# Probing the temperature gradient in the core boundary layer of stars with gravito-inertial modes: the case of KIC$\,$7760680

**Authors:** M. Michielsen, C. Aerts, D. M. Bowman  
**arXiv:** [2104.04531](https://arxiv.org/abs/2104.04531)  
**Date:** 2021-04-09  
**Summary page:** https://www.summarizepaper.com/en/paper/2104.04531v2/

## Key points

- The study investigates the thermal and chemical structure in the near-core region of stars with a convective core using gravito-inertial modes.
- KIC$\,$7760680, a B-type star rotating at a quarter of its critical rotation velocity, is focused on.
- Grids of 1D stellar structure and evolution models are computed for two different prescriptions of the temperature gradient and mixing profile in the near-core region.
- Period spacings of modes with consecutive radial order offer a better diagnostic than mode periods or mode frequencies for asteroseismic modelling of stars revealing only high-order gravito-inertial modes.
- KIC$\,$7760680 reveals a radiative temperature gradient in models with convective boundary mixing but less complex models without such mixing are statistically preferred for this rotating star.
- Measured individual period spacing values for modes of consecutive radial order should be used as an asteroseismic diagnostic for stellar modelling of B-type pulsators with gravito-inertial modes.
- Few B-type stars with gravito-inertial modes have been modelled asteroseismically, especially fast rotators which offer more interesting cases to probe stellar interiors with the aim to improve stellar evolution theory.
- Several prescriptions exist to describe the temperature gradient and chemical mixing profile in convective core boundary layers; convective penetration with an adiabatic temperature gradient and constant diffusion coefficient is often used for B type stars.

## Summary

This study aims to investigate the thermal and chemical structure in the near-core region of stars with a convective core by means of gravito-inertial modes. The authors focus on the case of KIC$\,$7760680, a B-type star rotating at a quarter of its critical rotation velocity. They compute grids of 1D stellar structure and evolution models for two different prescriptions of the temperature gradient and mixing profile in the near-core region, and determine which prescription is preferred according to the prograde dipole modes detected in 4-yr $\textit{Kepler}$ photometry of KIC$\,$7760680. The authors consider different sets of asteroseismic observables and compare the outcomes of the regression problem for a $\chi^2$ and Mahalanobis Distance merit function, where the latter takes into account realistic uncertainties for theoretical predictions. They find that period spacings of modes with consecutive radial order offer a better diagnostic than mode periods or mode frequencies for asteroseismic modelling of stars revealing only high-order gravito-inertial modes. The results suggest that KIC$\,$7760680 reveals a radiative temperature gradient in models with convective boundary mixing but less complex models without such mixing are statistically preferred for this rotating star, revealing extremely low vertical envelope mixing. The authors conclude that measured individual period spacing values for modes of consecutive radial order should be used as an asteroseismic diagnostic for stellar modelling of B-type pulsators with gravito-inertial modes. The study highlights that few B-type stars with gravito-inertial modes have been modelled asteroseismically, especially fast rotators which offer more interesting cases to probe stellar interiors with the aim to improve stellar evolution theory. The limited number is due to various reasons including lack of long time series photometry data, avoidance by Kepler space telescope (Borucki et al., 2010) because these stars are massive in nature, and complexity involved in performing modelling when dealing with gravito inertial modes. The study also notes that several prescriptions exist to describe the temperature gradient and chemical mixing profile in convective core boundary layers; convective penetration with an adiabatic temperature gradient and constant diffusion coefficient is often used for B type stars. However, this study shows that less complex models without such mixing are statistically preferred for KIC$\,$7760680.