The Late-Time Formation and Dynamical Signatures of Small Planets By Eve Jihyun Lee A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Astrophysics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Eugene Chiang, Chair Professor Eliot Quataert Professor David M. Romps Spring 2017 The Late-Time Formation and Dynamical Signatures of Small Planets Copyright 2017 by Eve Jihyun Lee 1 Abstract The Late-Time Formation and Dynamical Signatures of Small Planets by Eve Jihyun Lee Doctor of Philosophy in Astrophysics University of California, Berkeley Professor Eugene Chiang, Chair The riddle posed by super-Earths is that they are not Jupiters: their core masses are large enough to trigger runaway gas accretion, yet somehow super-Earths accreted atmospheres that weigh only a few percent of their total mass. In this thesis, I demonstrate that this puzzle is solved if super-Earths formed late, in the inner cavities of transitional disks. Super- puffs present the inverse problem of being too voluminous for their small masses. I show that super-puffs most easily acquire their thick atmospheres as dust-free, rapidly cooling worlds outside 1 AU, and then migrate in just after super-Earths appear. Super-Earths and Earth- sized planets around FGKM dwarfs are evenly distributed in log orbital period down to ∼10 days, but dwindle in number at shorter periods. I demonstrate that both the break at ∼10 days and the slope of the occurrence rate down to ∼1 day can be reproduced if planets form in disks that are truncated by their host star magnetospheres at co-rotation. Planets can be brought from disk edges to ultra-short (<1 day) periods by asynchronous equilibrium tides raised on their stars. Small planets may remain ubiquitous out to large orbital distances. I demonstrate that the variety of debris disk morphologies revealed by scattered light images can be explained by viewing an eccentric disk, secularly forced by a planet of just a few Earth masses, from different observing angles. The farthest reaches of planetary systems may be perturbed by eccentric super-Earths. i I dedicate this dissertation to my family. ii Contents List of Figures iv List of Tables vi Acknowledgments vii 1 Introduction1 2 Make Super-Earths, Not Jupiters: Accreting Nebular Gas onto Solid Cores at 0.1 AU and Beyond3 2.1 Introduction....................................3 2.1.1 For Super-Earths, Accretion of Solids Completes Before Accretion of Gas....................................4 2.1.2 Mission and Plan for this Chapter....................6 2.2 Time-Dependent Model Atmospheres......................7 2.2.1 Hydrostatic Snapshots..........................7 2.2.2 Connecting Snapshots in Time...................... 14 2.3 Results....................................... 16 2.3.1 Fiducial Model.............................. 16 2.3.2 Parameter Study............................. 24 2.4 Discussion: How Do Super-Earths Get Their Gas?............... 27 2.4.1 Supersolar Metallicity Gradients in Dusty Disks............ 30 2.4.2 Late-Stage Core Formation in Gas-Depleted Nebula.......... 32 2.5 Conclusions.................................... 35 3 To Cool is to Accrete: Analytic Scalings for Nebular Accretion of Planetary Atmospheres 37 3.1 Introduction.................................... 37 3.1.1 Planetesimal Accretion.......................... 37 3.2 Scaling Relations for GCR (Mcore; t; Z) ..................... 41 3.2.1 Dusty Atmospheres............................ 45 3.2.2 Dust-Free Atmospheres.......................... 50 3.3 Summary..................................... 53 Contents iii 4 Breeding Super-Earths and Birthing Super-Puffs in Transitional Disks 56 4.1 Introduction.................................... 56 4.2 Dangers of Runaway in Gas-Rich, Metal-Rich Nebulae (Scenario A)..... 57 4.2.1 High-µ Catastrophe............................ 58 4.2.2 Dust Coagulation: Low-κ Catastrophe................. 60 4.3 Acquiring Atmospheres in Gas-Poor Nebulae (Scenario B).......... 63 4.3.1 Gas Depletion Factors Compatible with GCRs and Disk Dispersal The- ories.................................... 63 4.3.2 Gas Depletion Factors Required to Merge Protocores......... 67 4.4 Super-Puffs as Migrated Dust-Free Worlds................... 71 4.5 Summary and Outlook.............................. 72 4.5.1 Future Directions............................. 75 5 Magnetospheric Truncation, Tidal Inspiral, and the Creation of Short and Ultra-Short Period Planets 79 5.1 Introduction.................................... 79 5.2 Monte Carlo Simulations............................. 83 5.2.1 Step 1: Draw Disk Truncation Periods from Stellar Rotation Periods 83 5.2.2 Step 2: Lay Down Planets Following Either “In Situ” Formation or “Disk Migration”............................. 83 5.2.3 Step 3: Apply Tidal Orbital Decay................... 87 5.2.4 Results for FGK Host Stars....................... 90 5.2.5 Results for M Host Stars......................... 93 5.3 Summary and Discussion............................. 96 5.3.1 Orbital Spacings of USPs......................... 97 5.3.2 Trends with Stellar Mass......................... 97 5.A Migration in Gas-poor Disks........................... 101 6 A Primer on Unifying Debris Disk Morphologies 102 6.1 Introduction.................................... 102 6.2 Model....................................... 103 6.3 Synthetic Scattered Light Images........................ 107 6.4 Summary and Discussion............................. 116 6.4.1 “Ring”................................... 116 6.4.2 “Moth”................................... 116 6.4.3 “Bar”.................................... 118 6.4.4 “Needle”.................................. 118 6.4.5 “Ship-and-Wake”............................. 120 6.4.6 Future Improvements........................... 120 Bibliography 122 iv List of Figures 2.1 Tabulated and extrapolated dusty and dust-free opacities vs. temperature at sev- eral densities..................................... 15 2.2 Atmospheric profiles for a fiducial model...................... 17 2.3 Profiles of temperature gradients, opacity, and number fractions of hydrogen species 18 2.4 Time evolution of gas-to-core mass ratio and cooling luminosity......... 19 2.5 Time evolution of different contributors to the atmospheric power budget and the luminosity neglected in radiative zones....................... 20 2.6 Cooling times of convective and radiative zones.................. 22 2.7 Runaway time vs. various boundary conditions................... 23 2.8 Runaway time vs. orbital radius for 10-M⊕ cores in a dusty disk with fixed solar metallicity and a disk with radially varying metallicity.............. 28 2.9 Atmospheric profiles just before runaway for 10-M⊕ cores at 0.1 AU and 5 AU. 29 2.10 Growth of envelope mass for 5-M⊕ and 10-M⊕ cores in a gas-depleted disk... 33 3.1 Planetesimal accretion rates required to keep dusty envelopes in thermal equilib- rium at a given gas-to-core mass ratio GCR..................... 39 3.2 Ratio of accretion luminosity to cooling luminosity at runaway for dusty and dust-free atmospheres................................ 40 3.3 Envelope mass evolution: analytic vs. numerical result.............. 47 3.4 Gas-to-core mass ratio vs. core mass at fixed time................. 48 3.5 Gas-to-core mass ratio vs. gas metallicity at fixed time.............. 49 3.6 Dust-free and dusty opacities vs. temperature for several densities........ 51 4.1 Critical core mass vs. metallicity.......................... 59 4.2 Envelope mass growth for a 5-M⊕ core in a metal-rich disk with dusty and dust- free opacities..................................... 61 4.3 The effect of dust on the radiative-convective boundary.............. 62 4.4 Envelope mass growth in disks with different surface densities.......... 64 4.5 Required level of gas density depletion to allow a giant impact of two 2.5-M⊕ cores as a function of their eccentricities (dusty opacity)............. 66 4.6 Required level of gas density depletion to allow a giant impact of two 2.5-M⊕ cores as a function of their eccentricities (dust-free opacity)............ 68 List of Figures v 4.7 Formation of super-puffs: envelope mass growth of a 2-M⊕ core beyond 1 AU as a dust-free world................................... 73 4.8 Observationally-inferred gas-to-core mass ratio vs. core mass........... 76 5.1 Occurrence rates of sub-Neptunes orbiting FGK and M dwarfs.......... 80 5.2 Histograms of pre-main-sequence stellar rotation periods in clusters of various ages 82 5.3 How Type I migration might play out for a system of sub-Neptunes....... 86 5.4 Model occurrence rates including Type I disk migration in a dissipating nebula but excluding tidal migration............................. 88 5.5 Occurrence rates of planets that have undergone both disk (Type I) migration in a dissipating nebula, and tidal migration over 5 Gyr................ 89 5.6 Occurrence rates of planets that form in situ and that subsequently undergo tidal migration over 5 Gyr.................................. 91 5.7 Best-fitting disk+tidal and in-situ+tidal models.................. 92 5.8 Model occurrence rate profiles of sub-Neptunes around M dwarfs......... 94 5.9 In-situ planet formation in disks truncated at co-rotation by host star magneto- spheres, in combination with tidal migration, can reproduce the observed occur- rence rates of sub-Neptunes.............................. 95 5.10 Observational evidence for how stellar tidal friction widens separations between