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We observed the rapidly rotating Delta Scuti star $\upsilon$ UMa with the Advanced Fiber Optic Echelle (AFOE) spectrometer at the Mt. Hopkins 1.5-m telescope on 5 successive nights in April 1993. Spectra covering a total of 730 $\AA$ were obtained at a 5-min cadence over about 4 hours on each night. The rotationally-broadened profiles of unblended strong lines clearly show previously-seen ``bumps" propagating from the blue side to the red side of the lines. We isolated moving features for each individual spectrum by subtracting the spectrum from the mean spectrum for that night, normalizing to the latter. We then calculated the cross-correlation function between each difference spectrum and a standard template spectrum, which was a very high signal-to-noise spectrum of a slowly-rotating star (Procyon) of similar spectral type, obtained with the same instrument. The cross-correlation combines the information from all the bumps moving across all spectral lines (including rotationally-blended lines) into a single function of displacement from line center, thereby significantly increasing the signal-to-noise ratio of the moving features. Analysis of the time-series of cross-correlation functions yields the rate of propagation of features and their separation in velocity, which may be interpreted in terms of effective azimuthal wavenumber and oscillation frequency. Modes are identified by remapping the cross-correlation functions in terms of longitude and performing two-dimensional Fourier transforms. For each night a different modal pattern was found, usually with several modes. The modes have effective azimuthal order m ranging from about 2 up to about 12, and frequencies between 120 and 170 uHz (i.e., 2.3 to 1.6 hours), with frequency gradually increasing with increasing m. The relative amplitude of the different modes changes substantially from night to night, suggesting either that the coherence time of the modes is not longer than about a day, or that beats are being observed between modes of similar wavelength and frequency.
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