For the first time, {\it all} available pseudo-Schwarzschild potentials are exhaustively used to investigate the possibility of shock formation in hydrodynamic, invicid, black hole accretion discs. It is shown that a significant region of parameter space spanned by important accretion parameters allows shock formation for flow in {\it all} potentials used in this work. This leads to the conclusion that the standing shocks are essential ingredients in accretion discs around non-rotating black holes in general. Using a complete general relativistic framework, equations governing multi-transonic black hole accretion and wind are also formulated and solved in the Schwarzschild metric. Shock solutions for accretion flow in various pseudo potentials are then compared with such general relativistic solutions to identify which potential is the best approximation of Schwarzschild space-time as far as the question of shock formation in black hole accretion discs is concerned.Comment: 34 pages. 7 black and white encapsulated post-script figures. Higher resolution Fig. 4 is available from http://www.astro.ucla.edu/~tapas/figure4.eps.gz Published in Ap

Abstract.We compute mass outflow rates from accretion disks around compact objects, such as neutron stars and black holes. These computations are done using combinations of exact transonic inflow and outflow solutions which may or may not form standing shock waves. Assuming that the bulk of the outflow is from the effective boundary layers of these objects, we find that the ratio of the outflow rate and inflow rate varies anywhere from a few percent to even close to a hundred percent (i.e., close to disk evacuation case) depending on the initial parameters of the disk, the degree of compression of matter near the centrifugal barrier, and the polytropic index of the flow. Our result, in general, matches with the outflow rates obtained through a fully time-dependent numerical simulation. In some region of the parameter space when the standing shock does not form, our results indicate that the disk may be evacuated and may produce quiescence states.

Transonic accretion onto astrophysical objects is a unique example of analogue black hole realized in nature. In the framework of acoustic geometry we study axially symmetric accretion and wind of a rotating astrophysical black hole or of a neutron star assuming isentropic flow of a fluid described by a polytropic equation of state. In particular we analyze the causal structure of multitransonic configurations with two sonic points and a shock. Retarded and advanced null curves clearly demonstrate the presence of the acoustic black hole at regular sonic points and of the white hole at the shock. We calculate the analogue surface gravity and the Hawking temperature for the inner and outer acoustic horizons.

We formulate and solve the equations governing the transonic behaviour of a general relativistic black-hole accretion disc with non-zero advection velocity. We demonstrate that a relativistic Rankine-Hugoniot shock may form leading to the formation of accretion powered outflow. We show that the critical points of transonic discs generally do not coincide with the corresponding sonic points. The collection of such sonic points forms an axisymmetric hypersurface, generators of which are the acoustic null geodesics, i.e. the phonon trajectories. Such a surface is shown to be identical with an acoustic event horizon. The acoustic surface gravity and the corresponding analogue horizon temperature TAH at the acoustic horizon are then computed in terms of fundamental accretion parameters. Physically, the analogue temperature is associated with the thermal phonon radiation analogous to the Hawking radiation of the black-hole horizon.Thus, an axisymmetric black-hole accretion disc is established as a natural example of the classical analogue gravity model, for which two kinds of horizon exist simultaneously. We have shown that for some values of astrophysically relevant accretion parameters, the analogue temperature exceeds the corresponding Hawking temperature. We point out that acoustic white holes can also be generated for a multi-transonic black-hole accretion with a shock. Such a white hole, produced at the shock, is always flanked by two acoustic black holes generated at the inner and the outer sonic points. Finally, we discuss possible applications of our work to other astrophysical events which may exhibit analogue effects.

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 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 can not accommodate shock solutions even if it produces multiple critical points. WHITHER SHOCKED ACCRETION DISC?For accretion of matter onto astrophysical black holes, the local radial Mach number M of the accreting fluid can be defined as the ratio of the radial component of the local dynamical flow velocity to that of the propagation of the acoustic perturbation embedded inside the accreting matter. The flow will be locally subsonic or supersonic according to M < 1 or > 1. The flow is transonic if at any moment it crosses the M = 1 hypersurface. This happens when a subsonic to supersonic or supersonic to subsonic transition takes place either continuously or discontinuously. The point(s) where such crossing takes place continuously is (are) called sonic point(s), and where such crossing takes place discontinuously are called shocks or discontinuities. The particular value of the radial distance r for which M = 1, is referred as the transonic point or the sonic point, and will be denoted by rs hereafter. For r < rs, infalling matter becomes supersonic. Any acoustic perturbation created in such a region is destined to be dragged toward the black hole, and can not escape to the domain r > rs. In othe...

In this work we address the issue of shock formation in black hole accretion disks. We provide a generalized two-parameter solution scheme for multitransonic accretion and wind around Schwarzschild black holes, mainly by concentrating on accretion solutions that may contain steady, standing isothermal shocks. Such shocks conserve flow temperature by dissipating energy at the shock location. We use a vertically integrated 1.5-dimensional model to describe the disk structure, where the equations of motion apply to the equatorial plane of the central accretor, assuming the flow to be in hydrostatic equilibrium in the transverse direction. Unlike previous works in this field, our calculation is not restricted to any particular kind of postNewtonian gravitational potentials; rather, we use all available pseudo-Schwarzschild potentials to formulate and solve the equations governing the accretion and wind only in terms of the flow temperature T and specific angular momentum of the flow. The accretion flow is assumed to be nondissipative everywhere, except possibly at the shock location, if any. We observe that a significant region of parameter space spanned by {, T} allows shock formation. Our generalized formalism ensures that the shock formation is not just an artifact of a particular type of gravitational potential; rather, the inclusion of all available black hole potentials demonstrates a substantially extended zone of parameter space allowing for the possibility of shock formation. We thus arrive at the conclusion that the standing shocks are essential components of rotating, advective accretion flows of isothermal fluid around a nonspinning astrophysical black hole. We identify all possible shock solutions that may be present in isothermal disk accretion and thoroughly study the dependence of various shock parameters on fundamental dynamical variables governing the accretion flow for all possible initial boundary conditions. Types of shocks discussed in this paper may appear to be '' bright '' because of the huge amount of energy dissipation at the shock, and the quick removal of such energy to maintain isothermality may power the strong X-ray flairs recently observed to be emerging from our Galactic center. The results are discussed in connection with other astrophysical phenomena of related interest, such as the quasi-periodic oscillation behavior of galactic black hole candidates.

Using mathematical formalism borrowed from dynamical systems theory, a complete analytical investigation of the critical behaviour of the stationary flow configuration for the low angular momentum axisymmetric black hole accretion provides valuable insights about the nature of the phase trajectories corresponding to the transonic accretion in the steady state, without taking recourse to the explicit numerical solution commonly performed in the literature to study the multi-transonic black hole accretion disc and related astrophysical phenomena. Investigation of the accretion flow around a non rotating black hole under the influence of various pseudo-Schwarzschild potentials and forming different geometric configurations of the flow structure manifests that the general profile of the parameter space divisions describing the 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 the another, since the numerical domain of the parameter space responsible to produce 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 linear perturbation for all kind of flow geometries, black hole potentials, and the corresponding equations of state used to obtain the critical transonic solutions. Finally, the structure of the acoustic metric corresponding to the propagation of the linear perturbation studied are discussed for various flow geometries used.

The material accreting on to Sgr A* most probably comes from the nearby stars. We analyse the pattern of this flow at distances of a fraction of a parsec, and we argue that the net angular momentum of this material is low but non‐negligible, and the initially supersonic disc accretion changes into subsonic flow with constant angular momentum. Next, we estimate the flow parameters at a distance RBHL from the black hole, and we argue that for the plausible parameter range the accretion flow is non‐stationary. The inflow becomes supersonic at a distance of ∼104Rg, but the solution does not continue below the horizon and the material piles up forming a torus, or a ring, at a distance of a few, up to tens of Schwarzchild, radii. Such a torus is known to be unstable and may explain strong variability of the flow in Sgr A*. Our considerations show that the temporary formation of such a torus seems to be unavoidable. Our best‐fitting model predicts a rather large accretion rate of around 4 × 10−6  M⊙ yr−1 directly on Sgr A*. We argue that magnetic fields in the flow are tangled, and this allows our model to overcome the disagreement with the Faraday rotation limits.