Optical Cross-Match of SRG/eROSITA X-ray Sources Using the Deep Lockman Hole Survey as an Example

We present a method for the optical cross-match of sources detected in wide-field X-ray sky surveys. For this purpose, we have constructed and trained a neural network model to characterize the photometric attributes of the populations of optical counterparts of X-ray sources and optical field objects. The photometric information processing result is used for the probabilistic cross-match of X-ray sources with optical DESI LIS sources. The efficiency of the method is illustrated using the deep Lockman Hole survey with the eROSITA telescope of the SRG observatory as an example. To estimate the accuracy of the method, we have produced a validation sample based on the Chandra and XMM-Newton catalogs of X-ray sources. The cross-match precision in our method reaches 94 % for the entire Lockman Hole X-ray catalog and 97 % for sources with a flux F_x,0.5-2>10^-14 erg cm ^-2 s ^-1 . We discuss the further development of the cross-match model and the steps needed for its application to the SRG/eROSITA all-sky survey data.