribution of the ARIEL space mission to the study of planetary formation, Exp. Astron. 46(1), 45–65 (Nov., 2018). DOI: 10.1007/s10686-017-9570-1. [8] N. Madhusudhan. Exoplanetary atmospheres: Key insights, challenges, and prospects, ARA&A. 57, 617–663 (Aug., 2019). DOI: 10.1146/annurev-astro-081817-051846.

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c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 0002

Chapter 2

The Mercurial Sun at the Heart of Our Solar System

Philip G. Judge High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO, USA [email protected]

As the powerhouse of our Solar System, the Sun’s electromagnetic planetary influences appear contradictory. On the one hand, the Sun for aeons emitted radiation which was “just right” for life to evolve in our terrestrial Goldilocks zone, even for such complex organisms as ourselves. On the other, in the dawn of Earth’s existence the Sun was far dimmer than today, and yet evidence for early liquid water is written into geology. Now in middle age, the Sun should be a benign object of little interest to society or even astronomers. However, for physical reasons yet to be fully understood, it contains a magnetic machine with a slightly arrhythmic 11 year magnetic heartbeat. Although these variations require merely 0.1% of the solar luminosity, this power floods the Solar System with rapidly changing fluxes of photons and particles at energies far above the 0.5-eV thermal energy characteristic of the photosphere. Ejected solar plasma carries magnetic fields into space with consequences for planets, the Earth being vulnerable to geomagnetic storms. This chapter discusses some physical reasons why the Sun suffers from such ailments, and examines consequences through time across

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the Solar System. A Leitmotiv of the discussion is that any rotating and convecting star must inevitably generate magnetic “activity” for which the Sun represents the example par excellence.

1.

Introduction

This chapter attempts to introduce astronomers concerned with exoplanetary studies to electromagnetic solar influences on its planetary system. The approach follows that of a recent book,1 presenting a viewpoint of a physicist and astronomer, not of a solar specialist. Table 1 lists gross solar properties, which could be used together with elemental abundances and data from elementary physics, to construct a theoretical star of the kind shown in Fig. 1. But this fictional star merely reflects a star without magnetic fields. Magnetism arises from the differential motions of ions and electrons within plasmas like the Sun, and because there are no magnetic charges (monopoles), magnetic fields are not shorted out, and can pervade plasmas. In contrast, large-scale electric fields cannot be supported in plasmas. The interactions between solar plasma and magnetism constitute the main focus of interest in modern solar physics. The clearest signature of magnetism in stars and the Sun is in spots (Fig. 2). Not only are these much darker than the granulated surface, but by using polarized light the magnetic flux can be measured through the Zeeman effect (a technique started by Hale et al.2,3 ). Table 1.

Some basic properties of the Sun.

Age Mass M Radius R Distance Luminosity L Irradiance at Earth Average rotation period∗ Tilt of rotation axis to ecliptic Stellar spectral type B − V color Absolute magnitude MV

4.54 Gyr 2 × 1030 kg 700,000 km 150,000,000 km ≡ 1 AU 4 × 1026 W 1.365 kW m−2 27 days 7◦ G2 V 0.65 4.83

Note: ∗ The surface rotates differentially, from 25 days at the equator to over 30 days near the poles.

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Normal modes of oscillation

T ( ) ≈ Teff

(

3 1 + 4 2

)

1 4

Surface convection

Fig. 1. A fictional star without magnetic fields. The equation shows the run of temperature with gray optical depth τ for a radiative equilibrium atmosphere. The left panel shows limb darkening and surface convection, with roughly 4 million granules on the solar surface at any moment. The right panel shows Doppler shifts associated with the incoherent superposition of normal modes of oscillation. The solar rotation is seen as an East–West gradient, spanning ±2 km s−1 .

The present discussion encompasses the Sun’s behavior as it affects the Solar System, from zero-age main sequence to the present day and beyond. On short timescales compared with thermonuclear processing, this magnetic “activity” is responsible for electromagnetic disturbances perturbing the planets. Over 5 decades, solar and stellar studies reveal that magnetically induced solar variations associated with sunspots are not exceptional among the stars. It is, however, somewhat mercurial a : on the one hand, the well-known sunspot cycle (an aspect of which is shown in Fig. 3) is the most regular 11-year cyclic variation of all stars.4 On the other, these cycles are punctuated by irregular epochs of weakened magnetic influences on timescales of centuries. Dynamic, unpredictable flares often associated with coronal mass ejections (CMEs) vary over timescales of minutes.5 CMEs are magnetized bubbles of energetic plasma into interplanetary space unleashed by the Sun, frequently with consequences for a society dependent on a stable global electromagnetic environment.5 The precise mechanisms underlying this behavior a A character described as changeable; volatile; lively; sprightly; fickle; flighty; erratic. From Greek mythology.

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Fig. 2. The images reveal observational signatures of solar magnetic fields. Outside of sunspots magnetism is best detected through the polarization of light by the Zeeman effect. Sunspots themselves are aligned mostly E–W and are believed to originate from the emergence of tori of magnetic field generated by differential rotation of fluid in the solar convection zone (Ω-effect). Polar magnetic fields are traced by coronal plasma along N–S oriented rays in the coronal image. The schematic “dynamo cycle” of magnetic field is illustrated demonstrating the continuous process of generating poloidal fields (seen at the pole) from toroidal fields (sunspots), and vice versa.

Fig. 3. The signed surface magnetic flux densities (units Mx cm−2 ) are shown as a function of time and latitude, derived from Stokes V profiles of spectral lines (lower right spectral image in Fig. 2). Poloidal components are seen as the shaded patches close to the two poles, and the (mostly) toroidal fields are seen in the “butterfly wings” which are mostly oriented E–W (Fig. 2). Between these, surface fields propagate toward the poles, mostly of opposite polarity to the polar fields, appearing to reverse the polarity of polar fields every 11 years. The butterfly wing pattern was originally discovered by Annie and Edward Maunder in 1904.

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remain beyond current understanding. However, some of the ingredients that are known are discussed in an Appendix, acknowledging that nonlinear and non-local physical effects still present us with significant fundamental challenges. Thus, our understanding is still largely driven by observations and not from consideration of first principles. This argument applies both to the regeneration of global solar magnetism discussed in the appendix, as well as effects such as coronal heating and dynamics (e.g., Ref. 6). 2.

A Nonmagnetic Sun

A fictional Sun-like star without magnetic fields (Fig. 1) has benign influences on its planetary system: • The star brightens on the main sequence by just 13% per Gyr, with a ZAMS effective temperature Teff of 5,660 K, increasing by ≈ 25 K per Gyr. • The planets are irradiated by a near black-body spectrum with temperature near Teff . • These irradiances would be weakly modulated by small amplitude random variations of surface convection (granules) on periods between 2 and 10 min, and the linear oscillations of normal modes of oscillation of the elastic sphere would peak near periods of 5 min.7 This fictional star would provide a stable input to interplanetary space over aeons, conducive to the slow evolution of life, necessary perhaps to develop complex multi-cellular life like ourselves.8 It would possess no reservoir to store free energy in its atmosphere outside of those in fluid wave modes, and emit almost no UV or Xradiation. In stark contrast, Fig. 4 also shows solar spectra between the maxima and minima of the 11-year cycle of sunspots. No solar magnetism means no ionosphere. 3.

Magnetic Sun

The reasons why the Sun must behave according to Figs. 2–4 are by no means obvious, either from a theoretical (see the Appendix) or empirical point of view. For example, there exist rapidly-rotating

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Fig. 4. Five flux spectra relevant to Sun-like stars are shown. Smooth lines show black body spectra. The lower line is a reference spectrum measured close to minimal solar magnetic activity,9 the black a representative spectrum close to sunspot maximum. The arrow indicates wavelengths at which the N2 molecule, dominant in the thermosphere, is photo-dissociated, indicating that a non-magnetic Sun would possess no permanent ionosphere. However, stratospheric ozone (O3 ) would be formed in either case.

Sun-like stars without spot cycles, with more energetic magnetic fields and lacking the level of symmetry exhibited in time and space by the Sun in Fig. 3. Sun-like stars can show spots on rotational time scales (weeks) but with no sunspot cycles (e.g., Ref. 4). The solar magnetic fields can usefully be projected on to poloidal and toroidal components (Fig. 2, see also the appendix), which are convenient also for modeling solar magnetic evolution (e.g., Ref. 10.) In the context of models described in the appendix, the solar cycle involves the repeated interplay between the toroidal and poloidal fields on a time scale of 11 years. Some effects of these variable surface magnetic fields are highlighted in Fig. 5, showing an image of the solar disk seen in the resonance line of He+ (orange) at 30.4 nm. It is seen as a prominent peak along with the H Lα line at 121.6 nm in the flux (irradiance) spectra shown in Fig. 4. These lines arise from plasma close to 100,000 and 20,000 K, respectively. It also shows the solar corona close to 1 million K observed in broadband light (darker orange), both images from instruments on the SoHO spacecraft. The dark orange “ear-like” structure is a CME extending over a solar radius above the surface. CMEs are enormous, hot magnetic plasmoids arising from and separated from the Sun by magnetic reconnection.5,11 The right half of the figure shows a

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Fig. 5. Two images of the real Sun observed by instruments on the SoHO spacecraft are shown (left) along with a sketch (not to scale) of the Earth and its magnetosphere (right). A non-magnetic star would show neither the solar disk nor corona, could not produce energetic particles (white dots) or a mass ejection, and the Earth’s magnetosphere would be unperturbed. Adapted from ESA.

sketch (not to scale) of the CME later as it has propagated through interplanetary space (diffuse tan), energetic particles (white dots), the Earth’s magnetosphere (blue) and the CME as it later impacts the magnetopause region of Earth’s atmosphere. The cartoon shows a quiescent phase before the blue (magnetospheric) and tan (CME) magnetic fields interact. More consequential are those phases where the CME plasma gains entry into the Earth’s magnetosphere through magnetic reconnection at the interface region (“magnetopause”) and in the stretched out tail of the magnetosphere, causing potentially damaging geomagnetic storms. These phenomena all arise from the storage and release of magnetic free energy in the corona, caused by the emergence and perturbation of magnetic fields generated by dynamo action in the solar interior.12 The measured irradiation of the Solar System varies on all time scales from seconds (flares) to decades (the waxing and waning of sunspots). Representative variations over decades are shown

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in Fig. 4, showing typical solar spectra, representative of a minimum and maximum in the number of spots on the Sun. These changes occur on a timescale of just 5 years! The figure also shows that little of the entire solar luminosity is carried shortward of 200 nm, but that the variations in the irradiance increase systematically with decreasing wavelength. Soft X-rays of 1 keV energy (wavelengths near 1 nm) vary over decades almost by a factor of 10 as sunspots come and go. By comparison, the total (wavelength-integrated irradiance as measured at Earth) varies only by about 0.1%. However, the passage of a single large sunspot group over several days can change the total irradiance for days by 1%. Numbers of short-lived but highly energetic solar flares and CMEs are statistically correlated with sunspot numbers,13 during which the EUV and X-ray irradiances can increase by orders of magnitude over minutes and hours. Later we will see that the Sun can produce far more energetic flares than have yet been recorded. In short, the differences between the fictional star and the Sun indicate that the Sun is a machine which generates magnetic fields, with a strong 22 year periodicity. The evolving magnetism emits high energy radiation and plasma particles into interplanetary space, which fluctuate on timescales down to minutes.

The appendix summarizes what this remarkable solar behavior implies about underlying physical causes. 4.

The Sun, Stars and Life on Earth

We inhabit a planet around an ordinary, middle-aged star in the outer parts of an ordinary spiral galaxy. Even before the first detections of extrasolar planets, astronomical evidence (in the distribution of elemental abundances), together with the remarkable success of the theory of stellar evolution (e.g., Ref. 14), suggests that the Solar System is an ordinary and natural product of stellar and galactic evolution. It arose from the debris of earlier generations of ordinary massive stars which lived their whole lives in the Galaxy. In terms of universal life, and assuming (as usual) that the laws of nature are universal, this mundane situation raises profound philosophical questions: is life nevertheless so rare that our Solar System is the

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only place in the universe with life? Or is life teeming across the universe,8 in which case, where is everyone (a question attributed to Enrico Fermi in 1950)? After Earth’s formation, bombardments, tectonic activity and the acquisition of water, the Earth entered a phase of relative stability suitable for the early creation of life. Threats to life over the following aeons include variations in global climate, asteroid and meteoroid collisions, and, perhaps, high energy events from the Sun. The remains of this discussion ask how did the Sun’s magnetic machinery evolve, and could there have been important consequences for evolution of complex life on Earth? After all, high energy electromagnetic disturbances were essential components leading to the “primordial soup” of amino acids from inorganic ingredients in the famous Miller–Urey experiments in the 1950s. In this “big picture” view, I am struck by a poetic parallel which can be drawn between planetary and stellar magnetism. After the formation of the first stars, young massive stars converted primordial H, He and a trace of Li into the array of elements generated both by fusion and neutron capture processes. Thanks in part to the decay of radioactive elements like 232 U in the interior, the Earth’s core is heated, and in part, molten and subject to convection. Coupled with Earth’s rotation, Walter Els¨asser16 first suggested that the convecting fluid then generates its own magnetic field. serving as a protective shield against hostile energetic charged particles of cosmic and solar origins. Thus, while the Sun’s magnetized fluid generates threats, the Earth naturally generates a natural defense, through the same kind of mechanism (a dynamo). The story of stellar rotation and associated magnetic evolution on the main sequence is also perhaps a poem of epic proportions: • rotation and convection are natural consequences of the formation and evolution of stars, • these are the essential ingredients to generate global and variable global magnetic fields (appendix), then • an increase in temperature is an unavoidable consequence of the motions of emerging magnetic fields and ion–neutral collisions,17 so that • all the elementary physical ingredients are naturally available to generate a magnetically active corona,18 then

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• the pressure of hot coronal plasma leads to expansion that cannot be contained by the interstellar medium, causing the solar wind,19 and then • the magnetic torque exerted by the Sun on the rotating, frozen-in wind plasma then slows solar rotation, and finally • on main sequence lifetimes, the slower rotation weakens the magnetic fields generated in the interior. This story, based on first principle ideas. is borne out by data. Beginning with the work of Skumanich in 1975,20 the rotation rates Ω of Sun-like stars were related to stellar age t as Ω(t) ∝ t−1/2 ,

(1)

based upon just four data points (open cluster stars and the Sun). The recent advent of asteroseismological stellar age determinations from missions such as Kepler and TESS has vastly extended Skumanich’s early picture, from a single relation Ω(t) to dependencies on more variables. As an example, Ω(t, [B − V ]0 ), for main sequence stars, is shown in Fig. 6.

Fig. 6. A modern summary of relations between stellar rotation and age. For each color index, a single curve along the surface gives the empirical rotation-age relationship. Measurements of rotation period can thus be used to estimate stellar ages, a method termed “gyro-chronology”. Adapted from Ref. 15.

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Fig. 7. Three possible histories of high energy (EUV) radiation of the Sun are plotted, depending on the assumed zero age main sequence rotation rate. The “Skumanich” law, derived from data between 40 and 4,000 Myr, would be a straight line with slope –1/2 in this plot. Various eras in the histories of Earth and Mars are indicated. The earliest fossil evidence for life on Earth is dated at 3,465 Myr ago, an age of ≈ 1,080 Myr, defining the beginning of the Archean era. Adapted from Ref. 21.

Armed with data from a variety of spacecraft over decades, we can consequently infer that the early Sun flooded the Solar System with far more intense UV and X-radiation than it does today. Figure 7 is a recent representation of possible histories of high energy radiation of Sun-like stars with age on the main sequence. The implications of this story of solar rotation are explored further in Section 5. 5. 5.1.

A Closer Look Stars like the Sun

The Sun does not belong to any known stellar group, but it is similar to the stars in the open cluster M67. Gyro-chronology suggests an age of 4 Gyr for the stars of M67. The Sun is 4.54 Gyr old (Table 1). The cluster is too distant (800–900 pc) to observe G2 V stars at UV and X-ray wavelengths (mV ≈ 14.5). Thus, we are left to compare the Sun’s magnetic activity mostly with nearer, brighter field stars.

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Many authors have sought a genuine “twin” for the Sun among the stars. Currently, the best candidates are HD 146233 (18 Sco) and HD 186302 (https://en.wikipedia.org/wiki/Solar analog). A group of genuine “solar twins” would be of enormous practical use and interest in our quest to relate solar behavior to other stars. Genuine twins would permit us to assess if there are any special properties about the Sun. However, nature presents us with challenges: • The Sun is “old” in the sense that spin-down by angular momentum loss has already occurred at 4.5 Gyr sufficient to have erased any “memory” of the ZAMS angular momentum (Fig. 7). As such it is therefore magnetically “inactive” among its younger stellar relatives, and it is not highly luminous in UV or X-ray wavelengths. • While there are ≈ 500 stars in our immediate neighborhood (d ≤ 30 pc), they reflect the known initial mass distributions and so of these, only about 25 are G stars of luminosity class V. Of these only about 13 have spectral types between G0 and G4. • The dimensionality of a “Sun-like” space of variables is a little subjective. But this space must contain at least ZAMS mass, metallicity, age and rotation rate. Figure 8 reveals the dearth of possible candidates in two scatter plots.

Fig. 8. Known solar twin candidates are plotted in terms of metallicity (left panel) and effective temperature (right panel) as a function of stellar age. The Sun is shown as an open black circle. Estimates of typical uncertainties are represented by the black box. Adapted from https://en.wikipedia.org/wiki/Solar analog.

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Not only are there few twin candidates, but the typical uncertainties are large: 4–5 different stars are identical with the Sun within the uncertainties. But this situation is expected to improve as Sunlike stars become the focus of the large number of exoplanetary scientists. Stars of solar mass through time

5.2.

Again our focus is on magnetic activity and not stellar evolution per se. Researchers have documented not only the high energy emission, but also bulk wind properties using observations at visible UV to X-ray wavelengths. Nice reviews are available from G¨ udel.22,23 Figure 9 highlights how high and low energy emission evolves in time, as represented by surface flux density measurements of several stars of 1 . The harder the radiation, the faster it decays with age. The generic “EUV” emission (wavelengths between about 10 and 91 nm) used in the geospace community cannot be measured for enough stars owing to large Lyman-continuum optical depths in the interstellar medium. The “EUV” emission presumably lies between the

103

1

10

100 EK Dra (130 Myr)

–1

10

1

π UMa (300 Myr) 1

κ Cet (750 Myr)

–2

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1

β Com (1.6 Gyr) β Hyi (6.7 Gyr)

–3

10

10–4

Flux density at 1 AU (erg s –1 cm–2 Å–1)

10 Flux at 1 AU (erg s –1 cm–2 Å–1)

14

O VI

2

12

0.1 Gyr (EK Dra) 1 0.3 Gyr (π UMa) 1 0.65 Gyr (κ Cet) 1.6 Gyr (β Com) 6.7 Gyr (β Hyi)

O VI

10 8 6

C II

4 2 0

1

10

100 Wavelength (Å)

1000

1030

1032

1034 1036 Wavelength (Å)

1038

Fig. 9. Levels of emission from Sun-like stars are shown as a function of age on the main sequence. Flux densities at the stellar surface can be derived by multiplying by (1AU/R = 215)2 = 4.6 · 104 . Note the logarithmic and linear scales plotted, and the gap between 120 and 1,000 ˚ A caused by interstellar absorption. Adapted from Ref. 22.

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UV and X-ray behaviors shown. The very steep trends in UV emission and X-ray emission are somewhat different, the latter indicating that coronal soft X-ray emission cannot exceed a limit near 2·1030 erg, 6 · 107 erg cm−2 s−1 , or 0.005 L . This “saturation” has been known for almost four decades, but the underlying reasons are still debated. Note that the present day Sun’s 100-nm UV spectrum (emission lines and continua are both important for upper atmospheric chemistry and dynamics) is some 1 and 2 orders of magnitude weaker than stars of age 2 and 0.1 Gyr, respectively. The (nonlinear) dynamical responses of the Earth’s atmosphere to between 1 and 10 times the mean solar EUV flux have been studied.24,25 The Earth’s atmosphere does not blow off (i.e., the thermal energy at the “exobase” does not exceed a critical fraction of the gravitational potential energy). This is because hydrodynamic flow and adiabatic expansion sap the available energy for heating the upper atmosphere for levels of EUV flux 5 times those of the mean presentday Sun. In contrast, Mars would have lost any initial atmosphere, only able to maintain a warm and wet period several hundred Myr after Mars formed (see Fig. 7) when the EUV fluxes dropped within an order of magnitude of the current Sun.26

5.3.

Flares and CMEs

The above arguments rely on data from “typical” observations, not those rarer phenomena such as flares. Again, a vast quantity of data has been analyzed for the Sun27 and significant progress again has been made with recent photometric asteroseismology missions for Sun-like stars.28 One might expect that flaring might be higher in intensity and frequency in younger stars. The story is even now unfolding as recent satellite databases undergo more and more scrutiny. Flares recorded on Sun-like stars (Fig. 10) extend far higher in energy than the largest in solar history,29 the “Carrington Event” of 1959, with an estimated energy of 1033 ergs. Flares last shorter than 24 hours, so that while the impact of flare radiation on surface life might be serious on the illuminated hemisphere, areas in shadow would not receive devastating doses of high energy radiation. We can speculate that this intermittent source of energy on genetic mutations might have been relevant to the evolution of complex life on Earth.

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Fig. 10. The occurrences of flares on Sun-like stars from the Kepler mission are shown as a function of flare energy in several stellar age bins. The strongest ever (“Carrington”) flare of 1859 is estimated to have released about 1033 erg. The figure suggests that a flare of 1034 erg might occur once every 2,000 years or so on the present Sun. In contrast, at 1 Gyr (a rotation period near 10 days) this flare would occur once every 30 years or so. Adapted from Ref. 28.

6.

Conclusions

Absent from this brief discussion is the importance of understanding why the Sun is obliged to produce sunspots with the pulse of a 22 year cycle (Figs. 2 and 3). Hopefully ground-based observations of chromospheric Ca+ lines begun in 1966 will continue over many more decades4 and for more stars, to improve our knowledge of what might cause and then suppress cycling behavior, for stars having the same convection and rotation properties. The answer to why the Sun and a few stars must do this is central to our understanding of magnetic evolution, also giving insight into the weaker pulse of sunspot signals during the Maunder Minimum (1645–1715, see Ref. 30). Curiously, the Sun presents the most ordered 22-year cycle of all field G stars, only about 10% of which show clear cycles.4 Young field G stars tend to show strong irregular variability, old stars weak, if any, secular variations. In terms of cycle properties, the Sun is more similar to field K stars.

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The magnetic machinery of Sun-like stars is only partly understood from first principles. Neither the operation modes of the global dynamo or the manner in which energy is released in the atmosphere with accompanying high energy particles and radiation are understood. They are relatively well documented in our observations. But because of the enormous challenges facing theorists, solar physics will continue to be an observationally driven field. The place of the Sun among the stars will remain of central interest to our understanding of astrophysical dynamos and plasma physics, and it will become clearer as our datasets improve. 7.

Q&A

Luisa M Lara: Why the “mercurial” Sun? Philip Judge: Mercurial means unpredictable or behaving in a way that is not easy to understand. So, just like the Sun. Thea Kozakis: What would a Carrington event do to Earth today? Philip Judge: UV and X-ray enhancement would change the conductivity of the ionosphere. Changing the conductivity and currents in the ionosphere would cause large induced fields that can induce currents in electronics, a bit like the electromagnetic pulse caused by atmospheric detonation of a hydrogen bomb. Your computer would be fried. Charged particles would bombard the planet and are capable of damaging DNA in exposed animals. How serious that would be depends on many unknown parameters, but the fact that Carrington events must be common and that we are still here means that it would not be devastating. However, the flaring Kepler stars do show events much larger than Carrington events (5 × 1023 erg), and maybe the Sun does that, too, although more rarely. Even large flares might not cause widespread extinction, but they still can do a lot of damage. Everything would be OK if you’re a dolphin (protected by water) or a tough bacterium, but it is less clear for humans. References [1] P. G. Judge, The Sun: A Very Short Introduction. Oxford University Press, Oxford, UK, 2020.

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[2] G. E. Hale, On the probable existence of a magnetic field in sun-spots, ApJ. 28, 315 (1908). [3] G. E. Hale et al., The magnetic polarity of Sun-spots, ApJ. 49, 153 (1919). [4] R. Egeland, Long-term variability of the sun in the context of solaranalog stars, Ph.D. thesis, Montana State University, Bozeman, Montana, USA, 2017. [5] J. A. Eddy, The Sun, the Earth and Near-Earth Space: A Guide to the Sun-Earth System NASA, 2009. [6] P. G. Judge, The enduring mystery of the solar corona, Physics World, 34(9), 38–42 (2021). [7] R. K. Ulrich, The five-minute oscillations on the solar surface, ApJ. 162, 933–1002 (1970). [8] D. C. Catling, Astrobiology, 1st edn., Oxford University Press, Oxford, UK, 2013. [9] T. Baltzer et al. The new LASP interactive solar irradiance datacenter (LISIRD). In EGU General Assembly Conference Abstracts (2018), EGU General Assembly Conference Abstracts, p. 10587. [10] M. Dikpati and P. Charbonneau, A Babcock-Leighton flux transport dynamo with solar-like differential rotation, ApJ. 518, 508–520 (1999). [11] E. Priest and T. Forbes, Magnetic Reconnection: MHD Theory and Applications. Cambridge University Press, Cambridge, UK (2000). [12] A. S. Brun and M. K. Browning, Magnetism, dynamo action and the solar-stellar connection, Living Rev. Solar Phys. 14, 4 (2017). [13] K. B. Ramesh, Coronal Mass Ejections and Sunspots—Solar Cycle Perspective, ApJL. 712, L77–L80 (2010). [14] E. M. Burbidge et al. Synthesis of the Elements in Stars, Rev. Modern Phys. 29, 547–650 (1957). [15] S. Meibom et al. A spin-down clock for cool stars from observations of a 2.5-billion-year-old cluster, Nature 517, 589–591 (2015). [16] W. M. Elsasser, Origin of the Earth’s Magnetic Field, Nature 143, 374–375 (1939). [17] P. G. Judge, Inevitable consequences of ion-neutral damping of intermediate MHD waves in Sun-like stars, MNRAS. 498 2018–2029 (2020). [18] E. N. Parker, Spontaneous Current Sheets in Magnetic Fields with Application to Stellar X-Rays, International Series on Astronomy and Astrophyics. Oxford University Press, Oxford, 1994. [19] E. N. Parker, Dynamics of the interplanetary gas and magnetic fields, ApJ. 128, 664 (1955). [20] A. Skumanich, Time scales for Ca II emission decay, rotational braking, and lithium depletion, Astrophys. J. 171, 565–567 (1972). [21] H. Lammer et al., Origin and evolution of the atmospheres of early Venus, Earth and Mars, A&APR 26, 2 (2018).

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[22] M. G¨ udel, The Sun in time: Activity and environment, Living Rev. Solar Phys. 4(3), (2007). [23] M. G¨ udel, The Sun through time, Space Sci. Rev. 216, 143 (2020). [24] F. Tian et al., Hydrodynamic planetary thermosphere model: 1. Response of the Earth’s thermosphere to extreme solar EUV conditions and the significance of adiabatic cooling, J. Geophys. Res. (Planets) 113, E05008 (2008). [25] A. N. Volkov, On the hydrodynamic model of thermal escape from planetary atmospheres and its comparison with kinetic simulations, MNRAS. 459, 2030–2053 (2016). [26] F. Tian, J. F. Kasting and S. C. Solomon, Thermal escape of carbon from the early Martian atmosphere, GRL 36, L02205 (2009). [27] L. Fletcher et al., An observational overview of solar flares, SSR 159, 19–106 (2011). [28] S. Okamoto et al., Statistical properties of superflares on solar-type stars: Results using all of the Kepler primary mission data, ApJ. 906, 72 (2021). [29] E. W. Cliver and W. F. Dietrich, The 1859 space weather event revisited: limits of extreme activity, J. Space Weather Space Clim. 3, A31 (2013). [30] J. A. Eddy, The maunder minimum., Science 192 1189–1202 (1976). [31] J. H. Holland, Complexity: A Very Short Introduction, Oxford University Press, Oxford, UK, 2014. [32] E. N. Parker, Hydromagnetic dynamo models, ApJ. 122, 293–314 (1955). [33] T. G. Cowling, The magnetic field of sunspots, MNRAS. 94, 39–48 (1933). [34] E. N. Parker, Solar magnetism: The state of our knowledge and ignorance, SSR 144, 15–24 (2009). [35] S. I. Braginskii, Transport processes in a plasma, Rev. Plasma Phys. 1, 205–311 (1965). [36] M. Rempel, Creation and destruction of magnetic fields. In Heliophysics I: Plasma Physics of the Local Cosmos, Cambridge University Press, Cambridge, UK, p. 42 (2009). [37] S. M. Hanasoge, T. L. Duvall, and K. R. Sreenivasan, Anomalously weak solar convection, Proc. Nat. Acad. Sci. 109, 11928–11932 (2012). [38] V. G. A. B¨oning et al., Helioseismological determination of the subsurface spatial spectrum of solar convection: Demonstration using numerical simulations, A&A 649, A59 (2021). [39] B. C. Low, Magnetohydrodynamic processes in the solar corona: Flares, coronal mass ejections, and magnetic helicity, Phys. Plasmas 1, 1684–1690 (1994). [40] P. Charbonneau, Dynamo models of the solar cycle, Living Rev. Solar Phys. 17, 4 (2020).

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Appendix: The Sun’s Magnetic Engine There is no reason a priori that the Sun should behave in this fashion. Although the required power of all this “activity” is a small fraction of the total solar luminosity, the oscillatory behavior has garnered attention of physicists. This behavior is striking because the implied magnetic order exists in spite of the fact that energy transport across the outer 28% of the Sun, by radius, is dominated by turbulent convection. Perhaps solar magnetism is a manifestation of emergent behavior arising from the complexity of a complex dynamical system.31 Alternatively, a more deterministic mechanism might be in action, perturbed by convection to produce the “noise” seen, for example, in Fig. 3, and others. The latter picture is almost universally adopted by solar physicists, and is adopted below because it has value pedagogically. Much observational evidence and physical considerations strongly argue in favor of the regeneration of magnetic fields within the solar interior (e.g., Ref. 12.) Since 1989, one critical ingredient of deterministic models has been measured through observations of the modulation of the Sun’s normal modes of oscillation (“helioseismology”). Until measurement of the internal profile for axial differential rotation Ωϕ (r, ϑ) as a function of radius r and latitude ϑ were available, only the surface and coronal rotation properties were accessible to observers. Helioseismology has identified three interior regions The solar interior has three shear layers in the interior (Fig. A.1). Radial shears in Ωϕ are found just below the convection zone (the “tachocline”) and just beneath the photosphere. A latitudinal shear is found near latitudes of |ϑ| = 55◦ . These large-scale shear zones can readily generate toroidal magnetic fields by stretching magnetic field lines around the axis of rotation. Called the Ω-effect, these shears are believed to be a critical component of credible large-scale, dynamos (see Fig. 2). But in order to make the Sun’s magnetism oscillate, another effect is needed, and one example of a model is discussed briefly here, the α-effect. To complete a deterministic model requires ingredients in addition to the helioseismic large-scale shear motions (e.g., Ref. 32): • sources and sinks of magnetic fields are needed to produce repetition over 22 years,

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Fig. A.1. The figure shows the internal rotation rates in the toroidal direction of the solar interior as a function of radius and latitude as derived from helioseismology. The lines are contours of constant rotation rate in units of 10−9 Hz. The closely packed contours in the figure are favorable locations for the amplification of magnetic fields through the Ω-effect. Adapted from Ref. 1.

• processes that convert poloidal fields to toroidal fields are needed, which must • break cylindrical symmetry.33 Asymmetries in the internal fluid dynamics arise directly from rotation, because the Coriolis force that acts upon convective flows of density ρ and velocity u, is a pseudo-vector, i.e., asymmetric under reflection. To proceed further, we can consider the Sun as a magnetohydrodynamic (MHD) system (e.g., Ref. 34). The magnetic field then evolves according to the induction equation:b ∂B = curl(u × B) + η∇2 B, ∂t

η = 1/μ0 σ,

(2)

where σ is a scalar electrical conductivity and μ0 the permeability of free space. To zeroth order the observations indicate that global surface magnetic fields (the left-hand side of Eq. (2)) must change b

A combination of Ohm’s law, Faraday’s law of electromagnetic induction, Amp´ere’s law and the lowest order transformation of electric fields in the frame of the fluid moving with velocity u.

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on timescales of a decade. Kinetic theory gives us fluid transport coefficients such as conductivities σ,35 from which η ∼ 1 m2 s−1 in the Sun’s interior. Choosing ∼ R /3 = 2 × 108 cm, the diffusive term in Eq. (2) has a timescale of 2 /η ∼ 109 years! Evidently, the “advective” term curl (u × B) must not only provide a source, but also must drive a sink for magnetic fields when integrated over the volume of the Sun. Correlations and anti-correlations between u and B can lead both to positive and negative contributions to Eq. (2). Such correlations must operate on spatial scales  R in order to produce time scales of years, but must have consequences on global length scales. Inspired by Parker’s notion of small-scale convective cyclonic turbulence32 one class of dynamo model seeks solutions to the development of large-scale vector fields X, X = X + X , where the vector field X is assumed to be consist of separate large and small scales X and X . The small-scale correlations are averaged out and written in terms of tensor coefficients, and the reader is referred to an excellent review by Rempel summarizing further ideas.36 Of the various tensor coefficients, the most important here is α which appearing as a source term in the poloidal magnetic field which is otherwise absent (e.g., Ref. 10).   ∂B = · · · + curl αB = · · · + αμ0 j, ∂t

(3)

i.e., the induced magnetic field induced by motions contributing to α is proportional to the mean current, completing the “circuit” shown in Fig. 2. Rempel36 shows that, when stratification exists (under a gravity vector g), then 2 Ω · grad ln(vrms ), α ≈ α0 (g · Ω) = τc2 vrms

(4)

where the rms turbulent speed urms and turnover time τc characterize the turbulence, and α0 is a constant. Note that Ro = (Ωτc )−1 is the well-known “Rossby” number. In short, we have physical ingredients to generate a cycling dynamo, summarized as follows (see Fig. 2): Ω

α

Ω

Bp −→ Bt −→ Bp −→ Bt . . . ,

(5)

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where both the α and Ω model parameters depend on the timescales for rotation, differential rotation and convection. In summary, observations can constrain physical models of evolving solar magnetism, suggesting that the quasi-deterministic picture has some merit. The native asymmetries, the roles of rotation and differential rotation are all essential components that are reasonably well understood. However helioseismology, while resolving the solar interior, has also shown more recently that subsurface convective motions urms are at least an order of magnitude weaker (at r ≈ 0.96R ) than theory suggests,37,38 which if confirmed begs the worrying question of what transports the solar luminosity there. Nevertheless it must generate some α-effect and link large- and small- scales through nonlinear terms that may be deterministic only in a global (i.e., highlyaveraged) sense. For more details including the fascinating global problem of secular hemispheric accumulation of magnetic helicity in such models,39 and non-mean-field models, such as the Babcock– Leighton picture where the α-effect takes place primarily in surface dynamics, the reader can should consult modern reviews, for example, Refs. 36 and 40.

c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 0003

Chapter 3

Twenty-Five Years of Exoplanet Discoveries: The Exoplanet Hosts

B´arbara Rojas-Ayala Instituto de Alta Investigaci´ on, Universidad de Tarapac´ a, Casilla 7D, Arica, Chile [email protected]

For centuries, humanity wondered if there were other worlds like ours in the Universe. For about a quarter of a century, we have known that planetary systems exist around other stars, and more than 3,800 exoplanetary systems have been discovered so far. However, the large majority of the exoplanets remain invisible to us since we usually infer their presence by their effect on their star. The chapter is devoted to stellar hosts and their characteristics, emphasizing their description by discovery method and links between the properties of the host stars and their planets. The star–planet connection is vital to constrain the theories on the formation and evolution of planetary systems, including our own.

1.

The Relevance of the Properties of the Planet Hosts

The discovery of new worlds has been inevitably linked to studying the stars for the past 25 years. The most successful detection methods for planets (radial velocity and transit techniques) measure the effect

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on the star caused by the exoplanet, not the exoplanet itself. Hence, the properties of those new worlds are derived from the observables and the properties of their host stars. For example, radial velocity semi-amplitude K,  K≈

2πG P M∗2

1 3

Mplanet sin i √ , 1 − e2

(1)

and transit depth δtra ,  δtra ≈

Rplanet R∗

2 

Iplanet (ttra ) 1− I∗

 (2)

are observables from the radial velocity and transit techniques. To obtain the bulk properties of the exoplanets, Rplanet and Mplanet , we need to know the bulk properties of the star R∗ and M∗ , respectively The properties of host stars are needed because: • we want to know how planet formation works and what determines their evolution, • we make target selection for exoplanet searches (e.g., input catalogs for space-based missions), • we want to ensure that what we are measuring is due to a planet around the star and not a false positive (e.g., activity, rotation). Figure 1 shows exoplanets with mass and radius estimates in the NASA Exoplanet Archive up to October 30, 2021, along with massradius relationships for planets with pure iron, rock (Mg2 SiO4 ) and water ice compositions from Ref. 1 and pure hydrogen composition from Ref. 2. The Mass–Radius (M–R) diagram for the discovered planets shows us the diversity of worlds being found and makes plainly evident the necessity to improve the precision of their mass and radius to constrain their composition. Over the past years, stable spectrographs and space telescopes have provided exquisite data to measure the observables precisely, but it is not enough for some hosts because the uncertainties on their masses and sizes are pretty significant. Therefore, the exact exoplanet flavor will depend on how well we know the bulk properties of the host star. The most fundamental property of a star is its mass. However, masses are not easy to directly measure for most stars. We can get

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Fig. 1. M–R relation: Observations vs. theoretical data. The circles correspond to the planets up to October 30, 2021, while the solid lines represent mass–radius relations for different planetary compositions.

precise masses for stars in binary systems, and if they are eclipsing binaries, we can get their accurate sizes. Stellar sizes can be obtained from interferometry if the star is relatively bright and we know how far the star is from us (e.g., from their Hipparcos/GAIA parallaxes). Asteroseismology is a powerful tool for insights into the stellar interior and obtaining the stellar mass, radius and ages with high precision if the star pulsates. In particular, all of the above becomes more challenging for the low-mass stars due to their low luminosities and lack of detected pulsations in photometric and spectroscopic data to date. Since the large majority of planet hosts do not satisfy the above conditions, the exoplanet community has relied mainly on the atmospheric stellar parameter (Teff , [M/H] and log g) estimates of their bulk properties. For example, you can get a precise estimate of the Teff of the star from high-resolution spectra, and if you know its parallax and luminosity, you can derive its radius. Then, from the estimate of the star’s surface gravity, you can obtain its mass. Stellar evolution models have been beneficial in deriving masses and sizes of stars from atmospheric stellar parameters.

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Characteristics of the Confirmed Stellar Hosts up to October 2021

According to the NASA Exoplanet Archive, up to October 30, 2021, there were 4451 planets in 3378 systems. The NASA Exoplanet Archive is an astronomical catalog and data service that collects and cross-correlates relevant information on exoplanetary systems such as stellar, exoplanet and discovery/characterization data. Thus, it serves as a census of exoplanetary systems constantly being updated and available to all. Unfortunately, not all the confirmed planet hosts in the NASA Exoplanet Archive are fully characterized, meaning they are missing estimates of effective temperature, metallicity, surface gravity, mass, radius and/or luminosity. In fact, the Hertzsprung–Russell diagram constructed with the data available up to October 30th in the archive shows only 3,247 hosts out of the 3,378 systems. About 4% of the hosts do not have effective temperature and/or luminosity estimations. Figure 2 shows a couple of peculiar hosts, such as white dwarfs and hot subdwarfs, since most hosts are main sequence, subgiant and giant stars. The lack of specific stellar

Fig. 2. The planet hosts with luminosity and effective temperature estimates from the NASA Exoplanet Archive up to October 30, 2021.

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parameters for the planet host is somewhat related to the detection technique involved in the exoplanet discovery. 2.1.

Radial velocity hosts

The locations of the hosts discovered by the radial velocity (RV) technique are shown in Fig. 3. The RV technique makes it easier to find planets around main-sequence (GK) stars and (sub)giant stars (bright/slow) since relatively bright stars provide high signal-to-noise observations. It is harder to find planets around F and earlier stars because of the lack of absorption lines to analyze the data correctly. It is also more challenging to find planets around young stars due to their activity and variability. Stellar activity can be a problematic signal to remove from the data. Spots, plages, convection, and pulsations can induce RV signals to reach amplitudes larger than a planet’s signal. However, RV observations with near-infrared spectrographs have facilitated the discovery of planets around M dwarfs and young stars.

Fig. 3. The stars with planets found with the radial velocity technique in the NASA Exoplanet Archive up to October 30, 2021 are shown in black.

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2.2.

Transit hosts

The locations of the hosts discovered by the transit technique are shown in Fig. 4. The transit technique works best in bright, small and inactive stars. Small stars are an advantage for the transits technique because the drop in luminosity is proportional to the ratio between the size of the planet and the star. It is easier to find planets around GK dwarfs and bright M dwarfs since relatively bright stars provide high signal-to-noise observations. It is harder to find planets around evolved stars since they are too large. It is also harder to find planets around young stars because of their variability. Most of the transit hosts in Fig. 4 were discovered by the Kepler and K2 missions. 2.3.

Direct imaging hosts

The locations in the Hertzsprung–Russell diagram of the hosts discovered by the direct imaging technique are shown in Fig. 5. This technique performs best around nearby and young stars. It is easier to find planets around young stars and nearby young associations because the worlds are still contracting and, therefore, are

Fig. 4. The stars with planets found with the transits technique in the NASA Exoplanet Archive up to October 30, 2021 are shown in black.

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Fig. 5. The stars with planets found with the direct imaging technique in the NASA Exoplanet Archive up to October 30, 2021 are shown in black.

brighter than in systems where the host has reached the mainsequence branch. On the other hand, it is harder to find planets around evolved and main-sequence stars because of the luminosity contrast between the host and the exoplanet. 2.4.

Microlensing hosts

The microlensing technique detects the effect of an unseen planetary system on the light emitted by a distant star. The host star and planets act as lenses, and the distant star gets magnified. This technique performs best in stars in front of dense stellar regions (e.g., galactic bulge). It is easier to find planets around M dwarfs since they are the most abundant type of star; it is harder to find planets in nearby stars. The hosts are difficult to characterize since they remain unseen or cannot be resolved. Microlensing hosts, therefore, are part of the stars that do not show up in the Hertzsprung–Russell diagram in Fig. 2. Stellar mass and distance estimates are a result of the fitting of the magnification curve. All hosts have masses less than 1.3 solar masses, as shown in Fig. 6. Effective temperatures for the star can be estimated from its mass, assuming that it is a main-sequence star.

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Fig. 6. The stars with planets found with the microlensing technique in the NASA Exoplanet Archive up to October 30, 2021 are shown in black.

2.5.

The sky distribution of the planet hosts

The techniques cover different regions of the Milky Way due to the performance characteristics listed in the above sections. In a 2D representation of the sky, the radial velocity planet hosts cover roughly all radial ascensions and declinations, as seen in Fig. 7. The transit hosts are also found everywhere in the projected 2D sky; however, they also bring out the Kepler and K2 fields since they cluster in those locations. The imaging hosts highlight where the young associations are found, while the majority of the microlensing hosts are located toward the bulge of the Milky Way. In a 3D representation, the limitations on the distance of the discovery methods become evident (Fig. 8). At 5pc, only systems discovered by the radial velocity show up, excluding the Sun (Fig. 8(a)). At 20pc, the RV systems dominate, but transit and direct imaging systems start to show up (Fig. 8(b)). At 100 pc, the RV systems begin to be encapsulated by the transit systems. At 500 pc, the transit systems dominate, the contribution of the Kepler mission can be clearly seen as a cone that extends from the center, and the

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79 All planet hosts Radial Velocity Transits Direct Imaging Microlensing

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6 60 0

0h 00 0

12h 00

00

30 30

–30 30

–9 90 0

Fig. 7. The 2D projection of the positions of all planet hosts in the NASA Exoplanet Archive up to October 30, 2021, coded by the discovery technique.

first microlensing system appears (Fig. 8(c)). The planetary systems found by the microlensing technique dominate at distances larger than ∼1,000 pc toward the center of the Galaxy (Fig. 8(d)). 3.

3.1.

Links between the Properties of the Host Stars and Their Planets Occurrence rates per star type

Each detection technique favors the discovery of planets around stars with specific characteristics. Hence, to answer how common rocky or gaseous planets are around particular groups of stars, we need to consider the limitations of such techniques and reach a certain level of completeness for each survey. This is why occurrence rate papers started to appear roughly 10 years after discovering 51 Peg b. Although the occurrence rates obtained from the detection methods may differ in the exact number, they are consistent in that M dwarfs have higher occurrence rates of rocky planets than FGK stars. Planet occurrence rates get updated almost every year, considering different samples that do get more complete as the searches continue. A list of articles related to planet occurrence rates can be found in the NASA Exoplanet Archive (footnote).

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(a)

(b)

(c)

(d)

Fig. 8. The 3D positions of all planet hosts in the NASA Exoplanet Archive up to October 30, 2021, coded by the discovery technique.

3.1.1.

Examples from RV surveys

The RV surveys with the HARPS and CORALIE spectrographs concluded that more than 50% of the solar-type stars host at least one planet of any mass with periods up to 100 days.3 For planets with orbital periods less than 50 days and minimum masses between 3 and 30 M⊕ , the occurrence rate is estimated between 15% and 27%.3,4 Reference 5 estimated that about 40% of the red dwarf stars have a super-Earth orbiting in their habitable zone, and that about 12% of

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the red dwarfs are expected to have giant planets (100–1,000 M⊕ ) from their M dwarf survey with HARPS. Using Lick data, Reference 6 concluded that the occurrence rate of giant planets in giant stars (2.7–5.0 M ) is less than 1.6%. Reference 7 estimated an occurrence rate of giant planets with periods lower than 1,000 days of ∼1% for young stars. 3.1.2.

Examples from transit surveys

Reference 8 concluded with the first results from the brightest half sample of the Kepler Mission that early M dwarfs were 7 times more likely to have a planet with an orbital period below 50 days than the hottest stars in the sample. Reference 9 estimated occurrence rates of ∼4 or ∼8 planets per M dwarfs considering sizes between 0.5 and 4 R⊕ and periods between 0.5 and 256 days. By considering only the planets with sizes between 0.75 and 1.5 R⊕ in the habitable zone of their stars, the occurrence rate is between 0.03 to 0.40 considering orbital periods between 237 and 500 days for FGK dwarfs10 and is 0.33 considering periods between 0.5 and 256 days for M dwarfs.9 3.1.3.

Examples from direct imaging surveys

If all spectral types surveyed are considered (B stars to M dwarfs), most works conclude that the occurrence rate is close to ∼1% for the most massive planets (∼0.5–13 Mjup ) at distances from few tens AU up to a few hundreds AU covered by the direct imaging technique.11,12 If masses consistent with brown-dwarfs (up to 20 Mjup ) and larger distances are considered (up to 5,000 AU), Ref. 13 estimated an occurrence rate frequency of f = 0.11+0.11 −0.05 using data from several direct imaging surveys. 3.1.4.

Examples from microlensing surveys

Reference 14 found that about 55% of microlensed stars host a snowline planet, and that Neptunes were about 10 times more common than Jupiter-mass planets, using OGLE, MOA and WISE data. However, from 20 years of OGLE survey data, Ref. 15 found a higher occurrence rate, estimating that, on average, every microlensing star hosts at least one giant planet at separations from ∼5 AU to ∼15 AU.

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B. Rojas-Ayala

Correlations with metallicity Giant planet — metallicity correlation

Soon after 51 Peg b and three other giant planets were discovered, Ref. 16 analyzed the hosts’ high-resolution spectra concluding they had a higher average metallicity than field stars hosting no planets. This led to what is known as the giant planet–metallicity correlation: the higher the star’s metallicity, the higher the probability of the star hosting a giant planet, as Fig. 9 shows. Although Ref. 16 proposed that pollution from infall material in the stellar convective envelope was the reason behind this correlation, it has been established that

Fig. 9. The planet–metallicity correlation: The iron metallicity distributions for planet host stars (hashed histogram) compared with the distributions of a volumelimited sample of stars (upper left) and of all the stars in the CORALIE program with at least five radial-velocity measurements (lower left). The percentage of planet hosts found amid the stars in the CORALIE sample as a function of stellar metallicity is shown in the lower right plot. Adapted from Ref. 17 with c permission from ESO.

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the metallicity of the host reflects the abundance of solids in the primordial cloud that formed the planetary system.17,18 The existence of this correlation favors the core-accretion model for planet formation, wherein disks with a higher metallic content, rocky and icy cores can form early enough to allow for runaway accretion to form giant planets before the dissipation of the disks happens, unlike the lower-metallicity disks.19–21 The exact functionality of the relation is still a matter of study, especially in the metal-poor regime where samples are still small to further constrain the occurrence rates of giants.22–24 The original giant planet–metallicity correlation was limited to FGK stars since solar-like stars were the preferred targets of the first RV surveys.17,18,25 However, it was soon evident that the correlation did hold for other stars. The few M dwarfs with giant planets discovered by the RV method showed a higher average metallicity when compared with field stars as well (e.g., Refs. 26–29). Giant stars with giant planets also showed higher average metallicities when compared with giants without planets, with an overabundance of planets around giant stars with iron metallicity of ∼ −0.3 dex.6,30 The spectroscopic characterization of Kepler host stars corroborated that large planets (Rp > 4 R⊕ ) are preferentially found around metal-rich stars.31–33 Results from wide-field ground-based surveys have found that hot Jupiters preferentially orbit metal-rich stars as well, concluding that probably all giants are formed by a similar process, but hot Jupiters have different migration histories.34 Unlike the giant planets, rocky and icy planets are not preferentially found around metal-rich stars.35,36 However, Ref. 37 found a “Universal” planet–metallicity connection for solar-type stars: terrestrial, gas-dwarf, and gas-giant planets occur more frequently in metal-rich stars, but the dependence on metallicity for terrestrial and gas-dwarf planets is lower than for gas giants. 3.2.2.

Planet distance/period — metallicity trend

Several works find trends in stellar metallicity with the orbital period or distance distributions of small and giant planets.38,39 For example, the occurrence rate of Kepler sub-Neptunes with orbital periods below 10 days as a function of metallicity is three times higher for stars with super-solar metallicity.40 Furthermore, planets with

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masses between 10 M⊕ and 4 Mjup orbiting metal-poor stars exhibit longer periods than those orbiting metal-rich stars.41 If the host’s metallicity is a proxy of the metal content in the disks, the above results may indicate that planets form farther out from their stars in metal-poor disks or that they form later and do not migrate as inward as planets in metal-rich disks. 3.3.

Correlations with stellar mass

The mass is the most fundamental property of a star since it determines its whole evolution. As planetary searches extended and samples grew, it was found that stellar mass may play a role in the type of planets that a star can host. Radial velocity surveys soon unraveled the scarcity of giant planets around the most petite stars in their samples. Giant planets with periods of few days should have been easier to discover than rocky planets around red dwarfs, given the favorable mass ratio Refs. 42 and 43 speculated that giant planets were necessary for the evolution of intelligent organisms. If this were so, a decrease in the incidence of radial velocity of giant companions around red dwarf could have enormous implications for the search for civilizations (note that the majority of stars in the Galaxy are red dwarfs). Reference 44 also found a lower frequency of close-in giant planets for M dwarfs from a sample of 90 red dwarfs with RV data from several spectrographs and concluded that their results confirmed theoretical predictions by Refs. 20 and 45 about the formation of giants by core-accretion Reference 46 calculated a functional form of the likelihood of a star (within a mass range from 0.2 to 1.9 M ), to harbor a giant planet as a function of mass and metallicity, using more than 1,000 stars observed by the California Planet Survey. Reference 46 found that at solar metallicity, the giant planet occurrence rises from 3% around M dwarfs to 14% around A stars, and concluded that, if disk masses correlate with stellar mass, this was strong supporting evidence of the core accretion model of planet formation from cool dwarfs to intermediate-mass subgiants. Radial velocity surveys also found correlations with mass for giant stars. References 6 and 30 found that the planet occurrence rate of close-in Jovians increases with stellar mass up to 2 M for giant stars, but it decreases rapidly and is consistent with zero at ∼3 M ,

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Fig. 10. The planet–stellar mass correlation: Planet occurrence rate as a function of stellar mass for giant stars, ignoring the effect of stellar metallicity. The filled histogram shows secure planets, whereas the open histogram includes planet candidates as well. The solid line denotes the best fit to the mass dependence of the giant planet occurrence rate computed for solar metallicity. The black dots correspond to the same model, but the true metallicity distribution within each bin has been taken into account. Adapted from Ref. 3 with permission from c ESO.

as shown in Fig. 10. Reference 6 proposes that stars massive than 2.5 M may lack giant planets at few AU because their snowline is further out, where gas densities and Kepler velocities are smaller, slowing down growth rates and increasing migration time scales that combine with a shorter lifetime of the protostellar disk, preventing these stars from forming close-in giant planets that would be observable today. There is a consensus regarding Neptunes and the sub-Neptune population that they occur more frequently around M dwarfs than FGK stars. Using the Kepler discoveries with periods between 2 and 50 days, Ref. 47 estimated that for minor planets (4 R⊕ ), the trend reverses, and more giant planets become

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more common around sun-like stars. These empirical results agree with model calculations, where the core-accretion scenario shows no difficulties in forming low-mass planets around red dwarfs and even predicts more Neptunes in short orbits around M dwarfs than G dwarfs.20,45 Recently, a correlation between protoplanetary disks gaps and stellar mass was found with ALMA observations of 500 young systems. Reference 48 found that higher mass stars in the sample have relatively more disks with gaps than lower mass stars and that the frequency of the gapped disks matches the observed frequency of giant planets at different stellar masses. If the openings are formed by planets of Neptune mass and above (i.e., giant planets), and they migrate inwards, this result is consistent with the stellar mass — giant planet correlation from exoplanet surveys. The correlation also applies to low-mass stars: disks without gaps are compact, and without giant planets, the dust will drift inwards, providing the necessary conditions for forming more minor, rocky planets with short periods, consistent with the observations of sub-Neptunes mentioned above. Therefore, the mass of host stars can directly relate the exoplanet to its planet-forming environment. 3.4.

Chemical signatures of planet formation

It is often assumed that a star and its planets form together from the same cloud and have similar compositions. There is a good match in the abundance of refractory elements between the Sun and the most primitive and undifferentiated meteorites in our Solar System, the CI carbonaceous chondrites.49 Therefore, the atmospheric abundances of refractory elements (such as Mg, Si, Ca, Ni and Fe) of solar-type stars can be considered a proxy for the composition of the protoplanetary disk. The chemical elements in the disk condensate at different temperatures and therefore condensate at distinct regions of the disk, separating themselves from the gas as dust, while the protostar continues accreting gas. Refractory elements have high condensation temperatures and condensate close to the star-forming rocky planetesimals, while the volatile elements have low condensation temperatures, forming icy planetesimals further away from the star. Chemical signatures related to the content of refractory elements in the atmosphere of stars have been searched using high-res, high

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signal-to-noise spectroscopic data to obtain high precisions in the measurement of element abundances. Reference 50 used a differential method to get precisions of ∼0.01 dex on solar twins to find that the sun was peculiar, having lower refractory abundances than the average of the solar twins, and proposing that the missing refractories were used to form rocky material in the solar system. Reference 51 extended the sample of Ref. 50 up to 79 solar twins, finding that the sun indeed has a deficiency in refractory material relative to more than 80% of the sample, suggesting that it could be a possible signpost for planetary systems like the solar system in the other refractory poor solar twins. Reference 52 found that the sun also has the lowest lithium abundance compared to the solar twins of the same age, and the most lithium-depleted solar twins were also depleted of refractory elements. The lack of refractory elements or different chemical compositions in planet hosts has been observed in binary systems, such as 16 Cygni,53–55 ζ 2 Reticuli,56 WASP-9457 and HD 133131.58 The overabundance of refractory elements and lithium in the atmospheres of stars has been linked to planetary formation, however, as a signpost of planetary accretion or engulfment in stars without detected planets. This is the case of a comoving pair analyzed in Ref. 59, where it is suggested that one of the components accreted 15 M⊕ of rocky material after birth to explain the enhancing of refractory elements and lithium found in its atmosphere. In a recent study, Ref. 60 analyzed 107 binary systems of Sun-like stars with similar effective temperatures and surface gravities, concluding that the discrepancies in chemical abundances in the binary systems favored the planet engulfment scenario and estimating that it occurs in about a quarter of all Sun-like stars. Pollution or engulfment of differentiated material has also been observed in the atmospheres of white dwarfs.61,62 Recently, a correlation between the compositions of rocky exoplanets and their host stars was found. By concentrating only on planets with masses below 10 M⊕ but avoiding mini-Neptunes, Ref. 63 found that the iron content of rocky planets (inferred from their estimated density) correlates with the iron content of the star, which reflects the iron content of the protoplanetary disk. However, it is not a one-to-one correlation as was expected. Instead, the planets are more enhanced in iron than their host stars. The reason behind

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this is still unknown, but Ref. 63 suggests that it can be related to rocky lines (condensation/sublimation lines of refractory materials) in the disk where the fraction of iron can be enhanced, as described in Ref. 64.

4.

Conclusions

The planet discovery techniques and methods probe different types of stars and distinct areas of our neighborhood and populations of the Galaxy. For most of the planetary systems known to date, all that we can see are the stars; hence, we need to know the stars in detail to obtain the exact bulk properties of the exoplanets and their orbital parameters, calculate the occurrence rates, and infer how the formation and evolution of the systems occurred. The stellar mass and metallicity are quantities showing connections with specific types of exoplanets in the stars surveyed. These two quantities are believed to depict the amount of material and the composition of the cloud that formed the planetary system. Knowing them in detail makes it possible to assume specific disk characteristics, figure out how relevant the initial conditions are for the formation of planets, and find possible explanations for the planetary systems that don’t follow the expected trends. Regarding the metallicity of the stars, hosts of giant planets on average have higher metallicities than field stars (i.e., are metalrich stars), a result known as the giant planet–metallicity correlation that supports the core accretion scenario for planet formation. On the other hand, hosts of only small planets exhibit a wide range of metallicities. Furthermore, if we consider the orbital period of the planets and metallicity, we find that Neptunes and super-Earths with short periods are found preferentially around metal-rich stars, while sub-Neptunes to giants with longer periods are found preferentially around metal-poor stars. Regarding the mass of the stars, the current samples of exoplanetary systems show that the occurrence rate of giant planets increases as stellar mass increases, however only up to 2 M , where it decreases as stellar mass increases. The occurrence rate of subNeptunes increases as stellar mass decreases.

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Regarding chemical signatures of planet formation, works have found the sun peculiar compared with samples of solar twins, being poor in refractory elements and lithium. The overabundance of refractory elements and lithium in the atmospheres of stars has been proposed as a signpost of planetary engulfment in stars without detected planets. The star–planet connection is an area in constant review, where newer discoveries allow the recognition and constraining of the physical processes involved in the formation and evolution of planetary systems. Therefore, it should not be surprising that the relationships presented in this chapter become increasingly specific concerning the characteristics and detection method of the system or exoplanet in question or are modified to include new observations, which allow new connections to be found. 5.

Q&A

Pedro Amado: M Dwarfs & Sun-like FGK stars are very different. What complications arise in understanding exoplanet systems around M stars because of this difference? B´arbara Rojas-Ayala: Sun-like stars are luminous and high quality spectra are “easy” to obtain. M Dwarfs (M∗ ∼ 0.1 − 0.6 M ) are less bright and cooler, with many more metal lines — so many that the blackbody shape is obscured. With no clear continuum, it is more difficult to characterize the M stars for gravity, metallicity, etc. Internally, the M stars are similar to the Sun except that with M∗ < 0.4 M , the radiative zone disappears. We have less understanding of M dwarf magnetic field generation in these lower mass stars, for example, because of the lack of a tachocline, where the Sun’s field is thought to originate. Gaia Lacedelli: Why did Kepler, unlike TESS, observe faint stars even though they cannot provide good enough radial velocity information? B´arbara Rojas-Ayala: Kepler did have a target list, and the first goal was to find a sun analog (G2V with an Earth at 1 AU). But they also targeted statistical studies of planets, and did a very good job, even though some of the lower mass planets cannot be accurately

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characterized. The Kepler discovery that the amazing planet results came from M dwarfs was a surprise. Thea Kozakis: What are the magnitude limits to be able to properly characterize stars? B´arbara Rojas-Ayala: I can’t remember. Andrea Mihayas: You said that different methods of detection give different rates of planet occurrence because of bias effects. Can you correct for that? B´arbara Rojas-Ayala: Yes, the authors all try really hard to get the bias out of their samples. What we would like is an accurate volume limited sample, but we can’t get that because some stars are more luminous & more visible at larger distances than others. There are other biases, like a bias against long period planets relative to short period planets. Unfortunately, different debiasing methods sometimes give different results. So, the situation is currently unclear. Andrea Mihayas: I read that some astronomers want to distinguish brown dwarfs from planets by formation mechanism not by mass. What do you think about that? B´arbara Rojas-Ayala: This has been a discussion since I was a graduate student. The idea is that planets form in disks, while stars form by collapse of a cloud. But, while we can measure the mass, we don’t know how a given object formed, except through models. So, using mass with a 13 MJ boundary is more direct, also less subject to changing models and their uncertainties and therefore seems better. Antonio Fernandez: You mentioned a stellar mass vs giant planet relation...is that a bias effect? B´arbara Rojas-Ayala: Could be.

References [1] S. Seager et al. Mass-radius relationships for solid exoplanets, ApJ. 669(2), 1279–1297 (Nov., 2007). DOI: 10.1086/521346. [2] J. J. Fortney, M. S. Marley, and J. W. Barnes, Planetary radii across five orders of magnitude in mass and stellar insolation: Application to transits, ApJ. 659(2), 1661–1672 (Apr., 2007). DOI: 10.1086/512120.

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[3] M. Mayor et al., The HARPS search for southern extra-solar planets XXXIV. Occurrence, mass distribution and orbital properties of superEarths and Neptune-mass planets, arXiv e-prints:arXiv:1109.2497 (Sept., 2011). [4] A. W. Howard et al., The Occurrence and Mass Distribution of Closein Super-Earths, Neptunes, and Jupiters, Science 330(6004), 653 (Oct., 2010). DOI: 10.1126/science.1194854. [5] X. Bonfils et al., The HARPS search for southern extra-solar planets. XXXI. The M-dwarf sample A&A. 549, A109 (Jan., 2013). DOI: 10. 1051/0004-6361/201014704. [6] S. Reffert et al., Precise radial velocities of giant stars. VII. Occurrence rate of giant extrasolar planets as a function of mass and metallicity, A&A. 574, A116 (Feb., 2015). DOI: 10.1051/0004-6361/201322360. [7] A. Grandjean et al., A SOPHIE RV search for giant planets around young nearby stars (YNS). A combination with the HARPS YNS survey, A&A. 650, A39 (Jun., 2021). DOI: 10.1051/0004-6361/202039672. [8] A. W. Howard et al., Planet occurrence within 0.25 AU of solartype stars from Kepler, ApJS. 201(2), 15 (Aug., 2012). DOI: 10.1088/ 0067-0049/201/2/15. [9] D. C. Hsu, E. B. Ford, and R. Terrien, Occurrence rates of planets orbiting M Stars: Applying ABC to Kepler DR25, Gaia DR2, and 2MASS data, MNRAS. 498(2), 2249–2262 (Oct., 2020). DOI: 10.1093/ mnras/staa2391. [10] D. C. Hsu et al., Occurrence rates of planets orbiting FGK stars: Combining Kepler DR25, Gaia DR2, and Bayesian Inference AJ. 158(3), 109 (Sept., 2019). DOI: 10.3847/1538-3881/ab31ab. [11] B. P. Bowler, Imaging extrasolar giant planets, PASP. 128(968), 102001 (Oct., 2016). DOI: 10.1088/1538-3873/128/968/102001. [12] M.-E. Naud et al., PSYM-WIDE: A survey for large-separation planetary-mass companions to late spectral type members of young moving groups, AJ. 154(3), 129 (Sept., 2017). DOI: 10.3847/15383881/aa826b. [13] F. Baron et al., Constraints on the occurrence and distribution of 1-20 MJup companions to stars at separations of 5-5000 Au from a compilation of direct imaging surveys, AJ. 158(5), 187 (Nov., 2019). DOI: 10.3847/1538-3881/ab4130. [14] Y. Shvartzvald et al., The frequency of snowline-region planets from four years of OGLE-MOA-Wise second-generation microlensing, MNRAS. 457(4), 4089–4113 (Apr., 2016). DOI: 10.1093/mnras/ stw191.

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[15] R. Poleski et al., Wide-orbit exoplanets are common. Analysis of nearly 20 years of OGLE Microlensing survey data, Acta Astron. 71(1), 1–23 (Mar., 2021). DOI: 10.32023/0001-5237/71.1.1. [16] G. Gonzalez, The stellar metallicity-giant planet connection, MNRAS. 285(2), 403–412 (Feb., 1997). DOI: 10.1093/mnras/285.2.403. [17] N. C. Santos, G. Israelian, and M. Mayor, Spectroscopic [Fe/H] for 98 extra-solar planet-host stars. Exploring the probability of planet formation, A&A. 415, 1153–1166 (Mar., 2004). DOI: 10.1051/0004-6361: 20034469. [18] D. A. Fischer and J. Valenti, The planet-metallicity correlation, ApJ. 622(2), 1102–1117 (Apr., 2005). DOI: 10.1086/428383. [19] J. B. Pollack et al., Formation of the giant planets by concurrent accretion of solids and gas, Icarus 124(1), 62–85 (Nov., 1996). DOI: 10.1006/icar.1996.0190. [20] S. Ida and D. N. C. Lin, Toward a deterministic model of planetary formation. I. A desert in the mass and semimajor axis distributions of extrasolar planets, ApJ. 604(1), 388–413 (Mar., 2004). DOI: 10.1086/ 381724. [21] C. Mordasini et al., Characterization of exoplanets from their formation. I. Models of combined planet formation and evolution, A&A. 547: A111 (Nov., 2012). DOI: 10.1051/0004-6361/201118457. [22] A. Mortier et al., New and updated stellar parameters for 71 evolved planet hosts. On the metallicity-giant planet connection, A&A. 557, A70 (Sept., 2013). DOI: 10.1051/0004-6361/201321641. [23] V. Adibekyan, Heavy metal rules. I. Exoplanet incidence and metallicity, Geosciences 9(3), 105 (Feb., 2019). DOI: 10.3390/geosciences 9030105. [24] K. M. Boley et al., Searching for transiting planets around halo stars. II. Constraining the occurrence rate of hot Jupiters, AJ. 162(3), 85 (Sept., 2021). DOI: 10.3847/1538-3881/ac0e2d. [25] N. C. Santos et al., Statistical properties of exoplanets. II. Metallicity, orbital parameters, and space velocities, A&A. 398, 363–376 (Jan., 2003). DOI: 10.1051/0004-6361:20021637. [26] X. Bonfils et al., The HARPS search for southern extra-solar planets. X. A m sin i = 11 M⊕ planet around the nearby spotted M dwarf GJ 674, A&A. 474(1), 293–299 (Oct., 2007). DOI: 10.1051/0004-6361: 20077068. [27] B. Rojas-Ayala et al., Metallicity and temperature indicators in M dwarf K-band spectra: Testing new and updated calibrations with observations of 133 solar neighborhood M dwarfs, ApJ. 748(2), 93 (Apr., 2012). DOI: 10.1088/0004-637X/748/2/93.

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[28] R. C. Terrien et al., An H-band spectroscopic metallicity calibration for M dwarfs, ApJL. 747(2), L38 (Mar., 2012). DOI: 10.1088/2041-8205/ 747/2/L38. [29] J. Maldonado et al., HADES RV programme with HARPS-N at TNG. XII. The abundance signature of M dwarf stars with planets, A&A. 644, A68 (Dec., 2020). DOI: 10.1051/0004-6361/202039478. [30] M. I. Jones et al., Four new planets around giant stars and the massmetallicity correlation of planet-hosting stars, A&A. 590, A38 (May, 2016). DOI: 10.1051/0004-6361/201628067. [31] L. A. Buchhave et al., An abundance of small exoplanets around stars with a wide range of metallicities, Nature 486(7403), 375–377 (Jun., 2012). DOI: 10.1038/nature11121. [32] L. A. Buchhave et al., Three regimes of extrasolar planet radius inferred from host star metallicities Nature 509(7502), 593–595 (May, 2014). DOI: 10.1038/nature13254. [33] K. C. Schlaufman, A continuum of planet formation between 1 and 4 Earth radii, ApJL. 799(2), L26 (Feb., 2015). DOI: 10.1088/2041-8205/ 799/2/L26. [34] A. Osborn and D. Bayliss, Investigating the planet-metallicity correlation for hot Jupiters, MNRAS. 491(3), 4481–4487 (Jan., 2020). DOI: 10.1093/mnras/stz3207. [35] S. G. Sousa et al., Spectroscopic parameters for 451 stars in the HARPS GTO planet search program. Stellar [Fe/H] and the frequency of exo-Neptunes, A&A. 487(1), 373–381 (Aug., 2008). DOI: 10.1051/0004-6361:200809698. [36] L. Ghezzi et al., Stellar parameters and metallicities of stars hosting jovian and Neptunian mass planets: A possible dependence of planetary mass on metallicity, ApJ. 720(2), 1290–1302 (Sept., 2010). DOI: 10.1088/0004-637X/720/2/1290. [37] J. Wang and D. A. Fischer, Revealing a universal planet-metallicity correlation for planets of different sizes around solar-type stars, AJ. 149(1), 14 (Jan., 2015). DOI: 10.1088/0004-6256/149/1/14. [38] C. Beaug´e and D. Nesvorn´ y, Emerging trends in a period-radius distribution of close-in planets, ApJ. 763(1), 12 (Jan., 2013). DOI: 10.1088/0004-637X/763/1/12. [39] R. I. Dawson, E. Chiang, and E. J. Lee, A metallicity recipe for rocky planets, MNRAS. 453(2), 1471–1483 (Oct., 2015). DOI: 10.1093/mnras/stv1639. [40] G. D. Mulders et al., A super-solar metallicity for stars with hot rocky exoplanets, AJ. 152(6), 187 (Dec., 2016). DOI: 10.3847/0004-6256/ 152/6/187.

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[41] V. Z. Adibekyan et al., Orbital and physical properties of planets and their hosts: new insights on planet formation and evolution, A&A. 560, A51 (Dec., 2013). DOI: 10.1051/0004-6361/201322551. [42] G. W. Wetherill, Possible consequences of absence of “Jupiters” in planetary systems, Astrophys. Space Sci. 212(1–2), 23–32 (Feb., 1994). DOI: 10.1007/BF00984505. [43] C. Laws et al., Parent Stars of Extrasolar Planets. VII. New Abundance Analyses of 30 Systems AJ. 125(5), 2664–2677 (May, 2003). DOI: 10.1086/374626. [44] M. Endl et al., Exploring the frequency of close-in Jovian planets around M dwarfs, ApJ. 649(1), 436–443 (Sept., 2006). DOI: 10.1086/506465. [45] G. Laughlin, P. Bodenheimer, and F. C. Adams, The core accretion model predicts few Jovian-mass planets orbiting red dwarfs, ApJL. 612(1), L73–L76 (Sept., 2004). DOI: 10.1086/424384. [46] J. A. Johnson, K. M. Aller, A. W. Howard, and J. R. Crepp, Giant planet occurrence in the stellar mass-metallicity plane, PASP. 122 (894), 905 (Aug., 2010). DOI: 10.1086/655775. [47] G. D. Mulders, I. Pascucci, and D. Apai, A Stellar-mass-dependent drop in planet occurrence rates, ApJ. 798(2), 112 (Jan., 2015). DOI: 10.1088/0004-637X/798/2/112. [48] N. van der Marel and G. D. Mulders, A stellar mass dependence of structured disks: A possible link with exoplanet demographics, AJ. 162(1), 28 (Jul., 2021). DOI: 10.3847/1538-3881/ac0255. [49] M. Asplund, N. Grevesse, A. J. Sauval, and P. Scott, The chemical composition of the Sun, ARA&A. 47(1), 481–522 (Sept., 2009). DOI: 10.1146/annurev.astro.46.060407.145222. [50] J. Mel´endez, M. Asplund, B. Gustafsson, and D. Yong, The peculiar solar composition and its possible relation to planet formation, ApJL. 704(1), L66–L70 (Oct., 2009). DOI: 10.1088/0004-637X/704/1/L66. [51] M. Bedell et al., The chemical homogeneity of Sun-like stars in the solar neighborhood, ApJ. 865(1), 68 (Sept., 2018). DOI: 10.3847/ 1538-4357/aad908. [52] M. Carlos et al., The Li-age correlation: The Sun is unusually Li deficient for its age, MNRAS. 485(3), 4052–4059 (May, 2019). DOI: 10.1093/mnras/stz681. [53] I. Ram´ırez et al., Elemental abundance differences in the 16 Cygni binary system: A signature of gas giant planet formation? ApJ. 740(2), 76 (Oct., 2011). DOI: 10.1088/0004-637X/740/2/76. [54] P. E. Nissen et al., High-precision abundances of elements in Kepler LEGACY stars. Verification of trends with stellar age, A&A. 608, A112 (Dec., 2017). DOI: 10.1051/0004-6361/201731845.

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c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 0004

Chapter 4

Exploration of the Atmospheres of the Terrestrial Planets

Ann C. Vandaele Planetary Atmospheres Research Unit, Royal Belgian Institute for Space Aeronomy, Brussels, Belgium [email protected]

In this chapter, we describe the atmospheres of the terrestrial planets of our Solar System. After a brief introduction on the concept of “comparative planetology”, we introduce different theoretical elements which permit us to better grasp the differences existing within the atmospheres of Mercury, Venus, Mars and Earth.

1.

Introduction: Comparative Planetology

Planetary atmospheres are gaseous envelopes surrounding celestial bodies. They differ in terms of temperature, pressure and composition, and therefore offer natural test beds to improve our knowledge on the physical, chemical and dynamical processes that can occur in such systems. Indeed one of the main objectives of comparative planetology is to study all atmospheres to better understand our own atmosphere, to understand its past and future evolution. Processes like the interaction of the atmosphere with the solar radiation or

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with its magnetosphere, exchange with the surface and with space, the dynamical circulation, or even seasonal cycles occur in all atmospheres, but they are shaped by the different conditions occurring on each celestial body, like its temperature and pressure or its proximity to its Sun. Comparing different planetary atmospheres allow to investigate the origin and history of the Solar System. It is possible to retrace its evolution from the collapsing of the rotating disk of gases around the Sun to the current composition of the different atmospheres. Measuring the abundance of noble gases, and in particular that of Helium or Argon, of hydrogen and carbon, provides precious information to validate (or not) different hypothesis. Comparative planetology can also be seen as the first step toward classifying and understanding the atmospheres of the numerous exoplanets that have been and will be detected. To illustrate the concept of comparative planetology, let’s consider the seasonal effect on Mars, Venus and Earth. Seasons on Mars and Earth are due to the high inclination of their rotation axis from the vertical of the plane of ecliptic. Seasons on Mars are exacerbated by its elongated elliptical orbit around the Sun, whereas that of Earth is almost circular. On Venus no seasons are expected because of its quasi-circular orbit and its very small inclination. Early Venus radio observations from Earth published in 1958 showed an amazingly hot temperature, upwards of 600 K, which was confirmed by the flybys of Mariner 2 in 1962. This high temperature could not be explained at that time. Slowly the idea of an exceptional greenhouse effect emerged. Scientists realized that the atmosphere of Venus was filled not only with CO2 but also with an opaque haze. Its nature was unknown, and in the 1960s scientists could only say that the haze was probably caused by some kind of tiny particles. At that time it was believed that the unraveling of the precise role of aerosols in the Venus atmosphere would certainly benefit studies of chemical contamination of Earth’s atmosphere.1 In the early 1970s, ground-based telescope observations produced extraordinarily precise data on the optical properties of these aerosols, and at last they were identified. The haze was made of sulfur compounds. The greenhouse effect of the sulfates could be calculated, and by the late 1970s, NASA’s findings about sulfate aerosols strengthened the belief

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that these particles could make a serious difference to the Earth’s climate as well. Sulfates were emitted by volcanoes and, increasingly, by human industry, so Venus had things to tell about climate change on Earth. In 1971, the spacecraft Mariner 9 settled into orbit around Mars and observed a great dust storm shrouding the entire planet. The observers immediately saw that the dust had profoundly altered the Martian climate, warming the planet by tens of degrees. The dust settled after a few months, but its lesson was clear. Haze, clouds and dust could warm an atmosphere. More generally, anyone studying the climate of any planet would have to consider dust very seriously. In particular, it seemed that on Mars the temporary warming had reinforced a pattern of winds that had kept the dust stirred up. It was a striking demonstration that feed-backs in a planet’s atmospheric system could flip weather patterns into a drastically different state. That was no longer speculation but an actual event in full view of scientists. The present atmosphere of Mars is thin, and its surface is too cold to allow liquid water. Still, the presence of ancient channels supports the belief that, in the past, a warmer climate allowed running water, possibly life sustaining. Venus was originally cooler and had a greater abundance of water. Because the planet was slightly closer to the Sun than the Earth, its water never liquefied and remained in the atmosphere to participate in the greenhouse effect. Being in gaseous form, water could reach higher altitudes where ultraviolet radiation would dissociate the molecule into H and O atoms. One clue to the Mars and Venus atmosphere evolutions is the ratio of deuterated water vapor HDO to normal water vapor H2 O. On Mars the D/H ratio has been measured to be, in the lower atmosphere, six times higher than on Earth. On Venus it is even higher, reaching 120 times the Earth value. Because D atoms are twice heavier than H atoms, their escape rate from the top of an atmosphere is much lower. This leads to believe that there has been in the past more H2 O on Mars or Venus than now. The exact determination of these past abundances depends on the ratio of escape rates of D and H, directly linked to the D/H ratio in the upper atmosphere. The total HDO remaining now in the planet is an indication of how much water the planet could have contained in the past.

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Mars has the advantage, compared to Earth, that it has preserved traces of its long gone history. Earth surface is indeed continuously remodeled by erosion and plate tectonics. There is almost no trace left of the time when microorganisms colonized it, before life was governed by the carbon chemistry. Mars could tell us this lost history and could reveal how life emerged. To conclude this long list of how solving scientific questions on other planets might help scientists to better understand their own world, we could cite H. Newell, who, in 1980 reported that the “study of the role of halogens in the atmosphere of Venus... led to the suspicion that chlorine produced in Earth’s stratosphere from the exhausts of Space Shuttle launches or from Freon used at the ground in aerosol sprays might dangerously deplete the ozone layer”.1 Maybe investigating the photochemistry of the PAH in the Mars atmosphere or analyzing the link between CO and the Venus circulation, to take only two examples, might one day give some insights to unsolved problems on Earth. In the following sections, we will provide some general information on planetary atmospheres and how that information can be obtained through observations.

2.

Generalities on Planetary Atmospheres

In this section, we will describe different characteristics shared by all planetary atmospheres, which will help understand their specificities, described in the following sections. The atmosphere usually refers to the gaseous envelope around a planet or body. Initially defined for rocky bodies having a solid surface, the definition has been extended to gaseous objects, such as the giant planets or even stars. In the case of the four giant planets of our Solar System (Jupiter, Saturn, Uranus and Neptune), their atmospheres are dominated by hydrogen and helium. The outer gas phase atmosphere blends into liquid once the atmosphere pressure has increased beyond a critical point. As a consequence, there is no clear boundary between the surface and the atmosphere. Within any atmosphere, temperature, pressure and density change with altitude. The pressure at a given altitude is the weight of air above that altitude per unit area (Fig. 1). The pressure decrease

Terrestrial Planets

Fig. 1.

101

Definition of atmospheric pressure.

with increasing altitude is described by the hydrostatic law: dp = −ρ(z)g(z), dz  ∞ ρ(z)g(z) dz, p(z) =

(1) (2)

z

where p is the pressure at altitude z, ρ is the density (ρ = m/V, with m the total mass of the species and V the volume occupied by the gas) and g is the acceleration due to gravity. Usually g can be considered constant, since the atmosphere depth is negligible compared to the radius of the planet. The equation of state describes the relationship between pressure, volume and the temperature of a real gas. The ideal gas law is a special case when the gas can be considered as ideal, i.e., as a theoretical gas composed of molecules between which there is no interaction. In this case, the pressure is expressed through the equation: ρ (3) p = RT. m When combining the hydrostatic law (Eq. (2)) and the ideal gas law (Eq. (3)), the following equation is obtained: g(z)m(z) dz dp = dz = , p RT (z) H

(4)

with H=

RT (z) , g(z)m(z)

(5)

where H has the dimensions of a distance, and is called the “scale height”. Values of the scale height for different atmospheres are given

A. C. Vandaele

102 Table 1. Parameter (unit) m (g) g (m/s2 ) Surface temperature (K) H (km)

Scale heights for different atmospheres.

Venus Earth Mars Jupiter Saturn Uranus Neptune 43.4 8.9 735

29.0 9.8 288

43.4 3.7 214

2.3 24 165

2.3 10 135

2.6 9 76

2.5 11 72

16

8.4

11

25

48

27

22

in Table 1. They were calculated considering the temperature at the surface of the planet. Scale heights are lower for massive planets and dense atmospheres. The higher the gravity or density or the lower the temperature, the more concentrated the atmosphere is toward the surface. However, the scale height varies with altitude as the temperature also varies. For example, on Earth, the scale height is about 8.4 km at the surface but only 6 km at an altitude of 13 km (210 K). Considering that the temperature is constant with altitude (or that the scale height is constant), the pressure decreases with altitude according to an exponential law. p(z) = p(0)e−z/H .

(6)

The scale height is the height above a reference level at which pressure decreases by a factor e (i.e., by about 2.7). The hydrostatic hypothesis states that the vertical acceleration of air masses is zero, not that vertical motion is impossible. This is a reasonable hypothesis on large spatial scales of several kilometers, but not in some kinds of clouds like cumulonimbus, where vertical accelerations can be important. In most of the atmospheres, all atmospheric constituents are uniformly mixed. Indeed in the lower layers of the atmosphere, convection and turbulent diffusion mix the different gases homogeneously. The hydrostatic law applies to the atmosphere considered as a whole, and all species share the same scale height. This region is called the homosphere. Above a certain altitude, called the homopause, the turbulent diffusion is less important and the different species separated under the effect of gravity according to their mass. The hydrostatic law applies to each species separately and each species

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has its own scale height. Light elements, like helium or hydrogen, have high scale heights and their partial pressure decreases slowly with altitude. They become more and more abundant with increasing altitudes compared to the heavier elements. As a consequence, the average molecular weight of the atmosphere decreases with increasing altitudes. This is illustrated in Fig. 2 for the Earth. Above 100 km, the density and pressure decrease exponentially but at a rate which differs from the region below. Below 100 km, where all constituents are well mixed, their densities decrease with altitude at the same exponential rate. Above 100 km, the mean free path becomes larger than the turbulent displacement of air. Diffusive transport becomes dominant. Because molecular diffusion depends on the molar weight of the species, species will be stratified differently, heavier molecules decreasing more rapidly with altitude.

Fig. 2. Global mean pressure (p), temperature (T), mean molar weight (M ) and number densities of several atmospheric constituents of the Earth atmosphere as functions of altitude. Adapted from Ref. 2.

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2.1.

Equilibrium temperature and greenhouse effect

The equilibrium temperature of a planet is the theoretical temperature that a planet would be at if it was in radiative equilibrium, i.e., the radiation the planet would emit as a black body at that temperature would compensate the energy received by its parent star. In this simple frame, the planet does not have any atmosphere nor internal heat source. Let’s consider the general case of a planet of radius R, with a surface temperature of Teq , and a planetary albedo A (percentage of the incident radiation which is reflected). Figure 3 represents schematically the different energetic fluxes: the incident solar flux, the fractions of this flux reflected and absorbed by the planet, and the black body flux emitted by the surface. By expressing that the absorbed flux should be in equilibrium with the emitted flux, one obtains the following expression for the equilibrium temperature, remembering that the radiation flux emitted by a blackbody at temperature T is given by the Stefan–Boltzmann law (σT 4 , where σ is the Stefan–Boltzmann constant):  Teq =

(1 − A)ES 4σ

1/4 .

(7)

Table 2 gives the values of the equilibrium temperatures for Venus, Mars and the Earth and compares these to the temperatures observed at the surface. Remember that one of the main differences in these

Fig. 3. Equilibrium temperature: (Left) Description of the fluxes; (Right) Definition of the surface intercepting the incoming solar radiation.

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Table 2. Comparison between equilibrium and surface temperatures for some planets. Parameter Bond albedo Incident flux (W/m2 ) Equilibrium temperature (K) Mean surface temperature (K) Excess of temperature (K)

Venus

Earth

Mars

0.75 2621 232 737 505

0.31 1370 254 288 34

0.25 590 210 215 ˜ 0

temperatures is the existence of an atmosphere surrounding the planets. For Mars, there is almost no difference, which is not surprising given the thinness of the martian atmosphere, as we will see in Section 4. The differences are quite significant for Earth and even more for Venus. For Earth, it makes it possible to find liquid water on its surface, which is crucial for supporting life. In both cases, these differences can be explained by the existence of a greenhouse effect within the atmospheres. Those are nearly transparent to the short wave radiation (from the Sun), but almost opaque to the long wave radiation (emitted by the planet’s surface). The radiation emitted by the surface will be absorbed by the atmospheric constituents, such as carbon dioxide, water vapor, ozone, nitrous oxide or methane. This will warm the atmosphere, which will then radiate this energy, both upwards and downwards, warming up the surface. This is the socalled greenhouse effect. The case of Venus, often called a runaway greenhouse effect, will be further developed in Section 4.2. 2.2.

Thermal escape to space

In the homosphere and the heterosphere, collisions between molecules are frequent. Above a critical altitude, called the exobase, those collisions become less frequent, so rare that some molecules never undergo a single collision. This is the exosphere. The exobase is defined as the altitude above which the free mean path is comparable to or larger than the atmospheric scale height.3 Once in this region, a molecule can escape the gravitational influence of the planet to reach space. These molecules follow ballistic trajectories determined by

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Fig. 4. Determination of the escape velocity. Here the altitude of the exobase is considered small compared to the radius of the planet.

their velocities. Most of these are captured by the gravitational field and return back to the denser regions of the atmosphere. However, some have velocities large enough to escape. The escape velocity (see Fig. 4) is the minimum speed needed to break free from the planet’s gravity. Whether an atmospheric molecule has sufficient speed or not depends on the temperature. As the temperature of a gas increases, its molecules move more quickly. In other words, their average speed increases. Different gases have different molecular masses and their average velocities are different at a given temperature. The velocities of individual molecules follow a Maxwellian distribution. The mostprobable velocity of a molecule of mass m is given by v therm = 2kT /m, where k is the Boltzmann constant. Typical values of the escape velocity and thermal velocities of H and O atoms calculated at the exobase are reported in Table 3 for different planets. The exobases of the Moon and Mercury correspond to their surface, and most of the elements ejected from their surface would be immediately lost to space. We speak of unstable or transient atmospheres. On Earth, Mars and Venus, H and He atoms can easily escape, and their atmospheres are essentially composed of molecules made of C, N and O.

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Table 3. Parameters of Terrestrial Planets and typical values of the escape velocity and thermal velocities of H and O atoms for different bodies. Parameter (unit) g (m/s2 ) R (km) ve (km/s) Exobase temperature (K) H v therm (km/s) O v therm (km/s)

3.

Mercury

Venus

Earth

Mars

Moon

3.7 2439.7 4.2

8.8 6051.8 10.3

9.8 6372 11.2

3.7 3389.9 5.0

1.62 1737 2.4

725 3.47 0.87

300 2.23 0.56

1000 4.08 1.02

350 2.41 0.60

260 2.08 0.52

Observation Techniques

The exploration of planetary atmospheres really started with the first astronomical observations made possible by the invention of telescopes. Still today many observations are made from Earth using powerful telescopes coupled with spectrometers operating in various spectral regions. Instruments embarked on satellites also provide a rich source of information on the planetary systems they probe. In the following, we will focus on observations carried out by spectroscopic instruments on platforms orbiting the planets of interest. Figure 5 illustrates the different observation modes used to sound the atmospheres. Nadir observations correspond to an instrument looking down to the surface of the planet, during day or night. This type of measurements is sensitive to different radiative contributions, such as the radiation emitted by the planet’s surface (being at a certain temperature and emitting like a blackbody), the atmosphere itself (again each layer of the atmosphere is at a certain temperature and also emits radiation), and the solar radiation being reflected by the planet. Limb observations directly sound the limb of the atmosphere investigating the emission from the atmosphere itself. Limb measurements can also be carried out when the Sun illuminates the atmosphere; in that case the signal seen by the instrument comes from solar light scattered by the atmosphere. During solar or stellar occultations the instrument points toward the Sun or a star while the Sun or the star sets down or rises.

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Fig. 5. Geometry of space observations: Nadir on the day side of the planet (1) or on the night side (2), solar (or stellar) occultation (3), and limb observation (4).

The theory of sounding atmospheres is based on the description of how radiation interacts with matter, in our case the atmosphere. Radiation is absorbed by the many molecules or atoms of the atmosphere. Indeed, any chemical element absorbs (or emits) radiation at specific wavelengths which are characteristic of this element. These spectral signatures cover the whole electromagnetic spectrum and correspond to transitions between two energy states of the element. In the far infrared or millimeter regions, we find essentially transitions between rotational levels, while in the mid infrared, the spectrum is due to transitions between ro-vibrational levels. In the visible and ultraviolet regions, transitions occur between electronic levels. Radiation can also be emitted by the atmosphere itself since it is lying at a certain temperature and thus radiating like any blackbody. A third mechanism of interaction is the scattering of light. Let’s consider a layer in the atmosphere with infinitesimal thickness ds as schematically represented in Fig. 6, where Lλ is the incoming radiance at wavelength λ. The attenuation of the incoming radiation after having passed through the layer, dLλ |abs , is given in Eq. (8), where βext is the

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Fig. 6. Radiative transfer in the atmosphere: The incoming radiation can be absorbed (1), emitted (2). Radiation coming from different directions can also be scattered (3) in the direction of propagation considered.

extinction coefficient which depends on the physical medium and the wavelength. dLλ |abs = −βext,λ Lλ ds.

(8)

This coefficient encompasses the attenuation by absorption (βa , i.e., the conversion of the energy of the radiation to heat), but also by scattering (βs , i.e., the redirection of the incoming light out of the incoming direction of propagation): βext,λ = βa + βs .

(9)

Absorption coefficients can be calculated using first principles spectroscopy theory. They will depend on the symmetry of the molecule, the temperature, the presence of other gases. Figure 7 shows the resulting absorption spectra for a series of species usually found in atmospheres. Each molecule is characterized by specific absorption features at different wavelengths which make their detection possible with spectroscopic space instruments. The position of absorption features will give information on which molecule absorbs, and their amplitude on their abundance. The layer of atmosphere will also emit radiation (Jλ,thermal ) and radiation coming from different directions will be scattered in the propagation direction (Jλ,scat ), so that the gain in radiation can be expressed by dLλ |emi = βext,λ (Jλ,thermal + Jλ,scat )ds = βext,λ Jλ ds.

(10)

dLλ = −Lλ + Jλ . βext,λ ds

(11)

Finally,

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Fig. 7.

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Absorption spectra of several atmospheric spectra. Adapted from Ref. 2.

the optical depth (or the optical thickness) τλ (s1 ; s2 ) Introducing s2 β ds, this expression becomes: s1 ext,λ dLλ = −Lλ + Jλ . dτλ

(12)

This is the Schwarzchild equation, which is the fundamental description of radiative transfer summarizing the gain and loss of radiation while going through the medium. It can be written as a differential equation (Eq. (12)) or under its integral form:  τ2 −(τ1 −τ2 ) − e−(τ −τ2 ) Jλ dτ. (13) Lλ (τ2 ) = Lλ (τ1 )e τ1

Let’s further introduce the transmittance of the atmosphere along the path as Tλ (τ1 ; τ2 ) = e−(τ1 −τ2 ) . The previous equation becomes:  1 Jλ dT, (14) Lλ (τ2 ) = Lλ (τ1 )Tλ (τ1 ; τ2 ) + T (τ1 ,τ2 )

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which can also be expressed as a function of the geometric distance s:  s2 dTλ (s) ds, (15) Jλ (s) Lλ (s2 ) = Lλ (s1 )Tλ (s1 ; s2 ) + ds s1  s2 = Lλ (s1 )Tλ (s1 ; s2 ) + Jλ (s)W (s)ds, (16) s1

where W (s) are the weighting functions. These functions are the derivatives of the transmittance profiles W (s) = dTλ (s)/ds. They indicate the relative contribution from a given layer of the atmosphere to the radiance received by the instrument at a given wavelength. Combining the definition of the weighting function with the definition of the transmittance and the optical depth, we see that the weighting function can also be described as the product of the transmittance by the extinction coefficient, W (s) = βext Tλ (s), as illustrated in Fig. 8. The typical form of a weighting function is a bell shape peaking at the altitude from which the measured radiation at that wavelength is originating. The radiation emitted by a layer of the atmosphere depends on the temperature of that layer, the abundances of the gases and the transmittance of the air between that layer and the measuring instrument. The radiation emitted by the lowest layers is

Fig. 8. Example of weighting functions corresponding to typical extinction and transmittance profiles.

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high because density is high, but most of the radiation is absorbed by the atmosphere above; for the highest layers, the transmittance to space is high but the emission is low because density decreases exponentially with altitude. Let’s consider the intensity of radiation reaching an instrument (Inst) looking backward along the direction of propagation, which is usually the case for an instrument in space (see Figs. 5 and 9). Equation 13 can be rewritten by considering that at the level of the instrument τ |Inst = τ2 = 0 in this geometry:  τSource e−τ Jλ dτ. (17) Lλ |Inst = Lλ (0) = Lλ (τSource )e−τSource + 0

On the left-hand side of this equation, Lλ |Inst is the intensity observed by the instrument. On the right-hand side, the first term represents the intensity of a radiation source (located at the end of the line-ofsight, LOS, of the instrument) attenuated by the atmosphere between the source and the sensor. For example, for nadir looking instrument Lλ (τSource ) would be the emission from the planet’s surface and e−τSource would be the total atmospheric transmittance from the surface to the instrument. The second term is the sum over all the contributions from individual infinitesimal layers along the line-ofsight, each of them emitting radiation, which will be attenuated by the atmosphere between that layer and the instrument.

Fig. 9. Definition of the parameters for an instrument looking backward along the propagation direction.

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Let’s now consider scattering. When radiation is extinguished by scattering, the energy is not converted into another form, but instead redirected into another direction. The loss of radiation along the line-of-sight will be associated with a gain of radiation originating from different directions. When scattering needs to be considered, the complexity of the radiative transfer equations greatly increases, because all directions need to be taken into account into the calculations. Scattering is a complex process, as it depends on the size, form and composition of the scattering particle and on the wavelength of the incoming light. Since energy is scattered in all directions, the Schwarzschild equation becomes also more complex. As an illustration the source term Jλ of Eq. (10) becomes:  ω ˜ ˜ )Jλ,thermal + p(Ω , Ω)Lλ (Ω )dω  , (18) dLλ |emi = (1 − ω 4π 4π where ω ˜ = βs /βext is the single scattering albedo of the medium. p(Ω , Ω) is the scattering phase function, which represents the probability that a photon arriving from direction Ω will be scattered within an infinitesimal element dω of solid angle centered around the Ω direction. Radiative transfer modeling means solving the Schwarzschild equation considering the different sources and losses of radiation which will directly depend on the composition of the atmosphere and its temperature. In nadir observations, different contributions need to be considered (thermal emission by the planet’s surface and by each layer of the atmosphere, reflection of the solar radiation on the surface, scattering of light on the aerosols) and the solution of the Schwarzchild equation is not trivial. In the following, we will illustrate two different cases often used by space instruments: the observation of the emission at the limb and solar occultation. In observations of the night side limb (see Fig. 5 case [4] and Fig. 10), the radiation reaching the instrument is emitted by the atmosphere itself; there is no other source (no Sun or star at the end of the line-of-sight; Lλ (τSource ) = 0) and scattering can be neglected. As a first approximation the atmosphere can be considered as a blackbody. A blackbody is an ideal object that totally absorbs all incoming radiation and reversely it is the ideal body that emits the theoretical maximum of radiation. The emitted radiation is isotopic, and nonpolarized, and only depends on the temperature of the blackbody.

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Fig. 10. Definition of the parameters for an instrument measuring the emission at the limb.

A blackbody emits more radiation than any object of the same temperature. The intensity of radiation emitted by a blackbody is given by the Planck function (Eq. (19)) Bλ (T ) =

2hc2 λ5 (ehc/kB λT − 1)

,

(19)

where c is the speed of light, h is the Planck constant and kB is the Boltzmann constant. The general Schwarzchild equation reduces to  0 dTλ (s; s∞ ) ds, (20) Bλ (s) Lλ (H) = ds ∞ where H is the tangential height, i.e., the lowest altitude sounded (see Fig. 10). Considering that the tangential height and the path along the line-of-sight (s, see Fig. 11) are linked to the altitude through: (Re + H)2 + s2 = (Re + z)2 ,

(21)

with Re the radius of the planet. The expression Eq. (20) can be written as  ∞  ∞  dTλ (s; s∞ ) ds   Bλ (z ) dz = Bλ (z  )Wλ (H, z∞ )dz  , Lλ (H) = ds dz  H H (22)

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where the weighting functions are defined as  0 z < H, Wλ (H, z∞ ) = dTλ (z;z∞ ) ds dTλ (z;z∞ )  Re /2(z − H) z > H. ds dz = ds (23) The sensitivity of the instrument is increased by a factor  Re /2(z − H) which is due to the long tangent optical path. The weighting functions are represented for a typical observation in Fig. 11, for different tangential heights sounded sequentially as the instrument probes from the top of the atmosphere down to lower altitudes. Limb observations usually provide high vertical resolution and are sensitive to low abundances. The second example is a particular case of limb observations, called solar occultations, which correspond to the instrument looking at the Sun. As atmospheric emission can be neglected, the equation simplifies in the known Beer Lambert law: Lλ (H) = Lλ (Sun)Tλ (Sun − Inst).

(24)

Usually solar occultation provide a very sensitive method to sound the atmosphere (long paths through the atmosphere) as well as a

Fig. 11.

Weighting functions for a typical limb observation. Adapted from Ref. 4.

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high vertical resolution. With limb observations, they allow for a detailed investigation of the vertical profiles of different trace gases in the atmosphere. In Section 4, we will describe what we know today of the atmospheres of the telluric planets of our Solar System, most of which has been obtained by spectroscopic observations carried out either from the Earth using sensitive telescopes or from space-borne instruments.

4.

Terrestrial Planets

Our Solar System has four terrestrial planets: Mercury, Venus, Earth and Mars. During the formation of the Solar System, there were probably many more planetesimals, but they have all merged with or been destroyed by the four remaining worlds in the solar nebula. Only one terrestrial planet, Earth, is known to have an active hydrosphere. Telluric planets are composed mostly of some combination of hydrogen, helium and water existing in various physical states. They all have roughly the same structure: a central metallic core, mostly iron, with a surrounding silicate mantle. Those planets possess secondary atmospheres, atmospheres generated through degassing, internal volcanism or comet impacts, as opposed to the gas giants, which possess primary atmospheres, atmospheres captured directly from the original solar nebula. Table 4 gives some general information on the orbital parameters of the terrestrial planets and on the composition of their atmospheres. Telluric planets have oxidized atmospheres, whereas the giant planets have reducing atmospheres. Indeed, in the atmospheres of Mars or Venus, carbon, for example, exists predominantly combined with oxygen as CO2 rather than combined with hydrogen as CH4 , while in the atmospheres of the giant planets, where the major gas is hydrogen, the contrary is found. The atmosphere of Earth is unusual in that it contains substantial amounts of molecular oxygen (O2 ) and is capable of oxidizing the surface. Therefore Earth’s atmosphere is an oxidizing one. In the following, we will shortly describe the atmospheres of the four terrestrial planets and illustrate also the exploration of these through selected missions and instruments. The latter will be done only for Mercury, Venus and Mars, Earth observation would need a separate chapter in itself and will not be included in this section.

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Table 4. Orbital parameters of terrestrial planets, as well as the composition of their atmospheres. Parameter

Mercury

Venus

Earth

Mars

Mean distance 0.387 0.723 1.0 1.524 to Sun (AU) Mean radius 2440 6051.8 6371.0 3389.9 (km) 5.427 5.204 5.515 3.933 Density (g/cm3 ) Eccentricity 0.2 0.007 0.02 0.09 Obliquity to 0.034 177.4 23.4 25.2 orbit (deg) Orbital period 88.0 224.7 365.2 687.0 (days) Rotation period 58.7 –243.0 0.98 1.025 (days) Length of day 176 117 1.0 1.029 (days) Surface 100–725 733 288 215 temperature (K) Surface pressure 0 92 1.013 0.0056 (bar) Equilibrium 446 238 263 222 temperature (K) Scale height 13–95 16 8.5 18 (km) Escape velocity 4.3 10.4 11.2 5.0 (km/s) Composition H2 He O2 CO2 (0.965) N2 (0.77) O2 (0.21) CO2 (0.95) H2 Ar CO2 H2 O N2 (0.027) N2 (0.035) CO O3 CH4 NO2 Ar O2 CO H2 O

4.1.

Mercury

Mercury, the smallest planet and the closest to the Sun, has the largest eccentric orbit of the Solar System’s planets. Mercury rotates around an axis that is perpendicular to its orbital plane (its obliquity is almost zero, see Table 4). The planet has a 3:2 spin–orbit resonance, i.e., it completes three rotations about its axis for every two revolutions around the Sun.

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Mercury has a significant, apparently global, magnetic field about 1.1% of the strength of Earth’s. It is still strong enough to deflect the solar wind, inducing a magnetosphere. Mercury’s magnetic field is distorted by the solar wind, which compresses it on the dayside and stretches it out to form a long tail on the nightside. As on Earth, it is likely that this magnetic field is generated by a dynamo effect. This dynamo effect would result from the circulation of the planet’s iron-rich liquid core. Particularly strong tidal effects caused by the planet’s high orbital eccentricity would serve to keep the core in the liquid state necessary for this dynamo effect. Mercury has a tenuous atmosphere with a surface pressure of the order of or less than 10−12 bar. The first observations of Mercury from space were done by Mariner 10, which detected oxygen, helium and hydrogen atoms. Later, using ground-based instruments, other atoms, like sodium (Na), potassium (K) or calcium (Ca) were discovered. The most abundant atoms are present with number densities of the order of a few thousand atoms cm−3 . Sodium, potassium, oxygen and calcium atoms are thought to be surface constituents that have been extracted and blasted into the atmosphere through sputtering from the solar wind or meteoroids.a Indeed, Mercury’s magnetic field interacts with the magnetic field of the solar wind to sometimes create intense magnetic tornadoes that funnel the fast solar wind ions down to the surface of the planet where they interact with atoms within the crust and eject them into space. Hydrogen and helium atoms are probably captured from the solar wind, of which they are major constituents. This tenuous atmosphere is not stable. It is continuously lost to space and replenished by the solar wind or impacts. Indeed escape to space is easy because of the high temperatures reigning on the day side. Along with its weak gravity field, it means that for almost any atom or molecule, their thermal velocity will be larger than the escape velocity (about 4 km/s, see Table 3). In fact, the exosphere, i.e., the upper layer of the atmosphere which gradually fades into space, starts at its surface. The huge temperature

a

When a fast atom or ion hits an atmospheric atom, the latter gains energy and may be able to escape the planet’s gravitational attraction. In the case of tenuous atmospheres, the fast ion or atom hits the surface directly, ejecting one or several atoms from the crust into space.

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difference between day (725 K) and night (80 K) comes from the fact that the planet rotates very slowly (a day on Mercury lasts 176 Earth days) and the atmosphere is so thin it does not retain heat. The surface is rocky with a multitude of craters, indicating that the planet has been geologically inactive for billions of years. There are no signs of volcanic activity or plate tectonics. The high number of craters on the surface is explained by its tenuous atmosphere. Mariner 10 was the first mission to use the gravity of one planet (in this case Venus) to reach another one. The spacecraft was launched in November 1973 toward Venus, and after a flyby of that planet, its trajectory was modified toward Mercury which was reached in March 1974. Mariner 10 was then set to orbit the Sun, flying above Mercury again in September 1974. A third flyby occurred in March 1975 at an altitude of 305 km. In total Mariner 10 took pictures of about half Mercury’s surface. MESSENGER (Mercury Surface, Space Environment, Geochemistry and Ranging5 ), the next mission to Mercury, was launched in 2004, so about 30 years after Mariner 10. The spacecraft entered orbit around Mercury in March 2011, and started acquiring data soon after. The mission discovered high concentrations of magnesium and calcium on the dark side of the planet,6,7 identified a significant northward offset of the planet’s magnetic field, found large amounts of water in the exosphere, evidence of water ice at the poles, frozen in locations that never see the sunlight,8,9 and revealed evidence of past volcanic activity on the surface. Beginning of the summer 2014, the orbit was lowered down to 25 km altitude to be able to carry out new research. However it was soon found out that the spacecraft propellant was running out and that it would soon impact the planet. As expected, on April 30, 2015, MESSENGER slammed into Mercury’s surface creating a new crater on the planet. BepiColombo,10 the first European mission to Mercury, has been launched in October 2018 for a 7-year journey to the planet. It comprises two spacecraft: the Mercury Planetary Orbiter (MPO) and the Mercury Magnetospheric Orbiter (Mio). BepiColombo is a joint mission between the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA). MPO will investigate the surface and internal composition of the planet; Mio will study its magnetosphere and magnetic field. As of today, BepiColombo has successfully performed its first flyby of the planet (see Fig. 12). BepiColombo’s main science mission will begin in early 2026.

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Fig. 12. The joint European-Japanese BepiColombo mission captured this view of Mercury on October 1, 2021 as the spacecraft flew past the planet for a gravity assist manoeuvre. The region shown is part of Mercury’s northern hemisphere. Credit: ESA/BepiColombo/MTM, CC BY-SA 3.0 IGO.

4.2.

Venus

Venus has an atmosphere very different from that of Earth. In comparison to Earth it is much denser, heavier and extends to a much higher altitude. The temperature and pressure at the surface are 740 K and 92 atm, respectively. Despite the harsh conditions on the surface, at about a 50-km to 65 km level above the surface of the planet, the atmospheric pressure and temperature are nearly the same as those on Earth’s surface. The atmosphere of Venus is mostly made up of CO2 (97%) and nitrogen (N2 , less than 3.5%), the rest being trace gases such as carbon monoxide (CO), water vapor (H2 O), halides (HF, HCl), sulfur-bearing species (SO2 , SO, OCS, H2 S) and noble gases. Sulfur compounds are extremely important to understand the formation of the Venusian clouds which are believed to be composed of sulfuric acid (H2 SO4 ) droplets. These clouds completely enshroud the planet in a series of layers, extending from 50 to 70 km altitude, and

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are composed of particles of different sizes and different H2 SO2 /H4 O compositions.11 These act also as a very effective separator between the atmospheres below and above the clouds, which show very distinctive characteristics. Water vapor is present in extremely low quantities (about 30 parts per million or ppm, 1 ppm = 0.001%), making Venus the driest planet of the solar system.12,13 As on Earth, the atmosphere can be divided into distinct regions based on the evolution of the temperature with altitude, as shown in Fig. 13. The troposphere on Venus extends from the surface up to about 70 km altitude which also corresponds to the top of the main cloud deck. No temperature variations (diurnal or seasonal) have been observed below the clouds. Above the clouds, the mesosphere extends up to about 100 km. At higher altitudes, in the thermosphere, very different temperatures for the night and day sides have been observed. The nightside is so cold that some are referring to it as the cryosphere. Due to the absence of a magnetosphere, the solar wind interacts directly with the ionosphere, confining the latter below 200 km altitude. The dynamics of the Venusian atmosphere is quite complex and characterized by two regimes of circulation: retrograde zonal superrotation in the troposphere and mesosphere and solar-antisolar circulation in the thermosphere. The zonal circulation is characterized by wind speeds decreasing from 100 m/s at the cloud top to

Fig. 13. Variation of the temperatures within the atmospheres of Venus, Earth and Mars.

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almost 0 at the surface. The mechanisms that maintain the superrotation are still not fully understood.14 The equilibrium temperature of Venus is only about 240 K, whereas the temperature at the surface reaches much higher values (see Table 4). This difference is attributed to the huge greenhouse effect experienced by the planet. Venus and Earth formed from the same interstellar gas and dust, and therefore their initial composition should be very similar.15 Liquid water has always been present at the surface of Earth, while Venus evolved toward a dry and hot planet. Some proposed that Venus could have been formed in a drier region of the Solar nebulae which would explain the current depletion in water.16 However, observations indicate that, in its past, Venus had more water than in the present epoch. This is evidenced by measurements of present-day D/H, which indicate an overabundance of deuterium (heavy hydrogen, D) relative to hydrogen. Venus might even have supported enough water to form an ocean. Over time, this water was vaporized17,18 then lost through photodissociation by ultraviolet (UV) radiation emitted by the Sun, providing hydrogen and oxygen atoms. The H atoms can escape the planet’s gravitational field under favorable conditions, i.e., when their thermal energy is high enough (see Section 2.2). The free oxygen reacted to create both carbon dioxide and sulfur dioxide. Thermal escape of hydrogen is a slow process; it would require at least hundreds of millions of years for Venus to lose its ocean.18 During that time water vapor evaporating from the ocean and trapped in the atmospheric participated to the increase of the atmosphere temperature, through the greenhouse effect. Water vapor is an even more powerful greenhouse gas than carbon dioxide. Increasing the temperature also accelerated the evaporation of the ocean, creating a positive feedback loop. At some point, the surface of Venus got so hot that the carbon trapped in rocks sublimated into the atmosphere and mixed with oxygen to form even more carbon dioxide, forming the dense atmosphere now surrounding the planet. The accumulation of CO2 was boosted by the lack of any efficient CO2 cycle, which could transfer CO2 back to the crust, as is happening on Earth: the CO2 emitted in the atmosphere, remained in the atmosphere. The composition and photochemical processes occurring below, within and above the clouds are quite different in nature. The chemistry in Venus’s atmosphere is controlled by ion–neutral and ion–ion

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reactions in the ionosphere, by photochemistry within and above the cloud global layer, and by thermal equilibrium chemistry, which prevails near the surface.19 Venus’s main cloud layers span the 50–70-km altitude range, with hazes reaching up to 90 km and down to 30 km. The main cloud deck is composed of different populations of particle sizes ranging from less than a micrometer up to 35 μm. Although Lomonosov was the first to suggest that Venus had an atmosphere, through observations of the 1761 Venus transit, the systematic observation of Venus started in the early 20th century with the detection of the main constituent of the atmosphere, CO2 , the determination of the cloud structure, the high surface temperature and the existence of the greenhouse effect gathered from Earth-based observations and the first fly-by of the planet by Mariner 2. This was followed by a long series of space missions, including the Venera and Mariner missions, Pioneer Venus or Magellan (see Ref. 20 for a review) and more recently Venus Express of the European Space Agency21,22 and Akatsuki,23 which is the last mission still orbiting the planet today. But already several space agencies have been supporting the future exploration of the planet, indeed several missions have been selected by ESA (EnVision, launch in 2031), NASA (with two missions DaVinci+ and Veritas, launches foreseen in the 2028–2030 timeframe) and the Indian space agency and are now being prepared. 4.3.

Earth

The average temperature and pressure on the surface of the Earth are 288 K and 985 hPa (1,013 mbar). This temperature is about 35 K warmer than the equilibrium temperature (see Section 2.1) as a result of the greenhouse effect due to the presence of water vapor, carbon dioxide (CO2 ) and other trace gases such as ozone (O3 ), nitrous oxide (N2 O) and methane (CH4 ). Figure 13 shows the different layers within the atmosphere of Earth: • The troposphere from the surface up to an altitude between 10 km above the poles and 20 km at the equator. The rapid decrease of the temperature with altitude is due to the heating of the surface and causes convection. • The stratosphere, characterized by an increase of temperature with altitude because of the presence of ozone, whose abundance is the

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highest in the stratosphere, forming what is called the ozone layer. Ozone is the only component that significantly absorbs the UV solar radiation penetrating the atmosphere. Despite its low concentration, ozone effectively absorbs the solar radiation between 230 and 300 nm, protecting the Earth against harmful ultraviolet radiation which therefore cannot reach the lower layers of the atmosphere, nor the surface. The energy absorbed by ozone is then transferred to kinetic energy, heating the stratosphere. This region is unique to Earth, and is not found in the other atmospheres of the telluric planets. • The mesosphere, in which the temperature decreases with altitude, caused by a decreasing production of ozone and an increase in the cooling rate due to CO2 . • The thermosphere, above 80–90 km, where temperature increases with altitude, following the absorption of the UV solar radiation and a rarefied atmosphere which prevents any efficient cooling through IR emission. The atmosphere of Earth primarily consists of nitrogen (N2 , 78%) and molecular oxygen (O2 , 21%), and a series of trace gases, including water (H2 O), argon (Ar) and CO2 (see Table 4). The main characteristics of the Earth and difference compared to the other planets of our Solar System is the presence of liquid water on its surface. It is likely that the presence of liquid oceans played an essential role in the development of life on Earth. The appearance of life also had irreversible impacts on the atmosphere, with the production of oxygen, whose photodissociation led to the formation of the ozone layer. 4.4.

Mars

Mars lost its magnetosphere 4 billion years ago, so the solar wind interacts directly with the Martian ionosphere, keeping the atmosphere thinner than it would otherwise be by stripping away atoms from the outer layer. Both Mars Global Surveyor and Mars Express have detected these ionized atmospheric particles trailing off into space behind Mars.24 Atmospheric pressure on the surface varies from around 30 Pa on Olympus Mons to over 1,155 Pa in the depths of Hellas Planitia, with a mean surface level pressure of 600 Pa. This is less

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than 1% of the surface pressure on Earth. The equivalent pressure of Mars surface is found at a height of 35 km above the Earth’s surface. The scale height of the atmosphere is about 11 km; higher than Earth’s 6 km due to the lower gravity. The average surface temperature is about 215 K, although large latitudinal, seasonal and diurnal variations are observed. For example, the temperature at the equator drops to 200 K at night and reaches 300 K during the day. The atmosphere on Mars consists of 95% carbon dioxide, 3% nitrogen, 1.6% argon and contains traces of oxygen and water. Liquid water cannot exist on the surface under the current temperature and pressure conditions, although the surface of the planet is covered by many evidences of liquid water, suggesting a warmer and wetter past. Mars surface is mostly composed of iron-rich basaltic and andesitic rock. Surface dust, also called regolith, is ubiquitous on the planet and can be lifted up in the atmosphere. The presence of hematite (Fe2 O3 ) and goethite (α-FeO(OH)) explains the reddish color of the planet. Because there is no plate tectonics taking place on Mars, the surface preserves traces of its past. Scientists could estimate the age of different areas on the planet, based on the number and size of craters, as far as 4.5 billion years ago, while on Earth the surface is younger than 2 billion years. Although Mars does not have any global magnetic field, observations revealed traces of remnant magnetic field25 resulting from the magnetization of some terrains in the past of the planet. Mars has an elliptical orbit with perihelion and aphelion of, respectively, 1.38 and 1.66 AU. The complete revolution around the Sun takes 687 terrestrial days. The rotation of the planet on itself, i.e., a martian day (also called “sol”) lasts a little longer than Earth’s, about 24 h 40 min. Obliquity is about 25◦ , more or less the same as Earth’s, implying that Mars has also a seasonal cycle. But due to its elliptical orbit, seasons on Mars differ more between northern and southern hemisphere than on Earth. On Mars, the Solar Longitude, LS , is used to define the seasons and more generally the time (see Fig. 14). LS ranges from 0◦ to 360◦ corresponding to a complete revolution around the Sun. LS represents thus the angle between Mars, the Sun and a reference position of Mars at LS = 0◦ corresponding to the spring equinox in the northern hemisphere. LS = 90◦

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6 5

7 8 perihelion

210°

180°

150°

9

90°

270° 10

4

120°

240°

300°

60° 330°

0°

3

30°

11

aphelion

12

2 1

Fig. 14.

Solar longitude on Mars. Adapted from Ref. 26.

corresponds then to the northern summer solstice, LS = 180◦ to the northern autumn equinox and LS = 270◦ to the northern winter solstice. The first Martian year (MY1) was arbitrarily chosen to start at the northern spring equinox (LS = 90◦ ) on April 11, 1955.27 Because the orbit of Mars is highly elliptical, the orbital revolution velocity is the highest while the planet is closest to the Sun and Mars receives up to 45% more energy than at aphelion. As a consequence, the duration and strength of the seasons in both hemispheres are quite different. The southern hemisphere undergoes more extreme seasons with a warm short summers and a cold long winters, while in the northern hemisphere, the seasons are more temperate with longer summers but less warm and shorter winters with less cold temperatures. Like Earth, Mars possesses polar caps whose extensions toward lower latitudes vary throughout the year. On Mars, the polar caps are characterized by a residual (present all year round) and a seasonal cap (appearing during the cold seasons). At both poles, a mix of sediments, dust and ice has accumulated over time to form a deposit, extending on about 1,000 km large and whose thickness reaches more than thousands of meters. These polar deposits are

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partly covered by the residual polar caps. The residual caps at the north and south poles differ in composition and size28 : in the north, the deposits are covered by a layer of water ice while in the south, the cap is smaller and is made of CO2 ice (see Fig. 15). As the temperature decreases, atmospheric CO2 condenses creating the seasonal cap, which is released back to the atmosphere when the temperature rises again. This leads to important variations of the atmospheric pressure. The atmosphere of Mars is constantly loaded with dust whose abundances depend on season and location.29 The amount of dust in the atmosphere of Mars has a seasonal cycle (see Fig. 16), with the first half of the year having less dust than the second half (in the northern hemisphere). During summer in the southern hemisphere, Mars is also at perihelion in its orbit around the Sun, which causes an increase in the amount of dust lifted from the surface and suspended in the atmosphere. There is large inter-annual variability in the dust activity, with some years having smaller regional scale dust storms and some years developing into a global, planet-encircling dust storm. The nature of this variability is still unknown and is an open question in Mars research. The dust and water cycles30 are coupled through cloud condensation processes, but dust also modifies the thermal

Fig. 15. Images of the Martian residual polar caps obtained by MOC on MGS. (Left) North polar cap (dimensions: roughly 1,100 km across); (Right) South polar cap (dimensions: from right to left, about 420 km across). Credit: NASA/ JPL/MSSS.

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Fig. 16.

Dust climatology. Adapted from Ref. 31.

structure of the atmosphere. Recent studies suggest that global dust storms effectively transport water vapor from the near-surface to the middle atmosphere and increase the escape rate of atmospheric hydrogen (a product of water vapor photolysis).32,33 Different kinds of clouds occur on Mars: water ice and CO2 ice clouds.34 Water ice clouds usually appear under situations of adiabatically cooled upward flows. The dust particles serve as condensation nuclei in the formation of the clouds. However, as dust warms the atmosphere, clouds occur only under low dust loading conditions. Such clouds can take several forms: polar hoods, topographically induced clouds, cloud belt forming at low latitudes during the aphelion season. CO2 ice clouds can only form when the temperature is low enough to allow CO2 to condense. Such clouds are found in the polar regions during the winter. High altitude mesospheric clouds have also been observed.35 The presence of methane in the atmosphere of Mars is still controversial. Methane, which is a tracer for life on Earth, was first noticed in Mars’ atmosphere by Michael J. Mumma (NASA/Goddard Space Flight Center), whose team first detected Martian methane in 2003.36 In March 2004, Mars Express confirmed the presence of methane in

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the Martian atmosphere with a concentration of about 10 ppb by volume.37,38 Since methane is an unstable gas that is broken down by ultraviolet radiation, typically lasting in the atmosphere for about 340 years, its presence on Mars could indicate that there is (or has been within the last few hundred years) a source of the gas on the planet. Volcanic activity, comet impacts, and the existence of life in the form of microorganisms such as methanogens have been proposed as possible sources, although some are now thought not to have been important.39 Methane appears to occur in patches, which suggests that it is being rapidly broken down before it has time to become uniformly distributed in the atmosphere, and so it is presumably also continually being released to the atmosphere. It has also been shown that methane could also be produced by a non-biological process involving water, carbon dioxide, and the mineral olivine, which is known to be common on Mars.40 One of the main science objectives of the ExoMars Trace Gas Orbiter mission is to confirm or refute the presence of the trace gas within the atmosphere of Mars. Since the beginning of its science phase in April 2016, methane has been continuously monitored by both spectrometers on board the spacecraft, i.e., NOMAD and ACS. Up to now, no detection of methane could be reported.41,42 The history of the exploration of the Red Planet is very rich; it started in the 1960s. Following the successful flyby in 1965 by Mariner 4, several missions were designed and launched by the Soviet Union and the USA with various success rates. Today six space agencies have successfully made it to Mars: NASA, the former Soviet Union space program, the European Space Agency (Mars Express, ExoMars Trace Gas Orbiter), the Indian Space Research Organization (MOM), the China National Space Administration (Tianwen-1), and the United Arab Emirates Space Agency (Hope). Today several spacecraft orbit around the planet continuing to deliver a wealth of information on its atmosphere, helped by a series of rovers crossing over the surface of the planet delivering ground truth about the surface composition and the lower layers of the atmosphere. NASA’s rover Curiosity, arrived at Gale Crater in 2012 to search for signs of ancient habitable environments. Mars InSight landed in 2018 to probe the interior structure of Mars in detail for the first time. Perseverance, which landed on Mars in Feb. 2021, will search for potential signs of life. Perseverance also carries a test helicopter, Ingenuity,

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which will assess the feasibility of flying on Mars. Perseverance will cache the most promising samples for a future sample-return mission, tentatively scheduled for later in the decade and involving both NASA and the European Space Agency. In the near future, the second element of the ExoMars mission will deliver a rover and a platform on the surface of Mars (launch expected in 2022). Japan is now building the Mars Moons Exploration (MMX) mission for a samplereturn mission from Phobos, one of the two moons of Mars. 5.

Q&A

Julia Maia: You said that indications of volcanism on Venus include SO2 and high emissivity surface rocks. What else could cause high emissivity? What other data could test that? Ann-Carine Vandaele: New missions are needed to study the emissivity problem. The high emissivity could be an artifact of higher temperature caused by internal heat, but could also result from compositional and even structural (e.g., particle size) differences. Multiple signs of volcanic activity are seen in the geology of the surface, but there is no direct evidence of current activity. Luisa M Lara: Volcanoes emit more than SO2 . If Venus is active, future missions could detect these other gases? Ann-Carine Vandaele: Water and carbon monoxide are two such gases that could be measured spectroscopically. We are planning a suitable spectrometer for next European mission to Venus. Maya Garcia-Comas: Why is there hemispheric asymmetry (more in the North) in the amount of polar cloud on Mars? Ann-Carine Vandaele: The orbit of the planet is quite eccentric, and Mars has a non-zero obliquity. So there is a seasonal effect that causes the asymmetry because one pole is pointing nearer the Sun at perihelion while the other is not. We do not notice this effect on Earth because, although we have an obliquity, the orbital eccentricity is very small. Maya Garcia-Comas: What are the conditions for a regional storm to become a global storm. Why do these storms start and stop?

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Ann-Carine Vandaele: It is still not really understood. The main idea is that it is somehow related to the orbit, but it is not clear. There may also be a kind of runaway once a lot of dust gets in the atmosphere and changes the thermal structure. But we don’t know. Julia Maia: Obs Cote d’Azur: Why is Mars so heavily explored yet Venus left aside? Ann-Carine Vandaele: Venus is easier to reach but harder to study, because the atmosphere is hotter, the pressure is higher and the cloud cover is total. Also, human exploration of Venus has no future, while human exploration of Mars has been on people’s minds for decades, or even centuries. Asier: How do you get vertical resolution from a limb profile of an atmosphere? Ann-Carine Vandaele: You have many lines of sight through the atmosphere each with different impact parameters, so you can take differences to probe the change between adjacent lines, like peeling an onion. Olga Mu˜ noz: Can you explain about the relation between dust in Mars’ atmosphere and water escape? Ann-Carine Vandaele: We see that there is more water at high altitudes and faster escape of hydrogen when the atmosphere is dusty. This is because the dust warms the atmosphere by absorbing sunlight and then the atmosphere expands upwards, exposing more water to the solar UV flux and dissociation. So, it’s nothing much to do with reactions, but with a change in the atmospheric structure. Mayer: How do you get to be a PI of a space instrument and how do you have time for science when you are a PI? Ann-Carine Vandaele: Like what you do, build your luck by participating, by networking, to show that you do good work, and have some luck. References [1] H. Newell, Beyond the Atmosphere: Early Years of Space Science, Dover Publication, Inc., Mineola, New York, USA (1980). [2] M. Salby, Physics of the Atmosphere and Climate. Cambridge University Press, New York, USA (2012).

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[11] [12] [13] [14] [15]

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[18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]

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A. Garcia-Munoz et al., in Handbook of Exoplanets, 2018. W.L. Smith, Bull. Am. Meteor. Society 53(11), 1074–1082 (1972). S.C. Solomon et al., PSS 49, 1445–1465 (2001). A.W. Merkel et al., Icarus 281, 46–54 (2017). P.N. Peplowski et al., PSS 108, 98–107 (2015). A.N. Deutsch, Icarus 280, 158–171 (2016). N.L. Chabot et al., GRL 43, 9461–9468 (2016). J. Benkhoff and M. Fujimoto, Comprehensive science investigations of Mercury: The scientific goals of the joint ESA/JAXA mission BepiColombo, Special Issue: PSS 58(1–2), 1–326 (2010). D. V. Titov et al., Space Sci. Rev. 214, 126 (2018). DOI: https:// doi.org/10.1007/s11214-018-0552-z. E. Marcq et al., Space Sci. Rev. 214 (2018). DOI: 10.1007/s11214-0170438-5. A.C. Vandaele. (2020). DOI: 10.1093/acrefore/9780190647926.013.4. A. S´anchez-Lavega et al., Space Sci. Rev. 212, 1541–1616 (2017). DOI: 10.1007/s11214-017-0389-x. D. Grinspoon, The surface and atmosphere of Venus: Evolution and present state. In L. Bengtsson, R.-M. Bonnet, D. Grinspoon, S. Koumoutsaris, S. Lebonnois, and D. Titov (eds.), Towards Understanding the Climate of Venus: ISSI Scientific Report Series, Springer Science + Business Media, New York, vol. 11 (2013). J.S. Lewis, Earth Planet. Sci. Lett. 22, 239–244 (1974). M. Bullock, and D. Grinspoon The atmosphere and climate of Venus. In S. Mackwell, A. Simon-Miller, J. Harder, and M. Bullock (eds.), Comparative Climatology of Terrestrial Planets, University of Arizona, Tucson, pp. 19–54 (2013). J. Kasting, Icarus 74, 472–494 (1988). F.P. Mills et al., Geophys. Monograph Series 176, 73–100 (2007). B. Fegley Jr., Venus. In Treatise on Geochemistry, vol. 21, Elsevier, Amsterdam, The Netherlands, pp. 1–56 (2004). H. Svedhem, et al., J. Geophys. Res. 114, 3–21 (2009). DOI: 10.1029/ 2008JE. F.W. Taylor, et al., Space Sci. Rev. 214, 35 (2018). DOI: 10.1007/ s11214-018-0467-8. M. Nakamura, et al. Earth, Planets and Space 68, 75 (2016). DOI: 10.1186/s40623-016-0457-6. R. Lundin, et al., Science 305, 1933–1936 (2004). M.H. Acuna, et al., JGR 106, 23403–23418 (2001). http://www-mars.lmd.jussieu.fr/mars/time/solar longitude.html. T. Clancy, et al., JGR 105 (2000) 9553–9572. J. P. Bibring et al., Science 307, 1576–1581 (2005).

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[29] F. Kahre, et al., The Atmosphere and Climate of Mars, Cambridge Univ. Press, pp. 295–337 (2017). [30] F. Montmessin et al., The Atmosphere and Climate of Mars, Cambridge Univ. Press, pp. 338–373 (2017). [31] Y. Willame et al., Planet. Space Sci. 142, 9–25 (2017). DOI: 10. 1016/j.pss.2017.04.011. [32] A. C. Vandaele, et al., Nature 568(7753), 517–520 (2019). DOI: 10.1038/s41586-019-1096-4. [33] M. Chaffin, et al., Nature Astron. 5, 1036–1042 (2021). DOI: 10.1038/ s41550-021-01425-w. [34] R.T. Clancy et al., The Atmosphere and Climate of Mars, Cambridge Univ. Press, pp. 76–105 (2017). [35] A. M¨a¨att¨anen et al., Icarus 209, 452–469 (2010). [36] M. J. Mumma, et al., Science 323(5917), 1041–1045 (2009). [37] V. Formisano, et al., Science 306, 1758–1761 (2004). [38] A. Geminale, et al., Planet. Space Sci. 56(9), 1194–1203 (2008). [39] S. K. Atreya, et al., Planet. Space Sci. 55(3), 358–369 (2007). [40] C. Oze and M. Sharma, Geophys. Res. Lett. 32(L10203), (2005). DOI: 10.1029/2005GL022691. [41] E. Knutsen et al., Icarus 367, 114266 (2021). [42] F. Montmessin et al., A&A. 650, A140 (2021). DOI: 10.1051/00046361/202140389.

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c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 0005

Chapter 5

Atmospheres and Climates of Telluric Planets of the Solar System (and a Bit of Giant Planets and Exoplanets)

Aymeric Spiga Laboratoire de M´et´eorologie Dynamique/Sorbonne Universit´e Institut Universitaire de France, Paris, France [email protected]

This short introductory course deals with atmospheres and climates of telluric planets of the solar system. We explore the basic principles governing key properties of planetary atmospheres, which are subsequently applied to the telluric planets of the solar system. Those principles are sometimes generic enough to mention applications to giant planets and extrasolar planets. Our point of view is to retain both the simplest and the most insightful formalism to provide an overview of planetary atmospheres’ radiative processes, vertical structure and atmospheric dynamics. It is an overview that must read as an encouragement for any interested reader to delve into more detailed references for further information.1–3 Let us start by simply highlighting the large diversity in planetary atmospheric environments by considering our closest neighbors.

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1. 1.1.

A Diversity of Planetary Atmospheres Earth

The Earth is the obvious reference against which other planetary atmospheres are compared (Fig. 1 and Table 1). Its atmosphere is made of 1 bar of mostly nitrogen and surface and atmospheric temperatures are propitious to the stable presence of liquid water, forming at places vast oceans. Clouds and continental surfaces means the part of incoming sunlight energy reflected to space (named the albedo) is about a third. The Earth features a complete water cycle, clouds are made of liquid water and ice particles, and water condensing in clouds fuels powerful thunderstorms which extend vertically toward the stratosphere, an inversion of temperature caused by the absorption of incoming sunlight by ozone. The Earth is a relatively fast-spinning planet, with atmospheric winds not globally super-rotating.

[The Earth seen from Apollo 17]

[Credits: Bjorn Stevens]

[Mars Global Surveyor, 2002]

[Mars Opportunity panorama, 2006]

[Pioneer Venus, 1979]

[Venera 13, 1982 (reprocessed)]

[Cassini Image PIA06139, 2004 (R,G > IR; B > UV)]

[Huygens Titan probe panorama, 2005]

Fig. 1. The typical global and local appearances of each telluric planet of the solar system having substantial atmosphere are shown: The Earth on the top-left panel, Mars on the top-right panel, Venus on the bottom-left panel, Titan on the bottom-right panel. Titan is planet-like but it is a satellite of Saturn. Relevant credits are indicated under each image. Credit: Earth surface image is by Bjorn Stevens and Venus surface image is processed by Don Mitchell.

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Table 1. Main properties of the atmospheres of telluric bodies of the solar system having substantial atmosphere.

Main composition Surface pressure Ps (bar) Surface temperature Ts Albedo Ab (%) Ocean Condensates Storms Stratosphere Rotation rate Ω (10−5 s) Global super-rotation

1.2.

Earth

Mars

Venus

Titan

N2 1 288 31 yes H2 O H2 O yes 7 no

CO2 0.006 220 25 no H2 O CO2 dust seasonal 7 no

CO2 92 730 75 no H2 SO4 no no 0.03 yes

N2 1.5 95 20 lakes CH4 C2 H6 CH4 C2 H6 yes 0.5 yes

Mars

Moving to Mars, the most visited planet in the solar system, leads to striking contrasts compared to the Earth — considering both the surface and atmosphere. Mars’ atmosphere is about a hundred times thinner than the Earth’s and is mainly composed of CO2 . Mars is characterized by a cold climate, it is devoid of any ocean or liquid water at the surface, and only thin clouds made of water ice or CO2 ice particles form in the atmosphere. The surface of Mars is, to first order, a large desert made of dust and sand particles, undergoing strong diurnal temperature changes (up to 80–100◦ C to the point that the average diurnal temperature is not meaningful. The albedo of the surface of Mars is thus typical of arid continental surfaces on Earth. The main atmospheric component on Mars, CO2 , condenses at the surface in polar night regions, causing surface pressure to vary significantly with season. Mars features dust storms, from local to planetary scales. While Mars is usually devoid of a stratospheric inversion and of a global super-rotation, the season during which dust storms are particularly active gives rise to a seasonal version of both phenomena. 1.3.

Venus

Venus is highly contrasted with both the Earth and Mars. The main component of Venus’s atmosphere is CO2 like on Mars but Venus has

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a very thick, massive 92-bar atmosphere which gives rise to a strong greenhouse effect with surface temperature reaching 430◦ C. This is all the more striking as 75% of the incoming sunlight is reflected back to space. Venus’s surface conditions make the presence of water oceans impossible. The visible appearance of Venus is the cloud deck made of sulfuric acid clouds located about 50–70 km above the surface. The atmospheric dynamics of Venus is rich with waves and turbulence at all scales, yet Venus does not have storms associated with condensates or aerosols. A very notable point is that Venus’s surface is spinning really slowly while the atmosphere is spinning much faster than the solid body, putting Venus’s atmosphere in a state of global super-rotation. 1.4.

Titan

Titan, satellite of Saturn, is characterized by an atmosphere having surface pressure and major component like the Earth’s. Titan’s climate and atmosphere are, nevertheless, far from Earth-like. The atmosphere’s vertical extent spans several hundreds of kilometers (see the blue limb color in Fig. 1). The visible appearance of Titan is uniform blurry orange color caused by a prominent photochemical haze — to see surface contrasts and clouds (respectively, yellow/green and white colors in Fig. 1) requires to observe in specific wavelengths. In the very cold Titan environment, lakes of methane and hydrocarbons are found — associated with clouds, rain and storms involving these chemical species. Titan’s photochemical haze entails a stratosphere. Akin to Venus’s atmosphere, Titan’s atmosphere is in global super-rotation above its slow-spinning planetary surface.

2. 2.1.

The Vertical Structure of Planetary Atmospheres Basic energy balance

How could we get the basic principles determining the temperature in the atmosphere at various altitudes and at the surface of a planet? A good starting point is energy balance; a convenient place to define

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it is at the top of the atmosphere (TOA), as follows: π Rp2 (1 − Ab ) Fs = 4 π Rp2 OLR. • The left-hand side is the incoming sunlight power, peaking in intensity in visible wavelengths, where Fs is incoming sunlight at the planet’s location and Ab is albedo integrated over all wavelengths, directions and the whole planetary surface. The planet has a spherical shape (of radius Rp ), so less flux is received at higher latitudes because the surface is inclined; moreover, part of the planet is not receiving flux on a given range of local times. An integral computation yields the result that the equivalent surface on which the incoming sunlight is received is π Rp2 the area of the disk contained in the planetary sphere — or, in other words, the shadow surface cast by the planetary sphere within the incoming sunlight. • The right-hand side is the outgoing planetary power, peaking in intensity in infrared wavelengths. It is emitted over the whole surface 4 π Rp2 of the planetary sphere. Here, to resist against the intent to characterize it further, we will simply name it explicitly: outgoing longwave radiation (OLR). An example often brought 4 (where σ forward as a first application is to consider OLR = σ Teq is the Stefan–Boltzmann constant), i.e., merely the thermal emission of a planet being at the equivalent temperature Teq . This diagnostic is meaningless since it ascribes a common temperature to surface and atmosphere; as could be expected, it leads to temperature estimates too far from reality for Earth and Venus. OLR has to be a bit more complex than this. The TOA equilibrium can also be recast in flux, i.e., Wm−2 , the units considered in what follows: (1 − Ab )

Fs = OLR. 4

To go further than simply the TOA equilibrium, we need to represent the radiative exchanges within the atmosphere. This is named radiative transfer and this can be very complex. To illustrate basic principles, we will use the simplest model retaining the major insights on atmosphere and surface structures.

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2.2.

Two-beam model

A simple yet insightful model is the two-beam formalism: consider simply an upward flux F + and a downward flux F − in the infrared wavelengths with a plane-parallel geometry of an atmosphere transparent in the visible, with the atmosphere and the surface considered as perfect blackbodies. The vertical coordinate we choose is not altitude z but optical depth τ , i.e., representing the equivalent depth dτ that a ray of infrared light experiences through a layer of atmosphere dz featuring green-house gases (GHGs), infrared absorbers of abundances ρGHG and absorption coefficient κ over all relevant infrared wavelengths: dτ = ρGHG κ dz. A small amount of GHG with large absorption coefficient may cause large infrared optical depth — a point we know all too well in the current human-induced climate change on Earth via CO2 and CH4 . To further illustrate the status of τ as being representative of a collection of GHG integrated over the atmosphere’s extent, τ is set to decrease with height so that it is τ = 0 at TOA and τ = τ∞ at the surface. 2.3.

Two-beam equations

Let us consider a layer dτ of temperature T (τ ) anywhere in the atmosphere (see the left part of Fig. 2). The variations of upward flux dF + = F + (τ + dτ ) − F + (τ ) through this layer are composed of (1) a term proportional to incoming upward flux F + from below, the factor being optical depth dτ (this is an equivalent Beer–Lambert– Bougher law in the infrared) and (2) a term corresponding to the thermal emission σ T (τ )4 of this layer of temperature T (τ ). A similar point can be made to consider downward fluxes F − . This entails the two equations of the two-beam formalism as follows: dF + = F + − σ T (τ )4 dτ

dF − = −F − + σ T (τ )4 . dτ

The educated reader may note that those equations could differ a bit from other books (different multiplying factors on some terms). This

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Fig. 2. The left part illustrates the TOA balance as well as radiative exchanges considered in the two-beam model with an upward infrared beam F + . The right part illustrates the radiative profile obtained with the two-beam model in black with additional processes defining atmospheric layers as described in the main text.

may come from slightly different hypothesis, for instance beams that are not perpendicular to atmospheric layers but propagating with a certain angle. This may also come from elements not being perfect black bodies. The essence of what is explained herein does not vary with those details. 2.4.

Radiative temperature profile

The system of coupled equations above is easy to solve, for instance by transforming it to two equations coupling Δ = F + − F − and Σ = F + − F − . Actually, the most important input is (as usual) boundary conditions. We consider that (1) we are at radiative balance, d Δ = 0 and (2) at TOA, there is no incoming which means that dτ − infrared flux Fτ =0 = 0 (it is mostly coming from visible wavelengths) and, well, outgoing flux was given an explicit name Fτ+=0 = OLR. This entails a first consequence of the two-beam equations: we are able to formulate the vertical profile of temperature T (τ ) governed by radiative equilibrium, found to be increasing with optical depth,

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hence decreasing with altitude:  T (τ ) =

4

OLR (1 + τ ) , 2σ

keeping in mind that, according to the TOA equilibrium, OLR = (1 − Ab ) F4s . The temperature profile in the atmosphere is obtained by integrating downward from the TOA equilibrium, which was our starting point. 2.5.

Greenhouse effect

The second consequence of the two-beam model is related to surface energy balance. The surface of temperature Ts receives both a sunlight flux (1 − Ab ) F4s (unaltered since the atmosphere is considered transparent in the visible) and an infrared flux from the atmospheric layer just above Fτ−=τ∞ ; it emits an infrared flux σ Ts4 . (1 − Ab )

Fs + Fτ−=τ∞ = σ Ts4 . 4

By using the two-beam system of equations above, a formula for Fτ−=τ∞ can be obtained and, using again the TOA equilibrium, the surface energy budget leads to surface temperature being expressed as  4 OLR (2 + τ∞ ) . Ts = 2σ This is one of the simplest models to describe the greenhouse effect: OLR, i.e., thermal emission outgoing from the atmosphere, is always smaller than the thermal emission of the surface as long as the atmosphere features GHG with non-negligible infrared optical depth τ∞ . The amount of GHG and their absorption properties in a given planetary atmosphere determine both the atmospheric temperature T (τ ) (see first consequence, a.k.a. the radiative profile of temperature decreasing with altitude) and the surface temperature Ts . More GHG, especially so if those GHG are more absorbant in the infrared, means larger surface temperature Ts with approximately a linear trend in the total infrared optical depth τ∞ integrated over the full atmospheric column.

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Discontinuity surface-atmosphere

A third consequence follows from the first two consequences obtained above. Those two preceding results are obtained independently: the atmospheric thermal profile by integrating downward from the TOA equilibrium and the surface temperature by considering the surface energy budget. What if we compare the atmospheric temperature T (τ∞ ) right above the surface to the surface temperature Ts ? The ratio between both reads  1 + τ∞ T (τ∞ ) = 4 < 1. Ts 2 + τ∞ In other words, the two-beam model adopted here illustrates the existence of a discontinuity between the surface and atmosphere: the temperature of the surface is always on average warmer than the atmosphere right above it. Since this is a situation leading to convective forcing, a practical and important implication of this result about the surface-atmosphere discontinuity is that a planetary atmosphere with a surface cannot be at rest, it is by nature unstable and experiences vertical convective motions that will tend to mix heat in the lower atmospheres. Hence, temperature would depart from the purely radiative profile. Actually, what we have found here for planetary atmospheres above a surface also applies to planetary atmospheres without surface; the fact that the radiative profile indicates that temperature increases as a power-law as one goes deeper within a planetary atmosphere means that, deeper in the atmosphere, the radiative profile becomes unstable with respect to convective motions, especially so given that the absorption coefficient κ increases due to pressure broadening of GHG absorption bands. 2.7.

Atmospheric vertical structure

Let us summarize what we have learned from the simple model described above: we have basically illustrated some of the main principles governing the vertical structure of planetary atmospheres (see the right part of Fig. 2). The lower atmosphere is governed by radiation and convection, exhibiting a so-called radiative–convective profile, in a layer usually named the troposphere. Convective turbulence may be particularly active close to the surface in a layer named

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the planetary boundary layer. Obviously, the educated reader may object to some subtleties where the boundaries of the radiative– convective layer could be slightly distinct from the boundaries of the troposphere; in this introductory course in a limited space, our simplified description remains valid to first order. Above the troposphere, where convection no longer acts efficiently to mix the atmosphere, the radiative profile dominates in a layer usually named the mesosphere where temperature decreases with altitude. In the rarefied upper atmosphere, when radiative processes can no longer be efficient for heat transfers, other energy transfers like conduction and photochemistry are dominant in a layer usually named the thermosphere where temperature could strongly increase with altitude. An important point for the vertical structure of planetary atmospheres is left out of the simplified two-beam model we presented. The atmosphere may not be transparent in the visible wavelengths (or wavelengths in the visible neighborhood). In the layer where radiative processes dominate, incoming sunlight may be absorbed by radiative species in the visible/ultraviolet range — e.g., by ozone O3 in Earth’s atmosphere, or haze particles in Titan’s atmosphere, or dust particles in Mars’ atmosphere — leading to an increase of atmospheric temperature in a specific layer named the stratosphere. Venus is devoid of a stratosphere; Mars is usually devoid of a stratosphere, except during global dust storms during which a “seasonal” stratosphere develops. 2.8.

Word of caution

Of course, we have neglected here key processes, but the picture we have drawn remains valid to first order, even considering those additional processes. (1) A key medium to exchange heat in planetary atmospheres is phase changes (e.g., when liquid or solid cloud particles form) which will heavily impact convective mixing in Earth’s and gas giants’ tropospheres. (2) All the radiative calculations we have described here are averaged over all infrared wavelengths; detailed radiative transfer computations in smaller distinct wavelength intervals are needed to compute realistic temperature profiles in planetary atmospheres. (3) In the case of gas giants, incoming sunlight is not the sole dominant source of energy for planetary atmospheres: internal heat originating from planetary contraction also plays a role.

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(4) In the case of cold stars (e.g., red dwarfs), the spectral range between incoming sunlight and atmospheric emission may become less clear than the visible/infrared distinction in solar system planetary atmospheres. 3.

Atmospheric Circulations

3.1. 3.1.1.

Impact of temperature gradients Scale heights

One of the conclusions of the previous section is that convective vertical motions are pretty inevitable in planetary atmospheres, especially so if the planetary atmosphere sits above a planetary surface. Let us illustrate now that horizontal motions in planetary atmospheres are pretty inevitable, too. The best, and maybe most straightforward, example is thermally direct circulations. To explore this, we simply need (1) the hydrostatic equation for the atmosphere — which is a great approximation for any actual atmosphere, static or not — that reads dP = −ρ g, dz where P is atmospheric pressure, z is altitude, ρ is atmospheric density, and (2) the ideal gas law that reads P = ρ R T, where T is atmospheric temperature and R is specific ideal gas law constant (i.e., divided by atmospheric molar mass M, which depends on the considered planetary atmosphere). Combining the two yields the equation for the scale height H for pressure: dz dP =− P H

with H =

RT . g

What this equation describes is the fact that pressure decreases faster with height in a colder layer compared to a warmer layer. Interestingly, this already allows us to start talking about atmospheric circulations.

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[Graphics by C. Petetin and A. Spiga]

Fig. 3. The top-left panel depicts the principle of thermally direct circulations described in the text: Warm region (W), cold region (C), isobars in full line, horizontal pressure force (arrows) and vertical motions in dashed lines. The topright panel summarizes the differences between northern summer Hadley cell on Mars and on the Earth. The bottom panels show planetary equivalent of sea/land breezes: Circulations from the cold seasonal CO2 cap on Mars and from the cold methane/ethane lakes on Titan, overlaid on respectively a Mars Orbiter Camera mosaic and a Cassini radar image.

3.1.2.

Thermally direct circulations

Let us consider a spatial gradient of temperature in the atmosphere (say, in the troposphere), with a warmer vs. a colder region (see Fig. 3 top-left). In the colder region, according to the scale height equation we just derived, pressure decreases faster with height compared to the warmer region. This means that in the upper part of the atmosphere, at a given altitude level z, the pressure is larger in the warmer part compared to the colder part, resulting in a pressure force from the former to the latter. The effect of this pressure force is to move air masses from the warmer to the colder region; as a result, close to the surface, pressure increases in the colder part of the atmosphere, since the hydrostatic equation implies that pressure varies

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directly with the integral air mass above a given point. This entails, close to the surface, a pressure force from the colder region to the warmer region. We thus obtain a situation where, in the warmer region, we have a near-surface convergence of air and an upperatmosphere divergence of air: upward motions are thus encouraged in this warmer region; the situation is reversed in the colder regions, in which downward motions are favored. To summarize, the horizontal gradients of temperature give rise to horizontal gradients of pressure that cause a circulation cell with motions being upward in the warmer region, from the warmer to the colder region at high altitude, downward in the colder region, from the colder to the warmer region at low altitude. This circulation cell is the so-called thermally direct circulation, because the cell can be obtained directly from the horizontal temperature gradients. It is absolutely not a convection cell since it is related to horizontal gradients of temperature and the hydrostatic equation, and has strictly nothing to do with convection which involves an unstable vertical gradient of temperature. 3.1.3.

Hadley cells and other thermally direct circulations

Thermally direct circulations are widely encountered in planetary atmospheres and it is crucial to understand these given their role in transporting heat, momentum and volatiles; clouds and chemical reactions in planetary atmospheres cannot be understood without the dynamical component. The thermal contrast between sea and land on Earth causes sea/land breezes whose direction depends on day or night conditions. Similar thermally direct circulations develop on Titan between methane/hydrocarbon lakes and organic-dust bare soil (see Fig. 3 bottom-right). On Mars, the seasonal polar CO2 caps are much colder than the lower-latitude bare soil, implying thermally direct circulations causing strong near-surface winds to originate from polar caps (see Fig. 3 bottom-left). Maybe the most famous thermally direct circulations are those that develop at global scales, named Hadley cells. Let us consider northern summer: a slow, seasonal, thermally direct Hadley cell results from the temperature differences implied by incoming sunlight contrasts between the warmer summer hemisphere in the north and the colder winter hemisphere in the south.

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Hadley cells’ impact on heat transport and clouds

The upper-altitude branch of the Hadley cell goes from the warmer region to the colder region, while the near-surface branch of the Hadley cell goes from the colder to the warmer region; warmer regions are prone to near-surface convergence and upward motions (on Earth, moist convection is encouraged there, in what is named the Inter-Tropical Convergence Zone, ITCZ) while colder regions are prone to downward motions capable of locally warming these colder regions by adiabatic compression, illustrating that Hadley cells are a means to transport heat and to mitigate the initial temperature gradients that gave rise to it — in other words, we note here how atmospheric temperatures and climates cannot be thought of only with radiative processes, but have to be determined by the influence of dynamical circulations, too. Hadley cells are found on Earth, Mars, Venus, Titan, exoplanets, etc. In tidally locked “eyeball” exoplanets, with a much-warmer region around the sub-stellar point and a much-colder rest of the planet, thermally direct Hadley cells may develop anywhere around the warmer region which becomes an area of strong near-surface convergence and upward motions, where convective clouds might be favored. In other words, the iris of eyeball exoplanets may be quite stormy. Heat transport by those thermally direct circulations may actually be efficient enough to homogenize temperature in this planet and make the eyeball’s warm iris to disappear — there is a possibility that the qualitative approach developed here is too limited, and for which quantitative approach to 3D climate models are needed. 3.1.5.

Hadley cells on Mars and the Earth

To explore the differences between the Hadley cells on Earth and on Mars, we can add an interesting point to those conclusions and those of Section 2: we assumed insofar that the surface and atmosphere reacted instantly to incoming sunlight. This is particularly not true for surfaces that have a so-called thermal inertia resulting from their thermal conductivity and heat capacity. Earth is, to first order, an ocean planet with large thermal inertia; Mars is, to first order, a dusty desert planet with very low thermal inertia (Fig. 1). In northern summer, both on Earth and on Mars which have similar obliquity,

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the diurnally averaged incoming sunlight flux peaks at 60◦ N — a common misconception places this peak at the tropics but, while higher latitudes receive less flux for geometrical reasons, the longer day duration largely compensates this term. This similar incoming sunlight situation in summertime for both Earth and Mars does not lead to similar surface temperature fields because of the much contrasted surface thermal inertia of the two planets. While the surface temperature peaks close to 60◦ N at northern summer in the lowthermal-inertia desert Mars, it peaks no further than 25◦ N in the high-thermal-inertia ocean-rich Earth. Hadley cells are thus much more extended toward the poles on Mars than on the Earth (see Fig. 3 top-right), which has strong implications for heat transport, cloud formation and volatile transport in the Red Planet. 3.2. 3.2.1.

Impact of planetary rotation Atmospheric dynamics in rotating planets

Obviously, planetary rotation plays a key role in atmospheric dynamics; basically this means that planetary surfaces are not inertial frames of reference for atmospheres, which subsequently undergo the impact of the Coriolis force if the planet is rotating fast enough. How much the planetary rotation rate Ω impacts atmospheric dynamics can be assessed by the Rossby number Ro =

U , ΩL

where U and L are typical scales for, respectively, wind speed and spatial scales. Fast-rotating planets like the Earth, Mars or gas giants exhibit a Rossby number much smaller than 1, meaning the Coriolis force plays a key role — this is not the case for slow-rotating planets like Venus and Titan which exhibit a Rossby number larger than 1. Another important point about the Rossby number is that it will be much larger than 1 whenever the considered planetary scales L are smaller than several thousands kilometers. In other words, whatever the planet is, planetary rotation and the Coriolis force play no role, for instance, in local sea/land breezes or small-scale vortices (or the sense of rotation of a kitchen sink).

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Fig. 4. Illustrating angular-momentum-conserving circulations associated with Hadley cells in the upper branch and the near-surface branch. Equatorial circulations in super-rotation correspond to the case of non-conservation of local angular–momentum and momentum transport by non-axisymmetric waves.

3.2.2.

Hadley cells in rotating planets

Let us immediately explore the effect of planetary rotation on atmospheric dynamics by returning to the Hadley cells (Fig. 4). The most straightforward way to illustrate this matter is to consider the conservation of axial angular momentum M M = Rp cos ϕ (Ω Rp cos ϕ + u), where u is the zonal wind, i.e., atmospheric motions along the west-to-east axis relative to the planetary surface, and ϕ is latitude. Atmospheric motions in the upper-atmosphere branch of the Hadley cell are directed from the equator toward the summer-hemisphere pole, meaning that ϕ increases in this upper branch where the conservation of M entails an increase in zonal wind u, leading to eastward jets (i.e., atmospheric currents) also named westerlies. In other words, if air masses gets closer from the planetary axis of rotation, they accelerate toward the east as a result of angular–momentum conservation. What is found here is that the poleward motion in the upper-branch of the Hadley cell is deflected toward the east. This deflection is all the more strong that the planet is rotating fast (large values of Ω) as a result of the Coriolis force — which appears naturally from angular–momentum conservation by taking the time

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derivative of M. In other words, planetary rotation strongly impacts the latitudinal extent of the Hadley cell: the slower the rotation, the more extended the Hadley cell. To summarize, we thus have two factors controlling the latitudinal extent of Hadley cells: (1) surface and atmosphere temperature gradients and (2) planetary rotation. Interestingly, both Mars and Venus/Titan exhibit Hadley cells extended toward the poles but for very distinct reasons: on low-thermal-inertia Mars, factor (1) dominates; on slow-rotating Venus and Titan, factor (2) dominates. On the high-thermal-inertia fast-rotating Earth, both factors (1) and (2) concur to limit strongly the latitudinal extent of the Hadley cell. 3.2.3.

Super-rotation and non-axisymmetric circulations

If we follow the angular–momentum conservation assumed above, atmospheric motions in the near-surface branch of the Hadley cell are directed from high latitudes to the equator, implying a decrease in ϕ (air masses gets further from the axis of rotation) hence a decrease in zonal wind u, thus leading to westward jets named easterlies. It thus appears in principle difficult for equatorial jets to be directed eastward, in the prograde direction, i.e., the direction of rotation of the planetary surface. Yet, strong equatorial jets in the prograde direction, in a so-called state of super-rotation with respect to the planetary surface (or a fixed reference at depth for planets devoid of surfaces), are observed on Venus, Titan, Mars (when the atmosphere is dusty), gas giants and even extrasolar hot Jupiters. This apparent paradox between angular–momentum conservation and these observed circulations can be solved by considering Hide’s principle that states, to put it simply, that angular–momentum conservation is only valid when considering steady axi-symmetric flows (i.e., with zonal symmetry). Planetary atmospheres are far from exhibiting zonal symmetry and feature planetary waves such as those giving rise through baroclinic instability to high- and low-pressure systems, regional waves such as gravity waves, large-scale turbulence such as observed in the flanks of Jupiter’s jet system, etc. Those non-axisymmetric waves imply transport of angular momentum from some regions of the planet to others and may give rise, as a notable example, to super-rotating equatorial prograde jets by

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transporting eastward momentum from higher latitudes to lower latitudes. Atmospheric waves may also force thermally indirect circulations, i.e., circulation cells which are, for a given spatial gradient of temperature, reversed compared to what is expected from thermally direct circulations explained in Section 3.1. This is the case for the Ferrel cell on the Earth, or circulation cells associated to banded jets in gas giants. Actually, atmospheric waves may also contribute to apparent thermally direct circulations in addition to temperature gradients: to reproduce realistic Hadley cells in climate model for planetary atmospheres requires to resolve planetary waves in addition to temperature gradients, even if the latter dominates the forcing. 4.

Concluding Remarks

We have shown that a handful of carefully chosen basic principles can be used to start to understand planetary atmospheres, their differences and similarities. We explored the vertical thermal structure and horizontal motions of planetary atmospheres, with applications ranging from the Earth to extrasolar planets. We have also understood that physical processes act in tight interrelation to define the weather and climate of planetary atmospheres. Radiation impacts dynamics which impacts chemistry and clouds/aerosols, the latter in turn impacting radiation. Other links, that we did not detail here, exist between radiation and chemistry, or between radiation and clouds. This short course on basic principles of planetary atmospheres leaves obviously many fascinating details off. We do hope, however, that we reinforce in the readers’ minds the idea that exploring planetary atmospheres — should they be telluric planets, gas giants, solar system or extrasolar planets — with observations, modeling, theory, laboratory experiments is ultimately an endeavor to better understand weather and climate for any possible planet. 5.

Q&A

Asier Munguira: When there is a lot of dust in the Mars atmosphere, it can affect the meridional circulation, right? How does this idea fit with the 2018 storm starting in the northern hemisphere?

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Aymeric Spiga: Good question. Usually, the regional storms start in the south, and the disturbance tends to reinforce the Hadley circulation. In 2018, it started in the north, but some dust was soon lifted in the south, and then the forcing was stronger in the south because it was southern summer. So, the start in the north put dust even in the south, is the answer. Gaia Lacedelli: What exactly do you mean by “condensates”? What creates these Mars storms? How long do the storms last? Aymeric Spiga: Condensate means any state other than gas. We don’t know in full detail what creates the dust storms, but we know some of the ingredients. We do know that condensation liberates latent heat and drives convection. On Mars, the air is very thin and there is not much water — latent heat of water is not important there. On Mars, storms fueled by dust particle heating is more likely if they can drive a runaway. The low density air allows the heating to be very rapid, which helps. The global storms happen when the dust affects the meridional circulation — it pumps dust everywhere. The local storms last a few days. The regional storms last weeks. The global storms can last a couple of months before all the dust falls out. Julia Maia: Do you ever take into account the planetary geothermal heat? Does Mercury have an atmosphere? Can you summarize what the InSight mission is doing? Aymeric Spiga: Geothermal heat is too small to worry about. Mercury has a very thin atmosphere caused by sputtering of atoms when the solar wind hits the surface. It is so thin that the exobase (bottom of the escape layer) is on the surface. InSight results are already in the literature so please look there. The main results are from the seismometer, which records geophysical vibrations, but also vibrations from the wind on the spacecraft. To interpret the latter, we measure the pressure with high accuracy, and atmospheric science comes from there, with results about turbulence, vortices, gravity waves and with a good view of diurnal variations. Camille Bergez-Casalou: Do we know why Titan has such a thick atmosphere? Aymeric Spiga: We don’t know. The amount is a puzzle and so is the composition (1 bar of N2 ).

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References [1] G. K. Vallis, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation, Cambridge University Press (2006). [2] A. Sanchez-Lavega, An Introduction to Planetary Atmospheres, CRC Press (2010). [3] R. T. Pierrehumbert, Principles of Planetary Climate, Cambridge University Press (2010).

c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 0006

Chapter 6

Habitability and Atmospheric Biosignatures in an Exoplanetary Context

John Lee Grenfell German Aerospace Centre (DLR), Berlin, Germany [email protected]

The extent of habitable conditions beyond the Solar System and the potential range of atmospheric biosignatures are central issues in exoplanetary science. We are currently at a fascinating juncture where the characterization of specific objects such as Proxima Centauri-b is an emerging theme for favored targets which lie in the habitable zone. It is the task of a new generation of atmospheric models and planned instruments to determine the climate and atmospheric compositions of these fascinating objects. This chapter reviews factors affecting planetary habitability and discusses the various definitions of the habitable zone. It also provides a brief overview of exoplanetary atmospheric biosignatures and their spectral signals.

1.

Introduction

Whether life could evolve beyond the Earth has been the subject of debate since the dawn of civilization. Rapid advances in exoplanetary

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science over the last few decades have helped move this debate into the realms of scientific discussion. A logical step in the path to finding extraterrestrial life is to identify regions with so-called habitable conditions favorable to life. The first part of this chapter (Section 2) therefore discusses central aspects of habitability in an exoplanetary context. The second part of this chapter (Section 3) discusses biosignatures (signs of life) in an exoplanetary context.

2.

Habitability

The word habitability is derived from the Greek habitablis meaning “to dwell”. Habitability denotes in a broad sense conditions which are favorable for life. 2.1.

Definition

Habitability is defined as the potential of an environment to sustain life. This does not necessarily imply that life has originated nor does it necessarily mean that life is present. Life as we know it has four essential requirements, namely a source of energy, the presence of complex molecular chains, a supply of nutrients and the presence of liquid water. In an exoplanetary context the key factor is the search for conditions which could enable existence of liquid water on the planet’s surface. Such conditions are determinable for a given pressure and temperature from the phase diagram of water as shown in Fig. 1. The green shaded area in Fig. 1 shows the pressure–temperature range, e.g., on a planet’s surface where liquid water hence habitable conditions can exist. Numbers in the blue shaded region mark the different ice states of water. In addition to the above four criteria for habitability, numerous other criteria have been suggested, for example, the presence of stable conditions without sudden, large changes in climate and protection from harmful influences such as cosmic rays. Note however that small changes in the environment have been proposed to favor life by driving Darwinian evolution. Further information on the criteria for habitability beyond the Earth can be found in, e.g., Refs. 1 and 2.

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Fig. 1. Phase diagram of water. Credit: Cmglee, CC BY-SA 3.0. https:// commons.wikimedia.org/w/index.php?curid=14939155.

2.2.

Historical context

In the mid-nineteenth century, William Whewell introduced the concept of the temperate zone 3 around a star where planets could feature habitable conditions favoring life as we know it. About 100 years later, Shapley4 discussed climate conditions in the so-called water belt and Strughold5 investigated the ecosphere in the Solar System. Huang6 introduced the term “habitable zone” (HZ) for liquid water (see the following discussion) which paved the way for modern climate model calculations estimating the HZ width. 2.3.

Factors affecting habitability

Numerous factors have been proposed to affect the evolution and maintenance of habitable conditions. These can be broadly divided

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Fig. 2. Factors affecting habitability in the planet–star system. Adapted from image design of Franck Selsis, CNRS/University of Bordeaux, France.

into four groups. First, stellar properties such as luminosity, metallicity and activity. Second, planetary orbital properties such as planet– star distance, obliquity and eccentricity. Third, planetary properties such as radius, mass, rotation rate and surface properties. Fourth, properties of the planetary atmosphere such as its mass and composition. These four factors are summarized in Fig. 2. Processes in the planet’s atmosphere can shape the development of atmospheric mass and composition hence drive the evolution of climate which is critical for the presence of surface oceans hence habitability. These processes include atmospheric escape and delivery of material from space, photochemistry, radiative transfer (the emission, absorption and scattering of photons in planetary atmospheres), surface processes such as removal of gas species via weathering and their emission via, e.g., biomass and geological activity. Over geological timescales of several thousand million years, the interplay of these processes shape atmospheric evolution on rocky planets hence influence the rise and fall of planetary habitability. Catling and Kasting7

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Fig. 3. Factors affecting habitability in Earth-like atmospheres. Adapted from the German Helmholtz Research Alliance “Planetary Evolution and Life (PEL)” Proposal.

review the main processes which influence atmospheric evolution on rocky planets. These processes are summarized in Fig. 3. The solid line in Fig. 3 denotes an illustrative temperature profile which is representative of Earth-like atmospheres. From the surface upwards temperature generally decreases adiabatically with decreasing pressure but can exhibit a temperature inversion in the middle atmosphere due to, e.g., absorption of ozone (O3 ) by shortwave radiation (as is the case on Earth). The shape of the temperature profile can strongly influence atmospheric mixing and transport. 2.4.

Evolution of habitability: Venus-Earth-Mars compared

Figure 4 illustrates schematically the evolution of habitability on Venus, Earth and Mars.

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Fig. 4. Schematic representation showing the evolution of habitability on Venus, Earth and Mars. Adapted from NASA/JPL Caltech.

Venus (Fig. 4, left panels) was likely habitable earlier in its history. The close proximity of Venus to the Sun however favored enhanced ocean evaporation (and atmospheric escape) compared with the Earth. This may have led to an early, so-called runaway greenhouse on Venus and Venus-like exoplanets as discussed in, e.g., Ref. 8. This process involves enhanced greenhouse heating from evaporating water vapor driving further evaporation which leads to a selfreinforcing, unstable climate feedback. Strong water loss on Venus led to its modern-day hot (Psurface ∼ 737 K) and thick (Psurface ∼ 92 bar) atmosphere. Earth (Fig. 4, middle panels) with its lower insolation than Venus took a somewhat different evolutionary pathway than its sister planet. Earth (unlike Venus and Mars) has featured active plate tectonics (PTs) over a large portion of its history although the factors which initiated and maintained this process are still the subject of debate. Mulyukova and Bercovici9 review PT generation theory. PT on Earth contributes to the carbonate-silicate cycle which recycles

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carbon between the atmosphere–ocean–lithosphere-interior and can significantly stabilize climate. Unlike its neighboring planets Earth also features a comparatively strong, intrinsic magnetospheric field, which arises due to ordered motion of liquid iron in our planet’s outer core. Earth’s strong magnetosphere is thought to mainly protect the atmosphere from erosion by the stellar wind, although the extent and nature of the processes involved are still debated.10 The origin and maintenance of life on Earth also likely influenced atmospheric evolution, e.g., photosynthesis drove the rise in atmospheric oxygen (O2 ) (hence the formation of the protective ozone layer) on our planet (see, e.g., Ref. 11). Mars (Fig. 4, outer columns) was also likely habitable earlier in its history. Mars however features only ∼11% of Earth’s mass and the weaker gravitational field together with the lack of magnetospheric field on Mars likely favored enhanced escape of its atmosphere to space compared with the Earth. Isotopic (D/H) measurements suggest that 20–200 m global equivalent water has escaped to space from Mars.12 Modern Mars features a thin (Psurface ∼ 6.4 mbar) and cool (Psurface ∼ 210 K) atmosphere. In summary, studying our neighboring planets provides useful insights into the processes driving the evolution of habitability on rocky planets in general. More details on the evolution of Venus, Earth and Mars can be found in Lammer et al.13 2.5.

Evolution of habitability: Case study Earth

We summarize here some central atmospheric processes affecting the evolution of habitability on our planet. Earth’s protoatmosphere refers to the initial gaseous envelope formed from gases present in the protoplanetary disk at the close of accretion. Abe14 suggested that our planet’s protoatmosphere contained a few hundred bars surface pressure of H2 and H2 O and several tens of bars of CO and CO2 based on the analysis of meteorites and impact degassing experiments. Such an atmosphere, if maintained, would lead to strong greenhouse heating preventing the Earth from reaching habitable conditions. Loss of the protoatmosphere on Earth is however estimated to occur within about 10 million years (Myr) after planetary formation (see, e.g., Ref. 15). More recent studies16 however noted that Earth’s building blocks could have been closer isotopically to enstatite meteorites,

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which suggests the presence of up to 0.7% volume mixing ratio (vmr) of CH4 in the protoatmosphere. Such gaseous envelopes lead to slower escape via radiative cooling and could have survived for up to several hundred million years after accretion. Atmospheric evolution during Earth’s magma ocean (MO) period is a central focus (see, e.g., Refs. 17–19). The end of the MO period is estimated to have occurred (20–160) MYr after Earth’s formation (see Ref. 2 and references therein) and is marked by the formation of a solid surface crust. Since the solidifying crust is less able to retain water in its lattice, this favored the expulsion of between several hundred up to possibly a few thousand bar surface pressure of steam from the cooling mantle into the atmosphere. This phenomenon is sometimes referred to as the catastrophic steam outgassing event (see, e.g., Ref. 20). Cooling and condensation of the giant steam atmosphere led to the formation of Earth’s oceans after ∼2 Myr.21 The presence of oceans favored the removal of CO2 from the atmosphere via rainout and wet deposition to form carbonates. Outgassing from the interior (and atmospheric escape to space) likely played important roles in shaping the subsequent so-called secondary atmosphere. Further information on the evolution of Earth’s earliest atmospheres can be found in Zahnle et al.22 The emergence and extent of habitable conditions on the Early Earth is contested. The faint young sun problem refers to the difficulty of climate models to reproduce habitable conditions during the Archaean. A review of this problem and suggested solutions are provided by Feulner.23 Studies investigating future loss of habitability on Earth (e.g., Ref. 24) suggested that a brightening Sun could lead to a warmer climate on Earth with increased atmospheric weathering of CO2 . Their study suggested that this could result in plant life becoming unsustainable for atmospheric abundances of CO2 below 10 parts per million (ppm). Another future limit of Earth’s habitability could involve our planet moving out of the HZ, e.g., due to the brightening Sun (see the following discussion on habitable zones). 2.6.

Habitability classes

Lammer et al.25 discussed four classes of habitability. Class 1 refers to Earth-like planets where multi-cellular life may evolve on the surface.

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Class II refers to bodies such as Mars where microbial life may have evolved in pockets on the sub-surface depending on the availability of water. Class III refers to, e.g., icy moons beyond the ice line where life forms may have evolved and exist in sub-surface oceans. Class IV refers to ice-rich worlds which migrate inwards into the HZ (sometimes referred to as ocean planets) where if life evolves, it will populate the oceans. Habitable zones

2.7.

Luminosity

The classical HZ 26 is defined as the region around a star where liquid water is stable over long periods. The Kasting study assumed an Earth-like planet with operational climate feedbacks such as the carbonate-silicate cycle. Figure 5 shows the classical HZ for different classes of main sequence stars. Figure 5 suggests that the HZ center shifts inwards, e.g., from ∼1 AU for the Solar System to ∼0.03 AU for small M-dwarf stars. The dashed gray line in Fig. 5 shows the orbit inside which the planet becomes tidally locked, i.e., where strong tidal forces result in the

0.1 –1 Planet–Star distance in AU (Astronomical Units) Fig. 5. Schematic representation showing the habitable zone (gray shaded band) for different stellar classes. Filled circles denote the planets in the Solar system. Adapted from Ref. 26.

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planet presenting the same hemisphere to the star hence features a constant dayside and constant nightside. The boundaries of the classical HZ are defined as follows. The first inner HZ limit (moist greenhouse) occurs where water (which is assumed to be present as a large surface reservoir) evaporates in the lower atmosphere to the extent that it overcomes the so-called cold trap (the temperature minimum at ∼12 km on Earth, see Fig. 3), which acts as a barrier due to mixing and freeze-out. Water then travels upwards into the stratosphere where it is rapidly photolyzed. The moist greenhouse limit is defined to occur where one Earth ocean equivalent of atomic hydrogen can escape within one Earth lifetime. The second inner HZ limit occurs at higher insolation where the critical point of water is reached. In the outer HZ region, the maximum greenhouse limit is reached at the point where further increases of CO2 into the atmosphere lead to cooling due to an anti-greenhouse effect (assuming a carbonate-silicate cycle is operating and a large CO2 reservoir is present) since scattering of radiation at high CO2 abundances attenuates the incoming shortwave radiation and leads to surface cooling. Climate feedbacks regulate the extent of the HZ. Near the inner HZ boundary two feedbacks are potentially important. First, the Planck feedback. Here, an initial heating leads to stronger topof-atmosphere emission of longwave radiation. This serves to cool the planet hence opposes the initial heating (a stabilizing, negative feedback). Second, the water vapor feedback. Here, an initial heating leads to stronger evaporation of water at the surface. This results in stronger greenhouse heating hence strengthens the initial heating (a de-stabilizing, positive feedback). The interplay between these two feedbacks can determine the position of the inner HZ boundary. Near the outer HZ boundary, a stabilizing climate feedback involving the carbonate-silicate cycle (see, e.g., Ref. 27) plays a potentially important role. Here, an initial decrease in atmospheric CO2 leads to a slowing in atmospheric washout, but CO2 outgassing rates are unaffected which overall serves to increase CO2 hence opposing the original change. Further details on the classical HZ boundaries can be found in Ref. 26. Numerous model studies have been applied to estimate the width of the classical HZ around different main sequence stars. In recent years the HZ boundaries have been revised due to improvements

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in, e.g., spectral linelists (see, e.g., Refs. 28 and 29); improved atmospheric transport30 and updated 3D cloud parameterizations.31 Godolt et al.32 noted the importance of consistently treating the relative humidity in 1D and 3D model studies estimating the HZ width. Various HZ concepts beyond the classical HZ have been discussed in the literature. The floating HZ refers to the region within an atmosphere where liquid water droplets can exist as discussed for Jupiter by Sagan and Saltpeter.33 Whether however life can evolve and be maintained without a planetary surface is the subject of debate. The continuously HZ (CHZ)34 refers to the region around a star which remains continuously habitable despite the increasing stellar luminosity over time as illustrated in Fig. 6. Figure 6 shows the HZ boundaries moving outwards from time, t0 to t1 , as the luminosity of the star increases over time. The region of overlap of the HZs for these two times denotes the CHZ.

HZ at time t0

t time

HZ a t1

Sun

CHZ

Fig. 6. Schematic representation showing the position of the continuously HZ. Credit: https://www.astro.psu.edu/users/williams.

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The delayed HZ (DHZ) refers to the habitable region around a star after post-main sequence stellar evolution. For example, the Pluto–Charon system could lie in the DHZ when the future Sun enters its Red Giant Phase.35 The weird life HZ considers life as we do not know it — which could utilize non-water solvents (e.g., CH4 , NH3 ) or/and could harvest energy sources other than insolation from the star (see e.g., Ref. 36). The extended HZ refers to the outward extension of the classical HZ for planets containing significant amounts of H2 in their atmospheres due to heating via collision-induced absorption.37 That study suggested habitable conditions out to ∼10 AU for a Super-Earth orbiting a G-star assuming a surface pressure of 40 bars H2 . In addition to stars on the main sequence, HZ boundaries have also been investigated for binary star systems (e.g., Ref. 38); white dwarves39 and brown dwarves.40 Numerous gas giants have been discovered in the HZ of their host stars, e.g., 55 Cancri f,41 which have been speculated to possess habitable moons. 2.8.

Exoplanets in the habitable zone

Figure 7 shows known exoplanets lying in or around the HZ. Figure 7 suggests that many of the currently detected rocky exoplanets lie inward of the HZ since hotter objects orbiting close-in are favored observationally. Many of the known exoplanets lying in the HZ orbit smaller, cooler stars, which leads to enhanced planet/star contrast ratios and faster orbits with a higher transit frequency. Figure 8 shows a mass–radius diagram for known terrestrial-type exoplanets where dashed lines denote bulk solid compositions. Figure 8 suggests that terrestrial exoplanets are diverse in their bulk composition. They include heavy objects with significant iron contents; planets with mostly rocky mantles and lighter objects with mostly icy interiors. In practice, it is likely that such planets consist of iron–rock–ice–gas mixtures and that further characterization, e.g., via atmospheric spectroscopy is required to separate the compositional degeneracies. To determine planetary habitability such studies will be necessary to separate potentially habitable rocky exoplanets from non-habitable mini gas planets, for example.

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Fig. 7. Exoplanets lying in or around the HZ (green-shaded region) color-coded according to detection method (transit, radial velocity (RV) or transit timing variation (TTV). Adapted from Heike Rauer, DLR Germany.

2.9. 2.9.1.

Examples of potentially habitable worlds Proxima Centauri-b

Proxima Centauri-b43 orbits in the HZ of our neighboring star Proxima Centauri, which is a red dwarf with spectral class M5.5. The planet receives ∼65% of the incoming stellar energy compared with Earth and has a minimum mass of 1.3 Earth masses. Its close proximity, potential habitability and favorable planet/star contrast ratio make it an important object of study. The model study by Meadows et al.44 investigated habitability and atmospheric detectability of Proxima Centauri-b for a range of assumed atmospheres including CO2 -dominated, O2 -dominated and Earth-like. Results suggested thermal phase curves could be detectable with ∼20 h on the James Webb Space telescope and that the O2 visible band could be detected assuming an Earth-like atmosphere using a 16-m Large UltraViolet Optical Infrared Surveyor telescope (LUVOIR) setup. Scheucher et al.45 found that an Earth-like

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Ice

Radius [Earth radii]

2.5

2 Silicate 1.5 Iron 1

0.5

PLATO error bar 0 0

2

4 6 Mass [Earth masses]

8

10

Fig. 8. Mass–radius diagram. Small solid dots denote terrestrial-type exoplanets. Solid black lines represent the error range. Dashed lines show the bulk composition for pure iron, silicate and ice. Thick line shows the PLATO error bar. Adapted from Heike Rauer, DLR Germany (see also Ref. 42).

atmosphere but with 20% CO2 by vmr replacing N2 would lead to habitable surface conditions. 2.9.2.

K2-18b

K2-18b46 is an object with 8.6 Earth masses lying in the HZ of the class M2.8 red dwarf K2-18. Scheucher et al.47 suggested a Po = 10 bar solar metallicity atmosphere based on comparison of modeled with observed transmission spectra. This suggests that the surface is likely not habitable. Madhusudhan et al.,48 however, calculated some habitable scenarios for K2-18b assuming hydrogen–helium atmospheres. More work is required to determine the extent of water evaporation and its influence upon the planetary radius when fitting theoretical with observed transmission spectra of K2-18b.

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2.9.3.

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LHS-1140b

LHS-1140b49 is a dense, rocky Super-Earth with ∼6.5 Earth masses orbiting the M4.5 red dwarf LHS-1140 in the HZ. The model study by Wunderlich et al.50 suggested that the JWST or the Extremely Large Telescope (ELT) could observe spectroscopic transmission features of, e.g., CH4 and H2 O assuming light, haze-free atmospheres. 2.10.

Observing planetary habitability

In an exoplanetary context the main criteria for classical habitability is the presence of liquid water on the surface. Indirect hints for this can be gathered by, e.g., searching for the presence of atmospheric water vapor via transmission spectroscopy. Note however that water vapor could maybe form in situ in Earth-like atmospheres from sources other than ocean evaporation, e.g., via CH4 oxidation. An additional hint that liquid water could (at least in theory) be present would come from constraining surface temperature from occultation spectroscopy. Detecting ocean glint (see, e.g., Lustig-Jaeger et al.51 ), which arises due to specular reflection, would provide more concrete evidence that oceans are present, although this is very challenging. Fujii et al.52 summarize future observing challenges and planned exoplanetary missions. 3.

Biosignatures and Life

A “biosignature” in general terms refers to a signal which arises due to the presence of life. Schwieterman et al.53 provide a comprehensive review of biosignatures in exoplanetary science. 3.1.

Defining life

Defining life is still the subject of debate although commonly cited is the NASA-based definition,54 namely a “self-sustaining chemical system capable of Darwinian evolution”. The basic requirements of life were discussed above, but briefly these are, an energy source, molecular complexity, a solvent and a supply of nutrients. Life as we know takes its energy mainly from the Sun, its molecular complexity from complex carbon chains, its solvent being water and its nutrients are

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commonly the “CHNOPS” elements. “Weird life”, on the other hand, is speculated to behave more flexibly in its requirements by utilizing, e.g., alternative energy sources, molecular complexity, solvents and nutrients from life as we know it. 3.2.

Biosignature methods

Figure 9 summarizes some biosignature methods commonly discussed in (exo)planetary science. Figure 9 divides biosignatures into two main groups, namely in situ and remote. Some biosignatures (e.g., based on chirality and isotopic properties) can be assigned to both groups. Assessing in situ fossils requires distinguishing morphological features of fossilized microorganisms from, e.g., potentially similar features due to geological processes, as reviewed in, e.g., Ref. 55. “Spikes” in the abundance distribution of carbon number give clues to biotic activity as discussed in Lovelock (Ref. 56, Fig. 1). Regarding chirality, life favors the left-handed form of amino acids, possibly due to the complex specificity of biochemical pathways or/and because prebiotic species were delivered to our planet with a built-in chirality. Sparks et al.57 discussed detecting chiral signals from, e.g., biological pigments on exoplanetary surfaces using circular spectropolarimetry.

Fig. 9.

Summary of biosignature methods applied in (exo)planetary science.

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Regarding isotopes, life favors the lighter isotope, possibly related to the kinetic isotope effect (see, e.g., Ref. 58). The red edge refers to an up to ∼50% increase in reflected light in the wavelength range [680– 750 nm] by vegetation and is suggested to arise in order to prevent leaf overheating. Seager et al.59 studied the red edge as an exoplanetary biosignature. Chemical (or redox ) disequilibrium refers to the simultaneous presence of oxidizing (e.g., O2 ) and reducing species (e.g., CH4 ) in a planet’s atmosphere.60,61 In Earth’s atmosphere, these two species would quickly react together in the gas-phase if they were not constantly replenished by life. Barge et al.62 discussed the role of thermodynamical disequilibrium in the context of the origin of life., Regarding intelligent life, the Search for Extraterrestrial Intelligence (SETI) project has been running for ∼60 years (see overview in Tarter et al., 2010). Assessing the spectroscopic detectability of technosignatures was recently reviewed in Socas-Navarro et al.63 A central focus of this chapter is atmospheric biosignatures, which we will now discuss.

3.3.

Atmospheric biosignatures: Photochemical effects

Table 1 shows some commonly discussed examples of atmospheric biosignatures based on the modern Earth together with their biotic and abiotic sources.

Table 1. Some common atmospheric biosignatures with their biotic and abiotic sources. Species

Biotic source

Abiotic source

Oxygen (Ozone)

Cyanobacteria

CO2 + hν H2 O + hν H escape

Nitrous oxide

(De)nitrifying Bacteria

Photochemistry Energetic Particles

Methane

Methanogens

Geology

Chloromethane

Seaweed

Photochemistry

CFCs (Technosignatures)

Humans

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Regarding molecular oxygen (O2 ), Earth’s modern atmosphere contains ∼21% vmr, which arises mainly due to photosynthetic activity (P) of cyanobacteria (see Table 1). O2 production via P is almost balanced by its consumption via the reverse process, respiration and decay (R) as shown by the general equation: CO2 + H2 O

P R

CH2 O + O2 · · · .

(1)

Organic material (denoted simplistically in equation (1) as “CH2 O”) sediments in the ocean (carbon rain) followed by removal via subduction into the mantle at the ocean floor. This removal introduces an imbalance in equation 1, which leads to a net release of ∼320 Tg/yr of O2 into the atmosphere (see, e.g., Ref. 64). Ozone (O3 ) is mostly formed from O2 in Earth’s atmosphere. O2 photolysis in the stratosphere in the Herzberg continuum (200 > λ > 240 nm) to form oxygen atoms which can react in the ground electronic state with O2 in a three-body reaction to form ozone (O3 ). The “third body” can be any gas phase species (typically N2 in Earth’s atmosphere) and is required to remove excess vibrational energy which would otherwise result in the two reactants moving apart elastically after collision. Earth’s O3 layer has its maximum at ∼30 km with peak O3 abundances of ∼10 ppmv. The O3 layer shields our planet’s surface by absorbing harmful incoming ultraviolet radiation. Abiotic sources of O2 (hence O3 ) (see Table 1) include first, photolysis of CO2 (in CO2 -dominated atmospheres such as on Mars and Venus, to form ground-state atomic oxygen. This can self-react in a three-body reaction to form O2 . Secondly, atmospheric water vapor (H2 O) photolysis in the upper atmosphere. If the resulting Hatoms escape into space, this leads to a net gain in abiotic oxygen in the atmosphere. Nitrous oxide (N2 O) is formed mainly as a by-product from microorganisms participating in the nitrifying and denitrifying cycles. Important (global) biomass sources include tropical rainforest soils [0.9–2.4] TgN/yr65 with weak abiotic sources from, e.g., cosmic rays, lightning and in situ gas-phase reactions in the atmosphere. N2 O currently has an abundance of 334 ppbv in Earth’s atmosphere. It is destroyed mainly via photolysis and reaction with electronically excited oxygen atoms in the stratosphere and has a long chemical lifetime of ∼300 years against atmospheric removal. This is long

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compared with Earth’s atmospheric transport timescales, therefore, N2 O spreads uniformly around the globe in the troposphere. Methane (CH4 ) is emitted mainly by methanogenic bacteria (∼550 Tg/yr globally) with a smaller source (several tens of Tg/yr) due to geological processes. CH4 currently has an atmospheric abundance of 1,889 ppbv. Its atmospheric lifetime is estimated to be ∼12 years and it is removed mainly via reaction with hydroxyl (OH) in the lower and middle atmosphere and via photolysis in the upper atmosphere. The global CH4 budget (i.e., the inventory of its sources and sinks) on modern Earth was recently reviewed by Saunois et al.66 Chloromethane (CH3 Cl) is formed from e.g., oceans, wetlands, seaweeds and industry.67 It presently has an abundance of (500–600) pptv in Earth’s atmosphere depending on latitude with an atmospheric lifetime of (1–2 years). Grenfell et al.68 provide a review of the photochemical responses of common atmospheric biosignatures on Earth. 3.4.

Atmospheric biosignatures: Transmission spectroscopy

Figure 10 illustrates infrared transmission spectroscopy for Venus (upper), Earth (middle) and Mars (lower panel). Figure 10 suggests clear differences between the atmospheric transmission spectra of Earth and its neighboring planets. The dry, CO2 -dominated atmospheres of Venus and Mars both feature a strong absorption band at the 15 microns CO2 fundamental band. Earth’s atmospheric spectrum however additionally shows water absorption features at around 8 microns as well as the O3 fundamental at ∼9.6 microns. 3.5.

False positives and negatives

A false positive biosignature detection refers to a claim that life is present when in actual fact it is not. This claim could arise, e.g., due to insufficient knowledge of abiotic production operating in the exoplanetary environment, which is then falsely interpreted as life. A false negative biosignature detection refers to a claim that life is not present when in actual fact life is there. This claim could arise, e.g., due to observational challenges such as a thick, absorbing atmosphere or the presence of a strong cloud layer which flattens

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Fig. 10. Atmospheric transmission spectra of Venus, Mars and Earth. Credit: R. Hanel [NASA GSFC], M. Goodman.

spectral features or/and prevents the lower atmospheric layers or the surface from being probed. 3.6.

The ideal atmospheric biosignature and reporting protocols

Ideally, a biosignature signal should be strongly statistically significant, unique and clearly attributable to life. O2 features a rather weak spectral band in the visible at 0.76 microns. O3 (which is commonly formed from O2 in Earth-like atmospheres) features a rather strong fundamental band in the infrared at ∼9.6 microns which remains significant over a range (several order of magnitude) of oxygen concentrations. Detections of both O2 and O3 however require careful investigation of the planetary environment in order to discount possible abiotic sources (see Table 1). The O3 fundamental band can overlap with a CO2 band in thick CO2 atmospheres. CH4 features rather weak, narrow bands in the infrared, e.g., at 3.4 microns, which are blended with H2 O bands at low spectral resolution (R < 20) and which require further investigation of the planetary environment in

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order to rule out possible geological sources. N2 O, on the one hand, features a rather weak spectral band at 7.8 microns. On the other hand, its known abiotic sources are rather weak which suggests that a successful detection could be more securely attributable to life compared with other atmospheric biosignatures. CH3 Cl features rather weak spectral bands, e.g., at ∼13.7 microns. Organizing a suitable reporting protocol for potential detections of extraterrestrial life is a central theme (see, e.g., Ref. 69). A suitable protocol, for example, would involve a broad spectrum of the relevant scientific community. It would aim to assign a confidence level and clearly impart uncertainties and caveats. Finally, it would organize its findings into logical steps involving, e.g., the confidence and attributability of a detection, its attributability to life, evidence of independent detections and related biological aspects.

4.

Summary

We live in interesting times regarding the search for habitable conditions and life beyond the Solar System. The field of exoplanets is unfolding and maturing at a rapid rate and this pace will quicken as data from the next generation missions emerge. Learning both from the Solar System as well as from the newly emerging exoplanetary data — which help place our planet into a new context — will be valuable guides in this challenging quest.

5.

Q&A

Denis Shulyak: Is the Faint Young Sun Paradox really a paradox, given that Mars probably had a much thicker atmosphere with a bigger greenhouse when it was young? John Lee Grenfell: The Sun was several tens of percent less luminous but maybe more UV active than now. Various models address how much CO2 one would need to keep the temperature up. The suggestion is that several bars of CO2 pressure are needed, but then, since this is no longer there, you have to have a way to get rid of it. So, it’s not really clear what happened, but we have ideas. It’s not a paradox if you are sure that Mars had a massive greenhouse, but nobody can be sure of that.

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Denis Shulyak: What is the role of the magnetic field? Could it prevent atmospheric erosion? John Lee Grenfell: We don’t know much about a global magnetic field on Mars, except that there isn’t one now. The history of Mars’ field depends on the past existence of a dynamo, which we also don’t know much about. Camille Bergez-Casalou: Why is chirality a biosignature? John Lee Grenfell: Terrestrial biology favors one sense of chirality. Outside of biology, the natural world does not in general exhibit a preference for one “handedness” over the other. So, the idea is that chirality suggests biology, but it is unclear why this is so. Jose Gomes: Which tools do you use to model habitability? John Lee Grenfell: Most exoplanet groups use rather straightforward 1D column models, which are generally less detailed than models used to study Earth’s atmosphere, for example. The reason is that we have very little data on the exoplanets, and therefore too few constraints to limit more elaborate models. Evandro Balbi: How important is plate tectonics for development and continuation of life? John Lee Grenfell: Tectonics is an important part of the carbonate-silicate cycle, which stabilizes the climate on long timescales. Maybe plate tectonics also helps with cycling of “nutrients”. So in this sense one can assert that tectonics is necessary for the development of life on Earth, although this is not well known. Luisa M Lara: Is it possible to know the ratio of several biomarker gases that reliably indicate life? John Lee Grenfell: This is a good question and is ongoing research. The answer depends on many things, including the nature of the star, the temperature of the planet and more. Pedro Amado: The CO2 band for Earth has a bump in the middle of the absorption band. What is that? John Lee Grenfell: It’s caused by the temperature structure of the atmosphere. The middle of the band is where the absorption is strongest, so it samples higher altitudes, where there is a local temperature maximum that is caused by ozone absorption of solar UV.

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With a retrieval model one can invert an emission spectrum to say something about temperature. Greg Cooke: If life is abundant, would you expect biosignature false positives or negatives to be more common, and why? John Lee Grenfell: A false negative could mean that we miss life (maybe because of thick clouds or another cause). A false positive would be like wrongly interpreting ozone as a biosignature when it has a photochemical cause. But unfortunately it is not possible to attach a number to this in order to address your question.

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c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 0007

Chapter 7

The Nature of Gas Giant Planets

Ravit Helled∗ , Naor Movshovitz† and Nadine Nettelmann‡ Institute for Computational Science, University of Zurich, Winterthurerstrasse, Zurich, Switzerland ∗

[email protected] [email protected] ‡ [email protected] †

Revealing the true nature of the gas giant planets in our Solar System is challenging. The masses of Jupiter and Saturn are about 318 and 95 Earth masses, respectively. While they mostly consist of hydrogen and helium, the total mass and distribution of the heavier elements, which reveal information about their origin, are still unknown. Recent accurate measurements of the gravitational fields of Jupiter and Saturn together with knowledge of the behavior of planetary materials at high pressures allow us to better constrain their interiors. Updated structure models of Jupiter and Saturn suggest that both planets have complex interiors that include composition inhomogeneities, non-convective regions, and fuzzy cores. In addition, it is clear that there are significant differences between Jupiter and Saturn and that each giant planet is unique. This has direct implications for giant exoplanet characterization and for our understanding of gaseous planets as a class of astronomical objects. In this review we summarize the methods used to model giant planet interiors and recent developments in giant planet structure models.

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1.

Introduction

The giant planets in the Solar System are mysterious and complex objects. They have been targets of detailed exploration from the ground and space for many decades and their characterization remains a key goal of planetary science. While significant progress in giant planet exploration has been made in the last few years, in particular thanks to the Juno and Cassini spacecraft, new questions have arisen, and there are many questions that still need to be answered. Constraining the composition of Jupiter and Saturn is of significant importance due to several reasons. First, the composition of the planets can be used to reveal information of the composition of the protoplanetary disk from which the Solar System formed. Second, exploration of Jupiter and Saturn allows for comparative planetology so we can understand whether Saturn is simply a small version of Jupiter (spoiler: the answer is no) and this knowledge can be reflected on the characterization of giant exoplanets. Third, the deep interiors of giant planets are natural laboratories for materials at extreme pressure and temperature conditions that cannot easily be achieved on Earth. Finally, a determination of the composition and internal structure of the planets can be used to constrain their formation and evolution histories. In this chapter, we summarize the key methods used to model the structure of giant planets and our current knowledge of the planets. Further information can be found in several recent reviews on giant planet interiors, including Refs. 1–6 and references therein.

2.

Modeling Planetary Interiors

For Earth, much of the information we have on its internal structure comes from seismology. For giant planets, there is no way to directly inter their compositions and internal structures, and therefore indirect methods must be used. 2.1.

Mass and radius

Before we discuss detailed structure models, it is worth noting that some information on a planet’s composition can be inferred from its

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mass and the radius alone. Jupiter has a mass of 1.89818(9)×10 27 kg and Saturn’s mass is 5.6834(2) × 1026 kg. Mass is relatively easya to measure (one or more natural satellites are helpful in that regard) with reliable precision. Radius is trickier because the planets are not perfect spheres. A simplification that will get us very close to the right volume is to assume the planet’s shape is an ellipsoid, estimate a surface radius at the equator and the pole, and solve for the volume or, equivalently, a mean radius. Jupiter has a mean radius of 69,911± 6 km, and Saturn, 58,232 ± 6 km. What do these values say about the planets’ composition? We know that we are dealing with, to first order, a mixture of hydrogen (H) and helium (He). But how much room is left in the mix for heavier elements? Figure 1 shows a theoretical mass–radius relation

Fig. 1. The mass–radius (M–MR) relation of H–He-dominated planets. The solid black curve corresponds to a H–He composition with a proto-soar ratio. The dotted line demonstrates the influence of a 15 M⊕ heavy-element core on the M–MR relation. Also shown are Jupiter and Saturn, and detected exoplanets in gray. Adapted from the Dace catalog, https://dace.unige.ch/dashboard/. a

Rather, it’s GM that is easy to measure, often with exquisite precision, and sometimes that is all we need. But here we really do need a mass, in kilograms. A measurement of G, the universal constant of gravity, is not easy, and includes a small but non-negligible uncertainty.

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for isolated H–He-rich planets. The solid curve assumes pure H–He mixture with a protosolar ratio and the dashed curved is the same mixture with a core of heavy elements. We see in the figure that both Jupiter and Saturn lie close to the H–He curves, confirming that they consist of mostly hydrogen and helium, but well below the curve for pure, protosolar H–He. This suggests that elements heavier than H–He are present in significant quantity, although it is not necessary that they are confined in a compact core. These heavier elements are typically assumed to be “rocks” (i.e., silicates and sometimes metals) and/or “ices” (mainly H2 O but also CH4 and NH3 ). In addition, since Saturn is farther from the pure-H–He curve than is Jupiter, it is expected to be more enriched with heavy elements. This prediction might appear to be contradicted by Saturn’s lower average density (687 kg m−3 compared with Jupiter’s 1,326 kg m−3 ). It’s the greater degree of compression of hydrogen and helium in Jupiter’s interior, due to its larger mass, that accounts for its higher overall bulk density. 2.2.

Polytropic models

A step beyond the mass–radius relation is the unit-index polytrope, the relationship: P = Kρ2

(1)

between pressure P and density ρ. This simple and artificial assumption can nevertheless be a surprisingly reasonable approximation of the compressibility of a H–He mixture at conditions typical of giant planet envelopes, with the polytropic constant K = 2.1 × 1012 m5 kg−1 s−2 . The polytropic relation and the condition of hydrostatic equilibrium (dP/dr = −ρ(r)g(r), where g(r) is the local acceleration due to gravity) combine to an integro-differential equation on ρ(r) which, with the assumption of a spherical planet (i.e., neglecting oblateness due to rotation), becomes the solvable ordinary differential equation   dρ d r = −k2 r 2 ρ(r), (2) dr dr

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Considering boundary conditions, the solution is ρ(r) = ρc

sin(kr) kr

(3)

 for 0 ≤ r ≤ R = πK 2G . The prediction then is that, neglecting the effects of rotation, a core, and heavy elements, an isolated body in the giant planet mass regime should have a predictable radius, which comes out to R = 70,300 km. Apparently the index-1 polytrope approximation is more appropriate for Jupiter than it is for Saturn. This is both because the P ∝ ρ2 approximation doesn’t fit Saturn’s present day envelope as well as Jupiter’s, and also that Saturn’s interior is more enriched with heavy elements compared with Jupiter, as we already suspected form the mass–radius relation. More information on polytropic models, extended to account for rotation and sometimes a core, can be found in Refs. 7–9. 3.

Interior Models

While the mass–radius and polytropic relations can be used to infer some basic predictions about the planetary bulk composition, they provide no information on the distribution of the materials. In order to constrain the density profile, and therefore the material distribution, additional constraints are required. For Solar System gas giants a critical measurement is their gravitational fields. Additionally, the magnetic fields, 1-bar temperatures, atmospheric composition, and static and dynamic rotation states are available and provide further constraints. The key measurable properties of Jupiter and Saturn that are used in interior models are listed in Table 1. Since giant planets consist of mostly fluid H and He, they do not have solid surfaces below the cloud layers and as a result the “surface” of the planet is defined as the location where the pressure is 1 bar, the pressure at the Earth’s surface. Often the measurement of the temperature at 1 bar is used to infer the entropy of the outer envelope and therefore of the planetary interior for adiabatic models where the temperature profile is set to be the adiabatic gradient (see Ref. 3 and references therein for details).

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Table 1. Basic observed properties of Jupiter and Saturn. Adapted from Ref. 5 and references therein. Property Distance to Sun (AU) Mass (1024 kg) Equatorial radius (km) Mean density (g/cm3 ) Effective temperature (K) 1-bar temperature (K) Rotation perioda J2 × 106 J4 × 106 J6 × 106 Love number k2

Jupiter

Saturn

5.204 1898.13 ± 0.19 71492 ± 4 1.3262 ± 0.0004 124.4 ± 0.3 165 ± 4 9h 55m 29.56s 14696.572 ± 0.014 −586.609 ± 0.004 34.24 ± 0.24 0.565 ± 0.018

9.582 568.319 ± 0.057 60268 ± 4 0.6871 ± 0.0002 95.0 ± 0.4 135 ± 5 10h 39m ± ∼10m 16290.557 ± 0.028 −935.318 ± 0.044 86.334 ± 0.112 0.382 ± 0.017

Notes: Gravity field data from Refs. 10, 11. The gravitational coefficients correspond to the reference equatorial radii of 71,492 km and 60,330 km for Jupiter and Saturn, respectively. a see Refs. 12 and 13 for discussion on Saturn’s rotation rate uncertainty.

An interior model of a giant planet is a self-consistent solution of the structure equations: dm = 4πr 2 ρ, dr Gm 2 1 dP = − 2 + ω 2 r, ρ dr r 3 T dP dT = ∇T, dr P dr

(4a) (4b) (4c)

where P is the pressure, ρ is the density, m is the mass inside a pressure level of mean radius r, and ω is the rotation rate. The first equation defines the transformation between a mass variable and radius variable. The second equation is the condition of hydrostatic equilibrium, including a correction term to account for oblateness due to uniform rotation. The third equation describes the energy transport outward from the interior of the object to its surface. The temperature gradient ∇T ≡ d ln T /d ln P depends on the energy transport mechanism. In convective regions the temperature gradient ln T is set to the adiabatic gradient ∇ad = ∂∂ ln P |S , where S is the entropy.

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If the energy transport is by radiation, the diffusion approximation is ∇ = ∇rad =

κR Lr P 3 = 16πGac mT 4



∂ ln T ∂ ln P

 .

(5)

rad

The derivative refers to the actual temperature–pressure variation in the planetary structure of the planet, and κR is the Rosseland mean opacity. Often, radiation and conduction are treated together using an effective opacity that accounts also for the contribution of conduction. Finally, a fourth equation, the equation of state (EoS), relates the density, pressure, and temperature at each level. More details on the EoS are given in Section 3.1. The hydrostatic condition as expressed in Eq. (4b) is only a firstorder approximation of the effects of rotation. The precise statement of the condition of hydrostatic equilibrium is 1 ∇P = −∇U, ρ

(6)

where U = V + Q is the sum of gravitational potential V (r) and centrifugal potential Q(r) = −(1/2)ω 2 r 2 sin2 θ. The gravitational potential field V is  V (r) = −G

d3 r 

ρ(r  ) , |r  − r |

(7)

where the integration is over the, as yet unknown, volume of the planet. An expansion in powers of r reads ∞   GM  r −n Jn Pn (μ) V (r, φ, θ) = − r a0 n=0   ∞  n   r −n (Cnm cos mφ + Snm sin mφ) Pnm (μ) , + a0 n=1 m=1

(8) where a0 denote the equatorial radius and μ = cos θ. In this form the information about the planet’s mass distribution is contained in the

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coefficients Jn , Cnm and Snm . The zonal harmonics Jn are  n d3 r  ρr n Pn (μ), M a0 Jn = − r  10−3 bar turb  (τ where τcoag grow and τnuc ). It is interesting to note that collisional particle–particle processes due to Brownian motion and gravitational settling are negligible compared to turbulence-driven collisional interactions for atmospheres where the turbulence cascade is driven by convective instabilities.27 Hence, turbulence-driven particle–particle collision may lead to coagulation or to fragmentation of the respective cloud particles. Further insight requires to model the processes in detail.

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241

Cloud Formation Modeling

An extensive description of cloud formation modeling in exoplanet and brown dwarf environments was provided by Ref. 28. Reference 29 (Chapters 6, and 9–14) present a textbook with detailed explanations of basic principles, hence applicable to the wide range of exoplanets. We refrain here from referring to more recent papers that present the same material in their own words. 4.1.

Modeling the formation of condensation seeds

To model the formation of condensation seeds means to describe the formation of subsequently larger molecules the biggest of which are called clusters (see Fig. 3). Ideally, the complete chemical path from

Fig. 3. The formation of condensation seeds leads to an increasing structural complexity, from the state of an unordered gas to a particle of a highly ordered structure.

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the gas phase to a solid particle could be modeled. This, however, is challenging since not only one path may exists and material data for all possible cluster sizes as well as their isomers will be required. If it is possible to identify one such chemical path that dominates the phase transition, then one can identify characteristic properties like a critical cluster and a bottle-neck reaction. Let us aim to incorporate as much microphysical knowledge as we possibly can into our model for condensation seed formation. The kinetic, steady-state approach describes the temporal evolution of the cluster size distribution function, f (N, t), as in Ref. 28, I

I

i=1

i=1

 df (N, t)  c = Ji (N, t) − Jic (N + i, t), dt

(1)

where f (N ) is the number density of a molecular cluster containing N i-mers that we are interested in. Jic (N, t) is the effective flux (or transition rate) for the growth of the cluster of size N − i to size N . This flux through cluster space is Jic (N, t)

=

Ri   ri −1

 f (N, t) f (N − i, t) − , τgr (ri , N − i, t) τev (ri , N, t)

(2)

summing over all chemical reactions ri in which an i-mer is involved. τgr (ri , N − i, t) is the growth time by reaction ri leading from cluster for size N − i to cluster size N . τev (ri , N, t) is the evaporation time leading from size N to size N − i, 1 = A(N − i) α(ri , N − i)vrel (nf (ri ), N − i) nf (ri ), τgr (ri , N − i, t) (3) 1 = A(N ) β(ri , N ) vrel (nr (ri ), N ) nr (ri ), (4) τev (ri , N, t) where nf (ri ) and nr (ri ) are the number densities of the molecule of the growth (forward) process and of the evaporation (reverse) process for reaction ri .30 A(N ) is the surface of the cluster of size N . vrel is the average relative velocity between the growing/evaporating TiO2

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molecule and the (TiO2 )N cluster. It is defined as the thermal velocity  vrel =

kB T 2π



 1 1 + . mN mTiO2

(5)

α(ri , N − i) and β(ri , N ) are the reaction efficiency for growth and evaporation via reaction ri . Note that α is also called the sticking probability. The growth and evaporation efficiency coefficients, α(ri , N ) and β(ri , N ), are often unknown for the different cluster sizes N . 3D MD molecular-dynamic-like simulations can help to study the effect of uncorrelated reaction efficiencies.31 Following Patzer et al. (1998), a reference equilibrium state is introduced to be able to solve Eq. (11) with Eqs. (3) and (4). Patzer et al. (1998) show in their Appendix A that if the temperatures of all components are equal, the supersaturation ratio of a cluster of size N with respect to the bulk is SN = (S1 )N . The reference equilibrium state is therefore characterized by phase equilibrium between monomers and between the clusters and the bulk solid, plus simultaneous chemical equilibrium in the gas phase, plus thermal equilibrium (i.e., all components have the same temperature). In such local thermodynamic equilibrium (LTE) between the gas phase and the clusters, the principle of detailed balance holds for a single microscopic growth process and its respective reverse, i.e., the evaporation process. This implies that under the condition of detailed balance, ◦

◦

f (N − 1)/τgr (N − 1) =f (N )/τev (N ), which allows to express the ◦

◦

◦

evaporation rate by the growth rate. f (N − i), f (N ), nf (ri ) and ◦ nr (ri ) are the equilibrium number densities for the clusters and the monomers. The law of mass action described the link between the equilibrium particle densities and Gibbs free energies, ⎛ ⎝

◦

◦

f(N − i) nf (ri ) ◦

◦

f(N ) nr (ri )

⎞ ⎠ = exp



◦ Δ− f G(ri , N, Td (N ))

R Td (N )

 .

(6)

◦ −1 Δ− f G(ri , N, Td (N )) [kJ mol ] is the Gibbs free energy of formation. It is calculated from the standard molar Gibbs free energy of

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formation of all reaction participants at the temperature Td (N ) = Tgas as ◦ − ◦ − ◦ Δ− f G(ri , N, Td (N )) = Δf G(N, Td (N )) − Δf G(N − i, Td (N )) ◦ + Δ− f G(nr (ri ), Td (N ))

(7)

◦ − Δ− f G(nf (ri ), Td (N )).

In LTE, the equilibrium cluster size distribution is therefore expressed by a Boltzmann distribution,   ◦ ◦ ΔG(N ) , (8) f(N ) =f(1) exp − RT ◦

with f(1) the equilibrium density of the monomer (e.g., TiO2 , SiO, NaCl). ΔG(N ) is the free energy change due to the formation of a cluster of size N from the saturated vapor. It is related to the stan◦ dard molar Gibbs free energy formation of the N -cluster Δ− f G(N ) by   psat (T ) − ◦ ◦ (9) − N Δ− ΔG(N ) = Δf G(N, T ) + RT ln f G1 (s, T ), p−◦ ◦ where Δ− f G1 (s), T is the standard molar Gibbs free energy of the formation of the solid phase, and p−◦ is the pressure of the standard state. Most often, p−◦ is the atmospheric pressure on Earth at which psat ◦ and Δ− f G(N, T ) are measured. The right-hand side of Eq. (9) contains now quantities which can be determined from lab experiments or quantum-chemical calculations. Note that the saturation vapor pressure is defined for an infinitely extended, planar surface but clusters do have a curvature. This surface curvature does affect the thermal stability of the cluster which was well recognized as a challenge within the astronomical community studying dust formation in late-type stars.32 In order for clusters to form, the gas needs to be considerably supersaturated (or super-cooled) in order to enter the regime of thermal stability for clusters. Furthermore, no assumptions were necessary with respect to size-independent surface tensions. Only a classical nucleation approach (droplet model) requires the consideration of the so-called Kelvin effect. The Kelvin effect is therefore used to include some representation of the curvature of the clusters/particles for the evaporation process. The use of thermodynamic cluster data in

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combination with the assumption of detailed balance conveniently side-steps calculating evaporation such that the concept of surface tension is not required to describe the effect of surface curvature on thermal stability. The final step is to derive an expression that enables to calculate the rate at which cloud condensation nuclei form. For this, we assume a stationary flow through the cluster space to occur. The slowest reaction will determine the flux through the cluster space during a chain of reaction. This bottle-neck reaction will lead to the formation of the critical cluster, N∗ Ref. 28, Eq. (15), which is the least stable cluster, and once it has formed, constructive cluster growth processes will dominate. This means that the nucleation rate, J∗ , is determined by the quantities of the critical cluster. For a homogeneous, homomolecular process in thermal equilibrium, one finds28 ◦   ΔG(N∗ ) f(1) Z(N∗ ) · exp (N∗ − 1) ln S(T ) − , (10) J∗ = τgr (1, N∗ ) RT

with Z(N∗ ) the Zeldovich factor (Ref. 28, Eq. (16)). Figure 4 demonstrates how the location in the (Tgas , pgas ) plane compares the results for the homogeneous, homomolecular nucleation rates for TiO2 and SiO (dashed lines, material data similar to Ref. 33) and the location of thermal stability where the supersaturation S = 1 for each of the solids (dotted lines). The modified nucleation theory is used to derive N∗ and cluster data to derive the required surface tension for TiO2 clusters is applied. Recall that no phase transition is possible in thermal equilibrium, which is represented by S = 1 here. Hence, the material will evaporate of T > T (S = 1) and it will be thermally stable for T ≤ T (S = 1). Therefore, CCN formation can only occur if Tgas  T (S = 1). The nucleation rates are calculated for prescribed 1D atmosphere profiles (solid gray line) for the dayside (left) and the nightside (right) of a tidally locked gas giant planet (for details, see Section 5). Figure 4 demonstrates that nucleation only occurs if the local gas temperature is sufficiently lower than Tgas (S = 1). The nucleation rate is lower on the dayside (left) where the local gas temperature (solid gray curve) decreases just below the Tgas (S = 1) compared to the nightside where a substantial supercooling below Tgas (S = 1) occurs. The dayside features Tgas ≈ Tgas (STiO2 = 1) at pgas ≈ 10−2.5 bar where

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Fig. 4. Comparing the location of the homogeneous, homomolecular nucleation rate for TiO2 (dashed dark blue line), SiO (dashed brown line), NaCl (not forming here), and KCl (not forming here) and the supersaturation ratio STiO2 [s],SiO[s],NaCl[s],KCl[s] = 1 in the (Tgas , pgas )-plane. The nucleation rates are calculated for (Tgas , pgas )-profiles (gray solid lines) of the dayside (left) and the nightside (right) for a tidally locked giant gas planet. The formation of CCNs is only possible if the gas is considerably colder than where thermal equilibrium (S = 1) occurs. Courtesy to D. Lewis.

consequently no TiO2 -nucleation occurs. The gas temperatures are too high for NaCl and KCl to nucleate. 4.2.

Modeling the bulk growth of cloud particles

Section 3 has shown that seed formation is the fastest process until the bulk growth supersedes it in higher density and warmer atmospheric regions. This section summarizes a method that allows to efficiently simulate the bulk growth of cloud condensation nuclei through surface reaction. The supersaturation ratio distinguishes now the constructive material growth (S > 1) from the destructive material evaporation (S < 1). Firstly, a conservation equation (the master equation) for the cloud particle size distribution, f (V ) [cm−6 ], in volume space is formulated as  ∂ (f (V )dV ) + ∇ (vd (V )f (V )dV ) = Rk dV. ∂t k

(11)

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Equation (11) can be solved directly by spectral binning methods34,35 or indirectly by defining moment of this equation. In order to derive a comprehensive set of equations that allow to derive cloud properties like particle sizes and material compositions, moments, Lj , are defined as ∞ f (V )V j/3 dV, (12) ρLj = Vl

which convert Eq. (11) into a set of moment equations for j = 0, 1, 2, . . . ∂ (ρLj ) + ∇(vd ρLj ) = ∂t



∞ Vl

Rk V j/3 dV.

(13)

k

The cloud particle velocity vd (V ) can be expressed in terms of the local gas velocity and the relative velocity between a cloud particle of volume V and the surrounding gas phase of density ρ as vd (V ) = vgas + vdr (V ). The frictional interaction of a cloud particle with the surrounding atmosphere does depend on its mass, size and the atmosphere density and different flow regimes may result.26 In a subsonic free molecular flow (large Knudsen numbers lKn), and 1D plane parallel geometry (z direction only), Eq. (13) becomes ∂ (ρLj ) + ∇(vgas ρLj ) ∂t   j net ∂ Lj+1 j/3 . = Vl J∗ + χlKn ρLj−1 + ξlKn ρd 3 ∂z cT

(14)

The first term on the r.h.s describes the nucleation process, the second, the surface growth, and the third, the effect of gravitational settling which transports the cloud particles with their relative velocities (raining particles). The lower integration boundary Vl represents the size of the CCNs and differs for the different nucleation key species (e.g., TiO2 , SiO, NaCl, KCl). χnet lKn ∼ nr (1 − 1/Sr ) is the total growth velocities for all materials s and defined in Eq. (43) in √ Ref. 28), and ξlKn = (3/4π)1/3 ( π/2)g. r annotates the chemical surface reactions. Various reactions r will contribute to the growth of a specific material s. The supersaturation is here defined with respect to a certain reaction r. For more in-depth details, please refer to

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our original papers as cited. Once the moment equations (Eqs. (14)) are solved, the moments ρLj j = 0, 1, 2, 3, . . .) can be used to derive cloud properties: • • • •

cloud particle number density: nd = ρL0 ,

3 A in Ref. 36), mean particle size a = 3/4π √ ·(L1 /L0 ) (Appendix tot /n , mean particle surface A = 3 36πL2 /L = A 0 s cloud d L3 /L0 with Vs = Ls3 /L0 . mean particle volume V  = L3 /L0 =

Average quantities represent an ensemble rather than individual particles. What may sound like a shortcoming is, in fact, a strength. By utilizing higher-order moments (L3 and L2 ) it is possible to derive an ensemble average more suitable, for example, for opacity calculation for which the surface area is more suited (opacity calculation).36

5.

The Resulting Cloud Structure, the Prerequisites for Extrasolar Weather Forecast

The numerical solution of the cloud formation model described in the previous sections in 1D and for a stationary cloud in an atmosphere that is well-mixed by convection allows to discuss the principle vertical cloud structures. In addition to the cloud model described, the element conservation has to be solved for each element involved and the chemical composition of the gas phase calculated. The cloud model in combination with the gas-phase chemistry calculation can be used as virtual laboratory in order to explore cloud details like the number of cloud particles forming, their material composition and the expansion of the cloud for a set of local gas temperatures, gas pressures and the vertical mixing efficiencies (τmix ). Here we compare the 1D vertical cloud structure at the dayside (substellar point) and the nightside (antistellar point) in Fig. 5 for a tidally locked, moderately warm giant gas planet that orbits a G-type host star at an orbital distance of 0.025 AU with a rotational period of 1.55 days. The same approach can be utilized to study many 1D profiles spanning the full planetary globe by extracting them from 3D GCMs in order to provide a first-order exploration of cloud properties and their distributions for different extrasolar planet atmosphere structures,38 hence, their local weather.

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Fig. 5. The cloud profiles for the substellar (φ = 0◦ , dayside) and the antistellar (φ = 180◦ , nightside) point of a tidally locked gas-giant orbiting a G-type host star. The gas-giant would have an effective temperature of Teff = 1,600 K and a log(g) = 3.0 for a set of solar element abundances. The 1D profiles are extracted from a 3D GCM simulation by Ref. 37. Courtesy to D. Lewis.

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The local gas temperature determines the chemical composition of the gas phase and, hence, the inset of the seed formation process. We note that the dayside of our model exoplanet in Fig. 5 has a gas temperature well above 1,300 K in the uppermost atmosphere where pgas < 10−2 bar. Consequently, only the nightside allows for an efficient formation of seed particles of TiO2 and SiO over three orders of pressure magnitude (2nd row, right, solid lines, J∗ ), whereas the region of efficient seed formation remains confined to a very narrow temperature interval on the substellar point (2nd row, left, solid lines). Only TiO2 (blue) contributes here to form cloud condensation nuclei. The nightside is cool enough that SiO (brown) contributes considerably to the formation of cloud condensation nuclei in the uppermost, coolest layers of our computational domain. The number density of cloud particle, nd , is a direct consequence of the seed formation process. Figure 5 (2nd row, dotted lines) furthermore demonstrates that nd expands into higher pressure regions compared to the nucleation rate. That shows that cloud particles have fallen (gravitational settling) into the deeper atmosphere where seed formation becomes thermally impossible. As particles fall through the atmosphere, they encounter different chemical gas compositions as a result of the changing thermodynamic conditions (top panels, solid black lines). Consequently, the material composition of the cloud particles changes throughout the atmosphere (3rd row, material volume fractions Vs /Vtot ). The very top layers are made of the cloud nucleation species TiO2 and SiO which lose in importance where other, more complex materials condense and compete for the elements that they are made of. The middle portion of the cloud layer is made of a wide mix of Mg/Fe/Si/O materials peppered with materials that contain elements of lesser (solar) abundances like Ca or Al. The warmest parts of the clouds are made of high-temperature condensates like Fe[s], Al2 O3 [s], CaTiO3 [s]. The detailed material composition in the optically thin part of the cloud (pgas < 10−3 bar) differs considerably between the day(φ = 0◦ ) and the nightside (φ = 180◦ ) reflecting the very different local temperatures. A very low nucleation rate at pgas < 10−3 bar causes a small number of cloud particles made of TiO2 [s], CaSiO2 [s], Al2 O3 [s] and CaTiO3 [s] to grow to considerable sizes of 10 μm from

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these rarified gases. A considerably larger number of cloud particles are able to form on the nightside where they are made of a large mix of silicates and grow to sizes of 0.1 μm only. Figure 5 (4th panel) shows how the larger particles (red line) on the dayside fall faster (dotted line) through the atmosphere than the smaller cloud particles on the nightside. Hence, cloud particles prevail for longer aloft on the nightside compared to the dayside. The size differences will matter hugely for the albedo of the night- and the daysides of such a planet. Cloud particles are a strong source of opacity in an atmosphere which will cause them to block our view into exoplanets and onto a potentially rocky surface. Cloud particles are also a chemically rather active component inside the gas that they are forming from. This is demonstrated in Fig. 5 (5th and 6th row) in terms of the supersaturation ratio and the element abundances after the cloud particles have formed. Section 2 has touched the idea of the supersaturation of a gas phase which needs to be sufficiently high (S 1) in order to enable a phase transition, hence, the formation of cloud condensation nuclei. Figure 5 (5th) shows three regimes: S 1, S = 1 and S  1. S 1 occurs where all constructive cloud formation processes (nucleation and surface growth) take place. S = 1 occurs where the growth process (which eventually supersedes the nucleation) can not progress any further and the respective materials are thermally stable. S  1 indicates that here the materials that have condensed onto the cloud particles are thermally unstable and evaporate. Since cloud particles have grown to considerable size of 100 μm on the nightside and 0.1 cm on the dayside at the cloud base, evaporation will not be instant, but it occurs over a certain distance within the cloud base. At the cloud base, a small increase of the element abundances (Fig. 5, x , 4th) indicates that the evaporating cloud particles have transported elements from the upper into the lower atmospheric regions. A considerable element depletion of the gas phase results from the cloud particle formation (seen as deep dips in which results in Ti , Mg , etc.) and a decreased number density of all gas-phase species that form from those molecules. Therefore, cloud particles do not only weaken the observability of spectroscopic features by adding a gray opacity source for λ < 1 μm, but they also weaken the spectral features by decreasing the number densities of species like TiO, VO, SiO and also H2 O.

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6.

Moving Forward

We can now stitch together a whole 3D cloud map by solving our cloud model for many such 1D profiles as in Fig. 5. Clearly, we cannot go into the amount of details discussed in Section 5 but need to select key quantities. Figure 6 shows two equatorial slices, for the gas temperature, Tgas [K], which is the result of a cloud-free 3D GCM solution (left) and the cloud particle mass load (in terms of dustto-gas mass ratios ρd /ρ) which is the result of our cloud formation simulation. Figure 6 shows that clouds form only on the nightside on ultra-hot Jupiters and that the amount of cloud particles is not homogeneous. The cloud reaches into the dayside on the morning terminator (270◦ ), but not on the evening terminator (90◦ ). The reason is an equatorial jet that transports cold gas from the night to the dayside. As cloud formation is determined by the local thermodynamic properties (unless in high photon-dominated regions), our cloud map traces nicely this temperature difference and sharply drops

Fig. 6. Equatorial slices of a 3D planetary globe modeling the ultra-hot, tidally locked Jupiter HAT-7b. The location of the host star is indicated on the right (yellow semicircle). The gas-phase temperature distribution is on the left and the resulting cloud mass load on the right. An extreme day/night asymmetry emerges for ultra-hot Jupiters which may be traced by transmission spectroscopy that measure the terminator regions.

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where thermal instability disables the presence of clouds. Note that cloud formation is prohibited inside the blue regions on our cloud map (left-hand side of Fig. 6). Similarly, no clouds can from until the hot dayside gas that is transported to the nightside has cooled sufficiently (e.g., like in Fig. 4) to allow cloud condensation seeds to form. Figure 6 also suggests that if transmission spectra could distinguish between the morning and the evening terminator, a geometrical asymmetry should emerge such that the morning terminator appears more extended in the optical.

7.

Final Thoughts

Any astrophysical cloud formation model (e.g., for exoplanets and brown dwarfs) needs to be fundamental enough to enable the application to the wide variety of exoplanets that we already know about (rocky planets, ultra-hot gas giants, mini-Neptunes). For those, we have no solar-system analogous to fly to and to take samples from. It is therefore essential that model approaches are compared39 and codes are not used as black boxes. Preferably, different methods are developed to solve the same problem.31 What is more, cloud formation requires the input from a variety of not-so adjacent research areas like quantum chemistry and geology, maybe even particle physics, and such fundamental research has been very timeconsuming in the past. A summary of challenges was presented elsewhere.40

8.

Q&A

Denis Shulyak: Cloud opacities are largest in the UV; what instruments (or prospects for instruments) do we have to observe at these wavelengths? Christiane Helling: The HST has been used to inspect the spectral part at wavelength less than the optical wavelength. Various instruments and missions are under development which would enable us to use the UV spectral range in the future, one example is Arago that would perform high-resolution spectropolarimetry simultaneously in the UV and Visible.

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Denis Shulyak: Higher dayside temperatures should drive more turbulent mixing than on the night side. Was that taken into account in Fig. 5? Christiane Helling: The turbulence will be driven by shear flows which do occur more vividly on the day-side, indeed. Our model does consider the velocity differences on the day and the night side according to the results of the pre-requisite 3D GCM results. Luisa M Lara: What is the difference among between atmospheric haze and clouds? Are there any chemical or physical processes that would allow to distinguish between them? Christiane Helling: ‘Haze’ is commonly used to represent photochemically produced complex molecules and potentially resulting cloud condensation nuclei. ‘Clouds’ is understood as the ensemble of particles that form in the deeper atmosphere (due to all the processes outlined in Fig. 1) and are richer in their chemical composition. However, I think this is a very artificial differentiation since photochemical processes will also effect the cloud particle formation in deeper atmospheric layers. Luisa M Lara: Could the entry of exogenic material (refractory material) at the top of the atmosphere trigger cloud layers clearly distinct from the ones originated by the atmosphere itself ? Christiane Helling: That is a very interesting idea and we know that exogenic materials do also reconvenes in the upper atmosphere of Earth. The same could happen in exoplanetary atmospheres. The lifetime of such a layer is then determined by how slowly the particles fall through the atmosphere compared to the replenishment by new exogenic material.

Acknowledgments Christiane Helling thanks Dominic Samra and David Lewis for their help with Figs. 2, 4 and 5. Christiane Helling acknowledges funding from the European Union H2020-MSCA-ITN-2019 under Grant Agreement no. 860470 (CHAMELEON).

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References [1] J. Wilson et al., Ground-based transmission spectroscopy with FORS2: A featureless optical transmission spectrum and detection of H2 O for the ultra-hot Jupiter WASP-103b, MNRAS. 497(4), 5155–5170 (Oct., 2020). DOI: 10.1093/mnras/staa2307. [2] K. D. Col´on et al., An unusual transmission spectrum for the subsaturn KELT-11b suggestive of a subsolar water abundance, AJ. 160(6), 280 (Dec., 2020). DOI: 10.3847/1538-3881/abc1e9. [3] L. Carone et al., Indications for very high metallicity and absence of methane in the eccentric exo-Saturn WASP-117b, A&A. 646, A168 (Feb., 2021). DOI: 10.1051/0004-6361/202038620. [4] K. L. Chubb et al., Aluminium oxide in the atmosphere of hot Jupiter WASP-43b, A&A. 639, A3 (Jul., 2020). DOI: 10.1051/0004-6361/ 201937267. [5] M. Braam et al., Evidence for chromium hydride in the atmosphere of hot Jupiter WASP-31b, A&A. 646, A17 (Feb., 2021). DOI: 10.1051/ 0004-6361/202039509. [6] N. Casasayas-Barris et al., Atmospheric characterization of the ultrahot Jupiter MASCARA-2b/KELT-20b. Detection of CaII, FeII, NaI, and the Balmer series of H (Hα, Hβ, and Hγ) with high-dispersion transit spectroscopy, A&A. 628, A9 (Aug., 2019). DOI: 10.1051/ 0004-6361/201935623. [7] N. Casasayas-Barris et al., Atmospheric characterization of the ultrahot Jupiter MASCARA-2b/KELT-20b. Detection of Ca II, Fe II, Na I, and the Balmer series of H (Hα, Hβ, and Hγ) with high-dispersion transit spectroscopy (Corrigendum), A&A. 640, C6 (Aug., 2020). DOI: 10.1051/0004-6361/201935623e. [8] T. S. Stallard et al., Identification of Jupiter’s magnetic equator through H3 + ionospheric emission, Nat. Astron. 2, 773–777 (Jul., 2018). DOI: 10.1038/s41550-018-0523-z. [9] S. Miller et al., Thirty years of H3 + astronomy, Rev. Modern Phys. 92(3), 035003 (Jul., 2020). DOI: 10.1103/RevModPhys.92.035003. [10] G. Hodosan et al., Exo-lightning radio emission: The case study of HAT-P-11b. In G. Fischer, G. Mann, M. Panchenko, and P. Zarka (eds.), Planetary Radio Emissions VIII, Austrian Academy of Sciences Press, Vienna, pp. 345–356 (Jan., 2017). DOI: 10.1553/PRE8s345. [11] P. Barth et al., MOVES - IV. Modelling the influence of stellar XUVflux, cosmic rays, and stellar energetic particles on the atmospheric composition of the hot Jupiter HD 189733b, MNRAS. 502(4), 6201– 6215 (Apr., 2021). DOI: 10.1093/mnras/staa3989.

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[12] G. Hodos´an et al., Lightning climatology of exoplanets and brown dwarfs guided by Solar system data, MNRAS. 461(4), 3927–3947 (Oct., 2016). DOI: 10.1093/mnras/stw1571. [13] H. R. Wakeford et al., The complete transmission spectrum of WASP39b with a precise water constraint, AJ. 155(1), 29 (Jan., 2018). DOI: 10.3847/1538-3881/aa9e4e. [14] J. K. Barstow, Unveiling cloudy exoplanets: the influence of cloud model choices on retrieval solutions, MNRAS. 497(4), 4183–4195 (Oct., 2020). DOI: 10.1093/mnras/staa2219. [15] L. Welbanks and N. Madhusudhan, Aurora: A generalized retrieval framework for exoplanetary transmission spectra, ApJ. 913(2), 114 (Jun., 2021). DOI: 10.3847/1538-4357/abee94. [16] S. V. Berdyugina et al., Remote sensing of life: polarimetric signatures of photosynthetic pigments as sensitive biomarkers, Inter. J. Astrobiol. 15(1), 45–56 (Jan., 2016). DOI: 10.1017/S1473550415000129. [17] C. R. Stark et al., Electrostatic activation of prebiotic chemistry in substellar atmospheres, Inter. J. Astro. 13(2), 165–172 (Apr., 2014). DOI: 10.1017/S1473550413000475. [18] S. Seager et al., Possibilities for an aerial biosphere in temperate sub neptune-sized exoplanet atmospheres, Universe. 7(6), 172 (May, 2021). DOI: 10.3390/universe7060172. [19] C. Helling, Exoplanet clouds, Ann. Rev. Earth Planetary Sci. 47, 583– 606 (May, 2019). DOI: 10.1146/annurev-earth-053018-060401. [20] P. Gao et al., Aerosols in exoplanet atmospheres, J. Geophys. Res. (Planets). 126(4), e06655 (Apr., 2021). DOI: 10.1029/2020JE006655. [21] X. Tan and A. P. Showman, Atmospheric circulation of brown dwarfs and directly imaged exoplanets driven by cloud radiative feedback: Global and equatorial dynamics, MNRAS. 502(2), 2198–2219 (Apr., 2021). DOI: 10.1093/mnras/stab097. [22] C. G¨ uttler et al., The outcome of protoplanetary dust growth: Pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments, A&A. 513, A56 (Apr., 2010). DOI: 10.1051/0004-6361/ 200912852. [23] J. Svensmark et al., The response of clouds and aerosols to cosmic ray decreases, J. Geophys. Res. (space physics). 121(9), 8152–8181 (Sept., 2016). DOI: 10.1002/2016JA022689. [24] C. Helling. Lightning in other planets. J. Phys. Conf. Ser., 1322, 012028 (Oct., 2019). DOI: 10.1088/1742-6596/1322/1/012028. [25] S. Witte et al., Dust in brown dwarfs and extra-solar planets. II. Cloud formation for cosmologically evolving abundances, A&A. 506(3), 1367–1380 (Nov., 2009). DOI: 10.1051/0004-6361/200811501.

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[26] P. Woitke and C. Helling, Dust in brown dwarfs. II. The coupled problem of dust formation and sedimentation, A&A. 399, 297–313 (Feb., 2003). DOI: 10.1051/0004-6361:20021734. [27] C. Helling et al., Dust in brown dwarfs. IV. Dust formation and driven turbulence on mesoscopic scales, A&A. 423, 657–675 (Aug., 2004). DOI: 10.1051/0004-6361:20034514. [28] C. Helling and A. Fomins, Modelling the formation of atmospheric dust in brown dwarfs and planetary atmospheres, Philosoph. Trans. Roy. Soc. Lond. Series A. 371(1994), 20110581–20110581 (Jun., 2013). DOI: 10.1098/rsta.2011.0581. [29] H.-P. Gail and E. Sedlmayr, Physics and Chemistry of Circumstellar Dust Shells, Cambridge University Press, Cambridge (2013). [30] A. B. C. Patzer et al., Dust formation in stellar winds. VII. Kinetic nucleation theory for chemical non-equilibrium in the gas phase, A&A. 337, 847–858 (Sep., 1998). [31] C. K¨ohn et al., Dust in brown dwarfs and extra-solar planets. VIII. TiO2 seed formation: 3D Monte Carlo versus kinetic approach, arXiv e-prints:arXiv:2108.04701 (Aug., 2021). [32] A. Goeres. Chemistry and thermodynamics of the nucleation in R CrB star shells. In C. S. Jeffery and U. Heber (eds.), Hydrogen Deficient Stars, vol. 96, Astronomical Society of the Pacific Conference Series, San Francisco, p. 69 (Jan., 1996). [33] E. K. H. Lee et al., Dust in brown dwarfs and extra-solar planets. VI. Assessing seed formation across the brown dwarf and exoplanet regimes, A&A. 614, A126 (Jul., 2018). DOI: 10.1051/0004-6361/ 201731977. [34] D. Powell et al., Formation of silicate and titanium clouds on hot Jupiters, ApJ. 860(1), 18 (Jun., 2018). DOI: 10.3847/1538-4357/ aac215. [35] Y. Kawashima et al., Detectable molecular features above hydrocarbon haze via transmission spectroscopy with JWST: Case studies of GJ 1214b-, GJ 436b-, HD 97658b-, and Kepler-51b-like Planets, ApJL. 876(1), L5 (May, 2019). DOI: 10.3847/2041-8213/ab16f6. [36] C. Helling et al., Mineral cloud and hydrocarbon haze particles in the atmosphere of the hot Jupiter JWST target WASP-43b, A&A. 641, A178 (Sept., 2020). DOI: 10.1051/0004-6361/202037633. [37] R. Baeyens et al., Grid of Pseudo-2D chemistry models for tidallylocked exoplanets. I. The role of vertical and horizontal mixing, MNRAS. (May, 2021). DOI: 10.1093/mnras/stab1310. [38] C. Helling et al., Cloud property trends in hot and ultra-hot giant gas planets (WASP-43b, WASP-103b, WASP-121b, HAT-P-7b, and

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WASP-18b), A&A. 649, A44 (May, 2021). DOI: 10.1051/0004-6361/ 202039911. [39] C. Helling et al., A comparison of chemistry and dust cloud formation in ultracool dwarf model atmospheres, MNRAS. 391(4), 1854–1873 (Dec., 2008). DOI: 10.1111/j.1365-2966.2008.13991.x. [40] C. Helling, Clouds in exoplanetary atmospheres, arXiv e-prints: arXiv:2011.03302 (Nov., 2020).

c 2023 World Scientific Publishing Europe Ltd.  https://doi.org/10.1142/9781800613140 0010

Chapter 10

Planetary Astrophysics of Small Bodies

David Jewitt Department of Earth, Planetary and Space Sciences, University of California, Los Angeles, USA [email protected]

This is an intentionally brief overview of Solar System science as seen from the perspective of an observational planetary astronomer. Instead of following the format used in my lectures for the school, I thought it would be more fun to focus on a set of topics that illustrate current problems and areas of activity in planetary science.

1.

Introduction

The small bodies of the Solar System are carriers of information from the earliest epochs and, therefore, objects of great scientific interest. Observationally, the small body populations tend to be difficult to study, both because small means “faint”, and because many of the bodies of greatest interest (the Kuiper belt objects, the Centaurs, the Trojans) are far-away residents of the middle and outer Solar System, rendering them fainter still. To add insult to injury, the albedos of

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many of the most primordial objects (notably the nuclei of comets but also the Trojans and many Kuiper belt objects), tend to be very small (few percent), making them even fainter still. This is why we can study self-luminous objects at the edge of the universe, but we can barely glimpse what’s in the Kuiper belt only 100 AU away. It’s also why the study of the small body populations is very fresh and new.

2.

The Comets

Comets are dynamically divided into two main groups, the shortperiod comets (SPCs) and the long-period comets (LPCs). The easy-to-remember but rather arbitrary distinction between them is that the SPCs have periods P < 200 years while the LPCs have P > 200 years. When separated by this simple criterion, the LPCs and the SPCs are remarkably dynamically distinct.a The SPCs occupy a disk-like distribution with modest inclinations and eccentricities and share the prograde motion of the planets around the Sun. The LPCs occupy an isotropic distribution, with equal numbers of prograde and retrograde orbits, and equal numbers arriving from the northern and southern hemispheres, as far as can be told. They have large eccentricities, up to e = 1. Objects in a third group, the Halley-type comets, (HTCs) are dynamically intermediate. Most are prograde but some retrograde HTCs exist. A famous example is the class prototype, 1P/Halley, which has P = 76 years like the SPCs but i = 162o like the LPCs. Seemingly less arbitrary but more involved classification systems exist, notably one based on the Tisserand parameter, TJ . This is a constant of the motion in the restricted, circular three-body (Sun– Jupiter–comet) problem, defined by  1/2 aJ 2 a + 2 (1 − e ) cos(i), TJ = a aJ

(1)

a The selection of 200 years is also not particularly critical. P = 100 and 1,000 years give roughly the same separation.

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where a, e and i are, respectively, the semi-major axis, eccentricity and inclination of the comet orbit and aJ = 5.2 AU is the semi-major axis of Jupiter’s orbit. By this parameter, the LPCs have TJ ≤ 2 while the SPCs have 2 < TJ ≤ 3. Although it looks superficially more formal, the TJ classification is itself not particularly rigorous because the solar system is not accurately represented by the restricted, circular three-body approximation (e.g., Jupiter’s orbit is not circular, there are many planets other than Jupiter, they have non-zero inclinations, and so-on). Happily, the period-defined and TJ -defined comet groups are roughly consistent. Most comets arrive in the inner Solar System from two distinct storage locations, known as the Kuiper belt (KB) and the Oort cloud (OC) (e.g., Ref. 1). The KB is the source of most SPCs (specifically the Jupiter family comets). It has an inner edge carved by Neptune at ∼30 AU and extends for thousands of AU outwards. It consists of four dynamically distinct components (the classical, resonant, scattered and detached Kuiper belt objects), each with a story to tell about the origin and dynamical evolution of the Solar System. The KB contains roughly 105 objects larger than 100 km and perhaps 1010 larger than 1 km, but the exact population is not well-defined for two reasons. First, KBOs smaller than a few × 10 km are too faint to be reliably detected in existing ground-based surveys. Second, the flux density, f [W m−2 Hz−1 ], of an object in scattered sunlight suffers from the inverse-square law twice (once from Sun to the object and again from the object to Earth), and so varies with distance from −4 . A given object at 50 AU appears 104 times the Sun, rH , as f ∝ rH fainter than it would at 5 AU (Jupiter’s orbit). In practice, this steep dependence means that we can say little about the contents of the KB beyond rH = 50–100 AU and there is room for almost any nonluminous object beyond a few hundred AU. Most SPCs originate in the scattered disk component of the KB. They are ejected as a result of dynamical chaos, at a rate estimated at a few per century. The OC is the source of LPCs. It holds ∼1012 comets in a spherical swarm that is not sharp-edged but which has a characteristic diameter ∼105 AU.1 This is a large fraction of the distance to the nearest stars (∼2 × 105 AU). Indeed, the extent of the cloud is set by erosion from the gravity of passing stars coupled with tides caused by the lop-sided distribution of mass in the Milky Way galaxy. The properties of the OC are inferred from the orbits of LPCs that have been

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deflected out of the cloud and enter the planetary region. A passing star of mass M∗ , relative velocity V∗ and with impact parameter (minimum distance) d perturbs the velocity of an orbiting OC comet by  ΔV ∼

2GM∗ V∗ d

1/2

.

(2)

Substituting G = 6.6 × 10−11 N kg−2 m2 , M∗ = M = 2 × 1030 kg, V∗ = 20 km s−1 and d = 1 pc (3 × 1016 m) gives ΔV ∼ 1 m s−1 . For comparison, the Keplerian velocity at 105 AU from the Sun is VK ∼ 100 m s−1 . Since field stars pass the Sun from random directions, the ΔV “kicks” accumulate randomly, and the total velocity change is equal to VK after about N ∼ (VK /(ΔV ))2 stellar flybys. Evidently, N ∼ 104 , which takes about a billion years (the process is aided by the galactic tide and the degree of orbit randomization depends as well on the comet semi-major axis and local stellar density2 ). On this and longer timescales, the OC, which began as a flattened disk sharing the midplane of the planets, was isotropized into a spherical cloud. Consequently, considerable uncertainties remain concerning the radial structure, the degree of isotropy, the mass and other parameters, and we do not know how or where the KB and the OC meet, except by theoretical conjecture. A third but much smaller comet reservoir has been recently located in the asteroid belt,3 where ice-rich asteroids unexpectedly survive. We will discuss these “main-belt comets” in another section. The three reservoirs are illustrated schematically in Fig. 1. The end-fates of comets are to impact planets or the Sun, to be ejected from the Solar System, or to spontaneously disintegrate. In between their demise and their origin in the source reservoirs, they are classified (for largely historical reasons) into numerous different groups. Damocloids are defunct LPCs.4 Centaurs are recently escaped KBOs in the process of crossing the giant planet region of the Solar System. Centaurs surviving the jump across Jupiter’s orbit are relabeled Jupiter family comets (JFCs). Defunct (i.e., thermally evolved) JFCs are known as dJFCs or Asteroids on cometary orbits (ACOs). The names don’t matter much; what is important is that the comets flow into the planetary region from distinct source reservoirs that have had different dynamical and thermal histories.

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Fig. 1. Schematic diagram showing the relationships between various cometary populations discussed in the text. The timescales on the right indicate the approximate lifetimes in each stage. Acronyms are defined in the text.

2.1.

Destruction of the comets

While we have made real progress in identifying and characterizing the different source regions of the comets, the ways in which they are destroyed are still not clear. As noted above, the likely processes are impact destruction, dynamical ejection to the interstellar medium (never to be seen again) and physical disintegration. Numerical integrations show that scattering by the planets limits the Jupiter family comets to a dynamical half life τd ∼ 0.4 Myr. On this timescale, the comets either strike a planet or the Sun or are ejected to infinity. The simulations also show that successive scattering interactions tend to pump up the inclinations of the orbits relative to the inclination distribution of objects arriving from the Kuiper belt. In order to prevent the model inclination distribution from growing fatter than the observed inclination distribution, the evolution must be truncated after about τ ∼ 12,000 years, which gives a measure of the “physical lifetime” of the comets. The question is “why is τ  τd ?” or, equivalently, “what determines τ ?”.

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Ice exposed to sunlight sublimates into the interplanetary vacuum, at a rate fs (kg m−2 s−1 ) that may be estimated from the energy balance equation, simplified hereb as   F 4 (1 − A) = χ εσT + f (T )H(T ) . (3) s 2 rH F = 1, 360 W m−2 is the solar constant, rH is the heliocentric distance expressed in AU, A and ε are the Bond albedo and emissivity of the ice surface (we assume A = 0 and ε = 1), T is the temperature and H(T ) is the latent heat of sublimation of the ice. The term on the left is the power per unit area absorbed from the Sun. The first term on the right is the power per unit area radiated by the ice into space and the second term on the right is the power per unit area used to break intermolecular bonds in the ice and so to drive sublimation. Parameter 1 ≤ χ ≤ 4 is a dimensionless number used to represent the distribution of the absorbed power over the nucleus surface. χ = 4 corresponds to the case where solar power is absorbed over πrn2 but radiated from 4πrn2 , as would be the case for an isothermal sphere of radius rn . χ = 1 corresponds to the case where the absorbing and radiating (and sublimating) areas are the same, as would be the case for a plane surface oriented normal to the Sun-comet line (e.g., as at midday). Equation (3) contains too many variables to be solved by itself, so must be considered simultaneously with a relation for fs (T ), provided by the Clausius–Clapeyron equation from thermodynamics. Solutions for water, carbon dioxide and carbon monoxide ices are shown in Fig. 2. In the limit as rH → 0, the sublimation term in Eq. (3) dominates over the radiation term (because sublimation is exponentially dependent on T , whereas radiation is proportional only to T 4 ) and we may write fs ∼

F (1 − A) 2 . χH(T )rH

(4)

−2 dependence in Eq. (4) is evident in all the curves in The fs ∝ rH Fig. 2 when rH  2 AU, precisely where most comet observations are b

A more detailed calculation would balance the energy at each element of the surface and include a term for thermal conduction into the interior. Nothing would be learned for our present purposes by pursuing this more detailed calculation.

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Fig. 2. Equilibrium sublimation rates of three common ices as a function of heliocentric distance. We show water ice, carbon dioxide ice and carbon monoxide ice as labeled. Each volatile is shown as two curves labeled “H” and “C”, for hot and cold temperature limits as described in the text. The orbits of the giant planets are marked by dashed vertical lines.

taken. For water ice, the least volatile of the plotted ices, fs shows a sharp downturn at larger rH , defining the region where comets are most active. For CO ice, the downturn lies beyond the orbit of −2 applies across the entire planetary system. Neptune, and fs ∝ rH CO2 ice is intermediate in volatility and behavior. Armed with the solutions to Eq. (3) we can make a crude guess as to the lifetimes of comets to the loss of volatiles. For a spherical nucleus of radius rn sublimating from an area 4πrn2 fA , the time over which the entire nucleus would sublimate away is τsub ∼

ρn rn , 3fs fA

(5)

where 0 ≤ fA ≤ 1 is the fraction of the nucleus surface which is losing mass. Measurements suggest fA ∼ 10−2 (e.g., as in Ref. 6), but a wide range of values exists in the active comets. From Fig. 2, water has fs ∼ 3 × 10−5 kg m−2 s−1 at rH = 3 AU and, with ρn = 500 kg m−3 , a 1 km radius nucleus would last τsub ∼ 1012 s (about 105 years). This is already longer than τ , and is a strong lower limit to the true

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sublimation lifetime because comet orbits are eccentric, and nuclei spend most of the time at larger rH where fs is greatly reduced. Moreover, comets grow refractory “mantles”, consisting of blocks too large to be lifted by gas drag, causing a gradual throttling of the outgassing. Volatile depletion by outgassing in comets is evidently rather slow. It turns out that outgassing can destroy comets in a less direct but much more devastating way. Outgassing, strongest on the hot dayside of the nucleus, exerts a net reaction force. The resulting non-gravitational acceleration is readily measurable on the orbital timescale (and, indeed, was the observational foundation of Whipple’s model of the cometary nucleus7 ). Significantly, the reaction force vector does not in general pass through the center of mass of the nucleus, creating a torque which can change the spin, both in magnitude and direction. A sustained torque can drive the spin to the limit, where centripetal forces can no longer be met by gravitational forces to the center of a rotating body. For a sphere, this critical period is given by Pc = (3π/(Gρn ))1/2 and, for ρn = 500 kg m−3 , is Pc ∼ 4.7 hours. A nucleus spinning with a shorter period is liable to break up unless held together by frictional or cohesive forces. The spin-up time is τ ∼ L/T , where L is the angular momentum and T is the torque. Neglecting considerations of shape, for the moment, we note that L ∝ Mn rn2 which, because Mn ∝ rn3 , gives L ∝ rn5 . The torque is proportional to the mass loss rate from the nucleus multiplied by the moment arm of the torque. Since mass loss rate is ∝ fs fA rn2 , and the moment arm ∝ rn , we see T ∝ rn5 /rn3 ∝ rn2 . Therefore, from dimensional considerations alone, we expect τ ∝ rn2 . The more detailed relation for a spherical nucleus is5    ρn rn2 1 4π , (6) τ= 15 kT (rn )fA (rn )Vth P fs (rH ) where fs (rH ) is the mass loss rate per unit area averaged around the cometary orbit, Vth is the speed of the outflowing gas, P is the instantaneous nucleus rotation period and 0 ≤ kT ≤ 1 is the “dimensionless moment arm” for the torque. Physically, kT is the fraction of the outflow momentum that exerts a torque on the nucleus. Limiting values are kT = 0 for isotropic outflow and kT = 1 for purely collimated, tangential outflow.

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Amazingly, we now possess good enough data to detect rotational period changes in comets, as shown in Fig. 3. Even more amazingly, the data are consistent with τ ∝ rn2 as expected from dimensional considerations; large nuclei are relatively unaffected by outgassing torques while small ones can be strongly affected. The empirical relation is

r 2 n , (7) τ ∼ 100 1 km with τ in years and rn in km. This relation is strictly applicable only to comets with orbits like those of the objects in Fig. 3, i.e., SPCs with perihelia in the range 1 to 2 AU, but it is sufficient to show that the lifetime to spin-up can be very short. The empirical median dimensionless moment arm is kT = 0.007. The very short subkilometer cometary nucleus spin-up times explain why sub-kilometer nuclei are rare. Larger comets cannot be so easily destroyed by rotational instabilities and linger until they are removed by the loss of volatiles or scattering by a planet (Fig. 4). The end state of volatile loss should

Fig. 3. Empirical spin-up times for comets as a function of radius. Filled circles indicate comets where spin changes are detected, while diamonds indicate that only upper limits to spin changes are available. Adapted from Ref. 5.

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Fig. 4. Model lifetimes for comets as a function of radius including the effects of volatile loss and spin-up instability. From Ref. 5.

be a dead comet, with an asteroid-like physical appearance but moving in the orbit of a comet. Such objects are known, but they are not as abundant as estimates of the relevant timescales would suggest, presenting a puzzle for future investigation.

3. 3.1.

Asteroids Spectral and compositional gradients

Asteroids in the main belt exhibit a wide range of surface properties. They are radially segregated from the inner edge (∼2 AU), where highly metamorphosed S-types (S for “stony”, having optically reddened surfaces and albedos ∼0.15) dominate, to the outer edge near

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3 AU, where less heated C-types (C for “carbonaceous”, colorimetrically more neutral, with low albedos ∼0.05) are more common. The gradient is too strong to be explained by the decrease of radiation equilibrium temperature from 2 to 3 AU. An early explanation for this compositional stratification invoked the varying influence of induction heating in an early, highly magnetic phase of the Sun. It is more widely accepted that strong heating of asteroids occurred through the decay of 26 Al (half-life 0.7 Myr, see Ref. 9). One way to cook inner belt asteroids more thoroughly than outer belt objects is to delay the accumulation of the latter relative to the former. In this picture, the radial gradient results from early-forming inner-belt objects being more strongly heated by 26 Al trapped in minerals relative to late-forming outer belt asteroids where the 26 Al has already decayed away. This explanation is not wholly unreasonable, because longer formation times automatically occur at larger distances in a protoplanetary disk whose density (and hence collision rate) falls with radius. Perhaps the asteroid belt compositional gradient simply reflects a formation time gradient. Various hydrated minerals in meteorites from the outer belt indicate chemical alteration reactions in liquid water, presumably from radioactively melted ice. Recent discovery of the so-called “main-belt comets” (see what follows) suggest that water ice has survived in some objects, preferentially those in the outer belt at 3 AU. The contrast with inner-belt S-types, some of which have been heated to 800◦ C, is extreme. Isotopic measurements of meteorites provide surprising evidence of a more complicated story. An isotopic dichotomy (Fig. 5), as opposed to a continuous spread, suggests that the asteroids formed in two spatially distinct reservoirs experiencing different thermal histories.8 The two groups also appear to be different in age, with the carbonaceous chondrites forming 1–2 Myr after the non-carbonaceous chondrites. The terrestrial planets (Earth, Moon and Mars — we have no known samples of Mercury or Venus) isotopically resemble the LL chondrites (S-type residents of the inner asteroid belt) and the HEDs (ejecta from large asteroid Vesta, semi-major axis 2.4 AU). Carbonaceous chondrites are more associated with the outer belt, where the C-types and main-belt comets reside. One idea is that the two reservoirs formed separately on either side of Jupiter’s orbit. Runaway growth then scattered and implanted material from beyond its orbit into the outer asteroid belt. However, it is difficult to see

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Fig. 5. Fractional isotopic concentrations in titanium and chromium show a bimodal distribution. Adapted from Ref. 8.

how any implantation mechanism would lead to fine compositional distinctions across the minuscule ∼1 AU width of the asteroid belt. 3.2.

Active asteroids

Figure 6 shows the distribution of asteroids and comets in the semimajor axis vs. eccentricity plane. Shown in red are a set of newlyidentified objects known as “active asteroids” because, while their orbits are asteroidal, their physical appearances resemble comets because of the intermittent ejection of dust. In addition to being a surprising and newly-identified population, the active asteroids are scientifically interesting because they result from an amazing suite of different physical processes capable of ejecting dust. 3.2.1.

Impact

Collisions underlie some of the active asteroids. Collision velocities in the asteroid belt, ΔV ∼ 5 km s−1 , are a significant fraction of the

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Fig. 6. Distribution of comets (blue dots) and asteroids (yellow dots) in the semi-major axis vs. eccentricity plane. Red circles show active asteroids, defined as objects with the orbits of asteroids but physical appearances like comets, resulting from mass-loss. Dashed, vertical lines mark the orbits of Mars and Jupiter, and the location of the 2:1 mean motion resonance with Jupiter. The diagonal arcs show the loci of points having aphelion equal to the perihelion distance of Jupiter and the perihelia equal to the aphelion of Mars. Objects above the arcs cross either the orbits of Mars or Jupiter and are, consequently, short-lived.

orbital velocity, VK ∼ 20 km s−1 , reflecting the non-negligible average inclinations (∼15◦ ) and eccentricities (∼0.15) of the asteroids. The kinetic energy of impact is more than enough to vaporize the projectile provided speed V > (2H)1/2 , where H is the latent heat of vaporization. For example, with representative H = 2 × 106 J kg−1 , we see that collisions with V > 2 km s−1 should involve substantial vaporization. With ΔV also being comparable to or greater than the speed of sound in rocks, the effect of impact is to shock process, vaporize and pulverize the asteroids, releasing a cascade of debris into the interplanetary space. 354P/(2010 A2)10 is the first identified impact-produced active asteroid. Although collisions have long been known as the main agent shaping the asteroid size distribution (an inverse radius3 power law produced by shattering into smaller

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and smaller pieces), the interval between major collisions per object is enormous (107 years in the case of 354P11 ). It is startling to be able to detect such rare events in nearly real-time, and a reminder of the vast numbers of small asteroids and collisions ongoing in the belt. 3.2.2.

Rotational instability

Whereas rotational instability in comets results from outgassing torques, in asteroids it is the “YORP” torque that plays the same role. The YORP torque results from the anisotropic radiation of infrared photons from an irregularly shaped, anisothermal body. It is ∼105 weaker than outgassing torques and so takes ∼105 times longer to act, on objects of a given size. Despite this, the time needed to approach rotational instability (a few to 10 Myr for a 1-km diameter asteroid at 3 AU) is still very short compared to the collisional lifetimes of these bodies. Several active asteroids are products of rotational instability, including 313P. Recent discoveries of main-belt asteroids which eject mass or even spontaneously fragment show that rotational break-up occurs and perhaps dominates asteroid destruction at small scales. 3.2.3.

Thermal destruction

Differential thermal expansion creates stresses large enough to crack rocks. The fractional expansion resulting from temperature change ΔT is αΔT , where expansivity α ∼ 10−5 K−1 is typical. The resulting strain is S ∼ Y αΔT , where Y is Young’s modulus and a multiplier of order unity called Poisson’s Ratio is ignored. Rock values of Y ∼ 1010 N m−2 to 1011 N m−2 are so large that huge stresses, S ∼ 105 ΔT to 106 ΔT (N m−2 ), can be developed. These stresses can overwhelm the strengths of the rocks, which are especially weak in tension (e.g., the tensile strength of basalt is only ∼ 4 × 106 N m−2 ). Thermal fracture operates most effectively on length scales comparable to the diurnal skin depth (i.e., where the temperature gradient is steepest) which, for a material of diffusivity κ on a body rotating with period P is

∼ (κP )1/2 . For solid rock, κ ∼ 10−6 m2 s−1 and a typical rotation period P = 5 h, ∼ 15 cm. Small rocks are thus strongly affected while larger boulders on asteroids are often surrounded by skirts of

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debris produced by thermal cracking of their surfaces owing to the day–night temperature cycle. Asteroid (3200) Phaethon, which is the source of the Geminid meteoroid stream, is the first object showing convincing evidence of particle ejection caused by thermal fracture. Phaethon has a very asteroidal Tisserand parameter (Eq. (1)) TJ = 4.5 and an orbit that is distinct from the comets in being completely decoupled from Jupiter. The perihelion is a remarkably small q = 0.14 AU, at which distance the sub-solar surface temperature approaches 1,000 K, while the local midnight temperature might be only 400 K, giving ΔT ∼ 600 K every rotation period of 3.5 h). Phaethon emits dust particles and sports a comet-like tail when near perihelion. The distribution of perihelion distances of the asteroids shows a depletion (lower curve in Fig. 7) relative to the expectation based on dynamical models (upper curve). The depletion begins at surprisingly large perihelion distances q ∼ 0.5 AU (peak sub-solar temperature ∼500 K) and affects C-types more than S-types. While currently lacking a widely-held explanation, this near-Sun depletion is very plausibly a result of thermal disintegration.

Fig. 7. Observed and expected numbers of near-Earth objects as a function of the perihelion distance. The two curves diverge at perihelion distances 0.5 AU, conceivably indicating an unknown error with the dynamical model but, more likely, a physical destruction of asteroids with small perihelia. Adapted from Ref. 13.

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3.2.4.

Sublimation

Some active asteroids, including the prototype object 133P/ Elst-Pizarro,3 appear to be driven by sublimation of embedded but near-surface ice; these are the main belt comets (MBCs) The evidence for this remains indirect, since sublimated gas production rates are orders of magnitude too small to be detected by existing spectroscopic techniques (JWST might change this), but nevertheless the distinctive properties of these objects are compelling. Most distinctive is the reappearance of dust activity near perihelion in different orbits, which establishes that the activity is thermally driven just as in “normal” comets from the Kuiper belt. The big difference between the normal comets and the active asteroids is that the latter have relatively circular orbits at 3 AU, and surface temperatures that are far too high (the subsolar temperature at 3 AU is ∼225 K) for the ice to survive for even a tiny fraction of their ∼billion year collisional destruction ages. For example, Fig. 2 shows that water ice exposed at the sub-solar point on an asteroid at 3 AU sublimates at fs ∼ 3×10−5 kg m−2 s−1 . If the density is ρ = 103 kg m−3 , a patch of ice would shrink at the rate dr/dt = fs /ρ = 3 × 10−8 m s−1 . This rate sounds small (coincidentally, it is about the same as the peak rate of a child), but a 1-km radius asteroid would, in the absence of intervention, last only ∼103 years given this dr/dt. We surmise that the ice, if present, must be stabilized against sublimation losses. A simple layer of dirt a few meters thick suffices to suppress the temperature at the buried ice surface and to inhibit the flow of sublimated gases to the surface. The scenario, then, is that MBCs are ice-containing asteroids in which the ice remains buried below the physical surface under a fragmented layer of refractory debris. Disturbances of this layer, by small impactors or perhaps by surface avalanches induced by rotational instability, occasionally expose the ice to the heat of the Sun, causing sublimation and the production of a temporary coma. After some time, the active surface again becomes clogged by refractory material and the ice recedes beneath the physical surface, stopping further sublimation. A key parameter in this conjectural model is the “duty cycle”, the fraction of the total time spent in the active state. Measurements show that the duty cycle must be 6:1 in Ref. 1; 5:3.1 in Ref. 7; 10:1 in Ref. 2; 3:1 in Ref. 8; >4.63 in Ref. 4; from 3.5 to 10.3 in Ref. 5; >5:1 in Ref. 3; 6 ± 1:1 in Ref. 9.

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Oblate

Elongated

Fractal

Fig. 2.

Some of the morphologies that have been suggested for 1I/’Oumuamua.

did not show any dust or gas outflow characteristic of cometary activity.1,2,6,13 The A/ denomination did not last long either because its orbit was unquestionably hyperbolic, like none of the solar system objects. Its current name is 1I/2017 U1, where I/ refers to all interstellar objects, whether cometary or asteroidal in nature. It is also known as 1I/’Oumuamua, that comes from the Hawaiian  ou (reach out for) and mua (first, in advance of). Despite the surprise, the arrival of this first interstellar visitor was not unexpected. On August 30, 2019 a second interstellar interloper was detected by amateur astronomer and optical engineer Guennadi Borisov, using a homemade 0.65 m telescope. Figure 3 shows 2I/Borisov’s trajectory. The detections of 1I/’Oumuamua and 2I/Borisov have opened a new era in astronomy because never before have we been able to study “up close” objects from outside our solar system. In Section 2, we will see that, even more extraordinary, these objects most likely originate from extrasolar planetary systems and have remained largely unchanged since their ejection, like time capsules of their planetary system most distant past. 2.

Interstellar Planetesimals are a Byproduct of Planet Formation and Evolution

Stars form from the collapse of dense regions of molecular clouds. A natural byproduct of this process is the formation of protoplanetary disks, where planet formation takes place.15–17 The dust particles in these disks, approximately 0.1 μm in size, are

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Saturn’s orbit

2I at discovery Aug. 30, 2019 Jupiter’s orbit

Sep. 30

2I/’Borisov Pre-encounter velocity = 32.2 km/s

Oct. 30 Mars

Nov. 30 Venus

e = 3.357 a = –0.851 AU q = 2.01 AU i = 44.05°

Mercury

Sun

Dec. 30 Earth

Jan. 30, 2020

Fig. 3. 2I/Borisov’s trajectory as it entered the inner Solar System (dashed line indicates the section that lies below the ecliptic plane). The open circles show the position of the planets at the time of 2I/Borisov’s discovery. Adapted from Ref. 14.

strongly coupled to the gas, resulting in small relative velocities and collisional energies that, together with “sticky” microphysical processes (like van der Waals and electromagnetic forces), result in their efficient collisional growth into cm-sized bodies;18–20 these pebbles eventually grow into km-sized planetesimals (see Fig. 4) and the processes by which these can grow into planetary embryos and planets, via collisions and gravitational interactions, is fairly well understood (Ref. 21, and references therein). However, the intermediate stage by which cm-sized pebbles grown into km-sized planetesimals poses several challenges, known as the m-sized barrier. As the cm-sized particles grow and become less coupled to the gas, their relative velocities and collisional energies increase, resulting in collisions that, rather than leading to efficient growth, lead to inefficient sticking, bouncing, or fragmentation22 ; in addition, because the particles are still coupled to the gas, they experience gas drag that results in short inward drift timescales, limiting significantly their lifetime in the disk and, consequently, their opportunity to grow to sizes unaffected by gas drag.18,23

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Fig. 4. Snapshots from a numerical simulation of planetesimal formation in a protoplanetary disk, viewed from above the plane. Credit: Michikoshi & Kokubo (NAOJ).

Giant planets can form if the planetesimal growth proceeds fast enough for the embryos to accrete gas from the protoplanetary disk before it dissipates. In the case of the solar system, it is thought that before 10 Myr after the Sun was formed, while the Sun was still embedded in its maternal stellar cluster, and before the gas in the primordial protoplanetary disk dispersed, Jupiter and Saturn formed and scattered planetesimals in the Jupiter–Saturn region to large distances; a fraction of this material had their perihelion lifted beyond the influence of the giant planets due to external perturbations by the stars and the gas in the star cluster, populating the Oort could; but most of the scattered material (75–85%; Ref. 24) was ejected into interstellar space. In systems where giant planets have not formed, the smaller-mass planets may not clear their feeding zone and continue to collide on longer timescales. After the gas is gone, giant planet formation comes to an end but the collisional growth of other planets may continue.25 At this point, a process that might have started in an orderly fashion quickly transitions into a fairly chaotic state. The swarms of planetesimals will interact with the growing planets and this can cause their migration and trigger episodes of dynamical instability and orbit readjustment, increasing the rate of collisions (Ref. 26; see Ref. 27 for a review).

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During these gravitational instabilities, planetesimals can be scattered in or scattered out. In the former case, they can become a source of volatiles to the terrestrial planets region28,29 where the collisional growth of planets is still continuing. In the latter case, it can result in the ejection of a significant fraction of planetesimals into the outer planetary system or into interstellar space. In fact, in the solar system, there is evidence that the planetesimal belts were heavily depleted leaving an asteroid and Kuiper belts that contain only a small faction of their original population. Evidence for a massive primordial Kuiper belt is the existence of KBOs larger than 200 km, whose formation by pairwise accretion must have required a number density of objects about two orders of magnitude higher than today. Evidence for a massive primordial asteroid belt comes from the minimum mass solar nebula, showing a strong depletion in the AB region unlikely to be primordial. Even though the efficiency of planetesimal ejection is very sensitive to the planetary architecture and its dynamical history, dynamical models (like those shown in Fig. 5) indicate that planetesimal clearing processes are a natural outcome of the planet-formation

Fig. 5. Numerical simulations of planet formation by Raymond et al.31,32 The planetary system starts with three giant planets and an inner and outer planetesimal belts. The panels show two snapshots of its dynamical evolution, encompassing a gravitational instability that ejects the majority of the planetesimals. Numerical simulations show that these types of planetesimal-clearing events, of which the Solar system also shows evidence, happen under a wide range of planetary configurations, enriching the interstellar medium with planetesimals. The insert to the top right shows the dust production: the solid line, corresponds to the emission from the dust as a function of wavelength and the dashed line, to the emission from the star.

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processes under a wide range of architectures (Ref. 30 and references therein). These processes enrich the interstellar medium with ejected planetesimals.

2.1.

Debris disks provide observational evidence that planetesimal formation is common and that the planetesimal belts are depleted with time

The processes described above trigger numerous collisions among planetesimals left in the disk, between planetesimals and the growing planets, or even among planets, and these collisions produce dust. Dust production also takes place in the outer disk where Pluto-sized objects stir the planetesimal swarms triggering mutual collisions.33 The timing, duration and amount of dust released in all these collisional processes vary widely: some of the disk collisional activity is in a pseudo-steady state during a long period,34 while other events associated with individual collisions are stochastic and shortlived.35–37 The properties of the dust also differ very significantly: some of the colliding bodies might have formed in situ, while others might have originated in different regions of the disk, inside or outside the different icelines, leading to different parent-body compositions; some of the colliding bodies might be pristine, while others might have been processed; in addition, some of the collisions will be very energetic, altering the composition of the debris, while others will be of low energy, with the composition of the debris dust tracing the parent bodies. The interpretation of the dust observations is therefore complex and we are still learning to unveil the clues that are hidden in the dust of planetary systems in the making. But we know that these types of collisions are the origin of the circumstellar dust observed around stars older than a few Myr. This is because once the gas of the protoplanetary disk is gone, the primordial dust is subject to more energetic collisions and to Poynting–Robertson drag, and both processes limit the lifetime of the dust particles to the order of 0.01–1 Myr. Poynting–Robertson drag is a relativistic effect that results from the interaction of the dust particle with the stellar radiations and can be intuitively understood because in the reference frame of the particle, the stellar radiation appears to come at a small angle forward from the radial direction (due to the aberration of

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light) that results in a force with a component against the direction of motion; in the reference frame of the star, the radiation appears to come from the radial direction, but the particle remits more momentum into the forward direction due to the photons blueshifted by the Doppler effect, resulting in a drag force.38 This means that the circumstellar dust observed around stars older than a few Myr old is not primordial, i.e., from the cloud of gas and dust where the star was born, but a debris dust that is replenished as a result of ongoing dust production. This dust is critically important to assess whether planetesimal formation is a common process because we cannot directly observe extrasolar planetesimals, like we do in the solar system, but when extrasolar planetesimals collide, they produce dust that can have a collective surface area large enough to allow its detection and characterization, shedding light on the underlying planetesimals population. Debris disks are therefore evidence that planetesimal formation is taking place in other systems (see Ref. 39 and references therein for a review). Figure 6 shows the frequency of debris disks around stars of different stellar types, derived from Spitzer and Herschel debris disk surveys. At 24 μm, the surveys are sensitive to warm dust at approximately 150 K, that for a solar-type star would be the temperature of dust particles located at 3–5 AU, a distance similar to that of the asteroid belt. At 70–100 μm, the surveys are sensitive to cold dust at around 50 K that corresponds to a distance of 30 AU, similar to the Kuiper belt. It is important to note that these surveys are limited by sensitivity. At 24 μm, the surveys are only able to detect warm dust in systems that contain more than 100 times the amount of warm dust in the solar system. While at 70 and 100 μm, the detection limit is 10–20 times the amount of cold dust in the solar system. This means that these surveys might only have been able to detect the tip of the iceberg. These surveys indicate that planetesimal disks exist around stars with luminosities that differ by several orders of magnitude; also around stars with a wide range of metallicities and with and without binary companions. And it is from these findings that we can infer that debris disks not only indicate that planetesimal formation is taking place in other systems, but that planetesimal formation is a robust process that can take place under a wide range of conditions. The Spitzer and Herschel debris disks surveys also allow to study how the debris disk frequency and the dust-to-star flux ratio depend

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Detection limit: >100x dust content in Solar system

Detection limit: >(10-20)x dust content in Solar system

Spitzer (FEPS)

Spitzer (FEPS)

24 µm

70 µm

150 K, 3-5 AU

Freq.

0.16 0 A

F

G

K

100 µm 50 K, 30 AU

0.32 Freq.

Young stars (100 Myr)

Freq.

Luminosity (Lsun) 5–25

0.2 0.1 0 A

F

G

K

M

0.4 0.3 0.2 0.1 0 A F G K M A F G K M

Fig. 6. Debris disk frequency derived from Spitzer and Herschel debris disks surveys for different stellar types. The mass and luminosity ranges corresponding to the different stellar types are shown below the top, left histogram. The diagrams correspond to: (left) warm dust emission at 24 μm; (right) cold dust emission at 70 and 100 μm; (top) young stars with ages 100 Myr. The debris disk frequencies are based on results from Refs. 40–45. Debris disks are found around stars with a wide range of metalicities and luminosities, in single and binary systems; because debris disks are evidence of planetesimals, this indicates that planetesimal formation is a robust process that can take place under a wide range of conditions.

on stellar age and, given that we cannot stare at a given system for millions of years, this is a proxy of how the dust-production rate evolves (see Ref. 34 for a review). From the left panels in Fig. 7, we can infer that the dust-producing planetesimals that are located closer to the stars (and produce dust that emits at 24 μm) disappear on a much shorter timescale than the planetesimals in the outer disk producing dust that can be observed at longer wavelengths (right panel). The reason why it is more common to find cold dust than warm dust around mature stars is because the dynamical times in the inner region of the disk are shorter than in the outer region and this makes planetesimals in the inner region collide more frequently and erode more rapidly, causing the production of warm dust to decay as 1/t. Another interesting aspect that is observed is that over the 1/t envelope there is a lot of dispersion, indicating that dust production in large stochastic collisions may have played an important role in the

Interstellar Planetesimals Detection limit: >100x dust content in Solar system

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Detection limit: >(10-20)x dust content in Solar system

Spitzer (FEPS)

Spitzer (FEPS)

24 µm

70 µm

150 K, 3-5 AU

100 µm 50 K, 30 AU

1.04–0.8 Msun 1.5–0.45 Lsun

Freq.

τ~300 Myr

00.000

Fluxdust/Fluxstar

FGK

Herschel (DEBRIS)

FGK

10.000 1.000 0.100 0.010 0.001 0.1

1.0

10.0

Age (Gyr) No evolution in Gyr, expect the most massive (τ~300 Myr) Log (Stellar Age)

Fluxdust/Fluxstar

A

1.4–2.1Msun 5–25 Lsun

τ~150 Myr

Age (Myr)

Fig. 7. Debris disk frequency and dust-to-star flux ratio as a function of stellar age derived from Spitzer and Herschel debris disks surveys. The diagrams correspond to: (left) warm dust emission at 24 μm; (right) cold dust emission at 70 and 100 μm; (top) FGK-type stars; (bottom) A-type stars. Based on results from Ref. 40. Dust production decays with time due to the erosion of the dustproducing planetesimals, more notable in the inner region where the dynamical times are shorter. The dispersion of the bottom panel maybe due to large stochastic collisions.

early evolution of the planetary systems (see bottom left panel from Su et al.41 The cold dust, on the other hand, shows no significant evolution on Gyr times scales. The wavy size distributions of the asteroids are a proof that this collisional activity played an important role in the early solar system history, in addition to the depletion of the planetesimal belts due to dynamical ejection discussed earlier.46,47 These studies use the current size distribution of the asteroid belt, together with other observational constraints and collisional evolution models, to calculate the size distribution in the “primordial” asteroid. They found that it would have been established early on as a result of a period of collisional activity before Jupiter formed (few Myr), and a period of collisional activity triggered by the planetary embryos (10–100 Myr). Similarly, the size distribution of the small objects in the Kuiper belt can help constrain its primordial size distribution.48

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To summarize, the presence of debris disks indicate that planetesimal formation is common and can take place under a wide range of conditions. The discovery of thousands of extrasolar planetary systems is evidence that, in some cases, this has led to the formation of planets in a wide range of planetary architectures,49 and dynamical models have shown that the dynamical history of these planetary systems generally involve planetesimal-clearing events. This has led to the idea that these ejected planetesimals, that would be predominantly icy because the majority would have formed outside the snowline in their parent systems, are a component of the interstellar medium. 2.2.

The unbinding of exo-Oort cloud objects enrich the interstellar medium with planetesimals

In the Solar System, the Oort cloud is thought to have formed due to the interplay of planetary scattering and external forces: the forming giant planets scattered the planetesimals in this region out to large distances where they were subject to external influences, like the slowly changing gravitational potential of the cluster, the Galactic tides and the stellar flybys, with different models favoring different perturbers. These external influences would have caused the perihelion distances of the scattered planetesimals to be lifted to distances 10 AU, where the planetesimals were no longer subject to further scattering events but were also safe from complete ejection and thus remained weakly bound to the Solar System, forming the Oort cloud (see, e.g., Ref. 50). Some authors argue that the Oort cloud formed while the Sun was in its birth cluster. Under this scenario, the main perturbers would be the stars and gas in the cluster. These models, however, fail to account for the circularization of the orbits due to the cluster gas (that would impede the comets to be scattered out into the Oort cloud,51 and for the stripping of the outer parts of the Oort cloud (≥3 · 104 ) by the cluster gravitational potential and neighboring stars. To account for these caveats, other authors argued that the Oort cloud formed during the late dynamical instability of the solar system, about 0.5 Gyr after it formed. The caveat of these latter models is that this process is not sufficiently efficient (by an order of magnitude) to account for the estimated number of bodies in the Oort cloud (derived from the flux of long-period comets) based on the estimated

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mass in planetesimals that would have remained ∼0.5 Gyr after the solar system formed, i.e., after most of the protoplanetary disk was dispersed.51 Even though the formation of the Solar System’s Oort cloud has still many unknowns, we can expect exo-Oort clouds to form around other stars as the result of the interplay of planetary scattering and external forces that would lead to the lifting of the periastrons of bodies initially orbiting closer to the star.52 Indirect evidence of the presence of a reservoir of comets around other stars are the debris disk systems. There is also evidence that some of these exocomets have been scattered into the inner regions of these systems, as suggested by the observation of variable absorption gas features in several of these debris disks,53,54 and by the dips in the lightcurve of some Kepler sources.55 The reason why we are interested in these exo-Oorts clouds as a potential source of interlopers like 1I/’Oumuamua is because dynamical models show that, over the lifetime of their parent stars, these weakly bound objects are subjected to ejection due to Galactic tides, post-main sequence mass loss, and encounters with other stars or with giant molecular clouds.56–58 For example, for the solar system, Hanse et al.59 indicated that over the Sun’s main sequence, the Oort cloud will lose 25–65% of its mass due mainly to stellar encounters, with a second stage of Oort cloud clearing to be triggered by the onset of mass loss as the Sun enters the post-main sequence stage.57 These ejected objects will contribute to the population of free-floating material and this contribution is expected to be more significant in the Galactic bulge than in the disk or the halo of the Galaxy (due to the more frequent stellar encounters in the former), and in the oldest regions than in the youngest regions (due to the timescale associated with the clearing processes58 ). The capture by the solar system of one of these ejected exoOort cloud objects today is highly unlikely due to their expected high relative velocity with respect to the Sun, but may have been possible when the Solar System was still embedded in its maternal birth cluster,60,61 with the higher transfer efficiencies being enabled by the lower relative stellar velocities, an order of magnitude lower than today. There is therefore the possibility that we have already observed, or will be able to observe, one of these objects captured from the interstellar medium, but its origin beyond the solar system will likely remain uncertain.

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Size Distribution of Interstellar Planetesimals

Needless to say that with only two interstellar objects detected it is not possible to constrain the size distribution of the population. Some of the studies that will be mentioned in what follows adopt a mono-size or an equilibrium size distribution n(r) ∝ r −3.5 (see Ref. 62). The only small-body population that can be studied in any detail is that of the solar system. Assuming initially that the source of the interstellar objects are planetesimal disks, it makes sense that the range of possible distributions should encompass that of the small body population in the early Solar System, that can be inferred from observations and models. However, it is a challenge for the latter to reproduce simultaneously the observed slopes for the large and small objects and the break radius because this requires to take into account the full dynamical history of the Solar System. It is also the case that other planetary systems will likely have experienced a wide range of dynamical and collisional histories and, as a consequence, the size distribution of their ejected bodies will depend significantly on the degree of dynamical/collisional evolution at the time of the ejection. This is why in the calculations of the number density of interstellar objects that will be discussed in what follows, instead of the equilibrium size distribution n(r) ∝ r −3.5 , informed by theoretical coagulation and accretion models, we consider a wide range of size distributions characterized by a broken power law of indexes q1 = 2−3.5 (in the small size end), q2 = 3−5 (in the large size end), break radius rb = 3−90 km, rmin ≈ 1 μm and rmax ≈ 1,000 km.

4.

Number Density of Interstellar Planetesimals

We need to think of interstellar planetesimals (that originate, e.g., from planetary systems in the making or from the release of exoOort clouds) as another component of the interstellar medium. It was therefore not a surprise that one of these objects would eventually cross paths with the solar system. And because of the velocity of the Sun with respect to the Local Standard of Rest (LSR; vLSR = 16.5 km s), it would appear as an interstellar interloper on a hyperbolic trajectory, making it clearly distinguishable from other

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solar system objects. Therefore, the detection of 1I/’Oumuamua, with a clearly hyperbolic orbit (eccentricity e = 1.197, semi-major axis a = −1.290, perihelion q = 0.254, and inclination i = 122.6) and high pre-encounter velocity (26.22 km s−1 , with U, V, W = −11.325, −22.384, −7.629 km s−1 ; Ref. 63) had been been anticipated for decades. In fact, McGlynn and Chapman64 had argued that the lack of extrasolar comet detections was actually problematic because, based on the number density of stars and expected contribution to the ejected planetesimal population, the number density of interstellar objects should be high enough to have a significant number entering the Solar System detected. Jewitt65 suggested to use PanSTARRS to constrain their number density. Based on current knowledge of star and planet formation, Moro-Mart´ın et al.66 predicted the number density of interstellar objects in the Galaxy to be so low that the detection of interstellar comets would require the deep survey capability of the Vera Rubin Observatory (LSST), able to detect smaller objects at greater distances. Engelhardt et al.67 reached a similar conclusion a few months prior to 1I/’Oumuamua’s detection in the much shallower PanSTARRS data. The visitor was expected, but it had arrived too early.

4.1.

Number density inferred from 1I/’Oumumua’s detection

Several studies were carried out to estimate the inferred number density of interstellar planetesimals from the detection of 1I/’Oumuamua, adopting different estimates for the detection volume, and what this would imply regarding the contribution per star and how this compares to expectations. These studies generally agree that the inferred number density is higher than expected in the context of a range of plausible origins. Some of the inferred number densities were the following: 0.1 AU−3 = 8 · 1014 pc−3 (see Refs. 1 and 2), 0.012–0.087 AU−3 = 1−7 · 1014 pc−3 (Ref. 68), 0.012 AU−3 = 1 · 1014 pc−3 (Ref. 69) and R1 Nr > R2

) ( )ƒ 1012

M∗ M

enc (M∗ ) dM∗ , eject

0.08–1 MSun

Nexo-OC ~ 1.7 1013 pc–3 1–8 M Sun

Number density of stars in Cumulative number with ejection due the main sequence sizes to encounters (based on solar enc system observations ƒeject (M∗ ) = 0.5 and on accretion and (based on collisional models). dynamical simulations; Hanse+ 2018)

Nexo-OC ~ 1.3 1012 pc–3

Contribution from post-main sequence mass loss: 8M S N PM exo -OC =

∫

ξ(M∗) ƒPM S (M∗ ))

(

Nr > R1 Nr > R2

) ( )ƒ 1012

M∗ M

PMS (M∗ ) dM∗ , eject

1-8 M Sun

Nexo-OC ~ 1013 pc-3

1M

Number density of stars that have left the main sequence

Cumulative number with sizes

due to post-main sequence mass loss 51.5% 74.7% 82.7% 85.3% 87.3% 87.8% 88.3% 89.0% 3 M 4M 1M 2M 5M 6M 7M 8M (based on dynamical simulations; Veras+ 2014)

Fig. 9. Estimate of the number density of interstellar planetesimals expected from the release of exo-Oorts objects due to stellar encounters and postmain sequence mass loss, compared to the number density inferred from 1I/’Oumuamua’s detection.71 Based on Ref. 75, M∗ is the stellar mass and ξ(M∗ ) is the number density of stars134 ; fPMS (M∗ ) is the fraction of stars that have reached the post-main sequence stage, star formation rate  a constant   N assuming M∗ is the cumulative numover the age of the Galactic disk. NrR1 1012 M  rR2

ber of bodies with sizes equal or larger than 1I/’Oumuamua’s, where R1 = 0.08 km (1I/’Oumuamua’s adopted effective radius) and R2 = 1.15 km; here, we are assuming that for a given exo-Oort cloud, the number of bodies with diameter larger than 2.3 km is similar to that of the Solar System’s Oort cloud, approxi N mated to be 1012 , scaled to the mass of the parent star. To calculate NrR1 , rR2 we assume that the size distribution can be approximated as the broken powerlaw, based on Solar System observations and on accretion and collisional models. PMS enc feject (M∗ ) and feject (M∗ ) are the efficiency of ejection of exo-OC bodies due to post-main sequence mass loss and stellar encounters, derived from dynamical models in Refs. 58 and 59, respectively.

Based on long-period comet observations, it is estimated that the solar system’s Oort cloud has an isotropic distribution with perihelion q  32 AU and inner and outer semi-major axes of aOC min ∼ 3 OC 5 3 · 10 and amax ∼ 10 AU, respectively. Following Hanse et al.,59 we

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scale the inner and outer edge of a given exo-Oort cloud to the Hill radius of its parent star in the Galactic potential. The two processes expected to dominate the exo-Oort clouds clearing are: (1) post-main sequence mass loss, for the stars in the 1–8 M mass range that have reached this stage of stellar evolution; and (2) stellar encounters, for the stars that are still on their main sequence. Their ejection efficiencies depend on where these objects are located and are based on dynamical models in the literature. The resulting number density from the calculations described above are listed on the right-hand side of Fig. 9 under “expected from the release of exo-Oort cloud objects”. The number density of interstellar planetesimals expected to be triggered by stellar encounters is ∼3 · 1013 pc−3 and from post-main sequence mass loss (of stars in the 1–8 M mass range) is ∼1013 pc−3 . Again, these values are significantly lower than the number density “inferred from observations” of Nr  R = 0.21 AU−3 ∼2 · 1015 pc−3 .71 In more intuitive units, this means that if we assume that 1I/’Oumuamua is representative of a population that is uniformly distributed, from its detection we can estimate that there are about 10,000 interstellar objects like 1I/’Oumuamua within the orbit of Neptune at any given time, that is a sphere of about 30 AU in radius, while from the ejection of planetesimals from protoplanetary disks or from the release of planetesimals from exo-Oort one would expect up to 100. There are many uncertainties in these calculations but this discrepancy points out that we still have a lot to learn about the population of interstellar planetesimals and their origin. 4.4.

4.4.1.

Proposed solutions for the discrepancy between the inferred and expected number density of interstellar planetesimals 1I/’Oumuamua could have originated in a young nearby system

One of the proposed solutions to address the discrepancy between the inferred and the expected number density of interstellar planetesimals is that 1I/’Oumuamua is not representative of an isotropic distribution of interstellar planetesimals, which could have led to an overestimate of the background density. This would be the case, for

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example, if it is originating from a nearby young planetary system, as suggested by Gaidos et al.69,81 In this case, the ejected population would likely have a highly anisotropic distribution, resulting in large fluctuations in space density. There are several observations that support a young age for 1I/’Oumuamua. One is the color of the object, found not to be as red as the ultra-red bodies in the outer solar system,1 thought to be reddened by space weathering (from cosmic rays and ISM plasma); some authors argue that this suggests that 1I/’Oumuamua has not been exposed to space weathering for Gyr.12,69,70 The second observation is 1I/’Oumuamua’s entering velocity, found to be within 3–10 km s of the velocity of the LSR;63,69,71 the fact that this velocity is similar to that of many young stellar associations also supports that 1I/’Oumuamua has not traveled in interstellar space during Gyr because otherwise dynamical heating (due to passing stars, clouds, spiral arms and star clusters) would have increased its relative velocity with respect to the LSR. Gaidos et al.69 estimate an age of 1 Gyr, while Feng and Jones70 indicate that the probability of observing the object with a velocity