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

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 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.

Binary asteroseismic modelling: isochrone-cloud methodology and application toKeplergravity mode pulsators

“…Additionally, the chemical mixing alters ∇ µ just outside of the core according to the chosen prescription. Recent asteroseismic modelling by Moravveji et al (2015Moravveji et al ( , 2016 has shown that a diffusive exponential overshooting better reproduces observed period-spacing patterns of B-type stars of ∼ 3M compared to a diffusive step overshooting implementation -see also Pedersen et al (2018) for the capacity of g modes to distinguish these two from mode trapping. Here, we use diffusive exponential overshooting in our grid, taking the values shown in Table 1.…”

Asteroseismology of High-Mass Stars: New Insights of Stellar Interiors With Space Telescopes

“…This is predicated on the non-zero inertia of convective bubbles at a convective boundary causing them to overshoot into a radiative layer. In massive stars, the overshooting of the convective core (also known as convective-boundary mixing) entrains hydrogen from the envelope into the core resulting in a longer main sequence lifetime and a larger helium core mass (Pedersen et al, 2018;Michielsen et al, 2019). This has a direct impact on the characteristic g-mode period, 0 , of main-sequence stars with convective cores (Mombarg et al, 2019).…”

“…Typically, these two prescriptions in the shape of convective core overshooting are referred to as α ov and f ov , respectively, in the literature and differ approximately by a factor of 10-12 (Moravveji et al, 2015). However, it is only recently that asteroseismology has demonstrated the potential to discriminate them in observations using g-mode period spacing patterns (Moravveji et al, 2015(Moravveji et al, , 2016Pedersen et al, 2018). Moreover, there is considerable ongoing work using 3D hydrodynamical simulations (Augustson and Mathis, 2019) and g-mode pulsations to probe the temperature gradient within an overshooting layer and ascertain if it is adiabatic, radiative, or intermediate between the two (Michielsen et al, 2019).…”

“…The mixing profile at the interface of convective and radiative regions, and the mixing profile within the envelope directly impact the amount of hydrogen available for nuclear burning. With more internal mixing, a massive star experiences a longer main sequence and produces a larger helium core mass at the end of the main sequence since fresh hydrogen from the envelope is readily supplied to the convective core (Miglio et al, 2008b;Kippenhahn et al, 2012;Pedersen et al, 2018;Michielsen et al, 2019). In the case of single, slowly rotating and non-magnetic massive stars, it is the internal mixing profile and helium core mass that dictates the evolution beyond the main sequence and determines the ultimate end state.…”

Convective boundary mixing in low- and intermediate-mass stars – I. Core properties from pressure-mode asteroseismology

“…The difference to Equation 1 is that the decay in the mixing velocities result a smoothly varying composition rather than a step in the mean-molecular weight profile. We refer the reader to Pedersen et al (2018) for a recent summary of the possible formulations of chemical mixing at convective boundaries (Herwig et al 2007;Rogers & McElwaine 2017).…”