Variation of the high-mass slope of the stellar initial mass function: Theory meets observations

Abstract: We present observational evidence of the correlation between the high-mass slope of the stellar initial mass function (IMF) in young star clusters and their stellar surface density, $\sigma_{}$. When the high-mass end of the IMF is described by a power law of the form $dN/d{\rm log}{M_{}}\propto M_{}^{-\Gamma}$, the value of $\Gamma$ is seen to weakly decrease with increasing $\sigma_{}$, following a $\Gamma=1.31~\sigma_{*}^{-0.095}$ relation. We also present a model that can explain these observations. The model is based on the idea that the coalescence of protostellar cores in a protocluster forming clump is more efficient in high density environments where cores are more closely packed. The efficiency of the coalescence process is calculated as a function of the parental clump properties and in particular the relation between its mass and radius as well as its core formation efficiency. The main result of this model is that the increased efficiency of the coalescence process leads to shallower slopes of the IMF in agreement with the observations of young clusters, and the observations are best reproduced with compact protocluster forming clumps. These results have significant implications for the shape of the IMF in different Galactic and extragalactic environments and have very important consequences for galactic evolution.