New formalism of second order perturbation for analysing the effects of moderate rotation on the axially symmetric modes frequencies of δ scuti

Rotation has several considerable effects on frequencies of the stellar oscillations. For moderately rotating stars, higher order pertubative terms of rotation have to be considered. Even axially sym- metric modes with azimuthal wave number m = 0 are also affected by rotation. We used a new formalism of perturbative method in co-rotating reference. For axially symmetric modes, toroidal component of displacement can be expanded in terms of the poloidal components of the displace- ment. The results based on our new formalism for axially symmetric modes in a δ scuti star are more compatible with observation and frequencies were extracted by the exact two dimensional methods.