Models Of Quasi-periodic Oscillations Research Articles

X-RAY BURSTS FROM THE TERZAN 5 TRANSIENT IGR J17480-2446: NUCLEAR RATHER THAN GRAVITATIONAL

The 2010 outburst of the transient neutron star low-mass X-ray binary IGR J17480-2446 has exhibited a series of unique X-ray bursts, as well as millihertz (mHz) quasi-periodic oscillations (QPOs) related to these bursts. It has been recently proposed that these are type-II bursts, powered by the gravitational energy. This implies that the current nuclear-burning based model of mHz QPOs is not correct, and this timing feature cannot be used as a tool to measure the neutron star parameters. We report the analysis of the Rossi X-ray Timing Explorer data of IGR J17480-2446 to show that the burst properties of this source are quite different from the properties of the type-II bursts observed from the rapid burster and GRO J1744-28. For example, the inferred ratio (~ 50-90) of the non-burst fluence to burst fluence is consistent with the thermonuclear origin of IGR J17480-2446 bursts, and is significantly different from this ratio (< 4) for type-II bursts. Our results suggest that the bursts and the mHz QPOs from IGR J17480-2446 are powered by the nuclear energy.

Magneto-elastic oscillations and the damping of crustal shear modes in magnetars

Abstract In a realistic model of magneto-elastic oscillations in magnetars, we find that crustal shear oscillations, often invoked as an explanation of quasi-periodic oscillations (QPOs) seen after giant flares in soft gamma-ray repeaters (SGRs), are damped by resonant absorption on time-scales of at most 0.2 s, for a lower limit on the dipole magnetic field strength of 5 × 1013 G. At higher magnetic field strengths (typical in magnetars) the damping time-scale is even shorter, as anticipated by earlier toy models. We have investigated a range of equations of state and masses and if magnetars are dominated by a dipole magnetic field, our findings exclude torsional shear oscillations of the crust from explaining the observed low-frequency QPOs. In contrast, we find that the Alfvén QPO model is a viable explanation of observed QPOs, if the dipole magnetic field strength exceeds a minimum strength of about several times 1014–1015 G. Then, Alfvén QPOs are no longer confined to the fluid core, but completely dominate in the crust region and have a maximum amplitude at the surface of the star.

The model constraints from the observed trends for the quasi-periodic oscillation in RE J1034+396

We analyze the time variability of the X-ray emission of RE J1034+396 -- an active galactic nucleus with the first firm detection of a quasi-periodic oscillations (QPO). Based on the results of a wavelet analysis, we find a drift in the QPO central frequency. The change in the QPO frequency correlates with the change in the X-ray flux with a short time delay. The data specifically suggest a linear dependence between the QPO period and the flux, and this gives important constraints on the QPO models. In particular, it excludes explanation in terms of the orbiting hot spot model close to a black hole. Linear structures such as shocks, spiral waves, or very distant flares are favored.

ON MASS CONSTRAINTS IMPLIED BY THE RELATIVISTIC PRECESSION MODEL OF TWIN-PEAK QUASI-PERIODIC OSCILLATIONS IN CIRCINUS X-1

Boutloukos et al. (2006) discovered twin-peak quasi-periodic oscillations (QPOs) in 11 observations of the peculiar Z-source Circinus X-1. Among several other conjunctions the authors briefly discussed the related estimate of the compact object mass following from the geodesic relativistic precession model for kHz QPOs. Neglecting the neutron star rotation they reported the inferred mass M_0 = 2.2 +/- 0.3 M_\sun. We present a more detailed analysis of the estimate which involves the frame-dragging effects associated with rotating spacetimes. For a free mass we find acceptable fits of the model to data for (any) small dimensionless compact object angular momentum j=cJ/GM^2. Moreover, quality of the fit tends to increase very gently with rising j. Good fits are reached when M ~ M_0[1+0.55(j+j^2)]. It is therefore impossible to estimate the mass without the independent knowledge of the angular momentum and vice versa. Considering j up to 0.3 the range of the feasible values of mass extends up to 3M_\sun. We suggest that similar increase of estimated mass due to rotational effects can be relevant for several other sources.

THE ENERGY DEPENDENCE OF THE CENTROID FREQUENCY AND PHASE LAG OF THE QUASI-PERIODIC OSCILLATIONS IN GRS 1915+105

We present a study of the centroid frequencies and phase lags of the quasi-periodic oscillations (QPOs) as functions of photon energy for GRS 1915+105. It is found that the centroid frequencies of the 0.5-10 Hz QPOs and their phase lags are both energy dependent, and there exists an anti-correlation between the QPO frequency and phase lag. These new results challenge the popular QPO models, because none of them can fully explain the observed properties. We suggest that the observed QPO phase lags are partially due to the variation of the QPO frequency with energy, especially for those with frequency higher than 3.5 Hz.

On the distribution of frequency ratios of kHz quasi-periodic oscillations

The width (W), root mean squared amplitude (Rs) of lower and upper kHz quasi-periodic oscillations (QPOs) from accreting neutron stars vary with frequency. Similarly, the QPO frequency varies with the source count rate (S). Hence, the significance of a QPO, scaling as S x Rs^2/W^(1/2) will also depend on frequency. In addition, the significance also scales up with the square root of the integration time of the Fourier power density spectrum (T). Consequently, depending on the way data are considered, kHz QPOs may be detected only over a limited range of their frequency spans or detected predominantly at some frequencies, leading potentially to biases in the observed distributions of frequencies or frequency ratios. Although subject of much controversy, an observed clustering of QPO frequency ratios around 3/2 in Sco X-1, also seen in other sources, has been previously used as an argument supporting resonance based models of neutron star QPOs. In this paper, we measure how the statistical significance of both kHz QPOs vary with frequency for three prototype neutron star kHz QPO sources, namely 4U1636-536, 4U0614+091 and Sco X-1. As the significance of QPO detection depends on frequency, we show that in sensitivity-limited observations (as in the case of the RXTE/PCA), a simultaneous detection of both the lower and upper kHz QPOs can only be achieved over limited frequency ranges. As a result, even a uniform distribution of QPO frequencies will lead to peaks (in particular around 3/2) in the histogram of frequency ratios. This implies that the observed clustering of ratios does not provide any evidence for intrinsically preferred frequency ratios, thus weakening the case for a resonance mechanism at the origin of neutron star kHz QPOs.

Low-frequency quasi-periodic oscillations spectra and Lense–Thirring precession

Abstract We show that the low-frequency quasi-periodic oscillations (QPOs) seen in the power-density spectra of black hole binaries (and neutron stars) can be explained by the Lense–Thirring precession. This has been proposed many times in the past, and simple, single-radius models can qualitatively match the observed increase in QPO frequency by decreasing a characteristic radius, as predicted by the truncated disc models. However, this also predicts that the frequency is strongly dependent on spin, and gives a maximum frequency at the last stable orbit which is generally much higher than the remarkably constant maximum frequency at ∼10 Hz observed in all black hole binaries. The key aspect of our model, which makes it match these observations, is the precession of a radially extended region of the hot inner flow. The outer radius is set by the truncation radius of the disc as above, but the inner radius lies well outside of the last stable orbit at the point where numerical simulations show that the density drops off sharply for a misaligned flow. Physically motivated analytic estimates for this inner radius show that it increases with a*, decreasing the expected frequency in a way which almost completely cancels the expected increase with spin, and ties the maximum predicted frequency to around 10 Hz for all a*. This is the first QPO model which explains both frequencies and spectrum in the context of a well-established geometry for the accretion flow.

A Magnetic Flux Tube Oscillation Model for QPOs in SGR Giant Flares

Giant flares from soft gamma-ray repeaters (SGRs) are one of the most violent phenomena in neutron stars. Quasi-periodic oscillations (QPOs) with frequencies ranging from 18 to 1840 Hz have been discovered in the tails of giant flares from two SGRs, and were ascribed to be seismic vibrations or torsional oscillations of magnetars. Here we propose an alternative explanation for the QPOs in terms of standing sausage mode oscillations of flux tubes in the magnetar coronae. We show that most of the QPOs observed in SGR giant flares could be well accounted for except for those with very high frequencies (625 and 1840 Hz).

Shock oscillation model for quasi-periodic oscillations in stellar mass and supermassive black holes

We numerically examine centrifugally supported shock waves in 2D rotating accretion flows around a stellar mass (10 M⊙) and a supermassive (10 6 M⊙) black holes over a wide range of input accretion rates of 10 7 ≥) M/ME≥ 10 -4 . The resultant 2D shocks are unstable with time and the luminosities show quasi-periodic oscillations (QPOs) with modulations of a factor of 2-3 and with periods of a tenth of a second to several hours, depending on the black hole masses. The shock oscillation model may explain the intermediate frequency QPOs with 1-10 Hz observed in the stellar mass black hole candidates and also suggest the existence of QPOs with the period of hours in active galactic nuclei. When the accretion rate M is low, the luminosity increases in proportion to the accretion rate. However, when M greatly exceeds the Eddington critical rate M E , the luminosity is insensitive to the accretion rate and is kept constantly around ∼3L E· On the other hand, the mass-outflow rate M loss increases in proportion to M and it amounts to about a few per cent of the input mass-flow rate.

Spin of Stellar-Mass Black Holes Estimated by a Model of Quasi-Periodic Oscillations

Abstract We have proposed in previous papers that the high-frequency pair of quasi-periodic oscillations observed in black-hole binaries with a frequency ratio of $3:2$ are inertial-acoustic oscillations (nearly horizontal oscillations with no node in the vertical direction) or g-mode oscillations, which are resonantly excited on warped relativistic disks. The resonance occurs through horizontal motions. In this model, the dimensionless spin parameter, $a_*$, of the central sources can be estimated when their masses are known from other observations. This estimate is done for three sources (GRO J1665$-$40, XTE J1550$-$564, GRS 1915$+$105). For all of them, we have $a_*\leq 0.45$.

QPOs in Microquasars: the Spin Problem

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

Quasi-periodic Oscillations from Magnetorotational Turbulence

Quasi-periodic oscillations (QPOs) in the X-ray lightcurves of accreting neutron star and black hole binaries have been widely interpreted as being due to standing wave modes in accretion disks. These disks are thought to be highly turbulent due to the magnetorotational instability (MRI). We study wave excitation by MRI turbulence in the shearing box geometry. We demonstrate that axisymmetric sound waves and radial epicyclic motions driven by MRI turbulence give rise to narrow, distinct peaks in the temporal power spectrum. Inertial waves, on the other hand, do not give rise to distinct peaks which rise significantly above the continuum noise spectrum set by MRI turbulence, even when the fluid motions are projected onto the eigenfunctions of the modes. This is a serious problem for QPO models based on inertial waves.

Twin-peak quasiperiodic oscillations as an internal resonance

Two inter-related peaks occur in high-frequency power spectra of X-ray lightcurves of several black-hole candidates. We further explore the idea that a non-linear resonance mechanism, operating in strong-gravity regime, is responsible for these quasi-periodic oscillations (QPOs). By extending the multiple-scales analysis of Rebusco, we construct two-dimensional phase-space sections, which enable us to identify different topologies governing the system and to follow evolutionary tracks of the twin peaks. This suggests that the original (Abramowicz and Kluzniak) parametric-resonance scheme can be viewed as an ingenuous account of the QPOs model with an internal resonance. We show an example of internal resonance in a system with up to two critical points, and we describe a general technique that permits to treat other cases in a systematical manner. A separatrix divides the phase-space sections into regions of different topology: inside the libration region the evolutionary tracks bring the observed twin-peak frequencies to an exact rational ratio, whereas in the circulation region the observed frequencies remain off resonance. Our scheme predicts the power should cyclically be exchanged between the two oscillations. Likewise the high-frequency QPOs in neutron-star binaries, also in black-hole sources one expects, as a general property of the non-linear model, that slight detuning pushes the twin-peak frequencies out of sharp resonance.

Radial Epicyclic Frequency in a Perfect Fluid Disk Around Compact Objects

The widely used expression of the radial epicyclic frequency, which is important in the relativistic precession model to interpret the observed quasi-periodic oscillation(QPO) in X-ray binaries, is derived by considering the perturbation of a circular-orbiting test particle around a compact object. However, this is not consistent with the real configuration of an accretion disk. Here we obtain the expressions of the radial epicyclic frequency of a perfect fluid disk in both Schwarzschild and Kerr metrics and find that they are different from the previous expressions if the pressure of fluid is considered. The effects of these new expressions on the theoretical QPO models are discussed.

A Resonance Model of Quasi-Periodic Oscillations of Low-Mass X-Ray Binaries

Abstract We try to understand the quasi-periodic oscillations (QPOs) in low-mass neutron-star and black-hole X-ray binaries by a resonance model in warped disks with precession. Our main concern is high-frequency QPOs, hectohertz QPOs, and horizontal-branch QPOs in the z sources and the atoll sources, and the corresponding QPOs in black-hole X-ray binaries. Our resonance model can qualitatively, but systematically, explain these QPOs by regarding hectohertz QPOs as a precession of warp.

Quasi-periodic oscillations: Resonant shear Alfvén waves in neutron star magnetospheres

We propose a new model for quasi-periodic oscillations (QPOs) based on oscillating magnetohydrodynamic modes in neutron star magnetospheres. We argue that the interaction of the accretion disk with the magnetosphere can excite resonant shear Alfvén waves in a region of enhanced density gradients, the region where accretion material flows along the magnetic field lines in the magnetosphere (see Fig.1). We demonstrate that depending on the distance of this region from the star and the magnetic field strength, the frequency of the field line resonance can range from several Hz (a weaker field, farther from the star), to approximately kHz frequencies (a stronger field, ~ stellar radii from the star). We show that such oscillations are able to significantly modulate inflow of matter from the high density region toward the star's surface and possibly produce the observed X-ray spectrum. In addition, we show that the observed 2:3 frequency ratio of QPOs is a natural result of our model.

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

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

On the high coherence of kHz quasi-periodic oscillations

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

Evidence for a Link between Fe Kα Emission-Line Strength and Quasi-periodic Oscillation Phase in a Black Hole

In X-ray binaries, the frequencies revealed in X-ray quasi-periodic oscillations (QPOs) are often interpreted as characteristic frequencies in the inner accretion disk, although the exact oscillation mechanism is unknown at present. Broadened Fe Kα lines are also excellent diagnostics of the inner accretion flow, if their broadening is indeed due to inner disk reflection. Here we present two cases where the flux and equivalent width of the Fe Kα emission lines in spectra of the Galactic black hole GRS 1915+105 vary with the phase of strong 1 and 2 Hz QPOs in the X-ray flux. These results provide strong evidence that both QPOs and the Fe Kα lines originate in the inner disk. If the 1 Hz QPO is only a Keplerian orbital frequency, the QPO comes from a distance of RSchw from the black hole; the 2 Hz QPO implies a radius of RSchw. At these radii, relativistic shaping of a disk line is inevitable. Moreover, the link holds in radio-bright and radio-faint phases, signaling that in systems like GRS 1915+105, the Fe Kα line is a disk line and not a jet line as per SS 433. A particularly interesting possibility is that a stable warp in the inner disk, e.g., due to Lense-Thirring precession, may produce the observed QPOs and line modulations. More broadly, the Fe K-QPO link provides an unprecedented mechanism for revealing the inner accretion flow and relativistic regime in accreting systems, in that it gives two measures of radius: for a given disk QPO model, the frequency translates into a specific radius, and relativistic line models yield radii directly.

X‐Ray Observations of XTE J1550−564 during the Decay of the 2000 Outburst. II. Timing

We investigate the timing behavior of XTE J1550-564 with the Rossi X-Ray Timing Explorer as the source made a transition to the hard state during the decay of the 2000 outburst. We detect a high-frequency quasi-periodic oscillation (QPO) at 65 Hz in one observation with a fractional rms amplitude of 4.9%. This is the first time that a high-frequency QPO has been detected in a transition to the hard state during outburst decay. We also observe low-frequency QPOs in the 0.36-4.1 Hz range and rich aperiodic variability. The changes in the temporal properties during the decay are very similar to the state transitions observed for other sources. We find a correlation between the low-frequency QPO and the break frequency in the continuum power spectra. We investigate the energy dependence of rms amplitudes of the QPOs. We compare these timing properties with those previously observed for XTE J1550-564 and other Galactic black hole candidates and discuss the implications for QPO models and black hole accretion.