Weak or strong: coupling of mixed oscillation modes on the red-giant branch

Abstract

Context. The high precision of recent asteroseismic observations of red-giant stars has revealed the presence of mixed dipole modes in their oscillation spectra. These modes allow for a look inside the stars. Among the parameters used to characterize mixed modes is the coupling strength q, which is sensitive to the stellar structure in the evanescent zone near the bottom of the convective envelope. Aims. The aim of this work is to probe the validity of the weak and strong coupling approximations, commonly used to calculate q, during stellar evolution along the red-giant branch (RGB). Methods. To test the approximations empirically, we calculate q-values in both, the weak and strong limit for stellar models on the RGB and compare them to the coupling derived from the mixed mode frequency pattern obtained from numerical solutions to the oscillation equations. Results. We find good agreement with the strong coupling approximation on the early RGB, when the evanescent zone lies in the radiative layer right above the hydrogen-burning shell; and with the weak coupling approximation once the evanescent zone is situated in the convective envelope. This is consistent with earlier studies. Additionally, we find that it is viable to use the weak coupling approximation as an estimate for q in the intermediate regime, in the mass range considered in this work (1.00 Msun <= M <= 2.00 Msun). Conclusions. The width of the evanescent zone serves as a good measure for which approximation to use. The serendipitous alignment of the weak coupling approximation with the observable q in the regime where neither approximation is expected to be valid simplifies the asymptotic calculation of mixed mode properties.