The coherence of kilohertz quasi-periodic oscillations in the X-rays from accreting neutron stars

We study in a systematic way the quality factor of the lower and upper kilohertz quasi-periodic oscillations (kHz QPOs) in a sample of low-luminosity neutron star X-ray binaries, showing both QPOs varying over a wide frequency range. The sample includes 4U 1636−536, 4U 1608−522, 4U 1735−44, 4U 1728−34, 4U 1820−303 and 4U 0614+09. We find that all sources except 4U 0614+09 show evidence of a drop in the quality factor of their lower kHz QPOs at high frequency. For 4U 0614+09 only the rising part of the quality factor versus frequency curve has been sampled so far. At the same time, in all sources but 4U 1728−34, the quality factor of the upper kHz QPO increases all the way to the highest detectable frequencies. We show that the high-frequency behaviours of both the lower and the upper kHz QPO quality factors are consistent with what is expected if the drop is produced by the approach of an active oscillating region to the innermost stable circular orbit: the existence of which is a key feature of general relativity in the strong field regime. Within this interpretation, our results imply gravitational masses around 2 M_⊙ for the neutron stars in those systems.     

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 4U 1636−53 with the Rossi X-ray Timing Explorer ( RXTE ) for more than 1.5 yr. Our campaign consisted of short (∼2 ks) pointings separated by 2 d, regularly monitoring the spectral and timing properties of the source. During the campaign we observed a clear long-term oscillation with a period of ∼30–40 d, 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.     

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  Δν= 274 ± 11 Hz  , significantly smaller than the constant value of  Δν∼ 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.     

kHz quasi-periodic oscillations in the low-mass X-ray binary 4U 0614+09

We report on a comprehensive analysis of the kilohertz (≥300 Hz) quasi-periodic oscillations (kHz QPOs) detected from the neutron star low-mass X-ray binary 4U 0614+09 with the Rossi X-ray Timing Explorer. With a much larger data set than previously analysed (all archival data from 1996 February up to 2007 October), we first investigate the reality of the 1330 Hz QPO reported by van-Straaten et al. This QPO would be of particular interest since it has the highest frequency reported for any source. A thorough analysis of the same observation fails to confirm the detection. On the other hand, over our extended data set, the highest QPO frequency we measure for the upper kHz QPO is at ∼1224 Hz; a value which is fully consistent with the maximum values observed in similar systems. Secondly, we demonstrate that the frequency dependence of the quality factor  ( Q =ν/Δν)  and amplitude of the lower and upper kHz QPOs follow the systematic trends seen in similar systems. In particular, 4U 0614+09 shows a drop of the quality factor of the lower kHz QPO above ∼700 Hz. If this is due to an approach to the innermost stable circular orbit, it implies a neutron star mass of  ∼1.9 M_⊙  . Finally, when analysing the data over fixed durations, we have found a gap in the frequency distribution of the upper QPO, associated with a local minimum of its amplitude. A similar gap is not present in the distribution of the lower QPO frequencies, suggesting some cautions when interpreting frequency ratio distributions, based on the occurrence of the lower QPO only.     

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

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.     

Morphological analysis on the coherence of kHz QPOs

We take the recently published data of twin kHz quasi-period oscillations (QPOs) in neutron star (NS) low-mass X-ray binaries (LMXBs) as the samples, and investigate the morphology of the samples, which focuses on the quality factor, peak frequency of kHz QPOs, and try to infer their physical mechanism. We notice that: (1) The quality factors of upper kHz QPOs are low (2～20 in general) and increase with the kHz QPO peak frequencies for both Z and Atoll sources. (2) The distribution of quality factor versus frequency for the lower kHz QPOs are quite different between Z and Atoll sources. For most Z source samples, the quality factors of lower kHz QPOs are low (usually lower than 15) and rise steadily with the peak frequencies except for Sco X-1, which drop abruptly at the frequency of about 750 Hz. While for most Atoll sources, the quality factors of lower kHz QPOs are very high (from 2 to 200) and usually have a rising part, a maximum and an abrupt drop. (3) There are three Atoll sources (4U 1728-34, 4U 1636-53 and 4U 1608-52) of displaying very high quality factors for lower kHz QPOs. These three sources have been detected with the spin frequencies and sidebands, in which the source with higher spin frequency presents higher quality factor of lower kHz QPOs and lower difference between sideband frequency and lower kHz QPO frequency.     

Type I X-ray bursts, burst oscillations and kHz quasi-periodic oscillations in the neutron star system IGR J17191−2821

We present a detailed study of the X-ray energy and power spectral properties of the neutron star transient IGR J17191−2821. We discovered four instances of pairs of simultaneous kilohertz quasi-periodic oscillations (kHz QPOs). The frequency difference between these kHz QPOs is between 315 and 362 Hz. We also report on the detection of five thermonuclear type I X-ray bursts and the discovery of burst oscillations at ∼294 Hz during three of them. Finally, we report on a faint and short outburst precursor, which occurred about two months before the main outburst. Our results on the broad-band spectral and variability properties allow us to firmly establish the atoll source nature of IGR J17191−2821.     

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  ν₁∼ν ^b ₂  between the upper and the lower kHz QPOs with different indices: b ≃ 1.5 for the Atoll source 4U 1728-34 and b ≃ 1.9 for the Z source Sco X-1. The implications of our results for the theoretical models for kHz QPOs are discussed.     

A detailed study of the 5-Hz quasi-periodic oscillations in the bright X-ray transient and black hole candidate GRS 1739–278

We present a detailed study of the 5-Hz quasi-periodic oscillation (QPO) recently discovered in the bright X-ray transient and black hole candidate (BHC) GRS     (Borozdin & Trudolyubov) during a Rossi X-ray Timing Explorer observation taken on 1996 March 31. In total 6.6 ksec of on-source data were obtained, divided in two data sets of 3.4 and 3.2 ksec which were separated by ∼2.6 ksec. The 5-Hz QPO was only present during the second data set. The QPO increased in strength from below 2 per cent rms amplitude for photon energies below 4 keV to ∼5 per cent rms amplitude for energies above 10 keV. The soft QPO photons (below 5 keV) lagged the hard ones (above 10 keV) by almost 1.5 rad. Besides the QPO fundamental, its first overtone was detected. The strength of the overtone increased with photon energy (from < 2 per cent rms below 5 keV to ∼8 per cent rms above 10 keV). Although limited statistics did not allow for an accurate determination of the lags of the first overtone, indications are that also for this QPO the soft photons lagged the hard ones. When the 5-Hz QPO was not detected (i.e., during the first part of the observation), a broad noise component was found for photon energies below 10 keV but it became almost a true QPO (with a Q value of ∼1.9) above that energy, with a frequency of ∼3 Hz. Its hard photons preceded the soft ones in a way reminiscent of the 5-Hz QPO, strongly suggesting that both features are physically related. We discuss our finding in the framework of low-frequency QPOs and their properties in BHCs.     

Accretion flow behaviour during the evolution of the quasi-periodic oscillation frequency of XTE J1550−564 in 1998 outburst

Low and intermediate frequency quasi-periodic oscillations (QPOs) are thought to be due to oscillations of Comptonizing regions or hot regions embedded in Keplerian discs. Observational evidence of evolutions of QPOs would therefore be very important as they throw lights on the dynamics of the hotter region. Our aim is to find systems in which there is a well-defined correlation among the frequencies of the QPOs over a range of time so as to understand the physical picture. In this paper, we concentrate on the archival data of XTE J1550−564 obtained during 1998 outburst, and study the systematic drifts during the rising phase from the 1998 September 7 to the 1998 September 19, when the QPO frequency increased monotonically from 81 mHz to 13.1 Hz. Immediately after that, QPO frequency started to decrease and on the 1998 September 26, the QPO frequency became 2.62 Hz. After that, its value remained almost constant. This frequency drift can be modelled satisfactorily with a propagatory oscillating shock solution where the post-shock region behaves as the Comptonized region. Comparing with the nature of a more recent 2005 outburst of another black hole candidate GRO 1655−40, where QPOs disappeared at the end of the rising phase, we conjecture that this so-called 'outburst' may not be a full-fledged outburst.     

Keck II spectroscopy of mHz quasi-periodic oscillations in Hercules X-1

We present Keck II spectroscopy of optical mHz quasi-periodic oscillations (QPOs) in the light curve of the X-ray pulsar binary Hercules X-1. In the power spectrum it appears as 'peaked noise', with a coherency ∼2, a central frequency of 35 mHz and a peak-to-peak amplitude of 5 per cent. However, the dynamic power spectrum shows it to be an intermittent QPO, with a lifetime of ∼100 s, as expected if the lifetime of the orbiting material is equal to the thermal time-scale of the inner disc. We have decomposed the spectral time series into constant and variable components and used blackbody fits to the resulting spectra to characterize the spectrum of the QPO variability and constrain possible production sites. We find that the spectrum of the QPO is best fitted by a small hot region, possibly the inner regions of the accretion disc, where the ballistic accretion stream impacts on to the disc. The lack of any excess power around the QPO frequency in the X-ray power spectrum, created using simultaneous light curves from RXTE , implies that the QPO is not simply reprocessed X-ray variability.     

The magnetohydrodynamics model of twin kilohertz quasi-periodic oscillations in low-mass X-ray binaries

We suggest an explanation for the twin kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binaries (LMXBs) based on magnetohydrodynamics (MHD) oscillation modes in neutron star magnetospheres. Including the effect of the neutron star spin, we derive several MHD wave modes by solving the dispersion equations, and propose that the coupling of the two resonant MHD modes may lead to the twin kHz QPOs. This model naturally relates the upper, lower kHz QPO frequencies with the spin frequencies of the neutron stars, and can well account for the measured data of six LMXBs.     

On The Low Frequency Quasi Periodic Oscillations Of X-Ray Sources

Based on the interpretation of the twin kilohertz Quasi Periodic Oscillations (kHz QPOs) of X-ray spectra of Low Mass X-Ray Binaries (LMXBs) ascribed to the Keplerian and the periastron precession frequencies at the inner disk respectively, we ascribe the low frequency (0.1–10 Hz) Quasi Periodic Oscillations (LFQPO) and HBO (15–60 Hz QPO for Z sources or Atoll sources) to the periastron precession at some outer disk radius. It is assumed that both radii are correlated by a scaling factor of 0.4. The conclusions obtained include: All QPO frequencies increase with increasing accretion rate. The theoretical relations between HBO (LFQPO) frequency and the kHz QPO frequencies are similar to the measured empirical formula.     

Superorbital variability in hard X-rays

We present the results of a study with the Swift Burst Alert Telescope in the 14–195 keV range of the long-term variability of five low-mass X-ray binaries with reported or suspected superorbital periods – 4U 1636−536, 4U 1820−303, 4U 1916−053, Cyg X-2 and Sco X-1. No significant persistent periodic modulation was detected around the previously reported periods in the 4U 1916−053, Cyg X-2 or Sco X-1 light curves. The ∼170-d period of 4U 1820−303 was detected up to 24 keV, consistent with variable accretion due to the previously proposed triple system model. The ∼46-d period in 4U 1636−536 was detected up to 100 keV, with the modulation in the low- and high-energy bands found to be phase shifted by ∼180° with respect to each other. This phase shift, when taken together with the near-coincident onset of the ∼46-d modulation and the low/hard X-ray state, leads us to speculate that the modulation could herald transient jet formation.     

Evolution of black hole intermediate-mass X-ray binaries: the influence of a circumbinary disc

We report the results of a systematic timing analysis of RXTE observations of GRS 1915+105 when the source was in its variability class θ, characterized by alternating soft and hard states on a time-scale of a few hundred seconds. The aim was to examine the high-frequency part of the power spectrum in order to confirm the hectohertz quasi-periodic oscillations (QPO) previously reported from observations from mixed variability behaviours. During the hard intervals (corresponding to state C in the classification of Belloni et al.), we find a significant QPO at a frequency of ∼170 Hz, although much broader (Q∼2) than previously reported. No other significant peak is observed at frequencies >30 Hz. A time-resolved spectral analysis of selected observations shows that the hard intervals from class θ show a stronger and steeper  (Γ= 2.8–3.0)  power-law component than hard intervals from other classes. We discuss these results in the framework of hectohertz QPOs reported from GRS 1915+105 and other black hole binaries.     

A Study on the Correlations between the Twin kHz QPO Frequencies in Sco X-1

For the bright neutron star low-mass X-ray binary Sco X-1, we analyzed all updated frequencies of the twin kilohertz quasi-periodic oscillations (kHz QPOs), their correlations and distributions. We found that the frequency separation of the kHz QPO peaks appears not to be a constant, rather, it decreases with increasing inferred mass accretion rate. We show that the currently available data of Sco X-1 by Rossi X-ray Timing Explorer are inconsistent with the proposals of the beat model that the frequency separation is a constant. Our conclusions are consistent with those of some previous researchers and we discuss further implications for the kilohertz QPO models.     

Comptonization and QPO origins in accreting neutron star systems

We develop a simple, time-dependent Comptonization model to probe the origins of spectral variability in accreting neutron star systems. In the model, soft 'seed photons' are injected into a corona of hot electrons, where they are Compton upscattered before escaping as hard X-rays. The model describes how the hard X-ray spectrum varies when the properties of either the soft photon source or the Comptonizing medium undergo small oscillations. Observations of the resulting spectral modulations can determine whether the variability is due to (i) oscillations in the injection of seed photons, (ii) oscillations in the coronal electron density, or (iii) oscillations in the coronal energy dissipation rate. Identifying the origin of spectral variability should help clarify how the corona operates and its relation to the accretion disc. It will also help in finding the mechanisms underlying the various quasi-periodic oscillations (QPOs) observed in the X-ray outputs of many accreting neutron star and black hole systems. As a sample application of our model, we analyse a kilohertz QPO observed in the atoll source 4U 1608–52. We find that the QPO is driven predominantly by an oscillation in the electron density of the Comptonizing gas.     

Are there three peaks in the power spectra of GX 339−4 and Cyg X-1?

Among the variability behaviours exhibited by neutron star systems are the so-called 'horizontal branch oscillations' (HBO, with frequencies ≈50 Hz), the 'lower-frequency kHz quasi-periodic oscillation' (QPO) and the 'upper-frequency kHz QPO', with the latter two features being separated in frequency by an amount comparable to, but varying slightly from, the suspected spin-frequency of the neutron star. Recently, Psaltis, Belloni & van der Klis have suggested that there exists a correlation between these three frequencies that, when certain identifications of variability features are made, even encompasses black hole sources. We consider this hypothesis by reanalysing a set of GX 339−4 observations. The power spectral density (PSD) constructed from a composite of seven separate, but very similar, observations shows evidence for three broad peaks in the PSD. If the peak frequencies of these features are identified with QPO, then their frequencies approximately fit the correlations suggested by Psaltis, Belloni, & van der Klis. We also reanalyse a Cyg X-1 observation and show that the suggested QPO correlation may also hold, but that complications arise when the QPOs (which, in reality, are fairly broad features) are considered as a function of energy band. These fits suggest the existence of at least three separate, independent physical processes in the accretion flow, a hypothesis that is also supported by consideration of the Fourier frequency-dependent time lags and coherence function between variability in different energy bands. If these variability features have a common origin in neutron star and black hole systems, then 'beat frequency models' of kHz QPO in neutron star systems are called into question.     

Normal-branch quasi-periodic oscillations during the high-intensity state of Cygnus X-2

Using data obtained with the Rossi X-ray Timing Explorer , we report the detection of a 5-Hz quasi-periodic oscillation (QPO) in the bright low-mass X-ray binary and Z source Cygnus X-2 during high overall intensities (the high-intensity state). This QPO was detected on the so-called normal-branch and can be identified with the normal-branch QPO or NBO. Our detection of the NBO is the first one during times when Cygnus X-2 was in the high-intensity state. The rms amplitude of this QPO decreased from 2.8 per cent between 2 and 3.1 keV to <1.9 per cent between 5.0 and 6.5 keV. Above 6.5 keV, its amplitude rapidly increased to ∼12 per cent rms above 16 keV. The time lags of the QPO were consistent with being zero below 5 keV (compared with the 2–3.1 keV band), but they rapidly increased to ∼70 ms (140°) around 10 keV, above which the time lags remained approximately constant near 70 ms. The photon energy dependences of the rms amplitude and the time lags are very similar to those observed for the NBO with other satellites ( Ginga , EXOSAT ) at different (i.e. lower) intensity states.     

A variable Quasi-Periodic Oscillation in M82 X-1. Timing and spectral analysis of XMM–Newton and RossiXTE observations

We report results from a spectral and timing analysis of M82 X-1, one of the brightest known ultraluminous X-ray sources. Data from a new 105-ks XMM–Newton observation of M82 X-1, performed in 2004 April, and of archival RossiXTE observations are presented. A very soft thermal component is present in the XMM spectrum. Although it is not possible to rule out a residual contamination from the host galaxy, modelling it with a standard accretion disc would imply a black hole (BH) mass of  ≈10³ M_⊙  . An emission line was also detected at an energy typical for fluorescent Fe emission. The power density spectrum of the XMM observation shows a variable Quasi-Periodic Oscillation (QPO) at frequency of 113 mHz with properties similar to those discovered by Strohmayer and Mushotzky. The QPO was also found in seven archival RXTE observations, that include those analysed by Strohmayer and Mushotzky, and Fiorito and Titarchuk. A comparison of the properties of this QPO with those of the various types of QPOs observed in Galactic black hole candidates strongly suggests an association with the type-C, low-frequency QPOs. Scaling the frequency inversely to the BH mass, the observed QPO frequency range (from 50 to 166 mHz) would yield a BH mass anywhere in the interval few tens to  1000  M_⊙  .