The Gaia-ESO survey: Calibrating a relationship between Age and the
  [C/N] abundance ratio with open clusters
  In the era of large high-resolution spectroscopic surveys, high-quality
spectra can contribute to our understanding of the Galactic chemical evolution,
providing chemical abundances belonging to the different nucleosynthesis
channels, and also providing constraints to stellar age. Some abundance ratios
have been proven to be excellent indicators of stellar ages. We aim at
providing an empirical relationship between stellar ages and [C/N] using, as
calibrators, open star clusters observed by both the Gaia-ESO and APOGEE
surveys. We use stellar parameters and abundances from the Gaia-ESO and APOGEE
of the Galactic field and open cluster stars. Ages of star clusters are
retrieved from the literature sources and validated using a common set of
isochrones. We use the same isochrones to determine, for each age and
metallicity, the surface gravity at which the first dredge-up and red giant
branch bump occur. We study the effect of extra-mixing processes in our sample
of giant stars, and we derive the mean [C/N] in evolved stars, including only
stars without evidence of extra-mixing. Combining the Gaia-ESO and APOGEE
samples of open clusters, we derive a linear relationship between [C/N] and
logarithmic cluster ages. We apply our relationship to selected giant field
stars in both Gaia-ESO and APOGEE. We find an age separation between thin and
thick disc stars and age trends within their populations, with an increasing
age towards lower metallicity populations. With such empirical relationship, we
are able to provide an age estimate for giant stars in which C and N abundances
are measured. Isochrone fitting is less sensitive for giant than dwarf stars at
the turn off. The present method can be thus considered as an additional tool
to give an independent estimate of the age of giant stars, with uncertainties
in their ages comparable to those obtained using isochrone fitting for dwarf
stars.
