Measurement of the dark matter velocity anisotropy in galaxy clusters

The internal dynamics of a dark matter structure may have the remarkable property that the local temperature in the structure depends on direction. This is parametrized by the velocity anisotropy beta which must be zero for relaxed collisional structures, but has been shown to be non-zero in numerical simulations of dark matter structures. Here we present a method to infer the radial profile of the velocity anisotropy of the dark matter halo in a galaxy cluster from X-ray observables of the intracluster gas. This non-parametric method is based on a universal relation between the dark matter temperature and the gas temperature which is confirmed through numerical simulations. We apply this method to observational data and we find that beta is significantly different from zero at intermediate radii. Thus we find a strong indication that dark matter is effectively collisionless on the dynamical time-scale of clusters, which implies an upper limit on the self-interaction cross-section per unit mass sigma/m < 1 cm2/g. Our results may provide an independent way to determine the stellar mass density in the central regions of a relaxed cluster, as well as a test of whether a cluster is in fact relaxed.