Characterising the AGB bump and its potential to constrain mixing processes in stellar interiors

In the 90's, theoretical studies motivated the use of the asymptotic-giant branch bump (AGBb) as a standard candle given the weak dependence between its luminosity and stellar metallicity. Because of the small size of observed asymptotic-giant branch (AGB) samples, detecting the AGBb is not an easy task. However, this is now possible thanks to the wealth of data collected by the CoRoT, Kepler, and TESS space-borne missions. It is well-know that the AGB bump provides valuable information on the internal structure of low-mass stars, particularly on mixing processes such as core overshooting during the core He-burning phase. In this context, we analysed ~ 4,000 evolved giants observed by Kepler and TESS, including red-giant branch stars and AGB stars, for which asteroseismic and spectrometric data are available. By using statistical mixture models, we detected the AGBb both in frequency at maximum oscillation power and in effective temperature. Then, we used the Modules for Experiments in Stellar Astrophysics MESA stellar evolution code to model AGB stars and match the AGBb occurrence with observations. From observations, we could derive the AGBb location in 15 bins of mass and metallicity. We noted that the higher the mass, the later the AGBb occurs in the evolutionary track, which agrees with theoretical works. Moreover, we found a slight increase of the luminosity at the AGBb when the metallicity increases, which complicates the use of the AGBb as a standard candle. By fitting those observations with stellar models, we noticed that low-mass stars (M < 1.0 \(M_{\odot}\)) require a small core overshooting region during the core He-burning phase. This core overshooting extent increases toward high mass, but above M > 1.5 \(M_{\odot}\) we found that the AGBb location cannot be reproduced with a realistic He-core overshooting alone, and instead additional mixing processes have to be invoked.