Saio (1981) evaluated frequency changes caused by rotation of a polytropic model, keeping the central pressure and density constant between the nonrotating and rotating model. Here we have evaluated the correction required to obtain the observationally more relevant change at fixed luminosity and effective temperature and shown that the result is quite similar to what is obtained for more realistic stellar models. We have shown that at least for higher-order modes the relative perturbation in dimensionless frequency , with the natural scaling factored out, can be obtained from Saio's results simply by adding 0.33. Thus, in particular, the second-order perturbation to the frequencies of the radial modes due to rotation, at fixed effective temperature and luminosity, is well-approximated from Saio's tabulated results as
where is in our notation and and Z are as defined by Saio (with for and Z is interpolated in frequency from Saio's Table 1). Although we have considered only radial modes, precisely the same correction must be applied in the case of nonradial modes.
Finally, we note that our analysis, as well as Saio's, was restricted to effects linear and quadratic in the angular velocity . It was pointed out by Soufi, Goupil & Dziembowski (1998) that terms of order must also be taken into account at the angular velocities found in some pulsating stars. Additional complications in the analysis of data from rapidly rotating stars arise from the fact that rotation affects the relation between observed intensities and colours and the true luminosity and effective temperature of the star (e.g. Maeder & Peytremann 1970; Collins & Smith 1985). Thus the proper interpretation of the frequency spectrum of rapidly rotating stars is evidently nontrivial; however, their prevalence dictates that this is an important problem in asteroseismology.
© European Southern Observatory (ESO) 1999
Online publication: October 14, 1999