Improved Asymptotic Expressions for the Eigenvalues of Laplace's Tidal Equations

Abstract

Laplace's tidal equations govern the angular dependence of oscillations in stars when uniform rotation is treated within the so-called traditional approximation. Using a perturbation expansion approach, I derive improved expressions for the eigenvalue associated with these equations, valid in the asymptotic limit of large spin parameter $q$. These expressions have a relative accuracy of order $q^{-3}$ for gravito-inertial modes, and $q^{-1}$ for Rossby and Kelvin modes; the corresponding absolute accuracy is of order $q^{-1}$ for all three mode types. I validate my analysis against numerical calculations, and demonstrate how it can be applied to derive formulae for the periods and eigenfunctions of Rossby modes.

10 pages, 2 figures, accepted by MNRAS

References in corpus (4)

• The interior rotation of a sample of gamma Doradus stars from ensemble modelling of their gravity mode period spacings
• Angular momentum transport by heat-driven g-modes in slowly pulsating B stars
• Period spacings of $\gamma$ Doradus pulsators in the \textit{Kepler} field: Rossby and gravity modes in 82 stars
• Dynamical Tides in Compact White Dwarf Binaries: Influence of Rotation

Cited by in corpus (8)

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• Nonlinear internal waves breaking in stellar radiation zones. Parametrisation for the transport of angular momentum: bridging geophysical to stellar fluid dynamics
• Constraining differential rotation in gamma Doradus stars from inertial dips properties
• KIC 4150611: A quadruply eclipsing heptuple star system with a g-mode period-spacing pattern Asteroseismic modelling of the g-mode period-spacing pattern
• Exploring the probing power of gamma-Dor's inertial dip for core magnetism: case of a toroidal field
• Foam: A Python package for forward asteroseismic modelling of gravity modes