$^{12}$C/$^{13}$C of Kepler giant stars: the missing piece of the mixing puzzle

Despite a rich observational background, few spectroscopic studies have dealt with the measurement of the carbon isotopic ratio in giant stars. However, it is a key element in understanding the mixing mechanisms that occur in the interiors of giant stars. We present the CNO and $^{12}$C/$^{13}$C abundances derived for 71 giant field stars. Then, using this new catalogue and complementary data from the Kepler and Gaia satellites, we study the efficiency of mixing occurring in the giant branch as a function of the stellar properties. We have determined the abundances of CNO and more specifically 12C/13C using the FIES Spectrograph on the Nordic Optical Telescope, for 71 giant field stars. In addition, asteroseismology is available for all stars, providing their mass, age as well as the evolutionary states. Finally, astrometry from Gaia data is also available for the majority of the sample. We compare these new determinations with stellar evolution models taking into account the effects of transport processes. To exploit the complete potential of our extensive catalogue and considering both the Galactic evolution and the impact of stellar evolution, we built mock catalogues using the Besancon Galaxy model in which stellar evolution models taking into account the effects of thermohaline instability are included. We confirm that 12C/13C at the surface of core He-burning stars is lower than that of first ascent RGB stars. 12C/13C measured at the surface of the core He-burning stars increases with [Fe/H] and mass while it decreases with age. These trends are all very well explained by the thermohaline mixing that occurs in red giants. We have shown that our models can explain the behaviour of 12C/13C versus N/O, although the observations seem to show a lower N/O than the models. We also note that more constraints on the thick disc core He-burning stars are needed to understand this difference.
Comment: Accepted for publication in A&A 18 pages 18 figures