Deriving Galaxy Cluster Velocity Anisotropy Profiles from a Joint Analysis of Dynamical and Weak Lensing Data

Abstract

We present an analytic approach to lift the mass-anisotropy degeneracy in clusters of galaxies by utilizing the line-of-sight velocity dispersion of clustered galaxies jointly with weak lensing inferred masses. More specifically, we solve the spherical Jeans equation by assuming a simple relation between the line-of-sight velocity dispersion and the radial velocity dispersion and recast the Jeans equation as a Bernoulli differential equation that has a well-known analytic solution. We first test our method in cosmological N -body simulations and then derive the anisotropy profiles for 35 archival data galaxy clusters with an average redshift of . The resulting profiles yield a weighted average global value of (stat) ±0.15 (sys). This indicates that clustered galaxies tend to globally fall on radially anisotropic orbits. We note that this is the first attempt to derive velocity anisotropy profiles for a cluster sample of this size utilizing joint dynamical and weak lensing data.