On the magnetospheric beat-frequency and lense-thirring interpretations of the horizontal-branch oscillation in the Z sources

Three types of quasi-periodic oscillations (QPOs) have been discovered so far in the persistent emission of the most luminous neutron star low-mass X-ray binaries, the Z sources: similar to 10-60 Hz horizontal-branch and similar to 6-20 Hz normal/flaring-branch oscillations and similar to 200-1200 Hz kilohertz QPOs, which usually occur in pairs. Here we study the horizontal-branch oscillations and the two simultaneous kilohertz QPOs, which were discovered using the Rossi X-Ray Timing Explorer, comparing their properties in five Z sources with the predictions of the magnetospheric beat-frequency and Lense-Thirring precession models. We find that the variation of the horizontal-branch oscillation frequency with accretion rate predicted by the magnetospheric beat-frequency model for a purely dipolar stellar magnetic field and a radiation-pressure-dominated inner accretion disk is consistent with the observed variation. The model predicts a universal relation between the horizontal-branch oscillation, stellar spin, and upper kilohertz QPO frequencies that agrees with the data on five Z sources. The model implies that the neutron stars in the Z sources are near magnetic spin equilibrium, that their magnetic field strengths are similar to 10(9)-10(10) G, and that the critical fastness parameter for these sources is greater than or similar to 0.8. If the frequency of the upper kilohertz QPO is an orbital frequency in the accretion disk, the magnetospheric beat-frequency model requires that a small fraction of the gas in the disk does not couple strongly to the stellar magnetic field at 3-4 stellar radii but instead drifts slowly inward in nearly circular orbits until it is within a few kilometers of the neutron star surface. The Lense-Thirring precession model is consistent with the observed magnitudes of the horizontal-branch oscillation frequencies only if the moments of inertia of the neutron stars in the Z sources are similar to 4-5 times larger than the largest values predicted by realistic neutron star equations of state. If instead the moments of inertia of neutron stars have the size expected and their spin frequencies in the Z sources are approximately equal to the frequency separation of the kilohertz QPOs, Lense-Thirring precession can account for the magnitudes of the horizontal-branch oscillation frequencies only if the fundamental frequency of the horizontal-branch oscillation is at least 4 times the precession frequency. We argue that the change in the slope of the correlation between the frequency of the horizontal-branch oscillation and the frequency of the upper kilohertz QPO, when the latter is greater than 850 Hz, is directly related to the varying frequency separation of the kilohertz QPOs.