Timing Spectroscopy of Quasi-Periodic Oscillations in the Low-Mass X-Ray Neutron Star Binaries

Abstract

Precise simultaneous measurements of the frequencies of the two kilohertz quasi-periodic oscillations (referred in the literature as upper and lower kHz QPOs) cast doubts on the validity of the simple beat-frequency interpretation and some of the modifications introduced to explain the results of the varying frequency difference. A new model explains the variation of the frequency difference, suggesting that the upper kHz QPO, namely nuh, is an upper hybrid frequency of the Keplerian oscillator under the influence of the Coriolis force and the lower kHz QPO is the Keplerian frequency nuK. Such an oscillator has two branches characterized by a high frequency nuh ( approximately 1 kHz) and by a low frequency nuL ( approximately 50 Hz). The frequency nuL depends strongly on the angle delta between the normal to the neutron star disk and Omega-the angular velocity of the magnetosphere surrounding the neutron star. In the lower part of the QPO spectrum ( approximately 10 Hz), this model identifies the frequency of radial viscous oscillations nuV (previously called "extra noise component") and the break frequency nub, which is associated with the diffusive process in the transition region (the innermost part of the disk). According to this model, all frequencies (namely nuh, nuL, nub, and nuV) have specific dependences on nuK. This Letter focuses on the verification of the predicted relations. For the source 4U 1728-34, the best theoretical fit is obtained for delta=8&fdg;3+/-1&fdg;0, which is slightly larger than the value of delta=5&fdg;5+/-0&fdg;5 previously found for Scorpius X-1. In addition, we show that the theoretically derived power-law relation nub~nu1.61V is consistent with the recent observations of other atoll and Z-sources.

Evidence of a decrease of kHz quasi-periodic oscillation peak separation towards low frequencies in 4U 1728-34 (GX 354-0)

“…We have also checked the relation between the upper and lower kHz QPOs as predicted by the two‐oscillator model. We have used the values of the constant parameters of equation (15) in Osherovich & Titarchuk (1999) as determined by Titarchuk et al (1999) for 4U 1728–34. For a low‐frequency QPO of 308 Hz the two‐oscillator model predicts an upper kHz QPO of ∼717 Hz, much higher than the one observed.…”

“…They identify the lower kHz QPO frequency as the Keplerian frequency of the blob and the upper kHz QPO frequency as the radial oscillator mode frequency, a non‐linear function of the Keplerian frequency. This model also gives a relation between the lower and the upper kHz QPOs (dependent on the source; see, for example, Titarchuk, Osherovich & Kuznetsov 1999) which can be tested by observations.…”

Energy dependent time delays of kHz oscillations due to thermal Comptonization

“…The relativistic precession model (Stella, & Vietri 1999) identifies the upper kHz QPO frequency as a Keplerian one with the lower kHz QPO generated due to modulation of the Keplerian frequency with the relativistic periastron precession frequency. In the two-oscillator model Titarchuk, Osherovich, & Kuznestov 1999), the lower kHz QPO is due to a blob moving in a Keplerian orbit, and the upper kHz QPO is generated by the influence of the Coriolis force on the blob when it enters the neutron star's rotating magnetosphere. Later, Titarchuk (2003) refined this model by connecting the QPO to a Rayleigh-Taylor gravity wave.…”

Correlations between X‐Ray Spectral and Timing Characteristics in Cygnus X‐2

“…Both lower and upper kHz QPO peaks are detected simultaneously only in an observation carried out on July 2, 1997 [see details of the data analysis and QPO identification in Kuznetsov (2001)]. We obtain the high frequency QPO values ν K = 464.9 ± 13.4 Hz , ν h = 830.7 ± 12.7 Hz, with significances 3.4σ and 5.8σ for the QPO low and the -Power Density Spectra of Z-sources Cyg X-2 (as a result of the presented study) and Sco X-1 [adopted from Titarchuk, Osherovich & Kuznetsov (1999)] in units of ν × P(ν), (rms/mean) 2 . Upper limits correspond to 1σ confidence level.…”