The formation of star clusters – I. Three-dimensional simulations of hydrodynamic turbulence

We present the results of a series of numerical simulations of compressible, self-gravitating hydrodynamic turbulence of cluster-forming clumps in molecular clouds. We examine the role that turbulence has in the formation of gravitationally bound cores, studying the dynamical state, internal structure and bulk properties of these cores. Complex structure in turbulent clumps is formed provided that the damping time of the turbulence, tdamp, is longer than the gravitational free-fall time tff in a region. We find a variety of density and infall velocity structures among the cores in the simulation, including cores that resemble the Larson–Penston collapse of an isothermal sphere (ρ∝r−2) and cores that resemble the McLaughlin–Pudritz collapse of logatropic spheres (ρ∝r−1). The specific angular momentum profiles range between j∝r1−r2. The masses of the bound cores that form fit the initial mass function, while the specific angular momentum distribution can be fit by a broken power law. While our hydrodynamic simulations reproduce many of the observed properties of cores, we find an upper limit for the star formation efficiency in clusters of 40–50 per cent.