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 ($<0.71 \, M_\odot$) main sequence companion does not survive. During the CEE phase $\approx 1 \, M_\odot$ of material is ejected from the system, and the final star reaches the CHeB stage after helium flashes as if it were a single star of mass $\approx 0.7 \, M_\odot$, which is what we observe today. Although the proposed scenario is consistent with photometric and spectroscopic observations, a quantitative comparison with detailed stellar evolution calculations is needed to quantify the systematic skewness of radius, luminosity, and effective temperature distributions towards higher values than observations.