SIMBAD references

In the framework of the Gaia DR3 survey, we study the chemical composition of asymptotic giant branch (AGB) stars that have a high probability of being members to Galactic open clusters. To our knowledge, this is the first time such a study has been conducted. We analyse 16 AGB candidates, all of which are brighter than the tip of the red giant branch. There are nine of the C-star spectral type, two K stars, three M stars, one MS star, and one S star. Some of these stars belong to open clusters with an age corresponding to an initial mass of M_ini≈1.6-2.1 M_⊙, where the existence of a possible discontinuity (kink) in the initial-final mass relation (IFMR) has recently been suggested. By combining high-resolution spectroscopy at visual and near-infrared wavelengths, Gaia DR3 astrometry and photometry, and stellar models, we characterise each star in terms of its chemical abundances, luminosity, initial mass, and core mass. We find that the chemical pattern of the stars is similar to those found in AGB stars of the Galactic field with a similar metallicity. Globally, we matched the abundances found in each star at the observed luminosity (within the observational uncertainty) using nucleosynthesis predictions from the FUNS code for initial stellar masses in the range of ∼1.3-5.0 M_⊙, with metallicities in agreement with the ones determined spectroscopically. The inferred stellar masses are compatible with the turn-off mass obtained by fitting the Hertzsprung-Russell diagram of the corresponding cluster. Then, we constructed a semi-empirical IFMR from the core masses calculated at the end of the AGB phase. We find the usual monotonic increasing trend without evidence of a non-linearity in the initial mass range where the kink in the IFMR could exist, similar to that recently inferred from the analysis of white dwarf binaries.