Spectroscopic determination of masses (and implied ages) for red giants
  The mass of a star is arguably its most fundamental parameter. For red giant
stars, tracers luminous enough to be observed across the Galaxy, mass implies a
stellar evolution age. It has proven to be extremely difficult to infer ages
and masses directly from red giant spectra using existing methods. From the
KEPLER and APOGEE surveys, samples of several thousand stars exist with
high-quality spectra and asteroseismic masses. Here we show that from these
data we can build a data-driven spectral model using The Cannon, which can
determine stellar masses to $\sim$ 0.07 dex from APOGEE DR12 spectra of red
giants; these imply age estimates accurate to $\sim$ 0.2 dex (40 percent). We
show that The Cannon constrains these ages foremost from spectral regions with
CN absorption lines, elements whose surface abundances reflect mass-dependent
dredge-up. We deliver an unprecedented catalog of 80,000 giants (including
20,000 red-clump stars) with mass and age estimates, spanning the entire disk
(from the Galactic center to R $\sim$ 20 kpc). We show that the age information
in the spectra is not simply a corollary of the birth-material abundances
[Fe/H] and [$\alpha$/Fe], and that even within a mono-abundance population of
stars, there are age variations that vary sensibly with Galactic position. Such
stellar age constraints across the Milky Way open up new avenues in Galactic
archeology.
