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Astron. Astrophys. 334, 911-924 (1998)

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Effects of moderate rotation on stellar pulsation

I. Third order perturbation formalism

F. Soufi 1, M.J. Goupil * 1 and W.A. Dziembowski ** 2

1 DASGAL, Observatoire de Paris, F-92195 Meudon, France
2 Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, PL-00-716 Warsaw, Poland

Received 20 October 1997 / Accepted 9 March 1998

Abstract

Interpretation of the available ground-based and forthcoming space observations of multiperiodic variable stars require accurate computations of oscillation frequencies. Typical rotational equatorial velocities of upper main sequence stars range between 50 and 200 km/s and the effect of rotation on the oscillation frequencies of these stars must be included. The rotation can still be considered as a perturbation, provided the expansion used in the perturbation method is carried out far enough to provide frequencies accurate enough to match that of the observations. For that purpose, we develop here a perturbation formalism for adiabatic oscillations of moderately rotating stars which is consistently valid up to third order in the rotation rate.

The formalism includes the case of near-degeneracy i.e. when the frequencies of two (or three) oscillation modes happen to be close to each other. This occurs systematically for [FORMULA] and [FORMULA] p -modes. Near-degeneracy leads to spherical harmonic mixing and affects frequencies. Consequences for mode identification are discussed.

Key words: stars: oscillations – stars: rotation – ffi Scu – stars: variables: other

* e-mail: mariejo.goupil @ obspm.fr
** e-mail: Wojciech-Dziembowski @ camk.edu.pl

Send offprint requests to: M.J. Goupil or W.A. Dziembowski

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998

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