Equilibrium configurations of slowly rotating stars
Keywords:
Slowly rotating stars, equation of structure, equilibrium stateAbstract
In this work we consider equilibrium configurations of slowly rotating classical stars on the basis of Hartle’s formalism. All calculations have been performed up to second order terms in the angular velocity of a star. Equations of structure have been derived for configurations in equilibrium in order to find the mass, radius, moment of inertia, ellipticity, eccentricity and quadrupole moment as a function of the central density and the rotation period. Obtained results allow to account for all changes appeared as a result of rotation in star and planets. It was shown that unlike non-rotating spherical stars, the shape of slowly rotating stars will be a rotating ellipsoid with equal major semi-axes relative to the rotation axis; the moment of inertia of the rotating ellipsoid is different from non-rotating object; the potential of the gravitational field is not only the function of the radial coordinate but also the function of the polar coordinate. Generally the gravitational potential of a spherical object is defined only by its mass, however for a deformed object in the following approximation the quadrupole moment must be accounted for. The matching procedure is shown for the internal and external potentials of the rotating ellipsoid. All expressions are written as ordinary first order total differential equations and their integration methods are presented.
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