Consequences of high effective Prandtl number on solar differential rotation and convective velocity

TL;DR

This study investigates how high effective Prandtl numbers, influenced by small-scale magnetic effects, impact solar convection and differential rotation, challenging previous solutions to the solar convective conundrum.

Contribution

It demonstrates that increased Prandtl number alters convective structures and rotation profiles, questioning the viability of high Prandtl number as a solution to the solar convective conundrum.

Findings

Convective velocity decreases with higher Prandtl number.

Low-$ Pr$ simulations form subadiabatic layers at the convection zone base.

Low-$ Pr$ plumes can induce anti-solar differential rotation.

Abstract

Observations suggest that the large-scale convective velocities obtained by solar convection simulations might be over-estimated (convective conundrum). One plausible solution to this could be the small-scale dynamo which cannot be fully resolved by global simulations. The small-scale Lorentz force suppresses the convective motions and also the turbulent mixing of entropy between upflows and downflows, leading to a large effective Prandtl number ($\Pr$). We explore this idea in three-dimensional global rotating convection simulations at different thermal conductivity ($\kappa$), i.e., at different $\Pr$. In agreement with previous non-rotating simulations, the convective velocity is reduced with the increase of $\Pr$ as long as the thermal conductive flux is negligible. A subadiabatic layer is formed near the base of the convection zone due to continuous deposition of low entropy plumes in low-$\kappa$ simulations. The most interesting result of our low-$\kappa$ simulations is that the convective motions are accompanied by a change in the convection structure that is increasingly influenced by small-scale plumes. These plumes tend to transport angular momentum radially inward and thus establish an anti-solar differential rotation, in striking contrast to the solar rotation profile. If such low diffusive plumes, driven by the radiative-surface cooling, are present in the Sun, then our results cast doubt on the idea that a high effective $\Pr$ may be a viable solution to the solar convective conundrum. Our study also emphasizes that any resolution of the conundrum that relies on the downward plumes must take into account angular momentum transport as well as heat transport.