The perils of stacking optically selected groups in eROSITA data. The Magneticum perspective

Abstract: Hydrodynamical simulation predictions are often compared with observational data without fully accounting for systematics and biases specific to observational techniques. Using the magnetohydrodynamical simulation Magneticum, we generate mock eROSITA eRASS:4 data, combined with GAMA-like spectroscopic surveys and optically selected galaxy catalogs from the same light-cone, to analyze hot gas properties in galaxy groups via a stacking technique. This study aims to (i) incorporate observational systematics into predictions and (ii) evaluate the reliability of stacking techniques for determining average X-ray properties of galaxy groups. Our analysis provides X-ray emission predictions from Magneticum, including contributions from AGN, X-ray binaries (XRBs), and the Intra-Group Medium (IGM) as a function of halo mass, covering Milky Way (MW)-like groups to poor clusters. We find that AGN and XRBs dominate the X-ray surface brightness profiles of low-mass halos. The reliability of stacking techniques is tested by reproducing input X-ray surface brightness and electron density profiles, accounting for completeness and contamination of prior samples, miscentering of optical group centers, uncertainties in X-ray emissivity due to gas temperature and metallicity assumption, and systematics in halo mass proxies. The halo mass proxy emerges as the primary source of systematics, affecting X-ray surface brightness and scaling relations. We show that stacked X-ray luminosity-mass relations are flatter than input relations but consistent with observations. Additionally, the retrieved hot gas fraction-mass relation aligns well with observational data. These results highlight the need to account for systematic errors when comparing stacking techniques to other methods using different prior catalogs or predictions.