  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 or
fixed-entropy-gradient. We find that the resulting differential rotation is
markedly different between the two sets. The fixed-entropy-gradient 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 fixed-entropy 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 fixed-entropy-gradient 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 a fixed-gradient outer boundary
condition.
