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X-ray observations of merging clusters provide many examples of bow shocksleading merging subclusters. While the Mach number of a shock can be estimatedfrom the observed density jump using Rankine-Hugoniot condition, it reflectsonly the velocity of the shock itself and is generally not equal to thevelocity of the infalling subcluster dark matter halo or to the velocity of thecontact discontinuity separating gaseous atmospheres of the two subclusters.Here we systematically analyze additional information that can be obtained bymeasuring the standoff distance, i.e. the distance between the leading edge ofthe shock and the contact discontinuity that drives this shock. The standoffdistance is influenced by a number of additional effects, e.g. (1) thegravitational pull of the main cluster (causing acceleration/deceleration ofthe infalling subcluster), (2) the density and pressure gradients of theatmosphere in the main cluster, (3) the non-spherical shape of the subcluster,and (4) projection effects. The first two effects tend to bias the standoffdistance in the same direction, pushing the bow shock closer to (farther awayfrom) the subcluster during the pre- (post-)merger stages. Particularly, in thepost-merger stage, the shock could be much farther away from the subclusterthan predicted by a model of a body moving at a constant speed in a uniformmedium. This implies that a combination of the standoff distance withmeasurements of the Mach number from density/temperature jumps can provideimportant information on the merger, e.g. differentiating between the pre- andpost-merger stages.

Standoff Distance of Bow Shocks in Galaxy Clusters as Proxy for Mach Number