Low-Frequency Nonradial Oscillations in Rotating Stars. I. Angular Dependence

Details Low-Frequency Nonradial Oscillations in Rotating Stars. I. Angular Dependence Low-Frequency Nonradial Oscillations in Rotating Stars. I. Angular Dependence

Dec 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997apj...491..839l&link_type=abstract

Astrophysical Journal v.491, p.839

Astronomy and Astrophysics

Astronomy

44

Methods: Numerical, Stars: Oscillations, Stars: Rotation

Scientific paper

We obtain the theta -dependence of the displacement vector of rotationally modulated low-frequency nonradial oscillations by numerically integrating Laplace's tidal equation as an eigenvalue problem with a relaxation method. This method of calculation is more tractable than our previous method in which the theta -dependence was represented by a truncated series of associated Legendre functions. Laplace's tidal equation has two families of eigenvalues. In one of these families, an eigenvalue lambda coincides with l(l + 1) when rotation is absent, where l is the latitudinal degree of the associated Legendre function, Pml({cos} theta ). The value of lambda changes as a function of nu = 2 Omega / omega , where Omega and omega are the angular frequencies of rotation and of oscillation (seen in the corotating frame), respectively. These eigenvalues correspond to rotationally modulated g-mode oscillations. In the domain of | nu | > 1, another family of eigenvalues exists. Eigenvalues belonging to this family have negative values for prograde oscillations, while they change signs from negative to positive for retrograde oscillations as | nu | increases. Negative lambda 's correspond to oscillatory convective modes. The solution associated with a lambda that has a small positive value after changing its sign is identified as an r-mode (global Rossby wave) oscillation. Amplitudes of g-mode oscillations tend to be confined to the equatorial region as | nu | increases. This tendency is stronger for larger lambda . On the other hand, amplitudes of oscillatory convective modes are small near the equator.

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