Symmetry breaking in stellar dynamos

Abstract

The generation of magnetic fields in stars like the Sun can be described by an azimuthally averaged dynamo model. Solutions of the linear (kinematic) problem have pure dipole or quadrupole symmetry, i.e. toroidal fields that are antisymmetric or symmetric about the equator. These symmetries can only be broken at bifurcations in the non-linear regime, which lead to the appearance of spatially asymmetric mixed-mode solutions. The symmetries of dipole, quadrupole and mixed-mode solutions, whether steady or periodic, form the same group for any axisymmetric dynamo. To establish the bifurcation structure it is necessary to follow unstable as well as stable solutions. This is only feasible for simple systems and a minimal non-linear aω dynamo is studied in detail in order to illustrate the formation of mixed-mode periodic solutions and to distinguish between their symmetries. The results are applied to the Sun (where there are persistent deviations from dipole symmetry) and to other late-type stars.