Magnetic helicity fluxes in interface and flux transport dynamos

Context. Dynamos in the Sun and other bodies tend to produce magnetic fields that possess magnetic helicity of opposite sign at large and small scales, respectively. The build-up of magnetic helicity at small scales provides an important saturation mechanism. Aims. In order to understand the nature of the solar dynamo we need to understand the details of the saturation mechanism in spherical geometry. In particular, we want to understand the effects of magnetic helicity fluxes from turbulence and meridional circulation. Methods. We consider a model with just radial shear confined to a thin layer (tachocline) at the bottom of the convection zone. The kinetic α owing to helical turbulence is assumed to be localized in a region above the convection zone. The dynamical quenching formalism is used to describe the build-up of mean magnetic helicity in the model, which results in a magnetic α effect that feeds back on the kinetic α effect. In some cases we compare with results obtained using a simple algebraic α quenching formula. Results. In agreement with earlier findings, the magnetic α effect in the dynamical α quenching formalism has the opposite sign compared with the kinetic α effect and leads to a catastrophic decrease of the saturation field strength with increasing magnetic Reynolds numbers. However, at high latitudes this quenching effect can lead to secondary dynamo waves that propagate poleward due to the opposite sign of α. Magnetic helicity fluxes both from turbulent mixing and from meridional circulation alleviate catastrophic quenching.