The treatment of mixing in core helium burning models - I. Implications for asteroseismology

The detection of mixed oscillation modes offers a unique insight into the internal structure of core helium burning (CHeB) stars. The stellar structure during CHeB is very uncertain because the growth of the convective core, and/or the development of a semiconvection zone, is critically dependent on the treatment of convective boundaries. In this study we calculate a suite of stellar structure models and their non-radial pulsations to investigate why the predicted asymptotic g-mode $\ell = 1$ period spacing $\Delta\Pi_1$ is systematically lower than is inferred from Kepler field stars. We find that only models with large convective cores, such as those calculated with our newly proposed "maximal-overshoot" scheme, can match the average $\Delta\Pi_1$ reported. However, we also find another possible solution that is related to the method used to determine $\Delta\Pi_1$: mode trapping can raise the observationally inferred $\Delta\Pi_1$ well above its true value. Even after accounting for these two proposed resolutions to the discrepancy in average $\Delta\Pi_1$, models still predict more CHeB stars with low $\Delta\Pi_1$ ($ < 270$ s) than are observed. We establish two possible remedies for this: i) there may be a difficulty in determining $\Delta\Pi_1$ for early CHeB stars (when $\Delta\Pi_1$ is lowest) because of the effect that the sharp composition profile at the hydrogen burning shell has on the pulsations, or ii) the mass of the helium core at the flash is higher than predicted. Our conclusions highlight the need for the reporting of selection effects in asteroseismic population studies in order to safely use this information to constrain stellar evolution theory.