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

We compare the peak optical luminosity with orbital period for a sample of 22 stellar-mass black hole candidates good measurements both quantities. find that absolute magnitude outbursts follows linear relation $M_{V,peak}=3.48 (\pm 0.85)-3.89 0.91) {\rm log}P_{orb}$, which corresponds to $L_V \propto P_{orb}^{1.56\pm 0.36}$ power law relation. Excluding V4641 Sgr is strong outlier and not likely have produced by standard disc instability model, in addition BW Cir V821 Ara -- highly uncertain distances; new correlation 19 sources found be $M_{V,peak}= 3.01\;(\pm 0.93)-3.21\;(\pm 1.04){\rm P_{orb}^{1.28 \pm 0.42}$. This an analogous relationship "Warner relation" between cataclysmic variables. discuss implications these results finding X-ray binaries other galaxies our own Galaxy Large Synoptic Survey Telescope future large time domain surveys.