No intermediate coupling prescription needed on the red-giant branch
Abstract
Red-giant stars resonate in two cavities - pressure modes can oscillate in the envelope, while the core allows for the propagation of gravity modes. Since the eigenfrequencies of these modes fall in a similar range, mixed modes form via coupling of the cavities across the intermediate evanescent zone (EZ). The asymptotic frequency pattern of mixed modes is governed by the coupling strength q. So far, the link of q to stellar structure has been derived for an explicitly narrow or wide EZ (i.e. strong or weak coupling, respectively). We aim to test the validity of both approximations during the evolution along the red-giant branch (RGB). To do so, we derived q from numerically calculated oscillation frequencies for a set of stellar models and compared the resulting values to those obtained from the strong and weak coupling approximation. We confirm that the EZ widens along the RGB, such that first the strong and later the weak coupling approximation is valid. Additionally, we find that the weak coupling approximation is serendipitously applicable in narrower EZs than expected. On the RGB, this allows to always estimate values for the coupling strength in one of the two well-known limits without a need for an intermediate prescription.