X-ray wakes as probes of galaxy cluster dynamics

Abstract

If a galaxy resides in a cluster, then its passage through the pervasive intracluster medium will produce a detectable signature in the X-ray emission from the cluster. The simplest kinematic information that can be extracted from this signature is the galaxy's direction of motion on the plane of the sky. This paper explores the constraints on cluster dynamics that could be derived from such information. In particular, we show that it is possible to define a projected anisotropy parameter, B(R), which is directly analogous to the usual orbital anisotropy parameter. We describe an estimator for this quantity, Bhat(R), which can be derived in a robust and straightforward manner. Using a simple dynamical model, we demonstrate the ambiguity between the distribution of mass and the distribution of galaxy orbits when interpreting the traditional measures of cluster kinematics (the projected density of galaxies and their line-of-sight velocity dispersion). As an example, we show how two very different dynamical models can fit the kinematic properties of the Coma cluster. We demonstrate that the measurement of Bhat using a relatively small sample of wake directions (N_{wake} ~ 50) would provide an effective mechanism for lifting this degeneracy. Thus, by combining X-ray measurements of wake directions with number counts and line-of-sight velocities derived from optical data, it will prove possible to measure both the orbit distribution and the form of the gravitational potential in clusters of galaxies.