On the Gravitational Collapse of a Gas Cloud in Presence of Bulk Viscosity

TL;DR

This paper investigates how bulk viscosity affects the gravitational collapse of a gas cloud, showing that strong viscous effects suppress sub-structure formation in adiabatic-like collapses but not in isothermal-like ones.

Contribution

It extends Newtonian models of gravitational collapse to include bulk viscosity effects, revealing their impact on structure formation and perturbation behavior.

Findings

Viscous effects suppress sub-structure formation in adiabatic-like collapse.

In isothermal-like collapse, sub-structures still form despite viscosity.

A threshold scale emerges where perturbations grow due to viscosity.

Abstract

We analyze the effects induced by the bulk viscosity on the dynamics associated to the extreme gravitational collapse. Aim of the work is to investigate whether the presence of viscous corrections to the evolution of a collapsing gas cloud influence the fragmentation process. To this end we study the dynamics of a uniform and spherically symmetric cloud with corrections due to the negative pressure contribution associated to the bulk viscosity phenomenology. Within the framework of a Newtonian approach (whose range of validity is outlined), we extend to the viscous case either the Lagrangian, either the Eulerian motion of the system and we treat the asymptotic evolution in correspondence to a viscosity coefficient of the form $\zeta=\zeta_0 \rho^{nu}$ ($\rho$ being the cloud density and $\zeta_0=const.$). We show how, in the adiabatic-like behavior of the gas (i.e. when the politropic index takes values $4/3<\gamma\leq5/3$), density contrasts acquire, asymptotically, a vanishing behavior which prevents the formation of sub-structures. We can conclude that in the adiabatic-like collapse the top down mechanism of structures formation is suppressed as soon as enough strong viscous effects are taken into account. Such a feature is not present in the isothermal-like (i.e. $1\leq\gamma<4/3$) collapse because the sub-structures formation is yet present and outlines the same behavior as in the non-viscous case. We emphasize that in the adiabatic-like collapse the bulk viscosity is also responsible for the appearance of a threshold scale beyond which perturbations begin to increase.