EFFECTS OF MODERATE ROTATION ON STELLAR PULSATION - I - 3RD-ORDER PERTURBATION FORMALISM

Interpretation of the available ground-based and forthcoming space obs ervations of multiperiodic variable stars require accurate computation s of oscillation frequencies. Typical rotational equatorial velocities of upper main sequence stars range between 50 and 200 km/s and the ef fect of rotation on the oscillation frequencies of these stars must be included. The rotation can still be considered as a perturbation, pro vided the expansion used in the perturbation method is carried out far enough to provide frequencies accurate enough to match that of the ob servations. For that purpose, we develop here a perturbation formalism for adiabatic oscillations of moderately rotating stars which is cons istently valid up to third order in the rotation rate. The formalism i ncludes the case of near-degeneracy i.e. when the frequencies of two ( or three) oscillation modes happen to be close to each other. This occ urs systematically for l = 0 and l = 2 p-modes. Near-degeneracy leads to spherical harmonic mixing and affects frequencies. Consequences for mode identification are discussed.