  The horizontal branch (HB) morphology of globular clusters (GCs) is most
strongly influenced by metallicity. The second parameter phenomenon
acknowledges that metallicity alone is not enough to describe the HB morphology
of all GCs. In particular, the outer Galactic halo contains GCs with redder HBs
at a given metallicity than are found inside the Solar circle. Thus, at least a
second parameter is required to characterize HB morphology. Here we analyze the
median color difference between the HB and the red giant branch (RGB), d(V-I),
measured from HST ACS photometry of 60 GCs within ~20 kpc of the Galactic
Center. Analysis of this homogeneous data set reveals that, after the influence
of metallicity has been removed, the correlation between d(V-I) and age is
stronger than that of any other parameter considered. Expanding the sample to
include HST photometry of the 6 most distant Galactic GCs lends additional
support to the correlation between d(V-I) and age. This result is robust with
respect to the adopted metallicity scale and the method of age determination,
but must bear the caveat that high quality, detailed abundance information is
not available for a significant fraction of the sample. When a subset of GCs
with similar metallicities and ages are considered, a correlation between
d(V-I) and central luminosity density is exposed. With respect to the existence
of GCs with anomalously red HBs at a given metallicity, we conclude that age is
the second parameter and central density is most likely the third. Important
problems related to HB morphology in GCs, notably multi-modal distributions and
faint blue tails, remain to be explained. (Abridged)

Solar and Stellar Astrophysics;Astrophysics of Galaxies