The study of stellar pulsations can improve our understanding of stellar structure. By measuring the photometric and spectral line-profile variations caused by pulsations, one can determine the time dependent state of the stellar surface, and eventually probe the interior of the star. The development of high-precision spectroscopy with solid-state detectors initiated the discovery of several classes of non-radially pulsating early-type stars (e.g., Smith 1977; Vogt & Penrod 1983; Baade 1984; Gies & Kullavanijaya 1988), and offered much higher accuracy in measuring time variability of line profiles. The increase in computing power allowed the numerical synthesis of line-profile variations, based on analytical descriptions of the surface velocity and/or temperature perturbations due to non-radial pulsations (Osaki 1971; Kambe & Osaki 1988; Lee & Saio 1990; Aerts & Waelkens 1993). Such numerical simulations are indispensable for the correct interpretation of observed line-profile variability. An excellent textbook on the theory of stellar pulsations is written by Unno et al. (1989).
Spectroscopic identifications of pulsation modes have been attempted by fitting theoretical line profiles to observed spectra (e.g. Smith 1977). A serious problem with such an approach is the large number of free parameters, and the associated question of the uniqueness of the solution. Currently, two powerful Fourier-analysis techniques are in use, which attempt to resolve this problem. The first is based on the Doppler imaging principle (Vogt et al. 1987), in which one assumes a mapping of photospheric features (e.g. local velocity, brightness or EW variations) onto line profiles that are Doppler broadened by the rotation of the star. From a Fourier transform applied to each velocity bin of a time series of observed spectra one obtains the power of variability as a function of frequency (periodogram), for all velocity positions in the line profile (e.g. Gies & Kullavanijaya 1988; Kambe et al. 1990; Reid et al. 1993; see Kennelly et al. 1992 for an alternative version of this technique which comprises a 2D Fourier transform). Additionally, the Fourier analysis provides information about the phase change of the periodic variations across the line profile. Using the power and phase information, some of the pulsation parameters can be derived.
The second technique involves the computation of velocity moments of the line profile (Balona 1986; Aerts et al.\ 1992). A comparison of the Fourier components derived from the observed moment variations with those of the velocity moments generated by means of a non-radial pulsation model, gives in principle all the desired pulsation parameters.
In this paper we apply a technique, that is similar to the first mentioned method, to theoretical spectra. Our aim is to illustrate the dependence of the observable diagnostics (which will be defined in Sect. 4 (click here)) on the relevant stellar and pulsational parameters. To allow a comparison with the work of Aerts et al.\ (1992), we calculated the first two velocity moments as well. We present calculations for rotating early-type stars, but in many cases our description applies to other types of stars as well.
We use a description of the pulsational velocity field of a rotating star that incorporates terms due to the Coriolis force, which is equivalent to the one presented by Aerts & Waelkens (1993, hereafter AW), but with a few modifications to allow straightforward calculation. We investigate only single spheroidal pulsation modes. A generalization of the velocity field to multiple modes in a rotating star is straightforward if a linear pulsation theory applies. In all our models, we assume the symmetry axis of the pulsation to be aligned with the axis of rotation. In our line profile synthesis we neglect the atmospheric variations due to the pulsation, which is justified for those absorption lines for which the pulsational velocity variations dominate the temperature effects (Simon 1991).
In subsequent papers we present the results of bulk computations of the diagnostics (Paper II, Telting & Schrijvers 1996a), we discuss the peculiar line-profile behavior of nearly equator-on tesseral modes with odd (Paper III, Telting & Schrijvers 1996b), and we investigate the effect of brightness and EW changes caused by the pulsation on the observational diagnostics (Paper IV, & Telting 1996). Preliminary results of the diagnostic value of phase diagrams derived from time series of spectra of non-radially oscillating stars are presented by Telting & Schrijvers (1995).
The outline of this paper is as follows. In Sects. 2.1 and 2.2 we briefly summarize the traditional model describing the surface velocity field of non-radial adiabatic pulsations, in the limit of no rotation. The effect of rotation on the velocity field of pulsation is included in Sect. 2.3. In Sect. 2.4 we derive an expression for the ratio of the horizontal to the vertical pulsational amplitude, k, which accounts for effects of the Coriolis force, and in Sect. 2.5 we verify this expression in the case of a polytropic model. The synthesis of line profiles is described in Sect. 3. We discuss the observable diagnostics in Sect. 4. The relevant domains of the pulsational and stellar parameters are discussed in Sect. 5. The results of our computations are presented in Sect. 6. We summarize our findings in Sect. 7.