Dynamical stability of giant planets: the critical adiabatic index in the presence of a solid core

Abstract

The dissociation and ionization of hydrogen, during the formation of giant planets via core accretion, reduces the effective adiabatic index $\gamma$ of the gas and could trigger dynamical instability. We generalize the analysis of Chandrasekhar, who determined that the threshold for instability of a self-gravitating hydrostatic body lies at $\gamma =4/3$, to account for the presence of a planetary core, which we model as an incompressible fluid. We show that the dominant effect of the core is to stabilize the envelope to radial perturbations, in some cases completely (i.e. for all $\gamma >1$). When instability is possible, unstable planetary configurations occupy a strip of $\gamma$ values whose upper boundary falls below $\gamma =4/3$. Fiducial evolutionary tracks of giant planets forming through core accretion appear unlikely to cross the dynamical instability strip that we define.

References in corpus (26)

• Streaming Instabilities in Protoplanetary Disks
• Stability of Standing Accretion Shocks, With an Eye Toward Core Collapse Supernovae
• Closed-form expressions for particle relative velocities induced by turbulence
• Forming Planetesimals in Solar and Extrasolar Nebulae
• Disk Accretion Onto High-Mass Planets
• Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core
• Models of Jupiter's Growth Incorporating Thermal and Hydrodynamic Constraints
• To Cool is to Accrete: Analytic Scalings for Nebular Accretion of Planetary Atmospheres
• Critical Protoplanetary Core Masses in Protoplanetary Disks and the Formation of Short-Period Giant Planets
• Distribution of Accreting Gas and Angular Momentum onto Circumplanetary Disks
• On the Minimum Core Mass for Giant Planet Formation at Wide Separations
• Final Stages of Planet Formation
• Reduced gas accretion on super-Earths and ice giants
• Minimum Core Masses for Giant Planet Formation With Realistic Equations of State and Opacities
• The fuzziness of giant planets' cores
• Angular Momentum Accretion onto a Gas Giant Planet
• Growth after the streaming instability: from planetesimal accretion to pebble accretion
• Polytropic gas spheres: An approximate analytic solution of the Lane-Emden equation
• Gravitational instability of polytropic spheres and generalized thermodynamics
• From Disks to Planets
• The Maximum Mass Solar Nebula and the early formation of planets
• The Endgame of Gas Giant Formation: Accretion Luminosity and Contraction Post-Runaway
• The Gravitational Instability of Adiabatic Filaments
• Weak Shock Propagation with Accretion. II. Stability of Self-similar Solutions to Radial Perturbations
• Self-gravitating planetary envelopes and the core-nucleated instability
• The Formation of Binaries