SRGz: Machine Learning Methods and Properties of the Catalog of SRG/eROSITA Point X-ray Source Optical Counterparts in the DESI Legacy Imaging Surveys Footprint

We describe the methods of the SRGz system for the physical identification of eROSITA point X-ray sources from photometric data in the DESI Legacy Imaging Surveys footprint. We consider the models included in the SRGz system (version 2.1) that have allowed us to obtain accurate measurements of the cosmological redshift and class of an X-ray object (quasar/galaxy/star) from multiwavelength photometric sky surveys (DESI LIS, SDSS, Pan-STARRS, WISE, eROSITA) for 87\({\%}\) of the entire eastern extragalactic region (\(0^{\circ}<l<180^{\circ}\), \(|b|>20^{\circ}\)). An important feature of the SRGz system is that its data handling model (identification, classification, photo-z algorithms) is based entirely on heuristic machine learning approaches. For a standard choice of SRGz parameters the optical counterpart identification completeness (recall) in the DESI LIS footprint is \(95{\%}\) (with an optical counterpart selection precision of \(94{\%}\)); the classification completeness (recall) of X-ray sources without optical counterparts in DESI LIS is \(82{\%}\) (\(85{\%}\) precision). A high quality of the photometric classification of X-ray source optical counterparts is achieved in SRGz: \({>}99{\%}\) photometric classification completeness (recall) for extragalactic objects (a quasar or a galaxy) and stars on a test sample of sources with SDSS spectra and GAIA astrometric stars. We present an analysis of the importance of various photometric features for the optical identification and classification of eROSITA X-ray sources. We have shown that the infrared (IR) magnitude \(W_{2}\), the X-ray/optical(IR) ratios, the optical colors (for example, \((g-r)\)), and the IR color (\(W_{1}-W_{2}\)) as well as the color distances introduced by us play a significant role in separating the classes of X-ray objects. We use the most important photometric features to interpret the SRGz predictions in this paper. The accuracy of the SRGz photometric redshifts (from DESI LIS, SDSS, Pan-STARRS, and WISE photometric data) has been tested in the Stripe82X field on a sample of 3/4 of the optical counterparts of eROSITA point X-ray sources (for which spectroscopic measurements are available in Stripe82X): \(\sigma_{NMAD}=3.1{\%}\) (the normalized median absolute deviation of the prediction) and \(n_{>0.15}=7.8{\%}\) (the fraction of catastrophic outliers). The presented photo-z results for eROSITA X-ray sources in the Stripe82X field are more than a factor of 2 better in both metrics (\(\sigma_{NMAD}\) and \(n_{>0.15}\)) than the photo-z results of other groups published in the Stripe82X catalog.