Stellar ages from [C/N] in giant stars: applicability and limitations
The [C/N] abundance ratio is a powerful age indicator for giant stars, enabling age estimates for spectroscopic samples where traditional methods are limited. We calibrate a multivariate [C/N]-age-[Fe/H] relationship using 9,122 giant stars observed by Kepler, with asteroseismic ages and APOGEE DR17 abundances. The calibration is performed separately for lower red giant branch (LRGB), upper RGB (URGB), and red clump (RC) stars. We validate the relationships using independent samples from K2, TESS, and open clusters, finding good agreement with reference ages, particularly for LRGB stars, with typical precision of ~30% for ages between ~2 - 10 Gyr. The performance degrades for URGB and RC stars and low metallicities, likely due to extra mixing processes, for young (<2 Gyr) and old (>10 Gyr) stars, where the [C/N]-age correlation weakens. We show that the [C/N]-based ages reproduce known Milky Way features, including the age distribution across the [alpha/Fe]-[Fe/H] plane and the flaring of the Galactic disc. Compared to other chemical clocks, [C/N] provides more robust and precise age estimates within its domain of validity. Our results demonstrate that [C/N], combined with metallicity, is an effective empirical tool for deriving stellar ages of giant stars from spectroscopic surveys, particularly for LRGB stars with [Fe/H] > -1, enabling Galactic archaeology studies beyond the reach of current asteroseismic samples.