# Spectroscopy of Quasi-Periodic Oscillations in the Low-Mass
X-ray Neutron Star Binaries

### Lev Titarchuk

### Vladimir Osherovich

### Sergey Kuznetzov

## Abstract

Precise measurements of the frequencies of the two simultaneous
kiloHertz quasiperiodic oscillations (kHz QPOs), n_{K} and n_{h},
in the atoll source 4U 1728-34 carried out by Mendez & van der Klis (1999)
cast additional doubts about the validity of the simple beat-frequency
interpretation and some of the modifications introduced to explain the results
of the varying Dn = n_{h}-n_{K}.
A new model (Osherovich and Titarchuk 1999, Titarchuk and Osherovich 1999)
explains the variation of Dn
suggesting that n_{h} is the upper hybrid frequency of the Keplerian
oscillator under the influence of the Coriolis force. Such an oscillator
has two branches characterized with high frequency n_{h} and with low
frequency n_{L}. The frequency n_{L} depends
strongly on the angle d between the normal to the neutron star
disk and W - the angular velocity of the magnetosphere surrounding
the neutron star. In the lower part of the QPO spectrum, this model
identifies the frequency of radial viscous oscillations n_{v} and
the break frequency n_{b}, which is associated with the diffusive process
in the transition region (the innermost part of the disk).
According to this model, all frequencies (namely n_{h}, n_{L}, n_{b}
and n_{v}) have
specific dependences on n_{K}. This paper focuses on the verification of the
predicted relations. For two sources, namely Sco X-1 and 4U 1728-34, we
present a comprehensive classification of QPO within the framework of
this model. For the source 4U 1728-34, the best theoretical fit is
obtained for d = 8.3±1^{o}, which is slightly larger than
d = 5.5±0.5^{o} previously found for Sco X-1. In addition, we
verify the theoretically derived power law relation n_{b} µ n_{v}^{1.61} using recent observations of other atoll and Z-sources.

File translated from T_{E}X by T_{T}H, version 2.32.

On 16 Jul 1999, 09:19.