Corpus ID: 118084613

A dynamical systems approach to a thin accretion disc and its time-dependent behaviour on large length scales

  title={A dynamical systems approach to a thin accretion disc and its time-dependent behaviour on large length scales},
  author={Arnab K. Ray and Jayanta K. Bhattacharjee},
  journal={arXiv: Astrophysics},
Modelling the flow in a thin accretion disc like a dynamical system, we analyse the nature of the critical points of the steady solutions of the flow. For the simple inviscid disc there are two critical points, with the outer one being a saddle point and the inner one a centre type point. For the weakly viscous disc, there are four possible critical points, of which the outermost is a saddle point, while the next inner one is a spiral. Coupling the nature of the critical points with the outer… Expand
The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion
Abstract Using mathematical formalism borrowed from dynamical systems theory, a complete analytical investigation of the critical behaviour of stationary flows in low angular momentum axisymmetricExpand
Hysteresis effects and diagnostics of the shock formation in low angular momentum axisymmetric accretion in the Kerr metric
Abstract 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 aExpand
An analytical study on the multi-critical behaviour and related bifurcation phenomena for relativistic black hole accretion
We apply the theory of algebraic polynomials to analytically study the transonic properties of general relativistic hydrodynamic axisymmetric accretion onto non-rotating astrophysical black holes.Expand
Transonicity in black hole accretion -- A mathematical study using the generalized Sturm chains
We apply the theory of algebraic polynomials to analytically investigate the transonic properties of hydrodynamic accretion onto non-rotating astrophysical black holes. We first construct theExpand
Low angular momentum accretion of fractal medium on to Kerr black holes and the emergence of the acoustic manifold
For three different geometric configurations of matter and two different thermodynamic equations of state, low angular momentum, multi-transonic, axially symmetric accretion flow of matter havingExpand
On spin dependence of relativistic acoustic geometry
This work makes the first ever attempt to understand the influence of the black hole background spacetime in determining the fundamental properties of the embedded relativistic acoustic geometry. ToExpand
Multi-criticality and related bifurcation in accretion discs around non-rotating black holes -- an analytical study
Low angular momentum, general relativistic, axially symmetric accretion of hydrodynamic fluid onto Schwarzschild black holes may undergo more than one critical transition. To obtain the stationaryExpand


Theory of Transonic Astrophysical Flows
This book presents methods of studying transonic flows applicable to various astrophysical circumstances. This is the first book of its kind and efforts have been made to be as thorough as possible.Expand
Nonlinear Partial Differential Equations for Scientists and Engineers
Partial differential equations (PDEs) originated from the study of geometrical surfaces and a wide variety of problems in mechanics. Since till today they are essential in modeling of naturalExpand
Accretion power in astrophysics
1. Accretion as a source of energy 2. Gas dynamics 3. Plasma concepts 4. Accretion in binary systems 5. Accretion discs 6. Accretion on to a compact object 7. Active galactic nuclei 8. AccretionExpand
Nonlinear ordinary differential equations
This new edition has been expanded to contain an introduction to areas of current importance such as bifurcation, structural stability and chaotic behavior. Other topics include linearization,Expand