SRGz: building an optical cross-match model for the X-ray SRG/eROSITA sources using the Lockman Hole data

We present a probabilistic model built for the optical cross-match between the SRG/eROSITA X-ray sources and photometric data from the DESI Legacy Imaging Surveys. The model relies both on positional and photometric information on optical objects nearby X-ray sources and allows performing selection with precision and recall $\approx94$% (for $F_{\rm X,0.5-2}>10^{-14}$ erg/s/cm$^2$). With this model, we calibrated positional error of the SRG/eROSITA sources detected in the Lockman Hole: $\sigma_{\rm corr} = 0.87\sqrt{ \sigma_{\rm det}^{2.53} + 1.12^2}$. The model will become a part of the SRGz system for data analysis of the X-ray data obtained from the all-sky SRG/eROSITA survey.