Low-frequency nonradial oscillations in rotating stars. I. Angular dependence

Umin Lee, Hideyuki Saio

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131 Citations (Scopus)


We obtain the θ-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 θ-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 λ coincides with l(l + 1) when rotation is absent, where l is the latitudinal degree of the associated Legendre function, Plm(cos θ). The value of λ changes as a function of v = 2Ω/ω, where Q and a 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 | v | > 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 | v | increases. Negative A'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 r-mode (global Rossby wave) oscillation. Amplitudes of g-mode oscillations tend to be confined to the equatorial region as | v | increases. This tendency is stronger for larger λ. On the other hand, amplitudes of oscillatory convective modes are small near the equator.

Original languageEnglish
Pages (from-to)839-845
Number of pages7
JournalAstrophysical Journal
Issue number2 PART I
Publication statusPublished - 1997
Externally publishedYes


  • Methods: Numerical
  • Stars: Oscillations
  • Stars: Rotation

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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