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A Convenient Method to Obtain Stellar Eigenfrequencies***

Published online by Cambridge University Press:  12 April 2016

M. Knölker  and
M. Stix
M. Knölker
Affiliation:
Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, D-7800 Freiburg i.Br., F.R.G.
M. Stix
Affiliation:
Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, D-7800 Freiburg i.Br., F.R.G.

Abstract

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The differential equations describing stellar oscillations are transformed into an algebraic eigenvalue problem. Frequencies of adiabatic oscillations are obtained as the eigenvalues of a banded real symmetric matrix. We employ the Cowling-approximation, i.e. neglect the Eulerian perturbation of the gravitational potential, and, in order to preserve selfadjointness, require that the Eulerian pressure perturbation vanishes at the outer boundary. For a solar model, comparison of first results with results obtained from a Henyey method shows that the matrix method is convenient, accurate, and fast.

Type
Research Article
Information
International Astronomical Union Colloquium , Volume 66: Problems of Solar and Stellar Oscillations , 1983 , pp. 331 - 341
Copyright
Copyright © Reidel 1983

Footnotes

*

Proceedings of the 66th IAU Colloquium: Problems in Solar and Stellar Oscillations, held at the Crimean Astrophysical Observatory, U.S.S.R., 1-5 September, 1981.

**

Mitteilungen aus dem Kiepenheuer-Institut Nr. 213.

References

Acton, F.S.: 1970, Numerical Methods That Work, Harper and Row, New York.Google Scholar
Ando, H. and Osaki, Y.: 1975, Pubi. Astron. Soc. Japan 27, 581.Google Scholar
Baker, N. and Kippenhahn, R.: 1962, Z. Astrophys. 54, 114.Google Scholar
Baker, N. and Kippenhahn, R.: 1965, Astrophys. J. 142, 868.CrossRefGoogle Scholar
Baker, N. and Temesváry, S.: 1966, Tables of Convective Stellar Envelope Models, 2nd ed., NASA, New York.Google Scholar
Böhm-Vitense, E.: 1958, Z. Astrophys. 46, 108.Google Scholar
Castor, J.I.: 1971, Astrophys. J. 166, 109.Google Scholar
Chandrasekhar, S.: 1964, Astrophys. J. 139, 664.Google Scholar
Cox, A.N. and Tabor, J.E.: 1916, Astrophys. J. Suppl. 31, 271.Google Scholar
Cox, J.P.: 1980, Theory of Stellar Pulsation, Princeton Univ. Press.Google Scholar
Cowling, T.G.: 1941, Monthly Notices Roy. Astron. Soc. 101, 367.Google Scholar
Grec, G., Fossat, E., and Pomerantz, M.: 1980, Nature 288, 541.Google Scholar
Henyey, L.G., Forbes, J.E., and Gould, N.L.: 1964, Astrophys. J. 139, 306.Google Scholar
Knölker, M.: 1978, Diplomarbeit, Univ. Göttingen.Google Scholar
Ledoux, P. and Walraven, Th.: 1958, in Flügge, S. ed.), Handbuch der Physik, Springer, Berlin, Vol. 51, p. 353.Google Scholar
Sobouti, Y.: 1977, Astron. Astrophys. 55, 327.Google Scholar
Unno, W., Osaki, Y., Ando, H., and Shibahashi, H.: 1979, Nonradial Oscillations of Stars, Univ. Tokyo Press.Google Scholar
Vernazza, J.E., Avrett, E.H., and Loeser, R.: 1976, Astrophys. J. Suppl. 30, 1.Google Scholar
Williams, G.P.: 1969, J. Fluid Mech. 37, 727.Google Scholar