On the Magnetospheric Beat‐Frequency and Lense‐Thirring Interpretations of the Horizontal‐Branch Oscillation in the Z Sources

We study the horizontal branch oscillations (HBO) and the two simultaneouskilohertz QPOs comparing their properties in five Z sources with thepredictions of the magnetospheric beat-frequency and Lense-Thirring precessionmodels. We find that the variation of the HBO frequency with accretion ratepredicted by the magnetospheric beat-frequency model for a purely dipolarstellar magnetic field and a radiation-pressure-dominated inner accretion diskagrees well with the observed variation. This model implies that the neutronstars in the Z sources are near magnetic spin equilibrium, that their magneticfield strengths are ~10^9-10^10 G, and that the critical fastness parameter forthese sources is >0.8. If the frequency of the upper kilohertz QPO is anorbital frequency in the accretion disk, the magnetospheric beat-frequencymodel requires that a small fraction of the gas in the disk does not couplestrongly to the stellar magnetic field at 3-4 stellar radii but instead driftsslowly inward in nearly circular orbits until it is within a few kilometers ofthe neutron star surface. The Lense-Thirring precession model is consistentwith the observed magnitudes of the HBO frequencies only if the moments ofinertia of the neutron stars in the Z sources are 4-5 times larger than thelargest values predicted by realistic neutron-star equations of state. Thetrend of the correlation between the HBO and upper kHz QPO frequencies is notconsistent with this model. We argue that the change in the slope of thecorrelation between the frequency of the horizontal branch oscillation and thefrequency 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.Comment: 29 pages, 12 figures, and 3 tables. To appear in the Astrophysical Journa