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Oscillations of a rotating star: a non-perturbative theory
Received 10 May 1999 / Accepted 16 September 1999
Nonradial gravity modes of a rotating ZAMS star are investigated using the anelastic approximation. Formulating the oscillation equations as a generalized eigenvalue problem, we first show that the usual second-order perturbative theory reaches its limits for rotation periods of about three days. Studying the rapid rotation régime, we develop a geometric formalism based on the integration of the characteristics of the governing mixed-type operator. These characteristics propagate in the star interior and the resulting web can be either ergodic (the web fills the whole domain) or periodic (the web reduces to an attractor along which characteristics focus). We further show the deep relation existing between the orbits of characteristics and the corresponding eigenmodes: (i) with ergodic orbits are associated regular eigenmodes which are similar to the usual gravity modes; (ii) with periodic orbits are associated singular eigenmodes for which the velocity diverges along the attractor. If diffusivity is taken into account, this singularity turns into internal shear layers tracing the attractor. As a consequence, the classical organization of eigenvalues along families with fixed disappears and leaves the place to an intricate low-frequency spectrum.
Key words: stars: individual: fl Doradus stars: oscillations stars: rotation
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