The salpeter slope of the IMF explained

Abstract

If we accept a paradigm that star formation is a self-similar, hierarchical process, then the Salpeter slope of the IMF for high-mass stars can be simply and elegantly explained as follows. If the intrinsic IMF at the smallest scales follows a simple –2 power-law slope, then the steepening to the –2.35 Salpeter value results when the most massive stars cannot form in the lowest-mass clumps of a cluster. It is stressed that this steepening must occur if clusters form hierarchically from clumps, and the lowest-mass clumps can form stars. This model is consistent with a variety of observations as well as theoretical simulations.