Mass Ratio Determination from H α Lines in Black Hole X-Ray Transients

We find that the mass ratio q in quiescent black hole (BH) X-ray transients is tightly correlated with the ratio of the double-peak separation (DP) to the full width half maximum (FWHM) of the H _α emission line, {log}q=-6.88-23.2\quad {log}({DP}/{FWHM}). This correlation is explained through the efficient truncation of the outer disk radius by the 3:1 resonance with the companion star. This is the dominant tidal interaction for extreme mass ratios q={M}₂/{M}₁≲ 0.25, the realm of BH (and some neutron star) X-ray transients. Mass ratios can thus be estimated with a typical uncertainty of ≈32%, provided that the H _α profile used to measure DP/FWHM is an orbital phase average. We apply the DP/FWHM-q relation to the three faint BH transients XTE J1650-500, XTE J1859+226, and Swift J1357-0933 and predict q={0.026}_-0.007^+0.038, {0.049}_-0.012^+0.023 and {0.040}_-0.005^+0.003, respectively. This new relation, together with the {FWHM}{--}{K}₂ correlation presented in Paper I, allows the extraction of fundamental parameters from very faint targets and, therefore, the extension of dynamical BH studies to much deeper limits than was previously possible. As an example, we combine our mass ratio determination for Swift J1357-0933 with previous reported values to yield a BH mass of 12.4 ± 3.6 M _⊙. This confirms Swift J1357-0933 as one of the most massive BH low-mass X-ray binaries in the Galaxy.