Nonlinear dynamical friction of a circular-orbit perturber in a gaseous medium

Abstract

We use three-dimensional hydrodynamic simulations to investigate the nonlinear gravitational responses of gas to, and the resulting drag forces on, very massive perturbers moving in circular orbits. This work extends our previous studies that explored the cases of low-mass perturbers in circular orbits and massive perturbers on straight-line trajectories. The background medium is assumed to be non-rotating, adiabatic with index 5/3, and uniform with density ρ0 and sound speed a0. We model the gravitating perturber using a Plummer sphere with mass Mp and softening radius rs in a uniform circular motion at speed Vp and orbital radius Rp, and run various models with differing R ≡ rs/Rp, M ≡ Vp/a0, and B ≡ GMp/(a20Rp). A quasi-steady density wake of a supersonic model consists of a hydrostatic envelope surrounding the perturber, an upstream bow shock, and a trailing low-density region. The continuous change in the direction of the perturber motion reduces the detached shock distance compared to the linear-trajectory cases,while the orbit-averaged gravity of the perturber gathers the gas toward the center of the orbit, modifying the background preshock density to ρ1 ≈ (1+0.46B1.1)ρ0 depending weakly onM. For sufficiently massive perturbers, the presence of a hydrostatic envelope makes the drag force smaller than the prediction of the linear perturbation theory, resulting in F = 4φρ1(GMp)2/V2p × (0.7η-1B ) for ηB≡ B/(M2 -1) ≥ 0.1; the drag force for low-mass perturbers with ηB ≤ 0.1 agrees well with the linear prediction. The nonlinear drag force becomes independent of R as long as R ≤ ηB/2, which places an upper limit on the perturber size for accurate evaluation of the drag force in numerical simulations. © 2010 The American Astronomical Society.