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On the Relative Ages of the $α$-Rich and $α$-Poor Stellar Populations in the Galactic Halo

We study the ages of $α$-rich and $α$-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 [$α$/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 [$α$/Fe] directly providing a new and widely applicable way to estimate [$α$/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 $α$-rich and $α$-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 $α$-rich and $α$-poor populations are coeval while in the high metallicity regime the $α$-rich population is older than the $α$-poor population. Our results indicate the $α$-rich halo population, which has shallow age-metallicity relation, was formed in a rapid event with high star formation, while the $α$-poor stars were formed in an environment with a slower chemical evolution timescale.