Mixed-mode coupling in the red clump. I. Standard single-star models

The investigation of global, resonant oscillation modes in red-giant stars offers valuable insights into their internal structures. In this study, we investigate the information we can recover on the structural properties of core-helium burning stars by examining how the coupling between gravity- and pressure-mode cavities depends on several stellar properties, including mass, chemical composition, evolutionary state, and core-to-envelope mass ratio. Using the structure of models computed with the stellar evolution code MESA, we compute the coupling coefficient implementing analytical expressions appropriate for the strong coupling regime, which well describes the structure of the evanescent region in core-helium burning stars. Our analysis reveals a notable anti-correlation between the coupling coefficient and both the mass and metallicity of stars in the regime M ≲ 1.8 M⊙, in agreement with Kepler data, attributing this primarily to variations in the density contrast between the stellar envelope and core. The strongest coupling is thus expected for red horizontal-branch stars, partially stripped stars, and stars in the higher-mass range exhibiting solar-like oscillations (M ≳ 1.8 M⊙). While our investigation emphasises some limitations of current analytical expressions, it also presents promising avenues. The frequency dependence of the coupling coefficient emerges as a potential tool for reconstructing the stratification of the evanescent region.