Evolution of Gas Giant Entropy During Formation by Runaway Accretion

Abstract

We calculate the evolution of gas giant planets during the runaway gas accretion phase of formation, to understand how the luminosity of young giant planets depends on the accretion conditions. We construct steady-state envelope models, and run time-dependent simulations of accreting planets with the Modules for Experiments in Stellar Astrophysics (MESA) code. We show that the evolution of the internal entropy depends on the contrast between the internal adiabat and the entropy of the accreted material, parametrized by the shock temperature $T_0$ and pressure $P_0$. At low temperatures ($T_0\lesssim 300$--$1000\mathrm{K}$, depending on model parameters), the accreted material has a lower entropy than the interior. The convection zone extends to the surface and can drive a large luminosity, leading to rapid cooling and cold starts. For higher temperatures, the accreted material has a larger entropy than the interior, giving a radiative zone that stalls cooling. For $T_0\gtrsim 2000\mathrm{K}$, the surface--interior entropy contrast cannot be accommodated by the radiative envelope, and the accreted matter accumulates with high entropy, forming a hot start. The final state of the planet depends on the shock temperature, accretion rate, and starting entropy at the onset of runaway accretion. Cold starts with $L\lesssim 5\times 10^{-6}{L}_{\odot }$ require low accretion rates and starting entropy, and that the temperature of the accreting material is maintained close to the nebula temperature. If instead the temperature is near the value required to radiate the accretion luminosity, $4\pi R^2\sigma T_0^4\sim (GM\dot{M}/R)$, as suggested by previous work on radiative shocks in the context of star formation, gas giant planets form in a hot start with $L\sim 10^{-4}{L}_{\odot }$.

20 pages, 14 figures, Accepted for publication in ApJ

References in corpus (18)

• Modules for Experiments in Stellar Astrophysics (MESA)
• Direct Imaging of Multiple Planets Orbiting the Star HR 8799
• On the Luminosity of Young Jupiters
• Line and Mean Opacities for Ultracool Dwarfs and Extrasolar Planets
• Synthetic Spectra and Colors of Young Giant Planet Atmospheres: Effects of Initial Conditions and Atmospheric Metallicity
• Formation of Jupiter using opacities based on detailed grain physics
• Global Models of Planet Formation and Evolution
• An Atmospheric Structure Equation for Grain Growth
• Recovery of the Candidate Protoplanet HD 100546 b with Gemini/NICI and Detection of Additional (Planet-Induced?) Disk Structure at Small Separations
• Grain opacity and the bulk composition of extrasolar planets. II. An analytical model for the grain opacity in protoplanetary atmospheres
• The opacity of grains in protoplanetary atmospheres
• Grain opacity and the bulk composition of extrasolar planets. I. Results from scaling the ISM opacity
• Direct Imaging Discovery of a Jovian Exoplanet Within a Triple Star System
• Ohmic Dissipation in the Interiors of Hot Jupiters
• An Exploration of Double Diffusive Convection in Jupiter as a Result of Hydrogen-Helium Phase Separation
• Thermodynamics of Giant Planet Formation: Shocking Hot Surfaces on Circumplanetary Disks
• A critical reassessment of the fundamental properties of GJ 504: Chemical composition and age
• A Search for Companions to Brown Dwarfs in the Taurus and Chamaeleon Star Forming Regions

Cited by in corpus (21)

• The Gemini Planet Imager Exoplanet Survey: Giant Planet and Brown Dwarf Demographics From 10-100 AU
• Retrieving scattering clouds and disequilibrium chemistry in the atmosphere of HR 8799e
• The Atmospheric Circulation of Ultra-hot Jupiters
• Characterization of exoplanets from their formation III: The statistics of planetary luminosities
• The Challenge of Forming a Fuzzy Core in Jupiter
• The Planetary Accretion Shock: I. Framework for Radiation-hydrodynamical Simulations and First Results
• Exploring the formation by core accretion and the luminosity evolution of directly imaged planets: The case of HIP 65426 b
• The First Dynamical Mass Measurement in the HR 8799 System
• Strong H$\alpha$ emission and signs of accretion in a circumbinary planetary mass companion from MUSE
• The End of Runaway: How Gap Opening Limits the Final Masses of Gas Giants
• Synthetic Evolution Tracks of Giant Planets
• Birth of convective low-mass to high-mass second Larson cores
• Hot Start Giant Planets Form With Radiative Interiors
• How does the mass and activity history of the host star affect the population of low-mass planets?
• The Endgame of Gas Giant Formation: Accretion Luminosity and Contraction Post-Runaway
• High-resolution survey for planetary companions to young stars in the Taurus Molecular Cloud
• Differentiating Formation Models with New Dynamical Masses for the PDS 70 Protoplanets
• Effects of Planetesimal Accretion on the Thermal and Structural Evolution of Sub-Neptunes
• LBT search for companions and sub-structures in the (pre)transitional disk of AB Aurigae
• Planetary Accretion Shocks with a Realistic Equation of State
• Spitzer phase curve observations and circulation models of the inflated ultra-hot Jupiter WASP-76b