We investigate the color-magnitude relation for globular clusters (GCs) -- the so-called blue tilt -- detected in the ACS Fornax Cluster Survey and using the combined sample of GCs from the ACS Fornax and Virgo Cluster Surveys. We find a tilt of gamma_z=d(g-z)/dz=-0.0257 +- 0.0050 for the full GC sample of the Fornax Cluster Survey (~5800 GCs). This is slightly shallower than the value gamma_z=-0.0459 +- 0.0048 found for the Virgo Cluster Survey GC sample (~11100 GCs). The slope for the merged Fornax and Virgo datasets (~16900 GCs) is gamma_z=-0.0293 +- 0.0085, corresponding to a mass-metallicity relation of Z ~ M^0.43. We find that the blue tilt sets in at GC masses in excess of M ~ 2*10^5 M_sun. The tilt is stronger for GCs belonging to high-mass galaxies (M_* > 5 * 10^10 M_sun) than for those in low-mass galaxies (M_* < 5 * 10^10 M_sun). It is also more pronounced for GCs with smaller galactocentric distances. Our findings suggest a range of mass-metallicity relations Z_GC ~ M_GC^(0.3-0.7) which vary as a function of host galaxy mass/luminosity. We compare our observations to a recent model of star cluster self-enrichment with generally favorable results. We suggest that, within the context of this model, the proto-cluster clouds out of which the GCs formed may have had density profiles slightly steeper than isothermal and/or star formation efficiencies somewhat below 0.3. We caution, however, that the significantly different appearance of the CMDs defined by the GC systems associated with galaxies of similar mass and morphological type pose a challenge to any single mechanism that seeks to explain the blue tilt. We therefore suggest that the merger/accretion histories of individual galaxies have played a non-negligible role determining the distribution of GCs in the CMDs of individual GC systems.
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