CHEX-MATE: Cluster multi-probes in three dimensions (CLUMP-3D)

II. Combined gas and dark matter analysis from X-ray, SZE, and WL

¹ California Institute of Technology, 1200 E. California Blvd., MC 367-17 Pasadena, CA 91125, USA
² Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
³ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
⁴ INFN, Sezione di Bologna, viale Berti Pichat 6/2, I-40127 Bologna, Italy
⁵ Université Paris Saclay, IRFU/CEA, 91191 Gif-sur-Yvette, France
⁶ Department of Astronomy, University of Geneva, Ch. d’Ecogia 16, CH-1290 Versoix, Switzerland
⁷ Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), No. 1, Section 4, Roosevelt Road, Taipei 106216, Taiwan
⁸ Dipartimento di Fisica, Università degli studi di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy
⁹ INFN, Sezione di Roma ‘Tor Vergata’, Via della Ricerca Scientifica, 1, 00133 Roma, Italy
¹⁰ Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41125 Modena, Italy
¹¹ Laboratoire d’Astrophysique de Marseille, Aix-Marseille Univ., CNRS, CNES, 13013 Marseille, France
¹² Institut d’Astrophysique de Paris, UMR7095 CNRS & Sorbonne Université, 98bis Bd Arago, 75014 Paris, France
¹³ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, UK
¹⁴ INAF, Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano, Via A. Corti 12, 20133 Milano, Italy
¹⁵ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
¹⁶ INAF – Osservatorio Astronomico di Trieste, Via Tiepolo 11, I-34131 Trieste, Italy
¹⁷ Department of Physics; University of Michigan, Ann Arbor, MI 48109, USA

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 15 July 2025
Accepted: 16 March 2026

Abstract

Under the standard model of hierarchical structure formation, the overall geometry of galaxy clusters is better described by a triaxial ellipse than by a sphere. As a result, the application of spherically symmetric models can result in significant biases, with masses derived from weak-lensing observations being particularly sensitive. These biases can be mitigated by fitting a triaxial model, but this requires deep multi-probe data along with a set of physically motivated models to describe them. We present a multi-probe triaxial analysis method based on the data available for galaxy clusters in the Cluster Heritage project with XMM-Newton – Mass Assembly and Thermodynamics at Endpoint of structure formation (CHEX-MATE), which includes X-ray data from XMM-Newton, Sunyaev-Zel’dovich effect maps from Planck and ACT, and weak-lensing data from Subaru. This work builds upon our previous development of a gas-only X-ray and Sunyaev-Zel’dovich triaxial fitting formalism in Paper I. After verifying our approach using mock observations of model clusters with known properties, we applied it to the CHEX-MATE galaxy cluster PSZ2 G313.33+61.13 (Abell 1689). We found that the cluster is elongated along the line of sight relative to the plane of sky by a factor of ℛ_LP = 1.20 ± 0.04. As a result, the weak-lensing mass obtained from our triaxial fit, M_200c = (13.88^+1.73_−1.43) × 10¹⁴ M_⊙, is significantly lower than the value of (17.77^+2.00_−1.75) × 10¹⁴ M_⊙ obtained from a spherically symmetric fit that otherwise employed the same method. Our triaxial fit finds a concentration of c_200c = 8.66^+2.08_−1.70, consistent with the spherically symmetric value of 9.99^+2.26_−1.8, which suggests that the unexpectedly high concentration in Abell 1689 is not due to triaxiality and orientation. We also measured the nonthermal pressure fraction at radii between 0.18–1.37 Mpc and found a minimum of approximately 20% at intermediate radii, increasing to near 30% at the smallest and largest radii, and with a typical measurement precision of ±5%.