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

Context. Hydrodynamical simulation predictions are often compared with observational data without fully accounting for systematics and biases specific to observational techniques. In this study, we used the magnetohydrodynamical simulation Magneticum to create a mock dataset that replicates the observational data available for analyzing hot gas properties in extensive galaxy group samples. Aims. Specifically, we simulated eROSITA eRASS:4 data along with a GAMA-like galaxy spectroscopic survey from the same lightcone and generated mock, optically selected galaxy catalogs using widely employed group-finding algorithms. We then applied an observational stacking technique to the mock eRASS:4 observations, and used the mock group catalogs as priors to determine the average properties of the underlying group population. This approach serves two primary purposes: (i) to produce predictions that incorporate observational systematics, and (ii) to assess these systematics and evaluate the reliability of the stacking technique in deriving the average X-ray properties of galaxy groups from eROSITA data. Methods. We provide the predicted X-ray emission of the Magneticum divided into all contributions of AGN, X-ray binaries (XRBs), and Intra-Group Medium (IGrM) per bin of halo mass. The predicted AGN and XRB contamination dominates the X-ray surface brightness profile emission in all halos with masses below 10¹³ M_⊙, which contains the majority of low X-ray luminosity AGN. We tested the reliability of the stacking technique in reproducing the input X-ray surface brightness and electron density profile for all tested optical group selection algorithms. We considered completeness and contamination of the prior samples, miscentering of the optical group center, uncertainties in determining the X-ray emissivity due to the assumptions of mean gas temperature and metallicity, and systematics in the available halo mass proxy. Results. The primary source of systematics in our analysis arises from the precision of the halo mass proxy, which might impact the estimation of X-ray surface brightness profiles when utilized as a prior, and derived scaling relations. Our analysis displays the L_X–mass relationships produced by stacking various optically selected group priors and reveals that, in each instance, the slope of these relations appears somewhat flatter than the input relation, though still in agreement with observational data. We retrieve the f_gas–mass relation within R₅₀₀ effectively and find agreement between the predictions and observational data. Conclusions. These systematic errors must be considered when comparing the results of any stacking technique with other works in the literature based on different prior catalogs, detections, or predictions.