Kilohertz Quasi-periodic Oscillations Research Articles

Resonance in Forced Oscillations of an Accretion Disk and Kilohertz Quasi-periodic Oscillations

We have performed numerical simulations of a radially perturbed accretion torus around a black hole or neutron star and find that the torus performs radial and vertical motions at the appropriate epicyclic frequencies. We find clear evidence that vertical motions are excited in a nonlinear resonance when the applied perturbation is periodic in time. The strongest resonant response occurs when the frequency difference of the two oscillations is equal to one-half the forcing frequency, precisely as recently observed in the accreting pulsar SAX J1808.4-3658, where the observed kilohertz quasi-periodic oscillation peak separation is half the spin frequency of 401 Hz.

Nonlinear Resonance in the Accretion Disk of a Millisecond Pulsar

Two simultaneous frequencies of quasi-periodic millisecond modulation of the X-ray flux (twin kilohertz quasi-periodic oscillations) have recently been detected in an accreting 2.5 ms X-ray pulsar. Their difference, equal to about of the neutron star spin rate, clearly indicates that resonant oscillations of the accretion disk have been observed. Similar nonlinear resonances may be spontaneously excited in the accretion disk in the absence of a pulsar, e.g., in black holes. We identify modes of disk oscillations whose frequencies are in agreement with the two observed ones when the rotating neutron star is modeled with realistic equations of state.

Screw Instability in Black Hole Magnetosphere and kHz QPOs inX-Ray Binaries

Screw instability of the magnetic field connecting a rotating blackhole (BH) with its surrounding disc is discussed in coexistence with theBlandford–Znajek (BZ) process and the magnetic coupling (MC) process. Ascenario for kilohertz quasi-periodic oscillations (kHz QPOs) in x-raybinaries is proposed by introducing inductance components in theequivalent circuit for BH magnetosphere. It turns out that the periodrelated to the screw instability is consistent with the observations ofkHz QPO x-ray binaries.

On the correlated spectral and timing properties of 4U 1636–53: An atoll source at high accretion rates

We analyze ~600 ks data from the X-ray observatory Rossi X-ray Timing Explorer of the neutron star low mass X-ray binary and atoll source 4U 1636–53. These observations span almost three years, from April 1996 to February 1999. The color-color and hardness-intensity diagrams show significant secular shifts of the atoll track, similar to what is observed for some Z sources. These are most evident in the hardness-intensity diagram, where shifts in intensity up to ~20% are observed. We find that the intensity shifts in the hardness-intensity diagram are responsible for the parallel tracks observed in the kilohertz quasi periodic oscillations frequency vs. intensity diagram. While the parallel tracks in the frequency vs. color plane partially overlap, systematic long term shifts are still evident. We also study the broad band power spectra of 4U 1636–53 as a function of the source position Sa along the track in the color-color diagram. These power spectra are all characteristic of the lower and upper banana state in atoll sources, showing very low frequency noise, band limited noise, and sometimes one or two kHz QPOs. We find that the very low frequency noise in some intervals is not well described by a power law because of an excess of power between 20 and 30 mHz, which can be fitted by a Lorentzian. Also, the characteristic frequency of the band limited noise shows a trend to decrease with increasing Sa at high Sa values.

Quasi-periodic X-ray brightness fluctuations in an accreting millisecond pulsar.

The relativistic plasma flows onto neutron stars that are accreting material from stellar companions can be used to probe strong-field gravity as well as the physical conditions in the supra-nuclear-density interiors of neutron stars. Plasma inhomogeneities orbiting a few kilometres above the stars are observable as X-ray brightness fluctuations on the millisecond dynamical timescale of the flows. Two frequencies in the kilohertz range dominate these fluctuations: the twin kilohertz quasi-periodic oscillations (kHz QPOs). Competing models for the origins of these oscillations (based on orbital motions) all predict that they should be related to the stellar spin frequency, but tests have been difficult because the spins were not unambiguously known. Here we report the detection of kHz QPOs from a pulsar whose spin frequency is known. Our measurements establish a clear link between kHz QPOs and stellar spin, but one not predicted by any current model. A new approach to understanding kHz QPOs is now required. We suggest that a resonance between the spin and general relativistic orbital and epicyclic frequencies could provide the observed relation between QPOs and spin.

An analytic model of a rotating hotspot and kilohertz quasi-periodic oscillations in X-ray binaries

To explain kilohertz quasi-periodic oscillations (QPOs) in X-ray binaries, an analytic model of a rotating hotspot is proposed, which is based on the magnetic coupling of a rotating black hole (BH) with its surrounding accretion disc. The hotspot in the inner region of the disc is produced by energy transferred from a spinning BH with non-axisymmetric magnetic field. The frequency and energy band of the hotspot turn out to be related to six parameters, in terms of which the strength and the azimuthal angular region of the bulging magnetic field on the BH horizon, the mass and spin of the BH, and the power-law index of the magnetic field varying with the radial coordinate on the disc are described. In addition, the correlation of the fluctuation of the bulging magnetic field with the widths of QPO frequency is discussed.

Origin and Interpretation of Kilohertz Quasi-periodic Oscillations from Strange Stars in an X-Ray Binary System: Theoretical Hydrodynamical Description

We model and interpret kilohertz quasi-periodic oscillations (QPOs) from the hydrodynamical description of an accretion disk around a rapidly rotating compact strange star. The higher QPO frequency is described by the viscous effects of an accretion disk leading to shocks, while the lower one is taken to be the Keplerian motion of the accreting matter. Comparing our results with the observations for two of the fastest rotating compact stellar candidates, namely, 4U 1636-53 and KS 1731-260, we find that they match to a very good approximation and thus interpret them as strange stars.

Probing the X-ray Variability of X-ray Binaries

Kilohertz quasi-periodic oscillations (kHz QPOs) has been regarded as representing the Keplerian frequency at the inner disk edge in the neutron star X-ray binaries. The so-called “parallel tracks” on the plot of the kHz QPO frequency vs. X-ray flux in neutron star X-ray binaries, on the other hand, show the correlation between the kHz QPO frequency and the X-ray flux on time scales from hours to days. This is suspected as caused by the variations of the mass accretion rate through the accretion disk surrounding the neutron star. We show here that by comparing the correlation between the kHz QPO frequency and the X-ray count rate on a certain QPO time scale observed approximately simultaneous in the Fourier power spectra of the X-ray light curve, we have found evidences that the X-ray flux of millihertz QPOs in neutron star X-ray binaries is generated inside the inner disk edge if adopting that the kilohertz QPO frequency is an orbital frequency at the inner disk edge.

Kilohertz quasi-periodic oscillations difference frequency exceeds inferred spin frequency in 4U 1636−53

Recent observations of the low-mass X-ray binary 4U 1636−53 with the Rossi X-ray Timing Explorer show, for the first time, a kilohertz quasi-periodic oscillation (kHz QPO) peak separation that exceeds the neutron star spin frequency as inferred from burst oscillations. This strongly challenges the sonic-point beat-frequency model for the kHz QPOs found in low-mass X-ray binaries. We detect two simultaneous kHz QPOs with a frequency separation of 323.3 ± 4.3 Hz in an average Fourier power spectrum of observations obtained in 2001 September and 2002 January. The lower kHz QPO frequency varied between 644 and 769 Hz. In previous observations of this source the peak separation frequency was ∼250 Hz when the lower kHz QPO frequency was ∼900 Hz. Burst oscillations occur in 4U 1636−53 at ∼581 Hz and also possibly at half that frequency (290.5 Hz). This is the first source where the peak separation frequency is observed to change from less than (half) the burst oscillation frequency to more than that. This observation contradicts all previously formulated implementations of the sonic-point beat-frequency model except those where the disc in 4U 1636−53 switches from prograde to retrograde.

Correlation of the Quasi‐Periodic Oscillation Frequencies of White Dwarf, Neutron Star, and Black Hole Binaries

Using data obtained in 1994 June/July with the Extreme Ultraviolet Explorer deep survey photometer and in 2001 January with the Chandra X-ray Observatory Low Energy Transmission Grating Spectrograph, we investigate the extreme-ultraviolet (EUV) and soft X-ray oscillations of the dwarf nova SS Cyg in outburst. We find quasi-periodic oscillations (QPOs) at nu_0 ~ 0.012 Hz and nu_1 ~ 0.13 Hz in the EUV flux and at nu_0 ~ 0.0090 Hz, nu_1 ~ 0.11 Hz, and possibly nu_2 ~ nu_0 + nu_1 ~ 0.12 Hz in the soft X-ray flux. These data, combined with the optical data of Woudt & Warner for VW Hyi, extend the Psaltis, Belloni, & van der Klis nu_high-nu_low correlation for neutron star and black hole low-mass X-ray binaries (LMXBs) nearly two orders of magnitude in frequency, with nu_low ~ 0.08 nu_high. This correlation identifies the high-frequency quasi-coherent oscillations (so-called ``dwarf nova oscillations'') of cataclysmic variables (CVs) with the kilohertz QPOs of LMXBs, and the low-frequency QPOs of CVs with the horizontal branch oscillations (or the broad noise component identified as such) of LMXBs. Assuming that the same mechanisms produce the QPOs in white dwarf, neutron star, and black hole binaries, we find that the data exclude the relativistic precession model and the magnetospheric and sonic-point beat-frequency models (as well as any model requiring the presence or absence of a stellar surface or magnetic field); more promising are models that interpret QPOs as manifestations of disk accretion onto any low-magnetic field compact object.

QUASI PERIODIC OSCILLATIONS IN X-RAY NEUTRON STAR AND PROBES OF PERIHELION PRECESSION OF GENERAL RELATIVITY

We ascribe the twin kilohertz Quasi Periodic Oscillations (kHz QPOs) of X-ray spectra of Low Mass X-Ray Binaries (LMXBs) to the pseudo-Newtonian Keplerian frequency and the apogee and perigee precession frequency of the same matter in the inner disk, and ascribe 15–60 Hz QPO (HBO) to the apogee (or perigee) precession and its second harmonic frequency to both apogee and perigee precession in the outer disk boundary of the neutron star (NS) magnetosphere. The radii of the inner and outer disks are correlated each other by a factor of two is assumed. The obtained conclusions include: all QPO frequencies increase and frequency difference of twin kHz QPOs decreases with increasing the accretion rate. The obtained theoretical relations between HBO frequency and twin kHz QPOs are simlilar to the measured empirical formula. Further, the theo-retical formula to calculate the NS mass by the twin kHz QPOs is proposed, and the resultant values are in the range of 1.4 to 1.8 M⊙. QPOs from LMXBs likely provide an accurate laboratory for a strong gravitational field, by which a new method to determine the NS masses of LMXBs is suggested.

Kilohertz Quasi-periodic Oscillation Frequency Anticorrelated with Megahertz Quasi-periodic Oscillation Flux in 4U 1608-52

We analyzed Rossi X-Ray Timing Explorer data of the low-mass X-ray binary and atoll source 4U 1608-52 obtained on 1996 March 3 in which the source simultaneously showed a strong single kilohertz quasi-periodic oscillation (kHz QPO) around 840 Hz and a 7.5 mHz QPO detected at energies below 5 keV. We find that the frequency of the kHz QPO is approximately anticorrelated with the 2-5 keV X-ray count rate associated with the mHz QPO. The average kHz QPO frequency varies by about 0.6 Hz (0.07%) during a mHz QPO cycle over which the average 2-5 keV count rate varies by about 60 counts s(-1) (4%). This is the opposite of the frequency-count rate correlation observed in the same data on longer timescales and, hence, constitutes the first example of a sign reversal in the frequency-flux correlation related to the origin of the flux. Such a sign reversal is predicted by the radiative disk truncation model for the case where the flux variations originate on the neutron star but are not due to disk accretion rate fluctuations. The results support the nuclear burning interpretation of the mHz QPO and the interpretation of the kHz QPO frequency as an indicator of the orbital frequency at the inner edge of the accretion disk. The varying radiative stresses exerted on the inner disk by the flux due to the quasi-periodic nuclear burning lead to changes in the inner disk radius and, hence, to the observed anticorrelation between kHz QPO frequency and X-ray count rate. We found a time lag of about 10 s of the X-ray count rate relative to the kHz QPO frequency in terms of the anticorrelation between these two quantities, which could be caused by the propagation of the nuclear burning front on the neutron star away from the equatorial region.

The Amplitude of the Kilohertz Quasi‐periodic Oscillations in 4U 1728−34, 4U 1608−52, and Aquila X‐1, as a Function of X‐Ray Intensity

We study the kilohertz quasi-periodic oscillations (kHz QPOs) in the low-mass X-ray binaries 4U 1728-34, 4U 1608-52, and Aql X-1. Each source traces out a set of nearly parallel tracks in a frequency versus X-ray count rate diagram. We find that between two of these tracks, for similar QPO frequency, the 2-60 keV source count rate can differ by up to a factor of ~4, whereas at the same time the rms amplitude of the kHz QPOs is only a factor of ~1.1 different. We also find that, for 4U 1608-52 and Aql X-1, the rms spectrum of the kHz QPOs does not depend upon which track the source occupies in the frequency versus X-ray count rate diagram. Our results for 4U 1728-34, 4U 1608-52, and Aql X-1 are inconsistent with simple extra source of X-rays scenarios for the parallel tracks, such as those in which the properties of the kHz QPOs are determined only by the mass accretion rate through the disk, whereas X-ray count rate also depends upon other sources of energy that do not affect the QPOs.

ITAL]B[/ITAL]-Field Determination from Magnetoacoustic Oscillations in Kilohertz Quasi-periodic Oscillation Neutron Star Binaries: Theory and Observations

We present a method for determining the B-field around neutron stars based on observed kilohertz and viscous quasi-periodic oscillation (QPO) frequencies used in combination with the best-fit optical depth and temperature of a Comptonization model. In the framework of the transition layer QPO model, we analyze the magnetoacoustic wave (MAW) formation in the layer between a neutron star surface and the inner edge of a Keplerian disk. We derive formulas for the MAW frequencies for different regimes of radial transition layer oscillations. We demonstrate that our model can use the QPO as a new kind of probe to determine the magnetic field strengths for 4U 1728-42, GX 340+0, and Scorpius X-1 in the zone where the QPOs occur. Observations indicate that the dependence of the viscous frequency on the Keplerian frequency is closely related to the inferred dependence of the MAW frequency on the Keplerian frequency for a dipole magnetic field. The MAW dependence is based on a single parameter, the magnetic moment of the star as estimated from the field strength in the transition layer. The best-fit magnetic moment parameter is about (0.5-1) × 1025 G cm3 for all studied sources. From observational data, the magnetic fields within distances less than 20 km from the neutron star for all three sources are strongly constrained to be dipole fields with the strengths of 107-108 G on the neutron star surface.

Classification of Power Density Spectrum Features and Estimation of the δ-invariant Value for the Z Source GX 340+0

We present a theoretical analysis of Rossi X-Ray Timing Explorer data of Z source GX 340+0 obtained by Jonker et al. In the frameworks of the recently formulated transition layer model, the δ-angle is an angle between the neutron star (NS) magnetospheric axis and the disk (presumably NS rotational) axis. We determine the angle δ = 63 ± 03, which is a combination of the simultaneously observed kilohertz quasi-periodic and horizontal-branch oscillation frequencies. While these three frequencies change by a factor of 3 or more, their δ-combination stays almost constant. GX 340+0 is the fourth source (in addition to 4U 0614+09, Scorpius X-1, and 4U 1702-42) for which δ has been determined. With one (constrained) parameter, at most, we make a complete classification of six observed power spectral features, including the two kilohertz frequencies, the first and second harmonics of the horizontal-branch oscillation frequency, the low-frequency noise component, and the break frequencies. We demonstrate that a new component discovered by Jonker et al. in the GX 340+0 power spectrum is related to the viscous-frequency branch that has in fact been reported earlier in 4U 1728-34 by Ford & van der Klis. Finally, we reclassify several previously misidentified features in the power spectrum.

Discovery of a Kilohertz Quasi‐periodic Oscillation in 2S 0918−549

We report the discovery of a kilohertz quasi-periodic oscillation (kHz QPO) in the low-mass X-ray binary (LMXB) 2S 0918-549. The kHz QPO has a frequency of 1156 ± 9 Hz, an FWHM of 70 ± 20 Hz, and a fractional rms amplitude of 18% ± 2%. We also detected for the first time a type I X-ray burst in this source. The compact object must therefore be a neutron star. Finally, we were able to classify the source as an atoll source exhibiting the full complement of spectral/timing states of this class (island and banana). From the peak burst flux, an upper limit on the persistent luminosity can be derived of 0.5% of the Eddington luminosity, making 2S 0918-549 one of the least luminous LMXBs showing a kHz QPO. We compare the fractional rms amplitudes of the upper kHz QPO across the ensemble of LMXBs. We find a strong anticorrelation with luminosity. In LMXBs with luminosities ~100 times lower than those of Z sources, the fractional rms amplitude is a factor ~10 larger.

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.

Discovery of a 270 Hertz X-Ray Burst Oscillation in the X-Ray Dipper 4U 1916−053

We report the discovery of a highly coherent oscillation in a type I X-ray burst observed from 4U 1916-053 by the Rossi X-Ray Timing Explorer (RXTE). The oscillation was most strongly detected ≈1 s after the burst onset at a frequency of 269.4 Hz, and it increased in frequency over the following 4 s of the burst decay to a maximum of 272 Hz. The total measured drift of 3.58 ± 0.41 Hz (1 σ) represents the largest fractional change in frequency (1.32% ± 0.15%) yet observed in any burst oscillation. If the asymptotic frequency of the oscillation is interpreted in terms of a decoupled surface burning layer, the implied neutron star spin period is around 3.7 ms. However, the expansion of the burning layer required to explain the frequency drift during the burst is around 80 m, substantially larger than expected theoretically (assuming rigid rotation). The oscillation was not present in the persistent emission before the burst, nor in the initial rise. When detected, its amplitude was 6%-12% (rms) with a roughly sinusoidal profile. The burst containing the oscillation showed no evidence for photospheric radius expansion, while at least five of the other nine bursts observed from the source by RXTE during 1996 and 1998 did. No comparable oscillations were detected in the other bursts. A pair of kilohertz quasi-periodic oscillations (kHz QPOs) has been previously reported from this source with a mean separation of 348 ± 12 Hz. 4U 1916-053 is the first example of a source where the burst oscillation frequency is significantly smaller than the frequency separation of the kHz QPOs.

A Compton Upscattering Model for Soft Lags in the Lower Kilohertz Quasi-periodic Oscillation in 4U 1608−52

An empirical Compton up-scattering model is described which reproduces both the fractional amplitude (RMS) vs. energy and the soft time lags in the 830 Hz QPO observed in 4U1608-52 on Mar. 3, 1996. A combination of two coherent variations in the coronal and soft photon temperatures (with their relative contributions determined by enforcing energy conservation) gives rise to the QPO's energy dependent characteristics. All input parameters to the model, save a characteristic plasma size and the fraction of Comptonized photons impinging on the soft photon source, are derived from the time-averaged photon energy spectrum of the same observation. Fits to the fractional RMS and phase lag data for this kilohertz QPO imply that the spatial extent of the plasma is in the range from 4 to 15 km.

The harmonic and sideband structure of the kilohertz quasi-periodic oscillations in Sco X-1

ABSTRA C T We use data from the Rossi X-ray Timing Explorer to search for harmonics and sidebands of the two simultaneous kilohertz quasi-periodic oscillations (kHz QPOs) in Sco X-1. We do not detect any of these harmonics or sidebands, with 95 per cent confidence upper limits to their power between ,1 and ,10 per cent of the power of the upper kHz QPO. The oscillations produced at these frequencies may be attenuated in a scattering corona around the neutron star. We find that upper limits to the unattenuated power of some of the strongest theoretically predicted harmonics and sidebands are as low as ,2 per cent of the unattenuated power of the high-frequency QPO in Sco X-1.