A model for the initial stellar mass function based on random sampling in a hierarchical cloud is reviewed. The Salpeter function is readily obtained, with a flattening at low mass where cloud pieces cannot become self-gravitating. Fluctuations around the IMF are considered.

Introduction

The initial stellar mass function (IMF) shares two properties with turbulence: it is partly scale-free, with nearly a power law distribution for a factor of ∼ 100 in mass, and it is ubiquitous. The scale-free behavior is also like turbulence in the sense that the power law appears beyond a physical boundary, which in this case is set by the inability of gas to form stars at very low mass (at a given temperature and pressure). There is probably an upper boundary for stellar mass too, but this has not been observed yet because high mass stars are rare.

The IMF is ubiquitous as well, having about the same power law slope for the mass distribution function in a wide variety of environments, from old globular clusters to OB associations and young clusters. There are clear deviations from this average slope, and there are sometimes gaps and bumps in the IMF for particular clusters, but it is possible that these deviations and features are within the range of statistical fluctuations, as in the model discussed here. It is also possible that really significant differences in the IMF occur as a result of differences in the one physical parameter that enters this distribution, the lower mass limit.