Eccentric orbits and QPOs in neutron star X-ray binaries

We investigate the suggestion that the frequencies of the kilohertz and other QPOs in the emission from neutron stars in low-mass X-ray binaries are generated by geodesic motion of gas clumps around the star. First we assume, following previous work, that the dominant frequencies produced by such motions are the azimuthal frequency \nuk, the apsidal precession frequency \nuap, and the first overtone of the nodal precession frequency \nunp. We investigate whether geodesics can be found for which these frequencies agree with the observed frequencies. Correcting calculational errors made when the geodesic precession hypothesis was first proposed, we find that \nuk and \nuap disagree qualitatively with the frequencies of the kilohertz QPOs for infinitesimally or even moderately eccentric geodesics. These frequencies are similar to the frequencies of the kilohertz QPOs only for highly eccentric geodesics, with apastron to periastron ratios \sim3--4; for these geodesics, 2\nunp differs qualitatively from the frequencies of the low-frequency QPOs. Next we investigate whether these frequencies would be the dominant frequencies produced by orbiting clumps. We find that they are not and that the dominant frequencies are instead harmonics and sidebands of the radial epicyclic frequency \nur. Finally, we show that gas dynamical constraints restrict the radii of orbiting clumps to be \ll 10^{-3} of the stellar radius; the fractional modulation that could be produced by clumps is therefore \ll 10^{-6}. We conclude that there are significant difficulties in interpreting the kilohertz and low-frequency QPOs as consequences of geodesic motion of gas clumps.