The maximum stellar mass, star-cluster formation and composite stellar populations

We demonstrate that the mass of the most massive star in a cluster correlates non-trivially with the cluster mass. A simple algorithm, according to which a cluster is filled up with stars that are chosen randomly from the standard initial mass function (IMF) but sorted with increasing mass, yields an excellent description of the observational data. Algorithms based on random sampling from the IMF without sorted adding are ruled out with a confidence larger than 0.9999. A physical explanation of this would be that a cluster forms by more-massive stars being consecutively added until the resulting feedback energy suffices to revert cloud contraction and stops further star formation. This has important implications for composite populations. For example, 104 clusters of mass 102 M⊙ will not produce the same IMF as one cluster with a mass of 106 M⊙. It also supports the notion that the integrated galaxial stellar IMF (IGIMF) should be steeper than the stellar IMF and that it should vary with the star formation rate of a galaxy.