A massive thick disc around a massive black hole and its runaway instability

We investigate the runaway instability of configurations consisting of a massive dense but non-self-gravitating thick disc/torus surrounding a massive black hole (MBH). We limit our model parameters to values that result in a self-consistent thick disc around an MBH. We identify, analytically, the index of the angular momentum distribution that will form a thick disc as an initial equilibrium state, and obtain the mass ratio of the disc to the central black hole for which the disc is dominated by the radiation pressure. In our theoretical framework we find that a self-consistent thick disc with constant angular momentum leads to a runaway instability on a dynamical time-scale. However, even a slight increase of the specific angular momentum outwards has a strong stabilizing effect on the accretion process. Finally, we discuss our results and present possible applications to high-energy emission.     

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.     

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.     

Dynamics of oscillating relativistic tori around Kerr black holes

We present a comprehensive numerical study of the dynamics of relativistic axisymmetric accretion tori with a power-law distribution of specific angular momentum orbiting in the background space–time of a Kerr black hole. By combining general relativistic hydrodynamics simulations with a linear perturbative approach we investigate the main dynamical properties of these objects over a large parameter space. The astrophysical implications of our results extend and improve two interesting results that have been recently reported in the literature. First, the induced quasi-periodic variation of the mass quadrupole moment makes relativistic tori of nuclear matter densities, as those formed during the last stages of binary neutron star mergers, promising sources of gravitational radiation, potentially detectable by interferometric instruments. Secondly, p-mode oscillations in relativistic tori of low rest-mass densities could be used to explain high-frequency quasi-periodic oscillations observed in X-ray binaries containing a black hole candidate under conditions more generic than those considered so far.     

Runaway instabilities in geometrically thin accretion disks around Kerr black holes

The stability of the innermost disk region orbiting a Kerr black hole is investigated for geometrically thin accretion disks. The infalling matter transports mass and angular momentum into the Kerr hole. This affects the inner disk boundary and leads to runaway instabilities in some cases.     

Numerical Simulations of Self-Gravitating Magnetized Disks

We present the first global simulations of self-gravitating magnetized tori. The simulations are performed with Zeus-2D and GLOBAL. We find the magnetorotational instability (MRI) to behave similarly in a self-gravitating environment as in previous simulations of non self-gravitating systems: enhancement of turbulent angular momentum transport follows the linear phase. The torus quickly develops a two component structure composed of an inner thick disk in Keplerian rotation and an outer massive disk. We compare this result with zero mass global simulations in 2D, and also present preliminary results of 3D simulations.     

辐射效率对黑洞质量增长的影响

考虑了在黑洞质量增长过程中,辐射效率的变化对黑洞质量增长的影响．随着吸积的进行,黑洞的角动量会发生变化,辐射效率也会随之发生变化,从而影响了质量增长．对于黑洞的指数增长模型,给出了考虑辐射效率对黑洞质量增长影响下的黑洞质量增长方程,用数值方法进行求解,并得到了黑洞质量随时间变化的曲线．与假定辐射效率为常数的模型对比,结果表明辐射效率的变化对黑洞质量的增长有较明显的影响,使黑洞的增长延迟．这个模型可以定量地说明最近的观测结果．     

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.     

A numerical solution of the dynamical instability of a thin accretion torus

We consider the non-axisymmetric, dynamical instability of a thin accretion torus with a non-zero shift of corotation radius. By numerical method we evaluated the wave number dependence of the linear rate of growth of instability and the co-rotation shift. The rate of growth is only slightly affected by the non-zero co-rotation shift, while the dispersion relation in the case of a shift is the same as that of the linear KdV equation. This shows that the “planet-like” solution found in numerical simulations of thin tori is very probably analogous to the soliton solution of the KdV equation.     

Blandford-Znajek过程对黑洞吸积盘演化的影响

本文详细讨论了在Blandford－Znajek过程中吸积盘中心黑洞的角动量和质量的总变化率与质量吸积率和能量提取率之比的关系，在此基础上讨论了BlandfordZnajek过程对黑洞吸积盘内边缘半径r_(ms)演化的影响，并证明在此过程中中心黑洞的熵总是增大的。     

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.     

Angular momentum transport by thermal emission in black hole accretion disks

We calculate the amount of angular momentum that thermal photons carry out of a viscous black hole accretion disk, due to the strong Doppler shift imparted to them by the high orbital velocity of the radiating disk material. While thermal emission can not drive accretion on its own, we show that along with disk heating it does nonetheless result in a loss of specific angular momentum, thereby contributing to an otherwise viscosity‐driven accretion flow. In particular, we show that the fraction of the angular momentum that is lost to thermal emission at a radius r in a standard, multi‐color disk is ∼0.4r_s/r, where r_s is the Schwarzschild radius of the black hole. We briefly highlight the key similarties between this effect and the closely related Poynting‐Robertson effect (© 2011 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.     

Eccentric instability of a two-dimensional fluid disc with a central massive object

In this paper we investigate, by linear modal analysis, the one-armed dynamical instability of a two-dimensional fluid disc that has a massive object at its centre. The model of the disc is chosen to avoid the artificial instabilities that originate from the unrealistic disc configurations that have been adopted in previous studies. We find a one-armed instability for which the central massive object is displaced from the centre, which is generally called the 'eccentric instability'. However, to excite the eccentric instability, the mass of the central object should be appreciably smaller than that of the disc, and this mass ratio is far smaller than what was originally proposed. The instability shown in this paper is likely to be excited in a stellar system with a central massive object, e.g. a galactic nucleus harbouring a massive black hole, and further studies are desirable via techniques such as numerical simulations.     

The circumnuclear material in the Galactic Centre: a clue to the accretion process

On the basis of 'sticky particle' calculations, it is argued that the gas features observed within 10 pc of the Galactic Centre — the circumnuclear disc (CND) and the ionized gas filaments — as well as the newly formed stars in the inner 1 pc can be understood in terms of tidal capture and disruption of gas clouds on low angular momentum orbits in a potential containing a point mass. The calculations demonstrate that a dissipative component forms a 'dispersion ring', an asymmetric elliptical torus precessing counter to the direction of rotation, and that this shape can be maintained for many orbital periods. For a range of plausible initial conditions, such a structure can explain the morphology and kinematics of the CND and of the most conspicuous ionized filament. While forming the dispersion ring, a small cloud with low specific angular momentum is drawn into a long filament which repeatedly collides with itself at high velocity. The compression in strong shocks is likely to lead to star formation even in the near tidal field of the point mass. This process may have general relevance to accretion on to massive black holes in normal and active galactic nuclei.     

Effect of angular momentum distribution on gravitational loss-cone instability in stellar clusters around a massive black hole

We study the small perturbations in spherical and thin disc stellar clusters surrounding a massive black hole. Because of the black hole, stars with sufficiently low angular momentum escape from the system through the loss cone. We show that the stability properties of spherical clusters crucially depend on whether the distribution of stars is monotonic or non-monotonic in angular momentum. It turns out that only non-monotonic distributions can be unstable. At the same time, instability in disc clusters is possible for both types of distribution.     

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.     

Magnetohydrodynamical non-radiative accretion flows in two dimensions

We present the results of axisymmetric, time-dependent magnetohydrodynamic simulations of accretion flows around black holes. The calculations begin from a rotationally supported thick torus which contains a weak poloidal field. Accretion is produced by growth and saturation of the magnetorotational instability (MRI) provided that the wavelength of the fastest growing mode is less than the thickness of the torus. Using a computational grid that spans more than two decades in radius, we compare the time-averaged properties of the flow with previous hydrodynamical simulations. The net mass accretion rate is small compared with the mass inflow and outflow rates at large radii associated with turbulent eddies. Turbulence is driven by the MRI rather than convection. The two-dimensional structure of the time-averaged flow is significantly different compared with the hydrodynamical case. We discuss the limitations imposed on our results by the assumption of axisymmetry and the relatively small radial domain.