Perturbation of mass accretion rate, associated acoustic geometry and stability analysis

TL;DR

This paper analyzes the stability of stationary accretion flows in static, spherically symmetric spacetimes by studying perturbations of the mass accretion rate, introducing a matrix formalism to compare with velocity potential perturbations.

Contribution

It develops a novel matrix-based approach to analyze the stability of accretion flows through mass accretion rate perturbations, extending previous velocity potential methods.

Findings

The perturbation propagation can be described by a 2x2 matrix with acoustic properties.

The formalism applies to both standing and traveling wave perturbations.

Results are exemplified in Schwarzschild spacetime, aligning with existing literature.

Abstract

We investigate the stability of stationary integral solutions of an ideal irrotational fluid in a general static and spherically symmetric background, by studying the profile of the perturbation of the mass accretion rate. We consider low angular momentum axisymmetric accretion flows for three different accretion disk models and consider time dependent and radial linear perturbation of the mass accretion rate. First we show that the propagation of such perturbation can be determined by an effective $2\times2$ matrix, which has qualitatively similar acoustic causal properties as one obtains via the perturbation of the velocity potential. Next, using this matrix we analytically address the stability issues, for both standing and travelling wave configurations generated by the perturbation. Finally, based on this general formalism we briefly discuss the explicit example of the Schwarzschild spacetime and compare our results of stability with the existing literature, which instead address this problem via the perturbation of the velocity potential.