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.     

Quasi-viscous accretion flow – I. Equilibrium conditions and asymptotic behaviour

In a novel approach to studying viscous accretion flows, viscosity has been introduced as a perturbative effect, involving a first-order correction in the α-viscosity parameter. This method reduces the problem of solving a second-order non-linear differential equation (Navier–Stokes equation) to that of an effective first-order equation. Viscosity breaks down the invariance of the equilibrium conditions for stationary inflow and outflow solutions, and distinguishes accretion from wind. Under a dynamical systems classification, the only feasible critical points of this 'quasi-viscous' flow are saddle points and spirals. On large spatial scales of the disc, where a linearized and radially propagating time-dependent perturbation is known to cause a secular instability, the velocity evolution equation of the quasi-viscous flow has been transformed to bear a formal closeness with Schrödinger's equation with a repulsive potential. Compatible with the transport of angular momentum to the outer regions of the disc, a viscosity-limited length-scale has been defined for the full spatial extent over which the accretion process would be viable.     

Hydrodynamical non-radiative accretion flows in two dimensions

Two-dimensional (axially symmetric) numerical hydrodynamical calculations of accretion flows that cannot cool through emission of radiation are presented. The calculations begin from an equilibrium configuration consisting of a thick torus with constant specific angular momentum. Accretion is induced by the addition of a small anomalous azimuthal shear stress which is characterized by a function ν . We study the flows generated as the amplitude and form of ν are varied. A spherical polar grid which spans more than two orders of magnitude in radius is used to resolve the flow over a wide range of spatial scales. We find that convection in the inner regions produces significant outward mass motions that carry away both the energy liberated by and a large fraction of the mass participating in the accretion flow. Although the instantaneous structure of the flow is complex and dominated by convective eddies, long-time averages of the dynamical variables show remarkable correspondence to certain steady-state solutions. The two-dimensional structure of the time-averaged flow is marginally stable to the Høiland criterion, indicating that convection is efficient. Near the equatorial plane, the radial profiles of the time-averaged variables are power laws with an index that depends on the radial scaling of the shear stress. A stress in which ν ∝ r ^1/2 recovers the widely studied self-similar solution corresponding to an ' α -disc'. We find that, regardless of the adiabatic index of the gas, or the form or magnitude of the shear stress, the mass inflow rate is a strongly increasing function of radius, and is everywhere nearly exactly balanced by mass outflow. The net mass accretion rate through the disc is only a fraction of the rate at which mass is supplied to the inflow at large radii, and is given by the local, viscous accretion rate associated with the flow properties near the central object.     

Magnetic field bending in accretion discs with dynamos

We consider the problem of poloidal magnetic field advection and bending of an initially vertical field owing to radial inflow in thin accretion discs. For a ratio of kinematic viscosity to magnetic diffusivity of order unity, significant bending of an externally applied vertical field cannot occur in a disc with no internal dynamo. However, we show that if poloidal field is generated by a dynamo operating near its critical state, then significant field bending may be possible. Our results are of particular relevance to wind launching from accretion discs.     

On the precession of accretion discs in X-ray binaries

In this Letter, recent results on the nodal precession of accretion discs in close binaries are applied to the discs in some X-ray binary systems. The ratio between the tidally forced precession period and the binary orbital period is given, as well as the condition required for the rigid precession of gaseous Keplerian discs. Hence the minimum precessional period that may be supported by a fluid Keplerian disc is determined. It is concluded that near-rigid body precession of tilted accretion discs can occur and generally reproduce observationally inferred precession periods, for reasonable system parameters. In particular, long periods in SS 433, Her X-1, LMC X-4 and SMC X-1 can be fitted by the tidal model. It is also found that the precession period that has been tentatively put forward for Cyg X-2 cannot be accommodated by a tidally precessing disc model for any realistic choice of system parameters.     

The effects of thermal conduction on the ADAF with a toroidal magnetic field

The observation of the hot gas surrounding Sgr A * and a few other nearby galactic nuclei imply that electron and proton mean free paths are comparable to the gas capture radius. So, the hot accretion flows are likely to proceed under week-collision conditions. Hence, thermal conduction has been suggested as a possible mechanism by which the sufficient extra heating is provided in hot advection-dominated accretion flow (ADAF) accretion discs. We consider the effects of thermal conduction in the presence of a toroidal magnetic field in an ADAF around a compact object. For a steady-state structure of such accretion flows, a set of self-similar solutions are presented. We find two types of solutions which represent high and slow accretion rate. They have different behaviours with saturated thermal conduction parameter, φ.     

Magnetized, mass-loaded, rotating accretion flows

We present a semi-analytical investigation of a simple one-dimensional, steady-state model for a mass-loaded, rotating, magnetized, hydrodynamical flow. Our approach is analogous to one used in early studies of magnetized winds. The model represents the infall towards a central point mass of the gas generated in a cluster of stars surrounding it, as is likely to occur in some active nuclei and starburst galaxies. We describe the properties of the different classes of infall solutions. We find that the flow becomes faster than the fast-mode speed, and hence decoupled from the centre, only for a limited range of parameter values, and when magnetic stresses are ineffective. Such flow is slowed as it approaches a centrifugal barrier, implying the existence of an accretion disc. When the flow does not become super-fast and the magnetic torque is insufficient, no steady solution extending inward to the centre exists. Finally, with a larger magnetic torque, solutions representing steady sub-Alfvénic flows are found, which can resemble spherical hydrodynamical infall. Such solutions, if applicable, would imply that rotation is not important and that any accretion disc formed would be of very limited size.     

A semi-analytic solution for the radial and vertical structure of accretion discs with a magnetic wind

A semi-analytic method is presented for solving for the radial and vertical structures of an accretion disc, with a magnetically channelled wind flowing from its surfaces. Both magnetic and turbulent viscous effects are taken into account, and the essential wind properties are related to the disc structure. The angular momentum removed by the wind plays a major part in driving the inflow through the disc, with photospheric temperatures being sufficient to generate the required wind mass flux. The magnetic field is generated by an αω-dynamo, but the method of solution should have application with other magnetic field sources. Self-consistent disc-wind solutions result, with rms turbulent Mach numbers which are in good agreement with those found in simulations of turbulence generated from magnetic shearing instabilities.     

Thermally driven outflows from pair-plasma pressure-mediated shock surfaces around Schwarzschild black holes

Introducing a spherical, steady, self-supported pair-plasma pressure-mediated shock surface around a Schwarzschild black hole as the effective physical atmosphere that may be responsible for the generation of astrophysical mass outflows from relativistic quasi-spherical accretion, we calculate the mass outflow rate R _̇ by simultaneously solving the set of equations governing transonic polytropic accretion and isothermal winds. R _̇ is computed in terms of only three inflow parameters, which, we believe, has been done for the first time in our work. We then study the dependence of R _̇ on various inflow as well as shock parameters, and establish the fact that the outflow rate is essentially controlled by the post-shock proton temperature.     

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.     

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.     

Instability of spherical accretion — I. Shock-free Bondi accretion

We examine the spatial stability of spherical adiabatic Bondi accretion on to a point gravitating mass against external perturbations. Both transonic critical and subsonic subcritical accretion are shown to be stable against purely radial acoustic, vortex or entropy perturbations. In the case of non-radial perturbations the amplitude of the perturbations grows without limit with smaller radii. Instability manifests itself only if the size of the accreting body is much less than the Bondi radius so that the inflow is highly supersonic or highly subsonic at the surface of the accretor in the case of critical or subcritical accretion respectively. These asymptotics hold and consequently the instability may develop for adiabatic index of accreting gas γ < 5/3. We suggest that this instability may lead to an essential thermalization of accreting flow thus, particularly, solving the problem of otherwise inefficient energy release in spherical accretion on to a black hole.     

'Stokes imaging' of the accretion region in magnetic cataclysmic variables — I. Conception and realization

Modelling the polarized cyclotron emission from magnetic cataclysmic variables has been a pivotal technique for determining the structure of the accretion zones on the white dwarf. To date, model solutions have been obtained from trial fits to the intensity and polarization data, which have been constructed from emission regions (for example arcs and spots) put in by hand. These models were all inferred indirectly from arguments based on the polarization and X-ray light curves.   We present a more analytical and objective technique using optimization by a genetic algorithm, Tikhonov regularization and Powell's method that robustly models the details of polarized emission.   To demonstrate the success of this technique, we show the results of several simulations in which we calculated the intensity and polarization curves from arbitrarily shaped emission regions on the surface of a sphere and then applied our code to these curves to recover the original test data. We also show how adding artificial noise affects the outcome of the optimization technique.     

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.     

Non-linear bending waves in Keplerian accretion discs

The non-linear dynamics of a warped accretion disc is investigated in the important case of a thin Keplerian disc with negligible viscosity and self-gravity. A one-dimensional evolutionary equation is formally derived that describes the primary non-linear and dispersive effects on propagating bending waves other than parametric instabilities. It has the form of a derivative non-linear Schrödinger (DNLS) equation with coefficients that are obtained explicitly for a particular model of a disc. The properties of this equation are analysed in some detail and illustrative numerical solutions are presented. The non-linear and dispersive effects both depend on the compressibility of the gas through its adiabatic index Γ. In the physically realistic case Γ < 3, non-linearity does not lead to the steepening of bending waves but instead enhances their linear dispersion. In the opposite case Γ > 3, non-linearity leads to wave steepening and solitary waves are supported. The effects of a small effective viscosity, which may suppress parametric instabilities, are also considered. This analysis may provide a useful point of comparison between theory and numerical simulations of warped accretion discs.     

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.     

A TRANSITION IN THE ACCRETION PROPERTIES OF AGN

This contribution focuses on the evidence for a bimodality in the luminosity believed to be associated with the accretion process in AGN. In particular, it will be stressed that this behavior does seem to be present in an analogous way both in radio-loud and radio-quiet AGN, as inferred from samples selected in an independent way. The found bimodality can be naturally – although not uniquely – interpreted in the frame of the ADIOS solution for radiative inefficient accretion flows. The (so far) qualitative analogy with the behavior of XRB provides an interesting perspective to find a unique framework for the accretion and jet production in accreting black hole systems.     

A unified description of the global structure of accretion disks

The global structure of accretion disks is investigated in a unified scheme. We use a general radiative cooling formula applicable to both optically thick and thin regimes and we include radial advection cooling. Within the -viscosity models, we found distinct families of global solutions. If the accretion rate is low, there are three non-intersecting solutions, corresponding to optically thick and thin, local cooling and optically thin advection cooling. If the accretion rate is high, and the viscosity coefficient is large, the two local cooling solutions coincide at radii R₁ and R₂ and exist independently below R₁ and above R₂ while the advection solution is stable at all radii. If the accretion is high and the viscosity is low, the two optically thin solutions will cross each other while the optically thick solution exists at all radii.     

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.     

An accretion disc model with a magnetic wind and turbulent viscosity

A model is presented for an accretion disc with turbulent viscosity and a magnetically influenced wind. The magnetic field is generated by a dynamo in the disc, involving the turbulence and radial shear. Disc-wind solutions are found for which the wind mass flux is sufficient to play a major part in driving an imposed steady inflow, but small enough for most material to be accreted on to the central object. Constraints arise for the magnetic Reynolds and Prandtl numbers in terms of the turbulent Mach number and vertical length-scale of the disc's horizontal magnetic field. It is shown that the imposition of a stellar boundary condition enhances the wind mass flux in the very inner region of the disc and may result in jet formation.