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

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 $2\times 2$ 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.

arXiv commentv4, 15pp; discussions pertaining the stability analysis emphasized; main results unchanged; accepted in New Astronomy

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Cited by in corpus (12)

• Shocks in the relativistic transonic accretion with low angular momentum
• Relativistic sonic geometry for isothermal accretion in the Schwarzschild metric
• Linear perturbations of low angular momentum accretion flow in the Kerr metric and the corresponding emergent gravity phenomena
• Acoustic geometry obtained through the perturbation of the Bernoulli's constant
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• Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole systems
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• Effect of matter geometry on low angular momentum black hole accretion in the Kerr metric
• Acoustic Analogue of Gravitational Wave
• Dynamical analogue spacetimes in non-relativistic flows
• Analog rotating black holes in a magnetohydrodynamic inflow
• Emergent gravity through non-linear perturbation