Pulsations of rapidly rotating stars: II. Realistic modelling for intermediate-mass stars

Very high precision seismic space missions such as CoRoT and Kepler provide the means for testing the modelling of transport processes in stellar interiors. For some stars, such as $\delta$ Scuti $\gamma$ Doradus and Be stars, for instance, the observed pulsation spectra are modified by rotation to such an extent that it prevents any fruitful interpretation. Our aim is to characterise acoustic pulsation spectra of realistic stellar models in order to be able to interpret asteroseismic data from such stars. The 2-dimensional oscillation code ACOR, which treats rotation in a non-perturbative manner, is used to study pulsation spectra of highly distorted evolved models of stars. 2D models of stars are obtained by a self-consistent method which distorts spherically averaged stellar models a posteriori, at any stage of evolution, and for any type of rotation law. Four types of modes are calculated in a very dense frequency spectrum, among which are island modes. The regularity of the island modes spectrum is confirmed and yields a new set of quantum numbers, with which an \'echelle diagram can be built. Mixed gravito-acoustic modes are calculated in rapidly rotating models for the first time.