Low‐Frequency Nonradial Oscillations in Rotating Stars. I. Angular Dependence
Citations Over TimeTop 20% of 1997 papers
Abstract
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, Pml(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 g-mode oscillations.
Related Papers
- → Some relations between Bessel and Legendre Functions(1956)20 cited
- → Zonal harmonic series expansions of Legendre functions and associated Legendre functions(1990)18 cited
- → Legendre Polynomials and Legendre Functions(2021)1 cited
- Antiderivatives and integral representations of associated Legendre functions with {\mu}={\pm}{\nu}(2013)
- → Asymptotic Expansion of the Associated Legendre Function Over the Interval $0 \leq \theta \leq \pi$(2011)