Basic Tools for Studies on the Formation and Disruption of Star
  Clusters: the Luminosity Function
  The luminosity function (LF) of young star clusters is often approximated by
a power law function. For clusters in a wide range of galactic environments
this has resulted in fit indices near -2, but on average slightly steeper. A
fundamental property of the -2 power law function is that the luminosity of the
brightest object (L_max) scales linearly with the total number of clusters,
which is close to what is observed. This suggests that the formation of Young
Massive Clusters (YMCs) is a result of the size of the sample, i.e. when the
SFR is high it is statistically more likely to form YMCs, but no particular
physical conditions are required. In this contribution we provide evidence that
the LF of young clusters is not a -2 power law, but instead is curved, showing
a systematic decrease of the (logarithmic) slope from roughly -1.8 at low
luminosities to roughly -2.8 at high luminosities. The empirical LFs can be
reproduced by model LFs using an underlying cluster IMF with a Schechter type
truncation around M*=2x10^5 M_sun. This value of M* can not be universal since
YMCs well in excess of this M* are known in merging galaxies and merger
remnants. Therefore, forming super massive clusters (>10^6 M_sun) probably
requires conditions different from those in (quiescent) spiral galaxies and
hence is not only the result of a size-of-sample effect. From the vertical
offset a cluster formation efficiency of ~10% is derived. We find indications
for this efficiency to be higher when the SFR is higher.
