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This paper discusses data reduction for an echelle spectrograph we have developed for an automatic telescope at Tennessee State University and are using to monitor radial velocities and line profiles of cool giant and supergiant stars. Although our approach to data reduction is rather conventional, we discuss flat‐fielding and extraction of velocities in ways that should be of general interest, establish a transformation to the IAU radial velocity system (+0.35 ± 0.09 km s−1), and determine the external precision for measured velocities (0.10–0.11 km s−1). Also, we present results of the first 2–3 years of monitoring radial velocities in about 120 cool giants and compare those results with the level of variability found with photometry. These new data confirm the widely held understanding that K and M giants are all radial velocity variables at the level of 0.1 km s−1.