The Role of Thermal Feedback in the Growth of Planetary Cores by Pebble Accretion in Dust Traps

High-resolution millimetre-imaging of protoplanetary discs has revealed many containing rings and gaps. These rings can contain large quantities of dust, often in excess of 10M$_\oplus$, providing prime sites for efficient and rapid planet formation. Rapid planet formation will produce high accretion luminosities, heating the surrounding disc. We investigate the importance of a planetary embryo's accretion luminosity by simulating the dynamics of the gas and dust in a dust ring, accounting for the energy liberated as a resident planetary embryo accretes. The resulting heating alters the flow structure near the planet, increasing the accretion rate of large, millimetre-to-centimetre-sized dust grains. We show how this process varies with the mass of dust in the ring and the local background gas temperature, demonstrating that the thermal feedback always acts to increase the planet's mass. This increase in planet mass is driven primarily by the formation of vortices, created by a baroclinic instability once the accreting planet heats the disc significantly outside its Hill radius. The vortices can then migrate with respect to the planet, resulting in a complex interplay between planetary growth, gap-opening, dust trapping and vortex dynamics. Planets formed within dust traps can have masses that exceed the classical pebble isolation mass, potentially providing massive seeds for the future formation of giant planets. Once pebble accretion ceases, the local dust size distribution is depleted in large grains, and much of the remaining dust mass is trapped in the system's L$_5$ Lagrange point, providing potentially observable signatures of this evolution.