Effective sound speed in relativistic accretion discs around Schwarzschild black holes

For low angular momentum axially symmetric accretion flow maintained in hydrostatic equilibrium along the vertical direction, the value of the Mach number at the critical points deviates from unity, resulting in the non-isomorphism of the critical and the sonic points. This introduces several undesirable complexities while analytically dealing with the stationary integral accretion solutions and the corresponding phase portraits. We propose that the introduction of an effective dynamical sound speed may resolve the issue in an elegant way. We linear perturb the full spacetime-dependent general relativistic Euler and the continuity equations governing the structure and the dynamics of accretion disc in vertical equilibrium around Schwarzschild black holes and identify the sonic metric embedded within the stationary background flow. Such metric describes the propagation of the linear acoustic perturbation inside the accretion flow. We construct the wave equation corresponding to that acoustic perturbation and find the speed of propagation of such perturbation. We finally show that the ordinary thermodynamic sound speed should be substituted by the speed of propagation of the linear acoustic wave which has been obtained through the dynamical perturbation. Such substitution will make the value of Mach number at the critical point to be equal to unity. Use of the aforementioned effective sound speed will lead to a modified stationary disc structure where the critical and the sonic points will be identical.     

The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion

Using mathematical formalism borrowed from dynamical systems theory, a complete analytical investigation of the critical behaviour of stationary flows in low angular momentum axisymmetric black hole accretion, provides significant insight about the nature of the phase trajectories corresponding to transonic accretion in the steady state, without taking recourse to any explicit numerical method commonly reported in the literature on multi-transonic black hole accretion discs and related astrophysical phenomena. Investigation of an accretion process around a non-rotating black hole, forming different geometrical configurations of the flow structure under the influence of various pseudo-Schwarzschild potentials, reveals that the general profile of the parameter space divisions describing multi-critical accretion, is roughly equivalent for various flow geometries. However, a mere variation of the polytropic index of the flow cannot map a critical solution from one flow geometry to another, since the numerical domain of the parameter space responsible for producing multi-critical accretion does not undergo a continuous transformation in multi-dimensional parameter space. The stationary configuration used to demonstrate the aforementioned findings is shown to be stable under time-dependent linearised perturbations for all kinds of flow geometries, driven by any pseudo-Schwarzschild potential, and using a standard equation of state. Finally, the structure of the acoustic metric corresponding to the propagation of the linear perturbation is discussed for various flow geometries used.     

Black hole spin dependence of general relativistic multi-transonic accretion close to the horizon

We introduce a novel formalism to investigate the role of the spin angular momentum of astrophysical black holes in influencing the behavior of low angular momentum general relativistic accretion. We propose a metric independent analysis of axisymmetric general relativistic flow, and consequently formulate the space and time dependent equations describing the general relativistic hydrodynamic accretion flow in the Kerr metric. The associated stationary critical solutions for such flow equations are provided and the stability of the stationary transonic configuration is examined using an elegant linear perturbation technique. We examine the properties of infalling material for both prograde and retrograde accretion as a function of the Kerr parameter at extremely close proximity to the event horizon. Our formalism can be used to identify a new spectral signature of black hole spin, and has the potential of performing the black hole shadow imaging corresponding to the low angular momentum accretion flow.     

Spectral properties of the accretion discs around rotating black holes

We study the radiation properties of an accretion disc around a rotating black hole. We solve the hydrodynamic equations and calculate the transonic solutions of accretion disc in the presence of shocks. Then we use these solutions to generate the radiation spectrum in the presence of radiative heating and cooling processes. We present the effect of spin parameter of the black hole on the emitted radiation spectrum. In addition, attention has also been paid to the variation in energy spectral index with Kerr parameter and accretion rate. We find that spectral index becomes harder as the spin parameter changes from negative (accretion disc is counter-rotating with respect to the black hole spin) to a positive value. Finally, we compute and compare the spectral characteristics due to a free-fall flow and a transonic flow. We notice significant differences in high energy contributions from these two solutions.     

A model of magnetically induced disc–corona for black hole binaries

We propose a model of magnetic connection (MC) of a black hole with its surrounding accretion disc based on large-scale magnetic field. The MC gives rise to transport of energy and angular momentum between the black hole and the disc, and the closed field lines pipe the hot matter evaporated from the disc, and shape it in the corona above the disc to form a magnetically induced disc–corona system, in which the corona has the same configuration as the large-scale magnetic field. We numerically solve the dynamic equations in the context of the Kerr metric, in which the large-scale magnetic field is determined by dynamo process and equipartition between magnetic pressure and gas pressure. Thus we can obtain a global solution rather than assuming the distribution of large-scale magnetic field beforehand. The main MC effects lie in three aspects. (1) The rotational energy of a fast-spinning black hole can be extracted, enhancing the dissipation in the accretion disc, (2) the closed field lines provide a natural channel for corona matter escaping from disc and finally falling into black hole and (3) the scope of the corona can be bounded by the conservation of magnetic flux. We simulate the high-energy spectra of this system by using Monte Carlo method, and find that the relative hardness of the spectra decreases as accretion rate or black hole spin a _* increases. We fit the typical X-ray spectra of three black hole binaries  (GRO J1655−40, XTE 1118+480 and GX 339−4)  in the low/hard or very high state.     

The evolution of misaligned accretion discs and spinning black holes

In this paper, we consider the process of alignment of a spinning black hole and a surrounding misaligned accretion disc. We use a simplified set of equations, that describe the evolution of the system in the case where the propagation of warping disturbances in the accretion disc occurs diffusively, a situation likely to be common in the thin discs in active galactic nuclei (AGN). We also allow the direction of the hole spin to move under the action of the disc torques. In such a way, the evolution of the hole–disc system is computed self-consistently. We consider a number of different situations and we explore the relevant parameter range, by varying the location of the warp radius R _w and the propagation speed of the warp. We find that the dissipation associated with the twisting of the disc results in a large increase in the accretion rate through the disc, so that AGN accreting from a misaligned disc are likely to be significantly more luminous than those accreting from a flat disc. We compute explicitly the time-scales for the warping of the disc and for the alignment process and compare our results with earlier estimates based on simplified steady-state solutions. We also confirm earlier predictions that, under appropriate circumstances, accretion can proceed in a counter-aligned fashion, so that the accreted material will spin-down the hole, rather than spinning it up. Our results have implication in a number of different observational features of AGN such as the orientation and shape of jets, the shape of X-ray iron lines and the possibility of obscuration and absorption of X-ray by the outer disc as well as the general issue of the spin history of black holes during their growth.     

Critical properties of spherically symmetric accretion in a fractal medium

Spherically symmetric transonic accretion of a fractal medium has been studied in both the stationary and the dynamic regimes. The stationary transonic solution is greatly sensitive to infinitesimal deviations in the outer boundary condition, but the flow becomes transonic and stable when its evolution is followed through time. The evolution towards transonicity is more pronounced for a fractal medium than it is for a continuum, and in the former case the static sonic condition is met on relatively larger length scales. The dynamic approach also shows that there is a remarkable closeness between an equation  of motion for a perturbation in the flow, and the metric of an analogue acoustic black hole. The stationary inflow solutions of a fractal medium are as much stable under the influence of linearized perturbations as they are for the fluid continuum.     

Is the Bardeen–Petterson effect responsible for the warping and precession in NGC 4258?

Strong evidence for the presence of a warped Keplerian accretion disc in NGC 4258 (M 106) has been inferred from the kinematics of water masers detected at subparsec scales. Assuming a power-law accretion disc and using constraints on the disc parameters derived from observational data, we have analysed the relativistic Bardeen–Petterson effect driven by a Kerr black hole as the potential physical mechanism responsible for the disc warping. We found that the Bardeen–Petterson radius is comparable to or smaller than the inner radius of the maser disc (independent of the allowed value for the black hole spin parameter). Numerical simulations for a wide range of physical conditions have shown that the evolution of a misaligned disc due to the Bardeen–Petterson torques usually produces an inner flat disc and a warped transition region with a smooth gradient in the tilt and twist angles. Since this structure is similar to that seen in NGC 4258, we propose that the Bardeen–Petterson effect may be responsible for the disc warping in this galaxy. We estimated the time-scale necessary for the disc inside of the Bardeen–Petterson radius to align with the black hole's equator, as a function of the black hole spin. Our results show that the Bardeen–Petterson effect can align the disc within a few billion years in the case of NGC 4258. Finally, we show that if the observed curvature of the outer anomalous arms in the galactic disc of NGC 4258 is associated with the precession of its radio jet/counterjet, then the Bardeen–Petterson effect can provide the required precession period.     

An introduction to the theory of internal structure of supermassive compact celestial bodies

Different in principle from the contemporary standard black hole accretion models, a new approach to the understanding of the internal structure of highly compact stationary supermassive celestial bodies has been worked out. The equations of equilibrium configurations of baryonic protomatter (ECBP) have been discussed. In a particular case of ideal degenerated neutron gas in absence of a process of inner distortion of the space and time, it has been shown that the theory suggested by Ter-Kazarian (1989c) leads to the same results as those obtained by Oppenheimer and Volkoff (1939) based on Einstein's theory. The numerical integration of equations of ECBP in the most simple case of equilibrium single-component configurations of degenerated ideal gas of neutrons in a presence of one-dimensional space-like inner distortion of space-time continuum is carried out. It has been shown that the stable stationary supermassive cores are formed in the central parts of the considered configurations. As the models of active galactic nuclei (AGNs) one has considered only the configurations that consisted of these cores surrounded by accretion disks. The fundamental difference from the standard black-hole accretion models is the fact that the central cores are in a stable equilibrium state with certain radial distributions of density and pressure and with a number of integral characteristics. The significant effect of metric singularity cut-off has been established, due to the action of which a singularity of metric ceased to be significant. The numerous integrations have also revealed the other fact of great importance, the presence within the outlined theory of a rigorous restriction on the upper limit of possible values of total masses of considered equilibrium configurations, which is to beM3.5×10⁸ M . In the last section one has proceeded to the direct modelling of concrete AGNs (for 61 sources), the whole point of which comes to the solving of the inverse problem. The results of all calculations that have been carried out in the present work are summarized in Tables I–VII and represented by means of numerous figures. Finally, one should emphasize the important fact of the existence of BL Lac objects OJ 287, 3C 66A, and B2 1308+32, the observed time-scale for flux variations of which are inconsistent with contemporary black hole aceretion models. The case is quite different within the scope of the suggested theory. It seems that a decisive significance for these objects has the action of metric singularity cut-off effect. Due to this their observed sizes are less than the sizes of corresponding spheres of the event horizon. This may serve as a further indication that the suggested theory is preferable to the standard models.     

Application of a relativistic accretion disc model to X-ray spectra of LMC X-1 and GRO J1655-40

We present a general relativistic accretion disc model and its application to the soft-state X-ray spectra of black hole binaries. The model assumes a flat, optically thick disc around a rotating Kerr black hole. The disc locally radiates away the dissipated energy as a blackbody. Special and general relativistic effects influencing photons emitted by the disc are taken into account. The emerging spectrum, as seen by a distant observer, is parametrized by the black hole mass and spin, the accretion rate, the disc inclination angle and the inner disc radius.
We fit the ASCA soft-state X-ray spectra of LMC X-1 and GRO J1655-40 by this model. We find that, having additional limits on the black hole mass and inclination angle from optical/UV observations, we can constrain the black hole spin from X-ray data. In LMC X-1 the constraint is weak, and we can only rule out the maximally rotating black hole. In GRO J1655-40 we can limit the spin much better, and we find 0.68 a 0.88 . Accretion discs in both sources are radiation-pressure dominated. We do not find Compton reflection features in the spectra of any of these objects.     

Jet disc coupling in black hole binaries

In the last decade multi-wavelength observations have demonstrated the importance of jets in the energy output of accreting black hole binaries. The observed correlations between the presence of a jet and the state of the accretion flow provide important information on the coupling between accretion and ejection processes. After a brief review of the properties of black hole binaries, I illustrate the connection between accretion and ejection through two particularly interesting examples. First, an INTEGRAL observation of Cygnus X-1 during a ‘mini-’ state transition reveals disc jet coupling on time scales of orders of hours. Second, the black hole XTEJ1118+480 shows complex correlations between the X-ray and optical emission. Those correlations are interpreted in terms of coupling between disc and jet on time scales of seconds or less. Those observations are discussed in the framework of current models.     

Effects of inflationary bubbles on the polarization and temperature anisotropies of the cosmic microwave background

The broad X-ray iron line, detected in many active galactic nuclei, is likely to be produced by fluorescence from the X-ray-illuminated central parts of an accretion disc close to a supermassive black hole. The time-averaged shape of the line can be explained most naturally by a combination of special and general relativistic effects. Such line profiles contain information about the black hole spin and the accretion disc, as well as the geometry of the emitting region, and may help to test general relativity in the strong gravity regime. In this paper we embark on the computation of the temporal response of the line to the illuminating flux. Previous studies concentrated on the calculation of reverberation signatures from static sources illuminating the disc. In this paper we focus on the more physically justified case of flares located above the accretion disc and corotating with it. We compute the time-dependent iron line, taking into account all general relativistic effects, and show that its shape is of a very complex nature, and we also present light curves accompanying the iron line variability. We suggest that present and future X-ray satellites like XMM or Constellation-X may be capable of detecting features present in the computed reverberation maps.     

Hysteresis effects and diagnostics of the shock formation in low angular momentum axisymmetric accretion in the Kerr metric

The secular evolution of the purely general relativistic low angular momentum accretion flow around a spinning black hole is shown to exhibit hysteresis effects. This confirms that a stationary shock is an integral part of such an accretion disc in the Kerr metric. The equations describing the space gradient of the dynamical flow velocity of the accreting matter have been shown to be equivalent to a first order autonomous dynamical systems. Fixed point analysis ensures that such flow must be multi-transonic for certain astrophysically relevant initial boundary conditions. Contrary to the existing consensus in the literature, the critical points and the sonic points are proved not to be isomorphic in general, they can form in a completely different length scales. Physically acceptable global transonic solutions must produce odd number of critical points. Homoclinic orbits for the flow possessing multiple critical points select the critical point with the higher entropy accretion rate, confirming that the entropy accretion rate is the degeneracy removing agent in the system. However, heteroclinic orbits are also observed for some special situation, where both the saddle type critical points of the flow configuration possesses identical entropy accretion rate. Topologies with heteroclinic orbits are thus the only allowed non-removable degenerate solutions for accretion flow with multiple critical points, and are shown to be structurally unstable. Depending on suitable initial boundary conditions, a homoclinic trajectory can be combined with a standard non-homoclinic orbit through an energy preserving Rankine-Hugoniot type of stationary shock, and multi-critical accretion flow then becomes truly multi-transonic. An effective Lyapunov index has been proposed to analytically confirm why certain class of transonic flow cannot accommodate shock solutions even if it produces multiple critical points.     

Perturbation of mass accretion rate,associated acoustic geometry and stability analysis

We investigate the stability of stationary integral solutions of an ideal irrotational fluid in a general static and spherically symmetric background, by studying the profile of the perturbation of the mass accretion rate. We consider low angular momentum axisymmetric accretion flows for three different accretion disk models and consider time dependent and radial linear perturbation of the mass accretion rate. First we show that the propagation of such perturbation can be determined by an effective 2 × 2 matrix, which has qualitatively similar acoustic causal properties as one obtains via the perturbation of the velocity potential. Next, using this matrix we analytically address the stability issues, for both standing and travelling wave configurations generated by the perturbation. Finally, based on this general formalism we briefly discuss the explicit example of the Schwarzschild spacetime and compare our results of stability with the existing literature, which instead address this problem via the perturbation of the velocity potential.     

Numerical Simulation of Small Perturbation on an Accretion Disk Due to the Collision of a Star with the Disk Near the Black Hole

In this paper, perturbations of an accretion disk by a star orbiting around a black hole are studied. We report on a numerical experiment, which has been carried out by using a parallel-machine code originally developed by Dönmez (2004). An initially steady state accretion disk near a non-rotating (Schwarzschild) black hole interacts with a “star”, modeled as an initially circular region of increased density. Part of the disk is affected by the interaction. In some cases, a gap develops and shock wave propagates through the disk. We follow the evolution for order of one dynamical period and we show how the non-axisymetric density perturbation further evolves and moves downwards where the material of the disk and the star become eventually accreted onto the central body. When the star perturbs the steady state accretion disk, the disk around the black hole is destroyed by the effect of perturbation. The perturbed accretion disk creates a shock wave during the evolution and it loses angular momentum when the gas hits on the shock waves. Colliding gas with the shock wave is the one of the basic mechanism of emitting the X-rays in the accretion disk. The series of supernovae occurring in the inner disk could entirely destroy the disk in that region which leaves a more massive black hole behind, at the center of galaxies.     

Variation of the gas and radiation content in the sub-Keplerian accretion disk around black holes and its impact to the solutions

We investigate the variation of the gas and the radiation pressure in accretion disks during the infall of matter to the black hole and its effect to the flow. While the flow far away from the black hole might be non-relativistic, in the vicinity of the black hole it is expected to be relativistic behaving more like radiation. Therefore, the ratio of gas pressure to total pressure (β) and the underlying polytropic index (γ) should not be constant throughout the flow. We obtain that accretion flows exhibit significant variation of β and then γ, which affects solutions described in the standard literature based on constant β. Certain solutions for a particular set of initial parameters with a constant β do not exist when the variation of β is incorporated appropriately. We model the viscous sub-Keplerian accretion disk with a nonzero component of advection and pressure gradient around black holes by preserving the conservations of mass, momentum, energy, supplemented by the evolution of β. By solving the set of five coupled differential equations, we obtain the thermo-hydrodynamical properties of the flow. We show that during infall, β of the flow could vary up to ∼300%, while γ up to ∼20%. This might have a significant impact to the disk solutions in explaining observed data, e.g. super-luminal jets from disks, luminosity, and then extracting fundamental properties from them. Hence any conclusion based on constant γ and β should be taken with caution and corrected.     

Alignment and precession of a black hole with a warped accretion disc

We consider the shape of an accretion disc whose outer regions are misaligned with the spin axis of a central black hole and calculate the steady state form of the warped disc in the case where the viscosity and surface densities are power laws in the distance from the central black hole. We discuss the shape of the resulting disc in both the frame of the black hole and that of the outer disc. We note that some parts of the disc and also any companion star maybe shadowed from the central regions by the warp. We compute the torque on the black hole caused by the Lense–Thirring precession, and hence compute the alignment and precession time-scales. We generalize the case with viscosity and hence surface density independent of radius to more realistic density distributions for which the surface density is a decreasing function of radius. We find that the alignment time-scale does not change greatly but the precession time-scale is more sensitive. We also determine the effect on this time-scale if we truncate the disc. For a given truncation radius, the time-scales are less affected for more sharply falling density distributions.     

Alignment time-scale of the microquasar GRO J1655−40

The microquasar GRO J1655−40 has a black hole with spin angular momentum apparently misaligned to the orbital plane of its companion star. We analytically model the system with a steady-state disc warped by Lense–Thirring precession and find the time-scale for the alignment of the black hole with the binary orbit. We make detailed stellar evolution models so as to estimate the accretion rate and the lifetime of the system in this state. The secondary can be evolving at the end of the main sequence or across the Hertzsprung gap. The mass-transfer rate is typically 50 times higher in the latter case but we find that, in both the cases, the lifetime of the mass-transfer state is at most a few times the alignment time-scale. The fact that the black hole has not yet aligned with the orbital plane is therefore consistent with either model. We conclude that the system may or may not have been counter aligned after its supernova kick but that it is most likely to be close to alignment rather than counter alignment now.     

Line emission from accretion discs around black holes: the analytic approach

The broad X-ray iron line observed in many active galactic nuclei spectra is thought to originate from the accretion disc surrounding the putative supermassive black hole. We show here how to perform the analytical integration of the geodesic equations that describe the photon trajectories in the general case of a rotating black hole (Kerr metric), in order to write a fast and efficient numerical code for modelling emission line profiles from accretion discs.