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Turbulence is thought to be a primary driving force behind the early stagesof star formation. In this framework large, self gravitating, turbulent cloudsfragment into smaller clouds which in turn fragment into even smaller ones. Atthe end of this cascade we find the clouds which collapse into protostars.Following this process is extremely challenging numerically due to the largedynamical range so in this paper we propose a semi analytic framework which isable to follow star formation from the largest, giant molecular cloud (GMC)scale, to the final protostellar size scale. Due to the simplicity of theframework it is ideal for theoretical experimentation to explore the principalprocesses behind different aspects of star formation, at the cost of strongassumptions. The basic version of the model discussed in this paper onlycontains turbulence, gravity and crude assumptions about feedback, neverthelessit can reproduce the observed core mass function (CMF) and provide theprotostellar system mass function (PSMF), which shows a striking resemblance tothe observed IMF. Furthermore we find that to produce a universal IMFprotostellar feedback must be taken into account otherwise the PSMF peak showsa strong dependence on the background temperature.

Star Formation in a Turbulent Framework: From Giant Molecular Clouds to Protostars