Measuring the extent of convective cores in low-mass stars using Kepler data: toward a calibration of core overshooting

¹ Université de Toulouse, UPS-OMP, IRAP, 31400 Toulouse, France
e-mail: sebastien.deheuvels@irap.omp.eu
² CNRS, IRAP, 14 avenue Édouard Belin, 31400 Toulouse, France
³ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
⁴ Centro de Astrofísica e Faculdade de Ciências, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
⁵ Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
⁶ LESIA, CNRS UMR 8109, Université Pierre et Marie Curie, Université Denis Diderot, Observatoire de Paris, 92195 Meudon, France
⁷ Observatoire de Paris, GEPI, CNRS UMR 8111, 92195 Meudon, France
⁸ Institut de Physique de Rennes, Université de Rennes 1, CNRS UMR 6251, 35042 Rennes, France
⁹ Univ. Paris-Sud, Institut d’Astrophysique Spatiale, UMR 8617, CNRS, Bâtiment 121, 91405 Orsay Cedex, France

Received: 15 December 2015
Accepted: 1 March 2016

Abstract

Context. Our poor understanding of the boundaries of convective cores generates large uncertainties on the extent of these cores and thus on stellar ages. The detection and precise characterization of solar-like oscillations in hundreds of main-sequence stars by CoRoT and Kepler has given the opportunity to revisit this problem.

Aims. Our aim is to use asteroseismology to consistently measure the extent of convective cores in a sample of main-sequence stars whose masses lie around the mass limit for having a convective core.

Methods. We first tested and validated a seismic diagnostic that was proposed to probe the extent of convective cores in a model-dependent way using the so-called r₀₁₀ ratios, which are built with l = 0 and l = 1 modes. We applied this procedure to 24 low-mass stars chosen among Kepler targets to optimize the efficiency of this diagnostic. For this purpose, we computed grids of stellar models with both the Cesam2k and mesa evolution codes, where the extensions of convective cores were modeled either by an instantaneous mixing or as a diffusion process.

Results. We found that 10 stars in our sample are in fact subgiants. Among the other targets, were able to unambiguously detect convective cores in eight stars, and we obtained seismic measurements of the extent of the mixed core in these targets with a good agreement between the Cesam2k and mesa codes. By performing optimizations using the Levenberg-Marquardt algorithm, we then obtained estimates of the amount of extra mixing beyond the core that is required in Cesam2k to reproduce seismic observations for these eight stars, and we showed that this can be used to propose a calibration of this quantity. This calibration depends on the prescription chosen for the extra mixing, but we found that it should also be valid for the code mesa, provided the same prescription is used.

Conclusions. This study constitutes a first step toward calibrating the extension of convective cores in low-mass stars, which will help reduce the uncertainties on the ages of these stars.