The ACS Fornax Cluster Survey. IX. The color-magnitude relation of globular cluster systems

We investigate the color-magnitude relation for globular clusters (GCs)-the so-called blue tilt-detected in the Advanced Camera for Surveys (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) equivalent to d(g - z)/dz = -0.0257 +/- 0.0050 for the full GC sample of the Fornax Cluster Survey (approximate to 5800 GCs). This is slightly shallower than the value gamma(z) = -0.0459 +/- 0.0048 found for the Virgo Cluster Survey GC sample (approximate to 11,100 GCs). The slope for the merged Fornax and Virgo data sets (approximate to 16,900 GCs) is gamma(z) = -0.0293 +/- 0.0085, corresponding to a mass-metallicity relation of Z alpha M(0.43+0.12). We find that the blue tilt sets in at masses in excess of M similar to 2 x 10(5)M(circle dot). The tilt is stronger for GCs belonging to high-mass galaxies (M(*) greater than or similar to 5 x 10(10) M(circle dot)) than for those in low-mass galaxies (M(*) less than or similar to 5 x 10(10) M(circle dot)). It is also more pronounced for GCs with smaller galactocentric distances. Our findings suggest a range of mass-metallicity relations Z(GC) alpha M(GC)(0.3-0.7) which vary as a function of host galaxy mass/luminosity, a scaling similar to that observed for dwarf spheroidal galaxies. 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 protocluster 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 color-magnitude diagrams (CMDs) defined by the GC systems associated with galaxies of similar mass and morphological type poses a challenge to any single mechanism, including self-enrichment, that seeks to explain generically the observed GC color-magnitude relations. We therefore suggest that the detailed (and stochastic) merger/accretion histories of individual galaxies have likely played a non-negligible role determining the distribution of GCs in the CMDs of individual GC systems