Abstract The exteriors of stellar and galactic dynamos are usually modeled as current-free potential fields. A more realistic description might instead be that of a force-free magnetic field. Here, we suggest that, in the absence of outflows, neither of these reflects the actual behavior when the magnetic field spreads diffusively into a more poorly conducting turbulent exterior outside dynamo. In particular, we explain why the usual ordering, in which the dipole magnetic field is the most slowly decaying one, is altered, and why the quadrupole can develop a toroidal component that decays even more slowly with radial distance. This is a robust feature that persists even for spatially nonuniform magnetic diffusivities. It is most clearly seen for spherical dynamo volumes and becomes more complicated for oblate ones. In either case, however, these fields are confined within a magnetosphere, beyond which the field strength drops exponentially. We demonstrate that the Faraday displacement current, which plays a role in a vacuum, can safely be neglected in all cases. The superposition of magnetic fields from galaxies in the outskirts of voids between galaxy clusters therefore cannot explain the magnetization of the intergalactic medium in voids, reinforcing the conventional expectation that these fields are of primordial origin. For quadrupolar configurations, the synchrotron emission from the magnetosphere is found to be constant along concentric rings. The dipolar and quadrupolar configurations display large-scale radial trends that are potentially distinguishable with existing radio telescopes.
Brandenburg et al. (Tue,) studied this question.