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 \mbox { $ { d } $ } L \propto L ^ { - \alpha } \mbox { $ { d } $ } L , with a mean exponent of < \alpha > = 2.0 \pm 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 M51 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 M51 this suggests a maximum mass of \mbox { $M _ { max } $ } = 0.5 - 1 \times 10 ^ { 6 } \mbox { $M _ { \odot } $ } , although the bend is only a 1-2 \sigma 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 M51 , corresponding to a maximum cluster mass of \mbox { $M _ { max } $ } = 1.3 - 2.5 \times 10 ^ { 6 } \mbox { $M _ { \odot } $ } .
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 M51 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 .