Radial Epicyclic Frequency Research Articles

Mass and spin measurements of black hole and neutron stars X-ray binaries through axisymmetric oscillation modes of thick torus

ABSTRACT This paper examines the oscillatory behaviour of relativistic, non-self-gravitating, charged-fluid toroidal structures within the context of the Kerr metric. The primary objective is to explore how thick accretion discs influence the mass and spin measurements of black holes and neutron stars in low-mass X-ray binaries (LMXBs) through quasi-periodic oscillations (QPOs) models. To achieve this, we conduct a local analysis within a general relativistic framework, determining the radial epicyclic and orbital frequencies in a perfect fluid disc. The tori are modelled using a non-Keplerian distribution of specific angular momentum, and we analyse how the oscillation properties depend on the model’s angular momentum distribution parameters. Subsequently, we connect these oscillatory frequencies to high-frequency QPOs observed in LMXBs, enabling us to calculate the optimal mass and spin values for each studied source.

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.

Epicyclic frequencies for a generic ultracompact object

Recently, it has been shown that the radial stability of a light-ring (LR) in a spacetime generated by a stationary, axisymmetric, asymptotically flat object with a $\mathbb{Z}_2$ symmetry determines the possibility and radial stability of timelike circular orbits (TCOs) around the LR. In this paper, we generalise this result by also considering the vertical (angular) stability of the orbits through the study of the radial and vertical epicyclic frequencies. We show that the vertical stability of the LR only determines the vertical stability of the TCOs around it. A relation between the sum of the squared epicyclic frequencies and the Ricci tensor is also provided. With such relation, we show that objects with radially and vertically unstable LRs (TCOs) violate the null (strong) energy condition.

Hydrodynamical evolution of black-hole binaries embedded in AGN discs

ABSTRACT Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs are possible progenitors of black hole mergers detected in gravitational waves by LIGO/VIRGO. To better understand the hydrodynamical evolution of BBHs interacting with the disc gas, we perform a suite of high-resolution 2D simulations of binaries in local disc (shearing-box) models, considering various binary mass ratios, eccentricities and background disc properties. We use the γ-law equation of state and adopt a robust post-processing treatment to evaluate the mass accretion rate, torque and energy transfer rate on the binary to determine its long-term orbital evolution. We find that circular comparable-mass binaries contract, with an orbital decay rate of a few times the mass doubling rate. Eccentric binaries always experience eccentricity damping. Prograde binaries with higher eccentricities or smaller mass ratios generally have slower orbital decay rates, with some extreme cases exhibiting orbital expansion. The averaged binary mass accretion rate depends on the physical size of the accretor. The accretion flows are highly variable, and the dominant variability frequency is the apparent binary orbital frequency (in the rotating frame around the central massive BH) for circular binaries but gradually shifts to the radial epicyclic frequency as the binary eccentricity increases. Our findings demonstrate that the dynamics of BBHs embedded in AGN discs is quite different from that of isolated binaries in their own circumbinary discs. Furthermore, our results suggest that the hardening time-scales of the binaries are much shorter than their migration time-scales in the disc, for all reasonable binary and disc parameters.

Epicyclic frequencies of spheroidal stars with non-uniform density

ABSTRACT We consider the gravitational potential of a rotating star with non-uniform density to derive the orbital and epicyclic frequencies of the particles orbiting the star. We assume that the star is composed of concentric spheroids of constant density, with a global power-law distribution of density inside the star. At the lowest order approximation, we recover the known result for the Maclaurin spheroid that the maximum in the radial epicyclic frequency occurs at $r=\sqrt{2}ae$, for eccentricities ${\ge} 1/\sqrt{2}$. We find that the nature of these characteristic frequencies differs based on the geometry of the rotating star. For an oblate spheroid, the orbits resemble retrograde Kerr orbits and the location of the radial epicyclic maximum approaches the stellar surface as the density variation inside the star becomes steeper. On the contrary, orbits around a prolate spheroid resemble prograde Kerr orbits, but the marginally stable orbit does not exist for prolate-shaped stars. The orbital frequency is larger (smaller) than the Keplerian value for an oblate (prolate) star with the equality attained as e → 0 or r → ∞. The radial profiles of the angular velocity and the angular momentum allow for a stable accreting disc around any nature of oblate/prolate spheroid.

Dynamics and fundamental frequencies of test particles orbiting Kerr–Newman–NUT–Kiselev black hole in Rastall gravity

The spacetime properties in the exterior of the Kerr–Newman–NUT–Kiselev black hole in the Rastall theory of gravity, through particle dynamics, are investigated with the aim to find possible degeneracy of the different black hole parameters. We show that the effective potential, the energy, and the angular momentum of a test particle moving in the spacetime of such a black hole strongly depend on the central black hole parameters. We also evaluate the innermost stable circular orbit radii of test particles and show how the spacetime parameters can act on them. Further, we show the results for the fundamental frequencies of test particles moving at small distances from the circular orbits in the equatorial plane. We demonstrate that change in the Rastall parameter $$\kappa \lambda $$ can make the radial epicyclic frequency to become zero at larger distances from the central source. We also notice that for the vertical epicyclic frequencies, in the case of the Kerr–Newman–NUT–Kiselev black hole in the Rastall theory of gravity lower frequencies, are observed as compared to the frequencies observed in the case of the Kerr black hole. Finally, we show that for the Kerr–Newman–NUT–Kiselev black hole in the Rastall gravity, the Keplerian frequencies are almost identical with the frequencies noticed in the case of the Kerr black hole and the difference between the two can only be observed in the regions in a very close vicinity to the central black hole, studied in the present work.

Epicyclic oscillations of test particles near marginally stable circular orbits around charged Kiselev black holes

The marginally stable circular orbits (MSCOs) of test particles in the spacetime exterior to a charged Kiselev black hole are investigated for three characteristic values of the equation of state parameter ${\ensuremath{\omega}}_{q}$, namely (i) ${\ensuremath{\omega}}_{q}=\ensuremath{-}1/3$, (ii) ${\ensuremath{\omega}}_{q}=\ensuremath{-}1$, and (iii) ${\ensuremath{\omega}}_{q}=\ensuremath{-}2/3$, and for different values of the normalization factor $\ensuremath{\alpha}$ and electric charge $Q$ of the black hole. It is found that the presence of the quintessence field shifts outward the innermost stable circular orbits (ISCOs) around the Kiselev black hole, having the same charge parameter $Q$, as compared to the ISCOs around a Riessner-Nordstrom black hole, while the effect of the quintessence field on the outermost stable circular orbits (OSCOs) is just opposite to that on the ISCOs. Further, the radii of the photon circular orbits are also calculated for different ranges of the parameters $\ensuremath{\alpha}$ and $Q$. It is observed that the photon orbits are also shifted outward as the value of $\ensuremath{\alpha}$ increases. The radial and latitudinal epicyclic motion of test particles, which can be related to the quasiperiodic oscillations of test particles slightly above the MSCOs in the vicinity of the charged Kiselev black hole, is analyzed for the three different values of ${\ensuremath{\omega}}_{q}$. It is seen that the azimuthal and latitudinal frequencies coincide, and the radial epicyclic frequency is different in dependence on the spacetime parameters. In the case of ${\ensuremath{\omega}}_{q}=\ensuremath{-}1/3$, the azimuthal and latitudinal frequencies depend on the radial position $r$ of the particle, the charge $Q$, and the mass $M$ of the black hole, and do not depend on the factor $\ensuremath{\alpha}$. However, for ${\ensuremath{\omega}}_{q}=\ensuremath{-}2/3$ and ${\ensuremath{\omega}}_{q}=\ensuremath{-}1$, these two frequencies, along with the black hole parameters---i.e., $M$ and $Q$ and the radial position $r$---also depend on the factor $\ensuremath{\alpha}$. The radial epicyclic frequency for all the values of ${\ensuremath{\omega}}_{q}$ depends on $M$, $Q$, $r$, and also on the normalization factor $\ensuremath{\alpha}$. We also compare the epicyclic frequencies with that for an uncharged black hole. With the increase of electric charge, the ISCO becomes closer to the central object, and one can observe epicyclic frequencies closer to the central object, which makes the epicyclic frequencies larger. The ISCO gets larger as $\ensuremath{\alpha}$ increases, and thus the epicyclic frequencies can be observed away from the central object and would be smaller as compared to the case of a pure Riessner-Nordstrom black hole without quintessence. As the effect of the parameters $Q$ and $\ensuremath{\alpha}$ on the OSCOs is just opposite to that on the ISCOs, the epicyclic frequencies near the OSCOs behave the other way around.

Quasiperiodic oscillations in rotating Ellis wormhole spacetimes

We analyze the properties of the circular orbits for massive particles in the equatorial plane of symmetric rotating Ellis wormholes. In particular, we obtain the orbital frequencies and the radial and vertical epicyclic frequencies, and consider their lowest parametric, forced and Keplerian resonances. These show that quasi-periodic oscillations in accretion disks around symmetric rotating Ellis wormholes have many distinct properties as compared to quasi-periodic oscillations in accretion disks around rotating Teo wormholes and the Kerr black hole. Still we can distinguish some common features which appear in wormhole spacetimes as opposed to black holes. The most significant ones include the possibility of excitation of stronger resonances such as lower order parametric and forced resonances and the localization of these resonances deep in the region of strong gravitational interaction near the wormhole throat, which will lead to further amplification of the signal.

Quasiperiodic oscillations from the accretion disk around distorted black holes

We study the quasi-periodic oscillations from the accretion disk around the distorted Schwarzschild black hole in the framework of the resonant models. We confine ourselves to the case of a quadrupole distortion which can be caused for example by the accreting matter flow in the vicinity of the compact object. For the purpose we examine the linear stability of the circular geodesic orbits in the equatorial plane and derive analytical expressions for the radial and vertical epicyclic frequencies. We investigate their properties in comparison with the isolated Schwarzschild black hole. Due to the influence of the external matter the vertical epicyclic frequency is not always positive anymore, and the stability of the circular orbits is determined by the interplay between both of the frequencies. As a result, the stable circular orbits do not extend to infinity, but are confined to a finite annular region between an inner and an outer marginally stable orbit. In addition, the degeneracy between the vertical epicyclic and the orbital frequency, which is characteristic for the Schwarzschild solution, is broken, and there are regions in the parametric space where the radial epicyclic frequency is larger than the vertical one. All these properties allow for much more diverse types of non-linear resonances to be excited than for the isolated Schwarzschild black hole, which can provide an explanation for the observed 3:2 ratio between the twin-peak frequencies of the quasi-periodic oscillations from the accretion disk.

Orbital mechanics and quasiperiodic oscillation resonances of black holes in Einstein-Æther theory

In this paper, we study the motion of test particles around two exact charged black-hole solutions in Einstein-{\AE}ther theory. Specifically, we first consider the quasi-periodic oscillations (QPOs) and their resonances generated by the particle moving in the Einstein-{\AE}ther black hole and then turn to study the periodic orbits of the massive particles. For QPOs, we drop the usually adopted assumptions $\nu_U=\nu_\theta$, $\nu_L=\nu_r$, and $\nu_U/\nu_L=3/2$ with $\nu_U$ ($\nu_L$) and $\nu_r$ ($\nu_\theta$) being the upper (lower) frequency of QPOs and radial (vertical) epicyclic frequency of the orbiting particles, respectively. Instead, we put-forward a new working ansatz for which the Keplerian radius is much closer to that of the innermost stable circular orbit and explore in detail the effects of the {\ae}ther field on the frequencies of QPOs. We then realize good curves for the frequencies of QPOs, which fit to data of three microquasars very well by ignoring any effects of rotation and magnetic fields. The innermost stable circular orbits (isco) of timelike particles are also analyzed and we find the isco radius increases with increasing $c_{13}$ for the first type black hole while decreases with increasing $c_{14}$ for the second one. We also obtain several periodic orbits and find that they share similar taxonomy schemes as the periodic equatorial orbits in the Schwarzschild/Kerr metrics, in addition to exact solutions for certain choices of the Einstein-\AE ther parameters. The equations for null geodesics are also briefly considered, where we study circular photon orbits and bending angles for gravitational lensing.

Relativistic, axisymmetric, viscous, radiation hydrodynamic simulations of geometrically thin discs. II. Disc variability

ABSTRACT An analysis of two-dimensional viscous, radiation hydrodynamic numerical simulations of thin α-discs around a stellar mass black hole reveals multiple robust, coherent oscillations. Our disc models are initialized on both the gas- and radiation-pressure-dominated branches of the thermal equilibrium curve, with mass accretion rates between $\dot{M} = 0.01 L_\mathrm{Edd}/c^2$ and $10\, L_\mathrm{Edd}/c^2$. In the initially radiation-pressure-dominated disc, we confirm the presence of global inertial–acoustic oscillations of frequency slightly above the maximum radial epicyclic one. In the gas-pressure-dominated Schwarzschild-metric models, we find a velocity oscillation occurring at the maximum value of the radial epicyclic frequency, $3.5\times 10^{-3}\, t_\mathrm{g}^{-1}$, which is most likely a trapped fundamental g-mode. For the Kerr-metric, gas-pressure-dominated disc with dimensionless black hole spin parameter a* = 0.5, the mode frequency is well below the epicyclic frequency maximum, thus confirming that this oscillation is a trapped g-mode. Additionally, the total pressure fluctuations in the discs strongly suggest standing-wave p-modes with frequencies below the apparent g-mode frequency, some trapped in the inner disc close to the innermost stable circular orbit (ISCO), others present in the middle/outer parts of the disc. The strongest oscillations occur at the breathing oscillation frequency and are present in all the numerical models we report here, as are weaker velocity oscillations at the vertical epicyclic frequencies. The vertical oscillations show a 3:2 frequency ratio with oscillations occurring approximately at the radial epicyclic frequency, which could be of astrophysical importance in systems with observed twin peak, high-frequency quasi-periodic oscillations.

Study of energy extraction and epicyclic frequencies in Kerr-MOG\xa0(modified gravity) black hole

We investigate the energy extraction by the Penrose process in Kerr-MOG black hole (BH). We derive the gain in energy for Kerr-MOG as ΔE≤1221+11+α-aM2-α1+α11+11+α-aM22-1\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\varDelta {{\\mathcal {E}}} \\le \\frac{1}{2}\\left( \\sqrt{\\frac{2}{1+\\sqrt{\\frac{1}{1+\\alpha }-\\left( \\frac{a}{{{\\mathcal {M}}}}\\right) ^2}} -\\frac{\\alpha }{1+\\alpha } \\frac{1}{\\left( 1+\\sqrt{\\frac{1}{1+\\alpha }-\\left( \\frac{a}{{{\\mathcal {M}}}}\\right) ^2} \\right) ^2}}-1\\right) \\end{aligned}$$\\end{document}where a is spin parameter, alpha is MOG parameter and {{mathcal {M}}} is the Arnowitt–Deser–Misner (ADM) mass parameter. When alpha =0, we obtain the gain in energy for Kerr BH. For extremal Kerr-MOG BH, we determine the maximum gain in energy is varDelta {{mathcal {E}}} le frac{1}{2} left( sqrt{frac{alpha +2}{1+alpha }}-1 right) . We observe that the MOG parameter has a crucial role in the energy extraction process and it is in fact diminishes the value of varDelta {{mathcal {E}}} in contrast with extremal Kerr BH. Moreover, we derive the Wald inequality and the Bardeen–Press–Teukolsky inequality for Kerr-MOG BH in contrast with Kerr BH. Furthermore, we describe the geodesic motion in terms of three fundamental frequencies: the Keplerian angular frequency, the radial epicyclic frequency and the vertical epicyclic frequency. These frequencies could be used as a probe of strong gravity near the black holes.

Viscous driving of global oscillations in accretion discs around black holes

We examine the role played by viscosity in the excitation of global oscillation modes (both axisymmetric and non-axisymmetric) in accretion discs around black holes using two-dimensional hydrodynamic simulations. The turbulent viscosity is modeled by the $\alpha$-ansatz, with different equations of state. We consider both discs with transonic radial inflows across the innermost stable circular orbit, and stationary discs truncated by a reflecting wall at their inner edge, representing a magnetosphere. In transonic discs, viscosity can excite several types of global oscillation modes. These modes are either axisymmetric with frequencies close to multiples of the maximum radial epicyclic frequency $\kappa_\mathrm{max}$, non-axisymmetric with frequencies close to multiples of of the innermost stable orbit frequency $\Omega_\mathrm{ISCO}$, or hybrid modes whose frequencies are linear combinations of these two frequencies. Small values of the viscosity parameter $\alpha$ primarily produce non-axisymmetric modes, while axisymmetric modes become dominant for large $\alpha$. The excitation of these modes may be related to an instability of the sonic point, at which the radial infall speed is equal to the sound speed of the gas. In discs with a reflective inner boundary, we explore the effect of viscosity on trapped $p$-modes which are intrinsically overstable due to the corotation resonance effect. The effect of viscosity is either to reduce the growth rates of these modes, or to completely suppress them and excite a new class of higher frequency modes. The latter requires that the dynamic viscosity scales positively with the disc surface density, indicating that it is a result of the classic viscous overstability effect.

Power density spectra of modes of orbital motion in strongly curved space–time: obtaining the observable signal

High frequency quasi-periodic oscillations (HF QPOs) appear in the X-ray variability of several accreting low-mass binaries. In a series of works it was suggested that these QPOs may have connection to inhomogeneities orbiting close to an inner edge of the accretion disc. In this paper we explore the appearance of an observable signal generated by small radiating circular hot spots moving along quasi-elliptic trajectories close to the innermost stable circular orbit in the Schwarzschild spacetime. Our consideration takes into account the capabilities of observatories that have been operating in the past two decades represented by the Rossi X-ray Timing Explorer (RXTE) and the proposed future instruments represented by the Large Observatory for X-ray Timing (LOFT). For these purposes we choose such model parameters that lead to lightcurves comparable to those observed in Galactic black hole sources, in particular the microquasar GRS 1915+105. We find that when a weak signal corresponding to the hot-spot Keplerian frequency is around the limits of the RXTE detectability, the LOFT observations can clearly reveal its first and second harmonics. Moreover, in some specific situations the radial epicyclic frequency of the spot can be detected as well. Finally, we also compare the signal produced by the spots to the signal produced by axisymmetric epicyclic disc-oscillation modes and discuss the key differences that could be identified via the proposed future technology. We conclude that the ability to recognize the harmonic content of the signal can help to distinguish between the different proposed physical models.

Orbital and epicyclic frequencies of Maclaurin spheroids

We present analytical formulae for the orbital and epicyclic frequencies in orbits around Maclaurin spheroids in Newtonian gravity. The Laplace equation for the gravitational potential implies that the orbital frequency squared is the arithmetic mean of the squares of the epicyclic frequencies, $\omega _r^2 + \omega _z^2 = 2\Omega _{\rm o}^2$. The radial epicyclic frequency has a maximum at radius $r=\sqrt{2}ae$ for spheroid ellipticities $e>1/\sqrt{2}$, while for e = 0.834 583 18 it vanishes at the stellar equator (at r = a). For still larger ellipticities the innermost stable circular orbit (ISCO) is separated from the surface of the spheroid by a gap and has radius r ms = 1.198 203 ae. The vertical epicyclic frequency is always larger than the orbital one, and always by a factor of $\sqrt{2}$ in the marginally stable orbit. The presence of periastron motion, nodal precession (whose sense is the same as in retrograde orbits in the Kerr metric) and of the ISCO makes the properties of orbital motion around Maclaurin spheroids analogous to those in the Kerr metric. We find that the condition for the existence of circular orbits in test-particle motion is $\omega _r^2 + \omega _z^2 >0$, equally for the Maclaurin spheroid and for the Kerr metric.

Corotation resonance and overstable oscillations in black hole accretion discs: general relativistic calculations

We study the dynamics of spiral waves and oscillation modes in relativistic rotating discs around black holes. Generalizing the Newtonian theory, we show that wave absorption can take place at the corotation resonance, where the pattern frequency of the wave matches the background disc rotation rate. We derive the general relativistic expression for the disc vortensity (vorticity divided by surface density), which governs the behaviour of density perturbation near corotation. Depending on the gradient of the generalized disc vortensity, corotational wave absorption can lead to the amplification or damping of the spiral wave. We apply our general theory of relativistic wave dynamics to calculate the non-axisymmetric inertial-acoustic modes (also called p-modes) trapped in the inner-most region of a black hole accretion disc. Because general relativity changes the profiles of the radial epicyclic frequency and disc vortensity near the inner disc edge close to the black hole, these p-modes can become overstable under appropriate conditions. We present the numerical results of the frequencies and growth rates of p-modes for various black hole spin and model disc parameters (the surface density profile and sound speed), and discuss their implications for understanding the enigmatic high-frequency quasi-periodic oscillations observed in black hole X-ray binaries.

Hidden symmetries and geodesics of Kerr spacetime in Kaluza-Klein theory

The Kerr spacetime in Kaluza-Klein theory describes a rotating black hole in four dimensions from the Kaluza-Klein point of view and involves the signature of an extra dimension that shows up through the appearance of the electric and dilaton charges. In this paper, we study the separability properties of the Hamilton-Jacobi equation for geodesics and the associated hidden symmetries in the spacetime of the Kerr-Kaluza-Klein black hole. We show that the complete separation of variables occurs only for massless geodesics, implying the existence of hidden symmetries generated by a second rank conformal Killing tensor. Employing a simple procedure built up on an "effective" metric, which is conformally related to the original spacetime metric and admits a complete separability structure, we construct the explicit expression for the conformal Killing tensor. Next, we study the properties of the geodesic motion in the equatorial plane, focusing on the cases of static and rotating Kaluza-Klein black holes separately. In both cases, we obtain the defining equations for the boundaries of the regions of existence, boundedness and stability of the circular orbits as well as the analytical formulas for the orbital frequency, the radial and vertical epicyclic frequencies of the geodesic motion. Performing a detailed numerical analysis of these equations and frequencies, we show that the physical effect of the extra dimension amounts to the significant enlarging of the regions of existence, boundedness and stability towards the event horizon, regardless of the classes of orbits.

Strong gravity effects of rotating black holes: quasi-periodic oscillations

We explore strong gravity effects of the geodesic motion in the spacetime of rotating black holes in general relativity and braneworld gravity. We focus on the description of the motion in terms of three fundamental frequencies: the orbital frequency, the radial and vertical epicyclic frequencies. For a Kerr black hole, we perform a detailed numerical analysis of these frequencies at the innermost stable circular orbits and beyond them as well as at the characteristic stable orbits, at which the radial epicyclic frequency attains its highest value. We find that the values of the epicyclic frequencies for a class of stable orbits exhibit good qualitative agreement with the observed frequencies of the twin peaks quasi-periodic oscillations (QPOs) in some black hole binaries. We also find that at the characteristic stable circular orbits, where the radial (or the vertical) epicyclic frequency has maxima, the vertical and radial epicyclic frequencies exhibit an approximate 2:1 ratio even in the case of near-extreme rotation of the black hole. Next, we perform a similar analysis of the fundamental frequencies for a rotating braneworld black hole and argue that the existence of such a black hole with a negative tidal charge, whose angular momentum exceeds the Kerr bound in general relativity, does not confront with the observations of high-frequency QPOs.

Observational phenomena related to primordial Kerr superspinars

String theory indicates the existence of primordial Kerr superspinars, extremely compact objects with exterior described by the Kerr naked-singularity geometry. The primordial superspinars have to be converted to a black hole due to accretion, but they could survive to the era of high-redshift quasars. We discuss observational phenomena caused by the primordial Kerr superspinars in this era, considering the properties of corotating Keplerian accretion discs orbiting such superspinars and the optical phenomena modified by their presence. The potential well around a near-extreme superspinar with spin a very close to the extreme black hole value a = 1 is very deep so that the efficiency of the accretion process reaches 157.7%, influencing thus significantly the spectral continuum of corotating Keplerian discs and giving a signature of near-extreme superspinars. Such superspinars can also serve as an efficient accelerator for extremely high-energy collisions. Phenomena enabling a clear distinction of primordial Kerr superspinars and black holes are related to the disc oscillations with the radial and vertical epicyclic frequencies and the most profound could be differences implied by the profiled spectral lines generated in the innermost parts of the corotating Keplerian discs.

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

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