We measured the radial-velocity curve of HD 77581, the B-supergiant compani
on 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 e
ach 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 combi
ne the resulting velocities with the ones derived from the new optical spec
tra presented here, as well as those derived from optical spectra published
earlier. As in previous analyses, the radial velocities show strong deviat
ions 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 nea
r 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 pro
nounced 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 lar
gest 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 explana
tion. As a result, our best estimate of the radial-velocity amplitude, K-op
t = 21.7 +/- 1.6 km s(-1), has an uncertainty not much reduced to that foun
d in previous analyses, in which the influence of the systematic, phase-loc
ked deviations had not been taken into account. Combining our velocity ampl
itude with the accurate orbital elements of the X-ray pulsar, we infer M-ns
sin(3) i = 1.78 +/- 0.15 M-.***.