  The eROSITA X-ray telescope on board the Spectrum-Roentgen-Gamma (SRG)
satellite has started to detect new X-ray sources over the full sky at an
unprecedented rate. Understanding the performance and selection function of the
source detection is important for the subsequent scientific analysis of the
eROSITA catalogs. Through simulations, we test and optimize the eROSITA source
detection procedures, and we characterize the detected catalog quantitatively.
Taking the eROSITA Final Equatorial-Depth Survey (eFEDS) as an example, we ran
extensive photon-event simulations based on our best knowledge of the
instrument characteristics, the background spectrum, and the population of
astronomical X-ray sources. We introduce a method of analyzing source detection
completeness, purity, and efficiency based on the origin of each photon.
According to the source detection efficiency measured in the simulation, we
chose a two-pronged strategy to build eROSITA X-ray catalogs, creating a main
catalog using only the most sensitive band (0.2-2.3 keV) and an independent
hard-band-selected catalog using multiband detection in a range up to 5 keV.
Because our mock data are highly representative of the real eFEDS data, we used
the mock catalogs to measure the completeness and purity of the eFEDS catalogs
as a function of multiple parameters, such as detection likelihood, flux, and
luminosity. These measurements provide a basis for choosing the eFEDS catalog
selection thresholds. The mock catalogs (available with this paper) can be used
to construct the selection function of active galactic nuclei and galaxy
clusters. A direct comparison of the output and input mock catalogs also gives
rise to a correction curve that converts the raw point-source flux distribution
into the intrinsic number counts distribution.
