Grand minima and intermittency in near-critical convection-driven dynamos

Abstract

Context: Solar magnetism exhibits long-term variations on timescales of decades to centuries. Aims: The main aim is to study how the supercriticality of the dynamo affects the variability of magnetic fields on timescales relevant to the Sun. Methods: Three-dimensional rotating magnetohydrodynamic simulations in a spherical wedge geometry are used to produce self-consistent convection-driven dynamos. The supercriticality of the dynamo is controlled by varying the magnetic diffusivity. Results: The main result is that long-term variability of the dynamo increases with decreasing supercriticality of the dynamo and that cases nearest to the onset of dynamo action show extended grand minima-like periods of low activity. The simulations fall in three classes where the least supercritical cases show the largest variations of magnetic activity and where the flow including differential rotation is almost unaffected by the magnetic field. In the cases with the highest supercriticality the magnetic field is permanently strong and differential rotation permanently quenched, both having relatively little temporal variation. In an intermediate regime both the magnetic fields and differential rotation exhibit strong anticorrelated fluctuations. Conclusions: The occurrence of grand minima in the Sun has been conjectured to be due to a weakly supercritical dynamo. The current results support this idea and suggest that the absence of grand minima in earlier global dynamo simulations is because their large-scale dynamos were too supercritical. Furthermore, the current results suggest that the effect of the magnetic field on differential rotation is negligible if the average rms-field is less than about 2~kG.