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

Abstract

For inviscid, rotational accretion ows, 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 any pseudo-potential by which the ow may be driven on to a Schwarzschild black hole. This allows for a complete classi cation of the critical points for a wide range of ow parameters, and shows that the only possible critical points for this kind of ow 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 ows, is invariant under the choice of any particular pseudo-potential. Under generically true outer boundary conditions, the inviscid ow has been shown to be stable under an adiabatic and radially propagating perturbation. The perturbation equation has also served the dual purpose of enabling an understanding of the acoustic geometry for inviscid and rotationalows.