The Mechanical Equilibrium of Rotating Stars

“Epur si muove” said Galileo Galilei when claiming that the Earth is rotating. Due to rotation, the equatorial radius of the Earth is about 21.4 km longer than its polar radius, so that the Mississippi from its source to the Gulf of Mexico is “raising” away from the Earth center. Of course, in terms of the equipotentials it is “descending” to the sea. The same can also be said about the stars, where the effects of rotation are on the average much larger than on the Earth. In stars, the equatorial radius can be much bigger than the polar radius, up to about 1.5 times the polar radius. This shows the importance of the possible rotational effects. In addition, while the Earth rotates like a solid body, stars may have an internal differential rotation, with for example a core rotating faster than the outer envelope. Moreover, stellar rotation not only produces a flattening of the equilibrium configuration, but it drives internal circulation motions and various instabilities which transport both the chemical elements and the angular momentum.