Transition from anti-solar to solar-like differential rotation: Dependence on Prandtl number

Abstract

(abridged) Context: Late-type stars such as the Sun rotate differentially due to the interaction of turbulent convection and rotation. Aims: The aim of the study is to investigate the effects of the thermal Prandtl number on the transition from anti-solar (slow equator, fast poles) to solar-like (fast equator, slow poles) differential rotation. Methods: Three-dimensional hydrodynamic and magnetohydrodynamic simulations in semi-global spherical wedge geometry are used to model convection zones of solar-like stars. Results: The overall convective velocity amplitude increases as the Prandtl number decreases in accordance with earlier studies. The transition from anti-solar to solar-like differential rotation is insensitive to the Prandtl number for Prandtl numbers below unity but for Prandtl numbers greater than unity, solar-like differential rotation becomes significantly harder to excite. Magnetic fields and more turbulent regimes with higher fluid and magnetic Reynolds numbers help in achieving solar-like differential rotation in near-transition cases. Solar-like differential rotation occurs only in cases with radially outward angular momentum transport at the equator. The dominant contribution to such outward transport near the equator is due to prograde propagating thermal Rossby waves. Conclusions: The differential rotation is sensitive to the Prandtl number only for large Prandtl numbers in the parameter regime explored in the current study. Magnetic fields have a greater effect on the differential rotation, although the inferred presence of a small-scale dynamo does not lead to drastically different results in the present study. The dominance of the thermal Rossby waves in the simulations is puzzling given the non-detection in the Sun. The current simulations are shown to be incompatible with the currently prevailing mean-field theory of differential rotation.

11 pages, 8 figures, submitted to Astron. Astrophys

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• Small-scale and large-scale dynamos in global convection simulations of solar-like stars
• Scale-dependent analysis of angular momentum flux in high-resolution magnetohydrodynamic simulations for solar differential rotation
• Scale-resolved turbulent Prandtl number for Rayleigh-Bénard convection at $\mathbf{Pr}=10^{-3}$
• Effects of the centrifugal force in stellar dynamo simulations
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• Differential rotation in convecting spherical shells with non-uniform viscosity and entropy diffusivity