Relating peak optical luminosity and orbital period of stellar-mass black holes in X-ray binaries

We compare the peak optical luminosity with the orbital period for a sample of 22 stellar-mass black hole candidates with good measurements of both quantities. We find that the peak absolute magnitude for the outbursts follows a linear relation with MV, peak = 3.48(± 0.85) − 3.89(± 0.91) logPorb, which corresponds to a $L_V \propto P_{orb}^{1.56\pm 0.36}$ power-law relation. Excluding V4641 Sgr which is a strong outlier and not likely to have outbursts produced by the standard disc instability model, in addition to BW Cir and V821 Ara – both of which have highly uncertain distances; the new correlation for the 19 sources is found to be MV, peak = 3.01 (± 0.93) − 3.21 (± 1.04) logPorb, which corresponds to $L_V \propto P_{orb}^{1.28 \pm 0.42}$. This is an analogous relationship to the ‘Warner relation’ between orbital period and peak luminosity 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 other future large time domain surveys.