The effects of stellar rotation must be taken into account in interpreting the spectrum of oscillations of many stars. In the case of a slow rotator, the effects of rotation are very simply interpreted: rotation removes the frequency degeneracy in the azimuthal order m of the modes, and in fact this allows the possibility of determining the angular velocity inside the star. The Sun is one such star: it has a rotation period of about one month, which is much longer than its global dynamical timescale of about one hour. (The dynamical timescale is essentially , where is the mean density and G is the gravitational constant.) Many pulsating stars rotate much more rapidly, however; delta Scuti stars, for example, are observed to rotate with surface velocities of the order 100-200 km s-1, corresponding to a rotation period of about one day. As well as the first-order effect of raising the m-degeneracy of the modes, rotation also makes the star oblate and perturbs the internal stratification. Such perturbations will result in a systematic change of all frequencies, if compared with a nonrotating star of similar mass and age. In this way even the frequencies of radial and axisymmetric modes are affected by the rotation of the star. These effects must evidently be taken into account, in order to identify the mode parameters and to use the observed frequencies to make inferences about the stars' internal structure and rotation.
An influential paper on the study of oscillations in rotating stars is that by Saio (1981). Saio's numerical results are still in use for interpreting observations. However, Saio's calculations were for simple polytropic models. More realistic models are required for the detailed mode interpretation and seismology of stars that modern observations make a possibility. For this reason, Kjeldsen et al. (1998) calculated stellar models with more realistic physics. This work raised a question about the proper interpretation of Saio's tabulated results, which is addressed in this note.
The full calculation of the normal modes of oscillation of the model of a rotating star is quite an undertaking; the usual approach to estimating the frequencies of such a star is therefore to evaluate the frequency changes induced by the effects of rotation, treating them as a perturbation about a nonrotating model. But to make use of such calculations to compare with the observed frequencies of stars, it is necessary to consider carefully what properties of the star are held fixed when making the perturbation.
Saio compared the frequencies of rotating and nonrotating polytropes. In that comparison, he kept the central density and central pressure (and hence polytropic constant) fixed. An observationally more relevant comparison, though, would be to keep fixed the observed global properties of the star. This is considered here.
© European Southern Observatory (ESO) 1999
Online publication: October 14, 1999