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We examine the correlation between globular cluster (GC) color and magnitudeusing HST/ACS imaging for a sample of 79 early-type galaxies (-21.7<M_B<-15.2mag) with accurate SBF distances from the ACS Virgo Cluster Survey. Using theKMM mixture modeling algorithm, we find a highly significant correlation,d(g-z)/dz = -0.037 +- 0.004, between color and magnitude for the subpopulationof blue GCs in the co-added GC color-magnitude diagram of the three brightestVirgo galaxies (M49, M87 and M60): brighter GCs are redder than their faintercounterparts. For the single GC systems of M87 and M60, we find similarcorrelations; M49 does not appear to show a significant trend. There is nocorrelation between (g-z) and M_z for GCs of the red subpopulation. Thecorrelation d(g-z)/dg for the blue subpopulation is much weaker than d(g-z)/dz.Using Monte Carlo simulations, we attribute this to the fact that the bluesubpopulation in M_g extends to higher luminosities than the red subpopulation,which biases the KMM fits. The correlation between color and M_z thus is a realeffect. This conclusion is supported by biweight fits to the same colordistributions. We identify two environmental dependencies of thecolor-magnitude relation: (1) the slope decreases in significance withdecreasing galaxy luminosity; and (2) the slope is stronger for GCs at smallergalactocentric distances. We examine several mechanisms that might give rise tothe observed color-magnitude relation: (1) presence of contaminators; (2)accretion of GCs from low-mass galaxies; (3) stochastic effects; (4) capture offield stars by individual GCs; and (5) GC self-enrichment. We conclude thatself-enrichment and field-star capture, or a combination of these processes,offer the most promising means of explaining our observations.Comment: 15 pages, 12 figures, accepted for publication in the Astrophysical  Journal. Uses emulateapj.cl

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