  It is well known that the combination of barotropic rotation and radiative
equilibrium are mutually incompatible in stars. The Sun's internal rotation is
far from barotropic, however, which allows at least the theoretical possibility
that the Sun's thermal balance is one of radiative equilibrium in the region of
the tachocline near the outer boundary of the radiative zone. We show here that
(i) the constraint of radiative equilibrium leads to a straightforward ordinary
differential equation for the Sun's rotation profile, and (ii) solutions of
this equation can be found that, to within current levels of accuracy, closely
resemble the rotation profile deduced from helioseismology. More generally, we
calculate how large a baroclinic deviation from uniform rotation is required to
maintain radiative equilibrium without meridional circulation throughout the
bulk of the radiative zone. Very little deviation is required, well below
detectability. The feasibility of radiative equilibrium for the tachocline
suggests that the issue of a spreading boundary layer may be less severe than
previously thought.
