Nonlinear Dynamical Friction in a Gaseous Medium

TL;DR

This study uses high-resolution simulations to explore nonlinear gravitational gas responses and drag forces on massive perturbers, revealing nonlinear effects like detached shocks and vortex rings that alter dynamical friction timescales.

Contribution

It provides a detailed analysis of nonlinear dynamical friction, showing how detached shocks and vortex rings influence the drag force beyond linear theory predictions.

Findings

Detached bow shocks form for supersonic perturbers.

Nonlinear drag force scales with ta as /F_{lin}=(ta/2)^{-0.45}.

Subsonic wakes are hydrostatic and produce linear-like drag.

Abstract

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.