Modelling rotational near-degeneracy effects

Understanding the internal distribution of angular momentum in evolved solar-like stars remains an open problem. Dipolar (l = 1) mixed modes consistently indicate a much weaker core–envelope rotation contrast than predicted by standard models. Quadrupolar (l = 2) mixed modes provide a valuable yet underexploited probe, sensitive to different regions of the stellar interior. Their low amplitudes and distortions due to near-degeneracy have, however, hindered their analysis. We develop a new asymptotic framework for l = 2 mixed modes that incorporates near-degeneracy via off-diagonal coupling terms, allowing analytical computation of asymmetric rotational splittings without relying on full stellar models. Applied within a global Bayesian framework to KIC 7341231, our method reproduces previous results while reducing uncertainties on core and envelope rotation rates by about a factor of two. We also present the first seismic study of KIC 8179973, a young red giant with strong l = 2 near-degeneracy, providing new constraints on angular momentum transport. This work paves the way for disentangling rotational and magnetic effects, and offers a new window into the internal magnetism of post-main-sequence stars.