kHz Quasi-periodic Oscillations Research Articles

A variable corona for GRS 1915+105

ABSTRACT Most models of the low-frequency quasi-periodic oscillations (QPOs) in low-mass X-ray binaries (LMXBs) explain the dynamical properties of those QPOs. On the other hand, in recent years reverberation models that assume a lamp-post geometry have been successful in explaining the energy-dependent time lags of the broad-band noise component in stellar mass black holes and active galactic nuclei. We have recently shown that Comptonization can explain the spectral-timing properties of the kilo-hertz (kHz) QPOs observed in neutron star (NS) LMXBs. It is therefore worth exploring whether the same family of models would be as successful in explaining the low-frequency QPOs. In this work, we use a Comptonization model to study the frequency dependence of the phase lags of the type-C QPO in the BH LMXB GRS 1915+105. The phase lags of the QPO in GRS 1915+105 make a transition from hard to soft at a QPO frequency of around 1.8 Hz. Our model shows that at high QPO frequencies a large corona of ∼100–150 Rg covers most of the accretion disc and makes it $100{{\ \rm per\ cent}}$ feedback dominated, thus producing soft lags. As the observed QPO frequency decreases, the corona gradually shrinks down to around 3–17 Rg, and at 1.8 Hz feedback on to the disc becomes inefficient leading to hard lags. We discuss how changes in the accretion geometry affect the timing properties of the type-C QPO.

A New Method to Constrain Neutron Star Structure from Quasi-periodic Oscillations

Abstract We develop a new method to measure neutron star (NS) parameters and derive constraints on the equation of state (EoS) of dense matter by fitting the frequencies of simultaneous quasi-periodic oscillation (QPO) modes observed in the X-ray flux of accreting NSs in low-mass X-ray binaries. To this aim, we calculate the fundamental frequencies of geodesic motion around rotating NSs based on an accurate general-relativistic approximation for their external spacetime. Once the fundamental frequencies are related to the observed frequencies through a QPO model, they can be fit to the data to obtain estimates of the three parameters describing the spacetime, namely the NS mass, angular momentum and quadrupole moment. From these parameters we derive information on the NS structure and EoS. We present a proof of principle of our method applied to pairs of kHz QPO frequencies observed from three systems (4U1608-52, 4U0614+09, and 4U1728-34). We identify the kHz QPOs with the azimuthal and the periastron precession frequencies of matter orbiting the NS, and via our Bayesian inference technique we derive constraints on the neutrons stars’ masses and radii. This method is applicable to other geodesic-frequency-based QPO models.

Estimating the masses of three neutron stars by twin kilohertz quasi-periodic oscillations and innermost stable circular orbits: constraining equations of state

ABSTRACT We test the magnetohydrodynamics (MHD) model derived by Shi, Zhang and Li by the like-standard deviations of the twin kilohertz (kHz) quasi-periodic oscillation (QPO) frequencies when the modes of the MHD waves in the MHD model are recalculated. A group of approximate equations derived from the MHD equations in the MHD model are proposed. Consequently, the dependence of the twin kHz QPO frequencies on several neutron star (NS) parameters is determined by the approximate equations. Based on the selection criterion that NS parameters corresponding to the minimum like-standard deviation are the most reasonable parameters, the masses of the three NSs in 4U 0614+09, 4U 1636–53 and 4U 1608–52 are estimated as M < 2.60 M⊙, 2.00 M⊙ < M < 2.31 M⊙ and 2.17 M⊙ < M < 2.62 M⊙, respectively. According to these NS masses, some equations of state for the nuclear matter in compact stars can be ruled out.

A possible origin of kilohertz quasi-periodic oscillations in low-mass X-ray binaries

Abstract A possible origin of kilohertz quasi-periodic oscillations (QPOs) in low-mass X-ray binaries is proposed. Recent numerical magnetohydrodynamic simulations of accretion disks with turbulent magnetic fields of magneto-rotational instability definitely show the presence of two-armed spiral structure in the quasi-steady state of accretion disks. In such deformed disks, two-armed ($m=2$) c-mode ($n=1$) oscillations are excited by wave–wave resonant instability. Among these excited oscillations, the fundamental in the radial direction ($n_{\rm r}=0$) will be the higher kHz QPO of twin QPOs, and the first overtone ($n_{\rm r}=1$) in the radial direction will be the lower kHz QPO of the twin. A possible cause of the twin high-frequency QPOs in black hole X-ray binaries is also discussed in the final section.

On the frequency correlations of low-frequency QPOs with kilohertz QPOs in accreting millisecond X-ray pulsars

ABSTRACT We investigate frequency correlations of low frequency (LF, <80 Hz) and kHz quasi-periodic oscillations (QPOs) using the complete RXTE data sets on six accreting millisecond X-ray pulsars (AMXPs) and compare them to those of non-pulsating neutron star (NS) low-mass X-ray binaries with known spin. For the AMXPs SAX J1808.4−3658 and XTE J1807−294, we find frequency-correlation power-law indices that, surprisingly, are significantly lower than in the non-pulsars, and consistent with the relativistic precession model (RPM) prediction of 2.0 appropriate to test-particle orbital and Lense–Thirring precession frequencies. As previously reported, power-law normalizations are significantly higher in these AMXPs than in the non-pulsating sources, leading to requirements on the NS specific moment of inertia in this model that cannot be satisfied with realistic equations of state. At least two other AMXPs show frequency correlations inconsistent with those of SAX J1808.4−3658 and XTE J1807−294, and possibly similar to those of the non-pulsating sources; for two AMXPs no conclusions could be drawn. We discuss these results in the context of a model that has had success in black hole (BH) systems involving a torus-like hot inner flow precessing due to (prograde) frame dragging, and a scenario in which additional (retrograde) magnetic and classical precession torques not present in BH systems are also considered. We show that a combination of these interpretations may accommodate our results.

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

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

NICER Detects a Soft X-Ray Kilohertz Quasi-periodic Oscillation in 4U 0614+09

Abstract We report on the detection of a kilohertz quasi-periodic oscillation (QPO) with the Neutron Star Interior Composition Explorer (NICER). Analyzing approximately 165 ks of NICER exposure on the X-ray burster 4U 0614+09, we detect multiple instances of a single-peak upper kHz QPO, with centroid frequencies that range from 400 to 750 Hz. We resolve the kHz QPO as a function of energy, and measure, for the first time, the QPO amplitude below 2 keV. We find the fractional amplitude at 1 keV is on the order of 2% rms, and discuss the implications for the QPO emission process in the context of Comptonization models.

A possible explanation of the parallel tracks in kilohertz quasi-periodic oscillations from low-mass-X-ray binaries

We recalculate the modes of the magnetohydrodynamics (MHD) waves in the MHD model (Shi, Zhang & Li 2014) of the kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low mass X-ray binaries (NS-LMXBs), in which the compressed magnetosphere is considered. A method on pointby- point scanning for every parameter of a normal LMXBs is proposed to determine the wave number in a NS-LMXB. The dependence of the twin kHz QPO frequencies on accretion rates ( DOt(M) ) is obtained with the wave number and magnetic field (B?) determined by our method. Based on the MHD model, a new explanation of the parallel tracks, i.e. the slowly varying effective magnetic field leads to the shift of parallel tracks in a source, is presented. In this study, we obtain a simple power-law relation between the kHz QPO frequencies and Dot(M) /B^2 ? in those sources. Finally, we study the dependence of kHz quasi-periodic oscillation frequencies on the spin, mass and radius of a neutron star. We find that the effective magnetic field, the spin, mass and radius of a neutron star lead to the parallel tracks in different sources.

Parallel Tracks as Quasi-steady States for the Magnetic Boundary Layers in Neutron-star Low-mass X-Ray Binaries

Abstract The neutron stars in low-mass X-ray binaries (LMXBs) are usually thought to be weakly magnetized objects accreting matter from their low-mass companions in the form of a disk. Albeit weak compared to those in young neutron-star systems, the neutron-star magnetospheres in LMXBs can play an important role in determining the correlations between spectral and temporal properties. Parallel tracks appearing in the kilohertz (kHz) quasi-periodic oscillation (QPO) frequency versus X-ray flux plane can be used as a tool to study the magnetosphere–disk interaction in neutron-star LMXBs. For dynamically important weak fields, the formation of a non-Keplerian magnetic boundary layer at the innermost disk truncated near the surface of the neutron star is highly likely. Such a boundary region may harbor oscillatory modes of frequencies in the kHz range. We generate parallel tracks using the boundary region model of kHz QPOs. We also present the direct application of our model to the reproduction of the observed parallel tracks of individual sources such as 4U 1608–52, 4U 1636–53, and Aql X-1. We reveal how the radial width of the boundary layer must vary in the long-term flux evolution of each source to regenerate the parallel tracks. The run of the radial width looks similar for different sources and can be fitted by a generic model function describing the average steady behavior of the boundary region over the long term. The parallel tracks then correspond to the possible quasi-steady states the source can occupy around the average trend.

AstroSat/LAXPC Detection of Millisecond Phenomena in 4U 1728-34

Abstract The low-mass X-ray binary 4U 1728-24 was observed with AstroSat/LAXPC on 2016 March 8th. Data from a randomly chosen orbit of over 3 ks was analyzed for detection of rapid intensity variations. We found that the source intensity was nearly steady but, toward the end of the observation, a typical Type-1 burst was detected. Dynamical power spectrum of the data in the 3–20 keV band, reveals the presence of a kHz Quasi-Periodic Oscillation (QPO) for which the frequency drifted from ∼815 Hz at the beginning of the observation to about 850 Hz just before the burst. The QPO is also detected in the 10–20 keV band, which was not obtainable by earlier RXTE observations of this source. Even for such a short observation with a drifting QPO frequency, the time lag between the 5–10 and 10–20 keV bands can be constrained to be less than 100 microseconds. The Type-1 burst that lasted for about 20 s had a typical profile. During the first four seconds, dynamic power spectra reveal a burst oscillation for which the frequency increased from ∼361.5 to ∼363.5 Hz. This is consistent with the earlier results obtained with RXTE/PCA, showing the same spin frequency of the neutron star. The present results demonstrate the capability of the LAXPC instrument for detecting millisecond variability even from short observations. After RXTE ceased operation, LAXPC on AstroSat is the only instrument at present with the capability of detecting kHz QPOs and other kinds of rapid variations from 3 keV to 20 keV and possibly at higher energies as well.

Links between quasi-periodic oscillations and accretion states in neutron star low-mass X-ray binaries

We analysed the Rossi X-ray Timing Explorer (RXTE) data from a sample of bright accreting neutron star (NS) low-mass X-ray binaries (LMXBs). With the aim of studying the quasi-periodic variability as a function of the accretion regime, we carried out a systematic search of the quasi-periodic oscillations (QPOs) in the X-ray time series of these systems, using the integrated fractional variability as a tracker for the accretion states. We found that the three QPO types originally identified in the '80s for the brightest LMXBs, the so-called Z-sources, i.e., horizontal, normal and flaring branch oscillations (HBOs, NBOs and FBOs, respectively), are also identified in the slightly less bright NS LMXBs, the so-called Atoll sources, where we see QPOs with a behaviour consistent with the HBOs and FBOs. We compared the quasi-periodic variability properties of our NS sample with those of a sample of black hole (BH) LMXBs. We confirm the association between HBOs, NBOs and FBOs observed in Z-sources, with the type-C, type-B and type-A QPOs, respectively, observed in BH systems, and we extended the comparison to the HBO-like and FBO-like QPOs seen in Atoll sources. We conclude that the variability properties of BH and weakly-magnetized NS LMXBs show strong similarities, with QPOs only weakly sensitive to the nature of the central compact object in both classes of systems. We find that the historical association between kHz QPOs and high-frequency QPOs, seen around NSs and BHs, respectively, is not obvious when comparing similar accretion states in the two kinds of systems.

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

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

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

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

Epicyclic frequencies for rotating strange quark stars: Importance of stellar oblateness

Kilohertz quasi periodic oscillations (QPOs) can be used as a probe of the inner regions of accretion disks in compact stars and hence also of the properties of the central object. Most models of kHz QPOs involve epicyclic frequencies to explain their origin. We compute the epicyclic frequencies of nearly circular orbits around rotating strange quark stars. The MIT bag model is used to model the equation of state of quark matter, and the uniformly rotating stellar configurations are computed in full general relativity. The vertical epicyclic frequency and the related nodal precession rate of inclined orbits are very sensitive to the oblateness of the rotating star. For rotating stellar models of moderate and high-mass strange stars, the sense of the nodal precession changes at a certain rotation rate. At lower stellar rotation rates, the orbital nodal precession is prograde, as it is in the Kerr metric, while at higher rotation rates, the precession is retrograde, as it is for Maclaurin spheroids. Thus, qualitatively, the orbits around rapidly rotating strange quark stars are affected more strongly by the effects of stellar oblateness than by the effects of general relativity. We show that epicyclic and orbital frequencies calculated numerically for small mass strange stars are in very good agreement with analytical formulas for Maclaurin spheroids.

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

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

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

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

Discovery of twin kHz quasi-periodic oscillations in the low-mass X-ray binary XTE J1701−407

We report the discovery of kHz quasi periodic oscillations (QPOs) in three Rossi X-ray Timing Explorer observations of the low mass X-ray binary (LMXB) XTE J1701-407. In one of the observations we detect a kHz QPO with a characteristic frequency of 1153 +/- 5 Hz, while in the other two observations we detect twin QPOs at characteristic frequencies of 740 +/- 5 Hz, 1112 +/- 17 Hz and 740 +/- 11 Hz, 1098 +/- 5 Hz. All detections happen when XTE J1701-407 was in its high intensity soft state, and their single trial significance are in the 3.1-7.5 sigma range. The frequency difference in the centroid frequencies of the twin kHz QPOs (385 +/- 13 Hz) is one of the largest seen till date. The 3-30 keV fractional rms amplitude of the upper kHz QPO varies between ~18 % and ~30 %. XTE J1701-407, with a persistent luminosity close to 1 % of the Eddington limit, is among the small group of low luminosity kHz QPO sources and has the highest rms for the upper kHz QPO detected in any source. The X-ray spectral and variability characteristics of this source indicate its atoll source nature.

SOFT LAGS IN NEUTRON STAR kHz QUASI-PERIODIC OSCILLATIONS: EVIDENCE FOR REVERBERATION?

High frequency soft reverberation lags have now been detected from stellar mass and super massive black holes. Their interpretation involves reflection of a hard source of photons onto an accretion disk, producing a delayed reflected emission, with a time lag consistent with the light travel time between the irradiating source and the disk. Independently of the location of the clock, the kHz Quasi-Periodic Oscillation (QPO) emission is thought to arise from the neutron star boundary layer. Here, we search for the signature of reverberation of the kHz QPO emission, by measuring the soft lags and the lag energy spectrum of the lower kHz QPOs from 4U1608-52. Soft lags, ranging from ~15 to ~40 microseconds, between the 3-8 keV and 8-30 keV modulated emissions are detected between 565 and 890 Hz. The soft lags are not constant with frequency and show a smooth decrease between 680 Hz and 890 Hz. The broad band X-ray spectrum is modeled as the sum of a disk and a thermal comptonized component, plus a broad iron line, expected from reflection. The spectral parameters follow a smooth relationship with the QPO frequency, in particular the fitted inner disk radius decreases steadily with frequency. Both the bump around the iron line in the lag energy spectrum, and the consistency between the lag changes and the inferred changes of the inner disk radius, from either spectral fitting or the QPO frequency, suggest that the soft lags may indeed involve reverberation of the hard pulsating QPO source on the disk.

LOW-FREQUENCY QUASI-PERIODIC OSCILLATION FROM THE 11 Hz ACCRETING PULSAR IN TERZAN 5: NOT FRAME DRAGGING

We report on 6 RXTE observations taken during the 2010 outburst of the 11 Hz accreting pulsar IGR J17480-2446 located in the globular cluster Terzan 5. During these observations we find power spectra which resemble those seen in Z-type high-luminosity neutron star low-mass X-ray binaries, with a quasi-periodic oscillation (QPO) in the 35-50 Hz range simultaneous with a kHz QPO and broad band noise. Using well known frequency-frequency correlations, we identify the 35-50 Hz QPOs as the horizontal branch oscillations (HBO), which were previously suggested to be due to Lense-Thirring precession. As IGR J17480-2446 spins more than an order of magnitude more slowly than any of the other neutron stars where these QPOs were found, this QPO can not be explained by frame dragging. By extension, this casts doubt on the Lense-Thirring precession model for other low-frequency QPOs in neutron-star and perhaps even black-hole systems.

High-frequency quasi-periodic oscillations in black hole binaries

We present the results of the analysis of a large database of X-ray observations of 22 galactic black-hole transients with the Rossi X-Ray timing explorer throughout its operative life for a total exposure time of ~12 Ms. We excluded persistent systems and the peculiar source GRS 1915+105, as well as the most recently discovered sources. The semi-automatic homogeneous analysis was aimed at the detection of high-frequency (100-1000 Hz) quasi-periodic oscillations (QPO), of which several cases were previously reported in the literature. After taking into account the number of independent trials, we obtained 11 detections from two sources only: XTE J1550-564 and GRO J1655-40. For the former, the detected frequencies are clustered around 180 Hz and 280 Hz, as previously found. For the latter, the previously-reported dichotomy 300-450 Hz is found to be less sharp. We discuss our results in comparison with kHz QPO in neutron-star X-ray binaries and the prospects for future timing X-ray missions.