Dipolar versus multipolar dynamos: the influence of the background density stratification

Context. Dynamo action in giant planets and rapidly rotating stars leads to a broad variety of magnetic field geometries including small-scale multipolar and large-scale dipole-dominated topologies. Previous dynamo models suggest that solutions become multipolar once inertia is influential. Being tailored for terrestrial planets, most of these models neglected the background density stratification. Aims. We investigate the influence of the density stratification on convection-driven dynamo models. Methods. Three-dimensional nonlinear simulations of rapidly rotating spherical shells were employed using the anelastic approximation to incorporate density stratification. A systematic parametric study for various density stratifications and Rayleigh numbers at two different aspect ratios allowed us to explore the dependence of the magnetic field topology on these parameters. Results. Anelastic dynamo models tend to produce a broad range of magnetic field geometries that fall on two distinct branches with either strong dipole-dominated or weak multipolar fields. As long as inertia is weak, both branches can coexist, but the dipolar branch vanishes once inertia becomes influential. The dipolar branch also vanishes for stronger density stratifications. The reason is that the convective columns are concentrated in a narrow region close to the outer boundary equator, a configuration that favors nonaxisymmetric solutions. In multipolar solutions, zonal flows can become significant and participate in the toroidal field generation. Parker-dynamo waves may then play an important role close to onset of dynamo action, leading to a cyclic magnetic field behavior. Conclusions. These results are compatible with the magnetic fields of gas planets that are likely generated in their deeper conducting envelopes where the density stratification is only mild. Our simulations also suggest that the dipolar or multipolar magnetic fields of late M dwarfs can be explained in two ways. They may differ either because of the relative influence of inertia or fall into the regime where both types of solutions coexist.