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F.6 dehnen

potname=dehnen potpars=$\Omega,M,a,\gamma$

Walter Dehnen (1993, MN 265, 250-256) introduced the following family of potential-density pairs for spherical systems:

The potential is given by: \begin{displaymath}
\Phi = - { M \over a } \times -{1\over{2-\gamma}} *
1 - (r\over{r+a})^{2-\gamma}
\end{displaymath} cumulative mass by \begin{displaymath}
M(r) = M { r \over {(r+a)}^{3-\gamma} }
\end{displaymath} and density by \begin{displaymath}
\rho = { {(3-\gamma)M} \over {4\pi}}
{ a \over {r^{\gamma} (r+a)^{4-\gamma}}}

Special cases are the Hernquist potential ($\gamma=1$), and the Jaffe model ($\gamma=2$). The model with $\gamma=3/2$ seems to give the best comparison withe de Vaucouleurs $R^{1/4}$ law.

(c) Peter Teuben