Line-profile variations of non-radial adiabatic pulsations of rotating stars II. The diagnostic value of amplitude and phase diagrams derived from time series of spectra

We discuss the possibilities to derive the pulsation parameters ` andm of non-radially pulsating rotating stars from spectroscopic observations.Wemodel the line-profile variations caused by the oscillatory velocity field and temperature variations at the surface of the star. In our description of the velocity field of the pulsations, we use the expressions for linear adiabatic pulsations, and include terms that account for the Coriolis force. For various stellar and pulsational parameters we generate time series of spectra, and analyse the phase and amplitude diagrams resulting from a Fourier analysis of the time series. We find that for stars with Ve sin i larger than approximately five times the half-width (HWHM) of the intrinsic profile, one can derive both the degree ` and the order |m| from the phase diagrams of the line-profile variations. We present linear relations between observable phase differences and the parameters ` and |m|. These relations can be used to identify pulsation modes. This method works for spheroidal and toroidal, sectoral and tesseral modes; it is possible to derive values of ` <∼ 15 and values of |m| <∼ 10. Themethod is also applicable tomulti-periodic multi-mode pulsations. We apply the method to analyse spectroscopic data sets of ζ Oph and Per, and present values of ` of the pulsation modes in these stars. We use harmonic phase diagrams to constrain values of |m| of some of these modes. We argue that the presence of the complex pattern of frequencies in the periodogram of the line-profile variations of Per, is consistent with the expectations for profile variations which are dominated by the oscillatory velocity field, rather than the oscillatory temperature variations.