Convection-driven spherical shell dynamos at varying Prandtl numbers

Abstract

Context. Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims. We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods. We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25 to 5, respectively). Differential rotation and large-scale magnetic fields are produced self-consistently. Results. We find that for high thermal diffusivity, the rotation profiles show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased, corresponding to an increase of the Prandtl number. This coincides with and results in a change of the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the clearly cyclic solutions disappear at the highest magnetic Reynolds numbers and give way to irregular sign changes or quasi-stationary states. The total (mean and fluctuating) magnetic energy increases as a function of the magnetic Reynolds number in the range studied here (5-151), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases, however, we find that two regimes are possible, where either differential rotation is strong and mean magnetic fields are relatively weak, or vice versa. Conclusions. Our simulations indicate a strong nonlinear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large-scale dynamos at high magnetic Reynolds numbers. Furthermore, we do not find indications of the simulations approaching an asymptotic regime where the results would be independent of diffusion coefficients in the parameter range studied here.

Effects of small‐scale dynamo and compressibility on the Λ effect

“…The small‐scale magnetic fields generated by a small‐scale dynamo lead to a significantly milder quenching of the Λ effect in comparison to cases where also a uniform large‐scale field is imposed (see, e.g., Käpylä ). Thus is appears that the small‐scale dynamo alone could not explain the severely quenched differential rotation in recent semi‐global convection simulations (Käpylä et al ). It is also conceivable that other MHD instabilities, such as the magnetorotational instability (e.g., Masada ), can be excited in the high‐resolution convection simulations, leading to repercussions for differential rotation.…”

“…Numerical simulations of magnetohydrodynamic (MHD) convection in spherical coordinates have reached sufficient spatial resolution that allows the excitation of small‐scale dynamo action (e.g., Hotta et al ; Käpylä et al ; Nelson et al ). The study of Käpylä et al () showed that differential rotation in simulations is strongly quenched at the highest magnetic Reynolds numbers where an efficient small‐scale dynamo is excited. Furthermore, the turbulent Reynolds and Maxwell stresses were found to have similar spatial distributions and magnitudes but opposite signs.…”

Robustness of oscillatoryα2dynamos in spherical wedges

“…On the other hand, the oscillatory solutions found in global simulations in wedge geometry might still be physical and not an artefact of using a perfect conductor boundary condition on the latitudinal boundaries. Some global simulations in wedge geometry with the SAS condition have already been performed (Käpylä et al 2016b), but their cases were in a regime where no oscillations occur.…”

Magnetism, dynamo action and the solar-stellar connection

“…However, it is worth noting that all these simulations have been computed with a magnetic Prandtl number Pm of order 1. See also Käpylä et al (2017) for recent dynamo simulations performed with various diffusivity ratios.…”