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The extended ROentgen Survey with an Imaging Telescope Array (eROSITA)onboard the Spectrum-Roentgen-Gamma (SRG) observatory is revolutionizing X-rayastronomy. It provides large samples of active galactic nuclei (AGN) andclusters of galaxies, with the potential of studying X-ray sources andmeasuring cosmological parameters using X-ray-selected samples with higherprecision than ever before. We aim to study the detection, and the selection ofAGN and clusters in the first eROSITA all-sky survey (eRASS1), and tocharacterize the properties of the source catalog. We produced a half-skyeRASS1 simulation, by combining models that truthfully represent the clustersand AGN. In total, we simulated 1 116 758 clusters and 225 583 320 AGN. We ranthe standard eROSITA detection algorithm. We matched the input and sourcecatalogs with a photon-based algorithm. We perfectly recovered the brightsources. We detected half of the AGN brighter than 2e-14 erg/s/cm2 as pointsources and half of the clusters brighter than 3e-13 erg/s/cm2 as extended inthe 0.5-2.0 keV band. We quantified the detection performance in terms ofcompleteness, false detection rate, and contamination. We studied the sourcecatalog according to multiple cuts of detection and extension likelihood. Wefind that the detection of clusters is mainly driven by flux and exposure. Itdepends on secondary effects, such as the size of the clusters and theirdynamical state. The cool core bias mostly affects faint clusters classified aspoint sources, while its impact on the extent-selected sample is small. Themeasured X-ray luminosity of the detected clusters is compatible with thesimulated values. We discuss how to best build samples of galaxy clusters forcosmological purposes, accounting for the nonuniform depth of eROSITA. Thissimulation provides a digital twin of the real eRASS1.

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