kHz Quasi-periodic Oscillations Research Articles

The estimations of neutron star mass and radius by the kHz QPOs

AbstractThe kHz quasi‐periodic oscillations (QPOs) have been detected by the RXTE satellite in about thirty neutron stars (NSs) in low mass X‐ray binaries (LMXBs), which are usually interpreted to be related to the Keplerian motions in the orbit close to NS surface where the accreted matter is sucked onto the star. Based on the MHD Alfvén wave oscillation model and the relativistic precession model for the neutron star (NS) kHz QPOs, estimations of mass M and radius R of some NSs are given, which can give clues to evaluate the models. Furthermore, comparisons with theoretical M ‐R relations by stellar equations of state (EOSs) are presented (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The highest dynamical frequency in the inner region of an accretion disc

In the inner regions of accretion discs around compact objects, the orbital frequency of the gas deviates from the local Keplerian value. For long-wavelength modes in this region, the radial epicyclic frequency K is higher than the azimuthal frequency Ω. This has significant implications for models of the twin kilohertz quasi-periodic oscillations (QPOs) observed in many neutron star sources that traditionally identify the frequencies of the 2 kHz QPOs with dynamical frequencies in the accretion disc. The recognition that the highest frequency in the transition or boundary region of the disc may be the epicyclic frequency also significantly affects the constraints imposed by the observation of high-frequency QPOs on the mass and radius of the compact objects.

Quasi‐Periodic Oscillations as Global Hydrodynamic Modes in the Boundary Layers of Viscous Accretion Disks

The observational characteristics of quasi-periodic oscillations (QPOs) from accreting neutron stars strongly indicate the oscillatory modes in the innermost regions of accretion disks as a likely source of the QPOs. The inner regions of accretion disks around neutron stars can harbor very high frequency modes related to the radial epicyclic frequency κ. The degeneracy of κ with the orbital frequency Ω is removed in a non-Keplerian boundary or transition zone near the magnetopause between the disk and the compact object. We show, by analyzing the global hydrodynamic modes of long wavelength in the boundary layers of viscous accretion disks, that the fastest growing mode frequencies are associated with frequency bands around κ and κ ± Ω . The maximum growth rates are achieved near the radius where the orbital frequency Ω is maximum. The global hydrodynamic parameters such as the surface density profile and the radial drift velocity determine which modes of free oscillations will grow at a given particular radius in the boundary layer. In accordance with the peak separation between kHz QPOs observed in neutron star sources, the difference frequency between two consecutive bands of the fastest growing modes is always related to the spin frequency of the neutron star. This is a natural outcome of the boundary condition imposed by the rotating magnetosphere on the boundary region of the inner disk.

Frequency ratio of twin kHz quasi-periodic oscillations: The case of 4U1820-303

By analyzing all archival Rossi X-ray timing explorer (RXTE) data of the neutron star low mass X-ray binary 4U1820-303, we investigate the detectability of simultaneous twin kHz quasi-periodic oscillations (QPOs) as a function of their frequency, width and root mean squared (RMS) amplitudes. In a blind search over the whole data set (spanning over about 10 years), we show that in continuous time intervals (2000–3000 s), twin QPOs are preferentially detected over narrow range of frequencies (∼100 Hz wide), leading to a clustering in the distribution of frequency ratios, and a gap around the point (600, 900) Hz in the correlation line that links the upper QPO frequency to the lower QPO frequency. A deficit of lower QPOs around 600 Hz had already been noticed by Belloni et al. [Belloni, T., Méndez, M., Homan, J., 2005. A&A 437, 209], it is now confirmed using a much larger data set. We show that the lack of twin QPOs within the gap is not due to a lack of sensitivity for QPO detection, if the parameters of the QPOs (RMS and width) can be interpolated within the gap, using values measured before and after. Since as previously noticed, the gap cannot be attributed to an incomplete sampling of the source states, it thus implies a sudden change of the QPO properties within the gap, either a loss of coherence or an amplitude decrease, or alternatively, that there may be forbidden frequencies in this system.

The variability plane of accreting compact objects

Recently, it has been shown that soft-state black hole X-ray binaries and active galactic nuclei populate a plane in the space defined by the black hole mass, accretion rate and characteristic frequency. We show that this plane can be extended to hard-state objects if one allows a constant offset for the frequencies in the soft and the hard state. During a state transition, the frequencies rapidly move from one scaling to the other depending on an additional parameter, possibly the disc fraction. The relationship among frequency, mass and accretion rate can be further extended by including weakly accreting neutron stars (NSs). We explore if the lower kHz quasi-periodic oscillations of NSs and the dwarf nova oscillations of white dwarfs can be included as well and discuss the physical implications of the found correlation.

Correlations between X‐Ray Spectral Characteristics and Quasi‐Periodic Oscillations in Scorpius X‐1

Correlations between 1-10 Hz quasi-periodic oscillations (QPOs) and spectral power-law index have been reported for black hole (BH) candidate sources and one neutron star source, 4U 1728-34. An examination of QPO frequency and index relationships in Sco X-1 is reported here. We discover that Sco X-1, representing Z-source groups, can be adequately modeled by a simple two-component model of Compton up-scattering with a soft photon electron temperature of about 0.4 keV, plus an Iron K line. The results show a strong correlation between spectral power-law index and kHz QPOs. Because Sco X-1 radiates near the Eddington limit, one can infer that the geometrical configuration of the Compton cloud (CC) is quasi-spherical from high radiation pressure in the CC. Thus, we conclude that the high Thomson optical depth of the Compton cloud, in the range of ~5-6 from the best-fit model parameters, is consistent with the neutron star's surface being obscured by material. Moreover, a spin frequency of Sco X-1 is likely suppressed due to photon scattering off CC electrons. In addition, we demonstrate how the power spectrum evolves when Sco X-1 transitions from the horizontal branch to the normal branch.

Rossi XTE monitoring of 4U 1636-53 - I. Long-term evolution and kHz quasi-periodic oscillations

We have monitored the atoll-type neutron star low-mass X-ray binary 4U1636-53 with the Rossi X-ray Timing Explorer (RXTE) for more than 1.5yr. Our campaign consisted of short (~2ks) pointings separated by 2d, regularly monitoring the spectral and timing properties of the source. During the campaign we observed a clear long-term oscillation with a period of ~30-40d, already seen in the light curves from the RXTE All-Sky Monitor, which corresponded to regular transitions between the hard (island) and soft (banana) states. We detected kilohertz (kHz) quasi-periodic oscillations (QPOs) in about a third of the observations, most of which were in the soft (banana) state. The distribution of the frequencies of the peak identified as the lower kHz QPO is found to be different from that previously observed in an independent data set. This suggests that the kHz QPOs in the system shows no intrinsically preferred frequency.

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 & Co. KGaA, Weinheim)

Frequency Correlations of QPOs Based on a Disk Oscillation Model in Warped Disks

Abstract In previous papers, we proposed a model that high-frequency quasi-periodic oscillations (QPOs) observed in black-hole and neutron-star X-ray binaries are disk oscillations (inertial-acoustic and/or g-mode oscillations) resonantly excited on warped disks. In this paper we examine whether time variations of the QPOs and their frequency correlations observed in neutron-star X-ray binaries can be accounted for by this disk-oscillation model. By assuming that a warp has a time-dependent precession, we can well describe the observed frequency correlations among kHz QPOs and low-frequency QPOs over a wide range of frequencies.

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.

Supporting evidence for the signature of the innermost stable circular orbit in Rossi X-ray data from 4U 1636-536

Analysis of archival Rossi X-ray Timing Explorer (RXTE) data on neutron star low-mass X-ray binaries has shown that for several sources the quality factor Q of the lower kilohertz quasi- periodic oscillations (QPO) drops sharply beyond a certain frequency. This is one possible signature of the approach to the general relativistic innermost stable circular orbit (ISCO), but the implications of such an interpretation for strong gravity and dense matter are important enough that it is essential to explore alternate explanations. In this spirit, Mendez has recently proposed that Q depends fundamentally on mass accretion rate (as measured by spectral hardness) rather than the frequency of the QPO. Specifically, he has suggested that analysis of multiple sources shows trends in Q similar to those previously reported in individual sources, and he surmises that the ISCO therefore does not play a role in the observed sharp drop in Q in any source. We test this hypothesis for 4U 1636−536 by measuring precisely spectral colours simultaneously with the lower QPO frequency and Q after correction for the frequency drift, over a data set spanning eight years of RXTE observations. We find that in this source there is no correlation between Q and spectral hardness. In particular, no apparent changes in hardness are observed when Q reaches its maximum before dropping off. We perform a similar analysis on 4U 1608−522; another source showing a sharp drop in the quality factor of its lower kHz QPO. We find that for this source, positive and negative correlations are observed between spectral hardness, frequency and Q. Consequently, if we are to search for a common explanation for the sharp drop in the quality factor seen in both sources, the spectral hardness is not a good candidate for the independent variable whereas the frequency remains. Therefore, we conclude that the ISCO explanation is viable for 4U 1636−536, and thus possibly for others.

QPOs in Microquasars: the Spin Problem

AbstractIn Galactic microquasars with double-peak kHz quasi-periodic oscillations (QPOs), the ratio of the two frequencies is 3:2. This supports the suggestion that double-peak kHz QPOs are due to a non-linear resonance between two modes of accretion disk oscillations. For the microquasars with known mass, we briefly compare the black hole spin estimates based on the orbital resonance model with the recently reported spin predictions obtained by fitting the spectral continua. Results of these two approaches are not in good agreement. We stress that if the spectral fit estimates are accurate and can be taken as referential (which is still questionable), the disagreement between the predicted and referential values would represent a rather generic problem for any relativistic QPO model, as no spin influence would appear in the observed 1/M scaling of the QPO frequencies. The epicyclic frequencies relevant in these models are often considered to be equal to those of a test particle motion. However modifications of the frequencies due to disc pressure or other non-geodesic effects may play an important role, and the inaccuracy introduced in the spin estimates by the test particle approximation could be crucial.

Stochastic modeling of kHz quasi-periodic oscillation light curves

Aims. Kluzniak & Abramowicz explain the high frequency, double peak, QPOs observed in neutron star and black hole sources in terms of a non-linear parametric resonance between radial and vertical epicyclic oscillations of an almost Keplerian accretion disk. The 3:2 ratio of epicyclic frequencies occurs only in strong gravity. Recently, a simple model incorporating their suggestion was studied analytically: the result is that a small forcing may indeed excite the parametric 3:2 resonance. However, no explanation has been provided on the nature of the forcing which is given an deterministic form. Methods. In the present paper the same model is considered. The equation are numerically integrated, dropping the ad hoc forcing and adding instead a stochastic term to mimic the action of the very complex processes that occur in accretion disks as, for example, MRI turbulence. Results. We demonstrate that the presence of the stochastic term is able to trigger the resonance in epicyclic oscillations of nearly Keplerian disks, and it influences their pattern.

Forced oscillations in a hydrodynamical accretion disk and QPOs

This is the second of a series of papers aimed to look for an explanation on the generation of high frequency quasi-periodic oscillations (QPOs) in accretion disks around neutron star, black hole, and white dwarf binaries. The model is inspired by the general idea of a resonance mechanism in the accretion disk oscillations as was already pointed out by Abramowicz and Klu’zniak (2001). In a first paper (P'etri, 2005a, paper I), we showed that a rotating misaligned magnetic field of a neutron star gives rise to some resonances close to the inner edge of the accretion disk. In this second paper, we suggest that this process does also exist for an asymmetry in the gravitational potential of the compact object. We prove that the same physics applies, at least in the linear stage of the response to the disturbance in the system. This kind of asymmetry is well suited for neutron stars or white dwarfs possessing an inhomogeneous interior allowing for a deviation from a perfectly spherically symmetric gravitational field. After a discussion on the magnitude of this deformation applied to neutron stars, we show by a linear analysis that the disk initially in a cylindrically symmetric stationary state is subject to {three kinds of resonances: a corotation resonance, a Lindblad resonance due to a driven force and a parametric resonance}. In a second part, we focus on the linear response of a thin accretion disk in the 2D limit. {Waves are launched at the aforementioned resonance positions and propagate in some permitted regions inside the disk, according to the dispersion relation obtained by a WKB analysis}. In a last part, these results are confirmed and extended via non linear hydrodynamical numerical simulations performed with a pseudo-spectral code solving Euler's equations in a 2D cylindrical coordinate frame. {We found that for a weak potential perturbation, the Lindblad resonance is the only effective mechanism producing a significant density fluctuation}. In a last step, we replaced the Newtonian potential by the so called logarithmically modified pseudo-Newtonian potential in order to take into account some general-relativistic effects like the innermost stable circular orbit (ISCO). The latter potential is better suited to describe the close vicinity of a neutron star or a black hole. However, from a qualitative point of view, the resonance conditions remain the same. The highest kHz QPOs are then interpreted as the orbital frequency of the disk at locations where the response to the resonances are maximal. It is also found that strong gravity is not required to excite the resonances.

The correlations between the twin kHz quasi-periodic oscillation frequencies of low-mass X-ray binaries

We analyzed the recently published kHz quasi-period oscillaiton (QPO) data in the neutron star low-mass X-ray binaries (LMXBs), in order to investigate the different correlations of the twin-peak kHz QPOs in bright Z sources and in the less luminous Atoll sources. We find a power-law relation nu(1)similar to nu(b)(2) between the upper and the lower kHz QPOs with different indices: b similar or equal to 1.5 for the Atoll source 4U 1728-34 and b similar or equal to 1.9 for the Z source Sco X-1. The implications of our results for the theoretical models for kHz QPOs are discussed.

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.

An abrupt drop in the coherence of the lower kHz quasi-periodic oscillations in 4U 1636−536

Using archival data from the Rossi X-ray Timing Explorer (RXTE), we study in a systematic way the variation of the quality factor and amplitude of the lower and upper kHz quasi-periodic oscillations (QPO) in the low-mass X-ray binary 4U1636-536, over a frequency range from ~550 Hz to ~1200 Hz. When represented in a quality factor versus frequency diagram, the upper and lower QPOs follow two different tracks, suggesting that they are distinct phenomena, although not completely independent because the frequency difference of the two QPOs, when detected simultaneously, remains within ~60 Hz of half the neutron star spin frequency (at 581 Hz). The quality factor of the lower kHz QPO increases with frequency up to a maximum of ~200 at ~850 Hz, then drops precipitously to Q~50 at the highest detected frequencies ~920 Hz. A ceiling of the lower QPO frequencies at 920 Hz is also clearly seen in a frequency versus count rate diagram. The quality factor provides a measure of the coherence of the underlying oscillator. For exponentially damped sinusoidal shots, the highest Q observed corresponds to an oscillator coherence time of ~ 0.1 seconds. All existing QPO models face challenges in explaining such a long coherence time and the significantly different behaviours of the quality factors of the upper and lower QPOs reported here. It is therefore difficult to be certain of the implications of the abrupt change in the lower QPO at ~850 Hz. We discuss various possible causes, including that the drop in coherence is ultimately caused by effects related to the innermost stable circular orbit (abridged).

On the high coherence of kHz quasi-periodic oscillations

We have carried out a systematic study of the properties of the kilo-Hertz quasi-periodic oscillations (QPO) observed in the X-ray emission of the neutron star low-mass X-ray binary 4U1608-52, using archival data obtained with the Rossi X-ray Timing Explorer. We have investigated the quality factor, Q, of the oscillations (defined as the ratio of the frequency of the QPO peak to its full width at half maximum). In order to minimise the effect of long-term frequency drifts, power spectra were computed over the shortest times permitted by the data statistics. We show that the high Q of ~200 reported by Berger et al. (1996) for the lower frequency kilo-Hz QPO in one of their observations is by no means exceptional, as we observe a mean Q value in excess of 150 in 14 out of the 21 observations analysed and Q can remain above 200 for thousands of seconds. The frequency of the QPO varies over the wide range 560--890 Hz and we find a systematic trend for the coherence time of the QPO, estimated as tau=Q /(pi nu), to increase with the frequency, up to a maximum level at ~ 800 Hz, beyond which it appears to decrease, at frequencies where the QPO weakens. There is a more complex relationship between tau and the QPO root mean squared amplitude (RMS), in which positive and negative correlations can be found. A higher-frequency QPO, revealed by correcting for the frequency drift of the 560-890 Hz one, has a much lower Q (~10) which does not follow the same pattern. We discuss these results in the framework of competing QPO models and show that those involving clumps orbiting within or above the accretion disk are ruled out.

On the incidence of kilohertz quasi-periodic oscillations in the neutron star system 4U 1636−53

Nearly 1.32 x 10 6 s of non-zero count rate data were obtained from five years of Rossi X-ray Timing Explorer (RXTE) observations of the atoll source 4U 1636-53. The data were divided into 10 309 segments of 128 s each. The histogram of the number of segments as a function of count rate shows that the system can naturally be classified into four flux states. For each segment, an automated search for kilohertz quasi-periodic oscillations (QPOs) was undertaken and the histograms of the maximum Leahy normalized power P max for the four flux states were created. These were fitted by probability distribution functions under the assumption that the intrinsic amplitude of the QPO has a normal distribution. The best-fitting distribution functions showed that the fraction f of the time the system exhibits a kHz QPO decreases from near unity for the lowest flux state (1400 count s -1 ) to zero for the highest (>2550 count s -1 ), whereas the average amplitude remains nearly constant. Based on the best-fitting probability distribution functions, a threshold P thre was defined, such that 95 per cent of the segments with P max > P thre correspond to a real QPO signal. For segments selected by this criterion, the frequency versus count rate plot reproduced the earlier known 'parallel track' variation with the tracks coinciding roughly with the flux states. It is shown that the gaps between the tracks are not caused by uneven sampling, but rather the QPO phenomenon is absent or weak when the system flux level is intermediate between two flux states.