LAUSR

Globular clusters (GC) are important objects for tracing the early evolution of a galaxy. We study the relation between the properties of globular cluster systems—as quantified by the GC specific frequency (SN$S_{N}$)—and the properties of their host galaxies. In order to understand the origin of the relation between the GC specific frequency (SN$S_{N}$) and galaxy mass, we devise a theoretical model for the specific frequency (SN,th$S_{N,th}$). GC erosion is considered to be an important aspect for shaping this relation, since observations show that galaxies with low densities have a higher SN$S_{N}$, while high density galaxies have a small SN$S_{N}$. We construct a model based on the hypothesis that star-formation is clustered and depends on the minimum embedded star cluster mass (Mecl,min$\mathrm{{M}_{ecl,min}}$), the slope of the power-law embedded cluster mass function (β$\beta $) and the relation between the star formation rate (SFR) and the maximum star cluster mass (Mecl,max$\mathrm{{M}_{ecl,max}}$). We find an agreement between the primordial value of the specific frequency (SNi$S_{Ni}$) and our model for β$\beta $ between 1.5 and 2.5 with Mecl,min≤104M⊙$\mathrm{{M}_{ecl,min} \leq 10^{4}~\mathrm {M}_{\odot }}$.