Development of Secular Instability in Different Disc Models of Black Hole Accretion

Abstract

Analytical treatment of black hole accretion generally presumes the stability of the stationary configuration. Various authors in the past several decades demonstrated the validity of such an assumption for inviscid hydrodynamic flow. Inviscid assumption is a reasonable approximation for low angular^M momentum advection dominated flow in connection to certain^M supermassive black holes at the^M centres of the galaxies (including our own) fed from a number of stellar donors.^M Introduction of a weak viscosity, however, may sometimes provide a more detail understanding of the observed spectrum. Recently it has been demonstrated that introduction of small amount of viscosity in the form of quasi-viscous flow makes a stationary accretion disc -- where the geometric configuration of matter is described by axisymmetric flow in hydrostatic equilibrium -- unstable. We perform similar analysis for other disc models (for all three possible geometric configurations of matter) for quasi-viscous models under the post-Newtonian scheme. We introduced perturbations on the stationary flow solution particularly in standing wave form and studied their time evolution to observe whether they grow with time. Our analysis shows that same sort of secular instability exists in other disc models too. We further argued that with sufficiently low value of viscosity in the realistic astrophysical perspective, the instability does not effectively jeopardize the stationary condition.