Deriving galaxy cluster velocity anisotropy profiles from a joint analysis of dynamical and weak lensing data

TL;DR

This paper introduces an analytic method to determine galaxy cluster velocity anisotropy profiles by combining dynamical and weak lensing data, successfully applied to simulations and real data, revealing radially anisotropic galaxy orbits.

Contribution

It presents the first analytic approach to derive velocity anisotropy profiles from joint dynamical and weak lensing data for galaxy clusters.

Findings

Average anisotropy parameter of 0.35 indicating radial orbits

Method validated with cosmological N-body simulations

Applied to 35 galaxy clusters with consistent results

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 $\langle {z}_{c}\rangle =0.25$. The resulting profiles yield a weighted average global value of $\langle \beta (0.2\leqslant R/{R}_{200}\leqslant 1)\rangle =0.35\pm 0.28$ (stat) \pm 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