  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.
