Unveiling complex magnetic field configurations in red giant stars

TL;DR

This paper investigates the detectability of complex magnetic field configurations inside red giant stars, emphasizing the importance of combined $\, ext{l}=1$ and $\, ext{l}=2$ mode measurements to resolve degeneracies and better understand stellar magnetic topologies.

Contribution

It introduces a theoretical formalism for identifying complex magnetic field geometries using mixed mode oscillation frequencies and demonstrates the potential to distinguish different magnetic topologies.

Findings

Degeneracy between dipole and quadrupole fields can be lifted with combined mode analysis.

Offset magnetic fields can be misinterpreted as weak centered fields, affecting strength estimates.

Characterizing $\, ext{l}=2$ modes is crucial for unveiling higher-order magnetic field components.

Abstract

Recent measurements of magnetic field strength inside the radiative interior of red giant stars open the way towards the characterization of the geometry of stable large-scale magnetic fields. However, current measurements do not properly constrain the topology of magnetic fields due to degeneracies on the observed magnetic field signature on such $\ell=1$ mode frequencies. Efforts focused towards unambiguous detections of magnetic field configurations are now key to better understand angular momentum transport in stars. We investigate the detectability of complex magnetic field topologies inside the radiative interior of red giants. We focus on a field composed of a combination of a dipole and a quadrupole (quadrudipole), and on an offset field. We explore the potential of probing such magnetic field topologies from a combined measurement of magnetic signatures on $\ell=1$ and quadrupolar ($\ell=2$) mixed mode oscillation frequencies. We first derive the asymptotic theoretical formalism for computing the asymmetric signature in frequency pattern for $\ell=2$ modes due to a quadrudipole magnetic field. The degeneracy of the quadrudipole with a dipole is lifted when considering both $\ell=1$ and $\ell=2$ 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 demonstrate that offset fields may be mistaken for weak and centered magnetic fields, resulting in underestimating magnetic field strength in stellar cores. We emphasize the need to characterize $\ell=2$ mixed-mode frequencies, (along with the currently characterized $\ell=1$ mixed modes), to unveil the higher-order components of the geometry of buried magnetic fields, and better constrain angular momentum transport inside stars.