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

TL;DR

This study analyzes nine massive clusters from CLASH-VLT to measure their velocity anisotropy profiles $β(r)$ from the core to near the virial radius. It combines CLUMPS-based membership, MAMPOSSt-driven mass-profile inference with lensing priors, and a Jeans-equation inversion (JEI) to obtain nonparametric $β(r)$ for each cluster. The results show a mildly radial average $β(r)$ that increases with radius, but with substantial cluster-to-cluster variance and a clear dependence on $M_{200}$ and $c_{200}$, indicating no universal $β(r)$ across clusters. Comparisons with nearby observations and hydrodynamical simulations reveal good agreement in the mean profile but larger observed scatter, reinforcing the connection between orbital structure and a cluster’s merging history and dynamical state.

Abstract

The velocity anisotropy profiles, $β(r)$, of galaxy clusters are directly related to the shape of the orbits of their member galaxies. Knowledge of $β(r)$ 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 $β(r)$ of nine massive clusters at redshift $0.19 \leq z \leq 0.45$ 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 $β(r)$ 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 $β(r)$ is slightly radial, with the anisotropy increasing from $β\simeq 0.2$ at the cluster center, to $β\simeq 0.5$ at the virial radius. There is substantial variance in the $β(r)$ 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 $β(r)$. A comparison with cluster-sized halos in cosmological hydrodynamical simulations indicates a very good agreement for the average $β(r)$, but a smaller variance in the profiles than observed. We conclude that massive clusters cannot be characterized by a unique universal $β(r)$ and that the orbital distribution of cluster galaxies carries information on the merging history of the cluster.

Figures (13)

• Figure 1: Projected phase-space diagram of the 427 galaxies selected as members of the M1206 cluster (other clusters are shown in Fig. \ref{['f:pps']}) by the CLUMPS method in the region $R \leq 1.36 \,r_{200}$. The three numbers at the bottom left indicate, from left to right, the number of galaxies selected for the dynamical analysis (black-circled green dots); the number of CLUMPS members that are excluded from the dynamical analysis because they are at $R \leq 0.05$ Mpc, which is the region dynamically dominated by the BCG (red circles), and the number of CLUMPS members that are not used in the dynamical analysis because they are flagged as interlopers by the escape-velocity criterion (gray circles). The vertical lines indicate $R=0.05$ Mpc and $R=r_{200}$. The values of $r_{200}$ and $v_{200}$ come from Umetsu+18.
• Figure 2: Dots with 1$\sigma$ error bars: los VDP of M1206. Dashed blue line and cyan shading: Best-fit MAMPOSSt solution within 68% confidence levels, estimated on a random selection of 3000 MCMC steps. Red solid line and orange shading: JEI-predicted VDP and 68% confidence levels. The values of $r_{200}$ (indicated by the vertical magenta line) and $v_{200}$ are the best fits of the MAMPOSSt analysis (other clusters are shown in Fig. \ref{['f:vdp']}.)
• Figure 3: Each panel shows the 1$\sigma$ confidence levels of a cluster JEI$\beta_{{\rm sym}}(r)$, as obtained from the procedure described in Sect. \ref{['ss:jeans']} (red shadings), and its central value (yellow line), the weighted mean of the nine profiles, $\langle \beta_{{\rm sym}}(r) \rangle$, as defined in eq. \ref{['e:wmean']} (black dash-dotted line), and the $\beta_{{\rm sym}}(r)$ of the other eight clusters (black dotted lines). The horizontal dashed black line indicates isotropic orbits. Orbits are radial above this line and tangential below it.
• Figure 4: Results of the stepwise regression analysis (forward approach). Each square is the value of the coefficient of determination, $R^2$, of ${\rm d}\beta$ vs. the quantities labeled on the x-axis, with the inclusion of an additional quantity at each new point from left to right.
• Figure 5: ${\rm d}\beta$ vs. $M_{200}$. The symbol size is proportional to $c_{200}$. The colors identify our nine clusters, in order of increasing redshift with increasing color wavelength (from blue to brown).