Effects of moderate rotation on stellar pulsation I. Third order perturbation formalism

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 l = 0 and l = 2 p-modes. Near-degeneracy leads to spherical harmonic mixing and affects frequencies. Consequences for mode identification are discussed.