The origin of scatter in the X-ray luminosity–halo mass relation of galaxy clusters

ABSTRACT Galaxy groups and clusters are excellent probes of large-scale structure and are shaped by some of the most energetic physical processes in the Universe. They follow a tight scaling relation of X-ray luminosity with halo mass. However, predicting the dependence of the scatter in this relation on mass and redshift is challenging, due to the statistical requirement of large simulation volumes. Using the large volume cosmological hydrodynamical simulations for galaxy cluster physics FLAMINGO and TNG300+TNG-Cluster, we fit this relation and its scatter, focusing on $M_{\rm 500c}\gt10^{13}~\mathrm{M_\odot }$ and $z \le 2$. We find qualitatively similar, but quantitatively different results for the two models. For the first time, we study ways to reduce the scatter using properties beyond X-ray luminosity, namely six ICM, six galaxy, and eleven dark matter halo properties. For both FLAMINGO and TNG300+TNG-Cluster, the gas fraction and thermal Sunyaev–Zeld́ovich (SZ) signal correlate strongest with X-ray scatter, reducing it by over 50 per cent when accounting for their partial correlations. Galaxy and halo properties correlate weakly with X-ray scatter, typically reducing it by 10–20 per cent. Our results are qualitatively robust across different FLAMINGO feedback variations, though the correlations weaken for stronger feedback and with increasing redshift. Differences between FLAMINGO and TNG300+TNG-Cluster are only apparent at the high-mass end – where e.g. the galaxy stellar age correlates strongly for FLAMINGO, but not for TNG300+TNG-Cluster – confirming robustness across physics implementations. We provide fitting formulas for the scatter and its corrections, for direct application to cosmological analyses and observational data.