Self-gravitating planetary envelopes and the core-nucleated instability

Abstract: Planet formation scenarios can be constrained by the ratio of the gaseous envelope mass relative to the solid core mass in the observed exoplanet populations. One-dimensional calculations find a critical (maximal) core mass for quasi-static envelopes to exist, suggesting that envelopes around more massive cores should collapse due to a `core-nucleated' instability. We study self-gravitating planetary envelopes via hydrodynamic simulations, progressively increasing the dimensionality of the problem. We characterize the core-nucleated instability and its non-linear evolution into runaway gas accretion in one-dimensional spherical envelopes. We show that rotationally-supported envelopes can enter a runaway accretion regime via polar shocks in a two-dimensional axisymmetric model. This picture remains valid for high-mass cores in three dimensions, where the gas gravity mainly adds up to the core gravity and enhances the mass accretion rate of the planet in time. We relate the core-nucleated instability to the absence of equilibrium connecting the planet to its parent disk and discuss its relevance for massive planet formation.