Dynamical friction in a gaseous medium

Using time-dependent linear perturbation theory, we evaluate the dynamical friction force on a massive perturber M-p traveling at velocity V through a uniform gaseous medium of density rho(0) and sound speed c(s). This drag force acts in the direction -(V) over cap and arises from the gravitational attraction between the perturber and its wake in the ambient medium. For supersonic motion (M = V/c(s) > 1), the enhanced-density wake is confined to the Mach cone trailing the perturber; for subsonic motion (M < 1), the wake is confined to a sphere of radius c(s)t centered a distance Vt behind the perturber. Inside the wake, surfaces of constant density are hyperboloids or oblate spheroids for supersonic or subsonic perturbers, respectively, with the density maximal nearest the perturber. The dynamical drag force has the form F-DF = -I x 4 pi(GM(p))(2)rho(0)/V-2. We evaluate I analytically; its limits are I --> M-3/3 for M much less than 1, and I --> In (Vt/r(min)) for M much greater than 1. We compare our results to the Chandrasekhar formula for dynamical friction in a collisionless medium, noting that the gaseous drag is generally more efficient when M > 1, but is less efficient when M < 1. To allow simple estimates of orbit evolution in a gaseous protogalaxy or proto-star cluster, we use our formulae to evaluate the decay times of a (supersonic) perturber on a near-circular orbit in an isothermal rho proportional to r(-2) halo, and of a (subsonic) perturber on a near-circular orbit in a constant-density core. We also mention the relevance of our calculations to protoplanet migration in a circumstellar nebula.