The Turbulent Shock Origin of Proto--Stellar Cores

The fragmentation of molecular clouds (MC) into protostellar cores is a central aspect of the process of star formation. Because of the turbulent nature of super-sonic motions in MCs, it has been suggested that dense structures such as filaments and clumps are formed by shocks in a turbulent flow. In this work we present strong evidence in favor of the turbulent origin of the fragmentation of MCs. The most generic result of turbulent fragmentation is that dense post shock gas traces a gas component with a smaller velocity dispersion than lower density gas, since shocks correspond to regions of converging flows, where the kinetic energy of the turbulent motion is dissipated. Using synthetic maps of spectra of molecular transitions, computed from the results of numerical simulations of super--sonic turbulence, we show that the dependence of velocity dispersion on gas density generates an observable relation between the rms velocity centroid and the integrated intensity (column density), Sigma(V_0)-I, which is indeed found in the observational data. The comparison between the theoretical model (maps of synthetic 13CO spectra), with 13CO maps from the Perseus, Rosette and Taurus MC complexes, shows excellent agreement in the Sigma(V_0)-I relation. The Sigma(V_0)-I relation of different observational maps with the same total rms velocity are remarkably similar, which is a strong indication of their origin from a very general property of the fluid equations, such as the turbulent fragmentation process.