Saturation Level of Turbulence in Collapsing Gas Clouds

Abstract

We investigate the physical mechanism that determines the saturation level of the turbulence in collapsing gas clouds. We perform a suite of high-resolution numerical simulations that follow the collapse of turbulent gas clouds, with various effective polytropic exponents γ eff , initial Mach numbers  0 , and initial turbulent seeds. Equating the energy injection rate from gravitational contraction and the dissipation rate of the turbulence, we obtain an analytic expression for the saturation level of the 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 the Jeans length of the collapsing core. These results indicate that the strength of the turbulence at first-core formations in the early universe/the present-day star formation process can be estimated solely by γ eff .