@article{21658,
  abstract     = {Dipolar (ℓ = 1) mixed modes have revealed a surprisingly weak differential rotation between the core and the envelope of evolved solar-like stars. Quadrupolar (ℓ = 2) mixed modes also contain information regarding 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 the broadly used asymptotic seismic diagnostics beyond ℓ = 1 mixed modes by developing an analogue asymptotic description of ℓ = 2 mixed modes while explicitly accounting for near-degeneracy effects that distort their rotational multiplets. We have derived 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. This formalism, expressed directly in the mixed-mode basis, provides analytical expressions for the near-degeneracy effects. We implemented 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 were 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. We applied our formalism to the Kepler target KIC 7341231, and it yielded core and envelope rotation rates consistent with previous numerical modelling while providing improved constraints from the global and model-independent approach. We also characterised the new target, KIC 8179973, measuring its rotation rate and mixed-mode parameters for the first time. As our framework relies on a direct global fit, it allows for much better precision on the asteroseismic parameters and rotation rate estimates than standard methods, yielding better constraints for rotation inversions. We have placed the first observational constraints on the asymptotic ℓ = 2 mixed-mode parameters (ΔΠ2, q2, and εg, 2), thus paving the way towards the use of asymptotic seismology beyond ℓ = 1 mixed modes.},
  author       = {Liagre, Bastien Raymond Bernard and Desai, Aayush A and Einramhof, Lukas and Bugnet, Lisa Annabelle},
  issn         = {1432-0746},
  journal      = {Astronomy and Astrophysics},
  publisher    = {EDP Sciences},
  title        = {{Near-degeneracy effects in quadrupolar mixed modes: From an asymptotic description to data fitting}},
  doi          = {10.1051/0004-6361/202558023},
  volume       = {707},
  year         = {2026},
}

@article{18528,
  abstract     = {The recent measurement of magnetic field strength inside the radiative interior of red giant stars has opened the way toward full 3D characterization of the geometry of stable large-scale magnetic fields. However, current measurements, which are limited to dipolar (ℓ = 1) mixed modes, do not properly constrain the topology of magnetic fields due to degeneracies on the observed magnetic field signature on such ℓ = 1 mode frequencies. Efforts focused toward unambiguous detections of magnetic field configurations are now key to better understand angular momentum transport in stars. We investigated the detectability of complex magnetic field topologies (such as the ones observed at the surface of stars with a radiative envelope with spectropolarimetry) inside the radiative interior of red giants. We focused on a field composed of a combination of a dipole and a quadrupole (quadrudipole) and on an offset field. We explored the potential of probing such magnetic field topologies from a combined measurement of magnetic signatures on ℓ = 1 and quadrupolar (ℓ = 2) mixed mode oscillation frequencies. We first derived the asymptotic theoretical formalism for computing the asymmetric signature in the frequency pattern for ℓ = 2 modes due to a quadrudipole magnetic field. To access asymmetry parameters for more complex magnetic field topologies, we numerically performed a grid search over the parameter space to map the degeneracy of the signatures of given topologies. We demonstrate the crucial role played by ℓ = 2 mixed modes in accessing internal magnetic fields with a quadrupolar component. The degeneracy of the quadrudipole compared to pure dipolar fields is lifted when considering magnetic asymmetries in both ℓ = 1 and ℓ = 2 mode frequencies. In addition to the analytical derivation for the quadrudipole, we present the prospect for complex magnetic field inversions using magnetic sensitivity kernels from standard perturbation analysis for forward modeling. Using this method, we explored the detectability of offset magnetic fields from ℓ = 1 and ℓ = 2 frequencies and demonstrate that offset fields may be mistaken for weak and centered magnetic fields, resulting in underestimating the magnetic field strength in stellar cores. We emphasize the need to characterize ℓ = 2 mixed-mode frequencies, (along with the currently characterized ℓ = 1 mixed modes), to unveil the higher-order components of the geometry of buried magnetic fields and to better constrain angular momentum transport inside stars.},
  author       = {Das, Srijan B and Einramhof, Lukas and Bugnet, Lisa Annabelle},
  issn         = {1432-0746},
  journal      = {Astronomy and Astrophysics},
  publisher    = {EDP Sciences},
  title        = {{Unveiling complex magnetic field configurations in red giant stars}},
  doi          = {10.1051/0004-6361/202450918},
  volume       = {690},
  year         = {2024},
}