CHEX-MATE: Towards a consistent universal pressure profile and cluster mass reconstruction

¹ IRAP, CNRS, Université de Toulouse, CNES, UT3-UPS, Toulouse, France
² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
³ Université Grenoble Alpes, CNRS, LPSC-IN2P3, 53, Avenue des Martyrs, 38000 Grenoble, France
⁴ Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405 Orsay, France
⁵ INAF, Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano, Via A. Corti 12, 20133 Milano, Italy
⁶ Dipartimento di Fisica, Università degli studi di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy
⁷ INFN, Sezione di Roma ‘Tor Vergata’, Via della Ricerca Scientifica, 1, 00133 Roma, Italy
⁸ Dipartimento di Fisica, Sapienza Universitá di Roma, Piazzale Aldo Moro 5, I-00185 Rome, Italy
⁹ Michigan State University (MSU) – Dept of Physics and Astronomy, 567 Wilson Road, East Lansing, Michigan 48824, USA
¹⁰ Department of Astronomy, University of Geneva, Ch. d’Ecogia 16, CH-1290 Versoix, Switzerland
¹¹ INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
¹² INFN, Sezione di Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy
¹³ Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41125 Modena, Italy
¹⁴ Dipartimento di Fisica e Astronomia (DIFA), Alma Mater Studiorum – Universitá di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
¹⁵ Istituto Nazionale di Astrofisica – Istituto di Radioastronomia (IRA), Via Gobetti 101, 40129 Bologna, Italy
¹⁶ IJCLab, Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
¹⁷ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK
¹⁸ Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
¹⁹ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
²⁰ HH Wills Physics Laboratory, University of Bristol, Bristol, UK
²¹ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
²² INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²³ INAF, Osservatorio Astronomico di Trieste, Via Tiepolo 11, I-34131 Trieste, Italy
²⁴ IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
²⁵ Department of Physics; University of Michigan, Ann Arbor, MI 48109, USA
²⁶ California Institute of Technology, 1200 East California Boulevard, Pasadena, CA, USA

^★ Corresponding author: miren.munoz-echeverria@irap.omp.eu

Received: 20 June 2025
Accepted: 17 October 2025

Abstract

In a self-similar paradigm of structure formation, the thermal pressure of the hot intra-cluster gas follows a universal distribution, once the profile of each cluster is normalised based on the proper mass and redshift dependencies. The reconstruction of such a universal pressure profile requires an individual estimate of the mass of each cluster. In this context, we present a method to jointly fit, for the first time, the universal pressure profile and individual cluster M₅₀₀ masses over a sample of galaxy clusters, properly accounting for correlations between the profile shape and amplitude, and masses that scale the individual profiles. We demonstrate the power of the method and show that a consistent exploitation of the universal pressure profile and cluster mass estimates when modelling the thermal pressure in clusters is necessary to avoid biases. In particular, the method, informed by a cluster mass scale, outputs individual cluster masses with the same accuracy and greater precision than input masses. Using data from the Cluster HEritage project with XMM-Newton: Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE), we investigate a sample of ∼25 galaxy clusters spanning mass and redshift ranges of 2 ≲ M₅₀₀/10¹⁴ M_⊙ ≲ 14 and 0.07 < z < 0.6.