Shear-driven and diffusive helicity fluxes in α dynamos

We present non-linear mean-field α dynamo simulations in spherical geometry with simplified profiles of kinetic α effect and shear. We take magnetic helicity evolution into account by solving a dynamical equation for the magnetic α effect. This gives a consistent description of the quenching mechanism in mean-field dynamo models. The main goal of this work is to explore the effects of this quenching mechanism in solar-like geometry, and in particular to investigate the role of magnetic helicity fluxes, specifically diffusive and Vishniac–Cho (VC) fluxes, at large magnetic Reynolds numbers (Rm). For models with negative radial shear or positive latitudinal shear, the magnetic α effect has predominantly negative (positive) sign in the Northern (Southern) hemisphere. In the absence of fluxes, we find that the magnetic energy follows an R−1 m dependence, as found in previous works. This catastrophic quenching is alleviated in models with diffusive magnetic helicity fluxes resulting in magnetic fields comparable to the equipartition value even for Rm = 107. On the other hand, models with a shear-driven Vishniac–Cho flux show an increase in the amplitude of the magnetic field with respect to models without fluxes, but only for Rm < 104. This is partly a consequence of assuming a vacuum outside the Sun which cannot support a significant VC flux across the boundary. However, in contrast to the diffusive flux, the VC flux modifies the distribution of the magnetic field. In addition, if an ill-determined scaling factor in the expression for the VC flux is large enough, subcritical dynamo action is possible that is driven by the action of shear and the divergence of magnetic helicity flux.