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 _ { \infty } .
We model the perturber as a Plummer potential with softening radius r _ { s } , and run various models with differing \mathcal { A } = GM _ { p } / ( a _ { \infty } ^ { 2 } r _ { s } ) and \mathcal { M } = V _ { p } / a _ { \infty } 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 \mathcal { \eta } = \mathcal { A } / ( \mathcal { M } ^ { 2 } -1 ) such that \delta / r _ { s } = \eta and F / F _ { lin } = ( \mathcal { \eta } / 2 ) ^ { -0.45 } for \mathcal { \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 .