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 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.
