# Instabilities in nonrelativistic spherically symmetric self-gravitating accretion

## TL;DR

This paper investigates the stability of nonrelativistic, spherically symmetric accretion flows with self-gravity, revealing instabilities caused by medium's gravity through a linear perturbation analysis.

## Contribution

It introduces a perturbative approach to analyze instabilities in self-gravitating accretion, highlighting the role of medium's gravity in flow stability.

## Key findings

- Self-gravity induces flow instabilities.
- Linear perturbation reveals emergent gravity effects.
- Instabilities are absent without self-gravity.

## Abstract

We consider time dependent problem in perturbative approach for a nonrelativistic inviscid spherically symmetric accretion model where the effect of the gravity of the medium is considered in Newtonian gravity framework. We consider spherically symmetric nonrelativistic accretion, i.e. Bondi accretion with self-gravity. Our approach is perturbative in the linear order of perturbation regime. We introduce linear perturbation over the existing steady state solution of the system. The analysis has two features, one is that the linear perturbation in mass accretion rate in such irrotational inviscid model of accretion gives rise to emergent gravity and on the other hand, we get some significant insights about instabilities in the flow due to the effect of gravity in the medium, whereas the instabilities are absent in the absence of self-gravity.