Standoff Distance of Bow Shocks in Galaxy Clusters as Proxy for Mach
  Number
  X-ray observations of merging clusters provide many examples of bow shocks
leading merging subclusters. While the Mach number of a shock can be estimated
from the observed density jump using Rankine-Hugoniot condition, it reflects
only the velocity of the shock itself and is generally not equal to the
velocity of the infalling subcluster dark matter halo or to the velocity of the
contact discontinuity separating gaseous atmospheres of the two subclusters.
Here we systematically analyze additional information that can be obtained by
measuring the standoff distance, i.e. the distance between the leading edge of
the shock and the contact discontinuity that drives this shock. The standoff
distance is influenced by a number of additional effects, e.g. (1) the
gravitational pull of the main cluster (causing acceleration/deceleration of
the infalling subcluster), (2) the density and pressure gradients of the
atmosphere in the main cluster, (3) the non-spherical shape of the subcluster,
and (4) projection effects. The first two effects tend to bias the standoff
distance in the same direction, pushing the bow shock closer to (farther away
from) the subcluster during the pre- (post-)merger stages. Particularly, in the
post-merger stage, the shock could be much farther away from the subcluster
than predicted by a model of a body moving at a constant speed in a uniform
medium. This implies that a combination of the standoff distance with
measurements of the Mach number from density/temperature jumps can provide
important information on the merger, e.g. differentiating between the pre- and
post-merger stages.
