The Maximum Mass of Star Clusters
Abstract
When an universal untruncated star cluster initial mass function (CIMF) described by a power-law distribution is assumed, the mass of the most massive star cluster in a galaxy (Mmax) is the result of the size-of-sample (SoS) effect. This implies a dependence of Mmax on the total number of star clusters (N). The SoS effect also implies that Mmax within a cluster population increases with equal logarithmic intervals of age. This is because the number of clusters formed in logarithmic age intervals increases (assuming a constant cluster formation rate). This effect has been observed in the SMC and LMC. Based on the maximum pressure (Pint) inside molecular clouds, it has been suggested that a physical maximum mass (Mmax[phys]) should exist. The theory predicts that Mmax[phys] should be observable, i.e. lower than Mmax that follows from statistical arguments, in big galaxies with a high star formation rate. We compare the SoS relations in the SMC and LMC with the ones in M51 and model the integrated cluster luminosity function (CLF) for two cases: 1) Mmax is determined by the SoS effect and 2) Mmax=Mmax[phys]=constant. The observed CLF of M51 and the comparison of the SoS relations with the SMC and LMC both suggest that there exists a Mmax[phys] of 5*105 Msun in M51. The CLF of M51 looks very similar to the one observed in the ``Antennae'' galaxies. A direct comparison with our model suggests that there Mmax[phys]=2*106 Msun.
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