Star formation in a turbulent framework: from giant molecular clouds to protostars

Turbulence is thought to be a primary driving force behind the early stages of star formation. In this framework large, self-gravitating, turbulent clouds fragment into smaller clouds which in turn fragment into even smaller ones. At the end of this cascade we find the clouds which collapse into protostars. Following this process is extremely challenging numerically due to the large dynamical range, so in this paper we propose a semi-analytic framework which is able to model star formation from the largest, giant molecular cloud scale, to the final protostellar size scale. Because of the simplicity of the framework it is ideal for theoretical experimentation to explore the principal processes behind different aspects of star formation, at the cost of introducing strong assumptions about the collapse process. The basic version of the model discussed in this paper only contains turbulence, gravity and crude assumptions about feedback; nevertheless it can reproduce the observed core mass function and provide the protostellar system mass function (PSMF), which shows a striking resemblance to the observed initial mass function (IMF), if a non-negligible fraction of gravitational energy goes into turbulence. Furthermore we find that to produce a universal IMF protostellar feedback must be taken into account otherwise the PSMF peak shows a strong dependence on the background temperature.