Ensemble seismic study of the properties of the core of Red Clump stars

TL;DR

Red clump stars offer a direct probe of core physics through mixed-mode asteroseismology, particularly the period spacing $\Delta\Pi$. The authors construct grids of core-helium-burning tracks with varying core-boundary-mixing (CBM) prescriptions and $\mathrm{^{12}C}(\alpha,\gamma)\mathrm{^{16}O}$ rates using MESA, then sample these grids with Kepler RC priors via Monte-Carlo to reproduce the observed $\Delta\Pi$ distribution. They find the best agreement for a maximal overshoot CBM scheme with mode trapping, which corresponds to a semi-convective-like region without core breathing pulses, and they show that reducing the $\mathrm{^{12}C}(\alpha,\gamma)\mathrm{^{16}O}$ rate by about 15% further improves the fit; an overabundance of early RC stars around $\Delta\Pi\approx250$ s is predicted by the models but not seen. The results favor a mode-trapping interpretation with quasi-semi-convective CBM and highlight sensitivity to the reaction rate, while pointing to future data (e.g., PLATO) to resolve the remaining discrepancies.

Abstract

Red clump stars still pose open questions regarding several physical processes, such as the mixing around the core, or the nuclear reactions, which are ill-constrained by theory and experiments. The oscillations of red clump stars, which are of mixed gravito-acoustic nature, allow us to directly investigate the interior of these stars and thereby better understand their physics. In particular, the measurement of their period spacing is a good probe of the structure around the core. We aim to explain the distribution of period spacings in red clump stars observed by Kepler by testing different prescriptions of core-boundary mixing and nuclear reaction rate. Using the MESA stellar evolution code, we computed several grids of core-helium burning tracks, with varying masses and metallicities. Each of these grids have been computed assuming a certain core boundary mixing scheme, or carbon-alpha reaction rate. We then sampled these grids, in a Monte-Carlo fashion, using observational spectroscopic metallicities and seismic masses priors, in order to retrieve a period spacing distribution that we compared to the observations. We found that the best fitting distribution was obtained when using a "maximal overshoot" core-boundary scheme, which has similar seismic properties as a model whose modes are trapped outside a semi-convective region, and which does not exhibit core breathing pulses at the end of the core-helium burning phase. If no mode trapping is assumed, then no core boundary mixing scheme is compatible with the observations. Moreover, we found that extending the core with overshoot worsens the fit. Additionally, reducing the carbon-alpha reaction rate (by around 15%) improves the fit to the observed distribution. Finally, we noted that an overpopulation of early red clump stars with period spacing values around 250s is predicted by the models but not found in the observations.

Figures (14)

• Figure 1: Period spacing distribution of the observed sample (data from Vrard2016). The uncertainties are computed following the procedure described in Appendix \ref{['uncertainty_bin']}.
• Figure 2: Brunt-Väisälä profiles of 4 models with different CBM schemes, all stopped at $Y_{\mathrm{c}} = 0.3$. We indicate in orange the overshoot region, that is fully chemically mixed with the convective core. The region in green indicates the semiconvective region, where $\nabla_{\mathrm{rad}} = \nabla_{\rm ad}$. Finally, we indicate the region over which $N/r$ is integrated in the trapped mode scenario (red) and in the non-trapped mode scenario (purple).
• Figure 3: Evolution of the period spacing during the CHeB phase for models computed with (dashed line) and without taking into account $\epsilon_g$ in the energy equation (full line).
• Figure 4: Period spacing uncertainties of the sample of Vrard2016, plotted against the period spacing values of the same work. The orange line shows the linear fit that we use to simulate the uncertainties in our simulations.
• Figure 5: Kernel density estimations of the distributions of luminosities and effective temperature of the observed (blue) and synthetic (orange) samples, substracted by the median value of the sample.