Regular patterns in the acoustic spectrum of rapidly rotating stars

Context. Rapid rotation modifies the structure of the frequency spectrum of pulsating stars, thus making mode identification difficult. Aims. We look for new forms of organisation for the frequency spectrum that can provide a basis for mode identification at high rotation rates. Methods. Acoustic modes in uniformly rotating polytropic models of stars are computed using a numerical code that fully takes the effects of rotation (centrifugal distortion and Coriolis acceleration) into account. All low-degree modes, = 0 to 3, with radial orders n = 1-10 and 21-25 for $N = 3$ polytropic models and n = 1-10 for $N = 1.5$ polytropic models are followed from a zero rotation rate up to 59% of the break-up velocity. Results. We find an empirical formula that gives a good description of the high-frequency range of the computed acoustic spectrum for high rotation rates. Differences between this formula and complete eigenmode calculations are shown to be substantially smaller than those obtained with a 3 rd order perturbative method valid at low rotation rates.