The Orbit of NGC 5907 ULX-1

We report on the orbit of the binary system powering the most extreme ultraluminous X-ray pulsar known to date: NGC 5907 ULX-1 (hereafter ULX1). ULX1 has been the target of a substantial multi-instrument campaign, mainly in the X-ray band, but no clear counterparts are known in other bands. Although ULX1 is highly variable and pulsations can be transient (regardless of the source flux), the timing data collected so far allow us to investigate the orbit of this system. We find an orbital period ${P}_{\mathrm{orb}}={5.7}_{-0.6}^{+0.1}\,\mathrm{days}$ and a projected semi-axis ${A}_{1}={3.1}_{-0.9}^{+0.8}\,\mathrm{lt}\mbox{--}{\rm{s}}$ . The most likely ephemeris is P _orb = 5.6585(6) days, A _1 = 3.1(4) lt-s, and the epoch of ascending nodes passage is T _asc = 57751.37(5) MJD. However, there are six similar solutions acceptable within 3 σ . We find further indications that ULX1 is a high-mass X-ray binary. This implies that we are observing its orbit face on, with an inclination