Searching for accreting compact binary systems from spectroscopy and photometry: Application to LAMOST spectra

Compact objects undergoing mass transfer exhibit significant (and double-peaked) $H_{\alpha}$ emission lines. Recently, new methods have been developed to identify black hole X-ray binaries (BHXBs) and calculate their systematic parameters using $H_{\alpha}$ line parameters, such as the full-width at half maximum (FWHM), equivalent width (EW), and separation of double peaks. In addition, the FWHM-EW plane from spectroscopy and the $H_{\alpha}$ color-color diagram from photometry can be used for rapid stellar classification. We measure the $H_{\alpha}$ and $H_{\beta}$ profiles (e.g., FWHM and EW) using the LAMOST DR9 low- and medium-resolution spectra, and calculate the systematic parameters (e.g., velocity semi-amplitude of the donor star, mass ratio, inclination angle, and mass of the accretor). A new correlation between FWHM and $K_{\rm 2}$, $K_{\rm 2} = 0.205(18)\ \rm{FWHM}$, is obtained for cataclysmic variables (CVs) in our sample. Both the FWHM-EW plane and the $H_{\alpha}$ color-color diagram can distinguish CVs with FWHM $\gtrsim$ 1000 km/s from Be stars and young stellar objects (YSOs) to some extent. To improve classification accuracy and enhance the selection of compact objects, we propose a new set of idealized filters with effective widths of 30 \AA, 130 \AA, and 400 \AA \ for the narrow $H_{\alpha}$ filter, broad $H_{\alpha}$ filter, and $r$-band filter, respectively.