Emden-chandrasekhar axisymmetric, rigidly rotating polytropes V Approximate equilibrium configurations with polytropic index differing slightly from n=0, 1, and 5

An approximate analytical method of solving the polytropic equilibrium equations, first developed by Seidov and Kuzakhmedov (1978), has been extended and generalized to equilibrium configurations of axisymmetric systems in rigid rotation, with polytropic index, n = np+δn, near np = 0, 1 and 5. Though the details of the method depend on the value of np, acceptable results are obtained for |δn| ⪉ 0.5 to describe slowly rotating configurations in the range 0 ≤ n ≤ 1.5, 4.5 ≤ n ≤ 5. In the limit of rotational equilibrium configurations, when the distorsion may be large enough, a satisfactory approximation holds only in the range 0 < n, 1 ≤ n <1.5, 4.5 < n ≤ 5.