It is well known that the combination of uniform rotation and radiative equilibrium are mutually incompatible in stars. The rotation of the radiative zone of the Sun is often expected to be uniform, and the data from helioseismology do seem to converge to uniform rotation in the deep interior. Consequently, an ordered motion of the fluid, known as Eddington-Sweet circulation, is thought to contribute to the energy transfer, together with the radiative processes.
I will explore alternatives to this view by studying the patterns of differential rotation that arise when the constraint of diffusive radiative equilibrium is imposed. The rotation must be non-barotropic to maintain radiative equilibrium, which is in fact what is observed in the Sun. I will investigate how large a deviation from uniform rotation is required to maintain radiative equilibrium without meridional circulation throughout the radiative zone. Very little deviation is required, well below detectability.
I will present solutions of the stellar structure equations that satisfy the radiative equilibrium constraint. These solutions, to within current levels of accuracy, closely resemble the rotation profile deduced from helioseismology both in the upper radiative zone and in the tachocline, the narrow transition between the radiative and convective zones. The solutions maintain radiative equilibrium, and are both circulation-free and steady. They provide the simplest interpretation of the physics of the tachocline that is compatible with the current data from helioseismology.