The shape of convective core overshooting from gravity-mode period spacings

¹ Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
e-mail: maygade.pedersen@kuleuven.be
² Department of Astrophysics/IMAPP, Radboud University Nijmegen, 6500 GL Nijmegen, The Netherlands
³ Department of Mathematics & Statistics, Newcastle University, Newcastle upon Tyne, UK
⁴ Planetary Science Institute, Tucson, AZ 85721, USA

Received: 17 November 2017
Accepted: 6 February 2018

Abstract

Context. The evolution of stars born with a convective core is highly dependent on the efficiency and extent of near core mixing processes, which effectively increases both the core mass and main-sequence lifetime. These mixing processes remain poorly constrained and therefore result in large uncertainties in the stellar structure and evolution models of such stars.

Aims. We investigate to what extent gravity-mode period spacings in slowly pulsating B-type stars observed by the Kepler mission can be used to constrain both the shape and extent of convective core overshoot and additional mixing in the radiative envelope.

Methods. We compute grids of 1D stellar structure and evolution models for two different shapes of convective core overshooting and three shapes of radiative envelope mixing. The models in these grids are compared to a set of benchmark models to evaluate their capability of mimicking the dipole prograde g-modes of the benchmark models.

Results. Through our model comparisons we find that at a central hydrogen content of X_c = 0.5, dipole prograde g-modes in the period range 0.8−3 d are capable of differentiating between step and exponential diffusive overshooting. This ability disappears towards the terminal age main sequence at X _c = 0.1. Furthermore, the g-modes behave the same for the three different shapes of radiative envelope mixing considered. However, a constant envelope mixing requires a diffusion coefficient near the convective core five times higher than chemical mixing from internal gravity waves to obtain a surface nitrogen excess of ~ 0.5 dex within the main-sequence lifetime.

Conclusions. Within the estimated frequency errors of the Kepler mission, the ability of g-modes to distinguish between step and exponential diffusive overshooting depends on the evolutionary stage. Combining information from the average period spacing and observed surface abundances, notably nitrogen, could potentially be used to constrain the shape of mixing in the radiative envelope of massive stars.