Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980ssrv...27..653s&link_type=abstract
(International Astronomical Union, Colloquium on Stellar Hydrodynamics, 58th, Los Alamos, N. Mex., Aug. 12-15, 1980.) Space Scie
Astronomy and Astrophysics
Astronomy
6
Perturbation Theory, Stellar Oscillations, Stellar Rotation, Adiabatic Conditions, Approximation, Displacement, Eigenvalues, Gravitational Fields, Time Dependence, Toroids
Scientific paper
The linear adiabatic oscillations of a uniformly rotating star are examined with respect to a co-rotating frame of reference. It is shown that time-independent displacement fields are allowed and can be represented as toroidal fields. The time-dependent oscillation modes are governed by a system of differential equations of the fourth order in time for axisymmetric perturbations, and of the fifth order for nonaxisymmetric perturbations. Therefore, in comparison to a nonrotating spherical star, a rotating star allows a new class of nonaxisymmetric oscillation modes with non-zero frequencies. These modes correspond to the r-modes, which originate from purely toroidal displacement fields in a nonrotating spherical star. For the r-modes of a slowly and uniformly rotating star, a perturbation method has been developed, with inclusion of the perturbation of the gravitational potential. It is seen that both dynamically stable and unstable r-modes do exist.
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