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It is thought that magnetic fields must be present in the interiors of starsto resolve certain discrepancies between theory and observation (e.g. angularmomentum transport), but such fields are difficult to detect and characterise.Asteroseismology is a powerful technique for inferring the internal structuresof stars by measuring their oscillation frequencies, and succeeds particularlywith evolved stars, owing to their mixed modes, which are sensitive to the deepinterior. The goal of this work is to present a phenomenological study of thecombined effects of rotation and magnetism in evolved stars, where both areassumed weak enough that first-order perturbation theory applies, and we focuson the regime where Coriolis and Lorentz forces are comparable. Axisymmetric"twisted-torus" field configurations are used, which are confined to the coreand allowed to be misaligned with respect to the rotation axis. Factors such asthe field radius, topology and obliquity are examined. We observe that fieldswith finer-scale radial structure and/or smaller radial extent produce smallercontributions to the frequency shift. The interplay of rotation and magnetismis shown to be complex: we demonstrate that it is possible for nearly symmetricmultiplets of apparently low multiplicity to arise even under a substantialfield, which might falsely appear to rule out its presence. Our results suggestthat proper modelling of rotation and magnetism, in a simultaneous fashion, maybe required to draw robust conclusions about the existence/non-existence of acore magnetic field in any given object.

Topology and obliquity of core magnetic fields in shaping seismic properties of slowly rotating evolved stars