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Using time-dependent linear perturbation theory, we evaluate the dynamical friction force on a massive perturber Mₚ traveling at velocity V through a uniform gaseous medium of density rho₀ and sound speed cₛ. This drag force acts in the direction -\ V, and arises from the gravitational attraction between the perturber and its wake in the ambient medium. For supersonic motion (M=V/cₛ>1), the enhanced-density wake is confined to the Mach cone trailing the perturber; for subsonic motion (M1 but 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 \\ 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.
Eve C. Ostriker (Mon,) studied this question.