The Origin of The Stellar Initial Mass Function

Observations and theories of the stellar initial mass function are reviewed. The universality and large total mass range of the power law portion of the IMF suggest a connection between stellar mass and cloud structure. The fractal patterns and formation times of young clusters suggest a further connection to turbulence. There is also a similarity between the characteristic mass at the lower end of the power law and the minimum self-gravitating mass in a typical star-forming cloud. All of this suggests that the power law part of the IMF comes from star formation in self-gravitating cloud pieces that are formed by compressible turbulence. Timing constraints involving cloud destruction and competition for gas might limit the upper stellar mass to several hundred suns. This upper limit has to be less than the mass of a clump that has a dynamical time equal to several times the dynamical time of the characteristic mass. The smallest stars and brown dwarfs may not come directly from cloud clumps, which are not self-gravitating at this mass in the cloudy phase, but from collapsed fragments or other pieces connected with the formation of more massive stars.