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

Context. The high precision of recent asteroseismic observations of red giant stars has revealed mixed dipole modes in the oscillation spectra of these stars. These modes offer a look inside the stars. One of the parameters that are 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. We probe the validity of the weak- and strong-coupling approximations, which are commonly used to calculate q, during stellar evolution along the red giant branch (RGB). Methods. To test the approximations empirically, we calculated q-values in the weak and strong limit for stellar models on the RGB and compared them to the coupling derived from the mixed-mode frequency pattern obtained from numerical solutions to the oscillation equations. Results. The strong-coupling approximation describes the mixed-mode frequency pattern well on the early RGB, when the evanescent zone lies in the radiative layer immediately above the hydrogen-burning shell; and the weak-coupling approximation is applicable when the evanescent zone is situated in the convective envelope. This is consistent with earlier studies. We additionally found that, in the mass range we considered here (1.00 M⊙ ≤ M ≤ 2.00 M⊙), the weak-coupling approximation can be used as an estimate for q in the intermediate regime. 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 in which neither approximation is expected to be valid simplifies the asymptotic calculation of mixed-mode properties.