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

Abstract

We obtain the h-dependence of the displacement vector of rotationally modulated low-frequency non-radial oscillations by numerically integrating LaplaceÏs tidal equation as an eigenvalue problem with a relaxation method. This method of calculation is more tractable than our previous method in which the h-dependence was represented by a truncated series of associated Legendre functions. LaplaceÏs tidal equation has two families of eigenvalues. In one of these families, an eigenvalue j coincides with l(l ] 1) when rotation is absent, where l is the latitudinal degree of the associated Legendre function, h). P l m(cos The value of j changes as a function of l 4 2)/u, where) and u are the angular frequencies of rotation and of oscillation (seen in the corotating frame), respectively. These eigenvalues correspond to rotation-ally modulated g-mode oscillations. In the domain of o l o [ 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 o l o increases. Negative jÏs correspond to oscillatory convective modes. The solution associated with a j that has a small positive value after changing its sign is identiÐed as an r-mode (global Rossby wave) oscillation. Amplitudes of g-mode oscillations tend to be conÐned to the equatorial region as o l o increases. This tendency is stronger for larger j. On the other hand, amplitudes of oscillatory convective modes are small near the equator.