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.     

Study of accretion disk dynamics in presence of cooling

We examine the behaviour of accretion flow around a rotating black hole in presence of cooling. We obtain global flow solutions for various accretion parameters that govern the accreting flow. We show that standing isothermal shock wave may develop in such an advective accretion flow in presence of cooling. This shocked solution has observational consequences as it successfully provides the possible explanations of energy spectra as well as generation of outflows/jets of various galactic and extra-galactic black hole candidates. We study the properties of isothermal shock wave and find that it strongly depends on the cooling efficiency. We identify the region in the parameter space spanned by the specific energy and specific angular momentum of the flow for standing isothermal shock as a function of cooling efficiencies and find that parameter space gradually shrinks with the increase of cooling rates. Our results imply that accretion flow ceases to contain isothermal shocks when cooling is beyond its critical value.     

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.     

Smoothed particle hydrodynamic simulations of viscous accretion discs around black holes

Viscous Keplerian discs become sub-Keplerian close to a black hole since they pass through sonic points before entering into it. We study the time evolution of polytropic viscous accretion discs (both in one- and two-dimensional flows) using smoothed particle hydrodynamics. We discover that for a large region of the parameter space spanned by energy, angular momentum and polytropic index, when the flow viscosity parameter is less than a critical value, standing shock waves are formed. If the viscosity is very high then the shock wave disappears. In the intermediate viscosity, the disc oscillates very significantly in the viscous time-scale. Our simulations indicate that these centrifugally supported high density regions close to a black hole play an active role in the flow dynamics, and consequently, the radiation dynamics.     

Standing shocks in magnetized dissipative accretion flow around black holes

We explore the global structure of the accretion flow around a Schwarzschild black hole where the accretion disc is threaded by toroidal magnetic fields. The accretion flow is optically thin and advection dominated. The synchrotron radiation is considered to be the active cooling mechanism in the flow. With this, we obtain the global transonic accretion solutions and show that centrifugal barrier in the rotating magnetized accretion flow causes a discontinuous transition of the flow variables in the form of shock waves. The shock properties and the dynamics of the post-shock corona are affected by the flow parameters such as viscosity, cooling rate and strength of the magnetic fields. The shock properties are investigated against these flow parameters. We further show that for a given set of boundary parameters at the outer edge of the disc, accretion flow around a black hole admits shock when the flow parameters are tuned for a considerable range.     

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.     

Global solutions of adiabatic accretion flows with isothermal shocks in Kerr black hole geometry

This paper presents global solutions of adiabatic accretion flows with isothermal shocks in Kerr black hole geometry. It is known that in the previously studied cases, where the flow including the shock is either entirely adiabatic or entirely isothermal, there can be no more than one stable shock solution, and the solution can only be of α –x type. However, the solution topology in the present case shows remarkable new characteristics: for the same flow parameters there can be two stable shock solutions satisfying physical boundary conditions, and the solution can be of three types, namely α– x , x –α and α–α type. In addition, shocks in the present case occur for a parameter region different from that for Rankine–Hugoniot shocks. These results greatly increase the possibilities of shock formation in astrophysical flows. It is also significant that the effects of frame-dragging of a rapid Kerr black hole on the shock formation are discovered. Finally, a brief comparison is made between shocked inviscid flows and two types of shock-free viscous flows, namely those of Shakura & Sunyaev and Narayan & Yi, and some comments are made about the fact that numerous authors who have studied transonic global solutions of accretion flows have found no shocks.     

Studies of accretion flows around rotating black holes – II. Standing shocks in the pseudo-Kerr geometry

Standing, propagating or oscillating shock waves are common in accretion and winds around compact objects. We study the topology of all possible solutions using the pseudo-Kerr geometry. We present the parameter space spanned by the specific energy and angular momentum and compare it with that obtained from the full general relativity to show that the potential can work satisfactorily in fluid dynamics also, provided the polytropic index is suitably modified. We then divide the parameter space depending on the nature of the solution topology. We specifically study the nature of the standing Rankine–Hugoniot shocks. We also show that as the Kerr parameter is increased, the shock location generally moves closer to the black hole. In future, these solutions can be used as guidelines to test numerical simulations around compact objects.     

黑洞吸积理论的新进展(Ⅰ):ADAF吸积理论

黑洞的吸积是天体物理学中最重要的基础理论之一。近年来该理论取得了引人瞩目的重大进展,具体表现在两个方面。其一是根据黑洞吸积必定跨声速这一特性,提出在一定条件下吸积流中会出现激波,这可称为含激波的吸积理论;其二是基于对一种局域致冷机制-贮导（advection）致冷的作用的重新认识而建立的,称为ADAF理论。在吸积盘的光学厚度很小或很大两种情况下,粘滞产生的大部分热量没有像在标准薄盘模型中那样辐射出去,而是贮存在流体中随流体的径向运动进入黑洞。与标准薄盘模型相比,贮导吸积盘具有高得多的温度和大得多的径向速度,但角动量小于开普勒角动量,吸积致能的效率要低得多。     

Models for jet power in elliptical galaxies: a case for rapidly spinning black holes

The power of jets from black holes is expected to depend on both the spin of the black hole and the structure of the accretion disc in the region of the last stable orbit. We investigate these dependencies using two different physical models for the jet power: the classical Blandford–Znajek (BZ) model and a hybrid model developed by Meier. In the BZ case, the jets are powered by magnetic fields directly threading the spinning black hole while in the hybrid model, the jet energy is extracted from both the accretion disc as well as the black hole via magnetic fields anchored to the accretion flow inside and outside the hole's ergosphere. The hybrid model takes advantage of the strengths of both the Blandford–Payne and BZ mechanisms, while avoiding the more controversial features of the latter. We develop these models more fully to account for general relativistic effects and to focus on advection-dominated accretion flows (ADAFs) for which the jet power is expected to be a significant fraction of the accreted rest mass energy.
We apply the models to elliptical galaxies, in order to see if these models can explain the observed correlation between the Bondi accretion rates and the total jet powers. For typical values of the disc viscosity parameter  α∼ 0.04 –0.3  and mass accretion rates consistent with ADAF model expectations, we find that the observed correlation requires   j ≳ 0.9  ; that is, it implies that the black holes are rapidly spinning. Our results suggest that the central black holes in the cores of clusters of galaxies must be rapidly rotating in order to drive jets powerful enough to heat the intracluster medium and quench cooling flows.     

Iron line profiles and self-shadowing from relativistic thick accretion discs

We present Fe Kα line profiles from and images of relativistic discs with finite thickness around a rotating black hole using a novel code. The line is thought to be produced by iron fluorescence of a relatively cold X-ray-illuminated material in the innermost parts of the accretion disc and provides an excellent diagnostic of accretion flows in the vicinity of black holes. Previous studies have concentrated on the case of a thin, Keplerian accretion disc. This disc must become thicker and sub-Keplerian with increasing accretion rates. These can affect the line profiles and in turn can influence the estimation of the accretion disc and black hole parameters from the observed line profiles. We here embark on, for the first time, a fully relativistic computation which offers key insights into the effects of geometrical thickness and the sub-Keplerian orbital velocity on the line profiles. We include all relativistic effects such as frame-dragging, Doppler boost, time dilation, gravitational redshift and light bending. We find that the separation and the relative height between the blue and red peaks of the line profile diminish as the thickness of the disc increases. This code is also well suited to produce accretion disc images. We calculate the redshift and flux images of the accretion disc and find that the observed image of the disc strongly depends on the inclination angle. The self-shadowing effect appears remarkable for a high inclination angle, and leads to the black hole shadow being in this case, completely hidden by the disc itself.     

XMM-EPIC observation of MCG–6-30-15: direct evidence for the extraction of energy from a spinning black hole?

We present XMM-Newton European Photon Imaging Camera (EPIC) observations of the bright Seyfert 1 galaxy MCG–6-30-15, focusing on the broad Fe K α line at ∼6 keV and the associated reflection continuum, which is believed to originate from the inner accretion disc. We find these reflection features to be extremely broad and redshifted, indicating an origin in the very central regions of the accretion disc. It seems likely that we have caught this source in the 'deep minimum' state first observed by Iwasawa et al. The implied central concentration of X-ray illumination is difficult to understand in any pure accretion disc model. We suggest that we are witnessing the extraction and dissipation of rotational energy from a spinning black hole by magnetic fields connecting the black hole or plunging region to the disc.     

Spectral signatures of dissipative standing shocks and mass outflow in presence of Comptonization around a black hole

Accretion flows having positive specific energy are known to produce outflows and winds which escape to a large distance. According to Two Component Advective Flow (TCAF) model, centrifugal pressure dominated region of the flow just outside the black hole horizon, with or without shocks, acts as the base of this outflow. Electrons from this region are depleted due to the wind and consequently, energy transfer rate due to inverse Comptonization of low energy photons are affected. Specifically, it becomes easier to cool this region and emerging spectrum is softened. Our main goal is to show spectral softening due to mass outflow in presence of Compton cooling. To achieve this, we modify Rankine-Hugoniot relationships at the shock front when post-shock region suffers mass loss due to winds and energy loss due to inverse Comptonization. We solve two-temperature equations governing an accretion flow around a black hole which include Coulomb exchange between protons and electrons and other major radiative processes such as bremsstrahlung and thermal Comptonization. We then compute emitted spectrum from this post-shock flow. We also show how location of standing shock which forms outer boundary of centrifugal barrier changes with cooling. With an increase in disc accretion rate \((\dot{m}_{d})\) , cooling is enhanced and we find that the shock moves in towards the black hole. With cooling, thermal pressure is reduced, and as a result, outflow rate is decreased. We thus directly correlate outflow rate with spectral state of the disc.     

Super-Eddington accretion discs around Kerr black holes

We calculate the structure of the accretion disc around a rapidly rotating black hole with a super-Eddington accretion rate. The luminosity and height of the disc are reduced by the advection effect. In the case of large viscosity parameter, α>0.03, the accretion flow deviates strongly from thermodynamic equilibrium and overheats in the central region. With increasing accretion rate, the flow temperature steeply increases, reaches maximum, and then falls off. The maximum is achieved in the advection-dominated regime of accretion. The maximum temperature in the disc around a massive black hole of M =10⁸ M⊙ with α=0.3 is of order 3×10⁸ K. The discs with large accretion rates can emit X-rays in quasars as well as in galactic black hole candidates.     

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.     

Investigating a fluctuating-accretion model for the spectral-timing properties of accreting black hole systems

The fluctuating-accretion model of Lyubarskii and its extension by Kotov, Churazov & Gilfanov seek to explain the spectral-timing properties of the X-ray variability of accreting black holes in terms of inward-propagating mass accretion fluctuations produced at a broad range of radii. The fluctuations modulate the X-ray emitting region as they move inwards and can produce temporal-frequency-dependent lags between energy bands, and energy-dependent power spectral densities (PSDs) as a result of the different emissivity profiles, which may be expected at different X-ray energies. Here, we use a simple numerical implementation to investigate in detail the X-ray spectral-timing properties of the model and their relation to several physically interesting parameters, namely the emissivity profile in different energy bands, the geometrical thickness and viscosity parameter of the accretion flow, the strength of damping on the fluctuations and the temporal coherence (measured by the 'quality factor', Q ) of the fluctuations introduced at each radius. We find that a geometrically thick flow with large viscosity parameter is favoured, and we confirm that the predicted lags are quite robust to changes in the emissivity profile and physical parameters of the accretion flow, which may help to explain the similarity of the lag spectra in the low/hard and high/soft states of Cyg X-1. We also demonstrate the model regime where the light curves in different energy bands are highly spectrally coherent. We compare model predictions directly to X-ray data from the narrow line Seyfert 1 galaxy NGC 4051 and the black hole X-ray binary (BHXRB) Cyg X-1 in its high/soft state, and we show that this general scheme can reproduce simultaneously the time lags and energy-dependence of the PSD.     

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.     

Non-axisymmetric instabilities in shocked adiabatic accretion flows

We investigate the linear stability of a shocked accretion flow on to a black hole in the adiabatic limit. Our linear analyses and numerical calculations show that, despite the post-shock deceleration, the shock is generally unstable to non-axisymmetric perturbations. The simulation results of Molteni, Tóth & Kuznetsov can be well explained by our linear eigenmodes. The mechanism of this instability is confirmed to be based on the cycle of acoustic waves between the corotation radius and the shock. We obtain an analytical formula to calculate the oscillation period from the physical parameters of the flow. We argue that the quasi-periodic oscillation should be a common phenomenon in accretion flows with angular momentum.