All Figures

$\begin{figure} \par\includegraphics[width=7cm,clip]{0426fig1.eps} % \end{figure}$ Figure 1: The scaled deflection angle $\alpha _{\rm norm} \equiv \alpha /\alpha _{\rm v}$ vs. the dimensionless radius $\xi$ for three values of the dimensionless scale radius $x_{\rm p}$ of the RTM model, i.e. $x_{\rm p} = 0.1$ (solid), $x_{\rm p} = 0.2$ (short dashed), $x_{\rm p} = 0.3$ (long dashed).
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0426fig2.eps} %\end{figure}$ Figure 2: The deflection angle at the virial radius $\alpha _{\rm v}$ vs. the dimensionless scale radius $x_{\rm p}$ of the RTM model. See the text for the values of the other parameters.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0426fig3.eps} \end{figure}$ Figure 3: Contours of equal Einstein radius $R_{\rm E}$ in the $(\log{M_{\rm v}}, x_{\rm p})$ plane. $R_{\rm E}$ ranges from 5 (the uppermost curve) to 35 arcsec (the lowermost one) in steps of 10 arcsec.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0426fig4.eps} \end{figure}$ Figure 4: Contours of equal radial critical curve distance $R_{\rm rad}$ from the cluster centre in the $(\log{M_{\rm v}}, x_{\rm p})$ plane. $R_{\rm rad}$ ranges from 2.5 (the uppermost curve) to 5.5 arcsec (the lowermost one) in steps of 1 arcsec.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0426fig5.eps} \end{figure}$ Figure 5: Zero level curves of the denominator in Eq. (28) in the plane $(R, \log{M_{\rm v}})$ for a RTM cluster with $x_{\rm p} = 0.5/7.13$ . The solid line refers to the case with no BCG, while the dashed line is obtained by adding a BCG with $(M_{\rm h}, R_{\rm e}) = (5 \times 10^{12}~{M_{\odot}}, 24.80~{\rm kpc})$ . For a given value of $M_{\rm v}$ , the intersections of the horizontal line $\log{M_{\rm v}} = \rm const.$ with the plotted curves are the values of $R_{\rm rad}$ and $R_{\rm E}$ respectively.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0426fig6.eps} % \end{figure}$ Figure 6: Same as Fig. 5 but now the value of $M_{\rm v}$ is fixed at $1.125 \times 10^{15}~{M_{\odot}}$ and $x_{\rm p}$ is changing. The solid line refers to the case with no BCG, and the dashed one to the case with a BCG with parameters fixed as before.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0426fig7.eps} \end{figure}$ Figure 7: Constraints in the $(\log{M_{\rm v}}, x_{\rm p})$ plane imposing $R_{\rm rad} = 4.5~{\rm arcsec}$ ( left) or $R_{\rm E} = 15.35 \ {\rm arcsec}$ ( right) for the RTM model with (dashed line) and without (solid line) taking into account the presence of a BCG. The galaxy parameters are set as $(M_{\rm h}, R_{\rm e}) = (5.0 \times 10^{12} \ {M_{\odot}}, 24.80~{\rm kpc})$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0426fig8.eps} \end{figure}$ Figure 8: Critical curves (solid) and caustics (dashed) for the RTM model with the addition of external shear. Upper panels are for $\gamma = 0.0$ ( left) and $\gamma = 0.05$ ( right), while lower panels refer to $\gamma = 0.10$ ( left) and $\gamma = 0.15$ ( right). The shear position angle is set at $\theta _{\gamma } = 0$ , and the cluster parameters are $(M_{\rm v}, x_{\rm p}) = (1.125 \times 10^{15} \ {M_{\odot }}, 0.03)$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0426fig9.eps} \end{figure}$ Figure 9: ${\cal {R}}_{\alpha }$ vs. $\xi$ for the average values of the concentration parameters of the NFW and RTM model.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0426fig10.eps} \end{figure}$ Figure 10: ${\cal {R}}_{\alpha }$ vs. $\xi$ setting the NFW concentration to the value predicted by Eq. (35) and $c_{{\rm RTM}} = 7.13$ for three values of the virial mass, namely $M_{\rm v} = 5 \times 10^{14}$ (short dashed), $M_{\rm v} = 7.5 \times 10^{14}$ (solid), $M_{\rm v} = 10^{15}$ (long dashed).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0426fig11.eps} \end{figure}$ Figure 11: Contour plot in the $(\log{M_{\rm v}}, c_{{\rm NFW}})$ plane for the Einstein radius of the NFW model. Left panel: contours corresponding to values of $R_{\rm E}$ for the RTM model with $x_{\rm p} = 1/\langle c_{{\rm RTM}} \rangle$ and $M_{\rm v}$ from 7.5 to $17.5 \times 10^{14}~{M_{\odot}}$ ( from left to right) in steps of $2.5 \times 10^{14}~{M_{\odot}}$ . Right panel: contours corresponding to values of $R_{\rm E}$ for the RTM model with $M_{\rm v} = 10^{15}$ and $x_{\rm p}$ from 0.06 to 0.14 (from right to left) in steps of 0.02. The dashed line refers to Eq. (35).
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig12.eps} \end{figure}$ Figure 12: The structure integral $\eta$ vs. $\xi$ . The upper curve has been obtained by fixing l = 1 in Eq. (47), while the lower one refers to the case $l \rightarrow \infty$ .
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig13.eps} \end{figure}$ Figure 13: The relative error $\varepsilon$ in the structure integral $\eta$ vs. $\xi$ . It is: $\varepsilon = [\eta (l \rightarrow \infty ) - \eta (l = 1)]/\eta (l = 1)$ .
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig14.eps} \end{figure}$ Figure 14: The structure integral $\eta$ vs. $\xi$ for the RTM model using the correct temperature profile ( upper curve) or the isothermality hypothesis ( lower curve).
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig15.eps} \end{figure}$ Figure 15: The relative error in the SZE signal induced by using the best fit $\beta$ -model instead of the correct RTM one as function of the dimensionless radius $\xi = r/R_{\rm v}$ .
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig16.eps} \end{figure}$ Figure 16: Dependence of $\epsilon_Y~$ on the distance from the cluster center (in units of $R_{\rm v}$ ).
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig17.eps} \end{figure}$ Figure 17: Comparison of the integrated SZE flux of a $\beta$ and RTM model with $\epsilon _{Y} = 1 - Y_{\beta }/Y_{{\rm RTM}}$ plotted as function of the dimensionless distance from the cluster centre.
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig18.eps} \end{figure}$ Figure 18: Relative discrepancy between the Componization parameter for an RTM model and its best fitting NFW model.
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig19.eps} \end{figure}$ Figure 19: Relative discrepancy between the integrated SZE fluxes for an RTM model and its best fitting NFW model.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0426fig1.eps} % \end{figure}$	Figure 1: The scaled deflection angle $\alpha _{\rm norm} \equiv \alpha /\alpha _{\rm v}$ vs. the dimensionless radius $\xi$ for three values of the dimensionless scale radius $x_{\rm p}$ of the RTM model, i.e. $x_{\rm p} = 0.1$ (solid), $x_{\rm p} = 0.2$ (short dashed), $x_{\rm p} = 0.3$ (long dashed).
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$\begin{figure} \par\includegraphics[width=7cm,clip]{0426fig2.eps} %\end{figure}$	Figure 2: The deflection angle at the virial radius $\alpha _{\rm v}$ vs. the dimensionless scale radius $x_{\rm p}$ of the RTM model. See the text for the values of the other parameters.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0426fig3.eps} \end{figure}$	Figure 3: Contours of equal Einstein radius $R_{\rm E}$ in the $(\log{M_{\rm v}}, x_{\rm p})$ plane. $R_{\rm E}$ ranges from 5 (the uppermost curve) to 35 arcsec (the lowermost one) in steps of 10 arcsec.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0426fig4.eps} \end{figure}$	Figure 4: Contours of equal radial critical curve distance $R_{\rm rad}$ from the cluster centre in the $(\log{M_{\rm v}}, x_{\rm p})$ plane. $R_{\rm rad}$ ranges from 2.5 (the uppermost curve) to 5.5 arcsec (the lowermost one) in steps of 1 arcsec.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0426fig6.eps} % \end{figure}$	Figure 6: Same as Fig. 5 but now the value of $M_{\rm v}$ is fixed at $1.125 \times 10^{15}~{M_{\odot}}$ and $x_{\rm p}$ is changing. The solid line refers to the case with no BCG, and the dashed one to the case with a BCG with parameters fixed as before.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0426fig7.eps} \end{figure}$	Figure 7: Constraints in the $(\log{M_{\rm v}}, x_{\rm p})$ plane imposing $R_{\rm rad} = 4.5~{\rm arcsec}$ ( left) or $R_{\rm E} = 15.35 \ {\rm arcsec}$ ( right) for the RTM model with (dashed line) and without (solid line) taking into account the presence of a BCG. The galaxy parameters are set as $(M_{\rm h}, R_{\rm e}) = (5.0 \times 10^{12} \ {M_{\odot}}, 24.80~{\rm kpc})$ .
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0426fig9.eps} \end{figure}$	Figure 9: ${\cal {R}}_{\alpha }$ vs. $\xi$ for the average values of the concentration parameters of the NFW and RTM model.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0426fig10.eps} \end{figure}$	Figure 10: ${\cal {R}}_{\alpha }$ vs. $\xi$ setting the NFW concentration to the value predicted by Eq. (35) and $c_{{\rm RTM}} = 7.13$ for three values of the virial mass, namely $M_{\rm v} = 5 \times 10^{14}$ (short dashed), $M_{\rm v} = 7.5 \times 10^{14}$ (solid), $M_{\rm v} = 10^{15}$ (long dashed).
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$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig12.eps} \end{figure}$	Figure 12: The structure integral $\eta$ vs. $\xi$ . The upper curve has been obtained by fixing l = 1 in Eq. (47), while the lower one refers to the case $l \rightarrow \infty$ .
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$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig13.eps} \end{figure}$	Figure 13: The relative error $\varepsilon$ in the structure integral $\eta$ vs. $\xi$ . It is: $\varepsilon = [\eta (l \rightarrow \infty ) - \eta (l = 1)]/\eta (l = 1)$ .
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$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig14.eps} \end{figure}$	Figure 14: The structure integral $\eta$ vs. $\xi$ for the RTM model using the correct temperature profile ( upper curve) or the isothermality hypothesis ( lower curve).
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$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig15.eps} \end{figure}$	Figure 15: The relative error in the SZE signal induced by using the best fit $\beta$ -model instead of the correct RTM one as function of the dimensionless radius $\xi = r/R_{\rm v}$ .
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$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig16.eps} \end{figure}$	Figure 16: Dependence of $\epsilon_Y~$ on the distance from the cluster center (in units of $R_{\rm v}$ ).
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$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig17.eps} \end{figure}$	Figure 17: Comparison of the integrated SZE flux of a $\beta$ and RTM model with $\epsilon _{Y} = 1 - Y_{\beta }/Y_{{\rm RTM}}$ plotted as function of the dimensionless distance from the cluster centre.
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$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig18.eps} \end{figure}$	Figure 18: Relative discrepancy between the Componization parameter for an RTM model and its best fitting NFW model.
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$\begin{figure} \par\includegraphics[width=6cm,clip]{0426fig19.eps} \end{figure}$	Figure 19: Relative discrepancy between the integrated SZE fluxes for an RTM model and its best fitting NFW model.
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