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 M_p moving at velocity V_p through a uniform
gaseous medium of adiabatic sound speed a_0. We model the perturber as a
Plummer potential with softening radius r_s, and run various models with
differing A=GM_p/(a_0^2 r_s) and M=V_p/a_0 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
$\delta$ and the nonlinear drag force F depend solely on \eta=A/(M^2-1) such
that \delta/r_s=\eta and F/F_{lin}=(\eta/2)^{-0.45} for \eta>2, where F_{lin}
is the linear drag force of Ostriker (1999). The reduction of F compared with
F_{lin} 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.
