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Steady State by Recycling prevents Premature Collapse of Protoplanetary Atmospheres

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. We investigate the efficacy of the recycling hypothesis in preventing the collapse of the atmosphere, check for the existence of a steady state configuration, and determine the final atmospheric mass to core mass ratio. 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. 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 steady state, 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. 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.