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 R_s moving at constant velocity V ₀ through a background homogeneous medium of adiabatic gas. Since the potential is non-diverging, there is no gas removal due to accretion. When R_s is larger than the Bondi radius R_B , the perturbation is linear at every point and the drag force is well fitted by the time-dependent Ostriker's formula with r _min = 2.25R_s , where r _min is the minimum impact parameter in the Coulomb logarithm. In the deep nonlinear supersonic regime (R_s Lt R_B ), the minimum radius is no longer related to R_s but to R_B . We find r_min=3.3 {M}^{-2.5}R_{B} for Mach numbers of the perturber between 1.5 and 4, although r_min = 2 {M}^{-2}R_{B}=2GM/V^{2}_{0} also provides a good fit at {M}>2. As a consequence, the drag force does not depend sensitively on the nonlinearity parameter {A}, defined as R_B /R_s , for {A} values larger than a certain critical value {A}_cr. We show that our generalized Ostriker's formula for the drag force is more accurate than the formula suggested by Kim and Kim.