Non-rotating and slowly rotating stars in classical physics
DOI:
https://doi.org/10.26577/2218-7987-2014-5-1-69-80Keywords:
Hartle’s formalism, equilibrium configurations, moment of inertia and quadrupole moment.Abstract
Equations are given for the calculation of the equilibrium configurations of slowly rotating stars in the framework of classical physics. In particular, prescriptions have been given to find the mass-radius, the mass-central density relations and the shapes of rotating stars. The equations which determine the relations between mass, central density and radius of rotating configurations take the form of an equation of hydrostatic equilibrium. These equations show the balance between the pressure, gravitational, and centrifugal forces correctly to second order in the angular velocity, but no other approximation is made. The equations which determine the moment of inertia and the quadru-pole moment of the rotating star have also been derived.References
1 Meynet, G., Maeder, A. Stellar evolution with rotation. V. Changes in all the outputs of massive star models // Astronomy and Astrophysics. –
2000. –Vol.361. - P.101-120.
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 evolutionof 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 elativity. – 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 Bondi H. Massive Spheres in General Relativity // Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences.
-1964. – Vol. 284. – Issue 1390. – P. 303-317.
9 Buchdahl H. General Relativistic Fluid Spheres // Physical Review. - 1959. – Vol. 116. –Issue 4. – P. 1027-1034.
10 Chandrasekhar S. Introductionto the Study of Stellar Structure. Chicago: University of Chicago Press. - 1939.
11 Harrison B., Thorne K., Wakano M.,
Wheeler J. Gravitation Theory and Gravitational
Collapse. Cambridge: Cambridge University Press.-1965.
12 Hartle, J. B., Sharp D. H. Variational Principle for the Equilibrium of a Relativistic, Rotating Star // Astrophysical Journal. – 1967. – Vol.147. –
P. 317.
13 Jeffreys H. The Earth. Cambridge: Cambridge University Press. - 959.
14 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.
15 Chandrasekhar S., Roberts P. The Ellipticity of a Slowly Rotating Configuration // Astrophysical Journal.-1963. – Vol. 138. – P. 801.
2000. –Vol.361. - P.101-120.
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 evolutionof 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 elativity. – 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 Bondi H. Massive Spheres in General Relativity // Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences.
-1964. – Vol. 284. – Issue 1390. – P. 303-317.
9 Buchdahl H. General Relativistic Fluid Spheres // Physical Review. - 1959. – Vol. 116. –Issue 4. – P. 1027-1034.
10 Chandrasekhar S. Introductionto the Study of Stellar Structure. Chicago: University of Chicago Press. - 1939.
11 Harrison B., Thorne K., Wakano M.,
Wheeler J. Gravitation Theory and Gravitational
Collapse. Cambridge: Cambridge University Press.-1965.
12 Hartle, J. B., Sharp D. H. Variational Principle for the Equilibrium of a Relativistic, Rotating Star // Astrophysical Journal. – 1967. – Vol.147. –
P. 317.
13 Jeffreys H. The Earth. Cambridge: Cambridge University Press. - 959.
14 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.
15 Chandrasekhar S., Roberts P. The Ellipticity of a Slowly Rotating Configuration // Astrophysical Journal.-1963. – Vol. 138. – P. 801.
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Boshkayev, K. (2014). Non-rotating and slowly rotating stars in classical physics. International Journal of Mathematics and Physics, 5(1), 69–80. https://doi.org/10.26577/2218-7987-2014-5-1-69-80
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Theoretical Physics and Plasma Physics
