High Frequency Quasi-periodic Oscillations Research Articles

Epicyclic Oscillations and Circular Orbits in Hairy Black Holes: Testing by High-Frequency Quasi-Periodic Oscillations Observed in Microquasars

Recently, Ovalle and his collaborators proposed an exact solution to Einstein’s equations. In this study, we investigate the main characteristics of the spherically symmetric spacetime determined by the hair parameter l, with a specific focus on circular orbits, particularly the innermost circular orbits (ISCOs), and the epicyclic oscillatory motion along these orbits. To assess the validity of this novel geometry, we employ the frequencies derived from the epicyclic resonance model of high-frequency quasi-periodic oscillations (HF QPOs) observed in microquasars, as well as the ISCOs. By analyzing the observed data from three selected microquasars, we establish constraints on the parameter l. Our findings suggest that this geometric framework can encompass the phenomena associated with HF QPOs and offer a partial explanation for the observed shift in the ISCOs, which is commonly attributed to the rotation of the black hole.

Truncated, tilted discs as a possible source of Quasi-Periodic Oscillations

ABSTRACT Many accreting black holes and neutron stars exhibit rapid variability in their X-ray light curves, termed quasi-periodic oscillations (QPOs). The most commonly observed type is the low-frequency (≲10 Hz), type-C QPO, while only a handful of sources exhibit high-frequency QPOs (≳60 Hz). The leading model for the type-C QPO is Lense-Thirring precession of a hot, geometrically thick accretion flow that is misaligned with the black hole’s spin axis. However, existing versions of this model have not taken into account the effects of a surrounding, geometrically thin disc on the precessing, inner, geometrically thick flow. In Bollimpalli et. al 2023, using a set of GRMHD simulations of tilted, truncated accretion discs, we confirmed that the outer thin disc slows down the precession rate of the precessing torus, which has direct observational implications for type-C QPOs. In this paper, we provide a detailed analysis of those simulations and compare them with an aligned truncated disc simulation. We find that the misalignment of the disc excites additional variability in the inner hot flow, which is absent in the comparable aligned-disc simulations. This suggests that the misalignment may be a crucial requirement for producing QPOs. We attribute this variability to global vertical oscillations of the inner torus at epicyclic frequencies corresponding to the transition radius. This explanation is consistent with current observations of higher frequency QPOs in black hole X-ray binary systems.

First detection of soft-lag in GRS 1915 + 105 at HFQPO using AstroSat observations

ABSTRACT The Galactic black hole GRS 1915 + 105 exhibits generic high-frequency quasi-periodic oscillations (HFQPOs) at ∼ 67 Hz only during the radio-quiet ‘softer’ variability classes. We present the time-lag properties associated with HFQPOs in the wide energy band (3–60 keV) using all AstroSat observations. For the first time, we detect soft-lag of 6–25 keV band w.r.t. 3–6 keV band for all ‘softer’ variability classes (δ, ω, κ, and γ). Moreover, our findings reveal that soft-lag increases gradually with the energy of the photons. These features are entirely opposite to the previous report of hard-lag obtained with the RXTE observations. The energy-dependent time-lag study exhibits a maximum soft-lag of ∼ 3 and ∼ 2.5 ms for the δ and ω classes, respectively, whereas the κ and γ classes both exhibit a maximum soft-lag of ∼2.1 ms. We find a coherent lag-energy correlation for all four variability classes, where the amplitude of soft-lag increases with energy and becomes maximum at ∼18 keV. We interpret this observed soft-lag as the reflection of hard photons in the ‘cooler’ accretion disc. A generic lag-rms correlation implies that the soft-lag increases with the rms amplitude of the HFQPO. The wideband (0.7–50 keV) spectral study suggests a high value of the optical depth (τ ∼ 6.90–12.55) of the Comptonized medium and the magnitude of the soft-lag increases linearly with the increase in optical depth (τ). We explain the observed time-lag features at the HFQPOs in the context of a possible accretion disc scenario.

Testing of Kerr black hole with quintessential dark energy through observational data by using quasi-periodic oscillations

A viable method to examine the wide range of intriguing phenomena that occur in a strong gravity regime is the study of the quasi-periodic oscillations (QPOs) of X-ray flux seen in stellar-mass black hole (BH) binaries. We take into account three well-known microquasars GRO 1655-40, XTE 1550-564, and GRS 1915+105 with their observational data and investigate the QPOs. We successfully fit the observational data of the high frequency (HF) QPO models, i.e., epicyclic resonance (ER) and its variants, relativistic precession (RP) and its variants, tidal disruption (TD), as well as warped disk (WD) models are explore under the effect of the involved parameter in the Kerr BH with quintessential dark energy (DE). We demonstrate that the conventional geodesic models of QPOs can explain the observationally established data from the microquasar models. Conclusively, it is found that our obtained findings are physically viable and well-matched with the observational data of GRO 1655-40, XTE 1550-564, and GRS 1915+105 microquasar models.

Disc tearing leads to low and high frequency quasi-periodic oscillations in a GRMHD simulation of a thin accretion disc

ABSTRACT Black hole X-ray binaries (BHXRBs) display a wide range of variability phenomena, from long duration spectral state changes to short-term broad-band variability and quasi-periodic oscillations (QPOs). A particularly puzzling aspect is the production of QPOs, which – if properly understood – could be used as a powerful diagnostic tool of black hole accretion and evolution. In this work, we analyse a high-resolution 3D general relativistic magnetohydrodynamic simulation of a geometrically thin accretion disc, which is tilted by 65° with respect to the black hole spin axis. We find that the Lense–Thirring torque from the rapidly spinning 10 M⊙ black hole causes several sub-discs to tear off within ∼10–20 gravitational radii. Tearing occurs in cycles on time-scales of seconds. During each tearing cycle, the inner sub-disc precesses for 1–5 periods before it falls into the black hole. We find a precession frequency of $\sim 3\rm Hz$, consistent with observed low-frequency QPOs. In addition, we find a high frequency QPO (HFQPO) with centroid frequency of ∼55 Hz in the power spectra of the mass-weighted radius of the inner disc and the radial mass flux. This signal is caused by radial epicyclic oscillations of a dense ring of gas at the tearing radius, which suggests a corresponding modulation of the X-ray light curve and may thus explain some of the observed HFQPOs.

Testing black holes in non-linear electrodynamics from the observed quasi-periodic oscillations

Quasi-periodic oscillations (QPOs), in particular, the ones with high frequencies, often observed in the power spectrum of black holes, are useful in understanding the nature of strong gravity since they are associated with the motion of matter in the vicinity of the black hole horizon. Interestingly, these high frequency QPOs (HFQPOs) are observed in commensurable pairs, the most common ratio being 3:2. Several theoretical models are proposed in the literature which explain the HFQPOs in terms of the orbital and epicyclic frequencies of matter rotating around the central object. Since these frequencies are sensitive to the background spacetime, the observed HFQPOs can potentially extract useful information regarding the nature of the same. In this work, we investigate the role of regular black holes with a Minkowski core, which arise in gravity coupled to non-linear electrodynamics, in explaining the HFQPOs. Regular black holes are particularly interesting as they provide a possible resolution to the singularity problem in general relativity. We compare the model dependent QPO frequencies with the available observations of the quasi-periodic oscillations from black hole sources and perform a χ2 analysis. Our study reveals that most QPO models favor small but non-trivial values of the non-linear electrodynamics charge parameter. In particular, black holes with large values of non-linear electrodynamics charge parameter are generically disfavored by present observations related to QPOs.

Deciphering signatures of Bardeen black holes from the observed quasi-periodic oscillations

Quasi-periodic oscillations (QPOs) observed in the power spectrum of black holes are unique observational probes to the background spacetime since they can be directly related to the timescales associated with the motion of matter orbiting in the vicinity of the black hole horizon. In this regard, the high frequency QPOs (HFQPOs) are particularly interesting as they occur in commensurable pairs, the most common ratio being the 3:2 twin peak QPOs. The theoretical models which aim to explain these QPOs express the observed frequencies in terms of the epicyclic motion of test particles in a given background spacetime. In this work, we study the signatures of Bardeen spacetime from the observed QPOs in the black hole power spectrum. Bardeen black holes are rotating, regular black holes with a magnetic monopole charge. Such regular backgrounds are theoretically interesting as they can potentially evade the curvature singularity, otherwise unavoidable in general relativistic black holes. We perform a χ2 analysis by comparing the available observations of the quasi-periodic oscillations from black hole sources with the relevant theoretical models and note that the Kerr black holes in general relativity are observationally more favored compared to black holes with a monopole charge. Our analysis reveals that black holes with very high monopole charges are disfavored from QPO related observations.

The evolution of the high-frequency variability in the black hole candidate GRS 1915+105 as seen by RXTE

ABSTRACT GRS 1915+105 can show type-C quasi-periodic oscillations (QPOs) in the power density spectrum. A high-frequency QPO (HFQPO) at 67 Hz has been observed in this source, albeit less often than the type-C QPOs. Besides these features, GRS 1915+105 sometimes shows a broad bump in the power spectrum at around 30–150 Hz. We study the power spectra of GRS 1915+105 with the Rossi X-ray Timing Explorer when the source was in the χ class. We find that the rms amplitude of the bump depends strongly upon both the frequency of the type-C QPO and the hardness ratio, and is correlated with the corona temperature and anticorrelated with the radio flux at 15 GHz. The characteristic frequency of the bump is better correlated with a combination of the frequency of the type-C QPO and the hardness ratio than with the frequency of the type-C QPO alone. The rms amplitude of the bump generally increases with energy from ∼1–2 per cent at ∼3 keV to ∼10–15 per cent at ∼30 keV. We suggest that the bump and the HFQPO may be the same variability component but the properties of the corona affect the coherence of this variability, leading either to a HFQPO when the spectrum is in the relatively soft γ class, or to a bump when the spectrum is in the hard χ class. Finally, we discuss the anticorrelation between the rms amplitude of the bump and the radio flux in the context of the relation between the corona and the jet.

Wide-band view of high-frequency quasi-periodic oscillations of GRS 1915+105 in ‘softer’ variability classes observed with AstroSat

ABSTRACT We present a comprehensive temporal and spectral analysis of the ‘softer’ variability classes (i.e. θ, β, δ, ρ, κ, ω and γ) of the source GRS 1915+105 observed by AstroSat during the 2016−2021 campaign. Wide-band (3−60 keV) timing studies reveal the detection of high-frequency quasi-periodic oscillations (HFQPOs) with frequencies of 68.14−72.32 Hz, significance of 2.75−11σ and rms amplitude of 1.48–2.66 per cent in δ, κ, ω and γ variability classes. Energy-dependent power spectra show that HFQPOs are detected only in the 6−25 keV energy band and rms amplitude is found to increase (1–8 per cent) with energy. The dynamical power spectra of the κ and ω classes demonstrate that HFQPOs seem to be correlated with high count rates. We observe that wide-band (0.7−50 keV) energy spectra can be described by the thermal Comptonization component (nthComp) with a photon index (Γnth) of 1.83−2.89 along with an additional steep (ΓPL ∼ 3) power-law component. The electron temperature (kTe) of 1.82−3.66 keV and optical depth (τ) of 2−14 indicate the presence of a cool and optically thick corona. In addition, nthComp components, 1.97 ≲ Γnth ≲ 2.44 and 1.06 × 10−8 ≲ Fnth (erg cm−2 s−1) ≲ 4.46 × 10−8, are found to dominate in the presence of HFQPOs. Overall, these findings infer that HFQPOs are possibly the result of the modulation of the ‘Comptonizing corona’. Further, we find that the bolometric luminosity (0.3−100 keV) of the source lies within the sub-Eddington (3–34 per cent LEdd) regime. Finally, we discuss and compare the obtained results in the context of existing models on HFQPOs.

Very-high-frequency oscillations in the main peak of a magnetar giant flare.

Magnetars are strongly magnetized, isolated neutron stars1-3 with magnetic fields up to around 1015 gauss, luminosities of approximately 1031-1036 ergs per second and rotation periods of about 0.3-12.0 s. Very energetic giant flares from galactic magnetars (peak luminosities of 1044-1047 ergs per second, lasting approximately 0.1 s) have been detected in hard X-rays and soft γ-rays4, and only one has been detected from outside our galaxy5. During such giant flares, quasi-periodic oscillations (QPOs) with low (less than 150 hertz) and high (greater than 500 hertz) frequencies have been observed6-9, but their statistical significance has been questioned10. High-frequency QPOs have been seen only during the tail phase of the flare9. Here we report the observation of two broad QPOs at approximately 2,132 hertz and 4,250 hertz in the main peak of a giant γ-ray flare11 in the direction of the NGC 253 galaxy12-17, disappearing after 3.5 milliseconds. The flare was detected on 15 April 2020 by the Atmosphere-Space Interactions Monitor instrument18,19 aboard the International Space Station, which was the only instrument that recorded the main burst phase (0.8-3.2 milliseconds) in the full energy range (50 × 103 to 40 × 106 electronvolts) without suffering from saturation effects such as deadtime and pile-up. Along with sudden spectral variations, these extremely high-frequency oscillations in the burst peak are a crucial component that will aid our understanding of magnetar giant flares.

Epicyclic oscillations in spinning particle motion around Kerr black hole applied in models fitting the quasi-periodic oscillations observed in microquasars and AGNs

The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries or quasars can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus fit the data of QPOs observed in the well known microquasars as well as active galactic nuclei (AGNs) in the framework of the model of geodesic oscillations of Keplerian disks modified for the epicyclic oscillations of spinning test particles orbiting Kerr BHs. We show that the modified geodesic models of QPOs can explain the observational fixed data from the microquasars and AGNs but not for all sources. We perform a successful fitting of the high frequency QPOs models of epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models, and discuss the corresponding constraints of parameters of the model, which are the spin of the test particle, mass and rotation of the BH.

Evolution of a Mode of Oscillation within Turbulent Accretion Disks

Abstract We investigate the effects of subsonic turbulence on a normal mode of oscillation (a possible origin of the high-frequency quasi-periodic oscillations (HFQPOs) within some black hole accretion disks). We consider perturbations of a time-dependent background (steady-state disk plus turbulence), obtaining an oscillator equation with stochastic damping, (mildly) nonlinear restoring, and stochastic driving forces. The (long-term) mean values of our turbulent functions vanish. In particular, turbulence does not damp the oscillation modes, so “turbulent viscosity” is not operative. However, the frequency components of the turbulent driving force near that of the mode can produce significant changes in the amplitude of the mode. Even with an additional (phenomenological constant) source of damping, this leads to an eventual “blowout” (onset of effects of nonlinearity) if the turbulence is sufficiently strong or the damping constant is sufficiently small. The infrequent large increases in the energy of the mode could be related to the observed low duty cycles of the HFQPOs. The width of the peak in the power spectral density (PSD) is proportional to the amount of nonlinearity. A comparison with observed continuum PSDs indicates the conditions required for the visibility of the mode.

Confrontation of Observation and Theory: High-frequency QPOs in X-Ray Binaries, Tidal Disruption Events, and Active Galactic Nuclei

Abstract We compile observations of high-frequency quasi-periodic oscillations (QPOs) around black holes, both stellar and supermassive, and compare their positions in the parameter space of black hole mass, spin, and oscillation frequency. We find that supermassive black holes occupy a separate region of parameter space than stellar, and further, that QPOs seen around tidal disruption events rather than Seyfert-type active galactic nuclei (AGN) occupy an entirely different space. We then compare these results to the orbital resonance, diskoseismic, warped disk, and disk–jet coupling theoretical models for the origin of high-frequency QPOs. We find that while oscillations around stellar mass black holes are generally consistent with the above models, supermassive black holes are decidedly not. Oscillations seen in tidal disruption events are consistent with oscillations near the frequency of the innermost stable circular orbit, while QPOs in AGN are not accounted for by any of the physical models in consideration. This indicates that despite the scale invariance of accretion processes implied by a decades-wide correlation between QPO frequency and black hole mass, any theory of high-frequency QPOs must relate the frequency to more than just the mass and spin.

AstroSat view of GRS 1915+105 during the soft state: detection of HFQPOs and estimation of mass and spin

ABSTRACT We report the results of AstroSat observations of GRS 1915+105 obtained using 100 ks Guaranteed Time during the soft state. The colour–colour diagram indicates a variability class of δ with the detection of high-frequency quasi-periodic oscillation (HFQPO) in the power density spectra. The HFQPO is seen to vary in the frequency range of 67.96–70.62 Hz with percentage rms ∼0.83–1.90 per cent and significance varying from 1.63 to 7.75. The energy dependent power spectra show that the HFQPO features are dominant only in 6–25 keV energy band. The broad-band energy spectra (0.7–50 keV) of Soft X-ray Telescope and Large Area X-ray Proportional Counter modelled with nthComp and powerlaw imply that the source has an extended corona in addition to a compact ‘Comptonizing corona’ that produces high-energy emission and exhibits HFQPOs. The broad-band spectral modelling indicates that the source spectra are well described by thermal Comptonization with electron temperature (kTe) of 2.07–2.43 keV and photon index (Γnth) between 1.73 and 2.45 with an additional powerlaw component of photon index (ΓPL) between 2.94 and 3.28. The norm of nthComp component is high (∼8) during the presence of strong HFQPO and low (∼3) during the absence of HFQPO. Further, we model the energy spectra with the kerrbb model to estimate the accretion rate, mass, and spin of the source. Our findings indicate that the source accretes at super-Eddington rate of $1.17\!-\!1.31~ \dot{M}_{\rm Edd}$. Moreover, we find the mass and spin of the source as 12.44–13.09 M⊙ and 0.990–0.997 with $90{{\ \rm per\ cent}}$ confidence suggesting that GRS 1915+105 is a maximally rotating stellar mass X-ray binary black hole source.

HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. II. Magnetohydrodynamic simulations

ABSTRACT Trapped inertial oscillations (r modes) provide a promising explanation for high-frequency quasi-periodic oscillations (HFQPOs) observed in the emission from black hole X-ray binary systems. An eccentricity (or warp) can excite r modes to large amplitudes, but concurrently, the oscillations are likely damped by magnetohydrodynamic (MHD) turbulence driven by the magnetorotational instability (MRI). We force eccentricity in global, unstratified, zero-net-flux MHD simulations of relativistic accretion discs and find that a sufficiently strong disc distortion generates trapped inertial waves despite this damping. In our simulations, eccentricities above ∼0.03 in the inner disc excite trapped waves. In addition to the competition between r-mode damping and driving, we observe that larger amplitude eccentric structures modify and in some cases suppress MRI turbulence. Given the variety of distortions (warps as well as eccentricities) capable of amplifying r modes, the robustness of trapped inertial wave excitation in the face of MRI turbulence in our simulations provides support for a discoseismic explanation for HFQPOs.

Limiting effects in clusters of misaligned toroids orbiting static SMBHs

ABSTRACT We consider agglomerates of misaligned, pressure supported tori orbiting a Schwarzschild black hole. A leading function is introduced, regulating the toroids distribution around the central static attractor – it enables us to model the misaligned tori aggregate as a single orbiting (macro-)configuration. We first analyse the leading function for purely hydrodynamical perfect fluid toroids. Later, the function is modified for presence of a toroidal magnetic field. We study the constraints on the tori collision emergence and the instability of the agglomerates of misaligned tori with general relative inclination angles. We discuss the possibility that the twin peak high-frequency quasi-periodic oscillations (HF-QPOs) could be related to the agglomerate inner ringed structure. The discrete geometry of the system is related to HF-QPOs considering several oscillation geodesic models associated to the toroids inner edges. We also study possible effect of the tori geometrical thickness on the oscillatory phenomena.

Quasi-periodic oscillations around Kerr-MOG black holes

The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus present and apply to three known microquasars the model of epicyclic oscillations of Keplerian discs orbiting rotating BHs governed by the modified theory of gravity (MOG). We show that the standard geodesic models of QPOs can explain the observationally fixed data from the three microquasars, GRO 1655-40, XTE 1550-564, and GRS 1915+105. We perform a successful fitting of the high frequency (HF) QPOs observed in these microquasars, under assumption of MOG BHs, for epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models and discuss the corresponding constraints of parameters of the model, which are the mass and spin and parameter alpha of the BH.

A variable-frequency HFQPO in GRS 1915+105 as observed with AstroSat

ABSTRACT From the analysis of more than 92 ks of data obtained with the Large Area X-Ray Proportional Counter (LAXPC) instrument onboard AstroSat we have detected a clear high-frequency quasi-periodic oscillation (HFQPO) whose frequency varies between 67.4 and 72.3 Hz. In the classification of variability classes of GRS 1915+105, at the start of the observation period the source was in class ω and at the end the variability was that of class μ: both classes are characterized by the absence of hard intervals and correspond to disc-dominated spectra. After normalization to take into account time variations of the spectral properties as measured by X-ray hardness, the QPO centroid frequency is observed to vary along the hardness–intensity diagram, increasing with hardness. We also measure phase lags that indicate that HFQPO variability at high energies lags that at lower energies and detect systematic variations with the position on the hardness–intensity diagram. This is the first time that (small) variations of the HFQPO frequency and lags are observed to correlate with other properties of the source. We discuss the results in the framework of existing models, although the small (7 per cent) variability observed is too small to draw firm conclusions.

Rossby wave instability and high-frequency quasi-periodic oscillations in accretion discs orbiting around black holes

Context. The rather elusive high-frequency quasi-periodic oscillations (HFQPOs) observed in the X-ray light curve of black holes have been seen in a wide range of frequencies, even within one source. Also notable is the detection of “pairs” of HFQPOs with a close-to-integer ratio between the frequencies. Aims. The aim of this paper is to investigate some of the possible observables that we could obtain from the Rossby wave instability (RWI) active in the accretion disc surrounding the compact object. Methods. Using the newly developed GR-AMRVAC code able to follow the evolution of the RWI in a full general relativistic framework, we explore how RWI can reproduce observed HFQPO frequency ratios and whether or not it is compatible with observations. In order to model the emission coming from the disc we have linked our general relativistic simulations to the general relativistic ray-tracing GYOTO code and delivered synthetic observables that can be confronted with actual data from binary systems hosting HFQPOs. Results. We demonstrate that some changes in the physical conditions prevailing in the part of the disc where RWI can be triggered lead to various dominant RWI modes whose ratio recovers frequency ratios observed in various X-ray binary systems. In addition we also show that when RWI is triggered near to the last stable orbit of a spinning black hole, the amplitude of the X-ray modulation increases with the spin of the black hole. Revisiting published data on X-ray binary systems, we show that this type of relationship actually exists in five systems where an indirect measurement of the spin of the black hole is available.

Quasi-periodic oscillations, trapped inertial waves, and strong toroidal magnetic fields in relativistic accretionwhen th discs

The excitation of trapped inertial waves (r-modes) by warps and eccentricities in the inner regions of a black hole accretion disc may explain the high-frequency quasi-periodic oscillations (HFQPOs) observed in the emission of Galactic X-ray binaries. However, it has been suggested that strong vertical magnetic fields push the oscillations' trapping region toward the innermost stable circular orbit (ISCO), where conditions could be unfavourable for their excitation. This paper explores the effects of large-scale magnetic fields that exhibit \textit{both} toroidal and vertical components, through local and global linear analyses. We find that a strong toroidal magnetic field can reduce the detrimental effects of a vertical field: in fact, the isolation of the trapping region from the ISCO may be restored by toroidal magnetic fields approaching thermal strengths. The toroidal field couples the r-modes to the disc's magneto-acoustic response and inflates the effective pressure within the oscillations. As a consequence, the restoring force associated with the vertical magnetic field's tension is reduced. Given the analytical and numerical evidence that accretion discs threaded by poloidal magnetic field lines develop a strong toroidal component, our result provides further evidence that the detrimental effects of magnetic fields on trapped inertial modes are not as great as previously thought.