A FWHM–K₂ correlation in black hole transients

We compare $H_{\alpha }$ emission profiles of 12 dynamically confirmed black holes (BHs) and 2 neutron star X-ray transients (SXTs) in quiescence with those of a sample of 43 Cataclysmic Variables (CVs), also quiescent. The FWHM of the $H_{\alpha }$ line in SXTs is tightly correlated with the velocity semi-amplitude of the donor star $K_2=0.233\left(13\right)FWHM$. This new correlation, when combined with orbital periods (i.e., through photometric light curves), allows for the possibility of estimating compact object mass functions from single integration, low-resolution spectroscopy. On the other hand, CVs above the period gap are found to follow a flatter correlation, a likely consequence of their larger mass ratios. We also find that the FWHM traces the disk velocity at $\approx$42% $R_{L1}$, independently of binary mass ratio. In addition, for a given FWHM, BHs tend to have lower EWs than CVs. This might be explained by the fact that CVs must be seen at higher inclinations to mimic the same projected disk velocities as BH SXTs. For the same reason, CVs with $FWHM\gtrsim 1500$ km s⁻¹ are mostly eclipsing while none of our sample BHs are. Furthermore, we show that there is a vacant/unoccupied region for CVs in the FWHM–EW plane defined by $FWHM>2568\sqrt{(1-{\left(9/EW\right)}^2)}$ $\left(km{s}^{-1}\right)$. Both the FWHM–K₂ correlation and the FWHM–EW plane can be exploited, together with photometric light curves, to efficiently discover quiescent BHs in deep $H_{\alpha }$ surveys of the Galactic plane.