Nonlinear Dynamical Friction in a Gaseous Medium

Using high-resolution, two-dimensional hydrodynamic simulations, we investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a very massive perturber Mp moving at velocity Vp through a uniform gaseous medium of adiabatic sound speed a∞. We model the perturber as a Plummer potential with softening radius rs, and run various models with differing A = GMp/(a 2 ∞rs) and M = Vp/a∞ by imposing cylindrical symmetry with respect to the line of perturber motion. For supersonic cases, a massive perturber quickly develops nonlinear flows that produce a detached bow shock and a vortex ring, which is unlike in the linear cases where Mach cones are bounded by low-amplitude Mach waves. The flows behind the shock are initially non-steady, displaying quasi-periodic, overstable oscillations of the vortex ring and the shock. The vortex ring is eventually shed downstream and the flows evolve toward a quasi-steady state where the density wake near the perturber is in near hydrostatic equilibrium. We find that the detached shock distance δ and the nonlinear drag force F depend solely on η = A/(M2 − 1) such that δ/rs = η and F/Flin = (η/2) −0.45 for η > 2, where Flin is the linear drag force of Ostriker (1999). The reduction of F compared with Flin is caused by front-back symmetry in the nonlinear density wakes. In subsonic cases, the flows without involving a shock do not readily reach a steady state. Nevertheless, the subsonic density wake near a perturber is close to being hydrostatic, resulting in the drag force similar to the linear case. Our results suggest that dynamical friction of a very massive object as in a merger of black holes near a galaxy center will take considerably longer than the linear prediction. Subject headings: black hole physics — hydrodynamics — ISM: general — shock waves