On the interaction of pebble accreting embryos with the gaseous disc: importance of thermal forces

Abstract

A planetary embryo embedded in a gaseous disc can grow by pebble accretion while subjected to a gravitational force from the disc that changes its orbital elements. Usually, that force is considered to arise from the Lindblad and corotation resonances with the embryo. However, more important contributions exist for low-mass planets. Radiative thermal diffusion in the vicinity of embryos yields an additional contribution to the disc's force that damps the eccentricity and inclination much more vigorously than the resonant interaction with the disc, and that in general induces fast inward migration. In addition, the irradiation of the disc by a hot embryo gives rise to an additional contribution that excites eccentricity and inclination, and induces outward migration. Which of the two contributions dominates depends on the embryo's luminosity. We assess the importance of these contributions (termed thermal forces) on the dynamics and growth of a set of pebble-accreting embryos initially of Martian mass, by means of N-body simulations that include analytic expressions for the disc's force. We find very different outcomes for the embryos subjected to thermal forces and those subjected only to resonant forces. Importantly, we find that the median final mass of the embryos subjected to thermal forces is nearly independent of the metallicity, whereas this mass roughly scales with the metallicity when they are subjected only to resonant forces. These results can be explained by the strong damping of eccentricity and inclination at low metallicity, which enhances the embryos' accretion efficiency.