Emden-chandrasekhar axisymmetric, rigidly rotating polytropes III - Determination of equilibrium configurations by an improvement of Chandrasekhar's method

The author determines equilibrium configurations of Emden-Chandrasekhar axisymmetric, solid-body rotating polytropes, defined as EC polytropes, for polytropic indices ranging from 0 (homogeneous bodies) to 5 (Roche-type bodies). To this aim, he improves Chandrasekhar's method to determine equilibrium configurations in two respects: namely, (1) no distinction exists between undistorted and distorted terms in the expression of the potential, and (2) the comparison between the expressions of gravitational potential and its first derivatives inside and outside the body has to be made on the boundary of a sphere of radius ξ0 ≥ ΞE, which does not necessarily coincide with the undistorted Emden's sphere of radius ΞE. The author also allows different values of ξ0 for different physical parameters, and chooses a special set which fits more refined results (involving more complicated and more expensive computer codes) by James (1964).