Criteria for gravitational instability and quasi-isolated gravitational collapse in turbulent medium

TL;DR

This paper derives an analytical criterion for gravitational collapse in turbulent media, linking turbulence properties to the critical mass and scale for collapse, and explaining star cluster progenitor sizes.

Contribution

It introduces a new analytical criterion for gravitational collapse in turbulent media, connecting turbulence energy dissipation to critical mass and scale for collapse.

Findings

Derived the critical mass and scale for gravitational collapse in turbulent media.

Explained the size dependence of star cluster progenitor masses.

Provided a formalism consistent with observed star cluster sizes.

Abstract

We study the evolution of structures in turbulent, self-gravitating media, and present an analytical criterion $M_{\rm crit} \approx \epsilon_{\rm cascade}^{2/3} \eta^{-2/3} G^{-1} l^{5/3}$ (where $M_{\rm crit}$ is the critical mass, $l$ is the scale, $\epsilon_{\rm cascade}\approx \eta \sigma_{\rm v}^3 /l $ is the turbulence energy dissipation rate of the ambient medium, $G$ is the gravitational constant, $\sigma_{\rm v}$ is the velocity dispersion, $l$ is the scale and $\eta\approx 0.2$ is an efficiency parameter) for an object to undergo quasi-isolated gravitational collapse. The criterion also defines the critical scale ($l_{\rm crit} \approx \epsilon_{\rm cascade}^{1/2} \eta^{-1/2} G^{-3/4} \rho^{-3/4}$) for turbulent gravitational instability to develop. The analytical formalism explains the size dependence of the masses of the progenitors of star clusters ($M_{\rm cluster} \sim R_{\rm cluster}^{1.67}$) in our Galaxy.