The Energy Transfer in the Convective Envelope of a Rotating Star And the Solar Differential Rotation

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Abstract
Energy transport in the convective envelope of a rotating star is studied under the assumption that large scale circulation currents may be neglected. The problem then reduces to a second order differential equation for the perturbed entropy with the exponent of the gravity-darkening law on the surface as an eigenvalue. This equation is solved when all the energy is transported by convection and a criterion obtained for the validity of Lucy's gravity-darkening law. If rotation reduces the efficiency of convective energy transport, small deviations from barotropy result. The possibility then arises that the differential rotation of the Sun is driven by this baroclinic stratification. An equatorial acceleration of the right order is obtained if rotation reduces the efficiency of convective energy transport in the direction perpendicular to the axis of rotation.

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