Monte-carlo Experiments on Star- Cluster Induced Integrated-galaxy Imf Variations

As most if not all stars are born in stellar clusters the shape of the mass function of the field stars is not only determined by the initial mass function of stars (IMF) but also by the cluster mass function (CMF). In order to quantify this Monte-Carlo simulations were carried out by taking cluster masses randomly from a CMF and then populating these clusters with stars randomly taken from an IMF. Two cases were studied. Firstly the star masses were added randomly until the cluster mass was reached. Secondly a number of stars, given by the cluster mass divided by an estimate of the mean stellar mass and sorted by mass, were added until the desired cluster mass was reached. Both experiments verified the analytical results of Kroupa & Weidner (2003) that the resulting integrated stellar initial mass function is a folding of the IMF with the CMF and therefore steeper than the input IMF above 1 M⊙. 1. The Integrated Galactic Initial Mass Function from Clustered Star Formation Kroupa & Weidner (2003) showed that the integrated galactic stellar initial mass function (IGIMF) is obtained by summing up the stellar IMFs contributed by all the star clusters that formed over the age of a galaxy. In their approach the mass of the most massive star in an embedded cluster with stellar mass Mecl is calculated from by 1 = ∫ mmax∗ mmax ξ(m) dm and Mecl = ∫ mmax ml mξ(m) dm. The resulting function mmax = fn(Mecl) is quantified by Weidner & Kroupa 2004 who infer that there exists a fundamental upper stellar mass limit, mmax∗ ≈ 150M⊙, because otherwise the populous cluster R136 would contain too many stars with m > 100M⊙.