The End of Runaway: How Gap Opening Limits the Final Masses of Gas Giants

Abstract

Gas giants are thought to form by runaway accretion: an instability driven by the self-gravity of growing atmospheres that causes accretion rates to rise super-linearly with planet mass. Why runaway should stop at a Jupiter or any other mass is unknown. We consider the proposal that final masses are controlled by circumstellar disc gaps (cavities) opened by planetary gravitational torques. We develop a fully time-dependent theory of gap formation and couple it self-consistently to planetary growth rates. When gaps first open, planetary torques overwhelm viscous torques, and gas depletes as if it were inviscid. In low-viscosity discs, of the kind motivated by recent observations and theory, gaps stay predominantly in this inviscid phase and planet masses finalize at $M_{\mathrm{final}}/M_{\star }\sim (\Omega t_{\mathrm{disc}}{)}^{0.07}(H/a{)}^{2.73}(G{\rho }_0/{\Omega }^2{)}^{1/3}$, with $M_{\star }$ the host stellar mass, $\Omega$ the planet's orbital angular velocity, $t_{\mathrm{disc}}$ the gas disc's lifetime, $H/a$ its aspect ratio, and ${\rho }_0$ its unperturbed density. This final mass is independent of the dimensionless viscosity $\alpha$ and applies to large orbital distances, typically beyond $\sim$10 AU, where disc scale heights exceed planet radii. It evaluates to a few Jupiter masses at 10-100 AU, increasing gradually with distance as gaps become harder to open.

arXiv commentAccepted to MNRAS

References in corpus (50)

• Spectral Energy Distributions of T Tauri Stars With Passive Circumstellar Disks
• Protoplanetary Disks and Their Evolution
• Towards a Deterministic Model of Planetary Formation I: a Desert in the Mass and Semi Major Axis Distributions of Extra Solar Planets
• Accretion Disks around Young Objects. I. The Detailed Vertical Structure
• Rossby Wave Instability of Keplerian Accretion Disks
• Dust and Gas in the disc of HL Tauri: Surface density, dust settling, and dust-to-gas ratio
• The Mass-Metallicity Relation for Giant Planets
• Forming Planetesimals in Solar and Extrasolar Nebulae
• Disk Accretion Onto High-Mass Planets
• The Disk Substructures at High Angular Resolution Project (DSHARP): VII. The Planet-Disk Interactions Interpretation
• Mass Flow and Accretion through gaps in Accretion Discs
• Imaging Extrasolar Giant Planets
• Rossby Wave Instability of Thin Accretion Disks -- II. Detailed Linear Theory
• Atmospheres of protoplanetary cores: critical mass for nucleated instability
• Planetary Torques as the Viscosity of Protoplanetary Disks
• The Runts of the Litter: Why planets formed through gravitational instability can only be failed binary stars
• Super-Earth Atmospheres: Self-Consistent Gas Accretion and Retention
• Breeding Super-Earths and Birthing Super-Puffs in Transitional Disks
• Models of Jupiter's Growth Incorporating Thermal and Hydrodynamic Constraints
• A Three-Dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk using DCO${}^{+}$
• Initial Conditions of Planet Formation: Lifetimes of Primordial Disks
• The TW Hya Disk at 870 microns: Comparison of CO and Dust Radial Structures
• Orbital Migration and Mass Accretion of Protoplanets in 3D Global Computations with Nested Grids
• Make Super-Earths, Not Jupiters: Accreting Nebular Gas onto Solid Cores at 0.1 AU and Beyond
• To Cool is to Accrete: Analytic Scalings for Nebular Accretion of Planetary Atmospheres
• Towards a Global Evolutionary Model of Protoplanetary Disks
• How Empty are Disk Gaps Opened by Giant Planets?
• Accretion of Jupiter-mass Planets in the Limit of Vanishing Viscosity
• On the Minimum Core Mass for Giant Planet Formation at Wide Separations
• A Millimeter Continuum Size-Luminosity Relationship for Protoplanetary Disks
• Mass Estimates of a Giant Planet in a Protoplanetary Disk from the Gap Structures
• Gap Opening by Extremely Low Mass Planets in a Viscous Disk
• Formation of a disc gap induced by a planet: Effect of the deviation from Keplerian disc rotation
• Final Masses of Giant Planets II: Jupiter Formation in a Gas-Depleted Disk
• Multiple Disk Gaps and Rings Generated by a Single Super-Earth: II. Spacings, Depths, and Number of Gaps, with Application to Real Systems
• Minimum Core Masses for Giant Planet Formation With Realistic Equations of State and Opacities
• Models of Accreting Gas Giant Protoplanets in Protostellar Disks
• On the Terminal Rotation Rates of Giant Planets
• Gap Opening in 3D: Single Planet Gaps
• Short dissipation times of proto-planetary discs - an artifact of selection effects?
• A Systematic Study of the Final Masses of Gas Giant Planets
• Evolution of Gas Giant Entropy During Formation by Runaway Accretion
• Thermodynamics of Giant Planet Formation: Shocking Hot Surfaces on Circumplanetary Disks
• A Balanced Budget View on Forming Giant Planets by Pebble Accretion
• Using Ice and Dust Lines to Constrain the Surface Densities of Protoplanetary Disks
• Save the Planet, Feed the Star: How Super-Earths Survive Migration and Drive Disk Accretion
• How do T Tauri stars accrete
• Rayleigh Adjustment of Narrow Barriers in Protoplanetary Discs
• Deep and wide gaps by super Earths in low-viscosity discs
• Restrictions on the Growth of Gas Giant Cores via Pebble Accretion

Cited by in corpus (31)

• Constraining the Nature of the PDS 70 Protoplanets with VLTI/GRAVITY
• Formation of Giant Planet Satellites
• How planets grow by pebble accretion. III. Emergence of an interior composition gradient
• Magnetospheric Accretion as a Source of H$\alpha$ Emission from Proto-planets around PDS 70
• Creating the Radius Gap without Mass Loss
• Final Masses of Giant Planets III: Effect of Photoevaporation and a New Planetary Migration Model
• Giant planet formation models with a self-consistent treatment of the heavy elements
• Accreting protoplanets: Spectral signatures and magnitude of gas and dust extinction at H alpha
• Envelopes of embedded super-Earths II. Three-dimensional isothermal simulations
• Heavy-metal Jupiters by major mergers: metallicity vs. mass for giant planets
• Steady State by Recycling prevents Premature Collapse of Protoplanetary Atmospheres
• Rapid Formation of Jupiter and Wide-Orbit Exoplanets in Disks with Pressure Bumps
• How Consumption and Repulsion Set Planetary Gap Depths and the Final Masses of Gas Giants
• The maximum accretion rate of a protoplanet: how fast can runaway be?
• Accretion of Gas Giants Constrained by the Tidal Barrier
• Breaking the centrifugal barrier to giant planet contraction by magnetic disc braking
• Recycling of the first atmospheres of embedded planets: Dependence on core mass and optical depth
• Vertical gas accretion impacts the carbon-to-oxygen ratio of gas giant atmospheres
• Retention of Long-Period Gas Giant Planets: Type II Migration Revisited
• Unified simulations of planetary formation and atmospheric evolution: Effects of pebble accretion, giant impacts, and stellar irradiations on super-Earth formation
• The Endgame of Gas Giant Formation: Accretion Luminosity and Contraction Post-Runaway
• The 3D dust and opacity distribution of protoplanets in multi-fluid global simulations
• Unified simulations of planetary formation and atmospheric evolution II: Rapid disk clearing by photoevaporation yields low-mass super-Earth atmospheres
• A Theoretical Framework for the Mass Distribution of Gas Giant Planets forming through the Core Accretion Paradigm
• Can Large-Scale Migration Explain the Giant Planet Occurrence Rate?
• Delivery of gas onto the circumplanetary disk of giant planets: Planetary-mass dependence of the source region of accreting gas and mass accretion rate
• Self-gravitating planetary envelopes and the core-nucleated instability
• An Approximation for the Capture Radius of Gaseous Protoplanets
• Multiverse Predictions for Habitability: Planetary Characteristics
• Testing planet formation from the ultraviolet to the millimeter
• Evolution and Observable Properties of Rocky Planet Atmospheres