Changing frequency separation of kilohertz quasi-periodic oscillations in the sonic-point beat-frequency model

We show that the sonic-point beat-frequency (SPBF) model of the pair of kilohertz quasi-periodic oscillations (QPOs) observed in neutron star X-ray binary systems predicts that the frequency separation Delta nu between them is usually not exactly equal to the spin frequency nu (s) of the star. Although the stellar spin interacts with the orbital motion of the accreting gas at the sonic radius with a frequency equal to sonic-point beat frequency, the X-ray oscillations are produced by interaction of the gas with the surface of the star, and their frequencies are therefore affected by the flow of the gas from the sonic radius to the stellar surface. For prograde disk flow near the star, Delta nu is comparable to but usually less than nu (s), consistent with the observed values of Delta nu and the values of nu (s) inferred from oscillations during X-ray bursts. We show that the SPBF model also explains naturally the decrease in Delta nu with increasing QPO frequencies seen in some sources and the plateau in the QPO frequency-X-ray flux correlation observed in 4U 1820-30. The model fits well the QPO frequency behavior observed in Sco X-1, 4U 1608-52, 4U 1728-34, and 4U 1820-30 (chi (2)/degrees of freedom =0.4-2.1, not including systematic errors), giving masses ranging from 1.59 to 2.0 M-circle dot and spin rates ranging from 279 to 364 Hz. Previous work on the model has shown that it naturally explains many other properties of the kilohertz QPOs. These include the existence of just two principal kilohertz QPOs in a given source, the approximate commensurability of the burst oscillation frequency and Delta nu, and the high frequencies, coherence, and amplitudes of these QPOs. In the SPBF model, the existence of kilohertz QPOs is an effect of strong-field general relativity. Thus, if the model is validated, observations of the kilohertz QPOs can be used not only to determine the properties of neutron stars but also to explore quantitatively general relativistic effects in the strong-field regime.