Differential Rotation in Stellar Convection Zones

The dynamical effects of rotation on thermal convection in a fluid layer of spherical shape induce an equatorial acceleration. Special properties of the convection zone assumed in earlier theories on the differential rotation of the Sun are not required. To demonstrate the mechanism, the mathematical problem of convection in a rotating Boussinesq fluid subject to temperature and gravity fields of spherical symmetry is considered. At the critical value of the Rayleigh number the onset of convection takes place predominantly in the equatorial region. The dynamical constraint of rotation, together with the geometry of the problem, leads to the equatorial acceleration at finite convection amplitudes. Estimates give reasonable agreement with values observed on the Sun.