The IMF in Young Galaxies: What Theory Might Tell Us
  Observations have not yielded convincing results concerning the form of the stellar initial mass function (IMF) or its variations in space and time, so it is proposed that theoretical models may provide useful guidance. Several classes of theoretical models for the physics controlling the IMF are reviewed, emphasizing the dependence of the results on the probability distribution of velocity and density fluctuations, the spatial density distribution, the softness of the equation of state as controlled by the dominant heating and cooling processes, the ambient radiation field, and the star formation rate itself. One particularly relevant result is the ability of turbulent interactions to form high-density condensations, which should vary with decreasing redshift as the dominant cooling mechanism changes from H$_2$, to fine structure lines, and finally to CO and gas-grain collisions, due to corresponding changes in the effective polytropic exponent. A second theme is the ability of some of these models to produce a characteristic or turnover mass in the IMF which has nothing to do with the Jeans mass. Further development of such models should provide IMFs whose functional dependence can be used as input for simulations of galaxy formation, in which the energy input from massive stars plays a crucial role, and for calculations of the consequences of protogalactic star formation on the subequent evolution of the universe. The probable irrelevance of the concepts of pressure-confined clouds and the formation of condensations by thermal instability in a turbulent interstellar medium is also discussed. 
John Scalo (The University of Texas at Austin)