Deriving accurate galaxy cluster masses using X-ray thermodynamic profiles and graph neural networks

¹ Univ. Lille, Univ. Artois, Univ. Littoral Côte d’Opale, ULR 7369 – URePSSS – Unité de Recherche Pluridisciplinaire Sport Santé Société, F-59000 Lille, France
² Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai 400005, India
³ INAF – Osservatorio Astronomico di Trieste, Via Tiepolo 11, I-34131 Trieste, Italy
⁴ IFPU, Via Beirut, 2, 3I-4151 Trieste, Italy
⁵ Department of Physics; University of Michigan, Ann Arbor, MI 48109, USA
⁶ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁷ Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Biología y Geología, Física y Química Inorgánica, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
⁸ Université Paris-Saclay, CEA, Département de Physique des Particules, 91191 Gif-sur-Yvette, France
⁹ Departamento de Física Teórica, Módulo 15 Universidad Autónoma de Madrid, 28049 Madrid, Spain

^★ Corresponding authors: asif-iqbal.ahangar@univ-lille.fr; subha@tifr.res.in

Received: 27 May 2025
Accepted: 29 September 2025

Abstract

The precise determination of galaxy cluster masses is crucial for establishing reliable mass-observable scaling relations in cluster cosmology. We employed graph neural networks (GNNs) to estimate galaxy cluster masses from radially sampled profiles of the intra-cluster medium (ICM) inferred from X-ray observations. GNNs naturally handle inputs of variable length and resolution by representing each ICM profile as a graph, enabling accurate and flexible modelling across diverse observational conditions. We trained and tested the GNN model using state-of-the-art hydrodynamical simulations of galaxy clusters from THE THREE HUNDRED PROJECT. The mass estimates using our method exhibit no systematic bias compared to the true cluster masses in the simulations. Additionally, we achieved a scatter in recovered mass versus true mass of about 6%, which is a factor of six smaller than obtained from a standard hydrostatic equilibrium approach. Our algorithm is robust to both data quality and cluster morphology, and it is capable of incorporating model uncertainties alongside observational uncertainties. Finally, we applied our technique to XMM-Newton observed galaxy cluster samples and compared the GNN derived mass estimates with those obtained with Y_SZ-M₅₀₀ scaling relations. Our results provide strong evidence, at the 5σ level, of a mass-dependent bias in SZ derived masses: higher-mass clusters exhibit a greater degree of deviation. Furthermore, we find the median bias to be (1−b) = 0.85_−0.14^+0.34, albeit with significant dispersion due to its mass dependence. This work takes a significant step towards establishing unbiased observable mass scaling relations by integrating X-ray, SZ, and optical datasets using deep learning techniques, thereby enhancing the role of galaxy clusters in precision cosmology.