Convection-driven spherical shell dynamos at varying Prandtl numbers

¹ Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, 11482 Potsdam, Germany
e-mail: pkapyla@aip.de
² ReSoLVE Centre of Excellence, Department of Computer Science, Aalto University, PO Box 15400, 00076 Aalto, Finland
³ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
⁴ NORDITA, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
⁵ Department of Astronomy, AlbaNova University Center, Stockholm University, 10691 Stockholm, Sweden
⁶ JILA and Department of Astrophysical and Planetary Sciences, Box 440, University of Colorado, Boulder, CO 80303, USA
⁷ Laboratory for Atmospheric and Space Physics, 3665 Discovery Drive, Boulder, CO 80303, USA

Received: 19 May 2016
Accepted: 3 October 2016

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.