The Stellar Initial Mass Function from Turbulent Fragmentation

The morphology and kinematics of molecular clouds (MCs) are best explained asthe consequence of super--sonic turbulence. Super--sonic turbulence fragmentsMCs into dense sheets, filaments and cores and large low density ``voids'', viathe action of highly radiative shocks. We refer to this process as "turbulentfragmentation". In this work we derive the mass distribution of gravitationallyunstable cores generated by the process of turbulent fragmentation. The massdistribution above one solar mass depends primarily on the power spectrum ofthe turbulent flow and on the jump conditions for isothermal shocks in amagnetized gas. For a power spectrum index \beta=-1.74, consistent withLarson's velocity dispersion--size relation as well as with new numerical andanalytic results on super--sonic turbulence, we obtain a power law massdistribution of dense cores with a slope equal to 3/(4-\beta) = 1.33,consistent with the slope of the stellar IMF. Below one solar mass, the massdistribution flattens and turns around at a fraction of a solar mass, asobserved for the stellar IMF in a number of stellar clusters, because only thedensest cores are gravitationally unstable. The mass distribution at low massesis determined by the probability distribution of the gas density, which isknown to be approximately Log--Normal for an isothermal turbulent gas. Theintermittent nature of the turbulent density distribution is thus responsiblefor the existence of a significant number of small collapsing cores, even ofsub--stellar mass. Since turbulent fragmentation is unavoidable insuper--sonically turbulent molecular clouds, and given the success of thepresent model in predicting the observed shape of the stellar IMF, we concludethat turbulent fragmentation is essential to the origin of the stellar IMF.Comment: 15 pages, 3 figures included, submitted to Ap