Context. Ageing stars for reconstructing the history of the Milky Way remains one of the most difficult tasks in astrophysics. This involves knowing when it is safe to relate the stellar mass with its age and when it is not. The young α−rich (YAR) stars present such a case in which we are still not sure about their ages because they are relatively massive, implying young ages, but their abundances are α−enhanced, which implies old ages. Aims. We report the results from new observations from a long-term radial velocity monitoring campaign complemented with high resolution spectroscopy, as well as new astrometry and seismology of a sample of 41 red giants from the third version of APOKASC (Pinsonneault et al. in prep), which includes YAR stars. The aim is to better characterize the YAR stars in terms of binarity fraction, mass, abundance trends and kinematic properties. Methods. The radial velocities of HERMES, APOGEE and Gaia were combined to determine the binary fraction among YAR stars. In combination with their mass estimate, their evolutionary status, chemical composition and kinematic properties, it allows to better constrain the nature of these objects. Results. We find that the frequency of binaries among over-massive stars is not significantly different than that of the other stars in our sample, but that the most massive YAR stars are indeed single, which has been predicted by population synthesis models. Studying their [C/N], [C/Fe] and [N/Fe] trends with mass, many over-massive stars do not follow the APOKASC stars, favouring the scenario that most of them are product of mass transfer. Our sample further includes two under-massive stars, with sufficiently low masses so that these stars could not have reached the red giant phase without significant mass loss. Both over-massive and under-massive stars might show some anomalous APOGEE abundances such as N, Na, P, K and Cr, although higher resolution optical spectroscopy might be needed to confirm these findings. Conclusions. Considering the significant fraction of stars that are formed in pairs and the variety of ways that make mass transfer possible, the diversity in properties in terms of binarity and chemistry of the over-massive and under-massive stars studied here implies that it is not safe to directly relate the mass of the YAR stars with age and that most of these objects are likely not young.
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