2025ApJ...991...56C

Galaxy clusters, the most massive, dark-matter-dominated, and most recently assembled structures in the Universe, are key tools for probing cosmology. However, uncertainties in scaling relations that connect cluster mass to observables like X-ray luminosity and temperature remain a significant challenge. In this paper, we present the results of an extensive investigation of 329 simulated clusters from IllustrisTNG300 cosmological simulations. Our analysis involves cross-correlating dark matter and the hot X-ray-emitting gas, considering both the 3D and 2D projected distributions to account for projection effects. We demonstrate that this approach is highly effective in evaluating the dynamical state of these systems and validating the often-utilized assumption of hydrostatic equilibrium, which is key for inferring cluster masses and constructing scaling relations. Our study revisits both the X-ray luminosity-mass and X-ray temperature-mass scaling relations, and demonstrates how the scatter in these relations correlates with the clusters' dynamical state. We demonstrate that matter-gas coherence enables the identification of an optimal set of relaxed clusters, reducing scatter in scaling relations by up to 40%. This innovative approach, which integrates higher-dimensional insights into scaling relations, might offer a new path to further reduce uncertainties in determining cosmological parameters from galaxy clusters.