We show that the masses of red giant stars can be well predicted from their photospheric carbon and nitrogen abundances, in conjunction with their spectroscopic stellar labels log g, Teff, and [Fe/H]. This is qualitatively expected from mass-dependent post main sequence evolution. We here establish an empirical relation between these quantities by drawing on 1,475 red giants with asteroseismic mass estimates from Kepler that also have spectroscopic labels from APOGEE DR12. We assess the accuracy of our model, and find that it predicts stellar masses with fractional r.m.s. errors of about 14% (typically 0.2 Msun). From these masses, we derive ages with r.m.s errors of 40%. This empirical model allows us for the first time to make age determinations (in the range 1-13 Gyr) for vast numbers of giant stars across the Galaxy. We apply our model to 52,000 stars in APOGEE DR12, for which no direct mass and age information was previously available. We find that these estimates highlight the vertical age structure of the Milky Way disk, and that the relation of age with [alpha/M] and metallicity is broadly consistent with established expectations based on detailed studies of the solar neighbourhood.
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