Dynamical friction on hot bodies in opaque, gaseous media
  We consider the gravitational force exerted on a point-like perturber of mass
$M$ travelling within a uniform gaseous, opaque medium at constant velocity
$V$. The perturber irradiates the surrounding gas with luminosity $L$. The
diffusion of the heat released is modelled with a uniform thermal diffusivity
$\chi$. Using linear perturbation theory, we show that the force exerted by the
perturbed gas on the perturber differs from the force without radiation (or
standard dynamical friction). Hot, underdense gas trails the mass, which gives
rise to a new force component, the heating force, with direction $+V$, thus
opposed to the standard dynamical friction. In the limit of low Mach numbers,
the heating force has expression $F_\mathrm{heat}=\gamma(\gamma-1)GML/(2\chi
c_s^2)$, $c_s$ being the sound speed and $\gamma$ the ratio of specific heats.
In the limit of large Mach numbers, $F_\mathrm{heat}=(\gamma-1)GML/(\chi
V^2)f(r_\mathrm{min}V/4\chi)$, where $f$ is a function that diverges
logarithmically as $r_\mathrm{min}$ tends to zero. Remarkably, the force in the
low Mach number limit does not depend on the velocity. The equilibrium speed,
when it exists, is set by the cancellation of the standard dynamical friction
and heating force. In the low Mach number limit, it scales with the luminosity
to mass ratio of the perturber. Using the above results suggests that Mars- to
Earth-sized planetary embryos heated by accretion in a gaseous protoplanetary
disc should have eccentricities and inclinations that amount to a sizeable
fraction of the disc's aspect ratio, for conditions thought to prevail at a few
astronomical units.
