The Stellar IMF from Turbulent Fragmentation

The morphology and kinematics of molecular clouds (MCs) are best explained as the consequence of super-sonic turbulence. Super-sonic turbulence fragments MCs into dense sheets, filaments and cores and large low density ``voids'', via the action of highly radiative shocks. We refer to this process as turbulent fragmentation. In this work we derive the mass distribution of dense cores due to turbulent fragmentation. The distribution of core masses depends primarily on the power spectrum of the turbulent flow and on the jump conditions for isothermal shocks in a magnetized gas. For a power spectrum index beta=-1.8, consistent with results of numerical experiments of super-sonic turbulence as well as with Larson's velocity-size relation, we obtain a power law mass distribution of dense cores with a slope equal to 3/(4-beta)=1.36, consistent with the slope of the stellar IMF. Given the fact that turbulent fragmentation is unavoidable in super-sonic turbulence, and given the success of the present model in predicting the correct slope of the stellar IMF without any free parameter, we conclude that turbulent fragmentation is the most important process at the origin of the stellar IMF. If the magnetic field is so weak that the magnetic pressure in the postshock gas is smaller than the thermal pressure the IMF is much steeper, with a power law slope 3/(5-2*beta)=2.1, which may be relevant for star formation at high redshift