Virial quantities of galaxy clusters from extrapolating strong-lensing mass profiles

¹ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133 Milano, Italy
² INAF – IASF Milano, Via A. Corti 12, I-20133 Milano, Italy
³ INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, I-40129 Bologna, Italy
⁴ INFN – Sezione di Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy

^⋆ Corresponding author: enrico.maraboli@unimi.it

Received: 12 March 2025
Accepted: 5 May 2025

Abstract

We study the radial total mass profiles of nine massive galaxy clusters (M_200c > 5 × 10¹⁴ M_⊙) in the redshift range 0.2 < z < 0.9. These clusters were observed as part of the CLASH, HFF, BUFFALO, and CLASH-VLT programs, which provided high-quality photometric and spectroscopic data. Additional high-resolution spectroscopic data were obtained with the integral-field spectrograph MUSE at the Very Large Telescope. Our research takes advantage of strong-lensing analyses that rely on deep panchromatic and spectroscopic measurements. From these data, we measure the projected total mass profiles of each galaxy cluster in our sample. We fit these mass profiles with simple one-component spherically symmetric mass models including the Navarro–Frenk–White (NFW) nonsingular isothermal sphere, dual pseudo-isothermal ellipsoidal, a beta model, and Hernquist profiles. We performed a Bayesian analysis to sample the posterior probability distributions of the free parameters of the models. We find that the NFW, Hernquist, and beta models are the most suitable profiles for fitting the measured projected total mass profiles of the clusters. Moreover, we tested the robustness of our results by changing the region in which we performed the fits: We slightly modified the center of the projected mass profiles and the radial range of the region. We employed the results obtained with the Hernquist profile to compare our total mass estimates (M_H^tot = M_H(r→+∞)) with the M_200c values from weak-lensing studies. Through this analysis, we found scaling relations between M_H^tot and M_200c and a value of the scale radius, r_S, and R_200c. Interestingly, we also found that the M_200c values we obtained by extrapolating the total mass profiles we fit are very close to the weak-lensing results. This feature can be exploited in future studies of clusters and cosmology because it provides an easy way to infer the virial masses of clusters.