Numerical study of dynamical friction with thermal effects - I. Comparison to linear theory

We investigate the force exerted on a massive and luminous perturber moving at constant speed through a homogeneous and opaque gas by means of numerical simulations with nested Cartesian meshes, taking into account thermal diffusion in the gas and the radiative feedback from the perturber. The force arising from the release of energy into the ambient medium by the perturber, or heating force, is directed along the direction of motion and induces an acceleration of the perturber. Its value is compared to analytic estimates in the low and high Mach number limits, and found to match those accurately. In addition, the drag exerted on a non-luminous perturber significantly departs from the adiabatic expression when thermal diffusion is taken into account. In the limit of a vanishing velocity, this drag tends to a finite value that we determine using linear perturbation theory and corroborate with numerical simulations. The drag on a non-luminous perturber in a non-adiabatic gas therefore behaves, in the low Mach number regime, like dry or solid friction. We work out the luminosity threshold to get a net acceleration of the perturber and find it to be generally much smaller than the luminosity of accreting low-mass planetary embryos embedded in a gaseous protoplanetary disc at a few astronomical units. We also present in some detail our implementation of nested meshes, which runs in parallel over several Graphics Processing Units.