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Description
We present a sample of 705 local giant stars observed using the New Mexico State University 1m telescope with the Sloan Digital Sky Survey-III/Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectrograph, for which we estimate stellar ages and the local star formation history (SFH). The high-resolution (R~22500), near infrared (1.51-1.7{mu}m) APOGEE spectra provide measurements of stellar atmospheric parameters (temperature, surface gravity, [M/H], and [{alpha}/M]). Due to the smaller uncertainties in surface gravity possible with high-resolution spectra and accurate Hipparcos distance measurements, we are able to calculate the stellar masses to within 30%. For giants, the relatively rapid evolution up the red giant branch allows the age to be constrained by the mass. We examine methods of estimating age using both the mass-age relation directly and a Bayesian isochrone matching of measured parameters, assuming a constant SFH. To improve the SFH prior, we use a hierarchical modeling approach to constrain the parameters of the model SFH using the age probability distribution functions of the data. The results of an {alpha}-dependent Gaussian SFH model show a clear age-[{alpha}/M] relation at all ages. Using this SFH model as the prior for an empirical Bayesian analysis, we determine ages for individual stars. The resulting age-metallicity relation is flat, with a slight decrease in [M/H] at the oldest ages and a ~0.5 dex spread in metallicity across most ages. For stars with ages <~1Gyr we find a smaller spread, consistent with radial migration having a smaller effect on these young stars than on the older stars.
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