The Sun looses its angular momentum through the solar wind and continually reduces its rotation. So, it is quite logical to think that the Sun might have a rapidly rotating core compared to its surface.This means that the shape of the Sun may be distorted. So the interesting question is how higher is the angular velocity of the Sun's surface than its center?

The Sun does not rotate like a rigid body. It's rotation varies with latitude - from a rotation period of about 25 days near the equator to a rotation period of about 33 days near the poles. This is due to the coupling between rotation and large-scale rotation in the convection zone. The analysis of data from SOHO suggests that the latitude variation of rotation is more or less same at the surface and through out the convection zone. Then there is sudden transition near the base of convection zone to almost uniform rotation in the radiative zone. Below this, the results are not certain but the indications are that the core is not rotating rapidly as was thought earlier!

The figure (click on it!) on the left shows the inferred rotation rate as a function of depth and latitude. Evidently the convection zone rotates uniformly along a radius with all depths showing the differential rotation seen at the surface. Below the convection zone is a layer of shear below which the radiative interior seems to rotate rigidly. This shear zone which coincides with the sound speed excess could be the region where the solar cycle dynamo operates. This Image is courtesy of the SOHO/SOI-MDI project of the Stanford Lockheed Institute for Space Research. SOHO is a project of international cooperation between ESA and NASA."