Rapidly Rotating Stars. VIII. Zero-Viscosity Polytropic Sequences

The sequence of uniformly rotating (Maclaurin) spheroids of uniform density is generalized to the case of sequences of axisymmetric centrally condensed configurations, with fixed distributions of angular momentum. Numerical results are presented for such sequences of differentially rotating polytropes with indices 0, 3/2, and 3, and differing assumptions regarding the distribution of angular momentum. The generalized polytropic sequences bear close resemblance to the Maclaurin sequence, in most respects. In particular, the generalized sequences do not terminate, they do not "rotationally eject" matter, but they do reach points of bifurcation beyond which secular stability probably ceases. Subject headings: instabilities - interiors, stellar - rotation