The Oscillations of Tau Pegasi

We present extensive spectroscopic time series observations of the multiperiodic, rapidly rotating, delta Scuti star tau Pegasi. Information about the oscillations is contained within the patterns of line-profile variation of the star's blended absorption-line spectrum. We introduce the new technique of Doppler deconvolution with which to extract these patterns by modeling the intrinsic stellar spectrum and the broadening functions for each spectrum in the time series. Frequencies and modes of oscillation are identified from the variations using the technique of Fourier-Doppler imaging and a two-dimensional least-squares cleaning algorithm. We find a rich mode spectrum with degrees up to l = 20 and with frequencies below about 35 cycles day-1. Those modes with the largest amplitudes have frequencies that lie within a narrow band. We conclude that the observed spectrum can be explained if the modes of tau Peg propagate in the prograde direction with l ~= |m| and with frequencies that are about equal in the corotating frame of the star. We discuss the implications of these results for the prospect of delta Scuti seismology.