On the effects of rotation on acoustic stellar pulsations: Validity domains of perturbative methods and close frequency pairs

Pulsation frequencies of acoustic modes are calculated for realistic rotating stellar models using both a perturbative and a two-dimensional approach. A comparison between the two yields validity domains which are similar to those previously obtained in Reese et al. for polytropic models. One can also construct validity domains based on polynomial fits to the frequencies from the two-dimensional approach, and these also turn out to be similar, thus further confirming the agreement between the perturbative and the two-dimensional approaches at low rotation rates. Furthermore, as was previously shown in Espinosa et al., adjacent frequencies in multiplets come close together, thus forming pairs. This phenomenon, exclusive to two-dimensional calculations, is shown to be an unlikely explanation of the close frequency pairs observed in δ Scuti stars. A systematic search for all close frequency pairs in the calculated spectrum is also carried out. The number of close frequency pairs is shown to agree with what is expected based on a Poisson distribution, but does not match the number or distribution of close pairs in stars such as FG Vir. Furthermore, a lack of close frequency pairs appears at low rotation rates, where frequency multiplets do not overlap. δ Scuti stars currently reported as having close frequency pairs do not fall in this interval.