Dynamical Friction in a Gas: The Supersonic Case
  Any gravitating mass traversing a relatively sparse gas experiences a
retarding force created by its disturbance of the surrounding medium. In a
previous contribution (Lee & Stahler 2011), we determined this dynamical
friction force when the object's velocity was subsonic. We now extend our
analysis to the supersonic regime. As before, we consider small perturbations
created in the gas far from the gravitating object, and thereby obtain the net
influx of linear momentum over a large, bounding surface. Various terms in the
perturbation series formally diverge, necessitating an approximate treatment of
the flow streamlines. Nevertheless, we are able to derive exactly the force
itself. As in the subsonic case, we find that F=Mdot*V, where Mdot is the rate
of mass accretion onto the object and V its instantaneous velocity with respect
to distant background gas. Our force law holds even when the object is porous
(e.g., a galaxy) or is actually expelling mass in a wind. Quantitatively, the
force in the supersonic regime is less than that derived analytically by
previous researchers, and is also less than was found in numerical simulations
through the mid 1990s. We urge simulators to revisit the problem using modern
numerical techniques. Assuming our result to be correct, it is applicable to
many fields of astrophysics, ranging from exoplanet studies to galactic
dynamics.
