LowFrequency Nonradial Oscillations in Rotating Stars. I. Angular Dependence
Abstract
We obtain the θdependence of the displacement vector of rotationally modulated lowfrequency 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 θdependence 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 λ coincides with l(l + 1) when rotation is absent, where l is the latitudinal degree of the associated Legendre function, P^{m}_{l}(cos θ). The value of λ changes as a function of ν ≡ 2Ω/ω, where Ω and ω are the angular frequencies of rotation and of oscillation (seen in the corotating frame), respectively. These eigenvalues correspond to rotationally modulated gmode oscillations.
In the domain of  ν  > 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  ν  increases. Negative λ's correspond to oscillatory convective modes. The solution associated with a λ that has a small positive value after changing its sign is identified as an rmode (global Rossby wave) oscillation.
Amplitudes of gmode oscillations tend to be confined to the equatorial region as  ν  increases. This tendency is stronger for larger λ. On the other hand, amplitudes of oscillatory convective modes are small near the equator.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 1997
 DOI:
 10.1086/304980
 Bibcode:
 1997ApJ...491..839L
 Keywords:

 Methods: Numerical;
 Stars: Oscillations;
 Stars: Rotation