Revisiting the fundamental parameters for the black hole X-ray transient Swift J1753.5-0127

Abstract: We present time-resolved Gran Telescopio Canarias optical spectroscopy and William Herschel Telescope $i$-band photometry of the X-ray transient SWIFT J1753.5-0127 in quiescence. The $i$-band light curve is dominated by flickering with an amplitude of $\sim 0.5$ mag and shows no evidence of the ellipsoidal modulation of the companion star. The telluric-corrected average spectrum, on the other hand, reveals the presence of weak (strongly veiled) TiO bands at $7055$ .A and $7589$ .A. We used them for a spectral classification, finding an M4-5 V companion star. However, as velocity shifts are not clearly detected in the individual spectra, we turned the analysis to the double-peaked H$\alpha$ emission line from the accretion disc. By exploiting the empirical correlations established for quiescent X-ray transients between the line morphology and fundamental binary parameters, we estimated the radial velocity semi-amplitude of the companion $K_2 = 820 \pm 36$ km s$^{-1}$, a mass ratio $q = 0.023 \pm 0.006$ and an inclination $i = 79 \pm 5$ deg. Moreover, an orbital period of $3.26 \pm 0.02$ h was measured from the modulation of the centroid velocities and the double-peak trough depth of the H$\alpha$ profile. These quantities yielded a mass function $f(M_1) = 7.8 \pm 1.0$ M$\odot$ and black hole and companion star masses of $M_1 = 8.8 \pm 1.3$ M$\odot$ and $M_2 = 0.20 \pm 0.06$ M$_\odot$, respectively. The companion star mass is in line with the spectral classification obtained from the relative depth of the TiO bands. Based on the mean quiescent magnitude ($i = 21.4 \pm 0.1$), orbital period, and interstellar extinction, we estimate the distance to the source to be $3.9 \pm 0.7$ kpc and a Galactic plane elevation of $0.8 \pm 0.2$ kpc, supporting the case for a large natal kick.