The mass function of GX 339-4 from spectroscopic observations of its donor star

We obtained 16 VLT/X-shooter observations of GX 339-4 in quiescence in the period May - September 2016 and detected absorption lines from the donor star in its NIR spectrum. This allows us to measure the radial velocity curve and projected rotational velocity of the donor for the first time. We confirm the 1.76 day orbital period and we find that $K_2$ = $219 \pm 3$ km s$^{-1}$, $\gamma = 26 \pm 2$ km s$^{-1}$ and $v \sin i = 64 \pm 8$ km s$^{-1}$. From these values we compute a mass function $f(M) =1.91 \pm 0.08~M_{\odot}$, a factor $\sim 3$ lower than previously reported, and a mass ratio $q = 0.18 \pm 0.05$. We confirm the donor is a K-type star and estimate that it contributes $\sim 45-50\%$ of the light in the $J$- and H-band. We constrain the binary inclination to $37^\circ < i < 78^\circ$ and the black hole mass to $2.3~M_{\odot} < M_\mathrm{BH} < 9.5~M_{\odot}$. GX 339-4 may therefore be the first black hole to fall in the 'mass-gap' of $2-5~M_{\odot}$.