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

• Published in: Monthly notices of the Royal Astronomical Society Vol. 373; no. 1; pp. 146 - 156
• Main Authors: Chaudhury, Soumini, Ray, Arnab K., Das, Tapas K.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 21.11.2006; Blackwell Science; Oxford University Press
• Subjects: accretion; accretion discs; Accretion disks; accretion, accretion discs; Astronomy; black hole physics; Black holes; Earth, ocean, space; Exact sciences and technology; hydrodynamics; Mathematical models; black hole physics; accretion, accretion discs; hydrodynamics; Invariant; Critical property; Accretion; Isothermal flow; Polytropes; Black holes; Schwarzschild metric; Critical points; Pseudopotential; Boundary conditions; Rotational flow; Accretion disks; Dynamical systems; Saddle point; Upper bound; Classification; Angular momentum; Disturbances; Cosmology; Steady state solution
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2006.11018.x

For inviscid, rotational accretion flows, both isothermal and polytropic, a simple dynamical system analysis of the critical points has given a very accurate mathematical scheme to understand the nature of these points, for any pseudo-potential by which the flow may be driven on to a Schwarzschild black hole. This allows us 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 perturbation. The perturbation equation has also served the dual purpose of enabling and understanding the acoustic geometry for inviscid and rotational flows.