The gravitational drag force on an extended object moving in a gas

Using axisymmetrical numerical simulations, we revisit the gravitational drag felt by a gravitational Plummer sphere with mass M and core radius Rs, moving at constant velocity V0 through a background homogeneous medium of adiabatic gas. Since the potential is non-diverging, there is no gas removal due to accretion. When Rs is larger than the Bondi radius RB, the perturbation is linear at every point and the drag force is well fitted by the time-dependent Ostriker's formula with r_{min}= 2.25Rs, where r_{min} is the minimum impact parameter in the Coulomb logarithm. In the deep nonlinear supersonic regime (Rs<< RB), the minimum radius is no longer related with Rs but with RB. We find r_min=3.3mach^{-2.5}RB, for Mach numbers of the perturber between $1.5$ and $4$, although r_{min} = 2\mach^{-2}RB=2GM/V0^{2} also provides a good fit at mach>2. As a consequence, the drag force does not depend sensitively on the nonlinearity parameter RB/Rs, for RB/Rs-values larger than a certain critical value. We show that our generalized Ostriker's formula for the drag force is more accurate than the formula suggested by Kim & Kim (2009).