Relativistic Precession Model Research Articles

Rethinking the 67 Hz QPO in GRS 1915+105: Type C quasi-periodic oscillations at the innermost stable circular orbit

Context. We study quasi-periodic oscillations (QPO) at low and high frequency in the variability of the high-energy emission from black hole binaries and their physical interpretation in terms of signatures of General Relativity in the strong-field regime. Aims. We wish to understand the nature of the 67 Hz QPOs observed in the X-ray emission of the peculiar black hole binary GRS 1915+105 within the general classification of QPOs, and to determine the spin of the black hole in the system by applying the relativistic precession model (RPM). Methods. Within the RPM, the only relativistic frequency that is stable in time over a wide range of accretion rates and can be as low as 67 Hz (for a dynamically measured black hole mass) is the nodal frequency at the innermost stable circular orbit (ISCO). In the application of the model, this corresponds to type C QPOs. Under this assumption, it is possible to measure the spin of the black hole by using the mass of the black hole previously obtained via dynamical measurements. We re-analysed a large number of Rossi-XTE observations to determine whether other timing features confirm this hypothesis. Results. The identification of the 67 Hz QPO as the nodal frequency at ISCO yields a value of 0.706 ± 0.034 for the black hole spin. With this spin, the only two QPO detections at higher frequencies available in the literature are consistent with being orbital frequencies at a radius outside ISCO. The high-frequency bumps often observed at frequencies between 10 and 200 Hz follow the correlation expected for orbital and periastron-precession frequencies at even larger radii.

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.

Measuring black hole spins through X-ray reflection spectroscopy and the relativistic precession model: the case of XTE J1859+226

ABSTRACT The development of techniques to measure accurately black hole spins is crucial to study the physics and astrophysics of these objects. X-ray reflection spectroscopy is currently the most popular method to estimate the spins of accreting black holes; so far it has provided a spin measurement of about 40 stellar-mass black holes in X-ray binaries and 40 supermassive black holes in active galactic nuclei. The relativistic precession model (RPM) is another method to measure the spins of stellar-mass black holes: it requires the measurement of the frequencies of three simultaneous quasi-periodic oscillations and can potentially provide precise estimates of the black hole mass and spin. However, the two methods do not seem to provide consistent results when applied to the same sources, which questions the reliability and accuracy of these measurements. Recently, the RPM has been applied to infer the spin of the black hole in XTE J1859+226. The authors found a* = 0.149 ± 0.005 (68 per cent CL). There are no other spin measurements of this source. We looked for archived RXTE observations of XTE J1859+226 with blurred reflection features and found 23 spectra suitable for measuring the spin. We employed two different models with relxill and relxillD and obtained a higher spin value from all these fits. From simultaneous fitting of seven spectra of higher quality, we found $a_* = 0.986^{+0.001}_{-0.004}$ and a* = 0.987 ± 0.003 (90 per cent CL, statistical) with relxill and relxillD, respectively. Our results confirm the discrepancy between the spin measurements inferred from the two techniques.

Constraints on the rotating self-dual black hole with quasi-periodic oscillations

An impressive feature of loop quantum gravity (LQG) is that it can elegantly resolve both the big bang and black hole singularities. By using the Newman-Janis algorithm, a regular and effective rotating self-dual black hole (SDBH) metric could be constructed, which alters the Kerr geometry with a polymeric function P from the quantum effects of LQG geometry. In this paper, we investigate its impact on the frequency characteristics of the X-ray quasi-periodic oscillations (QPOs) from 5 X-ray binaries and contrast it with the existing results of the orbital, periastron precession and nodal precession frequencies within the relativistic precession model. We apply a Monte Carlo Markov Chain (MCMC) simulation to examine the possible LQG effects on the X-ray QPOs. We found that the best constraint result for the rotating self-dual geometry from LQG came from the QPOs of X-ray binary GRO J1655-40, which establish an upper bound on the polymeric function P less than 6.15 × 10-3 at 95% confidence level. This bound leads to a restriction on the polymeric parameter δ of LQG to be 0.66.

Charged particles motion and quasiperiodic oscillation in Simpson–Visser spacetime in the presence of external magnetic fields

The present work is devoted to the study of the dynamics of charged particles around Simpson–Visser black holes (with the length parameter lle 2) and wormholes (l>2) immersed in an external asymptotically uniform magnetic field. To do this, first, we solve the Maxwell equation for 4-potentials of the electromagnetic field and show that the difference between the numerical solution and Wald’s solution is small enough to neglect it, which may allow us to use the solution obtained by Wald. We also study fundamental frequencies of in the vertical and radial oscillations of charged particles around circular stable orbits around the magnetized black hole. The effects of the magnetic interaction and length parameters on the fundamental frequencies. We investigate the quasiperiodic oscillations (QPOs) around the black hole in relativistic precession and epicyclic resonance models. It is also shown that the combined effects of magnetic interaction for negatively charged particles and length parameters can mimic the spacetime effects of the Schwarzschild black hole compensating for their effects, as well as the spin of rotating Kerr black holes. The distance between an orbit where a QPO is generated with the ratio of upper and lower frequencies 3: 2 and innermost stable circular orbits is also studied. It is found that the QPO orbits are very close to ISCO in the RP model at l<2. This implies that the obtained result helps to determine the ISCO around black holes. We also study the applications of observed QPOs around stellar-mass black holes in microquasars and supermassive black holes.

Quasiperiodic Oscillations and Dynamics of Test Particles around Quasi- and Non-Schwarzschild Black Holes

One of the open problems in black hole physics is testing spacetime around black holes through astrophysical observations in the strong field regime. In fact, black holes cannot produce radiation themselves in the electromagnetic spectrum. However, a black hole’s gravity plays an important role in the production of the radiation of the accretion disc around it. One may obtain valuable information from the electromagnetic radiation of accretion discs about the gravitational properties of the spacetime around black holes. In this work, we study particle dynamics in the spacetime of quasi- and non-Schwarzschild black holes. We compare the gravitational effects of the spacetime deformation parameters of both black hole solutions on the innermost stable circular orbit (ISCO) radius, position, energy, and angular momentum of test particles at the ISCO, together with the energy efficiency of the accretion disc in the thin Novikov–Thorn model. Furthermore, we study the frequencies of particle oscillations in the radial and angular directions along circular stable orbits around both deformed black holes. Furthermore, we investigate quasiperiodic oscillations around the black holes in the relativistic precession model. We show the dependence of the deviation parameters on the orbits of twin peak QPOs with the frequency ratio 3:2. In the obtained results, we compare the gravitational effects of deviation parameters with the spin of a rotating Kerr black hole. Finally, we obtain constraints on the values of the deviation parameter of the spacetime around the black hole at the center of the microquasars GRO J1655-40 and GRS 1915-105 and their mass, using the χ2 method.

Charged particles and quasiperiodic oscillations around magnetized Schwarzschild black holes

We study the motion of charged particles around Schwarzschild black holes immersed in external (i) asymptotically uniform, (ii) dipolar, and (iii) parabolic-like magnetic fields. The effect of the different magnetic-field configurations on the position of innermost stable circular orbits (ISCOs) for test-charged particles is analyzed. Furthermore, we investigated frequencies of radial and vertical oscillations of the charged particles along their stable circular orbits together with the Keplerian one. As an astrophysical application, we explore quasiperiodic oscillations (QPOs) observed in microquasars sourced by black hole candidates in the frame of the relativistic precession (RP) model. In order to obtain constraints on the values of the magnetic parameter and black hole mass for the microquasars GRO J1655-40 and GRS 1915-105, we use the method so-called chi ^2 in the Bayesian approach. Also, we get constraints on the magnetic field around the black hole in the microquasars by treating electrons and protons as oscillating test-charged particles in the accretion disc. Our performed analyses show that the masses of black hole candidates in the above-mentioned objects and magnetic parameters are different for the uniform and dipolar magnetic field configurations. However, no constraints on the magnetic field and black hole masses are obtained in the case of a parabolic magnetic field configuration. The obtained results on the black hole masses are compared with the measurements in independent astrophysical observations of these black hole masses.

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.

Quasiperiodic oscillations, weak field lensing and shadow cast around black holes in Symmergent gravity

In this work, we performed a systematic study of the Symmergent gravity (SG) in a black hole (BH) environment. Being an emergent gravity model in which gravity emerges to restore the gauge symmetries and stabilize the Higgs boson mass in a way giving a holographic ultraviolet (UV) completion of the underlying quantum field theory, the SG involves the general relativity (GR) plus quadratic-curvature term with a loop-induced coupling c0 being proportional to the boson–fermion number difference. We investigated c0 and other quantities by utilizing the various BHs observations. In this regard, we investigated particle dynamics, obtained Keplerian frequencies describing the harmonic oscillations, and determined quasi periodic oscillations (QPOs) about such orbits by using the relativistic precession (RP), warped disk (WD), and epicyclic resonant (ER) models. We also analyse the BH shadow and determine constraints on the loop parameter c0 from the Event Horizon Telescope (EHT) data for both the static observers and observers co-moving with the cosmological expansion. We explored the weak deflection angle by considering the effect of finite distance and studied the resulting Einstein rings. We conclude the work by giving an overall discussion of the quasiperiodic oscillations, shadow cast, and weak deflection angle, with a mention of future prospects concerning other possible investigations of the SG. We also study weak deflection angle and planetary perihelion shift and determined bounds on the SG parameters. Furthermore, we compute shadow radius for both static and co-moving observers near and far from the Symmergent BH and revealed the sensitivity of these observers to the model parameters. We conclude the work by giving an overall discussion and giving future prospects concerning other possible analyses of the SG.

Black hole mass and spin measurements through the relativistic precession model: XTE J1859+226

ABSTRACT The X-ray light curves of accreting black holes and neutron stars in binary systems show various types of quasi-periodic oscillations (QPOs), the origin of which is still debated. The relativistic precession model identifies the QPO frequencies with fundamental time-scales from General Relativity, and has been proposed as a possible explanation of certain types of such oscillations. Under specific conditions (i.e. the detection of a particular QPOs triplet) such a model can be used to obtain self-consistent measurements of the mass and spin of the compact object. So far this has been possible only in the black hole binary GRO J1655-40. In the RXTE/PCA data from the 1999–2000 outburst of the black hole transient XTE J1859+226 we found a QPO triplet, and used the relativistic precession model to obtain high-precision measurements of the black hole mass and spin – M = (7.85 ± 0.46) M⊙, a* = 0.149 ± 0.005 – the former being consistent with the most recent dynamical mass determination from optical measurements. Similarly to what has been already observed in other black hole systems, the frequencies of the QPOs and broad-band noise components match the general relativistic frequencies of particle motion close to the compact object predicted by the model. Our findings confirm previous results and further support the validity of the relativistic precession model, which is the only electromagnetic-measurement-based method that so far has consistently yielded spins close to those from the gravitational waves produced by merging binary black holes.

A refined dynamical mass for the black hole in the X-ray transient XTE J1859+226

ABSTRACT We present two contiguous nights of simultaneous time-resolved Gran Telescopio Canarias spectroscopy and William Herschel Telescope photometry of the black hole X-ray transient XTE J1859+226, obtained in 2017 July during quiescence. Cross-correlation of the individual spectra against a late K-type spectral template enabled us to constrain the orbital period to 0.276 ± 0.003 d and the radial velocity semi-amplitude of the donor star to K2 = 550 ± 59 km s−1. An ellipsoidal modulation is detected in the photometric r- and i-band light curves, although it is strongly contaminated by flickering activity. By exploiting correlations between the properties of the double-peaked H α emission-line profile and the binary parameters, we derived an orbital inclination of 66.6 ± 4.3 deg, a refined K2 = 562 ± 40 km s−1 and mass ratio q = M2/M1 = 0.07 ± 0.01. From these values, we obtained an updated black hole mass of M1 = 7.8 ± 1.9 M⊙. An independent mass estimate based on X-ray timing agrees well with our value, which gives further support for the outburst quasi-periodic oscillation triplet being explained by the relativistic precession model. We also obtained a companion star mass M2 = 0.55 ± 0.16 M⊙, which is consistent with its K5-K7 V spectral type.

Testing general relativity using quasi-periodic oscillations from X-ray black holes: XTE J1550-564 and GRO J1655-40

ABSTRACT We use the Relativistic Precession Model (RPM) and quasi-periodic oscillation (QPO) observations from the Rossi X-ray Timing Explorer to derive constraints on the properties of the black holes that power these sources and to test general relativity (GR) in the strong field regime. We build upon past techniques by using pairs of simultaneously measured QPOs, rather than triplets, and by including characteristic frequencies from the broad noise components of the power spectra in our fits. We find the inclusion of these broad noise components causes an overestimate in masses and underestimate in spins compared to values derived independently from optical spectra. We extend the underlying space-time metric to constrain potential deviations from the predictions of GR for astrophysical black holes. To do this, we modify the RPM model to a Kerr–Newman–deSitter space-time and model changes in the radial, ecliptic, and vertical frequencies. We compare our models with X-ray data of XTE J1550-564 and GRO J1655-40 using robust statistical techniques to constrain the parameters of the black holes and the deviations from GR. For both sources, using QPO and characteristic frequency data, we constrain particular deviations from GR to be less than one part per thousand.

Constraint on parameters of a rotating black hole in Einstein-bumblebee theory by quasi-periodic oscillations

We have studied quasi-periodic oscillations frequencies in a rotating black hole with Lorentz symmetry breaking parameter in Einstein-bumblebee gravity by relativistic precession model. We find that in the rotating case with non-zero spin parameter both of the periastron and nodal precession frequencies increase with the Lorentz symmetry breaking parameter, but the azimuthal frequency decreases. In the non-rotating black hole case, the nodal precession frequency disappears for arbitrary Lorentz symmetry breaking parameter. With the observation data of GRO J1655-40, XTE J1550-564, and GRS 1915+105, we find that the constraint on the Lorentz symmetry breaking parameter is more precise with data of GRO J1655-40 in which the best-fit value of the Lorentz symmetry breaking parameter is negative. This could lead to that the rotating black hole in Einstein-bumblebee gravity owns the higher Hawking temperature and the stronger Hawking radiation, but the lower possibility of exacting energy by Penrose process. However, in the range of 1 sigma , we also find that general relativity remains to be consistent with the observation data of GRO J1655-40, XTE J1550-564 and GRS 1915+105.

Simple Analytic Formula Relating the Mass and Spin of Accreting Compact Objects to Their Rapid X-Ray Variability

Abstract Following the previous research on epicyclic oscillations of accretion disks around black holes (BHs) and neutron stars (NSs), a new model of high-frequency quasiperiodic oscillations (QPOs) has been proposed, so-called cusp torus (CT) model, which deals with oscillations of fluid in marginally overflowing accretion tori (i.e., tori terminated by cusps). According to preliminary investigations, the model provides better fits of the NS QPO data compared to the relativistic precession (RP) model. It also implies a significantly higher upper limit on the Galactic microquasar BH spins. A short analytic formula has been noticed to well reproduce the model’s predictions on the QPO frequencies in Schwarzschild spacetimes. Here we derive an extended version of this formula that applies to rotating compact objects. We start with the consideration of Kerr spacetimes and derive a formula that is not restricted to a particular specific angular momentum distribution of the inner accretion flow, such as a Keplerian or constant one. Finally, we consider Hartle–Thorne spacetimes and include corrections implied by the NS oblateness. For a particular choice of a single parameter, our relation provides frequencies predicted by the CT model. For another value, it provides frequencies predicted by the RP model. We conclude that the formula is well applicable to rotating oblate NSs and both models. We briefly illustrate the application of our simple formula on several NS sources and confirm the expectation that the CT model is compatible with realistic values of the NS mass and provides better fits of data than the RP model.

Quasiperiodic oscillations from noncommutative inspired black holes

We investigate the dynamics of test particles in the spacetime of noncommutative inspired black holes (NCi BHs). In this context, we first analyse spacetime properties of the NCi BHs together with innermost stable circular orbits (ISCOs) for the particles. It is observed that whereas the ISCO radius does not depend on the NC parameter, the frequencies of the Keplerian orbits and harmonic oscillations are NC parameter dependent. As an application, we consider quasiperiodic oscillations (QPOs) to test effects of the NC gravity around the BHs using twin-peak QPOs frequencies. It is found that the frequency changes even in the presence of the critical NC parameter are smaller than the error in the frequency measurements. The method developed for testing gravity using data from twin peak QPOs may also be applied to other alternate theories of gravity to obtain restrictions on the central BH parameters. We show that the orbits of QPOs lie near ISCO. This assumption may be helpful in solving the ISCO measurement problems in astrophysical observations. In addition, we determine the mass of the central BH in microquasar GRS 1915-105 and the QPO orbit in both the relativistic precession and warped disk models. It is shown that these parameters do not depend on the quantum corrections in the NC gravity. Lastly, we investigate the gravitational capture cross-section for photons and show that the effect of the NC parameter is also less than the error in shadow measurements of the supermassive BH (SMBH) Messier 87 (M87).

Constraints on charged black hole parameters using quasiperiodic oscillations data

Testing gravity theories and constraining their parameters using data from astrophysical observations of quasiperiodic oscillations (QPOs) is a powerful approach to study the features of black holes (BHs) and gravity theories in the strong field regime. To this end, we investigate the dynamics of the test particles in the vicinity of some charged BHs such as Reissner–Nordström (RN), regular Bardeen and Ayon–Beato–Garcia (ABG). In particular, we calculate harmonic oscillations and the innermost stable circular orbits (ISCOs) of test particles around these BHs. As an astrophysical application, we discuss the twin peak QPOs in relativistic precession (RP) model and give the possible values of the upper and lower frequencies of the QPOs at the distance from ISCO to infinity around the extremely charged BHs. Moreover, we also investigate the position of the orbit, where twin peak QPO may take place around central (charged) BH in the microquasar GRS 1915-105. We also study the dependence of the distance between the QPO position and ISCO from the BH charge. Using the upper and lower frequencies of the QPO, we obtain the relationship between the mass and charge of the central BH in the microquasar. Finally, we compare the effects of the spin of the Kerr BH and BH charges on the QPO in microquasar GRS 1915-105. We find that the BH charge can mimic the spin up to [Formula: see text] in the Bardeen model and up to [Formula: see text] in the case of special regular BH, admitting the same QPO frequencies.

Quasi-periodic oscillation around regular Bardeen black holes in 4D Einstein–Gauss–Bonnet gravity

In this paper, we explore the dynamics of test particles in spacetime around regular Bardeen black holes (BHs) in the novel four-dimensional Einstein–Gauss–Bonnet (4D EGB) theory. First, we analyze properties of the spacetime around the Bardeen BH with respect to the Gauss–Bonnet (GB) coupling parameter [Formula: see text], and we show the range of values of the BH charge and the parameter [Formula: see text] that horizon exists as [Formula: see text] and [Formula: see text], respectively. We also investigate the effects of the magnetic charge of the regular BH on innermost stable circular orbits (ISCOs) radius and efficiency of energy release from infalling test particles to the regular Bardeen BH in 4D EGB gravity. Moreover, fundamental frequencies such as Keplerian and harmonic oscillations are also studied with the applications of quasi-periodic oscillations (QPOs) where we proposed a method to test gravity theories through data from astrophysical observations of twin-peak QPOs in relativistic precession (RP) model. Finally, we show the dependence of the distance from the central BH to the orbit where twin-peak QPOs shine from the spin of Kerr BH, magnetic charge of Bardeen and Reissner–Nordström (RN) BHs, and GB coupling parameter.

Testing Kerr black hole mimickers with quasi-periodic oscillations from GRO J1655-40

The measurements of quasi-periodic oscillations (QPOs) provide a quite powerful tool to test the nature of astrophysical black hole candidates in the strong gravitational field regime. In this paper, we use QPOs within the relativistic precession model to test a recently proposed family of rotating black hole mimickers, which reduce to the Kerr metric in a limiting case, and can represent traversable wormholes or regular black holes with one or two horizons, depending on the values of the parameters. In particular, assuming that the compact object of GRO J1655-40 is described by a rotating black hole mimicker, we perform a chi -square analysis to fit the parameters of the mimicker with two sets of observed QPO frequencies from GRO J1655-40. Our results indicate that although the metric around the compact object of GRO J1655-40 is consistent with the Kerr metric, a regular black hole with one horizon is favored by the observation data of GRO J1655-40.

Distinguishing regular and singular black holes in modified gravity

This paper is devoted to investigate the possible ways of distinguishing regular and singular black holes (BHs) in modified gravity (MOG) called regular MOG (RMOG) and Schwarzschild MOG (SMOG) BHs through observational data from twin peak quasiperiodic oscillations (QPOs) which are generated by test particles in stable orbits around the BHs. The presence of MOG field causes to sufficiently the mpeak in effective potential for a radial motion of test particles. The effect of MOG parameter on specific angular momentum and energy has also studied. As a main part of the paper, we focus on investigations of QPOs around SMOG and RMOG BHs in RP model and the relations of upper and lower frequencies of twin peak QPOs in SMOG and RMOG BH models together with extreme rotating Kerr and Schwarzschild BH. Moreover, possible parameters for the central BHs of the objects GRS J1915 + 105 and XTE 1550 – 564 have also obtained numerically in the relativistic precession (RP) model. Finally, we provide comparisons of the innermost stable circular orbit (ISCO) and the orbits where twin peak QPOs with the ratio 3:2 taken place and show that QPOs can not be generated at/inside ISCO and there is a correlation between the radius of ISCO and QPO orbits.

A timing-based estimate of the spin of the black hole in MAXI J1820+070

ABSTRACT MAXI J1820+070 (ASSASN-18ey) is a black hole (BH) X-ray binary discovered in 2018. The brightness of the source triggered multi-wavelength campaigns of this source from different observatories. We analyse the power density spectra (PDS) obtained from NICER high cadence observations of the source in the hard state. We obtain the evolution of the characteristic frequencies by modelling the PDS. We interpret the characteristic frequencies of various PDS components (both QPOs and broad-band noise components) as variability occurring at a particular radius, and explain them in the context of the Relativistic Precession Model (RPM). We estimate the dimensionless spin of the BH at $0.799^{+0.016}_{-0.015}$ by fitting the RPM.