Near-critical magnetic fields in Kepler red giants

The recent seismic detection of magnetic fields in red giants cores has given the opportunity to characterize these fields, potentially giving information about their origin and their role in the internal transport of angular momentum. We detect strong deviations from the regular pattern of g-mode periods in eight Kepler red giants showing $l=1$ doublets. In three of these stars, the modes show partial suppression. We investigate the magnetic origin of these features and determine the characteristics of the core fields that can produce such signatures. We need to invoke strong, near-critical fields. Assessing the effects of such fields on the mixed mode frequencies requires a non-perturbative approach. We use and adapt a formalism that was recently proposed following a similar development as the traditional approximation for rotation (TAR). We then compute asymptotic expressions of mixed mode frequencies including magnetic effects and attempt to reproduce the observed oscillation spectra. We show that for near-critical fields, information can be obtained about the radial profile of the radial field $B_r$, as opposed to weaker fields for which only a weighted average of $B_r^2$ can be measured. For the eight targets, we find that the $l=1$ doublets cannot be identified as the $m=\pm1$ components. Instead, we show that very good fits to all the observations can be obtained by identifying the two components as $m=0$ and $m=1$. These solutions correspond to fields with intensities ranging from 100 to 700 kG that are confined well below the H-burning shell. Our best-fit models for the eight stars have low masses (1.1-1.2 $M_\odot$) and the maximal size of their convective core during the main sequence approximately corresponds to the radial extent of the measured magnetic fields. The detected fields could thus have been generated by dynamo action in the main-sequence convective core.