Transonic behaviour and stability analysis of quasi-viscous black hole accretion

TL;DR

This paper analyzes the transonic behavior and stability of quasi-viscous black hole accretion flows, revealing how weak viscosity influences critical points and stability, with implications for understanding black hole spectra.

Contribution

It provides an analytical study of transonic solutions and stability in quasi-viscous accretion, extending inviscid models by including linear viscosity effects across various flow geometries.

Findings

Transonic solutions with one or three critical points are found for low viscosity.

Viscosity changes the nature of critical points from center to saddle or spiral types.

Disk models exhibit secular instability at large distances, but remain stable within certain length scales.

Abstract

Analytical studies of black hole accretion usually presumes the stability of the stationary transonic configuration. Various authors in the past several decades demonstrated the validity of such an assumption for inviscid hydrodynamic flow. Inviscid approximation is a reasonable approach for low angular momentum advection dominated flow in connection to certain supermassive black holes at the centres of the galaxies (including our own) fed from a number of stellar donors. Introduction of a weak viscosity, as a first order linear correction involving the viscosity parameter, however, may sometimes provide a more detail understanding of the observed black hole spectra. The transonic behaviour of the stationary solutions have been studied for the aforementioned quasi-viscous accretion for all possible geometric configurations of axisymmetric flow. For a sufficiently low range of the viscosity parameter, transonic solutions containing one or three critical points have been found for allowed ranges in the astrophysical parameters under the post-Newtonian pseudo-Schwarzschild scheme. With the introduction of such viscosity parameter, the only feasible critical points are of saddle and spiral types in contrary to the inviscid case where centre type points were formed instead of spiral ones. Introduction of linear perturbations on stationary flow solutions and their time evolution in both standing and radially propagating wave forms have been examined (completely analytically) in detail. Our analysis shows that similar kind of secular instability exists in all the considered disk models at large distance in the asymptotic limit, however, the model itself is valid only within a certain length scale and the disks sustain within that length scale only for at least a considerable time scale.