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

## TL;DR

This study uses numerical simulations to analyze dynamical friction with thermal effects, comparing results to linear theory, and finds that thermal diffusion significantly alters the drag force on perturbers, with implications for planetary formation.

## Contribution

It provides a detailed numerical analysis of thermal effects on dynamical friction, including the heating force and non-adiabatic drag, validated against linear theory and implemented with GPU-accelerated nested meshes.

## Key findings

- Heating force aligns with analytic estimates at low and high Mach numbers.
- Non-luminous drag behaves like dry or solid friction in non-adiabatic gases.
- Luminosity threshold for net acceleration is lower than typical planetary embryo luminosities.

## Abstract

We investigate by means of numerical simulations with nested Cartesian meshes the force exerted on a massive and luminous perturber moving at constant speed through a homogeneous and opaque gas, 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 which 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 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 \emph{Graphics Processing Units} (GPUs).