  (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.

Solar and Stellar Astrophysics