Changing Frequency Separation of Kilohertz Quasi‐periodic Oscillations in the Sonic‐Point Beat‐Frequency Model

Abstract

Previous work on the sonic-point beat-frequency (SPBF) model of the kilohertz quasi-periodic oscillations (QPOs) observed in the X-ray flux from neutron stars in low-mass binary systems has shown that it naturally explains many properties of these QPOs. These include the existence of just two principal QPOs in a given source, the commensurability of the frequency separation ∆ν of the two kilohertz QPOs and the spin frequency ν s inferred from burst oscillations, and the high frequencies, coherence, and amplitudes of these QPOs. Here we show that the SPBF model predicts that ∆ν is less than but close to ν s , consistent with the observed differences between ∆ν and ν s . It also explains naturally the decrease in ∆ν with increasing QPO frequency seen in some sources and the plateau in the QPO frequency-X-ray flux observed in 4U 1820−30. The model fits well the QPO frequency behavior observed in Sco X-1, 4U 1608−52, 4U 1728−34, and 4U 1820−30 (χ 2 /dof = 0.4-2.1), giving masses ranging from 1.59 to 2.0 M ⊙ and spin rates ranging from 279 to 364 Hz. In the SPBF model, the kilohertz QPOs are effects of strong-field gravity. Thus, if the model is validated, the kilohertz QPOs can be used not only to determine the properties of neutron stars but also to explore quantitatively general relativistic effects in the strong-field regime.

Discovery of Kilohertz Quasi‐periodic Oscillations and Shifted Frequency Correlations in the Accreting Millisecond Pulsar XTE J1807−294

“…In XTE J1807À294, we find instead that the twin kHz QPO separation is nearly once the inferred spin frequency; Á is larger than spin by 2.3 . This has previously been seen only in 4U 1636À53 (Jonker et al 2002) and may be difficult to accommodate in beat-frequency (Lamb & Miller 2001) or relativistic resonance (Kluźniak et al 2004) models.…”

“…The strict dichotomy expressed in conclusion 3 may be due to the small sample size; some overlap between the slow and fast rotator groups might well be found in further observations. The model of Lamb & Miller (2003) predicts that kHz QPOs separated by once and by half spin can occur simultaneously, but this has not yet been observed. In SAX J1808.4À3658, where twin kHz QPOs were detected only once, several commensurabilities between the centroid frequencies of the kHz QPOs and the spin frequency of the form j;0 ¼ jm k;0 À n spin j (where i;0 indicates the centroid frequency of component L i , j and k designate u and l or vice versa, and m and n are integers) were consistent with the data, with u;0 ¼ j3 l;0 À 2 spin j in particular a remarkably good match.…”

“…Although based on only a single simultaneous detection of twin kHz QPOs, this result carried important consequences for our understanding of LMXBs, as it falsifies simple spin-orbit beat-frequency models, yet requires an intimate link between spin and kHz QPOs. This led to several new proposed models for the nature of the interaction between disk flow and neutron star spin Lamb & Miller 2003;Kluźniak et al 2004;Lee et al 2004), replacing, modifying, or adding to earlier proposed models (e.g., Miller et al 1998;Stella & Vietri 1998;Abramowicz et al 2003). So far, all sources with inferred spin frequencies spin > 400 Hz (''fast rotators'') have Á % spin /2, and the ones with spin < 400 Hz (''slow rotators'') have Á % spin .…”

Accreting Neutron Stars in Low-Mass X-Ray Binary Systems

“…Magnetic forces may cause the gas in the accretion disk to become more clumped as it approaches the neutron star [69,48,49]. Consequently, the parameters that may be most important in determining whether the flow at the spin resonance radius r sr is clumpy or smooth are the star's spin frequency and magnetic field.…”

Statistical properties of twin kilohertz quasi‐periodic oscillations in neutron star low‐mass X‐ray binaries

“…Some researchers proposed the sonic-point and spin-resonance models (Lamb & Miller, 2001, 2003Miller et al, 1998), which explain that the frequency separation of the twin kHz QPOs is close to the spin frequency of NS or its half. Abramowicz et al (2003a,b); Kluźniak & Abramowicz (2001) introduced the resonance model with the upper frequency corresponding to the vertical epicyclic frequency and the lower frequency corresponding to the radial epicyclic frequency, which accords with observational data quite well in the black-hole binary systems (Török et al, 2005.…”