Rotation Curve Measurement using Cross‐Correlation1

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Abstract
Long‐slit spectroscopy is entering an era of increased spatial and spectral resolution and increased sample size. Improved instruments reveal complex velocity structure that cannot be described with a one‐dimensional rotation curve, yet samples are too numerous to examine each galaxy in detail. Therefore, one goal of rotation curve measurement techniques is to flag cases in which the kinematic structure of the galaxy is more complex than a single‐valued curve. We examine cross‐correlation as a technique that is easily automated and works for low signal‐to‐noise spectra. We show that the technique yields well‐defined errors which increase when the simple spectral model (template) is a poor match to the data, flagging those cases for later inspection. We compare the technique to the more traditional, parametric technique of simultaneous emission‐line fitting. When the line profile at a single slit position is non‐Gaussian, the techniques disagree. For our model spectra with two well‐separated velocity components, assigned velocities from the two techniques differ by up to ~52% of the velocity separation of the model components. However, careful use of the error statistics for either technique allows one to flag these non‐Gaussian spectra.
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