Pebble dynamics and accretion onto rocky planets. II. Radiative models

TL;DR

This study uses high-resolution hydrodynamic simulations to explore how radiative energy transfer influences the atmosphere and convection around Earth-mass planetary embryos, revealing limited cooling effects under typical disk conditions.

Contribution

It provides the first detailed analysis of radiative effects on gas and particle dynamics near rocky planetary embryos, highlighting the interplay between radiative cooling and convection.

Findings

Radiative transport reduces entropy but is offset by increased convection.

Temperature reduction in the Hill sphere is about 100K under typical conditions.

Radiative cooling becomes significant only at very low disk surface densities.

Abstract

We investigate the effects of radiative energy transfer on a series of nested-grid, high-resolution hydrodynamic simulations of gas and particle dynamics in the vicinity of an Earth-mass planetary embryo. We include heating due to the accretion of solids and the subsequent convective motions. Using a constant embryo surface temperature, we show that radiative energy transport results in a tendency to reduce the entropy in the primordial atmosphere, but this tendency is alleviated by an increase in the strength of convective energy transport, triggered by a correspondingly increased super-adiabatic temperature gradient. As a consequence, the amplitude of the convective motions increase by roughly an order of magnitude in the vicinity of the embryo. In the cases investigated here, where the optical depth towards the disk surface is larger than unity, the reduction of the temperature in the outer parts of the Hill sphere relative to cases without radiative energy transport is only $\sim$100K, while the mass density increase is on the order of a factor of two in the inner parts of the Hill sphere. Our results demonstrate that, unless unrealistically low dust opacities are assumed, radiative cooling in the context of primordial rocky planet atmospheres can only become important after the disk surface density has dropped significantly below minimum-mass-solar-nebula values.