Age Gradient and the Second Parameter Problem in the Galactic Halo

We establish a framework for determing absolute ages of Galactic globular clusters and then use these ages to investigate the age-metallicity and age-Galactocentric distance relations for the 36 clusters with the most reliable age data. The clusters span Galactocentric distances from 4 through 100 kpc and cover a metallicity range from $[Fe/H] = -0.6$ to $-2.3$. Adopting currently plausible choices for the relation between cluster metallicity and horizontal-branch luminosity, and alpha-enhancement ratios, we find that the majority of the globular clusters form an age distribution with a dispersion $\sigma(t)$ about $10^9$ years, and a total age spread smaller than 4 Gyr. Clusters in the lowest metallicity group ($[Fe/H] < -1.8$) appear to be the same age to well within 1 Gyr at all locations in the Milky Way halo, suggesting that star formation began throughout the halo nearly simultaneously in its earliest stages. We find no statistically significant correlation between mean cluster age and Galactocentric distance (no age gradient) from 4 to 100 kpc. The correlation between cluster age and horizontal-branch type suggests that causes in addition to metallicity and age are required to understand the distribution of stars along the horizontal branches in globular cluster color-magnitude diagrams.