Critical properties and stability of stationary solutions in multi-transonic pseudo-Schwarzschild accretion

Abstract

For inviscid, rotational accretion flows, both isothermal and polytropic, a simple dynamical systems analysis of the critical points has given a very accurate mathematical scheme to understand the nature of these points, for {\em any} pseudo-potential by which the flow may be driven on to a Schwarzschild black hole. This allows for a complete classification of the critical points for a wide range of flow parameters, and shows that the only possible critical points for this kind of flow are saddle points and centre-type points. A restrictive upper bound on the angular momentum of critical solutions has been established. A time-dependent perturbative study reveals that the form of the perturbation equation, for both isothermal and polytropic flows, is invariant under the choice of any particular pseudo-potential. Under generically true outer boundary conditions, the inviscid flow has been shown to be stable under an adiabatic and radially propagating perturbtion. The perturbation equation has also served the dual purpose of enabling an understanding of the acoustic geometry for inviscid and rotational flows.

arXiv commentFinal version to appear in MNRAS. 12 pages, one colour and 3 black and white figures

References in corpus (12)

• Acoustic black holes: horizons, ergospheres, and Hawking radiation
• Viscous accretion discs around rotating black holes
• Geometrically Thin Disk Accreting Into a Black Hole
• Generalized Shock Solutions for Hydrodynamic Black Hole Accretion
• Multi-transonic Black Hole Accretion Discs with Isothermal Standing Shocks
• Black-Hole Accretion Disc as an Analogue Gravity Model
• Acoustic horizons in axially symmetric relativistic accretion
• Dependence of General Relativistic Accretion on Black Hole Spin
• Hydrodynamic accretion onto rapidly rotating Kerr black hole
• Realizability of stationary spherically symmetric transonic accretion
• Pseudo-Schwarzschild description of transonic spherical accretion onto compact objects
• Linearized perturbation on stationary inflow solutions in an inviscid and thin accretion disc

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