Post first dredge-up [C/N] ratio as age indicator. Theoretical calibration

We performed a detailed analysis of the use of [C/N] measured in red giant branch stars between the completion of the first dredge up and the red giant branch bump ([C/N]_{FDU}) as age indicator. [C/N]_{FDU} cannot give accurate ages for individual stars, but may provide a general chronology for the formation of composite populations and add constraints to analyses of red giants from surface gravity-effective temperature diagrams. We provide a theoretical calibration of [C/N]_{FDU} in terms of total metallicity [M/H] and age, for ages greater than 1 Gyr, which we tested against variations in the initial heavy element distribution (scaled-solar vs alpha-enhanced), efficiency of overshooting from MS convective cores and from the convective envelopes, variations in the initial He abundance and in the mixing length parameter. Our calibration is compared with a small sample of available measurements of [C/N]_{FDU} in star clusters and halo field stars, which at least qualitatively confirm the overall trend of the predicted [C/N]_{FDU} with age and [M/H]. The use of [C/N]_{FDU}-[M/H]-age relations obtained from independent sets of stellar evolution calculations cause age differences (for a given [C/N]_{FDU} and [M/H] pair) up to about 2~Gyr. More accurate spectroscopic measurements of [C/N]_{FDU} in star clusters with well-established ages and metallicities are required to better test theoretical calibrations of this age indicator.