A Family of Potential-Density Pairs for Spherical Galaxies and Bulges. Dehnen, W. Monthly Notices of the Royal Astronomical Society, 265:250, 1993.
A Family of Potential-Density Pairs for Spherical Galaxies and Bulges [pdf]Paper  abstract   bibtex   
A family of spherical potential-density pairs is presented. The densities are proportional to r^-4^ at large radii and diverge in the centre as r^- gamma^ with 0 <= gamma <3. The models of Jaffe and Hernquist are included as special cases. The gravitational potential is analytical for all gamma. For specific values of gamma, most of the intrinsic and projected properties, such as distribution function, surface density and projected velocity dispersion, can be expressed in terms of elementary functions. A comparison to the de Vaucouleurs R^1/4^-profile shows that the model with gamma = 3/2 most closely resembles it in both surface density and distribution function. This particular model is completely analytical, and thus it is the best analytical approximation of the R^1/4^-model known so far.
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 abstract = {A family of spherical potential-density pairs is presented. The densities are proportional to r^-4^ at large radii and diverge in the centre as r^- gamma^ with 0 <= gamma <3. The models of Jaffe and Hernquist are included as special cases. The gravitational potential is analytical for all gamma. For specific values of gamma, most of the intrinsic and projected properties, such as distribution function, surface density and projected velocity dispersion, can be expressed in terms of elementary functions. A comparison to the de Vaucouleurs R^1/4^-profile shows that the model with gamma = 3/2 most closely resembles it in both surface density and distribution function. This particular model is completely analytical, and thus it is the best analytical approximation of the R^1/4^-model known so far.},
 bibtype = {article},
 author = {Dehnen, Walter},
 journal = {Monthly Notices of the Royal Astronomical Society}
}
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