CLASH-VLT: The variance in the velocity anisotropy profiles of galaxy clusters

Abstract

The velocity anisotropy profiles, ${\hat{I}}^2(r)$, of galaxy clusters are directly related to the shape of the orbits of their member galaxies. Knowledge of ${\hat{I}}^2(r)$ is important to understand the assembly process of clusters and the evolutionary processes of their galaxies, and to improve the determination of cluster masses based on cluster kinematics. We determined the ${\hat{I}}^2(r)$ of nine massive clusters at redshift $0.19\le z\le 0.45$ from the CLASH-VLT data set, with 150 to 950 spectroscopic members each. We selected spectroscopic cluster members with the CLUMPS algorithm calibrated on cosmological simulations. We applied the MAMPOSSt code to the distribution of cluster members in projected phase-space to constrain the cluster mass profile, $M(r)$, using priors derived from a previous gravitational lensing analysis. Given the MAMPOSSt best-fit solution for $M(r)$, we then solved the inversion of the Jeans equation to determine ${\hat{I}}^2(r)$ without assumptions of its functional form. We also ran the DS+ code to identify subclusters and characterize the dynamical status of our clusters. The average ${\hat{I}}^2(r)$ is slightly radial, with the anisotropy increasing from ${\hat{I}}^2\simeq 0.2$ at the cluster center, to ${\hat{I}}^2\simeq 0.5$ at the virial radius. There is substantial variance in the ${\hat{I}}^2(r)$ of the individual clusters, that cannot be entirely accounted for by the observational uncertainties. Clusters of lower mass and with a low concentration per given mass have more tangential ${\hat{I}}^2(r)$. A comparison with cluster-sized halos in cosmological hydrodynamical simulations indicates a very good agreement for the average ${\hat{I}}^2(r)$, but a smaller variance in the profiles than observed. We conclude that massive clusters cannot be characterized by a unique universal ${\hat{I}}^2(r)$ and that the orbital distribution of cluster galaxies carries information on the merging history of the cluster.

Accepted for publication in A&A on Jan 31, 2026