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The ACS Virgo Cluster Survey IX: The Color Distributions of Globular Cluster Systems in Early-Type Galaxies

We present the color distributions of globular cluster (GC) systems for 100 Virgo cluster early-type galaxies observed in the ACS Virgo Cluster Survey. The color distributions of individual GC systems are consistent with continuous trends across galaxy luminosity, color, and stellar mass. On average, almost all galaxies possess a component of metal-poor GCs, with the average fraction of metal-rich GCs ranging from 15 to 60%. The colors of both subpopulations correlate with host galaxy luminosity and color, with the red GCs having a steeper slope. To convert color to metallicity, we also introduce a preliminary (g-z)-[Fe/H] relation calibrated to Galactic, M49 and M87 GCs. This relation is nonlinear with a steeper slope for [Fe/H] < -0.8. As a result, the metallicities of the metal-poor and metal-rich GCs vary similarly with respect to galaxy luminosity and stellar mass, with relations of [Fe/H]_MP ~ L^0.16 ~ M_star^0.17 and [Fe/H]_MR ~ L^0.26 ~ M_star^0.22, respectively. Although these relations are shallower than the mass-metallicity relation predicted by wind models and observed for dwarf galaxies, they are very similar to the mass-metallicity relation for star forming galaxies in the same mass range. The offset between the two GC populations varies slowly (~ M_star^0.05) and is approximately 1 dex across three orders of magnitude in mass, suggesting a nearly universal amount of enrichment between the formation of the two populations of GCs. We also find that although the metal-rich GCs show a larger dispersion in color, it is the *metal-poor GCs* that have an equal or larger dispersion in metallicity. Like the color-magnitude relation, these relations derived from globular clusters present stringent constraints on the formation and evolution of early-type galaxies. (Abridged)