Dynamical friction on hot bodies in gaseous, opaque media, and application to embedded protoplanets

A massive and luminous perturber moving across an opaque gas is subjected to a force different from the gravitational friction that it would experience if it were cold. The heat released by the perturber diffuses in the surrounding gas, where it gives rise to a low density region behind the perturber that exerts a force (that we call heating force) in the direction of motion, thus opposed to the standard dynamical friction. We present numerical simulations with nested meshes that confirm the analytical expression of the heating force in the limits of a low and high Mach number, respectively, and we present simulations that show that the dynamical friction exerted on a cold perturber in a gas with thermal diffusion is markedly different from that in an adiabatic gas. We then present numerical simulations of low-mass protoplanets embedded in opaque, viscous discs, that show that when these bodies have a sufficiently large luminosity their eccentricity and inclination can be excited to values comparable to the aspect ratio of the disc. We finally present numerical experiments with very high resolution that try to resolve the flow within the Bondi sphere, in an attempt to study the dependence of the heating force as a function of the ratio of the diffusive to acoustic times across the Bondi radius.