CLASH-VLT velocity anisotropy profiles in a stack of massive galaxy clusters

¹ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133 Milano, Italy
² INAF – Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, 34143 Trieste, Italy
³ IFPU – Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
⁴ INAF – IASF Milano, Via A. Corti 12, I-20133 Milano, Italy
⁵ INAF – Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
⁶ Università di Salerno, Dipartimento di Fisica “E.R. Caianiello”, Via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy
⁷ Dipartimento di Fisica G. Occhialini, Università degli Studi di Milano Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
⁸ Department of Physics and Earth Sciences, University of Ferrara, Via G. Saragat, 1, 44122 Ferrara, Italy
⁹ INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, I-40129 Bologna, Italy

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Received: 28 October 2025
Accepted: 13 February 2026

Abstract

We measured the velocity anisotropy profile, β(r), of different galaxy cluster member populations by analysing the stacked projected phase space of nine massive (M_200c > 7 × 10¹⁴ M_⊙) galaxy clusters at intermediate redshifts (0.18 < z < 0.45). We selected our sample of galaxy clusters by choosing the most round and virialised objects among the targets of the CLASH-VLT spectroscopic programme, which offers a large spectral database. Complementary MUSE observations of most of these clusters allowed us to identify an unprecedented number of cluster members, strongly enhancing the precision of our measurement with respect to previous studies. Our sample of cluster members is divided into four classes: the first two are based on colour (red and blue galaxies), and the other two on stellar mass (high and low). To study the velocity anisotropy profile of each cluster-member population, we employed two parallel techniques, namely the MAMPOSSt method (parametric in β(r)) and the inversion of the Jeans equation (non-parametric in β(r)). The results from both techniques are found to be in agreement for any given cluster member population, and suggest that the orbital anisotropy in galaxy clusters grows from the centre (where β ≈ 0.2 − 0.4) to the virial radius (β ≳ 0.8), and it is similar for the different cluster-member populations. We also find an interesting dynamical feature emerging from the Jeans inversion results, that is, a sudden drop in β(r) at a distance of ∼250 kpc from the cluster centre. We provide robust anisotropy estimates from our exploration of a highly significant number of model combinations: 72 with MAMPOSSt (varying the mass, surface number density, β(r) model, and galaxy population) and 18 (varying total mass model and galaxy population) in the Jeans inversion. Such an extensive investigation of the velocity anisotropy profile in galaxy clusters is a wide basis for future studies of cluster dynamical masses and cluster cosmology in the era of large spectroscopic surveys.