On dynamical friction in a gaseous medium with a boundary
  Dynamical friction arises from the interaction of a perturber and the
gravitational wake it excites in the ambient medium. We study the effects of
the presence of a boundary on dynamical friction by studying analytically the
interaction of perturber with uniform rectilinear motion in a uniform
homogeneous medium with a reflecting planar boundary. Wake reflection at a
medium's boundary may occur at the edges of truncated disks perturbed by
planetary or stellar companions as well as in numerical simulations of
planet-disk interaction with no-outflow boundary conditions. In this paper, we
show that the presence of the boundary modifies the behaviour of dynamical
friction significantly. We find that perturbers are invariably pushed away from
the boundary and reach a terminal subsonic velocity near Mach 0.37 regardless
of initial velocity. Dynamical friction may even be reversed for Mach numbers
less than 0.37 thereby accelerating instead of decelerating the perturber.
Perturbers moving parallel to the boundary feel additional friction orthogonal
to the direction of motion that is much stronger than the standard friction
along the direction of motion. These results indicate that the common use of
the standard Chandrasekhar formula as a short hand estimate of dynamical
friction may be inadequate as observed in various numerical simulations.
