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Acaba49a-645E-4700-B27c-Bc00c217b347.Pdf Exoplanetary Atmospheres PRINCETON SERIES IN ASTROPHYSICS Edited by David N. Spergel Theory of Rotating Stars, by Jean-Louis Tassoul Theory of Stellar Pulsation, by John P. Cox Galactic Dynamics, Second Edition, by James Binney and Scott Tremaine Dynamical Evolution of Globular Clusters, by Lyman S. Spitzer, Jr. Supernovae and Nucleosynthesis: An Investigation of the History of Matter, from the Big Bang to the Present, by David Arnett Unsolved Problems in Astrophysics, edited by John N. Bahcall and Jeremiah P. Ostriker Galactic Astronomy, by James Binney and Michael Merrifield Active Galactic Nuclei: From the Central Black Hole to the Galactic Environment, by Julian H. Krolik Plasma Physics for Astrophysics, by Russell M. Kulsrud Electromagnetic Processes, by Robert J. Gould Conversations on Electric and Magnetic Fields in the Cosmos, by Eugene N. Parker High-Energy Astrophysics, by Fulvio Melia Stellar Spectral Classification, by Richard O. Gray and Christopher J. Corbally Exoplanet Atmospheres: Physical Processes, by Sara Seager Physics of the Interstellar and Intergalactic Medium, by Bruce T. Draine The First Galaxies in the Universe, by Abraham Loeb and Steven R. Furlanetto Exoplanetary Atmospheres: Theoretical Concepts and Foundations, by Kevin Heng Exoplanetary Atmospheres Theoretical Concepts and Foundations Kevin Heng PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright c 2017 by Princeton University Press Published by Princeton University Press 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press 6 Oxford Street, Woodstock, Oxfordshire, OX20 1TR press.princeton.edu All Rights Reserved ISBN 978-0-691-16697-1 (cloth) ISBN 978-0-691-16698-8 (paperback) Library of Congress Control Number: 2016950505 British Library Cataloging-in-Publication Data is available This book has been composed in LATEX The publisher would like to acknowledge the author of this volume for providing the print-ready files from which this book was printed Printed on acid-free paper. ∞ Printed in the United States of America 10987654321 Dedications Dick McCray, for showing me that science is to be enjoyed Helmer Aslaksen, who believed in me when no one else did Scott Tremaine, for teaching me how to read the literature Rashid Sunyaev, for giving me a chance to learn from greatness Sara Seager, for inspiring me to think big Willy Benz, for teaching me the business of science Ray Pierrehumbert, for being a fountain of energy and creativity Claudia, my little black cat, the dearest creature I have ever known Felix Hetzenecker-Heng, who forced the first draft 7 months before deadline Stefanie Hetzenecker, my wife and best friend, who stood by me in all times Contents Foreword by Sara Seager xi Preface xiii 1 Observations of Exoplanetary Atmospheres: ATheorist’sReviewofTechniquesinAstronomy 1 1.1 The birth of exoplanetary science . 1 1.2 Transits and occultations . 2 1.3 Radial velocity measurements . 8 1.4 Direct imaging . 11 1.5 Gravitational microlensing . 12 1.6 Futuremissionsandtelescopes . 12 2 Introduction to Radiative Transfer 14 2.1 The optical depth: The most fundamental quantity in radiative transfer................................ 14 2.2 Basic quantities in radiative transfer . 16 2.3 Theradiativetransferequation. 20 2.4 Simple solutions of the radiative transfer equation . 20 2.5 A practical checklist for radiative transfer calculations . 23 2.6 Clouds ................................ 24 2.7 Atmosphericretrieval ........................ 27 2.8 Problemsets............................. 31 3 The Two-Stream Approximation of Radiative Transfer 35 3.1 Whatisthetwo-streamapproximation?. 35 3.2 The radiative transfer equation and its moments . 36 3.3 Two-stream solutions with isotropic scattering . 39 3.4 Thescatteringphasefunction . 45 3.5 Two-stream solutions with non-isotropic scattering . 46 3.6 Different closures of the two-stream solutions . 49 3.7 The diffusion approximation for radiative transfer . 51 3.8 Problemsets............................. 53 viii CONTENTS 4 Temperature-Pressure Profiles 56 4.1 A myriad of atmospheric effects: Greenhouse warming and anti- greenhousecooling.......................... 56 4.2 The dual-band or double-gray approximation . 57 4.3 The radiative transfer equation and the scattering parameter . 58 4.4 Treatmentofshortwaveradiation . 60 4.5 Treatmentoflongwaveradiation . 64 4.6 Assembling the pieces: Deriving the general solution . 65 4.7 Exploration of different atmospheric effects . 67 4.8 Milne’s solution and the convective adiabat . 71 4.9 Problemsets............................. 72 5 AtmosphericOpacities: HowtoUseaLineList 74 5.1 From spectroscopic line lists to synthetic spectra . 74 5.2 TheVoigtprofile........................... 76 5.3 Thequantumphysicsofspectrallines . 78 5.4 The million- to billion-line radiative transfer challenge . 81 5.5 Differenttypesofmeanopacities. 88 5.6 Problemsets............................. 89 6 Introduction to Atmospheric Chemistry 92 6.1 Why is atmospheric chemistry important? . 92 6.2 Basic quantities: Gibbs free energy, equilibrium constant, rate coefficients .............................. 93 6.3 Chemical kinetics: Treating chemistry as a set of mass conser- vationequations ........................... 101 6.4 Self-consistent atmospheric chemistry, radiation and dynamics: A formidable computational challenge . 106 6.5 Problemsets............................. 107 7 AHierarchyofAtmosphericChemistries 110 7.1 A hierarchy of models for understanding atmospheric chemistry 110 7.2 Equilibrium chemistry with only hydrogen . 110 7.3 Equilibrium C-H-O chemistry: Forming methane, water, carbon monoxideandacetylene. 113 7.4 Equilibrium C-H-O chemistry: Adding carbon dioxide . 115 7.5 Equilibrium C-H-O chemistry: Adding ethylene . 121 7.6 Problemsets............................. 122 8 Introduction to Fluid Dynamics 123 8.1 Why is the study of fluids relevant to exoplanetary atmospheres? 123 8.2 What exactly is a fluid? . 124 8.3 The governing equations of fluid dynamics . 124 8.4 Potential temperature and potential vorticity . 128 8.5 Dimensionless fluid numbers . 130 CONTENTS ix 8.6 Problemsets............................. 132 9 Deriving the Governing Equations of Fluid Dynamics 135 9.1 Preamble............................... 135 9.2 The mass continuity equation (mass conservation) . 135 9.3 The Navier-Stokes equation (momentum conservation) . 136 9.4 The thermodynamic equation (energy conservation) . 138 9.5 The conservation of potential vorticity . 139 9.6 Various approximate forms of the governing equations of fluid dynamics............................... 143 9.7 Magnetohydrodynamics. 147 9.8 Problemsets............................. 151 10 The Shallow Water System: A Fluid Dynamics Lab on Paper 155 10.1 A versatile fluid dynamics laboratory on paper . 155 10.2 Deriving the shallow water equations . 156 10.3 Gravity as the restoring force: The generation of gravity waves . 158 10.4 Friction in an atmosphere: Molecular viscosity and Rayleigh drag 160 10.5 Forcing the atmosphere: Stellar irradiation . 162 10.6 Like plucking a string: Alfv´en waves . 163 10.7 Rotation: The generation of Poincar´eand Rossby waves . 165 10.8 Generalcouplingofphysicaleffects . 167 10.9 Shallow atmospheres as quantum harmonic oscillators . 168 10.10 Shallow water systems and exoplanetary atmospheres . 174 10.11Problemsets............................. 175 11 The de Laval Nozzle and Shocks 182 11.1 WhatisthedeLavalnozzle? . 182 11.2 Whatareshocks? .......................... 184 11.3 What does the de Laval nozzle teach us about shocks? . 187 11.4 Applications to, and consequences for, exoplanetary atmospheres 191 11.5 Problemsets............................. 192 12Convection, Turbulence and Fluid Instabilities 196 12.1 Fluid motion induced by physically unstable configurations . 196 12.2 Hot air rises and cold air sinks: Schwarzschild’s criterion for convective stability . 196 12.3 A simplified “theory” of convection: Mixing length theory . 199 12.4 Implementing convection in numerical calculations: Convective adjustmentschemes . 200 12.5 A simple “theory” of turbulence: The scaling laws of Kolmogorov 202 12.6 Water over oil: The Rayleigh-Taylor instability . 204 12.7 Shearing fluids: The Kelvin-Helmholtz instability . 206 12.8 Weather at mid-latitudes: The baroclinic instability . 207 12.9 Problemsets............................. 209 x CONTENTS 13 Atmospheric Escape 211 13.1 TheKnudsennumberandJeansparameter . 211 13.2 Jeansescape ............................. 213 13.3 The classical Parker wind solution . 213 13.4 Non-isothermal Parker winds: Using the nozzle solutions . 216 13.5 Detailed processes: Photo-ionization, radiative cooling and non- thermalmechanisms. 218 13.6 Problemsets............................. 221 14 Outstanding Problems of Exoplanetary Atmospheres 223 AppendixA:SummaryofStandardNotation 228 Appendix B: Essential Formulae of Vector Calculus 233 Appendix C: Essential Formulae of Thermodynamics 235 Appendix D: Gibbs Free Energies of Various Molecules and Re- actions 237 Appendix E: Python Scripts for Generating Figures 240 Bibliography 250 Index 271 Foreword by Sara Seager The field of research of exoplanet atmospheres is flourishing in observation and theory. Both the quality and quantity of observations are increasing rapidly—for a variety of planet types including transiting planets and directly imaged giant planets. With the James Webb Space Telescope on the horizon, the promise of large numbers of a huge variety of exoplanet atmospheres with observations at
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