Line-profile variations due to adiabatic non-radial pulsations in rotating stars .1. Observable characteristics of spheroidal modes

We present a useful formulation of the surface velocity field of a rotating, adiabatically pulsating star, which accounts for the effects of the Coriolis force. We use this model to investigate the observable spectroscopic characteristics of non-radial pulsations. We calculate time series of absorption line profiles in a carefully chosen domain of parameter space. Only mono-periodic spheroidal modes are investigated; atmospheric changes due to the pulsation are neglected. The line-profile variations, as well as their behavior inferred from two well-defined diagnostics, are presented in two-dimensional parameter grids. We show that the intensity variations in time series of theoretical spectra, at each position in the line profile, cannot be described by a single sinusoid: at least one harmonic sinusoid needs to be included. Across the line profile the relative amplitudes and phases of these sinusoids vary independently. The blue-to-red phase difference found at the main pulsation frequency turns out to be an indicator of the degree l, rather than the azimuthal order \m\; the phase difference of the variations with the first harmonic frequency is an indicator of \m\ Hence, the evaluation of the variability at the harmonic frequency can improve the results derived from an analysis of observed line profiles. We find, that if line-profile variations at the line center dominate over the variations in the line wings, this does not give conclusive information on the ratio of the horizontal to the vertical pulsational surface motions. Tesseral modes, when observed at not too high inclinations, are as much capable of producing considerable line-profile variations as sectoral modes. We find that, within the limits of our model, the effects of rotation on the appearance of the line-profile variations are important for low-degree sectoral modes, and for the sub-class of the tesseral modes with l - m an even number.