Protoplanetary Disk Accretion, Hot Jupiter Climates, and the Evaporation of Rocky Planets

165 Pages·2013·5.3 MB·English

From Dust to Dust:
Protoplanetary Disk Accretion, Hot Jupiter Climates,
and the Evaporation of Rocky Planets
By
Daniel Alonso Perez-Becker
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Physics
in the
Graduate Division
of the
University of California, Berkeley
Committee in charge:
Professor Eugene Chiang, Co-chair
Professor Christopher McKee, Co-chair
Professor Eliot Quataert
Professor Geoffrey Marcy
Fall 2013
From Dust to Dust:
Protoplanetary Disk Accretion, Hot Jupiter Climates,
and the Evaporation of Rocky Planets
Copyright 2013
by
Daniel Alonso Perez-Becker
1
Abstract
From Dust to Dust:
Protoplanetary Disk Accretion, Hot Jupiter Climates,
and the Evaporation of Rocky Planets
by
Daniel Alonso Perez-Becker
Doctor of Philosophy in Physics
University of California, Berkeley
Professor Eugene Chiang, Co-chair
Professor Christopher McKee, Co-chair
This dissertation is composed of three independent projects in astrophysics concerning
phenomena that are concurrent with the birth, life, and death of planets. In Chapters
1 & 2, we study surface layer accretion in protoplanetary disks driven stellar X-ray and
far-ultraviolet (FUV) radiation. In Chapter 3, we identify the dynamical mechanisms that
control atmospheric heat redistribution on hot Jupiters. Finally, in Chapter 4, we characterize
the death of low-mass, short-period rocky planets by their evaporation into a dusty wind.
Chapters 1 & 2: Whether protoplanetary disks accrete at observationally significant rates
by the magnetorotational instability (MRI) depends on how well ionized they are. We find
that disk surface layers ionized by stellar X-rays are susceptible to charge neutralization by
condensates—rangingfrom µm-sizeddusttoangstrom-sized polycyclic aromatichydrocarbons
(PAHs). Ion densities in X-ray-irradiated surfaces are so low that ambipolar diffusion weakens
the MRI. In contrast, ionization by stellar FUV radiation enables full-blown MRI turbulence
in disk surface layers. Far-UV ionization of atomic carbon and sulfur produces a plasma
so dense that it is immune to ion recombination on grains and PAHs. Even though the
FUV-ionized layer is 10–100 times more turbulent than the X-ray-ionized layer, mass
∼
accretion rates of both layers are comparable because FUV photons penetrate to lower surface
densities than do X-rays. We conclude that surface layer accretion occurs at observationally
significant rates at radii (cid:38) 1–10 AU. At smaller radii, both X-ray- and FUV-ionized surface
layers cannot sustain the accretion rates generated at larger distance and an additional means
of transport is needed. In the case of transitional disks, it could be provided by planets.
Chapter 3: Infrared light curves of transiting hot Jupiters present a trend in which
the atmospheres of the hottest planets are less efficient at redistributing the stellar energy
absorbed on their daysides than colder planets. Here we present a shallow water model
of the atmospheric dynamics on synchronously rotating planets that explains why heat
2
redistribution efficiency drops as stellar insolation rises. To interpret the model, we develop a
scaling theory which shows that the timescale for gravity waves to propagate horizontally
over planetary scales, τ , plays a dominant role in controlling the transition from small to
wave
large temperature contrasts. This implies that heat redistribution is governed by a wave-like
process, similar to the one responsible for the weak temperature gradients in the Earth’s
tropics. When atmospheric drag can be neglected, the transition from small to large day-night
(cid:112)
temperature contrasts occurs when τ τ /Ω, where τ is the radiative relaxation
wave rad rad
∼
time of the atmosphere and Ω is the planetary rotation frequency. Our results subsume the
more widely used timescale comparison for estimating heat redistribution efficiency between
τ and the horizontal day-night advection timescale, τ .
rad adv
Chapter 4: Short-period exoplanets can have dayside surface temperatures surpassing 2000
K, hot enough to vaporize rock and drive a thermal wind. Small enough planets evaporate
completely. Here we construct a radiative-hydrodynamic model of atmospheric escape from
strongly irradiated, low-mass rocky planets, accounting for dust-gas energy exchange in
the wind. Rocky planets with masses (cid:46) 0.1M (less than twice the mass of Mercury) and
⊕
surface temperatures (cid:38) 2000 K are found to disintegrate entirely in (cid:46) 10 Gyr. When our
model is applied to Kepler planet candidate KIC 12557548b—which is believed to be a rocky
body evaporating at a rate of M˙ (cid:38) 0.1M /Gyr—our model yields a present-day planet
⊕
mass of (cid:46) 0.02M or less than about twice the mass of the Moon. Mass loss rates depend
⊕
so strongly on planet mass that bodies can reside on close-in orbits for Gyrs with initial
masses comparable to or less than that of Mercury, before entering a final short-lived phase
of catastrophic mass loss (which KIC 12557548b has entered). We estimate that for every
object like KIC 12557548b, there should be 10–100 close-in quiescent progenitors with sub-day
periods whose hard-surface transits may be detectable by Kepler—if the progenitors are
as large as their maximal, Mercury-like sizes. KIC 12557548b may have lost 70% of its
∼
formation mass; today we may be observing its naked iron core.
i
A mis padres
ii
Contents
List of Figures v
List of Tables viii
Acknowledgments ix
1 Surface Layer Accretion in Transitional and Conventional Disks: from
Polycyclic Aromatic Hydrocarbons to Planets 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 The Need for Companions . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Companions are Not Enough: The Case for the Magnetorotational
Instability for the Origin of Disk Viscosity . . . . . . . . . . . . . . . 5
1.1.3 The Threat Posed by Polycyclic Aromatic Hydrocarbons to the MRI 6
1.2 Model for Disk Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 X-ray and Cosmic-ray Ionization Rates and Gas Densities . . . . . . 8
1.2.2 Gas Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.3 Chemical Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.4 Properties and Abundances of Trace Species . . . . . . . . . . . . . . 14
1.2.5 Collisional Charging of PAHs and Grains . . . . . . . . . . . . . . . . 17
1.2.6 Numerical Method of Solution . . . . . . . . . . . . . . . . . . . . . . 19
1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.1 Charge Distributions on PAHs and Grains . . . . . . . . . . . . . . . 21
1.3.2 Ionization Fraction vs. PAH Abundance . . . . . . . . . . . . . . . . 21
1.3.3 Degree of Magnetic Coupling: Re and Am . . . . . . . . . . . . . . . 31
1.3.4 Comparison with Previous Work: Ionization Fractions . . . . . . . . . 37
1.4 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.4.1 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2 Surface Layer Accretion in Conventional and Transitional Disks Driven by
Far-Ultraviolet Ionization 45
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2 Model for FUV ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Contents iii
2.2.1 FUV Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.2.2 Total Gas Columns and Densities . . . . . . . . . . . . . . . . . . . . 51
2.2.3 Gas Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2.4 Very Small Grains (VSGs) . . . . . . . . . . . . . . . . . . . . . . . . 52
2.2.5 Polycyclic Aromatic Hydrocarbons (PAHs) . . . . . . . . . . . . . . . 53
2.2.6 H : Photodissociation and Re-Formation on Grains . . . . . . . . . . 54
2
2.2.7 Carbon: Abundance and Ionization Equilibrium . . . . . . . . . . . . 55
2.2.8 Sulfur: Abundance and Ionization Equilibrium . . . . . . . . . . . . . 56
2.2.9 Numerical Method of Solution . . . . . . . . . . . . . . . . . . . . . . 57
2.3 Results for MRI-Active Surface Densities . . . . . . . . . . . . . . . . . . . . 57
2.3.1 Photodissociation and Ionization Fronts . . . . . . . . . . . . . . . . 57
2.3.2 MRI-Active Surface Density Σ∗ . . . . . . . . . . . . . . . . . . . . . 59
2.3.3 Parameter Survey, Including Sensitivity to PAHs . . . . . . . . . . . 62
2.3.4 Hall Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.3.5 The Possibility of Turbulent Mixing: Chemical Equilibration Timescale
vs. Dynamical Timescale . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.4 Summary and Implications for Disk Accretion . . . . . . . . . . . . . . . . . 66
2.4.1 Transitional Disks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3 Atmospheric Heat Redistribution on Hot Jupiters 74
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3 Numerical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.1 Basic Behavior of the Solutions . . . . . . . . . . . . . . . . . . . . . 87
3.3.2 Physical Explanation for Forcing Amplitude Dependence . . . . . . . 88
3.3.3 Metric for the Day-Night Contrast . . . . . . . . . . . . . . . . . . . 89
3.4 Analytic Theory for Day-Night Differences . . . . . . . . . . . . . . . . . . . 91
3.4.1 Drag-dominated: Valid for Both Equatorial and Non-equatorial Regions 96
3.4.2 Coriolis-dominated: Valid for Non-equatorial Regions Only . . . . . . 96
3.4.3 Advection- or Vertical-transport-dominated: Valid for Ro (cid:38) 1 . . . . 97
3.5 Interpretation of Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5.1 Timescale Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5.2 Vertical Advection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.5.3 Wave Adjustment Mechanism . . . . . . . . . . . . . . . . . . . . . . 102
3.6 Application to Hot Jupiter Observations . . . . . . . . . . . . . . . . . . . . 104
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4 Catastrophic Evaporation of Rocky Planets 108
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.1.1 KIC 12557548b: A Catastrophically Evaporating Planet . . . . . . . 109
4.1.2 Plan of This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Contents iv
4.2.1 Base Conditions of the Atmosphere . . . . . . . . . . . . . . . . . . . 112
4.2.2 Equations Solved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.2.3 Relaxation Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.1 Isothermal Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.2 Full Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3.3 Mass-Loss Histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.3.4 Possible Mass Loss Histories for KIC 1255b . . . . . . . . . . . . . . 127
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.4.1 Mass Loss is Not Energy-Limited . . . . . . . . . . . . . . . . . . . . 131
4.4.2 Dust-Gas Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.4.3 Time Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.4.4 Long-Term Orbital Evolution . . . . . . . . . . . . . . . . . . . . . . 134
4.4.5 Flow Confinement by Stellar Wind . . . . . . . . . . . . . . . . . . . 135
4.4.6 Occurrence Rates of Close-In Progenitors . . . . . . . . . . . . . . . . 136
4.4.7 Iron Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.4.8 Dust Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Bibliography 143
v
List of Figures
1.1 Diagram of X-ray ionized disk surface layers . . . . . . . . . . . . . . . . . . . . 8
1.2 Diagram of our chemical reaction network . . . . . . . . . . . . . . . . . . . . . 13
1.3 Equilibrium charge distribution on PAHs . . . . . . . . . . . . . . . . . . . . . . 22
1.4 Equilibrium charge distribution on grains . . . . . . . . . . . . . . . . . . . . . . 23
1.5 Average charge state of PAHs ad a function of PAH abundance . . . . . . . . . 24
1.6 Average charge state of grains ad a function of grain abundance . . . . . . . . . 25
1.7 Ionization fraction as a function of PAH abundance for the standard metal
abundance (x = 10−8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
M
1.8 Ionization fraction as a function of PAH abundance for the metal-rich case (x =
M
10−6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.9 Magnetic Reynolds number Re and ambipolar diffusion number Am as a function
of surface density Σ at a = 3 AU . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.10 Magnetic Reynolds number Re and ambipolar diffusion number Am as a function
of surface density Σ at a = 30 AU . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.11 Ratio of the chemical equilibration timescale t to the dynamical time t = Ω−1,
eq dyn
for a = 3 AU and x = 10−8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
M
1.12 Test comparison with the model of Bai & Goodman (2009) . . . . . . . . . . . . 39
1.13 Test comparison with the model of Turner et al. (2010) . . . . . . . . . . . . . . 40
2.1 H photodissociation front, and C and S ionization fronts, for our standard model
2
at a = 3 AU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.2 Magnetic Reynolds number Re and ambipolar diffusion number Am versus vertical
surface density Σ for standard model parameters and a = 3 AU . . . . . . . . . 60
2.3 Maximumtransportparameterα andmassaccretionrateM˙ versusverticalsurface
density Σ for standard model parameters and a = 3 AU . . . . . . . . . . . . . . 61
2.4 Dependence of Σ∗ to model parameters . . . . . . . . . . . . . . . . . . . . . . . 63
2.5 Electron fraction as a function of PAH abundance for FUV and X-ray ionized
surface layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.6 Hall parameter Ha as a function of a in FUV-ionized surface layers . . . . . . . 65
2.7 Ratio of the ion-electron recombination timescale t to the dynamical time t ,
rec dyn
as a function of a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.8 Accretion rates for conventional (hole-less) disks as a function of a . . . . . . . . 69
List of Figures vi
2.9 Disk accretion rates driven by the combined effects of X-ray and sideways cosmic
ray ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.10 Accretion rates for transitional disks driven by FUV ionization of gas at the inner
rim of the disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.1 Fractional day-night infrared flux variations A vs. global-mean equilibrium
obs
temperature T for hot Jupiters with measured light curves . . . . . . . . . . . 76
eq
3.2 Diagram of the two-layer shallow water model . . . . . . . . . . . . . . . . . . . 79
3.3 Equirectangular maps of steady-state geopotential (gh) contours for the equili-
brated solutions of the shallow-water model for a forcing amplitude of ∆h /H = 1 81
eq
3.4 Equirectangular maps of steady-state geopotential (gh) contours for the equili-
brated solutions of the shallow-water model for a forcing amplitude of ∆h /H =
eq
0.001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.5 Absolute values of the zonal components of individual terms in the momentum
equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.6 Contours of day-night height amplitude A and τ /τ for the numerical and
adv wave
analytical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.7 Contoursofnormalizedday-nightamplitudeAofourfullshallowwatersimulations
for different ∆h /H values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
eq
3.8 Contours of equatorial day-night amplitude A of our full shallow water
equator
simulations and our analytical model for different ∆h /H values . . . . . . . . 93
eq
3.9 Simplified diagram of the upper layer of the shallow water model . . . . . . . . 94
3.10 Contours of day-night height amplitude A as would be predicted by comparing
τ vs. τ —the horizontal advective timescale . . . . . . . . . . . . . . . . . . 99
rad adv
3.11 Comparisonbetweenobservedfractionalday-nightinfraredfluxvariationsA (T )
obs eq
and shallow water model results A(T ) . . . . . . . . . . . . . . . . . . . . . . . 106
eq
4.1 Equilibrium vapor pressures of pyroxene and olivine vs. temperature . . . . . . . 113
4.2 Evaporative mass loss rates M˙ vs. planet mass M for isothermal dust-free winds 120
4.3 Radial dependence of wind properties in the full solution for a planet of mass
M = 0.03M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
⊕
4.4 Dependence of M˙ and τ on dust abundance for a planet of mass M = 0.03M 123
surface ⊕
4.5 Radial dependence of wind properties in the full solution for a planet of mass
M = 0.01M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
⊕
4.6 Radial dependence of wind properties in the full solution for a planet of mass
M = 0.07M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
⊕
4.7 Dependence of M˙ on dust abundance for a planet of mass M = 0.006M or
⊕
M = 0.1M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
⊕
4.8 Maximum mass loss rates M˙ vs. planet mass M for the full model . . . . . . . . 129
4.9 Mass-loss histories M(t) for the isothermal and full models . . . . . . . . . . . . 130
4.10 Mass loss rates M˙ , computed using the isothermal model at T = 2145 K, for iron
planets and olivine planets of varying M . . . . . . . . . . . . . . . . . . . . . . 137