# Supersonic Turbulence and the Fragmentation of a Cold Medium

The role played by velocity fields in the fragmentation of a cold medium and in the formation of protostars is studied. The velocity field is modeled with a compressible turbulent flow. A supersonic turbulent velocity field can fragment the medium into clumps of mass smaller than a local Jeans' mass, and therefore stabilize the medium against the formation of protostars. Based on this idea, the protostar formation efficiency and the protostar mass distribution are determined as functions of the following ambient parameters: average density $n_{0}$, average temperature $T_{0}$, r.m.s. turbulent velocity $\sigma_{v,0}$ (or its Mach number ${\cal{M}}_{t}$), postshock cooling time (e.g. chemistry). The main results are: i) the protostar mass distribution and its dependence on the ambient parameters are quantified; ii) the characteristic protostar mass is $M_{J,cl}\propto n_{0}^{-1/2}T_{0}^{2} \sigma_{v,0}^{-1}$; iii) the protostar formation efficiency $e$ is higher for larger mean density, larger mean temperature, lower velocity dispersion on a given scale and longer postshock cooling time (e.g. lower metallicity): $e\propto n_{0}^{{3/2}(\beta-1)}T_{0}^{\beta -1} \sigma_{v,0}^{-5(\beta-1)}L_{0}^{3(\beta-1)}$, where $\beta>1$ is the exponent of the clump mass distribution; iv) the efficiency is quite sensitive to the ambient parameters and therefore to the dynamical evolution of the star forming system.