Astronomy & Astrophysics

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$\begin{figure} \par\includegraphics[width=16.2cm,clip]{3587fig1.eps} \end{figure}$ Figure 1: Edge-on, major axis projected streaming velocity $v_{\rm p}$ ( left panels), and aperture velocity dispersion $\sigma _{\rm a}$ ( right panels) for one ( upper panels) and two-component ( lower panels) galaxy models. Projected streaming velocity is shown for isotropic models only, while $\sigma _{\rm a}$ for isotropic and fully tangentially anisotropic (i.e. not rotating) models. Aperture radii corresponding to $R_{\rm e}/8$ and $R_{\rm e}$ are marked as empty dots ( $\circ$ ) and solid dots ( $\bullet$ ), respectively. In two-component models the dark matter halo is described by a spherical Hernquist (1990) model ( $\gamma = 1$ , q = 1 in Eq. (3)), with $M_{h} = 5 ~ M_{\ast}$ and $R_{\rm h} = 2 ~ R_{\rm c}$ .
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In the text

$\begin{figure} \par\includegraphics[width=16.5cm,clip]{3587fig2.eps} \end{figure}$ Figure 2: Left panel: intrinsic (solid line) and projected (dashed line) streaming velocities on the equatorial plane (z = 0) of a model with $\gamma = 1$ , q = 0.3, k = 1, and a SMBH with $M_{\rm BH}= 10^{-3}~ M_{\ast}$ normalized to the corresponding quantity of the same model without the SMBH. Right panel: intrinsic (solid line), line-of-sight (dashed line), and aperture velocity dispersion ratios (dotted line) for the same model. The aperture velocity dispersion is calculated for a circular aperture $R_{\rm a} = R$ . The empty ( $\circ$ ) and solid ( $\bullet$ ) dots correspond to $R_{\rm e}/8$ and $R_{\rm e}$ , respectively.
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{3587fig3.eps} \end{figure}$ Figure 3: Left panel: projection effects on the galaxy models in the space where the FP for Coma cluster galaxies is seen edge-on (solid line) with 1-rms scatter (dashed line) from JFK. The intrinsic model parameters are given by labels, and $\gamma = 1$ for all models. For each model three spectroscopic apertures for $\sigma _{\rm a}= \sigma _0$ are considered ( $R_{\rm e}/8$ : dots, $R_{\rm e}$ : square, $10 R_{\rm e}$ : triangles). The los inclination increases from $\theta = 0$ (face-on) to $\theta = \pi / 2$ (edge-on) along the arrows, and the cases $\theta = 0$ , $R_{\rm a}= R_{\rm e}$ are arbitrarily placed on the FP best-fit line. Right panel: maximum rotational effects as a function of intrinsic flattening and spectroscopic aperture $R_{\rm a}$ for three edge-on models ( $\gamma = 0, ~ 1, ~ 1.5$ ). The isotropic rotators with q = 0.6 are arbitrarily placed on the FP while, on each horizontal line, the middle points correspond to models with k=0 and q = 0.6, while the rightmost points to models with k=0 and q = 0.3.
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In the text

$\begin{figure} \resizebox{8.5cm}{!}{\includegraphics[]{3587fig4.eps}}\end{figure}$ Figure 4: Rotational parameter for isotropic, edge-on models as a function of their ellipticity. The solid thick curve I is the locus of isotropic, classical ellipsoids as obtained from the tensor virial theorem (Binney 1978; see also Eq. (4.95) in BT), while solid line II is derived from the sky-averaged tensor virial theorem (Eq. (26) of Binney (2005), with $\delta = 0$ and $\alpha = 0$ ) . The upper set of curves represents our models when $v_{\rm p}= v_{{\rm p},{\max}}$ , while the lower set of curves represents our models when $v = v_{\rm p}(R_{\rm e}/8)$ . In all cases we adopt $\sigma = \sigma _{\rm a}(R_{\rm e}/ 8)$ .
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In the text