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The Roche Problem for Stratified Polytropes

Published online by Cambridge University Press:  25 April 2016

Leigh Brookshaw
Leigh Brookshaw*
Affiliation:
Mathematics Department, Monash University
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Extract

Roche (1850) made the first study of the stability of binary systems. The problem he studied, and which now bears his name, is concerned with the stability of a liquid star in a synchronous, circular orbit about a point mass. Roche’s calculations predicted that if the separation between the liquid star and the point mass is S2.5rs’/3, where r is the unperturbed radius of the liquid star and s the ratio of the mass of the point to the mass of the liquid star, then the liquid star would be unstable. This result was generalised to two liquid stars orbiting each other by Darwin (1910, p. 436). Using the tensor virial method Chandrasekhar (1969) has given a uniform analysis of the classical result. The classical results have been extended by Hachisu and Eriguchi (1984a, b) who looked for the onset of instability in polytropes in binary orbits.

Type
Contributions
Information
Publications of the Astronomical Society of Australia , Volume 6 , Issue 4 , 1986 , pp. 461 - 464
Copyright
Copyright © Astronomical Society of Australia 1985

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References

Chandrasekhar, S., 1933, An Introduction to the Study of Stellar Structure, Dover Publications. Chandrasekhar, S., 1969, Classical Ellipsoidal Figures of Equilibrium, Yale University Press.Google Scholar
Darwin, G. H., 1910, Collected Works Vol. III, Cambridge University Press.Google Scholar
Gingold, R. A.and Monaghan, J. J., 1979, Mon. Not. R. Astron. Soc, 188, 45.CrossRefGoogle Scholar
Gingold, R. A.and Monaghan, J. J., 1980, Mon. Not. R. Astron. Soc, 191, 897.CrossRefGoogle Scholar
Hachisu, I. and Eriguchi, Y., 1984a, Pubi. Astron. Soc. Japan, 36, 239.Google Scholar
Hachisu, I. and Eriguchi, Y., 1984b, Pubi. Astron. Soc. Japan, 36, 259.Google Scholar
Milgrom, M. and Shapiro, S. L., 1978, Astrophys. J., 223, 991.CrossRefGoogle Scholar
Nduka, A., 1971, Astrophys. J., 170, 131.CrossRefGoogle Scholar
Press, W. H.and Teukolsky, S. A., 1977, Astrophys. J., 213, 183.CrossRefGoogle Scholar
Roche, Ed., Acad, des Sci. de Montpellier, 1, 243 (1847-1850).Google Scholar