Dynamical models of cluster members to probe the total mass properties of cluster subhalos

I. A comparison with parametric strong lensing models

¹ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133 Milano, Italy
² INAF – IASF Milano, Via Corti 12, I-20133 Milano, Italy
³ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, I-44122 Ferrara, Italy
⁴ Institute of Cosmology and Gravitation, University of Portsmouth, Burnaby Rd, Portsmouth PO1 3FX, UK
⁵ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
⁶ Università di Salerno, Dipartimento di Fisica “E.R. Caianiello”, Via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy
⁷ INAF – Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Napoli, Italy
⁸ INFN – Gruppo Collegato di Salerno – Sezione di Napoli, Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, Via Giovanni Paolo II, 132, I-84084 Fisciano (SA), Italy
⁹ Independent researcher, Ismaning 85737, Germany

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Received: 23 December 2025
Accepted: 1 June 2026

Abstract

In this series of papers, we present dynamical models of cluster members in strong lensing galaxy clusters to independently probe the persistent discrepancy reported between strong lensing models and cosmological hydrodynamical simulations, in terms of total mass properties for the cluster subhalos. In this work, we focused our study on early-type galaxies within the clusters Abell 2744 (z = 0.309) and MACS J0416.1−2403 (z = 0.397). We took advantage of deep spectroscopic data from the Multi Unit Spectroscopic Explorer (MUSE), on the Very Large Telescope, complemented with Hubble Frontier Fields photometry. We used a pipeline based on spectral fitting to perform kinematic measurements of the line-of-sight velocity dispersion profiles of 109 cluster members, extending, in the best cases, up to approximately 15 kpc from the galactic centers. We modeled the cluster members assuming a dual pseudo-isothermal total mass density distribution and a Jaffe stellar mass density distribution. From the models, we inferred the values of the central stellar velocity dispersion, σ₀, and the truncation radius, r_t, for the galaxies in our sample. We found that σ₀ is accurately recovered for all of the cluster members and varies approximately from 40 km s⁻¹ to 370 km s⁻¹, while r_t is reliably measured for a fraction of galaxies in our sample, with sufficiently extended radial kinematic coverage. Our dynamical models predicted line-of-sight velocity dispersion profiles that fit the measured ones better than those inferred from strong lensing models. To tackle the discrepancy from the strong lensing side, we exploited the σ₀ measurements obtained from the dynamical models to calibrate the Faber-Jackson scaling relations for the cluster members in both galaxy clusters. When comparing our relations to those obtained in previous kinematics and strong lensing works, we found systematically higher normalization and compatible slope and scatter values. We conclude that our dynamical measurements of σ₀ and r_t, along with calibrated scaling relations, are more robust than previous kinematic estimates (which are biased due to not taking into account the effects of the point spread function and of averaging inside the aperture) and should therefore be adopted as improved initial prescriptions in future strong lensing models.