Context: In recent years, space missions such as Kepler and TESS have discovered many close-in planets with significant atmospheres consisting of hydrogen and helium: mini-Neptunes. This indicates that these planets formed early in gas-rich disks while avoiding the runaway gas accretion that would otherwise have turned them into hot-Jupiters. A solution is to invoke a long Kelvin-Helmholtz contraction (or cooling) timescale, but it has also been suggested that thermodynamical cooling can be prevented by hydrodynamical planet atmosphere-disk recycling.
Aim: We investigate the efficacy of the recycling hypothesis in preventing the collapse of the atmosphere for core masses from 1 to 10 earth masses and different optical depths at 0.1 au.
Methods: We use three-dimensional radiation-hydrodynamic simulations to model the formation of planetary proto-atmospheres. Equations are solved in a local frame centered on the planet.
Results: Ignoring small oscillations that average to zero over time, the simulations converge to a steady state where the velocity field of the gas becomes constant in time. In a thermodynamic equilibrium, the energy loss by radiative cooling is fully compensated by the recycling of the low entropy gas in the planetary atmosphere with high entropy gas from the circumstellar disk. Higher core masses generally result in less efficient recycling. However, for a core mass greater than 2 M_earth the onset of turbulence enhances recycling. The increase in pressure for lower optical depths results in significantly larger atmospheres.
Conclusions: For close-in planets, recycling naturally halts the cooling of planetary proto-atmospheres, preventing them from contracting toward the runaway regime and collapsing into gas giants.