The orbital parameters of the gamma-ray binary LMC P3

LMC P3 is the most luminous gamma-ray binary discovered to date and the first detected outside of the Galaxy, with an orbital period of 10.301 d. We report on optical spectroscopic observations undertaken with the Southern African Large Telescope (SALT) using the High Resolution spectrograph (HRS). We find the binary is slightly eccentric, $e = 0.40\pm0.07$, and place the time of periastron at HJD $2457412.13 \pm 0.29$. Stellar model fitting finds an effective temperature of $T_{\rm eff} = 36351 \pm 53$ K. The mass function, $f = 0.0010 \pm 0.0004$ M$_{\odot}$, favours a neutron star compact object. The phases of superior and inferior conjunctions are $0.98$ and $0.24$, respectively (where phase 0 is at the Fermi-LAT maximum), close to the reported maxima in the GeV and TeV light curves. Published in MNRAS. This version: a few minor typo corrections