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 follow star formation from the largest, giant molecular cloud (GMC)
scale, to the final protostellar size scale. Due to 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 strong
assumptions. 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 (CMF) and provide the
protostellar system mass function (PSMF), which shows a striking resemblance to
the observed IMF. 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.
