SRG/ART-XC Galactic Bulge deep survey. I. Maximum likelihood source detection algorithm for X-ray surveys

We describe an X-ray source detection method entirely based on the maximum likelihood analysis, in application to observations with the ART-XC telescope onboard the Spectrum Roentgen Gamma observatory. The method optimally combines the data taken at different conditions, a situation commonly found in scanning surveys or mosaic observations with a telescope with a significant off-axis PSF distortion. The method can be naturally extended to include additional information from the X-ray photon energies, detector grades, etc. The likelihood-based source detection naturally results in an optimal use of available information for the sources detection and stable and uniform definition of detection thresholds under different observing conditions (PSF, background level). This greatly simplifies the statistical calibration of the survey needed to, e.g. obtain the $\log N - \log S$ distribution of detected sources or their luminosity function. The method can be applied to the data from any imaging X-ray telescope.