The U - shaped distribution of globular cluster specific frequencies in a biased globular cluster formation scenario

Using high-resolution numerical simulations, we investigate massand luminosity-normalized specific frequencies (TN and SN, respectively) of globular cluster systems (GCSs) in order to understand the origin of the observed Ushaped relation between SN and V -band magnitude (MV) 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, ztrun. TN is derived for galaxies with GCs today and converted into SN for reasonable galaxy mass-tolight-ratios (M/L). We find that TN depends on halo mass (Mh) in the sense that TN can be larger in more massive halos with Mh > 10 M⊙, if ztrun is as high as 15. We however find that the dependence is too weak to explain the observed SN-MV relation and the wide range of SN in low-mass early-type galaxies with −20.5 < MV < −16.0 mag for a reasonable constant M/L. The MV-dependence of SN for the low-mass galaxies can be well reproduced, if the mass-to-light-ratio Mh/LV ∝ Mh , where α is as steep as −1. Based on these results, we propose that the origin of the observed U-shaped SN-MV relation of GCSs can be understood in terms of the bimodality in the dependence of Mh/LV on Mh of their host galaxies. We also suggest that the observed large dispersion in SN in low-mass galaxies is due partly to the large dispersion in TN. Subject headings: globular clusters: general – galaxies: star clusters – galaxies: evolution – galaxies: stellar content