A systematic study of the line profiles expected in the outer parts |(R Rc)| of non-rotating elliptical galaxies is reported. For a family of quasi-separable spherical models the line-of-sight velocity profiles |$l(v)$| are calculated analytically in both a Keplerian and a scale-free halo potential. These velocity profiles (VPs) can take a wide variety of shapes; they illustrate that tangentially anisotropic distribution functions (DFs) generally lead to VPs with flat tops, while radially anisotropic DFs lead to more nearly Gaussian VPs. Strongly radial DFs in a halo potential develop prominent wings.
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Ortwin Gerhard (1993) studied this question.
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