Relating Peak Optical Luminosity and Orbital Period of Stellar-Mass Black Holes in X-ray Binaries

TL;DR

This study finds a linear relation between peak optical luminosity and orbital period in stellar-mass black hole X-ray binaries, which could aid in identifying such systems in distant galaxies through large-scale surveys.

Contribution

It establishes a new correlation between optical peak luminosity and orbital period for black hole X-ray binaries, extending the analogy of the Warner relation to these systems.

Findings

Peak optical luminosity scales with orbital period as a power law.

Excluding certain outliers refines the correlation for 19 sources.

The relation can help identify black hole binaries in large surveys.

Abstract

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 $M_{V,peak}=3.48 (\pm 0.85)-3.89 (\pm 0.91) {\rm log}P_{orb}$, 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 $M_{V,peak}= 3.01\;(\pm 0.93)-3.21\;(\pm 1.04){\rm log}P_{orb}$, 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.