The Equilibrium Structure of Rapidly Rotating Gaseous Polytropes and Completely Degenerate Systems

The equilibrium structures of axially symmetric, uniformly rotating gaseous masses in the polytropic and white-dwarf cases are determined. We have studied the effects of rotation to the second order in w2 (i.e., up to w4) by Chandrasekhar's series-expansion method, where w is the angular velocity of rota- tion. We have obtained the mass, volume relation between central and mean densities, central pressure, and central temperature for rotating polytropes. We have also obtained ~3 (ratio of gas pressure to total pressure due to gas and radiation) for distorted polytropes. Similar structural parameters are also ob- tained in the case of a rotating white dwarf. Further, it is found that rotation increases Chandrasekhar's limiting mass for non-rotating white dwarfs by 3 per cent at the maximum angular velocity consistent with equilibrium. The numerical values of various functions and structural parameters for rotating poiy- tropes are given in tabular form at the end of the paper