THE OSCILLATIONS OF TAU-PEGASI

We present extensive spectroscopic time series observations of the mul tiperiodic, rapidly rotating, delta Scuti star tau Pegasi. Information about the oscillations is contained within the patterns of line-profi le variation of the star's blended absorption-line spectrum. We introd uce the new technique of Doppler deconvolution with which to extract t hese patterns by modeling the intrinsic stellar spectrum and the broad ening functions for each spectrum in the time series. Frequencies and modes of oscillation are identified from the variations using the tech nique of Fourier-Doppler imaging and a two-dimensional least-squares c leaning algorithm. We find a rich mode spectrum with degrees up to l = 20 and with frequencies below about 35 cycles day(-1). Those modes wi th the largest amplitudes have frequencies that lie within a narrow ba nd. We conclude that the observed spectrum can be explained if the mod es of tau Peg propagate in the prograde direction with l similar or eq ual to \m\ and with frequencies that are about equal in the corotating frame of the star. We discuss the implications of these results for t he prospect of delta Scuti seismology.