Static and dynamic aspects of transonicity in Bondi accretion

TL;DR

This paper investigates the stability and behavior of transonic flows in Bondi accretion, revealing that while stationary solutions are unstable, time-dependent evolution leads to stable transonic flows and draws parallels with analog black hole metrics.

Contribution

It demonstrates that transonic accretion flows are inherently unstable in stationary analysis but become stable when analyzed dynamically over time, and connects flow perturbations to acoustic black hole metrics.

Findings

Stationary transonic flows are highly unstable to boundary deviations.

Time evolution results in stable transonic flows.

Flow perturbations resemble metrics of acoustic black holes.

Abstract

Transonicity in a spherically symmetric accreting system has been considered in both the stationary and the dynamic regimes. The stationary flow, set up as a dynamical system, has been shown to be greatly unstable to even the minutest possible deviation in the boundary condition for transonicity. With the help of a simple analytical model, and some numerical modelling, it has then been argued that the flow indeed becomes transonic and stable, when the evolution of the flow is followed through time. The time-dependent approach also shows that there is a remarkable closeness between an equation of motion for a perturbation in the flow, and the metric of an analog acoustic black hole.