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tokens: Note the systemic velocity is relative to the template file used. We do note the systemic velocity we find, Γ = 321.18 ± 0.85 km s −1 , is higher than the 295.8 ± 2.0 km s −1 previously reported (Corbet et al. 2016 ). We undertook additional analysis to confirm that the wavelength calibration performed by the HRS pipeline was correct and that the comparison to the radial velocity standards was accurate to within the expected performance. We found no evidence of any discrepancy in the calibration, nor any long-term systematic shift in the wavelength calibration over the period of observations. We believe that there are two possible reasons for this difference; there may be a possible systematic offset arising from the fit of the high-resolution template fit to the medium resolution MILES libraries (however there is no significant offset to the radial velocity standards) or there may have been a systematic offset in the zero velocity in the field O-type star used in the previous analysis. However, this difference does not change the main results of determining the orbital parameters. If this difference in the systemic velocity is removed the radial velocities are in agreement with the previous results. The final radial velocity curve and the best-fitting model are shown in Fig. 2 , and the data are given in Table 3 . We find the binary is slightly eccentric, e = 0.40 ± 0.07, and place the time of periastron at HJD 2457412.13 ± 0.29. Figure 2. Radial velocity of the O5 iii star in the binary system, as determined from cross-correlation. The solid line shows the best fit to this data, with a fixed 10.301 d orbital period. For clarity the plot is reported over two orbital phases with phase φ = 0 at MJD = 57 410.25, which corresponds to the given phase in Corbet et al. ( 2016 ). The error bars show the statistical errors reported by the rvsao package. Table 3. Radial velocities obtained from cross-correlation. 3 DISCUSSION 3.1 Mass of the compact object The binary parameter solution gives a mass function of f = 0.0010 ± 0.0004 M and the constraints on the mass of the compact object are shown in Fig. 3 . The mass of an O5 iii (f) star is ∼40 M (Martins et al. 2005 ), but due to the binary evolution could be different. A mass range of 25–42 M was considered in Seward et al. ( 2012 ). For this mass range both a neutron star or black hole mass is compatible with the mass function, though a neutron star is favoured. For a 40 M star, the mass of the compact object will be >5 M for inclinations i ≤ 15 ± 2°, and while the inclination must be i ≤ 11 ± 1° for a 25 M optical companion. Assuming the compact object is a pulsar, with a mass of 1.4 M , the inclination will lie between i = 39 ± 6° and i = 59 ± 11° for a 25 M and 40 M star, respectively. Figure 3. The constraint on the mass of the compact object in LMC P3. The shaded area marks the range of assumed masses of the optical companion. 3.2 Binary orientation The orientation of the binary system is