Unveiling complex magnetic field configurations in red-giant stars

Magnetic fields are the missing key to unlocking our understanding of angular momentum transport inside stars. Recently, strong radial magnetic fields have been unveiled in the radiative interior of red-giant stars. However, the full topology of internal magnetic fields remains a mystery, due to the degeneracies of the signatures of various magnetic field configurations in asteroseismic data, strongly impacting our ability to evaluate the impact of magnetism on angular momentum transport. We investigate how complex magnetic field structures, similar to those observed at the radiative surface of intermediate-mass main-sequence stars, can be probed in the interior of red giants. To do so, we demonstrate the complementary sensitivity of dipolar and quadrupolar oscillation modes to the complexity of the magnetic field topology. In addition, we discuss how the inclination of the star's rotation axis compared to our line of sight affects the visibility of the magnetic signature in asteroseismic data. This magnetically-induced visibility modulation, along with the intrinsic nuances of disentangling the signatures of a dipolar field from that of higher multipoles (such as a quadrupole), makes the characterization of magnetic field configurations an outstanding challenge. Probing magnetic field topologies inside the core of red giants from such a combined study of dipolar and quadrupolar oscillation modes would revolutionize our understanding of angular momentum transport inside stars, and therefore on the current global picture of stellar evolution.