What determines the mass of the most massive star cluster in a galaxy: statistics, physics or disruption?

Abstract

In many different galactic environments the cluster initial mass function (CIMF) is well described by a power law with index −2. This implies a linear relation between the mass of the most massive cluster (M max ) and the number of clusters. Assuming a constant cluster formation rate and no disruption of the most massive clusters it also means that M max increases linearly with age when determining M max in logarithmic age bins. We observe this increase in five out of the seven galaxies in our sample, suggesting that M max is determined by the size of the sample. It also means that massive clusters are very stable against disruption, in disagreement with the mass-independent disruption (MID) model. For the clusters in M51 and the Antennae galaxies, the size-of-sample prediction breaks down around 106 M⊙, suggesting that this is a physical upper limit to the masses of star clusters in these galaxies. In this method there is a degeneracy between MID and a CIMF truncation. We show how the cluster luminosity function can serve as a tool to distinguish between the two.