Axial vs. equatorial dipolar dynamo models with implications for planetary magnetic fields

We present several numerical simulations of a self-consistent dynamo model in a rotating spherical shell. The solutions have two different field configurations. Besides magnetic fields dominated by the axial dipole component, we also find configurations where a dipole in the equatorial plane is the dominating component. Both types are stable in a parameter regime of intermediate shell thickness and Rayleigh numbers close to onset of convection. Axial dipole solutions are subcritical in all the simulations explored while the equatorial dipole cases are supercritical at low Rayleigh numbers but become metastable at higher Rayleigh numbers. The magnetic field strength saturates at a much lower amplitude for the equatorial dipole dynamos, and the Elsasser number is significantly smaller than in the axial configuration. The reason is that the mainly horizontal field in the equatorial dipole solution is incompatible with the motion of convective cyclones and anticyclones. The axial dipole field, on the other hand, is predominantly aligned with the axis of anticyclones, only cyclones are disrupted by horizontal field lines passing through. This configuration can therefore accomodate stronger convective flows and, consequently, is the only one remaining stable at higher Rayleigh numbers. These arguments should pertain in all planetary dynamos that are governed by strong rotational constraints. They offer an explanation why the Elsasser numbers inferred for Uranus and Neptune are much lower than the Elsasser numbers of Jupiter, Saturn, and Earth.