Acoustic oscillations of rapidly rotating polytropic stars. II. Effects of the Coriolis and centrifu

Context. With the launch of space missions devoted to asteroseismology (like COROT), the scientific community will soon have accurate measurements of pulsation frequencies in many rapidly rotating stars. Aims. The present work focuses on the effects of rotation on pulsations of rapidly rotating stars when both the Coriolis and centrifugal accelerations require a non-perturbative treatment. Methods. We develop a 2-dimensional spectral numerical approach which allows us to compute acoustic modes in centrifugally distorted polytropes including the full influence of the Coriolis force. This method is validated through comparisons with previous studies, and the results are shown to be highly accurate. Results. In the frequency range considered and with COROT's accuracy, we establish a domain of validity for perturbative methods, thus showing the need for complete calculations beyond $v \sin i=50\,\mathrm{km\,s}^{-1}$ for a $R = 2.3\,R_\odot$, $M=1.9\,M_\odot$ polytropic star. Furthermore, it is shown that the main differences between complete and perturbative calculations come essentially from the centrifugal distortion.