Changing Frequency Separation of Kilohertz Quasi-Periodic Oscillations in the Sonic-Point Beat-Frequency Model

Previous work on the sonic-point beat-frequency (SPBF) model of the kilohertz quasi-periodic oscillations (QPOs) observed in the X-ray flux from neutron stars in low-mass binary systems has shown that it naturally explains many properties of these QPOs. These include the existence of just two principal QPOs in a given source, the commensurability of the frequency separation \Dnu\ of the two kilohertz QPOs and the spin frequency \nus inferred from burst oscillations, and the high frequencies, coherence, and amplitudes of these QPOs. Here we show that the SPBF model predicts that \Dnu is less than but close to \nus, consistent with the observed differences between \Dnu and \nus. It also explains naturally the decrease in \Dnu with increasing QPO frequency seen in some sources and the plateau in the QPO frequency--X-ray flux 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 (chisqdof = 0.4-2.1), giving masses ranging from 1.59 to 2.0 Msun and spin rates ranging from 279 to 364 Hz. In the SPBF model, the kilohertz QPOs are effects of strong-field gravity. Thus, if the model is validated, 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.