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

Using high-resolution numerical simulations, we investigate mass- andluminosity-normalized specific frequencies (T_N and S_N, respectively) ofglobular cluster systems (GCSs) in order to understand the origin of theobserved U-shaped relation between S_N and V-band magnitude (M_V) of their hostgalaxies. We adopt a biased GC formation scenario in which GC formation is truncated ingalaxy halos that are virialized at a later redshift, z_trun. T_N is derivedfor galaxies with GCs today and converted into S_N for reasonable galaxymass-to-light-ratios (M/L). We find that T_N depends on halo mass (M_h) in thesense that T_N can be larger in more massive halos with M_h > 10^9 M_sun, ifz_trun is as high as 15. We however find that the dependence is too weak toexplain the observed S_N-M_V relation and the wide range of S_N in low-massearly-type galaxies with -20.5 < M_V < -16.0 mag for a reasonable constant M/L.The M_V-dependence of S_N for the low-mass galaxies can be well reproduced, ifthe mass-to-light-ratio M_h/L_V \propto M_h^{\alpha}, where \alpha is as steepas -1. Based on these results, we propose that the origin of the observedU-shaped S_N-M_V relation of GCSs can be understood in terms of the bimodalityin the dependence of M_h/L_V on M_h of their host galaxies. We also suggestthat the observed large dispersionin S_N in low-mass galaxies is due partly tothe large dispersion in T_N.Comment: 12 pages, 4 figures (two color), accepted by ApJ