Implications of nonlinearity for spherically symmetric accretion

TL;DR

This paper investigates how nonlinear radial perturbations affect the stability of spherically symmetric accretion flows, revealing potential instabilities that hinder the flow's transition to a stable transonic state.

Contribution

It introduces a nonlinear perturbation analysis using a Liénard system, showing the development of instabilities in accretion flows that were previously considered stable.

Findings

Nonlinear perturbations lead to saddle points indicating instabilities.

Instabilities prevent the flow from reaching a stable transonic state.

Nonlinearity significantly influences the evolution of accretion flows.

Abstract

We subject the steady solutions of a spherically symmetric accretion flow to a time-dependent radial perturbation. The equation of the perturbation includes nonlinearity up to any arbitrary order, and bears a form that is very similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave on subsonic solutions, and maintaining nonlinearity in it up to the second order, we get the time-dependence of the perturbation in the form of a Li\'enard system. A dynamical systems analysis of the Li\'enard system reveals a saddle point in real time, with the implication that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. The instability of initial subsonic states also adversely affects the temporal evolution of the flow towards a final and stable transonic state.