EQUILIBRIA OF RAPIDLY ROTATING POLYTROPES

The equilibrium structures of self-gravitating polytropes are found in the limit of rapid rotation by the method of matched asymptotic expansions. For physical values of the polytropic index, the discs are thin throughout most of their radii, but they flare out at their edges where the local Jeans length of the configuration becomes large. This signals a breakdown in the asymptotic expansion that we correct by including a boundary layer at the rim of the disc. A variety of results are illustrated for differing rotation curves and polytropic indices.