The relation between the most-massive star and its parental star cluster mass

We present a thorough literature study of the most-massive star, m(max), in several young star clusters in order to assess whether or not star clusters are populated from the stellar initial mass function (IMF) by random sampling over the mass range 0.01 < m < 150 M-circle dot without being constrained by the cluster mass, M-ecl. The data reveal a partition of the sample into lowest mass objects (M-ecl < 102 M-circle dot), moderate mass clusters (102 M-circle dot < M-ecl < 103 M-circle dot) and rich clusters above 103 M-circle dot. Additionally, there is a plateau of a constant maximal star mass (m(max) approximate to 25 M-circle dot) for clusters with masses between 103 M-circle dot and 4 x 103 M-circle dot. Statistical tests of this data set reveal that the hypothesis of random sampling from the IMF between 0.01 and 150 M-circle dot is highly unlikely for star clusters more massive than 102 M-circle dot with a probability of p approximate to 2 x 10-7 for the objects with M-ecl between 102 and 103 M-circle dot and p approximate to 3 x 10-9 for the more massive star clusters. Also, the spread of m(max) values at a given M-ecl is smaller than expected from random sampling. We suggest that the basic physical process able to explain this dependence of stellar inventory of a star cluster on its mass may be the interplay between stellar feedback and the binding energy of the cluster-forming molecular cloud core. Given these results, it would follow that an integrated galactic IMF (IGIMF) sampled from such clusters would automatically be steeper in comparison to the IMF within individual star clusters.