Oscillation modes of relativistic slender tori

Accretion flows with pressure gradients permit the existence of standing waves which may be responsible for observed quasi-periodic oscillations (QPO's) in X-ray binaries. We present a comprehensive treatment of the linear modes of a hydrodynamic, non-self-gravitating, polytropic slender torus, with arbitrary specific angular momentum distribution, orbiting in an arbitrary axisymmetric space–time with reflection symmetry. We discuss the physical nature of the modes, present general analytic expressions and illustrations for those which are low order, and show that they can be excited in numerical simulations of relativistic tori. The mode oscillation spectrum simplifies dramatically for near Keplerian angular momentum distributions, which appear to be generic in global simulations of the magnetorotational instability. We discuss our results in light of observations of high frequency QPO's, and point out the existence of a new pair of modes which can be in an approximate 3:2 ratio for arbitrary black hole spins and angular momentum distributions, provided the torus is radiation pressure dominated. This mode pair consists of the axisymmetric vertical epicyclic mode and the lowest order axisymmetric breathing mode.     

On an excitation mechanism for trapped inertial waves in discs around black holes

According to one model, high-frequency quasi-periodic oscillations (QPOs) can be identified with inertial waves, trapped in the inner regions of accretion discs around black holes due to relativistic effects. In order to be detected, their amplitudes need to reach large enough values via some excitation mechanism. We work out in detail a non-linear coupling mechanism suggested by Kato, in which a global warping or eccentricity of the disc has a fundamental role. These large-scale deformations combine with trapped modes to generate 'intermediate' waves of negative energy that are damped as they approach either their corotation resonance or the inner edge of the disc, resulting in amplification of the trapped waves. We determine the growth rates of the inertial modes, as well as their dependence on the spin of the black hole and the properties of the disc. Our results indicate that this coupling mechanism can provide an efficient excitation of trapped inertial waves, provided the global deformations reach the inner part of the disc with non-negligible amplitude.     

Resonant Oscillations of Accretion Flow and Khz QPOS

High-frequency quasi-periodic variations (HF QPOs) in the X-ray light curves of black hole X-ray novae can be understood as oscillations of the accretion disk in a nonlinear 3:2 resonance. An m = 0 vertical oscillation near a black hole modulates the X-ray emission through gravitational lensing (light-bending) at the source. Certain oscillations of the accretion disk will also modulate the mass accretion rate, and in neutron-star systems this would lead to nearly periodic variations in brightness of the luminous boundary layer on the stellar surface – the amplitude of the neutron-star HF QPOs would be thus increased relative to the black hole systems. The “kHz QPOs” in black holes are in the hecto-Hz range.     

The runaway instability of self-gravitating tori with non-constant specific angular momentum around black holes

We discuss the runaway instability of axisymmetric tori with non-constant specific angular momentum around black holes, taking into account self-gravity of the tori. The distribution of specific angular momentum of the tori is assumed to be a positive power law with respect to the distance from the rotational axis. By employing the pseudo-Newtonian potential for the gravity of the spherical black hole, we have found that self-gravity of the tori causes a runaway instability if the amount of the mass which is transferred from the torus to the black hole exceeds a critical value, i.e. 3 per cent of the mass of the torus. This has been shown by two different approaches: (1) by using equilibrium models and (2) by dynamical simulations. In particular, dynamical simulations using an SPH code have been carried out for both self-gravitating and non-self-gravitating tori. For non-self-gravitating models, all tori are runaway stable. Therefore we come to the conclusion that self-gravity of the tori has a stronger destabilizing effect than the stabilizing effect of the positive power-law distribution of the angular momentum.     

Quasi-periodic oscillations in low-mass X-ray binaries and constraints on the equation of state of neutron star matter

Recently discovered quasi-periodic oscillations in the X-ray brightness of low-mass X-ray binaries are used to derive constraints on the mass of the neutron star component and the equation of state of neutron star matter. The observations are compared with models of rapidly rotating neutron stars which are calculated by means of an exact numerical method in full relativity. For the equations of state we select a broad collection of models representing different assumptions about the many-body structure and the complexity of the composition of superdense matter. The mass constraints differ from their values in the approximate treatment by ∼10 per cent. Under the assumption that the maximum frequency of the quasi-periodic oscillations originates from the innermost stable orbit, the mass of the neutron star is in the range M ∼1.92–2.25 M_⊙. The quasi-periodic oscillation in the Atoll-source 4U 1820−30 in particular is only consistent with equations of state that are rather stiff at high densities, which is explainable, so far, only with pure nucleonic/leptonic composition. This interpretation contradicts the hypothesis that the protoneutron star formed in SN 1987A collapsed to a black hole, since this would demand a maximum neutron star mass below 1.6 M_⊙. The recently suggested identification of quasi-periodic oscillations with frequencies of about 10 Hz with the Lense–Thirring precession of the accretion disc is found to be inconsistent with the models studied in this work, unless it is assumed that the first overtone of the precession is observed.     

Studies of accretion flows around rotating black holes – III. Shock oscillations and an estimation of the spin parameter from QPO frequencies

In the present communication of our series of papers dealing with the accretion flows in the pseudo-Kerr geometry, we discuss the effects of viscosity on the accretion flow around a rotating black hole. We find the solution topologies and give special attention to the solutions containing shocks. We draw the parameter space where standing shocks are possible and where the shocks could be oscillating and could produce quasi-periodic oscillations (QPOs) of X-rays observed from black hole candidates. In this model, the extreme locations of the shocks give the upper limits of the QPO frequencies  (ν_QPO)  which could be observed. We show that both the viscosity of the flow and the spin of the black hole a increase the QPO frequency while, as expected, the black hole mass reduces the QPO frequencies. Our major conclusion is that the highest observed frequency gives a strict lower limit of the spin. For instance, a black hole exhibiting  ν_QPO∼ 400  and  700 Hz  must have the spin parameters of   a > 0.25  and  >0.75  , respectively, provided viscosity of the flow is small. We discuss the implications of our results in the light of observations of QPOs from black hole candidates.     

Warp and eccentricity propagation in discs around black holes

We consider the inward propagation of warping and eccentric disturbances in discs around black holes under a wide variety of conditions. In our calculations, we use secular theories of warped and eccentric discs and assume the deformations to be stationary and propagating in a disc model similar to regions (a) and (b) of Shakura & Sunyaev discs. We find that the propagation of deformations to the innermost regions of the disc is facilitated for low viscous damping and high accretion rate. We relate our results to the possible excitation of trapped inertial modes, and to the observations of high-frequency quasi-periodic oscillations (QPOs) in black hole systems in the very high spectral state.     

Dissipative accretion flows around a rotating black hole

We study the dynamical structure of a cooling dominated rotating accretion flow around a spinning black hole. We show that non-linear phenomena such as shock waves can be studied in terms of only three flow parameters, namely the specific energy     , the specific angular momentum (λ) and the accretion rate     of the flow. We present all possible accretion solutions. We find that a significant region of the parameter space in the     plane allows global accretion shock solutions. The effective area of the parameter space for which the Rankine–Hugoniot shocks are possible is maximum when the flow is dissipation-free. It decreases with the increase of cooling effects and finally disappears when the cooling is high enough. We show that shock forms further away when the black hole is rotating compared to the solution around a Schwarzschild black hole with identical flow parameters at a large distance. However, in a normalized sense, the flow parameters for which the shocks form around the rotating black holes are produced shocks closer to the black hole. The location of the shock is also dictated by the cooling efficiency in that higher the accretion rate     , the closer is the shock location. We believe that some of the high-frequency quasi-periodic oscillations may be due to the flows with higher accretion rate around the rotating black holes.     

Magnetized tori around Kerr black holes: analytic solutions with a toroidal magnetic field

The dynamics of accretion discs around galactic and extragalactic black holes may be influenced by their magnetic field. In this paper, we generalize the fully relativistic theory of stationary axisymmetric tori in Kerr metric of Abramowicz, Jaroszynski & Sikora by including strong toroidal magnetic field and construct analytic solutions for barotropic tori with constant angular momentum. This development is particularly important for the general relativistic computational magnetohydrodynamics that suffers from the lack of exact analytic solutions that are needed to test computer codes.     

On the source of quasi-periodic oscillations of the black hole candidate GRS 1915+105: some new observations and their interpretation

A few classes of the light curve of the black hole candidate GRS 1915+105 have been analysed in detail. We discover that unlike the previous findings, quasi-periodic oscillations (QPOs) occasionally occur even in the so-called 'On' or softer states. Such findings may require a revision of the accretion/wind scenario of the black hole candidates. We conjecture that considerable winds that are produced in 'Off' states cool down as a result of Comptonization and fall back to the disc, creating an excess accretion rate and producing the so-called 'On' state. After the drainage of the excess matter, the disc goes back to the 'Off' state. Our findings strengthen the shock oscillation model for QPOs.     

Evolution of black hole intermediate-mass X-ray binaries: the influence of a circumbinary disc

We report the results of a systematic timing analysis of RXTE observations of GRS 1915+105 when the source was in its variability class θ, characterized by alternating soft and hard states on a time-scale of a few hundred seconds. The aim was to examine the high-frequency part of the power spectrum in order to confirm the hectohertz quasi-periodic oscillations (QPO) previously reported from observations from mixed variability behaviours. During the hard intervals (corresponding to state C in the classification of Belloni et al.), we find a significant QPO at a frequency of ∼170 Hz, although much broader (Q∼2) than previously reported. No other significant peak is observed at frequencies >30 Hz. A time-resolved spectral analysis of selected observations shows that the hard intervals from class θ show a stronger and steeper  (Γ= 2.8–3.0)  power-law component than hard intervals from other classes. We discuss these results in the framework of hectohertz QPOs reported from GRS 1915+105 and other black hole binaries.     

The jet power extracted from a magnetized accretion disc

We consider the power of a relativistic jet accelerated by the magnetic field of an accretion disc. It is found that the power extracted from the disc is mainly determined by the field strength and configuration of the field far from the disc. Comparing it with the power extracted from a rotating black hole, we find that the jet power extracted from a disc can dominate over that from the rotating black hole. However, in some cases, the jet power extracted from a rapidly rotating hole can be more important than that from the disc, even if the poloidal field threading the hole is not significantly larger than that threading the inner edge of the disc. The results imply that the radio-loudness of quasars may be governed by its accretion rate, which might be regulated by the central black hole mass. It is proposed that the different disc field generation mechanisms might be tested against observations of radio-loud quasars if their black hole masses are available.     

The runaway instability of thick discs around black holes I. The constant angular momentum case

We present results from a numerical study of the runaway instability of thick discs around black holes. This instability is an important issue for most models of cosmic gamma-ray bursts, where the central engine responsible for the initial energy release is such a system consisting of a thick disc surrounding a black hole. We have carried out a comprehensive number of time-dependent simulations aimed at exploring the appearance of the instability. Our study has been performed using a fully relativistic hydrodynamics code. The general relativistic hydrodynamic equations are formulated as a hyperbolic flux-conservative system and solved using a suitable Godunov-type scheme. We build a series of constant angular momentum discs around a Schwarzschild black hole. Furthermore, the self-gravity of the disc is neglected and the evolution of the central black hole is assumed to be that of a sequence of exact Schwarzschild black holes of varying mass. The black hole mass increase is thus determined by the mass accretion rate across the event horizon. In agreement with previous studies based on stationary models, we find that by allowing the mass of the black hole to grow the disc becomes unstable. Our hydrodynamical simulations show that for all disc-to-hole mass ratios considered (between 1 and 0.05), the runaway instability appears very fast on a dynamical time-scale of a few orbital periods, typically a few 10 ms and never exceeding 1 s for our particular choice of the mass of the black hole (2.5 M) and a large range of mass fluxes  ( m 10^-3 M s^-1)  . The implications of our results in the context of gamma-ray bursts are briefly discussed.     

Comptonization and QPO origins in accreting neutron star systems

We develop a simple, time-dependent Comptonization model to probe the origins of spectral variability in accreting neutron star systems. In the model, soft 'seed photons' are injected into a corona of hot electrons, where they are Compton upscattered before escaping as hard X-rays. The model describes how the hard X-ray spectrum varies when the properties of either the soft photon source or the Comptonizing medium undergo small oscillations. Observations of the resulting spectral modulations can determine whether the variability is due to (i) oscillations in the injection of seed photons, (ii) oscillations in the coronal electron density, or (iii) oscillations in the coronal energy dissipation rate. Identifying the origin of spectral variability should help clarify how the corona operates and its relation to the accretion disc. It will also help in finding the mechanisms underlying the various quasi-periodic oscillations (QPOs) observed in the X-ray outputs of many accreting neutron star and black hole systems. As a sample application of our model, we analyse a kilohertz QPO observed in the atoll source 4U 1608–52. We find that the QPO is driven predominantly by an oscillation in the electron density of the Comptonizing gas.     

Weighing the black holes in ultraluminous X-ray sources through timing

We describe a new method to estimate the mass of black holes in Ultraluminous X-ray Sources (ULXs). The method is based on the recently discovered 'variability plane', populated by Galactic stellar-mass black-hole candidates (BHCs) and supermassive active galactic nuclei (AGNs), in the parameter space defined by the black-hole mass, accretion rate and characteristic frequency. We apply this method to the two ULXs from which low-frequency quasi-periodic oscillations have been discovered, M82 X-1 and NGC 5408 X-1. For both sources we obtain a black-hole mass in the range  100–1300 M_⊙  , thus providing evidence for these two sources to host an intermediate-mass black hole.     

Magnetic connection and current distribution in black hole accretion discs

We discuss one of the possible origins of large-scale magnetic fields based on a continuous distribution of toroidal electric current flowing in the inner region of the disc around a Kerr black hole (BH) in the framework of general relativity. It turns out that four types of configuration of the magnetic connection (MC) are generated, i.e. MC of the BH with the remote astrophysical load (MCHL), MC of the BH with the disc (MCHD), MC of the plunging region with the disc (MCPD) and MC of the inner and outer disc regions (MCDD). It turns out that the Blandford–Znajek process can be regarded as one type of MC, i.e. MCHL. In addition, we propose a scenario for fitting the quasi-periodic oscillations in BH binaries based on MCDD associated with the magnetic reconnection.     

Equations of general relativistic radiation hydrodynamics in Kerr space–time

Equations of fully general relativistic radiation hydrodynamics in Kerr space–time are derived. While the interactions between matter and radiation are introduced in the comoving frame, the derivatives used when describing the global evolutions of both the matter and the radiation are given in the Boyer–Lindquist frame (BLF) which is a frame fixed to the coordinate describing the central black hole. Around a rotating black hole, both the matter and the radiation are influenced by the frame-dragging effects due to the black hole's rotation. As a fixed frame, we use the locally non-rotating reference frame (LNRF) which is one of the orthonormal frame. While the special relativistic effects such as beaming effects are introduced by the Lorentz transformation connecting the comoving frame and the LNRF, the general relativistic effects such as frame dragging and gravitational redshift are introduced by the tetrads connecting the LNRF and the BLF.     

吸积盘物理:稳定性和振动

研究了环绕致密天体的吸积盘的稳定性质和振动模式。特别关注了在热致和粘滞扰动作用下稳定的对流起支配作用的盘外流。还研究了相对论性吸积盘的振动模式。一些在盘内的捕获的 ,非衰减的模式也许可以用来解释X射线双星和活动星系核中所观测到的准周期振动。     

A short review of relativistic iron lines from stellar‐mass black holes

In this contribution, I briefly review recent progress in detecting and measuring the properties of relativistic iron lines observed in stellar‐mass black hole systems, and the aspects of these lines that are most relevant to studies of similar lines in Seyfert‐1 AGN. In particular, the lines observed in stellar‐mass black holes are not complicated by complex low‐energy absorption or partial‐covering of the central engine, and strong lines are largely independent of the model used to fit the underlying broad‐band continuum flux. Indeed, relativistic iron lines are the most robust diagnostic of black hole spin that is presently available to observers, with specific advantages over the systematics–plagued disk continuum. If accretion onto stellar‐mass black holes simply scales with mass, then the widespread nature of lines in stellar‐mass black holes may indicate that lines should be common in Seyfert‐1 AGN, though perhaps harder to detect. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-axisymmetric relativistic Bondi–Hoyle accretion on to a Schwarzschild black hole

We present the results of an exhaustive numerical study of fully relativistic non-axisymmetric Bondi–Hoyle accretion on to a moving Schwarzschild black hole. We have solved the equations of general relativistic hydrodynamics with a high-resolution shock-capturing numerical scheme based on a linearized Riemann solver. The numerical code was previously used to study axisymmetric flow configurations past a Schwarzschild black hole. We have analysed and discussed the flow morphology for a sample of asymptotically high Mach number models. The results of this work reveal that initially asymptotic uniform flows always accrete on to the hole in a stationary way, which closely resembles the previous axisymmetric patterns. This is in contrast with some Newtonian numerical studies where violent flip-flop instabilities were found. As discussed in the text, the reason can be found in the initial conditions used in the relativistic regime, as they cannot exactly duplicate the previous Newtonian setups where the instability appeared. The dependence of the final solution on the inner boundary condition as well as on the grid resolution has also been studied. Finally, we have computed the accretion rates of mass and linear and angular momentum.