Abstract: Globular clusters (GC) are important objects for tracing
the early evolution of a galaxy. We study the correlation between the
cluster population and the global properties of the host galaxy. We
found that the correlation between cluster population (NGC) and
the baryonic mass (Mb) of the host galaxy are best described as
10
−5.6038Mb. In order to understand the origin of the U -shape
relation between the GC specific frequency (SN) and Mb (caused
by the high value of SN for dwarfs galaxies and giant ellipticals
and a minimum SN for intermediate mass galaxies≈ 1010M), we
derive a theoretical model for the specific frequency (SNth). The
theoretical model for SNth is based on the slope of the power-law
embedded cluster mass function (β) and different time scale (Δt) of
the forming galaxy. Our results show a good agreement between the
observation and the model at a certain β and Δt. The model seems
able to reproduce higher value of SNth of β = 1.5 at the midst
formation time scale.