A systematic study of planetary envelope growth with 3D radiation-hydrodynamics simulations

ABSTRACT In the core accretion model of planet formation, envelope cooling regulates the accretion of material and ultimately sets the time-scale to form a giant planet. Given the diversity of planet-forming environments, opacity uncertainties, and the advective transport of energy by three-dimensional (3D) recycling flows, it is unclear whether one-dimensional models can adequately describe envelope structure and accretion in all regimes. Even in 3D models, it is unclear whether approximate radiative transfer methods sufficiently model envelope cooling, particularly at the planetary photosphere. To address these uncertainties, we present a suite of 3D radiation-hydrodynamics simulations employing methods that directly solve the transfer equation. We perform a parameter space study, formulated in terms of dimensionless parameters, for a variety of envelope optical depths and cooling times. We find that the thermodynamic structure of the envelope ranges from adiabatic to isothermal based on the cooling time and, by extension, the background disc temperature and density. By adopting a dimensionless framework, these models can be applied to a wide range of formation conditions and assumed opacities. In particular, we dimensionalize them to the case of a super-Earth and proto-Jupiter and place upper limits on the 3D mass accretion rates prior to runaway growth. Finally, we evaluate the fidelity of approximate radiative transfer methods and find that even in the most challenging cases more approximate methods are sufficiently accurate and worth their savings in computational cost.