The High Mass Slope of the IMF

TL;DR

This paper investigates how local sampling biases and galactic environment affect the observed high-mass IMF slope, explaining why local measurements often show steeper slopes than the universal value.

Contribution

It models the impact of small sample volumes and galactic location on the apparent high-mass IMF slope, reconciling discrepancies in observational data.

Findings

Small sample volumes can cause the apparent IMF slope to be significantly steeper.

Location in an interarm region increases the likelihood of observing a steeper slope.

Observed steep slopes can be explained by sampling effects and galactic environment, not necessarily a different universal IMF.

Abstract

Recent papers have found that the inferred slope of the high-mass ($>1.5$ M$_\odot$) IMF for field stars in the solar vicinity has a larger value ($\sim 1.7-2.1$) than the slopes ($\sim 1.2-1.7$; Salpeter= 1.35) inferred from numerous studies of young clusters. We attempt to reconcile this apparent contradiction. Stars mostly form in Giant Molecular Clouds, and the more massive stars ($\gtrsim 3$ M$_\odot$) may have insufficient time before their deaths to uniformly populate the solar circle of the Galaxy. We examine the effect of small sample volumes on the {\it apparent} slope, $\Gamma_{\rm app}$, of the high-mass IMF by modeling the present day mass function (PDMF) over the mass range $1.5-6$ M$_\odot$. Depending on the location of the observer along the solar circle and the size of the sample volume, the apparent slope of the IMF can show a wide variance, with typical values steeper than the underlying universal value $\Gamma$. We show, for example, that the PDMFs observed in a small (radius $\sim 200$ pc) volume randomly placed at the solar circle have a $\sim 15-30$\% likelihood of resulting in $\Gamma_{\rm app} \gtrsim \Gamma+ 0.35$ because of inhomogeneities in the surface densities of more massive stars. If we add the a priori knowledge that the Sun currently lies in an interarm region, where the star formation rate is lower than the average at the solar circle, we find an even higher likelihood ($\sim 50-60\%$ ) of $\Gamma_{\rm app} \gtrsim \Gamma+0.35$, corresponding to $\Gamma_{\rm app} \gtrsim 1.7$ when the underlying $\Gamma= 1.35$.