Abstract
Precise masses of red giant stars enable a robust inference of their ages, but there are cases where these age estimates are very precise but also 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 Kepler database represent a unique opportunity to identify such stars because they combine exquisite asteroseismic constraints with independent age information (members of a star cluster share a similar age and chemical composition). We focus on the single metal-rich (Z approximate to Z(circle dot)) Li-rich low-mass CHeB star KIC4937011, which is a member of the open cluster NGC 6819 (turn-off mass of approximate to 1.6 M-circle dot, i.e. an age of approximate to 2.4 Gyr). This star has a lower mass by approximate to 1 M-circle dot than expected for its age and metallicity, which might be explained by binary interactions or mass loss along the red giant branch (RGB). To infer formation scenarios for this object, we performed a Bayesian analysis by combining the binary stellar evolutionary framework BINARY_C V2.2.3 with the dynamic nested-sampling approach contained in the DYNESTY V2.1.1 package. We find that this star probably is 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-circle dot) main-sequence companion does not survive. The mass of the primary star at the zero-age main sequence is in the range [1.46, 1.71] M-circle dot, with a log-orbital period in the range [0.06, 2.4] log(10)(days). During the CEE phase, approximate to 1 M-circle dot 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 with a mass of approximate to 0.7 M-circle dot, 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 the radius, luminosity, and effective temperature distributions towards higher values than observations.