The IMF of simple and composite populations

TL;DR

This paper discusses the constraints on the stellar initial mass function (IMF) in star clusters and galaxies, proposing that while the IMF appears universal, variations occur due to environmental factors, supported by observational data.

Contribution

It introduces the Cluster IMF Theorem and IGIMF Theorem, explaining how the IMF can be statistically constrained and varies with galaxy properties despite the universality hypothesis.

Findings

All well-resolved stellar populations are consistent with a common parent IMF.

Galaxy-wide IMFs vary with star-formation rate, as observed in SDSS data.

Evidence suggests IMF variations in extreme environments like the Galactic center and primordial stars.

Abstract

The combination of a finite time-scale for star formation, rapid early stellar evolution and rapid stellar-dynamical processes imply that the stellar IMF cannot be inferred for any star cluster independently of its age (the Cluster IMF Theorem). The IMF can nevertheless be constrained statistically by evolving many theoretical populations drawn from one parent distribution and testing these against observed populations. It follows that all known well-resolved stellar populations are consistent with having been drawn from the same parent mass distribution. The IMF Universality Hypothesis therefore cannot be discarded despite the existence of the Cluster IMF Theorem. This means that the currently existing star-formation theory fails to describe the stellar outcome, because it predicts a dependency of the IMF on the physical boundary conditions not observed. The IGIMF Theorem, however, predicts a variation of galaxy-wide IMFs in dependence of the galaxy's star-formation rate even if the IMF Universality Hypothesis is valid. This variation has now been observed in SDSS galaxy data. Detailed analysis of the binary properties in the very-low-mass star and brown dwarf (BD) mass regime on the one hand, and in the stellar regime on the other, shows there to be a discontinuity in the IMF near 0.1Msun such that BDs follow a separate distribution function. Very recent observations of the stellar population within 1pc of the nucleus of the MW do suggest a top-heavy IMF, perhaps hinting at a variation of the star-formation outcome with tidal field and temperature thereby violating the IMF Universality Hypothesis under these physically extreme conditions. Another violation of this hypothesis appears to emerge for extremely metal-poor stars such that the primordial IMF appears to have been depleted in low-mass stars.