Context. Whether or not there exists a physical upper mass limit for star clusters is as yet unclear. For small cluster samples the mass function may not be sampled all the way to the truncation, if there is one. Data for the rich cluster population in the interacting galaxy M 51 enables us to investigate this in more detail. Aims. Using HST/ACS data, we investigate whether the cluster luminosity function (LF) in M 51 shows evidence for an upper limit to the mass function. The variations of the cluster luminosity function parameters with position on the disk are addressed. Methods. We determine the cluster LF for all clusters in M 51 falling within our selection criteria, as well as for several subsets of the sample. In that way we can determine the properties of the cluster population as a function of galactocentric distance and background intensity. By comparing observed and simulated LFs we can constrain the underlying cluster initial mass function and/or cluster disruption parameters. A physical upper mass limit for star clusters will appear as a bend dividing two power law parts in the LF, if the cluster sample is large enough to sample the full range of cluster masses. The location of the bend in the LF is indicative of the value of the upper mass limit. The slopes of the power laws are an interplay between upper mass limits, disruption times and evolutionary fading. Results. The LF of the cluster population of M 51 is better described by a double power law than by a single power law. We show that the cluster initial mass function is likely to be truncated at the high mass end. We conclude from the variation of the LF parameters with galactocentric distance that both the upper mass limit and the cluster disruption parameters are likely to be a function of position in the galactic disk. At higher galactocentric distances the maximum mass is lower, cluster disruption slower, or both
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