Anomalously low-mass core-He-burning star in NGC 6819 as a post-common-envelope phase product

Precise masses of red-giant stars enable a robust inference of their ages, but there are cases where these age estimates are highly precise yet very inaccurate. Examples are core-helium-burning (CHeB) stars that have lost more mass than predicted by standard single-star evolutionary models. Members of star clusters in the \({\it Kepler}\) database represent a unique opportunity to identify such stars, because they combine exquisite asteroseismic constraints with independent age information. In this work we focus on the single, metal-rich, Li-rich, low-mass, CHeB star KIC4937011, which is a member of the open cluster NGC 6819 (turn-off mass of \(\approx 1.6 \, M_\odot\), i.e. age of \(\approx 2.4\) Gyr). This star has \(\approx 1 \, M_\odot\) less mass than expected for its age and metallicity, which could be explained by binary interactions or mass-loss along the red-giant branch (RGB). To infer formation scenarios for this object, we perform a Bayesian analysis by combining the binary stellar evolutionary framework \(\texttt{binary_c v2.2.3}\) with the dynamic nested sampling approach contained in the \(\texttt{dynesty v2.1.1}\) package. We find that this star is likely the result of a common-envelope evolution (CEE) phase during the RGB stage of the primary star in which the low-mass (\(