eROSITA(eRASS1) study of the Canis Major overdensity: Developing a multi-wavelength algorithm for classifying faint X-ray sources

Using data from Roentgen Survey with an Imaging Telescope Array) on board Spektrum-Roentgen-Gamma (Spektr-RG, SRG) taken during the first all-sky survey (eRASS1), we performed the first X-ray classification and population study in the field of the Canis Major overdensity\,(CMa OD), which is an elliptical-shaped stellar overdensity located at $l= circ b=-80^ circ This study aims to identify the X-ray sources in CMa OD. We developed a classification algorithm using multi-wavelength criteria as a preliminary method for the classification of faint X-ray sources, specifically in regions with a high source number density. We used the brightness of the multi-wavelength counterparts (mainly from infrared and optical catalogues), along with the X-ray flux and X-ray hardness ratios (HRs) to classify the sources. Out of a total number of 8311 X-ray sources, we classified 1029 sources as Galactic stars and binaries in the foreground, 946 sources as active galactic nuclei (AGNs) and galaxies in the background, and 435 sources with stellar counterparts that may belong to either the MW or CMa OD. Among the sources with a stellar counterpart, we identified 34 symbiotic star candidates, plus 335 sources, of which the infrared (IR) counterparts have properties of M-giants in CMa OD. Moreover, there is a known high-mass X-ray binary (HMXB, 4U\,0728-25) in the field of our study; according to the of its companion, it appears to be a member of CMa OD. There is also a recently detected transient low-mass X-ray binary\,(LMXB, SRGt\,J071522.1-191609) is also present; it may be a member of CMa OD based on its companion, which is most likely highly absorbed and is thus located behind the Galactic disk. In addition, we present the X-ray luminosity function\,(XLF) of members and candidate members of CMa OD. It is dominated by sources with luminosities of $<2 $ in the energy range of 0.2--2.3 keV. These sources are expected to be either accreting white dwarfs or quiescent LMXBs.