Revisiting the Sun's Strong Differential Rotation along Radial Lines

Current state-of-the-art models of the solar convection zone consist ofsolutions to the Navier-Stokes equations in rotating, 3D spherical shells. Suchmodels are highly sensitive to the choice of boundary conditions. Here, wepresent two suites of simulations differing only in their outer thermalboundary condition, which is either one of fixed-entropy orfixed-entropy-gradient. We find that the resulting differential rotation ismarkedly different between the two sets. The fixed-entropy-gradient simulationshave strong differential rotation contrast and isocontours tilted along radiallines (in good agreement with the Sun's interior rotation revealed byhelioseismology), whereas the fixed-entropy simulations have weaker contrastand contours tilted in the opposite sense. We examine in detail the forcebalances in our models and find that the poleward transport of heat by Bussecolumns drives a thermal wind responsible for the different rotation profiles.We conclude that the Sun's strong differential rotation along radial lines mayresult from the solar emissivity being invariant with latitude (which issimilar to the fixed-entropy-gradient condition in our models) and the polewardtransport of heat by Busse columns. In future work on convection in the solarcontext, we strongly advise modelers to use a fixed-gradient outer boundarycondition.