Turbulent Fragmentation and the Initial Conditions for Star Formation
  Super-sonic turbulence fragments molecular clouds (MC) into a very complex density field with density contrasts of several orders of magnitude. A fraction of the gas is locked into dense and gravitationally bound cores, which collapse as proto-stars. This process can be studied with numerical simulations of super-sonic self-gravitating turbulence.   In this work, we use numerical simulations of magneto-hydrodynamic (MHD), super-sonic, super-Alfv\'{e}nic and self-gravitating turbulence to compute the mass distribution of collapsing proto-stellar cores, which are selected as local density maxima. We find that the mass distribution of collapsing cores is consistent with the stellar initial mass function (IMF), suggesting that super-sonic turbulence may be responsible for the generation of the IMF.   To support this conclusion we also show that the physical properties of the numerically selected cores are in agreement with the properties of observed NH$_3$ cores and that their magnetic field strength is consistent with Zeeman splitting measurements.   In turbulent MCs, star formation occurs via the gravitational collapse of super-critical cores, formed by the turbulent flow, sub-critical cores being irrelevant for the process of star formation. 
Paolo Padoan, AAke Nordlund, Ornolfur Einar Rognvaldsson & Alyssa   Goodman