Equilibrium configurations of slowly rotating stars
Кілттік сөздер:
Slowly rotating stars, equation of structure, equilibrium stateАннотация
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.
Библиографиялық сілтемелер
2. Meynet G., Maeder A. Stellar evolution with rotation. X. Wolf-Rayet star populations at solar metallicity // Astronomy and Astrophysics. – 2003. - Vol. 404.- P. 975-990.
3. Ekstrom S., Meynet G., Chiappini C., Hirschi R., Maeder A. Effects of rotation on the evolution of primordial stars // Astronomy and Astrophysics.- 2008. - Vol. 489. - Issue 2.- P. 685-698.
4. Chandrasekhar S. The Maximum Mass of Ideal White Dwarfs // Astrophysical Journal. - 1931. - Vol. 74. - P. 81-82.
5. Chandrasekhar S., Roberts P. On Highly Rotating Polytropes. II // Astrophysical Journal. -1963. – Vol. 138. – P. 809.
6. Stergioulas N. Rotating Stars in Relativity // Living Reviews in Relativity. – 2003. – Vol. 6. – P. 3.
7. Hartle J. B. Slowly Rotating Relativistic Stars. I. Equations of Structure // Astrophysical Journal. -1967. - Vol. 150. – P. 1005.
8. Chandrasekhar S. Introduction to the Study of Stellar Structure. Chicago: University of Chicago Press. - 1939.
9. Jeffreys H. The Earth. Cambridge: Cambridge University Press. - 1959.
10. Chandrasekhar S. The equilibrium of distorted polytropes. I. The rotational problem // Monthly Notices of the Royal Astronomical Society. – 1933. – Vol. 93. – P. 390-406.
11. Chandrasekhar S., Lebovitz N. R. On the Oscillations and the Stability of Rotating Gaseous Masses. III. The Distorted Polytropes. // Astrophysical Journal. – 1962. – Vol. 136. – P.1082.
12. James R.A. The Structure and Stability of Rotating Gas Masses // Astrophysical Journal. – 1964. – Vol. 140. – P.552.
13. Roxburgh L W. On stellar rotation, I. The rotation of upper main-sequence stars // Monthly Notices of the Royal Astronomical Society. – 1964. – Vol. 128. – P.157.
14. Monaghan F.F., Roxburgh I.W. The structure of rapidly rotating polytropes // Monthly Notices of the Royal Astronomical Society. – 1965 . – Vol. 131. – P.13.
15. Anand S.P.S. The Equilibrium Structure of Rapidly Rotating Gaseous Polytropes and Completely Degenerate Systems // Astrophysical Journal. – 1968. – Vol. 153. – P.135.
16. Sedrakian D.M., Papoian V.V., Chubarian E.V. On the theory of rapidly rotating white dwarfs // Monthly Notices of the Royal Astronomical Society. - 1970. - Vol. 149. - P. 25.
17. Papoyan V.V., Sedrakyan, D. M., Chubaryan E.V. Newtonian theory of rapidly rotating white dwarfs // Astrophysics. - 1971. - Vol. 7. - Issue 1. -P.55-61.
18. Harrison B., Thorne K., Wakano M., Wheeler J. Gravitation Theory and Gravitational Collapse. Cambridge: Cambridge University Press. -1965.
19. Chandrasekhar S., Roberts P. The Ellipticity of a Slowly Rotating Configuration // Astrophysical Journal. - 1963. – Vol. 138. – P. 801.
20. Hartle J. B. Slowly Rotating Relativistic Stars. IX: Moments of Inertia of Rotationally Distorted Stars // Astrophysics and Space Science. - 1973. – Vol. 24. – P. 385-405.