7 Tidally induced non-radial oscillations

The strongest peaks in the power spectrum of the residuals after the first fit, at 0.111 d^-1 and 0.457 d^-1, are suggestively close to the orbital frequency and $4\times$ the orbital frequency ( $f_{\rm orb} = 0.11155~{\rm d}^{-1}$) respectively. This leads us to speculate that they may both represent tidally excited non-radial oscillation modes (see also Willems & Aerts 2002; Handler et al. 2002).

From a theoretical point of view, the tidal action exerted by one binary component on the other is governed by the tide-generating potential which can be expanded in a Fourier series in terms of multiples of the mean motion $n=2~\pi~f_{\rm orb}$ (e.g. Polfliet & Smeyers 1990). The oscillations that are most likely to be excited are those associated with the lower-order harmonics of the Fourier series. In the particular case of GP Vel, the dominant contributions to the Fourier series of the tide-generating potential are associated with the first ten harmonics. This supports the possibility that the oscillation associated with the frequencies $\approx$ $f_{\rm orb}$ and $\approx$ $4~ f_{\rm orb}$ may be induced by the tidal action of the neutron star.

An in-depth analysis of the possibility that a tidally excited oscillation mode exists in GP Vel requires an accurate knowledge of the stellar and orbital parameters. In particular, the internal structure of the B-type companion to the neutron star must be known to derive the spectrum of the eigenfrequencies present in the star. The radii quoted in Table 2 indicate that the B-type star might be in the Hertzsprung-gap. An additional complication arises from the unknown evolutionary history of the binary as the B-type star may be "polluted'' by mass-transfer episodes prior to the formation of the neutron star. In view of these complications, a detailed study of the oscillation spectrum of GP Vel and its possible use in an asteroseismological study is beyond the scope of our present investigation.