On the absence of winds in advection-dominated accretion flows

We show that recently published assertions that advection-dominated accretion flows (ADAFs) require the presence of strong winds are unfounded because they assume that low radiative efficiency in flows accreting at low rates on to black holes implies vanishing radial energy and angular momentum fluxes through the flow (which is also formulated in terms of the 'Bernoulli function' being positive). This, however, is a property only of self-similar solutions which are an inadequate representation of global accretion flows. We recall general properties of accretion flows on to black holes and show that such, necessarily transonic, flows may have either d positive or negative Bernoulli function depending on the flow viscosity. Flows with low viscosities ( α ≲0.1 in the α -viscosity model) have a negative Bernoulli function. Without exception, all 2D and 1D numerical models of low-viscosity flows constructed to date experience no significant outflows. At high viscosities the presence of outflows depends on the assumed viscosity, on the equation of state and on the outer boundary condition. The positive sign of the Bernoulli function invoked in this context is irrelevant to the presence of outflows. As an illustration, we recall 2D numerical models with moderate viscosity that have positive values of the Bernoulli function and experience no outflows. ADAFs, therefore, do not differ from this point of view from thin Keplerian discs: they may have, but they do not have to have, strong winds.     

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.     

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.     

On some transonic aspects of general relativistic spherical accretion on to Schwarzschild black holes

The equations governing general relativistic, spherically symmetric, hydrodynamic accretion of polytropic fluid on to black holes are solved in the Schwarzschild metric to investigate some of the transonic properties of the flow. Only stationary solutions are discussed. For such accretion, it has been shown that real physical sonic points may form even for flow with   γ <4/3  or   γ >5/3  . The behaviour of some flow variables in the close vicinity of the event horizon is studied as a function of specific energy and the polytropic index of the flow.     

Emission-line profiles from self-gravitating toroids around black holes

We have computed line profiles from self-gravitating toroids around black holes. The specific angular momentum of the toroids is assumed to be constant in space. The images of the toroids show peculiar features in the far sides of the black holes. Concerning the line profiles, the red wing extends to the very low frequency region because the location of the inner edge is rather near the event horizon of the black hole and consequently the velocity of the inner edges of the toroids can be greater than that of the Kepler discs.     

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.     

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。     

Slim accretion discs: a model for ADAF–SLE transitions

We numerically construct slim, global, vertically integrated models of optically thin, transonic accretion discs around black holes, assuming a regularity condition at the sonic radius and boundary conditions at the outer radius of the disc and near the black hole. In agreement with several previous studies, we find two branches of shock-free solutions, in which the cooling is dominated either by advection or by local radiation. We also confirm that the part of the accretion flow where advection dominates is in some circumstances limited in size: it does not extend beyond a certain outer limiting radius. New results found in our paper concern the location of the limiting radius and the properties of the flow near to it. In particular, we find that beyond the limiting radius the advective-dominated solutions match on to Shapiro, Lightman &38; Eardley (SLE) discs through a smooth transition region. Therefore, the full global solutions are shock-free and unlimited in size. There is no need to postulate an extra physical effect (e.g. evaporation) for triggering the ADAF–SLE transition. It occurs as a result of standard accretion processes described by the classic slim disc equations.     

Mini-discs around spinning black holes

Accretion on to black holes in wind-fed binaries and in collapsars forms small rotating discs with peculiar properties. Such 'mini-discs' accrete on the free-fall time without the help of viscosity and nevertheless can have a high radiative efficiency. The inviscid mini-disc model was previously constructed for a non-rotating black hole. We extend the model to the case of a spinning black hole, calculate the structure and radiative efficiency of the disc and find their dependence on the black hole spin. If the angular momenta of the disc and the black hole are anti-aligned, a hydrodynamic analogue of Penrose process takes place.     

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.     

Unipolar outflows and global meridional circulations in rotating accretion flows

Using two-dimensional simulations of non-radiative viscous rotating black hole accretion flows, we show that the flows with α ∼0.1–0.3 self-organize to form stationary unipolar or bipolar outflows accompanied by global meridional circulations. The required energy comes, with efficiency ∼0.001–0.01, from the matter directly accreted on to the black hole. Observational implications are discussed.     

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.     

Effects of Kerr space–time on spectral features from X-ray illuminated accretion discs

We performed detailed calculations of the relativistic effects acting on both the reflection continuum and the iron line from accretion discs around rotating black holes. Fully relativistic transfer of both illuminating and reprocessed photons has been considered in Kerr space–time. We calculated overall spectra, line profiles and integral quantities, and present their dependences on the black hole angular momentum. We show that the observed EW of the lines is substantially enlarged when the black hole rotates rapidly and/or the source of illumination is near above the hole. Therefore, such calculations provide a way to distinguish between different models of the central source.     

Effects of the Blandford–Znajek process on the evolution of the central black holes of accretion discs

The effects of the Blandford–Znajek (BZ) process on the evolution of the central black holes of accretion discs are investigated by an analytical method and numerical calculations in this paper. It is shown that the BZ process reduces the rates of change of some parameters of the black hole, such as mass, angular momentum, dimensionless angular momentum and temperature, and the evolution of the central black hole towards the extreme Kerr black hole is depressed effectively. However, the rate of change of entropy of the central black hole is augmented in the BZ process. In addition, the consistency of the BZ process with the three laws of black hole thermodynamics is discussed.     

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.     

Transfer of energy and angular momentum in the magnetic coupling between a rotating black hole and the surrounding accretion disc

The transfer of energy and angular momentum in the magnetic coupling (MC) of a rotating black hole (BH) with its surrounding accretion disc is discussed based on a mapping relation derived by considering the conservation of magnetic flux with two basic assumptions: (i) the magnetic field on the horizon is constant, (ii) the magnetic field on the disc surface varies as a power law with the radial coordinate of the disc. The following results are obtained: (i) the transfer direction of energy and angular momentum between the BH and the disc depends on the position of a co-rotation radius relative to the MC region on the disc, which is eventually determined by the BH spin; (ii) the evolution characteristics of a rotating BH in the MC process without disc accretion are depicted in a parameter space, and a series of values of the BH spin are given to indicate the evolution characteristics; (iii) the efficiency of converting accreted mass into radiation energy of a BH–disc system is discussed by considering the coexistence of disc accretion and the MC process; (iv) the MC effects on disc radiation and the emissivity index are discussed and it is concluded that they are consistent with the recent XMM–Newton observation of the nearby bright Seyfert 1 galaxy MCG–6-30-15 with reference to a variety of parameters of the BH–disc system.