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

Abstract

We study the evolution of structures in turbulent, self-gravitating media, and present an analytical criterion $M_{\mathrm{crit}}\approx {\epsilon }_{\mathrm{cascade}}^{2/3}{\eta }^{-2/3}{G}^{-1}{l}^{5/3}$ (where $M_{\mathrm{crit}}$ is the critical mass, $l$ is the scale, ${\epsilon }_{\mathrm{cascade}}\approx \eta {\sigma }_{\mathrm{v}}^3/l$ is the turbulence energy dissipation rate of the ambient medium, $G$ is the gravitational constant, ${\sigma }_{\mathrm{v}}$ 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 ($l_{\mathrm{crit}}\approx {\epsilon }_{\mathrm{cascade}}^{1/2}{\eta }^{-1/2}{G}^{-3/4}{\rho }^{-3/4}$) for turbulent gravitational instability to develop. The analytical formalism explains the size dependence of the masses of the progenitors of star clusters ($M_{\mathrm{cluster}}\sim R_{\mathrm{cluster}}^{1.67}$) in our Galaxy.

arXiv commentAccepted by MNRAS

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