# Probing the shape of the mixing profile and of the thermal structure at the convective core boundary through asteroseismology

## TL;DR

This study explores how asteroseismology can differentiate the thermal structure and mixing profiles near the convective core boundary in massive stars, revealing that temperature gradient changes have a more significant impact on mode frequencies than mixing shape.

## Contribution

It demonstrates that asteroseismic observations can distinguish between different thermal and mixing profiles near the core, especially with high-precision data and over various evolutionary stages.

## Key findings

- Mode frequencies are more sensitive to temperature gradient changes than mixing profile shape.
- Longer light curves improve the ability to distinguish between thermal and mixing profile differences.
- Higher-frequency pressure modes in β Cep stars show the largest frequency differences.

## Abstract

Aims: We investigate from a theoretical perspective if space asteroseismology can be used to distinguish between different thermal structures and shapes of the near-core mixing profiles for different types of coherent oscillation modes in massive stars with convective cores, and if this capacity depends on the evolutionary stage of the models along the main sequence. Methods: We compute 1D stellar structure and evolution models for four different prescriptions of the mixing and temperature gradient in the near-core region. Their effect on the frequencies of dipole prograde gravity modes in both Slowly Pulsating B and $\beta$ Cep stars is investigated, as well as for pressure modes in $\beta$ Cep stars. Results: A comparison between the mode frequencies of the different models at various stages during the main sequence evolution reveals that they are more sensitive to a change in temperature gradient than to the exact shape of the mixing profile in the near-core region. Depending on the duration of the observed light curve, one can distinguish between either just the temperature gradient, or also between the shapes of the mixing coefficient. The relative frequency differences are in general larger for more evolved models, and are largest for the higher-frequency pressure modes in $\beta$ Cep stars. Conclusions:In order to unravel the core boundary mixing and thermal structure of the near-core region, one must have asteroseismic masses and radii with $\sim 1\%$ relative precision for hundreds of stars.