Eccentricity driving of pebble accreting low-mass planets

Abstract

By means of high resolution hydrodynamical, three-dimensional calculations with nested-meshes, we evaluate the eccentricity reached by a low-mass, luminous planet embedded in an inviscid disc with constant thermal diffusivity and subjected to thermal forces. We find that a cell size of at most one tenth of the size of the region heated by the planet is required to get converged results. When the planet's luminosity is supercritical, we find that it reaches an eccentricity of order $10^{-2}$--$10^{-1}$, which increases with the luminosity and broadly scales with the disc's aspect ratio. Restricting our study to the case of pebble accretion, we incorporate to our model the dependence of the accretion rate of pebbles on the eccentricity. There is therefore a feedback between eccentricity, which determines the accretion rate and hence the planet's luminosity, and the luminosity, which yields the eccentricity attained through thermal forces. We solve for the steady state eccentricity and study how this quantity depends on the disc's turbulence strength parameter $α_z$, on the dimensionless stopping time of the pebbles $τ_s$, on the inward mass flux of pebbles and on the headwind (the difference between the gas velocity and the Keplerian velocity). We find that in general low-mass planets (up to a few Earth masses) reach eccentricities comparable to the disc's aspect ratio, or a sizeable fraction of the latter. Eccentric, low-mass protoplanets should therefore be the norm rather than the exception, even if they orbit far from other planets or from large scale disturbances in the disc.