Models Of Quasi-periodic Oscillations Research Articles

Strong gravitational lensing, quasi-periodic oscillations and constraints from EHT observations for quantum-improved charged black hole

We investigate strong gravitational lensing by quantum-improved charged black holes characterized by an additional parameter denoted as ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}, in addition to the mass M and charge Q. Our findings reveal that when both the parameters Q/2M and ω/4M2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega /4M^2$$\\end{document} increase simultaneously, various astrophysical consequences, such as the deflection angle αD(u)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _D(u)$$\\end{document} and angular image separation increase. Concurrently, the angular position θ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{\\infty }$$\\end{document}, relative magnification rmag\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{mag}$$\\end{document}, and the time delay ΔT2,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta T_{2,1}$$\\end{document} between the first and second relativistic images also decrease with the growing values of the parameters Q/2M and ω/4M2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega /4M^2$$\\end{document}. It is also observed that the Einstein ring θ1E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _1^E$$\\end{document} for the quantum-improved charged black hole is more significant than those for Schwarzschild, quantum-improved Schwarzschild, and Reisner–Nordström black holes. As with supermassive black holes such as M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document} and SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SgrA^*$$\\end{document}, it is observed that to be a viable astrophysical black hole, the EHT results constrain the parameter space (ω/4M2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega /4M^2$$\\end{document}, Q/2M). Remarkably, the EHT results for SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SgrA^*$$\\end{document} impose more stringent limits on the parameter space of quantum-improved charged black holes compared to those established by the EHT results forM87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document}. We investigate the radial profiles of orbital and radial harmonic oscillation frequencies as a function of the dimensionless coupling constants and black hole mass. The main characteristics of test particle quasi-periodic oscillations close to stable circular orbits in the black hole equatorial plane are also examined. We study the positioning of resonant radii in the background of quantum-improved charged black holes for high-frequency quasi-periodic oscillations models: warped disc (WD) models, relativistic precession (RP) and its types, and epicyclic resonance (ER) and its variants.

Testing alternative spacetimes by high-frequency quasi-periodic oscillations observed in microquasars and active galactic nuclei

In this article, we try to capture the influence of deviation from standard Kerr black hole (BH) spacetime on observed high-frequency quasi-periodic oscillations (QPOs) signal. We explore the dynamics of test particles in the field of rotating compact objects governed by the various modifications of the standard Kerr BH spacetime and apply the model of epicyclic oscillations of Keplerian discs to the observed microquasars and active galactic nuclei high-frequency QPOs data. We present a generalized formalism for fitting two well-known high-frequency QPO models: the epicyclic resonance model and the relativistic precession model. This is done assuming stationary, axisymmetric, and asymptotically flat spacetimes. Recently, we have used the same set of stationary, axisymmetric, and asymptotically flat spacetimes, and estimated the restrictions of spacetime parameters with the help of hot-spot data of three flares observed at Sgr A* by GRAVITY instrument (Misbah Shahzadi et al 2022 Eur. Phys. J. C 82 407). The aim of this work is not to test a particular theoretical model or to determine and constrain its parameters, but to map a set of well-astrophysically motivated deviations from classical Kerr BH spacetime and demonstrate which ones provide the best fit for high-frequency QPOs data and could be fruitful for future exploration.

Disc corona radii and QPO frequencies in black hole binaries: testing Lense– Thirring precession origin

ABSTRACT Stellar-mass black hole binary systems in the luminous X-ray states show a strong quasi-periodic oscillation (QPO) in their Comptonized emission. The frequency of this feature correlates with the ratio of a disc to Comptonized emission rather than with total luminosity. Hence, it changes dramatically during spectral transitions between the hard and soft states. Its amplitude is also strongest in these intermediate states, making them an important test of QPO models. However, these have complex spectra which generally require a disc and two separate Comptonization components, making it difficult to uniquely derive the spectral parameters. We build a new energy-conserving model of the accretion flow, SSsed model, which assumes a fixed radial emissivity but with a changing emission mechanism. This is similar to the agnsed model in xspec but tuned to be more suitable for stellar mass black holes. It uses a combination of the disc luminosity and temperature to constrain the inner radius of the (colour temperature corrected) blackbody disc, separating this from the more complex Comptonization spectra emitted inwards of this radius. We show a pilot study of this model fit to hundreds of RXTE spectra of the black hole binary XTE J1550 − 564. We show that the derived disc radius tightly anticorrelates with the central frequencies of the low-frequency QPO detected in the same observations. The relation is consistent with the quantitative predictions of Lense–Thirring precession of the entire inner Comptonization regions for the assumed system parameters. This supports the scenario that low-frequency QPOs are caused by Lense–Thirring precession.

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.

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.

Axisymmetric oscillation modes of relativistic tori in the vicinity of a distorted, deformed compact object

ABSTRACT This paper studies the oscillation properties of relativistic, non-self-gravitating tori in the background of a distorted, deformed compact object. This work concentrates on a static and axially symmetric metric containing two quadrupole parameters; relating to the central object and the external fields. This metric may associate the observable effects of these parameters as dynamical degrees of freedom. The astrophysical motivation for choosing such a field is the possibility of constituting a reasonable model for an actual scenario occurring in the vicinity of compact objects. Following our previous works, this paper aims to investigate the radial epicyclic frequency in a perfect fluid disc and not a test particle scenario via a local analysis. To achieve this goal, we employ the vertically integrated technique to be able to treat the equations analytically. The tori configuration is also modelled with Keplerian and non-Keplerian distributions of specific angular momentum. In this set-up, we also discuss the dependence of oscillation properties on the model’s variables related to angular momentum distribution and quadrupoles. In the present contribution, we further explore these properties with the possibility of relating oscillatory frequencies to some high-frequency quasi-periodic oscillations models and observed data in some microquasar and neutron star sources, and test the ability of this fluid approach to fit with observational data.

Orbital motion and quasi-periodic oscillations with periastron and Lense–Thirring precession of slowly rotating Einstein–Æther black hole

We study the orbital and oscillatory motion of test particles moving around slowly rotating first and second kinds of Einstein–Æther black holes. In relation to the black hole parameters, we find analytical solutions for the radial profiles of specific energy and specific angular momentum of the equatorial stable circular orbits. The properties of the co-rotating as well as contra-rotating innermost stable circular orbits are analyzed. We examine the radial profiles of the frequencies of latitudinal and radial harmonic oscillations as a function of the black hole mass and dimensionless coupling constants of the theory. The key features of quasi-periodic oscillations of test particles near the stable circular orbits in an equatorial plane of the black hole are discussed. We investigate the positions of resonant radii for high-frequency quasi-periodic oscillations models, namely epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models, considered in the background of slowly rotating first and second kinds of slowly rotating Einstein–Æther black holes. Furthermore, Periastron and Lense–Thirring precessions have been discussed. We demonstrate that the dimensionless coupling parameters of the theory have a strong influence on particle motion around Einstein–Æther black holes.

Quasiperiodic oscillations around hairy black holes in Horndeski gravity

Testing gravity theories and their parameters using observations is an important issue in relativistic astrophysics. In this context, we investigate the motion of test particles and their harmonic oscillations in the spacetime of non-rotating hairy black holes (BHs) in Hordeski gravity, together with astrophysical applications of quasiperiodic oscillations (QPOs). We show possible values of upper and lower frequencies of twin-peak QPOs which may occur in the orbits from innermost stable circular orbits to infinity for various values of the Horndeski parameter q in relativistic precession, warped disk models, and three different sub-models of the epicyclic resonant model. We also study the behaviour of the QPO orbits and their position relative to innermost stable circular orbits (ISCOs) with respect to different values of the parameter q. It is obtained that at a critical value of the Horndeski parameter ISCO radius takes 6M which has been in the pure Schwarzschild case. Finally, we obtain mass constraints of the central BH of microquasars GRS 1915+105 and XTE 1550-564 at the GR limit and the possible value of the Horndeski parameter in the frame of the above-mentioned QPO models. The analysis of orbits of twin peak QPOs with the ratio of upper and lower frequencies 3:2, around the BHs in the frame of relativistic precession (RP) and epicyclic resonance (ER4) QPO models have shown that the orbits locate close to the ISCO. It is obtained that the distance between QPO orbits and ISCO is less than the error of the observations.

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.

The NICER “Reverberation Machine”: A Systematic Study of Time Lags in Black Hole X-Ray Binaries

We perform the first systematic search of all NICER archival observations of black hole (and candidate) low-mass X-ray binaries for signatures of reverberation. Reverberation lags result from the light travel time difference between the direct coronal emission and the reflected disk component, and therefore their properties are a useful probe of the disk-corona geometry. We detect new signatures of reverberation lags in eight sources, increasing the total sample from three to 11, and study the evolution of reverberation lag properties as the sources evolve in outbursts. We find that in all of the nine sources with more than one reverberation lag detection, the reverberation lags become longer and dominate at lower Fourier frequencies during the hard-to-soft state transition. This result shows that the evolution in reverberation lags is a global property of the state transitions of black hole low-mass X-ray binaries, which is valuable in constraining models of such state transitions. The reverberation lag evolution suggests that the corona is the base of a jet that vertically expands and/or gets ejected during state transition. We also discover that in the hard state, the reverberation lags get shorter, just as the quasiperiodic oscillations (QPOs) move to higher frequencies, but then in the state transition, while the QPOs continue to higher frequencies, the lags get longer. We discuss the implications of the coronal geometry and physical models of QPOs in light of this new finding.

Dynamics of test particles around magnetically charged regular black holes

In this work, we have provided detailed studies of motion test neutral, photon, neutrino-like, magnetized, and magnetically charged particles around a magnetically charged regular black hole (BH) together with properties of the spacetime curvature and event horizon around the BH. In order to see differences of linear electrodynamic (LED) and nonlinear electrodynamic (NED) charge effects in these studies, we have compared all the obtained results with the results obtained in Reissner–Nordstöm (RN) BH. It has been shown that an increase of the magnetic charge causes a decrease in the curvature invariants and event horizon radius. The study of the impact parameter for photons and neutrino-like particles has shown the effect of the magnetic charge of the regular BH, stronger than the RN one. Harmonic oscillations of test particles around regular BHs are studied. As an astrophysical application of the study, we also have provided comparisons of the effects of rotating Kerr BH spin and magnetic charge of the BH on upper, [Formula: see text] and lower, [Formula: see text] frequencies of twin peak quasi-periodic oscillations (QPOs) and represented possible values of the upper and lower frequencies of the twin-peak QPOs around these BHs in various QPO models. Finally, it is shown that the effect of magnetic charge on the ISCO radius of magnetized particles becomes stronger in higher values of magnetized parameters of the magnetized particles, where the effects of RN BH and regular BH charges become distinguishable.

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.

Supermassive black holes surrounded by dark matter modeled as anisotropic fluid: epicyclic oscillations and their fitting to observed QPOs

Recently introduced exact solution of the Einstein gravity coupled minimally to an anisotropic fluid representing dark matter can well represent supermassive black holes in galactic nuclei with realistic distribution of dark matter around the black hole, given by the Hernquist-like density distribution. For these fluid-hairy black hole spacetimes, properties of the gravitational radiation, quasinormal ringing, and optical phenomena were studied, giving interesting results. Here, using the range of physical parameters of these spacetimes allowing for their relevance in astrophysics, we study the epicyclic oscillatory motion of test particles in these spacetimes. The frequencies of the orbital and epicyclic motion are applied in the epicyclic resonance variant of the geodesic model of quasiperiodic oscillations (QPOs) observed in active galactic nuclei to demonstrate the possibility to solve the cases where the standard vacuum black hole spacetimes are not allowing for explanation of the observed data. We demonstrate that the geodesic model can explain the QPOs observed in most of the active galactic nuclei for the fluid-hairy black holes with reasonable halo parameters.

Tangled magnetic field model of QPOs

ABSTRACT The highly tangled magnetic field of a magnetar supports shear waves similar to Alfvén waves in an ordered magnetic field. Here, we explore if torsional modes excited in the stellar interior and magnetosphere can explain the quasi-periodic oscillations (QPOs) observed in the tail of the giant flare of SGR 1900+14. We solve the initial value problem for a tangled magnetic field that couples interior shear waves to relativistic Alfvén shear waves in the magnetosphere. Assuming stellar oscillations arise from the sudden release of magnetic energy, we obtain constraints on the energetics and geometry of the process. If the flare energy is deposited initially inside the star, the wave energy propagates relatively slowly to the magnetosphere which is at odds with the observed rise time of the radiative event of ≲ 10 ms. Nor can the flare energy be deposited entirely outside the star, as most of the energy reflects off the stellar surface, giving surface oscillations of insufficient magnitude to produce detectable modulations of magnetospheric currents. Energy deposition in a volume that straddles the stellar surface gives agreement with the observed rise time and excites a range of modes with substantial amplitude at observed QPO frequencies. In general, localized energy deposition excites a broad range of modes that encompasses the observed QPOs, though many more modes are excited than the number of observed QPOs. If the flare energy is deposited axisymmetrically, as is possible for a certain class of MHD instabilities, the number of modes that is excited is considerably reduced.

A two-component Comptonization model for the type-B QPO in MAXI J1348−630

ABSTRACT Spectral-timing analysis of the fast variability observed in X-rays is a powerful tool to study the physical and geometrical properties of the accretion/ejection flows in black hole (BH) binaries. The origin of type-B quasi-periodic oscillations (QPO), predominantly observed in BH candidates in the soft-intermediate state, has been linked to emission arising from the relativistic jet. In this state, the X-ray spectrum is characterized by a soft-thermal blackbody-like emission due to the accretion disc, an iron emission line (in the 6–7 keV range), and a power-law-like hard component due to inverse-Compton scattering of the soft-photon source by hot electrons in a corona or the relativistic jet itself. The spectral-timing properties of MAXI J1348−630 have been recently studied using observations obtained with the NICER observatory. The data show a strong type-B QPO at ∼4.5 Hz with increasing fractional rms amplitude with energy and positive lags with respect to a reference band at 2–2.5 keV. We use a variable-Comptonization model that assumes a sinusoidal coherent oscillation of the Comptonized X-ray flux and the physical parameters of the corona at the QPO frequency, to fit simultaneously the energy-dependent fractional rms amplitude and phase lags of this QPO. We show that two physically connected Comptonization regions can successfully explain the radiative properties of the QPO in the full 0.8–10 keV energy range.

Models of high-frequency quasi-periodic oscillations and black hole spin estimates in Galactic microquasars

We explore the influence of nongeodesic pressure forces present in an accretion disc on the frequencies of its axisymmetric and nonaxisymmetric epicyclic oscillation modes. We discuss its implications for models of high-frequency quasi-periodic oscillations (QPOs), which have been observed in the X-ray flux of accreting black holes (BHs) in the three Galactic microquasars, GRS 1915+105, GRO J1655−40, and XTE J1550−564. We focus on previously considered QPO models that deal with low-azimuthal-number epicyclic modes, |m| ≤ 2, and outline the consequences for the estimations of BH spin, a ∈ [0, 1]. For four out of six examined models, we find only small, rather insignificant changes compared to the geodesic case. For the other two models, on the other hand, there is a significant increase of the estimated upper limit on the spin. Regarding the falsifiability of the QPO models, we find that one particular model from the examined set is incompatible with the data. If the spectral spin estimates for the microquasars that point to a > 0.65 were fully confirmed, two more QPO models would be ruled out. Moreover, if two very different values of the spin, such as a ≈ 0.65 in GRO J1655−40 and a ≈ 1 in GRS 1915+105, were confirmed, all the models except one would remain unsupported by our results. Finally, we discuss the implications for a model that was recently proposed in the context of neutron star (NS) QPOs as a disc-oscillation-based modification of the relativistic precession model. This model provides overall better fits of the NS data and predicts more realistic values of the NS mass compared to the relativistic precession model. We conclude that it also implies a significantly higher upper limit on the microquasar’s BH spin (a ∼ 0.75 vs. a ∼ 0.55).

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.

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.

Time-scale of twin-peak quasi-periodic oscillations and mass of accreting neutron stars

ABSTRACT Einstein’s general relativity predicts that orbital motion of accreted gas approaching a neutron star (NS) in a NS low-mass X-ray binary (LMXB) system occurs on a time-scale proportional to the NS mass. Radiation of the gas accounts for most of the observed LMXBs variability. In more than a dozen of sources twin-peak quasi-periodic oscillations (QPOs) have been observed. Inspired by the expected proportionality between periods of orbital motion and NS mass we present a straightforward comparison among these sources. We investigate relations between QPO periods and their ratios and identify characteristic time-scales of QPOs associated with individual sources. These time-scales are likely determined by the relative mass of each NS. We show that the characteristic time-scale of the millisecond pulsar XTE J1807.4−294 is longer than for most other NS LMXBs. Consequently, models of QPOs that consider geodesic orbital frequencies imply that the X-ray pulsars’ mass has to be about $50{{\ \rm per\ cent}}$ higher than the average mass of other sources. Consideration of other X-ray pulsars indicates that the exceptionality of XTE J1807.4−294 cannot be related to NS magnetic field in any simple manner. We suggest that QPOs observed in this source can help to discriminate between the proposed versions of the NS equation of state.

Epicyclic Oscillations in the Hartle–Thorne External Geometry

Abstract The external Hartle–Thorne geometry, which describes the spacetime outside a slowly rotating compact star, is characterized by the gravitational mass M, angular momentum J, and quadrupole moment Q of the star and gives a convenient description, which, for the rotation frequencies of more than 95% of known pulsars, is sufficiently accurate for most purposes. We focus here on the motion of particles in these spacetimes, presenting a detailed systematic analysis of the frequency properties of radial and vertical epicyclic motion and of orbital motion. Our investigation is motivated by X-ray observations of binary systems containing a rotating neutron star that is accreting matter from its binary companion. In these systems, twin high-frequency quasi-periodic oscillations (QPOs) are sometimes observed with a frequency ratio approaching 3:2 or 5:4, and these may be explained by models involving the orbital and epicyclic frequencies of quasi-circular geodesic motion. In our analysis, we use realistic equations of state for the stellar matter and proceed in a self-consistent way, following the Hartle–Thorne approach in calculating both the corresponding values of Q, M, and J for the stellar model and the properties of the surrounding spacetime. Our results are then applied to a range of geodetical models for QPOs. A key feature of our study is that it implements the recently discovered universal relations among neutron-star parameters so that the results can be directly used for models with different masses M, radii R, and rotational frequencies f rot.