Saturation level of turbulence in collapsing gas clouds

TL;DR

This study combines high-resolution simulations and analytic modeling to determine how turbulence saturation levels in collapsing gas clouds depend on physical parameters, aiding understanding of star formation processes.

Contribution

It provides an analytic expression for turbulence saturation in collapsing clouds and validates it with numerical simulations, linking turbulence strength to the effective polytropic exponent.

Findings

Numerical results agree with the analytic model.

Turbulent driving scale is about one-third of the Jeans length.

Turbulence strength can be estimated from $\gamma_{ m eff}$.

Abstract

We investigate the physical mechanism that decides the saturation level of turbulence in collapsing gas clouds. We perform a suite of high-resolution numerical simulations following the collapse of turbulent gas clouds with various effective polytropic exponents $\gamma_{\rm eff}$, initial Mach numbers $\mathcal{M}_0$, and initial turbulent seeds. Equating the energy injection rate by gravitational contraction and the dissipation rate of turbulence, we obtain an analytic expression of the saturation level of turbulence, and compare it with the numerical results. Consequently, the numerical results are well described by the analytic model, given that the turbulent driving scale in collapsing gas clouds is one-third of Jeans length of collapsing core. These results indicate that the strength of turbulence at the first core formation in the early universe/present-day star-formation process can be estimated solely by $\gamma_{\rm eff}$.