Supersonic turbulent flows 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 modelled 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 n₀ average temperature T₀, rms turbulent velocity σ_v,0 (or its Mach number M_t), and post-shock cooling time (e.g. chemistry). The main results are as follows. (i) The protostar’s mass distribution and its dependence on the ambient parameters are quantified. (ii) The characteristic protostar mass is $$M_{J,c1}\propto n_{0}^{-1/2}T_{0}^{2}\sigma_{v,0}^{-1}$$. (iii) The protostar formation efficiency e grows with increasing mean density and mean temperature, decreasing velocity dispersion on a given scale and increasing post-shock 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 $$\beta\gt1$$ 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.