Modeling the Formation of Globular Cluster Systems in the Virgo Cluster

Abstract: The mass distribution and chemical composition of globular cluster (GC) systems preserve fossil record of the early stages of galaxy formation. The observed distribution of GC colors within massive early-type galaxies in the ACS Virgo Cluster Survey (ACSVCS) reveals a multi-modal shape, which likely corresponds to a multi-modal metallicity distribution. We present a simple model for the formation and disruption of GCs that aims to match the ACSVCS data. This model tests the hypothesis that GCs are formed during major mergers of gas-rich galaxies and inherit the metallicity of their hosts. To trace merger events, we use halo merger trees extracted from a large cosmological N-body simulation. We select 20 halos in the mass range of $2\times 10^{12}$ to $7\times 10^{13}M_\odot$ and match them to 19 Virgo galaxies with K-band luminosity between $3\times 10^{10}$ and $3\times 10^{11}L_\odot$. To set the [Fe/H] abundances, we use an empirical galaxy mass-metallicity relation. We find that a minimal merger ratio of 1:3 best matches the observed cluster metallicity distribution. A characteristic bimodal shape appears because metal-rich GCs are produced by late mergers between massive halos, while metal-poor GCs are produced by collective merger activities of less massive hosts at early times. The model outcome is robust to alternative prescriptions for cluster formation rate throughout cosmic time, but a gradual evolution of the mass-metallicity relation with redshift appears to be necessary to match the observed cluster metallicities. We also affirm the age-metallicity relation, predicted by an earlier model, in which metal-rich clusters are systematically several billion years younger than their metal-poor counterparts.