Dynamical friction for accelerated motion in a gaseous medium
  Dynamical friction arises from the interaction of a perturber and the
gravitational wake it excites in the ambient medium. This interaction is
usually derived assuming that the perturber has a constant velocity. In
realistic situations, motion is accelerated as for instance by dynamical
friction itself. Here, we study the effect of acceleration on the dynamical
friction force. We characterize the density enhancement associated with a
constantly accelerating perturber with rectilinear motion in an infinite
homogeneous gaseous medium and show that dynamical friction is not a local
force and that its amplitude may depend on the perturber's initial velocity.
The force on an accelerating perturber is maximal between Mach 1 and Mach 2,
where it is smaller than the corresponding uniform motion friction. In the
limit where the perturber's size is much smaller than the distance needed to
change the Mach number by unity through acceleration, a subsonic perturber
feels a force similar to uniform motion friction only if its past history does
not include supersonic episodes. Once an accelerating perturber reaches large
supersonic speeds, accelerated motion friction is marginally stronger than
uniform motion friction. The force on a decelerating supersonic perturber is
weaker than uniform motion friction as the velocity decreases to a few times
the sound speed. Dynamical friction on a decelerating subsonic perturber with
an initial Mach number larger than 2 is much larger than uniform motion
friction and tends to a finite value as the velocity vanishes in contrast to
uniform motion friction.
