Kepler red-clump stars in the field and in open clusters: constraints on core mixing

Convective mixing in Helium-core-burning (HeCB) stars is one of the outstanding issues in stellar modelling. The precise asteroseismic measurements of gravity-modes period spacing (ΔΠ1) has opened the door to detailed studies of the near-core structure of such stars, which had not been possible before. Here we provide stringent tests of various core-mixing scenarios against the largely unbiased population of red-clump stars belonging to the old open clusters monitored by Kepler, and by coupling the updated precise inference on ΔΠ1 in thousands field stars with spectroscopic constraints. We find that models with moderate overshooting successfully reproduce the range observed of ΔΠ1 in clusters. In particular we show that there is no evidence for the need to extend the size of the adiabatically stratified core, at least at the beginning of the HeCB phase. This conclusion is based primarily on ensemble studies of ΔΠ1 as a function of mass and metallicity. While ΔΠ1 shows no appreciable dependence on the mass, we have found a clear dependence of ΔΠ1 on metallicity, which is also supported by predictions from models.