Nonlinear Dynamical Friction of a Circular-Orbit Perturber in a Gaseous
  Medium
  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 on circular orbits. This work extends our
previous studies that explored the cases of low-mass perturbers on 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 rho0 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, Mach=Vp/a0, and B=G*Mp/(a0^2*Rp). 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 makes the detached shock distance
reduced 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 rho1=(1 + 0.46B)*rho0 depending
weakly on Mach. 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 = 4*pi*rho1*(G*Mp/Vp)^2 * (0.7/etaB)
for etaB = B/(Mach^2 -1) > 0.1; the drag force for low-mass perturbers with
etaB < 0.1 agrees well with the linear prediction. The nonlinear drag force
becomes independent of R as long as R < etaB/2, which places an upper limit on
the perturber size for accurate evaluation of the drag force in numerical
simulations.
