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F. K. Lamb (U. Illinois), M. C. Miller (U. Chicago), D. Psaltis (CfA)
The frequency relationships observed between the upper and lower kilohertz QPOs and the ~10--60~Hz horizontal branch oscillations (HBOs) in the Z sources are important indicators of the mechanisms that produce them. We show that in the sonic point model of the kilohertz QPOs, the frequency separation between them is approximately equal to the stellar spin frequency \nu\rm spin, but generally differs from \nu\rm spin and varies with the mass accretion rate. For plausible models of the inner accretion disk, the frequency separation decreases with increasing accretion rate, in quantitative agreement with the variation of the frequency separation observed in Sco~X-1. If the moments of inertia of neutron stars have the sizes expected theoretically and their spin frequencies in the Z sources are approximately equal to the frequency separation of the kilohertz QPOs, the Lense-Thirring precession model of the HBOs can account for the frequencies of the HBOs only if the HBO frequency is at least four times the precession frequency. Moreover, the correlation observed between the frequencies of the HBO and the upper kilohertz QPO cannot be accounted for in the Lense-Thirring precession model, even when the effects of classical precession are taken into account. In contrast, the magnetospheric beat-frequency model of the HBOs predicts a power-law relation between HBO frequency and upper kilohertz QPO frequency that is consistent with the relation observed, if the frequency of the upper kilohertz QPO is an orbital frequency in the inner disk. The Z-source magnetic fields inferred from the model are ~109--1010~G.
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