The Salpeter Slope of the IMF Explained

TL;DR

This paper explains the Salpeter slope of the stellar initial mass function (IMF) as a consequence of hierarchical star formation, where the steepening from an intrinsic -2 slope to -2.35 arises due to the inability of low-mass clumps to form the most massive stars.

Contribution

It provides a simple, observationally consistent explanation for the Salpeter slope based on hierarchical star formation and the limitations of low-mass clumps in forming massive stars.

Findings

The intrinsic IMF slope at small scales is -2.

Steepening to -2.35 occurs due to hierarchical formation constraints.

Model aligns with observations and simulations.

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 instrinsic 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.