# On the primordial specific frequency of globular clusters in dwarf and giant elliptical galaxies

## TL;DR

This paper develops a theoretical model linking globular cluster specific frequency to galaxy properties, considering star formation clustering and erosion effects, to explain observed variations across galaxy types.

## Contribution

It introduces a new model for the primordial globular cluster specific frequency based on star formation parameters and cluster erosion, aligning with observations.

## Key findings

- Model agrees with observed specific frequencies for certain parameters.
- Star formation clustering influences globular cluster system properties.
- Erosion impacts the relation between galaxy density and globular cluster frequency.

## Abstract

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) - and the properties of their host galaxies. In order to understand the origin of the relation between the GC specific frequency (SN) and galaxy mass, we devise a theoretical model for the specific frequency (SN,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, while high density galaxies have a small SN. We construct a model based on the hypothesis that star-formation is clustered and depends on the minimum embedded star cluster mass (Mecl,min), the slope of the power-law embedded cluster mass function (beta) and the relation between the star formation rate (SFR) and the maximum star cluster mass (Mecl,max). We find an agreement between the primordial value of the specific frequency (SNi) and our model for beta between 1.5 and 2.5 with Mecl,min <10^4 Msun.