A New Scaling Law for Non-Dipolar Magnetic Fields in Rapidly Rotating Stars and Planets

Magnetic field generation in giant planets and rapidly rotating stars produces a diverse range of field geometries, from large-scale dipole-dominated configurations to complex, small-scale multipolar structures. Earlier dynamo studies have suggested that multipolar solutions tend to arise when rotational effects become less dominant. We investigate the strength of non-dipolar magnetic fields generated in systems dominated by rotation. 40 three-dimensional, spherical-shell dynamo simulations were carried out using the MagIC code, primarily made up of bistable pairs - simulations with the same control parameters that can settle in both a dipolar and non-dipolar steady-state regime. We use this suite of models to test how their magnetic field strength scales with heat flux and velocity. Our dynamo simulations produce magnetic fields with morphologies that fall on the two distinct branches, dipolar or non-dipolar, yet have very similar convective velocities. The strength of the dipole component differs by an order of magnitude between the two regimes, when scaled as a function of driving power. However, their non-dipolar magnetic field strengths are very similar. We conclude that when attempting to predict the magnetic field strength of rapidly rotating planets and stars, one cannot assume that it will have a dipole-dominated geometry. In particular, the amplitude of the dipole component is expected to be an order of magnitude smaller in the non-dipolar regime.