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Precise simultaneous measurements of the frequencies of the two kilohertz quasi-periodic oscillations (referred in the literature as upper and lower kHz QPOs) cast doubts on the validity of the simple beat-frequency interpretation and some of the modifications introduced to explain the results of the varying frequency difference. A new model explains the variation of the frequency difference, suggesting that the upper kHz QPO, namely nuh, is an upper hybrid frequency of the Keplerian oscillator under the influence of the Coriolis force and the lower kHz QPO is the Keplerian frequency nuK. Such an oscillator has two branches characterized by a high frequency nuh ( approximately 1 kHz) and by a low frequency nuL ( approximately 50 Hz). The frequency nuL depends strongly on the angle delta between the normal to the neutron star disk and Omega-the angular velocity of the magnetosphere surrounding the neutron star. In the lower part of the QPO spectrum ( approximately 10 Hz), this model identifies the frequency of radial viscous oscillations nuV (previously called "extra noise component") and the break frequency nub, which is associated with the diffusive process in the transition region (the innermost part of the disk). According to this model, all frequencies (namely nuh, nuL, nub, and nuV) have specific dependences on nuK. This Letter focuses on the verification of the predicted relations. For the source 4U 1728-34, the best theoretical fit is obtained for delta=8&fdg;3+/-1&fdg;0, which is slightly larger than the value of delta=5&fdg;5+/-0&fdg;5 previously found for Scorpius X-1. In addition, we show that the theoretically derived power-law relation nub~nu1.61V is consistent with the recent observations of other atoll and Z-sources.

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Correlations between 1-10 Hz quasi-periodic oscillations (QPOs) and spectral power law index have been reported for black hole (BH) candidate sources and one neutron star source, 4U 1728-34. An examination of QPO frequency and index relationships in Sco X-1 is reported herein. We discovered that Sco X-1, representing Z-source groups, can be adequately modeled by a simple two-component model of Compton up-scattering with a soft photon electron temperature of about 0.4 keV, plus an Iron K-line. The results show a strong correlation between spectral power law index and kHz QPOs. Because Sco X-1 radiates near the Eddington limit, one can infer that the geometrical configuration of the Compton cloud (CC) is quasi-spherical because of high radiation pressure in the CC. Thus, we conclude that the high Thomson optical depth of the Compton cloud, in the range of ∼ 5 − 6 from the best-fit model parameters, is consistent with the neutron star's surface being obscured by material. Moreover, a spin frequency of Sco X-1 is likely suppressed due to photon scattering off CC electrons. Additionally, we demonstrate how the power spectrum evolves when Sco X-1 transitions from the horizontal branch to the normal branch.