Determining Ages of APOGEE Giants with Known Distances
  We present a sample of local red giant stars observed using the New Mexico
State University 1 m telescope with the APOGEE spectrograph, for which we
estimate stellar ages and the age distribution from the high-resolution
spectroscopic stellar parameters and accurate distance measurements from
Hipparcos. The high-resolution (R ~ 23,000), near infrared (H-band, 1.5-1.7
micron) APOGEE spectra provide measurements of the 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 40%. For red giants, the relatively rapid evolution of
stars up the red giant branch allows the age to be constrained based on 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 star formation history (SFH). To improve the prior on the SFH, we use
a hierarchical modeling approach to constrain the parameters of a model SFH
from the age probability distribution functions of the data. The results of an
alpha dependent Gaussian SFH model shows a clear relation between age and
[alpha/M] at all ages. Using this SFH model as the prior for an empirical
Bayesian analysis, we construct a full age probability distribution function
and determine ages for individual stars. The age-metallicity relation is flat,
with a slight decrease in [M/H] at the oldest ages and a ~ 0.5 dex spread in
metallicity. For stars with ages < 1 Gyr we find a smaller spread, consistent
with radial migration having a smaller effect on these young stars than on the
older stars.
