Pairs Of Quasi-periodic Oscillations Research Articles

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.

Mass of the active galactic nucleus black hole XMMUJ134736.6+173403

A recent study of the X-ray source XMMUJ134736.6+173403 has revealed a strong quasi-periodic modulation in the X-ray flux. The observation of two quasiperiodic oscillations (QPOs) that occur on a daily timescale and exhibit a 3:1 frequency ratio strongly supports the evidence for the presence of an active galactic nucleus black hole (AGN BH). Assuming an orbital origin of QPOs, we calculated the upper and lower limit on AGN BH mass M and found M ≈ 107 − 109 M⊙. When we compare this to mass estimates of other sources, XMMUJ134736.6+173403 appears to be the most massive source with commensurable QPO frequencies, and its mass represents the current observational upper limit on AGN BH mass based on QPO observations. We note that it will be crucial for the falsification of particular resonance models of QPOs whether only a single QPO with a frequency that completes the harmonic sequence 3 : 2 : 1 is found in this source, or if a new different pair of QPOs with frequencies in the 3 : 2 ratio is found. The former case would agree with the prediction of the 3 : 2 epicyclic resonance model and BH mass M ≈ (5a2 + 8a + 8)×107 M⊙, where a is a dimensionless BH spin.

ON THE HIGH-FREQUENCY QUASI-PERIODIC OSCILLATIONS FROM BLACK HOLES

We apply the global mode analysis, which has been recently developed for the modeling of kHz quasi-periodic oscillations (QPOs) from neutron stars, to the inner region of an accretion disk around a rotating black hole. Within a pseudo-Newtonian approach that keeps the ratio of the radial epicyclic frequency $\kappa$ to the orbital frequency $\Omega$ the same as the corresponding ratio for a Kerr black hole we determine the innermost disk region where the hydrodynamic modes grow in amplitude. We find that the radiation flux emerging from the inner disk has the highest values within the same region. Using the flux weighted averages of the frequency bands over this region we identify the growing modes with highest frequency branches $\Omega +\kappa $ and $\Omega $ to be the plausible candidates for the high-frequency QPO pairs observed in black hole systems. The observed frequency ratio around 1.5 can therefore be understood naturally in terms of the global free oscillations in the innermost region of a viscous accretion disk around a black hole without invoking a particular resonance to produce black hole QPOs. Although the frequency ratio $<\Omega +\kappa>/<\Omega>$ is found to be not sensitive to the black hole's spin which is good for explaining the high-frequency QPOs it may work as a limited diagnostic of the spin parameter to distinguish black holes with very large spin from the slowly rotating ones. Within our model we estimate the frequency ratio of a high-frequency QPO pair to be greater than 1.5 if the black hole is a slow rotator. For fast rotating black holes, we expect the same ratio to be less than 1.5.

TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. III. QUASI-PERIODIC VARIABILITY

According to the no-hair theorem, astrophysical black holes are uniquely described by their masses and spins. An observational test of the no-hair theorem can be performed by measuring at least three different multipole moments of the spacetime of a black hole and verifying whether their values are consistent with the unique combinations of the Kerr solution. In this paper, we study quasi-periodic variability observed in the emission from black holes across the electromagnetic spectrum as a test of the no-hair theorem. We derive expressions for the Keplerian and epicyclic frequencies in a quasi-Kerr spacetime, in which the quadrupole moment is a free parameter in addition to mass and spin. We show that, for moderate spins, the Keplerian frequency is practically independent of small deviations of the quadrupole moment from the Kerr value, while the epicyclic frequencies exhibit significant variations. We apply this framework to quasi-periodic oscillations in black-hole X-ray binaries in two different scenarios. In the case that a pair of quasi-periodic oscillations can be identified as the fundamental g- and c-modes in the accretion disk, we show that the no-hair theorem can be tested in conjunction with an independent mass measurement. If, on the other hand, the pairs of oscillations are identified with non-parametric resonance of dynamical frequencies in the accretion disk, then testing the no-hair theorem also requires an independent measurement of the black-hole spin. In addition, we argue that VLBI observations of Sgr A* may test the no-hair theorem through a combination of imaging observations and the detection of quasi-periodic variability.

Correlation between 3 : 2 QPO Pairs and Jets in Black Hole X‐Ray Binaries

We argue, following our earlier works (the CEBZMC model), that the phenomenon of twin peak high frequency quasi-periodic oscillations (QPOs) observed in black hole X-ray binaries is caused by magnetic coupling (MC) between accretion disk and black hole (BH). Due to MC, two bright spots occur at two separate radial locations r_{in} and r_{out} at the disk surface, energized by a kind of the Blandford-Znajek mechanism (BZ). We assume, following the Kluzniak-Abramowicz QPO resonance model, that Keplerian frequencies at these two locations are in the 3:2 ratio. With this assumption, we estimate the BH spins in several sources, including GRO J1655-40, GRS 1915+105, XTE J1550-564, H1743-322 and Sgr A*. We give an interpretation of the jet line in the hardness-intensity plane discussing the parameter space consisting of the BH spin and the power-law index for the variation of the large-scale magnetic field in the disk. Furthermore, we propose a new scenario for the spectral state transitions in BH X-ray binaries based on fluctuation in densities of accreting plasma from a companion star.

2:3 Twin Quasi-Periodic Oscillations in Magnetohydrodynamic Accretion Flows

We have studied the radial and vertical oscillations in three-dimensional magnetohydrodynamic (MHD) accretion flows around black holes. General-relativistic effects were taken into account by using a pseudo-Newtonian potential. We found that the structure of MHD flows is changed at $3.8 \,r_{\mathrm{s}} \leq r \leq 6.3 \,r_{\mathrm{s}}$, and that two pairs of quasi-periodic oscillations (twin QPOs) are excited in that region. The time evolution of the power spectrum density (PSD) indicates that these twin QPOs are most likely to be produced by a resonance between the Keplerian frequency, $\nu_\mathrm{K}$, and the epicyclic frequency, $\nu_{\kappa}$. The PSD shows that the lower peak frequency, $\nu_\mathrm{l}$, corresponds to, $\nu_\mathrm{K}$, while the upper peak frequency, $\nu_\mathrm{u}$, corresponds to $\nu_\mathrm{K} + \nu_{\kappa}$. The ratio of two peak frequencies is close to $2:3$. The results provide the first direct evidence for the excitation of resonant disk oscillation in MHD accretion flows.

“Stable” Quasi-periodic Oscillations and Black Hole Properties from Diskoseismology

We compare our calculations of the frequencies of the fundamental g-, c-, and p-modes of relativistic thin accretion disks with recent observations of high-frequency quasi-periodic oscillations (QPOs) in X-ray binaries with black hole candidates. These classes of modes encompass all adiabatic perturbations of such disks. The frequencies of these modes depend mainly on the mass and angular momentum of the black hole; their weak dependence on disk luminosity is also explicitly indicated. Identifying the recently discovered, relatively stable QPO pairs with the fundamental g- and c-modes provides a determination of the mass and angular momentum of the black hole. For GRO J1655-40, M = 5.9 ± 1.0 M☉ and J = (0.917 ± 0.024)GM2/c, in agreement with spectroscopic mass determinations. For GRS 1915+105, M = 42.4 ± 7.0 M☉ and J = (0.926 ± 0.020)GM2/c or (less favored) M = 18.2 ± 3.1 M☉ and J = (0.701 ± 0.043)GM2/c. We briefly address the issues of the amplitude, frequency width, and energy dependence of these QPOs.

Recent Observations of X-ray Emission from Galactic Binary Neutron Stars

Recent measurements of young, accreting binary neutron stars are determining more precise magnetic field and accretion parameters. A low magnetic field, accreting, millisecond pulsar has finally been found in a binary burster. At least 20 low-mass binaries have exhibited high frequency oscillations, 300–1200 hertz. The majority have, for some range of luminosity, the pair of quasiperiodic oscillations that have never been seen in a black hole candidate. Recent evidence from burst oscillations strengthens the case that the difference frequency of this pair is close to the spin frequency of the neutron star. These oscillations are correlated with the spectra, luminosity, and low frequency oscillations. Quasiperiodic oscillations are also seen sometimes in strong magnetic field pulsars, where their origin can be closely examined.

The Beat-Frequency Interpretation of Kilohertz Quasi-periodic Oscillations in Neutron Star Low-Mass X-Ray Binaries

Pairs of quasi-periodic oscillations (QPOs) at kilohertz frequencies are a common phenomenon in several neutron-star low-mass X-ray binaries. The frequency separation of the QPO peaks in the pair appears to be constant in many sources and directly related to the neutron star spin frequency. However, in Sco X-1 and possibly in 4U 1608-52, the frequency separation between the QPO peaks decreases with increasing inferred mass accretion rate. We show that the currently available Rossi X-Ray Timing Explorer data are consistent with the hypothesis that the peak separations in all sources vary by amounts similar to the variation in Sco X-1. We discuss the implications for models of the kilohertz QPOs.