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

TL;DR

This study investigates how the thermal Prandtl number influences the transition between anti-solar and solar-like differential rotation in stars, revealing that magnetic fields and Rossby waves play significant roles in this process.

Contribution

The paper demonstrates that the Prandtl number affects differential rotation only at high values and highlights the importance of magnetic fields and Rossby waves in achieving solar-like rotation.

Findings

Transition to solar-like rotation is insensitive to Prandtl number below unity.

Magnetic fields facilitate the onset of solar-like differential rotation.

Prograde thermal Rossby waves dominate angular momentum transport near the equator.

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.