Quasi-periodic Oscillation Peak Research Articles

Hilbert–Huang Transform Analysis of Quasiperiodic Oscillations in MAXI J1820+070

We present a time-frequency analysis, based on the Hilbert–Huang transform, of the evolution of the low-frequency quasiperiodic oscillations observed in the black hole X-ray binary MAXI J1820+070. Through the empirical mode decomposition method, we decompose the light curve of the quasiperiodic oscillation (QPO) component and measure its intrinsic phase lag between photons from different energy bands. We find that the QPO phase lag is negative (low-energy photons lag behind high-energy photons); meanwhile, the absolute value of the lag increases with energy. By applying the Hilbert transform to the light curve of the QPO, we further extract the instantaneous frequency and amplitude of the QPO. Comparing these results with those from the Fourier analysis, we find that the broadening of the QPO peak is mainly caused by frequency modulation. Through further analysis, we find that these modulations could share a common physical origin with the broadband noise, and can be well explained by the internal shock model of the jet.

Centroid frequency ratios of simultaneous low-frequency QPOs in black hole low-mass X-ray binaries

ABSTRACT We measure the centroid frequency ratios of simultaneous quasi-periodic oscillations (QPOs) that occur at low frequency (0.1–30 Hz) in a selection of accreting black hole (BH) low-mass X-ray binaries. We use all data in the RXTE archive on GX 339–4, GRO J1655–40, 4U 1630–47, XTE J1550–564, and H 1743–322. We select the power spectra that show at least two simultaneous QPOs, and empirically divide them into four main categories, whose occurrence correlates systematically to X-ray spectral state. In the hard/hard-intermediate state, all sources show sets of QPO peaks with near-harmonic frequency relations, which we measure as precisely as possible using an improved analysis method. We find small but significant offsets from purely harmonic frequency relations that in most cases can be explained by the fit function not describing the QPOs accurately; for some QPO pairs, however, the ‘sub-harmonic’ is at a higher frequency than expected. In the intermediate and ultraluminous states, in all sources we find non-harmonic QPO pairs, some previously reported. We distinguish several different types of non-harmonic QPO pairs that occur across sources. We discuss these findings in the framework of classification schemes and models proposed for black hole low-frequency QPOs. We conclude that the phenomenology of the frequency ratios indicates that in addition to the physical mechanism (possibly precession) explaining the common harmonically related sets of (Type B and C) QPO peaks, at least one additional mechanism is required to explain the occurrence of pairs of QPOs in other states that are not only not harmonically related, but also stand out by the absence of harmonics to either of them.

Investigation of the Outburst Activity of the Black Hole Candidate GRS 1739-278

We have performed a joint spectral and timing analysis of the outburst of GRS 1739-278 in 2014 based on Swift and INTEGRAL data. We show that during this outburst the system exhibited both intermediate states: hard and soft. Peaks of quasi-periodic oscillations (QPOs) in the frequency range 0.1-5 Hz classified as type-C QPOs have been detected from the system. Using Swift/BAT data we show that after the 2014 outburst the system passed to the regime of mini-outburst activity: apart from the three mini-outbursts mentioned in the literature, we have detected four more mini-outbursts with a comparable (~20 mCrab) flux in the hard energy band (15-50 keV). We have investigated the influence of the accretion history on the outburst characteristics: the dependence of the peak flux in the hard energy band in the low/hard state on the time interval between the current and previous peaks has been found (for the outbursts during which the system passed to the high/soft state).

Fractal analysis of light curves for the microquasar GX 339-4

Results of a fractal analysis of the X-ray light curves from accreting black holes in low-mass binary systems are presented for the object GX 339-4 as an example. The fractal dimension of the light curves is shown to be strongly dependent on the presence of quasi-periodic oscillations (QPOs) in the observations. A correlation between the fractal dimension of the light curves and the frequency of the QPO peak has been revealed. A method supplementary to a Fourier analysis that allows the pattern of accretion disk emission as a function of time scales to be investigated is proposed. The results of this analysis can be explained if the accretion disk is separated by the QPO region into two zones with different emission parameters.

A search for periodicities from a ULX in the LINER galaxy NGC 4736

We report our findings on a new quasi-periodic oscillation (QPO) and a long period from the ultraluminous X-ray source (ULX) X-2 in nearby galaxy NGC 4736 based on the Chandra and XMM-Newton archival data. To examine the timing properties, power density spectra of the source have been obtained using Fast Fourier Transform. Also the spectral parameters of the source have been calculated by obtaining and fitting the energy spectra. Power density spectrum of this source reveals a QPO peak at $0.73_{-0.14}^{+0.16}$ mHz with an fractional rms variability of 16% using the Chandra data (in the year 2000-lower state of the source). The XMM-Newton data analysis indicates a peak at $0.53_{-0.35}^{+0.09}$ mHz with a fractional rms variation of 5% (in the year 2006-higher state of the source). These recovered QPOs overlap within errors and may be the same oscillation. In addition, we detect a long periodicity or a QPO in the Chandra data of about $(5.2\pm2.0)\times10^{-5}$ Hz ($\sim$ 5.4 hrs) over 3 $\sigma$ confidence level. If this is a QPO, it is the lowest QPO detected from a ULX. The mass of the compact object in ULX X-2 is estimated using the Eddington luminosity and a disk blackbody model in the range (10$-$80) M_{\sun}.

Quasi-periodic oscillations in XTE J1550−564: the rms–flux relation

Abstract We present an analysis of the short time-scale variations in the properties of the strong (type ‘C’) quasi-periodic oscillation (QPO) observed in XTE J1550−564 during its 1998 outburst. In particular, the QPO shows a correlation between absolute rms amplitude and mean source flux over time-scales shorter than ∼3 ks. A linear rms–flux relation has been observed to be a common property of broad-band noise, but here we report the first detection of rms–flux dependence in a QPO. The gradient of the rms–flux relation is correlated with the QPO peak frequency: from a strong positive correlation when the QPO peak frequency is below ∼4 Hz, through no correlation, to a strong negative correlation when the peak frequency is above 6 Hz. This is the first time a negative short term rms–flux relation has been observed in any component of the power spectrum. Previous work on both the broad-band noise and QPOs in a range of sources have suggested the presence of a filter reducing the amplitude of QPOs with increasing frequency. We attempt to remove the possible effects of this filter and find that the previously negative rms–flux relations above ∼5 Hz become constant.

Discovery of drifting high-frequency quasi-periodic oscillations in global simulations of magnetic boundary layers

We report on the numerical discovery of quasi-periodic oscillations (QPOs) associated with accretion through a non-axisymmetric magnetic boundary layer in the unstable regime, when two ordered equatorial streams form and rotate synchronously at approximately the angular velocity of the inner disk The streams hit the star's surface producing hot spots. Rotation of the spots leads to high-frequency QPOs. We performed a number of simulation runs for different magnetospheric sizes from small to tiny, and observed a definite correlation between the inner disk radius and the QPO frequency: the frequency is higher when the magnetosphere is smaller. In the stable regime a small magnetosphere forms and accretion through the usual funnel streams is observed, and the frequency of the star is expected to dominate the lightcurve. We performed exploratory investigations of the case in which the magnetosphere becomes negligibly small and the disk interacts with the star through an equatorial belt. We also performed investigation of somewhat larger magnetospheres where one or two ordered tongues may dominate over other chaotic tongues. In application to millisecond pulsars we obtain QPO frequencies in the range of 350 Hz to 990 Hz for one spot. The frequency associated with rotation of one spot may dominate if spots are not identical or antipodal. If the spots are similar and antipodal then the frequencies are twice as high. We show that variation of the accretion rate leads to drift of the QPO peak.

Quasi‐Periodic Oscillations in Cen X‐3 and the Long‐Term Intensity Variations

We have investigated the properties of the quasi-periodic oscillation (QPO) features in the accretion-powered X-ray pulsar Cen X-3 over a period of about 4 years using observations carried out with the Proportional Counter Array (PCA) of the Rossi X-ray Timing Explorer (RXTE). The observations cover a wide range of X-ray intensity of the source in excess of the binary intensity modulation. In 11 of 81 pointings with the PCA, we have detected QPOs with rms intensity fluctuation up to 10%. The QPO peak frequency shows clustering around 40 and 90 mHz, with the QPO frequency having no dependence on X-ray intensity. This indicates that either (1) the observed X-ray luminosity of the source is not related to the mass accretion rate or inner radius of the accretion disk, or (2) the QPO generation mechanism in Cen X-3 is different from the beat frequency model or Keplerian frequency model that is believed to operate in most other transient and persistent X-ray pulsars. We have also found that the rms variation in the 40 mHz QPO feature is not dependent on the X-ray energy, indicating that the origin of the QPO is unlikely to be related to disk absorption.

Detection of a 1258-Hz high-amplitude kilohertz quasi-periodic oscillation in the ultracompact X-ray binary 1A 1246–588

We have observed the ultracompact low-mass X-ray binary (LMXB) 1A 1246-588 with the Rossi X-ray Timing Explorer (RXTE). In this paper we report the discovery of a kilohertz quasi-periodic oscillation (QPO) in 1A 1246-588. The kilohertz QPO was only detected when the source was in a soft high-flux state reminiscent of the lower banana branch in atoll sources. Only one kilohertz QPO peak is detected at a relatively high frequency of 1258 +/- 2 Hz and at a single trial significance of more than 7sigma. Kilohertz QPOs with a higher frequency have only been found on two occasions in 4U 0614+09. Furthermore, the frequency is higher than that found for the lower kilohertz QPO in any source, strongly suggesting that the QPO is the upper of the kilohertz QPO pair often found in LMXBs. The full width at half-maximum is 25 +/- 4 Hz, making the coherence the highest found for an upper kilohertz QPO. From a distance estimate of ~6 kpc from a radius expansion burst we derive that 1A 1246-588 is at a persistent flux of ~0.2-0.3 per cent of the Eddington flux, hence 1A 1246-588 is one of the weakest LMXBs for which a kilohertz QPO has been detected. The rms amplitude in the 5-60 keV band is 27 +/- 3 per cent; this is the highest for any kilohertz QPO source so far, in line with the general anticorrelation between source luminosity and rms amplitude of the kilohertz QPO peak identified before. Using the X-ray spectral information we produce a colour-colour diagram. The source behaviour in this diagram provides further evidence for the atoll nature of the source.

Autoregressive Spectral Estimation for Quasi-Periodic Oscillations

Modern methods of spectral estimation based on parametric time-series models are useful tools in power spectral analysis. We apply the autoregressive (AR) model to study quasi-periodic oscillations (QPOs). An empirical formula to estimate the expectation and standard deviation of the noise AR power densities is derived, which can be used to estimate the statistical significance of an apparent QPO peak in an AR spectrum. An iterative adding-noise algorithm in AR spectral analysis is proposed and applied to studying QPOs in the X-ray binary Cir X-1.

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.

Interpreting the High‐Frequency Quasi‐periodic Oscillation Power Spectra of Accreting Black Holes

In the context of a relativistic hot spot model, we investigate different physical mechanisms to explain the behavior of quasi-periodic oscillations (QPOs) from accreting black holes. The locations and amplitudes of the QPO peaks are determined by the calculations presented previously by Schnittman & Bertschinger: the black hole mass and angular momentum give the geodesic coordinate frequencies, while the disk inclination and the hot spot size, shape, and overbrightness give the amplitudes of the different peaks. In this paper additional features are added to the existing model to explain the broadening of the QPO peaks as well as the damping of higher frequency harmonics in the power spectrum. We present a number of analytic results that closely agree with more-detailed numerical calculations. Three primary pieces are developed: the addition of multiple hot spots with random phases, a finite width in the distribution of geodesic orbits, and the scattering of photons from the hot spot through a corona of hot electrons around the black hole. Finally, the complete model is used to fit the observed power spectra of both type A and type B QPOs seen in XTE J1550-564, giving confidence limits on each of the model parameters.

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.

A transient variable 6 Hz QPO from GX 339-4

We report the results of an observation with the Rossi X-ray Timing Explorer of the black hole candidate GX 339-4 during its 2002/2003 outburst. This observation took place during a spectral transition from the hard to the soft state. A strong (6% rms) transient quasi-periodic oscillation (QPO) appears suddenly in the power density spectrum during this observation. The QPO centroid is ∼6 Hz, but it varies significantly between 5 and 7 Hz with a characteristic time scale of ∼10 s, correlated with the 2-30 keV count rate. The appearance of the QPO is related to spectral hardening of the flux, due to a change in the relative contribution of the soft and hard spectral components. We compare this peculiar behavior with results from other systems that show similar low frequency QPO peaks, and discuss the results in terms of possible theoretical models for QPO production.

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.

Kilo-Second Quasi-Periodic Oscillations in the Cataclysmic Variable DW Cancri

Abstract Our photometric monitoring revealed that DW Cnc, which was originally classified as a dwarf nova ($ V=15 \hbox{--} 17.5$), remained at a bright state of $ R_\mathrm{c}=14.68\pm 0.07$ for 61 days. In conjunction with optical spectra lacking a strong He II emission line, we propose that the object is not a dwarf nova, but a non-magnetic nova-like variable. Throughout our monitoring, the object showed strong quasi-periodic oscillations (QPOs) with amplitudes reaching about 0.3 mag. Our period analysis yielded a power spectrum with two peaks of QPOs, whose center periods are $ 37.5\pm 0.1$ and $ 73.4\pm 0.4 \,\mathrm{min}$ and, furthermore, with a significant power in frequencies lower than the QPOs. DW Cnc is a unique cataclysmic variable in which kilo-second QPOs were continuously detected for 61 days. We propose two possible interpretations of DW Cnc: (i) A permanent superhumper below the period minimum of hydrogen-rich cataclysmic variables. (ii) A nova-like variable having an orbital period over 3 hours. In this case, the QPOs may be caused by trapped disk oscillations.

Correlation between break frequency and power-density spectrum slope for the X-ray source Cygnus X-2: RXTE/PCA data

We present RXTE observations of the X-ray source Cyg X-2 during 1996–1999. Its power-density spectra in the 0.1–128-Hz band are fitted by a model that takes into account the power-law spectral behavior at frequencies below and above the break frequency, with an introduction of one or more Lorenz lines to describe the peaks of quasi-periodic oscillations that correspond to the horizontal branch of the Z track. The RXTE observations revealed a positive correlation between the break frequency and the indices of the two parts of the spectrum. The spectrum steepens with increasing break frequency both above and below the break frequency.

The X‐Ray Properties of Low‐Frequency Quasi‐periodic Oscillations from GRS 1915+105 Up to 120 keV

We present a study of the properties of strong 0.8-3.0 Hz quasi-periodic oscillations (QPOs) that occurred during 1997 Rossi X-Ray Timing Explorer (RXTE) observations of the microquasar GRS 1915+105 in the low-hard state. The high count rates allow us to track individual QPO peaks, and we exploit this to develop a QPO folding technique. In contrast to previous QPO studies with RXTE, we emphasize the high-energy QPO properties and report the detection of a QPO in the 60-124 keV energy band. Our technique allows us, for the first time, to measure the phase of the QPO harmonics relative to the fundamental. Variation in this phase difference leads to changes in the shape of the QPO profile with energy and over time. The strength of the QPO fundamental increases up to 19 keV, but the data do not suggest that the strength continues to increase above this energy. In some cases, the QPO amplitudes in the 30-60 and 60-124 keV energy bands are significantly less than in the 13-19 and 19-29 keV energy bands. We also use our technique to measure the phase lag of the QPO fundamental and harmonics. In the case where negative phase lags are detected for the fundamental, positive phase lags are detected for the second harmonic.

The Power Spectral Properties of the Z Source GX 340+0

We present an analysis of ~390 ksec of data of the Z source GX 340+0 taken during 24 observations with the Rossi X-ray Timing Explorer satellite. We report the discovery of a new broad component in the power spectra. The frequency of this component varied between 9 and 14 Hz, and remained close to half that of the horizontal branch quasi-periodic oscillations (HBO). Its rms amplitude was consistent with being constant around ~5%, while its FWHM increased with frequency from 7 to 18 Hz. If this sub-HBO component is the fundamental frequency, then the HBO and its second harmonic are the second and fourth harmonic component, while the third harmonic was not detected. This is similar to what was recently found for the black hole candidate XTE J1550-564. The profiles of both the horizontal- and the normal branch quasi-periodic oscillation peaks were asymmetric when they were strongest. We describe this in terms of a shoulder component at the high frequency side of the quasi-periodic oscillation peak, whose rms amplitudes were approximately constant at ~4% and \~3%, respectively. The peak separation between the twin kHz quasi-periodic oscillations was consistent with being constant at 339+-8 Hz but a trend similar to that seen in, e.g. Sco X-1 could not be excluded. We discuss our results within the framework of the various models which have been proposed for the kHz QPOs and low frequency peaks.

Quasi‐periodic Oscillations Associated with Spectral Branches inRossi X‐Ray Timing ExplorerObservations of Circinus X‐1

We present Rossi X-Ray Timing Explorer (RXTE) All-Sky Monitor observations of the X-ray binary Circinus X-1 that illustrate the variety of intensity profiles associated with the 16.55 day flaring cycle of the source. We also present eight observations of Cir X-1 made with the RXTE Proportional Counter Array over the course of a cycle wherein the average intensity of the flaring state decreased gradually over ~12 days. Fourier power density spectra for these observations show a narrow quasi-periodic oscillation (QPO) peak that shifts in frequency between 6.8 and 32 Hz, as well as a broad QPO peak that remains roughly stationary at ~4 Hz. We identify these as Z-source horizontal and normal branch oscillations (HBOs/NBOs), respectively. Color-color and hardness-intensity diagrams (CDs/HIDs) show curvilinear tracks for each of the observations. The properties of the QPOs and very low frequency noise allow us to identify segments of these tracks with Z-source horizontal, normal, and flaring branches that shift location in the CDs and HIDs over the course of the 16.55 day cycle. These results contradict a previous prediction, based on the hypothesis that Cir X-1 is a high- atoll source, that HBOs should never occur in this source.