The Peak Optical Luminosity versus the Orbital Period of Black Hole X-ray Binaries

We compare the peak optical luminosity with the orbital period for a sample of 21 stellar-mass black hole candidates with good measurements of both quantities. We find that the peak absolute magnitude for the outbursts follows a relation with $M_V=−3.07 {\rm log} P + 2.99$, which corresponds to a $L_V \propto P^{1.23}$ relation. This is a similar relationship to that found for cataclysmic variables. We discuss the implications of these results for finding black hole X-ray binaries in other galaxies and in our own Galaxy with the Large Synoptic Survey Telescope and with other future large time domain surveys.