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 f orce acts in the direction -(V) over cap and arises from the gravitational attraction between the perturber and its wake in the ambient medium. For su personic 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 o r oblate spheroids for supersonic or subsonic perturbers, respectively, wit h the density maximal nearest the perturber. The dynamical drag force has t he form F-DF = -I x 4 pi(GM(p))(2)rho(0)/V-2. We evaluate I analytically; i ts 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 form ula for dynamical friction in a collisionless medium, noting that the gaseo us 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 protogalax y 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 pro portional to r(-2) halo, and of a (subsonic) perturber on a near-circular o rbit in a constant-density core. We also mention the relevance of our calcu lations to protoplanet migration in a circumstellar nebula.