Exoplanetary Atmospheres: Theoretical Concepts and Foundations

291 Pages·2017·4.57 MB·English

by  Kevin Heng

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
Conversationson 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 (cid:13)c 2017 by Princeton UniversityPress
Published by Princeton University Press
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In theUnited Kingdom: Princeton University Press
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ISBN 978-0-691-16697-1 (cloth)
ISBN 978-0-691-16698-8 (paperback)
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Printed in theUnited States of America
10 9 8 7 6 5 4 3 2 1
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:
A Theorist’s Review of Techniques in Astronomy 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 Future missions and telescopes . . . . . . . . . . . . . . . . . . . 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 The radiative transfer equation. . . . . . . . . . . . . . . . . . . 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 Atmospheric retrieval . . . . . . . . . . . . . . . . . . . . . . . . 27
2.8 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 The Two-Stream Approximation of Radiative Transfer 35
3.1 What is the two-stream approximation?. . . . . . . . . . . . . . 35
3.2 The radiative transfer equation and its moments . . . . . . . . . 36
3.3 Two-stream solutions with isotropic scattering . . . . . . . . . . 39
3.4 The scattering phase function . . . . . . . . . . . . . . . . . . . 45
3.5 Two-stream solutions with non-isotropic scattering . . . . . . . 46
3.6 Different closures of the two-streamsolutions . . . . . . . . . . . 49
3.7 The diffusion approximation for radiative transfer . . . . . . . . 51
3.8 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
viii CONTENTS
4 Temperature-Pressure Profiles 56
4.1 Amyriadofatmosphericeffects: Greenhousewarmingandanti-
greenhouse cooling. . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 The dual-band or double-gray approximation . . . . . . . . . . . 57
4.3 The radiative transfer equation and the scattering parameter . . 58
4.4 Treatment of shortwave radiation . . . . . . . . . . . . . . . . . 60
4.5 Treatment of longwave radiation . . . . . . . . . . . . . . . . . . 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 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5 Atmospheric Opacities: How to Use a Line List 74
5.1 From spectroscopic line lists to synthetic spectra . . . . . . . . . 74
5.2 The Voigt profile. . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3 The quantum physics of spectral lines . . . . . . . . . . . . . . . 78
5.4 The million- to billion-line radiative transfer challenge . . . . . . 81
5.5 Different types of mean opacities . . . . . . . . . . . . . . . . . . 88
5.6 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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-
vation equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.4 Self-consistent atmospheric chemistry, radiation and dynamics:
A formidable computational challenge . . . . . . . . . . . . . . . 106
6.5 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7 A Hierarchy of Atmospheric Chemistries 110
7.1 A hierarchy of models for understanding atmospheric chemistry 110
7.2 Equilibrium chemistry with only hydrogen . . . . . . . . . . . . 110
7.3 EquilibriumC-H-Ochemistry: Formingmethane,water,carbon
monoxide and acetylene . . . . . . . . . . . . . . . . . . . . . . . 113
7.4 Equilibrium C-H-O chemistry: Adding carbon dioxide . . . . . . 115
7.5 Equilibrium C-H-O chemistry: Adding ethylene . . . . . . . . . 121
7.6 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Frictionin anatmosphere: MolecularviscosityandRayleighdrag 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 General coupling of physical effects . . . . . . . . . . . . . . . . 167
10.9 Shallow atmospheres as quantum harmonic oscillators . . . . . . 168
10.10 Shallow water systems and exoplanetary atmospheres . . . . . . 174
10.11 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
11 The de Laval Nozzle and Shocks 182
11.1 What is the de Laval nozzle? . . . . . . . . . . . . . . . . . . . . 182
11.2 What are shocks? . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
12 Convection, 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
adjustment schemes . . . . . . . . . . . . . . . . . . . . . . . . . 200
12.5 Asimple “theory”ofturbulence: The scalinglaws ofKolmogorov 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 Problem sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209