D. Psaltis et al., On the magnetospheric beat-frequency and lense-thirring interpretations ofthe horizontal-branch oscillation in the Z sources, ASTROPHYS J, 520(2), 1999, pp. 763-775
Three types of quasi-periodic oscillations (QPOs) have been discovered so f
ar 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 simi
lar to 6-20 Hz normal/flaring-branch oscillations and similar to 200-1200 H
z kilohertz QPOs, which usually occur in pairs. Here we study the horizonta
l-branch oscillations and the two simultaneous kilohertz QPOs, which were d
iscovered using the Rossi X-Ray Timing Explorer, comparing their properties
in five Z sources with the predictions of the magnetospheric beat-frequenc
y and Lense-Thirring precession models. We find that the variation of the h
orizontal-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 betwe
en 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 th
at the critical fastness parameter for these sources is greater than or sim
ilar to 0.8. If the frequency of the upper kilohertz QPO is an orbital freq
uency in the accretion disk, the magnetospheric beat-frequency model requir
es that a small fraction of the gas in the disk does not couple strongly to
the stellar magnetic held at 3-4 stellar radii but instead drifts slowly i
nward in nearly circular orbits until it is within a few kilometers of the
neutron star surface. The Lense-Thirring precession model is consistent wit
h the observed magnitudes of the horizontal-branch oscillation frequencies
only if the moments of inertia of the neutron stars in the Z sources are si
milar to 4-5 times larger than the largest values predicted by realistic ne
utron 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 a
re approximately equal to the frequency separation of the kilohertz QPOs, L
ense-Thirring precession can account for the magnitudes of the horizontal-b
ranch oscillation frequencies only if the fundamental frequency of the hori
zontal-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 kilohe
rtz QPO, when the latter is greater than 850 Hz, is directly related to the
varying frequency separation of the kilohertz QPOs.