Detecting clusters of galaxies and active galactic nuclei in an eROSITA all-sky survey digital twin

Context. The extended ROentgen Survey with an Imaging Telescope Array (eROSITA) on board the Spectrum-Roentgen-Gamma (SRG) observatory is revolutionizing X-ray astronomy. The mission provides unprecedented samples of active galactic nuclei (AGN) and clusters of galaxies, with the potential of studying astrophysical properties of X-ray sources and measuring cosmological parameters using X-ray-selected samples with higher precision than ever before. Aims. We aim to study the detection, and the selection of AGN and clusters of galaxies in the first eROSITA all-sky survey, and to characterize the properties of the source catalog. Methods. We produced a half-sky simulation at the depth of the first eROSITA survey (eRASS1), by combining models that truthfully represent the population of clusters and AGN. In total, we simulated 1 116 758 clusters and 225 583 320 AGN. We ran the standard eROSITA detection algorithm, optimized for extragalactic sources. We matched the input and the source catalogs with a photon-based matching algorithm. Results. We perfectly recovered the bright AGN and clusters. We detected half of the simulated AGN with flux larger than 2 × 10−14 erg s−1 cm−2 as point sources and half of the simulated clusters with flux larger than 3 × 10−13 erg s−1 cm−2 as extended sources in the 0.5–2.0 keV band. We quantified the detection performance in terms of completeness, false detection rate, and contamination. We studied the population in the source catalog according to multiple cuts of source detection and extension likelihood. We find that the latter is suitable for removing contamination, and the former is very efficient in minimizing the false detection rate. We find that the detection of clusters of galaxies is mainly driven by flux and exposure time. It additionally depends on secondary effects, such as the size of the clusters on the sky plane and their dynamical state. The cool core bias mostly affects faint clusters classified as point sources, while its impact on the extent-selected sample is small. We measured the fraction of the area covered by our simulation as a function of limiting flux. We measured the X-ray luminosity of the detected clusters and find that it is compatible with the simulated values. Conclusions. We discuss how to best build samples of galaxy clusters for cosmological purposes, accounting for the nonuniform depth of eROSITA. This simulation provides a digital twin of the real eRASS1