The mass of the neutron star in Vela X-1

We measured the radial-velocity curve of HD 77581, the B-supergiant companion of the X-ray pulsar Vela X-1, using 183 high-resolution optical spectra obtained in a nine-month campaign. We derive radial-velocity amplitudes for different lines and wavelength regions, and find all are consistent with each other, as well as with values found in previous analyses. We show that one apparent exception, an anomalously low value derived from ultra-violet spectra obtained with the International Ultraviolet Explorer, was due to an error in the analysis procedures. We re-analyse all IUE spectra, and combine the resulting velocities with the ones derived from the new optical spectra presented here, as well as those derived from optical spectra published earlier. As in previous analyses, the radial velocities show strong deviations from those expected for a pure Keplerian orbit, with root-mean-square amplitudes of similar to 7 km s(-1) for strong lines of Si IV and N III near 4100 Angstrom, and up to similar to 20 km s(-1) for weaker lines of N II and Al III near 5700 Angstrom. The deviations likely are related to the pronounced line-profile variations seen in our spectra. Our hope was that the deviations would average out when a sufficient number of spectra were added together. It turns out, however, that systematic deviations as a function of orbital phase are present as well, at the 3 km s(-1) level, with the largest deviations occurring near inferior conjunction of the neutron star and near the phase of maximum approaching velocity. While the former might be due to a photo-ionisation wake, for which we observe direct evidence in the profiles of H delta and H alpha, the latter has no straightforward explanation. As a result, our best estimate of the radial-velocity amplitude, K-opt = 21.7 +/- 1.6 km s(-1), has an uncertainty not much reduced to that found in previous analyses, in which the influence of the systematic, phase-locked deviations had not been taken into account. Combining our velocity amplitude with the accurate orbital elements of the X-ray pulsar, we infer M-ns sin(3) i = 1.78 +/- 0.15 M-.***.