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

¹ Georg-August-Universität Göttingen, Institut für Astrophysik und Geophysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
e-mail: pkaepyl@uni-goettingen.de
² KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 10691 Stockholm, Sweden

Received: 1 July 2022
Accepted: 21 November 2022

Abstract

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 effective thermal Prandtl number, which is the ratio of kinematic viscosity to thermal diffusivity, 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 were used to model the 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 to achieve solar-like differential rotation in near-transition cases where anti-solar rotation is found in more laminar simulations. Solar-like differential rotation occurs only in cases with radially outward turbulent angular momentum transport due to the Reynolds stress at the equator. The dominant contribution to this 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 this study. Magnetic fields have a greater effect on the differential rotation, although the inferred presence of a small-scale dynamo did not lead to drastically different results. The dominance of the thermal Rossby waves in the simulations is puzzling because they are not detected in the Sun. The current simulations are shown to be incompatible with the currently prevailing mean-field theory of differential rotation.