Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981ap%26ss..78..483s&link_type=abstract
Astrophysics and Space Science, vol. 78, no. 2, Aug. 1981, p. 483-501. Fonds de la Recherche Fondamentale Collective
Astronomy and Astrophysics
Astrophysics
30
Perturbation Theory, Spherical Coordinates, Stellar Rotation, Approximation, Boundary Value Problems, Eigenvalues, Modal Response, Partial Differential Equations, Stellar Gravitation
Scientific paper
A perturbation method is derived for r-modes in a slowly and uniformly rotating star. In contrast to previous studies, the perturbation of the gravitational potential is included in the perturbation method. On the assumption that the effects of the centrifugal force are taken into account in the equilibrium model up to the second order in the angular velocity, an eigenvalue problem of sixth-order in the radial coordinate is derived that allows one to determine the zeroth-order toroidal displacement field and the third-order term in the expansion of the eigenfrequency. Furthermore, another eigenvalue problem is derived that governs the first-order toroidal displacement field and the fourth-order term in the expansion of the eigenfrequency. This second eigenvalue problem is also of the sixth-order in the radial coordinate. It is shown that the third-order term in the expansion of the eigenfrequency is real, and that the fourth-order term is zero.
Craeynest D.
Martens L.
Smeyers Paul
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