Mass distributions of star clusters for different star formation
  histories in a galaxy cluster environment
  Clusters of galaxies usually contain rich populations of globular clusters
(GCs). We investigate how different star formation histories (SFHs) shape the
final mass distribution of star clusters. We assume that every star cluster
population forms during a formation epoch of length dt at a constant
star-formation rate (SFR). The mass distribution of such a population is
described by the embedded cluster mass function (ECMF), which is a pure power
law extending to an upper limit M_max. Since the SFR determines M_max, the ECMF
implicitly depends on the SFR. Starting with different SFHs, each SFH is
divided into formation epochs of length dt at different SFRs. The requested
mass function arises from the superposition of the star clusters of all
formation epochs. An improved optimal sampling technique is introduced that
allows generating number and mass distributions, both of which accurately agree
with the ECMF. Moreover, for each SFH the distribution function of all involved
SFRs, F(SFR), is computed. For monotonically decreasing SFHs, F(SFR) always
follows a power law. With F(SFR), we develope the theory of the integrated
galactic embedded cluster mass function (IGECMF). It describes the distribution
function of birth stellar masses of star clusters that accumulated over a
formation episode much longer than dt. The IGECMF indeed reproduces the mass
distribution of star clusters created according to the superposition principle.
Interestingly, all considered SFHs lead to a turn-down with increasing star
cluster mass in their respective IGECMFs. In the past, a turn-down at the
high-mass end has been observed for GC systems in different galaxy clusters and
in the cluster initial mass function. This behavior can be explained naturally
if the observed star cluster ensembles are superpositions of several individual
star cluster populations that formed at different times at different SFRs.
