The luminosity function of young star clusters: implications for the maximum mass and luminosity of clusters

We introduce a method to relate a possible truncation of the star cluster mass function at the high mass end to the shape of the cluster luminosity function (LF). We compare the observed LFs of five galaxies containing young star clusters with synthetic cluster population models with varying initial conditions. The LF of the SMC, the LMC and NGC 5236 are characterized by a power-law behavior N d L ∝ L^-α d L, with a mean exponent of < α> = 2.0 ± 0.2. This can be explained by a cluster population formed with a constant cluster formation rate, in which the maximum cluster mass per logarithmic age bin is determined by the size-of-sample effect and therefore increases with log (age/yr). The LFs of NGC 6946 and M 51 are better described by a double power-law distribution or a Schechter function. When a cluster population has a mass function that is truncated below the limit given by the size-of-sample effect, the total LF shows a bend at the magnitude of the maximum mass, with the age of the oldest cluster in the population, typically a few Gyr due to disruption. For NGC 6946 and M 51 this suggests a maximum mass of M_max = 0.5-1×10^6 M_⊙, although the bend is only a 1-2 σ detection. Faint-ward of the bend the LF has the same slope as the underlying initial cluster mass function and bright-ward of the bend it is steeper. This behavior can be well explained by our population model. We compare our results with the only other galaxy for which a bend in the LF has been observed, the "Antennae" galaxies (NGC 4038/4039). There the bend occurs brighter than in NGC 6946 and M 51, corresponding to a maximum cluster mass of M_max = 1.3-2.5×10⁶ M_⊙. Hence, if the maximum cluster mass has a physical limit, then it can vary between different galaxies. The fact that we only observe this bend in the LF in the "Antennae" galaxies, NGC 6946 and M 51 is because there are enough clusters available to reach the limit. In other galaxies there might be a physical limit as well, but the number of clusters formed or observed is so low, that the LF is not sampled up to the luminosity of the bend. The LF can then be approximated with a single power-law distribution, with an index similar to the initial mass function index.