On the evolution of pebble-accreting planets in evolving protoplanetary discs

We examine the migration of luminous low-mass cores in laminar protoplanetary discs where accretion occurs mainly because of disc winds and where the planet luminosity is generated by pebble accretion. Using 2D hydrodynamical simulations, we determine the eccentricities induced by thermal forces as a function of gas and pebble accretion rates, and also evaluate the importance of the torque exerted by the solid component relative to the gas torque. For a gas accretion rate $\dot{M}= 2\times 10^{-8}\, \mathrm{ M}_\odot$  yr ⁻¹ and pebble flux $\dot{M}_{\mathrm{ peb}}=170\, \mathrm{ M}_\oplus$  Myr ⁻¹ , we find that embryo eccentricities attain values comparable to the disc aspect ratio. The planet radial excursion in the disc, however, causes the torque exerted by inflowing pebbles to cancel on average and migration to transition from outward to inward. This is found to arise because the magnitude of thermal torques decreases exponentially with increasing eccentricity, and we provide a fitting formula for the thermal torque attenuation as a function of eccentricity. As the disc evolves, the accretion luminosity becomes at some point too small to make the core eccentricity grow such that the solid component can exert a non-zero torque on the planet. This torque is positive and for gas accretion rates $\dot{M} \lesssim 5\times 10^{-9}$ M ⊙  yr ⁻¹ and pebble fluxes $\dot{M}_{\rm {peb}} \lesssim 120\, \mathrm{ M}_\oplus $  Myr ⁻¹ , it is found to overcome the gas torque exerted on cores with mass $m_\mathrm{ p}\lesssim \, 1\,\mathrm{ {M}}_\oplus$ , resulting in outward migration.