A new asymptotic expression for near degeneracy effects

Near-degeneracy effects in Quadrupolar Mixed Modes. From an Asymptotic Description to Data Fitting Dipolar (l=1) mixed modes revealed surprisingly weak differential rotation between the core and the envelope of evolved solar-like stars. Quadrupolar (l=2) mixed modes also contain information on the internal dynamics, but are very rarely characterised due to their low amplitude and the challenging identification of adjacent or overlapping rotationally split multiplets affected by near-degeneracy effects. We aim to extend broadly used asymptotic seismic diagnostics beyond l=1 mixed modes by developing an analogue asymptotic description of l=2 mixed modes, explicitly accounting for near-degeneracy effects that distort their rotational multiplets. We derive a new asymptotic formulation of near-degenerate mixed l=2 modes that describes off-diagonal terms representing the interaction between modes of adjacent radial orders. We implement the formalism within a global Bayesian mode-fitting framework, for a direct fit of all l=0,1,2 modes in the power spectrum density. We are able to asymptotically model the asymmetric rotational splitting present in various radial orders of l=2 modes observed in young red giant stars without the need for any numerical stellar modelling. Applied to the Kepler target KIC 7341231, our formalism yields core and envelope rotation rates consistent with previous numerical modelling, while providing improved constraints from the global and model-independent approach. We also characterise the new target KIC 8179973, measuring its rotation rate and mixed-mode parameters for the first time. The global fit allows for much better precision than standard methods, yielding better constraints for rotation inversions. We place the first observational constraints on the asymptotic l=2 mixed mode parameters (DPi_2,q_2,eps_g2), paving the way towards the use of asymptotic seismology beyond l=1 mixed modes.