All Figures

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig1.eps} \end{figure}$ Figure 1: Relation $\gamma (\Psi )$ for the $f^{(\nu )}$ family of models, for selected values of $\nu$ . To fit the adopted frame, the $\gamma$ values corresponding to $\nu =3/8$ have been multiplied by a factor 1/6 and the ones corresponding to $\nu =1/2$ by a factor 2/3.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig2.eps} \end{figure}$ Figure 2: Density contrast between the center and the half-mass radius along the equilibrium sequence for different values of $\nu$ . The solid line refers to $\nu =3/8$ ; at fixed $\Psi$ , models with higher values of $\nu$ are less concentrated.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig3.eps} \end{figure}$ Figure 3: Density profile of some representative $f^{(\nu )}$ models, with $\nu =3/8$ , 1/2, and 1, and $\Psi = 5$ and 10. The most concentrated model corresponds to (3/8;10) and the least concentrated to (1;5). If the scales are fixed so that $r_M = 10~\rm kpc$ and $M = 10^{11}~M_{\odot}$ , the units for the density are $10^{-1}~M_{\odot}/\rm pc^3$ . The density profiles overlap in the outer parts, beyond a radius that becomes smaller and smaller as $\Psi$ increases. In the plot we also record the $\rho _J$ profile, shown here on an arbitrary scale for a convenient comparison.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig4.eps} \end{figure}$ Figure 4: Best fit value of the index n (of the R^1/n law) associated with the projected density profile of the $f^{(\nu )}$ models, for selected values of $\nu$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig5.eps} \end{figure}$ Figure 5: Residuals $\mu -\mu ^{1/n}$ , in magnitudes, obtained by fitting the R^1/n law to the projected density profiles of the $f^{(\nu )}$ models for $\nu =1/2$ and selected values of $\Psi$ . The quality of the fit is excellent for concentrated models ( $\Psi > 7$ ).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig6.eps} \end{figure}$ Figure 6: Anisotropy profiles $\alpha (r)$ of $\Psi = 5$ models for different values of $\nu$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig7.eps} \end{figure}$ Figure 7: Global anisotropy of the $f^{(\nu )}$ models shown in terms of the parameter $2K_{\rm r}/K_{\rm T}$ (group of curves starting from the top left) and of the ratio $r_{\alpha }/r_M$ (anisotropy radius to half-mass radius; group of curves starting from the bottom left) as a function of $\Psi$ . For low values of $\Psi$ the global anisotropy $2K_{\rm r}/K_{\rm T}$ is basically independent of $\nu$ . At fixed value of $\Psi$ the global anisotropy decreases with $\nu$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig8.eps} \end{figure}$ Figure 8: Intrinsic "pressure" profiles ( $\sigma_{\rm T}^2/2 = (\langle w^2_{\theta}\rangle + \langle w^2_{\phi}\rangle)/2$ and $\sigma_{\rm r}^2 = \langle w^2_{\rm r}\rangle$ ) for selected $f^{(\nu )}$ models with $\nu =1/2$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig9.eps} \end{figure}$ Figure 9: Projected velocity dispersion profile for selected $f^{(\nu )}$ models. If the scales are fixed so that $r_M = 10~\rm kpc$ and $M = 10^{11}~M_{\odot}$ , the velocity dispersion $\sigma _{\rm proj}$ is given in units of $207.4~\rm km~s^{-1}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fi10.eps} \end{figure}$ Figure 10: Profiles of the h₄ parameter for selected $f^{(\nu )}$ models with $\nu = 3/4$ and different values of $\Psi$ (the $\Psi = 2$ model is denoted by squares, $\Psi = 6$ by triangles, and $\Psi = 10$ by stars).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1023fi11.eps} \end{figure}$ Figure 11: The phase space density N(E,J²) for the (1/2;6.2) $f^{(\nu )}$ model. The graph has been obtained by a Monte Carlo sampling of the distribution function with $2 \times 10^6$ points.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1023fi12.eps} \end{figure}$ Figure 12: On the left frames, density and anisotropy profiles of the end-products of a simulation starting from the unstable (1;3.2) model (error bars) fitted by the marginally stable (1;4.2) model of the $f^{(\nu )}$ family (solid line); units for $\rho$ are the units adopted in the simulation. The right frames show the residuals $\Delta \rho = \rho ^{(4.2)} - \rho$ and $\Delta \alpha = \alpha ^{(4.2)} - \alpha$ .
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{1023fi13.eps} \end{figure}$ Figure 13: Evolution of the fractional mass radii (of the sphere containing, from the bottom to the top, $6.25 \times 10^{-5}$ , $1.25 \times 10^{-4}$ , 0.01, 0.05, 0.5, 0.7, 0.95, 0.99 M, respectively) for a simulation with $8 \times 10^5$ particles of the concentrated $f^{(\nu )}$ model (1/2;9.4). The model is stable over the time interval considered (about 10 dynamical times). The radius r and the time t are given in units of $10~\rm kpc$ and $10^8~\rm yr$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fi14.eps} \end{figure}$ Figure 14: Comparison between the photometric profile of NGC 3379 and the (1/2; 9.4) model of the $f^{(\nu )}$ family. The photometric profile in B is taken from de Vaucouleurs & Capaccioli (1979). Other members of the family (e.g. the (1; 9.2) model) could better reproduce the observed data especially at large radii, but they would perform less well on the velocity dispersion profile.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fi15.eps} \end{figure}$ Figure 15: Kinematic data for NGC 3379 described in terms of the (1/2; 9.4) model of the $f^{(\nu )}$ family. The inner data (plain error bars) are taken from the stellar spectroscopy of Statler & Smecker-Hane (1999), while the outer data (crosses with error bars) refer to the binned velocity dispersion determined from the study of planetary nebulae (Romanowsky et al. 2003).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig1.eps} \end{figure}$	Figure 1: Relation $\gamma (\Psi )$ for the $f^{(\nu )}$ family of models, for selected values of $\nu$ . To fit the adopted frame, the $\gamma$ values corresponding to $\nu =3/8$ have been multiplied by a factor 1/6 and the ones corresponding to $\nu =1/2$ by a factor 2/3.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig2.eps} \end{figure}$	Figure 2: Density contrast between the center and the half-mass radius along the equilibrium sequence for different values of $\nu$ . The solid line refers to $\nu =3/8$ ; at fixed $\Psi$ , models with higher values of $\nu$ are less concentrated.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig4.eps} \end{figure}$	Figure 4: Best fit value of the index n (of the R^1/n law) associated with the projected density profile of the $f^{(\nu )}$ models, for selected values of $\nu$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig5.eps} \end{figure}$	Figure 5: Residuals $\mu -\mu ^{1/n}$ , in magnitudes, obtained by fitting the R^1/n law to the projected density profiles of the $f^{(\nu )}$ models for $\nu =1/2$ and selected values of $\Psi$ . The quality of the fit is excellent for concentrated models ( $\Psi > 7$ ).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig6.eps} \end{figure}$	Figure 6: Anisotropy profiles $\alpha (r)$ of $\Psi = 5$ models for different values of $\nu$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig8.eps} \end{figure}$	Figure 8: Intrinsic "pressure" profiles ( $\sigma_{\rm T}^2/2 = (\langle w^2_{\theta}\rangle + \langle w^2_{\phi}\rangle)/2$ and $\sigma_{\rm r}^2 = \langle w^2_{\rm r}\rangle$ ) for selected $f^{(\nu )}$ models with $\nu =1/2$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fig9.eps} \end{figure}$	Figure 9: Projected velocity dispersion profile for selected $f^{(\nu )}$ models. If the scales are fixed so that $r_M = 10~\rm kpc$ and $M = 10^{11}~M_{\odot}$ , the velocity dispersion $\sigma _{\rm proj}$ is given in units of $207.4~\rm km~s^{-1}$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fi10.eps} \end{figure}$	Figure 10: Profiles of the h₄ parameter for selected $f^{(\nu )}$ models with $\nu = 3/4$ and different values of $\Psi$ (the $\Psi = 2$ model is denoted by squares, $\Psi = 6$ by triangles, and $\Psi = 10$ by stars).
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1023fi11.eps} \end{figure}$	Figure 11: The phase space density N(E,J²) for the (1/2;6.2) $f^{(\nu )}$ model. The graph has been obtained by a Monte Carlo sampling of the distribution function with $2 \times 10^6$ points.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fi14.eps} \end{figure}$	Figure 14: Comparison between the photometric profile of NGC 3379 and the (1/2; 9.4) model of the $f^{(\nu )}$ family. The photometric profile in B is taken from de Vaucouleurs & Capaccioli (1979). Other members of the family (e.g. the (1; 9.2) model) could better reproduce the observed data especially at large radii, but they would perform less well on the velocity dispersion profile.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1023fi15.eps} \end{figure}$	Figure 15: Kinematic data for NGC 3379 described in terms of the (1/2; 9.4) model of the $f^{(\nu )}$ family. The inner data (plain error bars) are taken from the stellar spectroscopy of Statler & Smecker-Hane (1999), while the outer data (crosses with error bars) refer to the binned velocity dispersion determined from the study of planetary nebulae (Romanowsky et al. 2003).
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