Magnetic fields of low-mass stars and planets are thought to originate from self-excited dynamo action in their convective interiors. Observations reveal a variety of field topologies ranging from large-scale, axial dipole to more structured magnetic fields. In this article, we investigate more than 70 three-dimensional, self-consistent dynamo models obtained by direct numerical simulations. The control parameters, the aspect ratio and the mechanical boundary conditions have been varied to build up this sample of models. Both, strongly dipolar and multipolar models have been obtained. We show that these dynamo regimes can in general be distinguished by the ratio of a typical convective length-scale to the Rossby radius. Models with a predominantly dipolar magnetic field were obtained, if the convective length scale is at least an order of magnitude larger than the Rossby radius. Moreover, we highlight the role of the strong shear associated with the geostrophic zonal flow for models with stress-free boundary conditions. In this case the above transition disappears and is replaced by a region of bistability for which dipolar and multipolar dynamos co-exist. We interpret our results in terms of dynamo eigenmodes using the so-called test field method. We can thus show that models in the dipolar regime are characterized by an isolated 'single mode'. Competing overtones become significant as the boundary to multipolar dynamos is approached. We discuss how these findings relate to previous models and to observations.

Context. Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid of constant density, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation.Aims. The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular, with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Methods. Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. Results. The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings.

Context. Large-scale magnetic fields resulting from hydromagnetic dynamo action may differ substantially in their time dependence. Cyclic field variations, characteristic for the solar magnetic field, are often explained by an important Ω-effect, i.e., by the stretching of field lines because of strong differential rotation. Aims. The dynamo mechanism of a convective, oscillatory dynamo model is investigated. Methods. We solve the MHD-equations for a conducting Boussinesq fluid in a rotating spherical shell. We computed the dynamo coefficients for the resulting oscillatory model with the help of the so-called test-field method. Subsequently, these coefficients were used in a mean-field calculation to explore the underlying dynamo mechanism. Results. The oscillatory dynamo model we consider is an α 2 Ω one. Although the fairly strong differential rotation of this model influences the magnetic field, the Ω-effect alone is not responsible for its cyclic time variation. If the Ω-effect is suppressed, the resulting α 2 -dynamo remains oscillatory. Surprisingly, the corresponding αΩ-dynamo leads to a non-oscillatory magnetic field. Conclusions. The assumption of an αΩ-mechanism does not explain the occurrence of magnetic cycles satisfactorily.

Abstract.In addition to the weak-dipolar state and to the fluctuating-multipolar state, widely discussed in the literature, a third regime has been identified in (Dormy 2016). It corresponds to a strong-dipolar branch which appears to approach, in a numerically affordable regime, the magnetostrophic limit relevant to the dynamics of the Earth's core. We discuss the transitions between these states and point to the relevance to this strong-dipolar state to Geodynamo modelling.