On the Relative Ages of the $\alpha$-Rich and $\alpha$-Poor Stellar
  Populations in the Galactic Halo
  We study the ages of $\alpha$-rich and $\alpha$-poor stars in the halo using
a sample of F and G dwarfs from the Sloan Digital Sky Survey (SDSS). To
separate stars based on [$\alpha$/Fe], we have developed a new semi-empirical
spectral-index based method and applied it to the low-resolution, moderate
signal-to-noise SDSS spectra. The method can be used to estimate the
[$\alpha$/Fe] directly providing a new and widely applicable way to estimate
[$\alpha$/Fe] from low-resolution spectra. We measured the main-sequence
turnoff temperature and combined it with the metallicities and a set of
isochrones to estimate the age of the $\alpha$-rich and $\alpha$-poor
populations in our sample. We found all stars appear to be older than 8 Gyr
confirming the idea that the Galactic halo was formed very early on. A
bifurcation appears in the age-metallicity relation such that in the low
metallicity regime the $\alpha$-rich and $\alpha$-poor populations are coeval
while in the high metallicity regime the $\alpha$-rich population is older than
the $\alpha$-poor population. Our results indicate the $\alpha$-rich halo
population, which has shallow age-metallicity relation, was formed in a rapid
event with high star formation, while the $\alpha$-poor stars were formed in an
environment with a slower chemical evolution timescale.
