## Effects of moderate rotation on stellar pulsation## I. Third order perturbation formalism
^{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
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 and
* e-mail: mariejo.goupil @ obspm.fr
## Contents- 1. Introduction
- 2. Computing frequencies of rotating stars: outline
- 3. Equilibrium structure of rotating models
- 4. Third order perturbation formalism
- 5. Near-degeneracy
- 6. Summary
- Acknowledgements
- Appendix
- References
© European Southern Observatory (ESO) 1998 Online publication: June 2, 1998 |