Numerical study of coorbital thermal torques on cold or hot satellites

TL;DR

This study uses high-resolution 3D hydrodynamics simulations to analyze thermal torques on low-mass planets in protoplanetary discs, confirming their dominance over other torques and their dependence on planetary offset and disc properties.

Contribution

The paper provides detailed numerical validation of thermal torque behavior, including their magnitude, dependence on offset, and comparison with analytic and dynamical friction estimates.

Findings

Thermal torques depend on the offset between planet and corotation.

Thermal torques generally dominate Lindblad and corotation torques for low-mass planets.

Thermal disturbance resolution of about 10 zones is necessary for accurate results.

Abstract

We evaluate the thermal torques exerted on low-mass planets embedded in gaseous protoplanetary discs with thermal diffusion, by means of high-resolution three-dimensional hydrodynamics simulations. We confirm that thermal torques essentially depend on the offset between the planet and its corotation, and find a good agreement with analytic estimates when this offset is small compared to the size of the thermal disturbance. For larger offsets that may be attained in discs with a large pressure gradient or a small thermal diffusivity, thermal torques tend toward an asymptotic value broadly compatible with results from a dynamical friction calculation in an unsheared medium. We perform a convergence study and find that the thermal disturbance must be resolved over typically 10 zones for a decent agreement with analytic predictions. We find that the luminosity at which the net thermal torque changes sign matches that predicted by linear theory within a few percents. Our study confirms that thermal torques usually supersede Lindblad and corotation torques by almost an order of magnitude for low mass planets. As we increase the planetary mass, we find that the ratio of thermal torques to Lindblad and corotation torques is progressively reduced, and that the thermal disturbance is increasingly distorted by the horseshoe flow. Overall, we find that thermal torques are dominant for masses up to an order of magnitude larger than implemented in recent models of planetary population synthesis. We finally briefly discuss the case of stellar or intermediate-mass objects embedded in discs around AGNs.