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Journal of Physical Studies 24(3), Article 3902 [20 pages] (2020)
DOI: https://doi.org/10.30970/jps.24.3902 NEW APPROACH IN THE THEORY OF STELLAR EQUILIBRIUM WITH AXIAL ROTATION
M. V. Vavrukh
Ivan Franko National University of Lviv, Department for Astrophysics,
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The study proposes a new method for the calculation of the equilibrium configuration of polytropes with rigid-body axial rotation. Self-consistency is based on the simultaneous use of differential and integral forms of the mechanical equilibrium equation and a new variant of the perturbation theory, which is relative to the rotation influence. 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 define the set of the integration constants (the expansion coefficients, 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 fixed 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.
Key words: polytropic stars, heterogeneous ellipsoids, axial rotation, mechanical equilibrium equation, stability of stars
