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

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 T<ns0:sc>HE</ns0:sc> T<ns0:sc>HREE</ns0:sc> H<ns0:sc>UNDRED</ns0:sc> P<ns0:sc>ROJECT</ns0:sc>. 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 YSZ-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.