Three-dimensional kinematic dynamos with equatorial symmetry: Application to the magnetic fields of Uranus and Neptune

Abstract

Previous studies of kinematic dynamo theory have sought solutions dominated by the axial dipole component of magnetic field, so as to model the field of the Earth. Motivated by the observed magnetic fields of the planets Uranus and Neptune, we obtain 3D kinematic dynamos with a different morphology: specifically, fields possessing equatorial symmetry, and so lacking an axial dipole component, where the axis is that of the differential rotation present in most of the flows studied. We base our investigations on the standard Kumar-Roberts flow, and find that with a small alteration this flow is capable of supporting a wide range of dynamos with equatorial symmetry, albeit in a different region of parameter space from the Earth-like solutions. A particularly interesting example is a dynamo generated by a flow with no toroidal component. We include an impenetrable inner core within the dynamo region, but find its effect to be slight compared with small alterations in the chosen flow, and observe no effect on the preferred symmetry of the solution. Solutions for a conducting or insulating inner core are very similar, although there is evidence that this is due to our particular choice of flow. On the evidence of kinematic dynamos, the axial dipole morphology seems to be strongly preferred only in the presence of strong axial differential rotation. However, our results are sensitive to the ad hoc choice of steady flow, which may limit the applicability of our conclusions.