The U-shaped Distribution of Globular Cluster-specific Frequencies in a Biased Globular Cluster Formation Scenario

Abstract

Using high-resolution numerical simulations, we investigate mass- and luminosity-normalized specific frequencies (T_N and S_N, respectively) of globular cluster systems (GCSs) in order to understand the origin of the observed U-shaped relation between S_N and V-band magnitude (M_V) of their host galaxies. We adopt a biased GC formation scenario in which GC formation is truncated in galaxy halos that are virialized at a later redshift, z_trun. T_N is derived for galaxies with GCs today and converted into S_N for reasonable galaxy mass-to-light-ratios (M/L). We find that T_N depends on halo mass (M_h) in the sense that T_N can be larger in more massive halos with M_h > 10^9 M_sun, if z_trun is as high as 15. We however find that the dependence is too weak to explain the observed S_N-M_V relation and the wide range of S_N in low-mass early-type galaxies with -20.5 < M_V