Modelling the selection of galaxy groups with end-to-end simulations

Context. Feedback from supernovae and active galactic nuclei (AGN) shapes the galaxy formation and evolution, but its impact remains unclear. Galaxy groups offer a crucial probe to determine this impact because their gravitational binding energy is comparable to the energy that is available from their central AGN. The XMM-Newton Group AGN Project (X-GAP) is a sample of 49 groups that were selected in the X-ray (ROSAT) and optical (SDSS) bands and provides a benchmark for hydrodynamical simulations. Aims. For this comparison, it is essential to understand the selection effects. We model the selection function of X-GAP by forward-modelling the detection process in the X-ray and optical bands. Methods. Using the Uchuu N-body simulation, we built a dark matter halo light cone, predicted X-ray group properties with a neural network trained on hydrodynamical simulations, and assigned matching observed properties to the galaxies. We compared the selected sample to the parent population in the light cone. Results. Our method provided a sample that matched the observed distribution of the X-ray luminosity and velocity dispersion. A completeness of 50% was reached at a velocity dispersion of 450 km/s in the X-GAP redshift range. The selection is driven by X-ray flux, with a secondary dependence on the velocity dispersion and redshift. We estimated a purity level of 93% for the X-GAP parent sample. We calibrated the relation of the velocity dispersion to the halo mass. We found a normalisation and slope that agree with the literature and an intrinsic scatter of about 0.06 dex. The measured velocity dispersion is only accurate within 10% for rich systems with more than about 20 members, and the velocity dispersion for groups with fewer than 10 members is biased at more than 20%. Conclusions. The X-ray follow-up refines the optical selection and enhances the purity, but reduces completeness. In an SDSS-like set-up, measurement errors for the velocity dispersion dominate the intrinsic scatter. Our selection model enables unbiased comparisons of thermodynamic properties and gas fractions between X-GAP groups and hydrodynamical simulations.