The mass of the neutron star in Vela X-1 and tidally induced non-radial oscillations in GP Vel

We report new radial velocity observations of GP Vel / HD 77581, the optical companion to the eclipsing X-ray pulsar Vela X-1. Using data spanning more than two complete orbits of the system, we detect evidence for tidally induced non-radial oscillations on the surface of GP Vel, apparent as peaks in the power spectrum of the residuals to the radial velocity curve fit. By removing the effect of these oscillations (to first order) and binning the radial velocities, we have determined the semi-amplitude of the radial velocity curve of GP Vel to be K0 = 22.6 ± 1.5 km s-1. Given the accurately measured semi-amplitude of the pulsar's orbit, the mass ratio of the system is 0.081 ± 0.005. We are able to set upper and lower limits on the masses of the component stars as follows. Assuming GP Vel fills its Roche lobe then the inclination angle of the system, i, is 70.1° ± 2.6°. In this case we obtain the masses of the two stars as Mx = 2.27 ± 0.17 M⊙ for the neutron star and Mx = 27.9 ± 1.3 M⊙ for GP Vel. Conversely, assuming the inclination angle is i = 90°, the ratio of the radius of GP Vel to the radius of its Roche lobe is β = 0.89 ± 0.03 and the masses of the two stars are Mx = 1.88 ± 0.13 M⊙ and M0 = 23.1 ± 0.2 M⊙. A range of solutions between these two sets of limits is also possible, corresponding to other combinations of i and β. In addition, we note that if the zero phase of the radial velocity curve is allowed as a free parameter, rather than constrained by the X-ray ephemeris, a significantly improved fit is obtained with an amplitude of 21.2 ± 0.7 km s-1 and a phase shift of 0.033 ± 0.007 in true anomaly. The apparent shift in the zero phase of the radial velocity curve may indicate the presence of an additional radial velocity component at the orbital period. This may be another manifestation of the tidally induced non-radial oscillations and provides an additional source of uncertainty in the determination of the orbital radial velocity amplitude.