Revisiting the Sun's Strong Differential Rotation along Radial Lines

Current state-of-the-art models of the solar convection zone consist of solutions to the Navier-Stokes equations in rotating, 3D spherical shells. Such models are highly sensitive to the choice of boundary conditions. Here we present two suites of simulations differing only in their outer thermal boundary condition, which is either one of fixed entropy (FE) or fixed flux (FF; corresponding to a fixed gradient in the entropy). We find that the resulting differential rotation is markedly different between the two sets. The FF simulations have strong differential rotation contrast and isocontours tilted along radial lines (in good agreement with the Sun's interior rotation revealed by helioseismology), whereas the FE simulations have weaker contrast and contours tilted in the opposite sense. We examine in detail the force balances in our models and find that the poleward transport of heat by Busse columns drives a thermal wind responsible for the different rotation profiles. We conclude that the Sun's strong differential rotation along radial lines may result from the solar emissivity being invariant with latitude (which is similar to the FF condition in our models) and the poleward transport of heat by Busse columns. In future work on convection in the solar context, we strongly advise modelers to use an FF outer boundary condition.