kHz Quasi-periodic Oscillations Frequency Research Articles

The possible origin of high frequency quasi-periodic oscillations in low mass X-ray binaries

AbstractWe summarize our model that high frequency quasi-periodic oscillations (QPOs) both in the neutron star low mass X-ray binaries (NS-LMXBs) and black hole LMXBs may originate from magnetohydrodynamic (MHD) waves. Based on the MHD model in NS-LMXBs, the explanation of the parallel tracks is presented. The slowly varying effective surface magnetic field of a NS leads to the shift of parallel tracks of QPOs in NS-LMXBs. In the study of kilohertz (kHz) QPOs in NS-LMXBs, we obtain a simple power-law relation between the kHz QPO frequencies and the combined parameter of accretion rate and the effective surface magnetic field. Based on the MHD model in BH-LMXBs, we suggest that two stable modes of the Alfv́en waves in the accretion disks with a toroidal magnetic field may lead to the double high frequency QPOs. This model, in which the effect of the general relativity in BH-LMXBs is considered, naturally accounts for the 3:2 relation for the upper and lower frequencies of the QPOs and the relation between the BH mass and QPO frequency.

Testing the relativistic precession model using low-frequency and kHz quasi-periodic oscillations in neutron star low-mass X-ray binaries with known spin

We analyze all available RXTE data on a sample of 13 low mass X-ray binaries with known neutron star spin that are not persistent pulsars. We carefully measure the correlations between the centroid frequencies of the quasi-periodic oscillations (QPOs). We compare these correlations to the prediction of the relativistic precession model (RPM) that, due to frame dragging, a QPO will occur at the Lense-Thirring precession frequency $\nu_{LT}$ of a test particle orbit whose orbital frequency is the upper kHz QPO frequency $\nu_u$. Contrary to the most prominent previous studies, we find two different oscillations in the range predicted for $\nu_{LT}$ that are simultaneously present over a wide range of $\nu_u$. Additionally, one of the low frequency noise components evolves into a (third) QPO in the $\nu_{LT}$ range when $\nu_u$ exceeds 600 Hz. The frequencies of these QPOs all correlate to $\nu_u$ following power laws with indices between 0.4$-$3.3, significantly exceeding the predicted value of 2.0 in 80$\%$ of the cases (at 3 to >20$\sigma$). Also, there is no evidence that the neutron star spin frequency affects any of these three QPO frequencies as would be expected for frame dragging. Finally, the observed QPO frequencies tend to be higher than the $\nu_{LT}$ predicted for reasonable neutron star specific moment of inertia. In the light of recent successes of precession models in black holes, we briefly discuss ways in which such precession can occur in neutron stars at frequencies different from test particle values and consistent with those observed. A precessing torus geometry and other torques than frame dragging may allow precession to produce the observed frequency correlations, but can only explain one of the three QPOs in the $\nu_{LT}$ range.

PULSE AMPLITUDE DEPENDS ON kHz QPO FREQUENCY IN THE ACCRETING MILLISECOND PULSAR SAX J1808.4-3658

We study the relation between the 300-700 Hz upper kHz quasi-periodic oscillation (QPO) and the 401 Hz coherent pulsations across all outbursts of the accreting millisecond X-ray pulsar SAX J1808.4-3658 observed with the Rossi X-ray Timing Explorer. We find that the pulse amplitude systematically changes by a factor of ~2 when the upper kHz QPO frequency passes through 401 Hz: it halves when the QPO moves to above the spin frequency and doubles again on the way back. This establishes for the first time the existence of a direct effect of kHz QPOs on the millisecond pulsations and provides a new clue to the origin of the upper kHz QPO. We discuss several scenarios and conclude that while more complex explanations can not formally be excluded, our result strongly suggests that the QPO is produced by azimuthal motion at the inner edge of the accretion disk, most likely orbital motion. Depending on whether this azimuthal motion is faster or slower than the spin, the plasma then interacts differently with the neutron-star magnetic field. The most straightforward interpretation involves magnetospheric centrifugal inhibition of the accretion flow that sets in when the upper kHz QPO becomes slower than the spin.

A possible link between kHz quasi-periodic oscillations and the magnetospheric boundary

The quasi-periodic oscillations (QPOs) observed with a 200-1300 Hz fre- quency range in the X-ray power spectra of low mass X-ray binaries (LMXBs) might be considered as one of the observational clues to the physics at the innermost regions of accretion disks around neutron stars. In a neutron star LMXB, the magnetospheric boundary is likely to be close to the surface of the neutron star because of its presumably weak magnetic dipole field. The kHz QPOs can therefore be interpreted as the modula- tion of X-ray emission with smallest timescales associated with the dynamics of accreting disk matter at the magnetospheric boundary. As a result of magnetosphere-disk interac- tion we expect the rotational dynamics of the disk matter in the boundary region to be characterized by either sub-Keplerian or super-Keplerian flow depending on the fastness of the neutron star. We summarize our current understanding of the kHz QPO frequency correlations in terms of the oscillatory modes amplified in the magnetic boundary region and discuss the future prospects related to the possible link between kHz QPOs and the rotational dynamics at the magnetospheric boundary.

Constraints on kilohertz quasi-periodic oscillation models and stellar equations of state from SAX J1808.4–3658, Cyg X-2 and 4U 1820–30

We test the relativistic precession model (RPM) and the magnetohydrodynamics Alfvén wave oscillation model (AWOM) for the kilohertz (kHz) quasi-periodic oscillations (QPOs) from sources with measured neutron star (NS) masses and twin kHz QPO frequencies. For the RPM, the derived NS masses of Cyg X-2, SAX J1808.4–3658 and 4U 1820–30 are 1.96 ± 0.10, 2.83 ± 0.04 and 1.85 ± 0.02 M⊙, respectively. These are, respectively, ∼30, 100 and 40 per cent higher than the measured results 1.5 ± 0.3, <1.4 and |$1.29^{+0.19}_{-0.07}$| M⊙. For the AWOM, where the free parameter of the model is the density of the star, we infer the NS radii to be around 10–20 km for the above three sources. Based on this, we can infer the matter compositions inside the NSs with the help of the equations of state. In particular, for SAX J1808.4–3658, the AWOM shows a lower mass density for its NS than those of the other known kHz QPO sources, with a radius range of 17–20 km, which excludes the strange quark matter inside its star.

The correlations between kHz and LF QPOs in the NSXBs

AbstractWe study the correlations between low frequency (LF) and kHz quasi-periodic oscillations (QPOs) for 20 neutron star X-ray bianaries (NSXBs). We find that both upper and lower kHz QPOs correlate with the LF QPOs. However, the correlations show 5 parallel branches in the kHz QPO frequency vs. LF QPO frequency relation diagram. We notice that the source will jump from one parallel branch to another when different harmonic frequency of the LF QPO is used to plot the correlation between kHz and LF QPOs. We infer that the parallel branches maybe due to the multi-harmonic QPOs in the NSXBs.

The applications of the MHD Alfvén wave oscillation model for kHz quasi‐periodic oscillations

AbstractIn this paper, we improve the previous work on the MHD Alfvén wave oscillation model for the neutron star (NS) kHz quasi‐periodic oscillations (QPOs), and compare the model with the updated twin kHz QPO data. For the 17 NS X‐ray sources with the simultaneously detected twin kHz QPO frequencies, the stellar mass M and radius R constraints are given by means of the derived parameter A in the model, which is associated with the averaged mass density of the star as 〈ρ 〉 = 3M /(4πR3) ≃ 2.4 × 1014 (A /0.7)2 g/cm3, and we also compare the M ‐R constraints with the stellar equations of state. Moreover, we also discuss the theoretical maximum kHz QPO frequency and maximum twin peak separation, and some expectations on SAX J1808.4–3658 are mentioned, such as its highest kHz QPO frequency ∼ 870 Hz, which is about 1.4–1.5 times less than those of the other known kHz QPO sources. The estimated magnetic fields for both Z sources (about Eddington accretion rate $ {\dot M}_{\rm Edd} $) and Atoll sources (∼ 1% $ {\dot M}_{\rm Edd} $) are approximately ∼109 G and ∼108 G, respectively. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Interpretations for Low‐ and High‐Frequency QPO Correlations of X‐Ray Sources among White Dwarfs, Neutron Stars, and Black Holes

ABSTRACTAn empirical linear relation is found to exist between the high and low frequencies (νhigh, νlow) of quasi‐periodic oscillations (QPOs) for black hole candidates (BHCs), neutron stars (NSs), and white dwarfs (WDs) in binary systems, spanning 5 orders of magnitude in frequency. For the NS Z (atoll) sources, νhigh and νlow are identified as the lower kHz QPO frequency and horizontal‐branch oscillation (HBO) frequency νHBO (broad noise components); for the BHCs and low‐luminosity NSs, they are the QPOs and broad noise components at frequencies between 1 and 10 Hz; for WDs, they are the “dwarf nova oscillations” (DNOs) and QPOs of cataclysmic variables (CVs). To interpret this relation, our model ascribes νhigh to the Alfvén wave oscillation frequency at a preferred radius, and νlow to the same mechanism at another radius. We can then obtain νlow = 0.08νhigh and the relation between the upper kHz QPO frequency ν2 and the HBO frequency, νHBO≃(56 Hz)(ν2/kHz)2, which are in accordance with the observed empirical relations. Furthermore, some implications of the model are discussed, including why QPO frequencies of WDs and NSs span 5 orders of magnitude.

On the kHz QPO frequency correlations in bright neutron star X-ray binaries

We re-examine the correlation between the frequencies of upper and lower kHz quasi-periodic oscillations (QPO) in bright neutron-star low-mass X-ray binaries. By including the kHz QPO frequencies of the X-ray binary Cir X-1 and two accreting millisecond pulsars in our sample, we show that the full sample does not support the class of theoretical models based on a single resonance, while models based on relativistic precession or Alfven waves describe the data better. Moreover, we show that the fact that all sources follow roughly the same correlation over a finite frequency range creates a correlation between the linear parameters of the fits to any sub-sample.

A Toy Model for 3:2 Ratio of kHz QPO Frequency in Black Hole X-ray Binaries

Production of pairs of high frequency quasi-periodic oscillations (QPOs) in black hole X-ray binaries is discussed based on a model of non-axisymmetric magnetic coupling of a rotating black hole (BH) with its surrounding accretion disk, in which a puzzling 3:2 ratio of the upper frequency to the lower frequency is explained. In addition, the correlation of the pairs of high frequency QPOs with the jets from microquasars is discussed.

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

We have produced the colour‐colour diagram of all the observations of 4U 1728‐34 available in the Rossi X-ray Timing Explorer public archive (from 1996 to 2002) and found observations filling in a previously reported ‘gap’ between the island and the banana X-ray states. We have made timing analysis of these gap observations and found, in one observation, two simultaneous kHz quasi-periodic oscillations (QPOs). The timing parameters of these kHz QPOs fit in the overall trend of the source. The ‘lower’ kHz QPO has a centroid frequency of ∼308 Hz. This is the lowest ‘lower’ kHz QPO frequency ever observed in 4U 1728‐34. The peak frequency separation between the ‘upper’ and the ‘lower’ kHz QPO is �ν = 274 ± 11 Hz, significantly smaller than the constant value of �ν ∼ 350 Hz found when the ‘lower’ kHz QPO frequency is between ∼500 and 800 Hz. This is the first indication in this source for a significant decrease of kHz QPO peak separation towards low frequencies. We compare the result briefly to theoretical models for kHz QPO production.

RXTEObservations of the Neutron Star Low‐Mass X‐Ray Binary GX 17+2: Correlated X‐Ray Spectral and Timing Behavior

We have analyzed ~600 ks of Rossi X-Ray Timing Explorer data of the neutron star low-mass X-ray binary and Z source GX 17+2. A study was performed of the properties of the noise components and quasi-periodic oscillations (QPOs) as a function of the broadband spectral properties, with the main goal to study the relation between the frequencies of the horizontal branch (HBO) and upper kHz QPOs. It was found that when the upper kHz QPO frequency is below 1030 Hz these frequencies correlate, whereas above 1030 Hz they anticorrelate. GX 17+2 is the first source in which this is observed. We also found that the frequency difference of the high-frequency QPOs was not constant and that the quality factors (Q-values) of the HBO, its second harmonic, and the kHz QPOs are similar and vary almost hand in hand by a factor of more than 3. Observations of the normal branch oscillations during two type I X-ray bursts showed that their absolute amplitude decreased as the flux from the neutron star became stronger. We discuss these and other findings in terms of models that have been proposed for these phenomena. We also compare the behavior of GX 17+2 and other Z sources with that of black hole sources and consider the possibility that the mass accretion rate might not be the driving force behind all spectral and variability changes.

A Possible Explanation for the “Parallel Tracks” Phenomenon in Low‐Mass X‐Ray Binaries

An explanation is proposed for the observation that in low-mass X-ray binaries (LMXBs), the correlation between most observable X-ray spectral and timing parameters on the one hand, and X-ray luminosity on the other, while generally good in a given source on a timescale of hours, is absent both on longer timescales and between sources. This phenomenon, particularly evident in kHz quasi-periodic oscillation (QPO) sources, leads to parallel tracks in plots of such parameters versus luminosity. It is pointed out that where previously proposed explanations require at least two time-variable independent parameters, such as accretion rate through the disk and through a more radial inflow, just one independent variable is in fact sufficient, provided that the systemic response to time variations in this variable has both a prompt and a time-averaged component. A specific scenario is explored in which most observable spectral and timing parameters to first order depend on the disk accretion rate normalized by its own long-term average, rather than on any individual accretion rate (luminosity, on the contrary, just depends on the total accretion rate). This provides a way in which parameters can be uncorrelated with accretion rate, yet vary in response to variations in accretion rate. Numerical simulations are presented of such a model, describing the relation between kHz QPO frequency and X-ray luminosity, which observationally is characterized by a striking pattern of parallel tracks in the frequency versus luminosity plane, both in individual sources and across sources. The model turns out to reproduce the observations remarkably well. Physical interpretations are suggested that would produce such a scenario; particularly promising seems an interpretation involving a radial inflow with a rate that derives through a time-averaging process from the disk accretion rate, and an inner disk radius that depends on the balance between the accretion through the disk and the total luminosity. The consequences of this idea for our understanding of states and tracks in LMXBs are discussed, and the applicability of the idea to black hole candidates, where the observational situation is more complex, is briefly addressed.

Dependence of Kilohertz Quasi-periodic Oscillation Properties on the Normal-Branch Oscillation Phase in Scorpius X-1

We analysed RXTE data of Sco X-1 which show kHz quasi-periodic oscillations (QPOs) and the $\sim$6--8 Hz normal-branch oscillation (NBO) simultaneously. Using power spectra of 0.03--0.5 s data segments, we find that both the upper kHz QPO frequency $\nu_2$ and the ratio of lower to upper kHz QPO amplitude are anticorrelated to variations in the X-ray count-rate taking place on the NBO time scale. The frequency dependence is similar to (but probably weaker than) that found on longer time scales, but the power ratio dependence is opposite to it. A model where radiative stresses on the disk material, modulated at the NBO frequency, lead to changes in $\nu_2$ can explain the data; this implies some of the NBO flux changes originate from inside the inner disk radius. We discuss how these findings affect our understanding of kHz QPOs and of the low-frequency variability of low-mass X-ray binaries.

Testing the Transition Layer Model of Quasi‐periodic Oscillations in Neutron Star X‐Ray Binaries

We compare the theoretical predictions of the transition layer model with some observational features of quasi-periodic oscillations (QPOs) in neutron star X-ray binaries. We found that the correlation between horizontal branch oscillation (HBO) frequencies and kilohertz (kHz) QPO frequencies, the difference between the low-frequency QPOs in atoll sources and HBOs in Z sources, and the correlation between the frequencies of low-frequency QPOs and break frequencies can be well explained by the transition layer model, provided the neutron star mass is around 1.4 M☉ and the angle between magnetosphere equator and accretion disk plane is around 6°. The observed decrease of peak separation between the two kHz QPO frequencies with the increase of the kHz QPO frequencies and the increase of QPO frequencies with the increase of inferred mass accretion rate are also consistent with the theoretical predictions of the transition layer model. In addition, we derive a simple equation that can be adopted to estimate the angle (δ) between magnetosphere equator and accretion disk plane by use of the simultaneously observed QPO frequency data. We estimate this angle, in the range of 4°-8°, for five Z sources and two atoll sources. The nearly constant δ value for each source, derived from the different sets of simultaneously observed QPO frequency data, provides a strong test of the theoretical model. Finally, we suggest that similar transition layer oscillations may be responsible for the observed QPOs in accretion-powered millisecond X-ray pulsars and Galactic black hole candidates.

Lense-thirring precession and QPOs in low mass x-ray binaries

The relativistic dragging of inertial frames around fast rotating collapsed stars is substantial and can give rise to observable effects. We apply this to the kHz quasi periodic oscillations (QPOs) sources, low mass X-ray binaries (LMXRBs) containing an accreting neutron star. Within the beat frequency model, both the Keplerian frequency of the innermost region of the accretion disk (∼ 0.3 − 1.2 kHz) and the neutron star spin frequency (∼ 0.3 − 0.4 kHz) are directly observed. From these the Lense-Thirring precession frequency (tens of Hz) of the same material in the innermost disk regions which gives rise to the kHz QPOs is deternined within a factor of ∼ 4, depending on the neutron star equation of state. The classical contribution from neutron star oblateness decreases the precession frequently slightly. The broad peaks at frequencies ∼ 20 − 40 Hz in the power spectra of the “Atoll”-sources 4U 1728-34, 4U 0614+091 and KS 1731-260 and their variations with the higher kHz QPO frequency are well matched by Lense-Thirring precession of material in the innermost disk region. We also suggest that the ∼ 15 – 60 Hz horizontal branch QPOs of GX 5-1 and GX 17+2 (and likewise other “Z”-type low mass X-ray binaries) arise from the same mechanism.

Discovery of Kilohertz Quasi-periodic Oscillations in 4U 1735−44

We discovered a single kHz quasi-periodic oscillation (QPO) near 1150 Hz in the Rossi X-ray Timing Explorer X-ray light curve of the low mass X-ray binary and atoll source 4U 1735-44. The rms amplitude of this peak was 2-3%, and the FWHM 6-40 Hz. There are indications that the kHz QPO frequency decreased from 1160 Hz to 1145 Hz when the count rate increased, which would be quite different from what is observed in other atoll sources for which kHz QPOs have been discovered. In the X-ray color-color diagram and hardness-intensity diagram the source traced out the curved branch (the so-called banana branch) which has been found by previous instruments. The kHz QPO was only detected when the source was at the lowest count rates during our observations, i.e. on the lower part of the banana branch. When 4U 1735-44 was at higher count rates, i.e. on the upper part of the banana branch and at higher inferred mass accretion rate with respect to that on the lower part of the banana branch, the QPO was not detected. Besides the kHz QPO we discovered a low frequency QPO with a frequency near 67 Hz, together with a complex broad peaked noise component below 30 Hz. This 67 Hz QPO may be related to the magnetospheric beat-frequency QPO, which is observed on the horizontal branch of Z sources. This idea is supported by the (peaked) noise found in both 4U 1735-44 and Z sources at frequencies just below the QPO frequency.

Lense-Thirring Precession and Quasi-periodic Oscillations in Low-Mass X-Ray Binaries

Relativistic dragging of inertial frames around fast-rotating collapsed stars is substantial and can give rise to observable effects. We consider kHz quasi-periodic oscillation (QPO) sources, low-mass X-ray binaries (LMXRBs) containing an accreting neutron star. Within beat frequency models, both the Keplerian frequency of the innermost region of the accretion disk (~0.3-1.2 kHz) and the neutron star spin frequency (~0.3-0.4 kHz) are directly observed. From these, the Lense-Thirring precession frequency (tens of Hz) of the same material as gives rise to the kHz QPOs is determined within a factor of ~4, depending on the neutron star equation of state. The classical contribution from neutron star oblateness decreases the precession frequency slightly. The broad peaks at frequencies ~20-40 Hz in the power spectra of the Atoll sources 4U 1728-34, 4U 0614+091, and KS 1731-260 and their variations with the higher kHz QPO frequency are well matched by Lense-Thirring precession of material in the innermost disk region. We also suggest that the ~15-50 Hz horizontal branch QPOs of GX 5-1 and GX 17+2 (and likewise other Z-type LMXRBs) arise from the same mechanism.