On the relation between the maximum stellar mass and the star cluster mass

It has been suggested for some time from observations (Larson 1982, 2003) and theory (Elmegreen 1983, 2000) that the mass of a star cluster probably limits the mass of the most massive star in the cluster. In this contribution we further investigate this relation with the use of three different sets of Monte-Carlo simulations. In the first set a number N of stars is randomly sampled from the IMF and than added to give the cluster mass. These cluster masses are then binned and the mean maximum mass for each bin is calculated. For the second set the cluster mass is given as a condition value and stars are drawn from the IMF until the cluster mass is reached. This is done 10000 times for a set of 10 different cluster masses and the mean maximum mass is calculated for each. Finally in the third set, again the cluster mass is a condition value but the number of stars in the cluster is calculated by dividing the cluster mass through the mean mass of the IMF. This number of stars is then drawn from the IMF but sorted by mass before being added. If the cluster mass is not reached, additional stars, determined by the cluster mass minus the sum of the stars divided by the mean mass, are drawn from the IMF. Then the stars are sorted and added again. This is again done 10000 times for a set of 10 different cluster masses and the mean maximum mass is calculated for each. We show that the observations of massive stars in young clusters favour the sorted sampling procedure, indicating that stars in star clusters starting with the lowest masses until the feedback stops the star-formation. Further, we discuss the implications of this for the stellar IMF in cluster systems. For example,