New approach in the theory of stellar equilibrium with axial rotation

The study proposes a new method for the calculation of the equilibrium con(cid:28)guration of polytropes with rigid-body axial rotation. Self-consistency is based on the simultaneous use of di(cid:27)erential and integral forms of the mechanical equilibrium equation and a new variant of the perturbation theory, which is relative to the rotation in(cid:29)uence. The solutions are shown in the form of expansions for the Legendre polynomials and the functions of radial coordinate. The integral form of the equilibrium equation allows us to correctly de(cid:28)ne the set of the integration constants (the expansion coe(cid:30)cients, which depend on the angular velocity). The geometrical parameters of the stellar surface as well as the mass, volume and the moment of inertia were calculated as the functions of the angular velocity at (cid:28)xed values of the polytropic index n = 0; 1 . 0; 1 . 5; 2 . 0; 2 . 5; 3 . 0 . A comparison with the results of other authors was performed.