Astronomy & Astrophysics

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$\begin{figure} \par\includegraphics[width=7cm,clip]{4125f001.eps} \end{figure}$ Figure 1: Definition and convention of triangle variables.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{4125f002.eps}\par\vspace*{2mm} \includegraphics[width=8cm,clip]{4125f003.eps} \end{figure}$ Figure 2: The top ( bottom) panel shows the positive ( $\gamma _{\mu \nu \rho }^{\oplus }$ ) and negative ( $\gamma _{\mu \nu \rho }^{\otimes }$ ) parity three-point functions for the center of mass (orthocenter) projection convention. We have assumed an isothermal sphere profile (n=2) and a fixed ratio ( $\ell _{2}/\ell _{3}=1$ ) and plotted as a function of the angle $\psi _{1}$ (see Fig. 1 for a definition). Line styles for parity positive three-point functions are $\gamma _{+++}$ (solid), $\gamma _{+\times \times }$ (long-dashed), $\gamma _{\times +\times }$ (dotted) and $\gamma _{\times \times +}$ (dashed) whereas for negative parity $\gamma _{\times \times \times }$ (solid), $\gamma _{\times ++}$ (long-dashed), $\gamma _{+\times +}$ (dotted) and $\gamma _{++\times }$ (dashed).
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{4125f004.eps}\par\vspace*{2mm} \includegraphics[width=8.1cm,clip]{4125f005.eps} \end{figure}$ Figure 3: Same as Fig. 2 but for the real (positive-parity) and imaginary (negative parity) parts of $\Gamma _{i}$ . Line styles are as follows: $\Gamma _{0}$ (solid), $\Gamma _{1}$ (long-dashed), $\Gamma _{2}$ (dashed), $\Gamma _{3}$ (dotted).
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{4125f006.eps}\par\vspace*{2mm} \includegraphics[width=8.1cm,clip]{4125f007.eps} \end{figure}$ Figure 4: Same as Fig. 3 but only in the center of mass projection, for sides ratio $\ell _{2}/\ell _{3}=2$ ( top panel) and $\ell _{2}/\ell _{3}=3$ ( bottom panel).
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{4125f008.eps}\par\vspace*{2mm} \hspace*{1.3mm}\includegraphics[width=8.07cm,clip]{4125f009.eps} \end{figure}$ Figure 5: The real part of $\Gamma _{0}$ ( top) and the imaginary part of $\Gamma _{2}$ ( bottom) for different values of the profile index of the halo nand $\ell _{2}=\ell _{3}$ . Line styles are n=1.2 (long-dashed), n=2 (solid), n=2.1 (dotted), n=2.5 (dot-dashed).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{4125f010.eps} \end{figure}$ Figure 6: The real ( top) and imaginary part of $\daleth$ for the $\ell _{2}/\ell _{3}=2$ case as a function of $\psi _{1}$ . The non-zero imaginary part shows that there is no preferred projection convention where all negative-parity three-point functions vanish.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=7.8cm,clip]{4125f011.ps} \end{figure}$ Figure 7: Scaling test for $\ell _{0}=1.125'$ . The points with error bars represent $S=\bar{\ell\Gamma_{1}}(\ell)/(\ell_{0}\bar{\Gamma_{1}}(\ell_{0}))$ . The solid line is S=1 (n=2), whereas the dotted line denotes to which according to Eq. (32) correspond to $n\approx 2.3$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{4125f012.eps}\par\vspace*{2mm} \includegraphics[width=8cm,clip]{4125f013.eps} \end{figure}$ Figure 8: Predictions from our n=2 model compared against measurements in simulations for isosceles triangles with $\ell =2.25$ arcmin. The top ( bottom) panel shows the real (imaginary) part of $\Gamma _{1}$ , and the model arbitrary amplitude has been adjusted to match $\Gamma _{2}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{4125f014.eps}\par\vspace*{2mm} \hspace*{1mm} \includegraphics[width=7.85cm,clip]{4125f015.eps} \end{figure}$ Figure 9: Same as previous figure, but modifying the model prediction to mimic the effect of binning in the simulations, approximately, as in Eq. (37).
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=6.8cm,clip]{4125f023.eps}\pa... ...e*{2mm} \includegraphics[angle=270,width=6.8cm,clip]{4125f025.eps} \end{figure}$ Figure 10: $\Gamma _{i}$ measured for $\ell _{2}=0.42'$ . In each panel top ( bottom) part shows positive (negative) parity three-point functions. Panels correspond to isoceles triangles ( top), $\ell {}_{2}=2\ell _{3}$ ( middle) and $\ell _{2}=3\ell _{3}$ ( bottom). Symbols are as follows $\Gamma _{0}$ (plus), $\Gamma _{1}$ (cross), $\Gamma _{2}$ (star) and $\Gamma _{3}$ (box).
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=6.8cm,clip]{4125f026.eps}\pa... ...e*{2mm} \includegraphics[angle=270,width=6.8cm,clip]{4125f028.eps} \end{figure}$ Figure 11: Same as previous figure for $\ell _{2}=2.8'$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{4125f016.eps} \end{figure}$ Figure 12: Predictions for the $\vec{\mathcal{F}}$ estimator. Left panel presents the real/parity positive ( top) and imaginary/parity negative ( bottom) parts. Right panel shows the resulting pattern. The points $\theta _{2}$ and $\theta _{3}$ are fixed to (0,-1/2) and (0,1/2). The coordinate gives the position of $\theta _{1}$ . We only shows one fourth of the plane. The rest of it can be determined from parity properties. ${\mathcal{F}}_{\times}$ goes go to zero on the x and y axis.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4125f017.eps} \end{figure}$ Figure 13: $\mathcal{I}_{0}$ measured in our three datasets.Results for all datasets are combined into this composite figure. In the top panel, top to bottom set of points corresponds to measurement for $\ell _{2}=r\ell _{3}$ for r=1,2,3,4. The corresponding theoretical prediction for n=2 are shown on top of the points for r=1 (solid line), r=2 (long dashed), r=3 (dashed) and r=4 (dotted). Bottom panel shows the ratio between the measurement and theoretical prediction for r=1.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4125f018.eps} \end{figure}$ Figure 14: $\mathcal{I}_{1}$ measured in our medium resolution dataset. The solid line is a power law proportional to $1/\ell ^{2}$ and shows the expected scaling. Other curves are semi analytical results (the covariance matrix has been evaluated from the simulations). They correspond to r=1 (long dashed), r=2 (dashed), 3 (dotted), r=4 (dot-dashed). Measurements partially agree with the semi-analytical predictions
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4125f019.eps} \end{figure}$ Figure 15: Same as Fig. 13 for our improved version of the BvWM estimator.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4125f020.eps} \end{figure}$ Figure 16: Signal to noise for $\mathcal{I}_{0}$ (solid line), $\mathcal{I}_{1}$ (dashed) and our improved version of the BvWM estimator (dotted). Only isoceles configurations have been taken into account. Data are projected on the n=2 model predictions. Only the medium resolution datasets are used.
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{4125f021.eps} \end{figure}$ Figure B.1: Power spectrum of $\kappa$ measured on the 40 lensing pseudo-realization. Lines are the predicted power spectrum using the PD (Peacock & Dodds 1996) (dashed) or halofit (Smith et al. 2003) (solid) prescription for the small scales. Points are the measurements in the simulations, without smoothing (crosses), and with smoothing (xs) to remove the Poisson noise (see text). Bottom panel shows the ratio between the smoothed measured power spectrum and the two predictions using PD (xs) and halofit (crosses).

In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{4125f022.eps} \end{figure}$ Figure B.2: The shear two-point functions in the simulations. Lines are the predicted power spectrum, taking into account the survey size and resolution. Solid line is $\xi _{+}$ , dashed, $\xi _{-}$ . Points show the measurements in the 40 realizations, for our three different datasets. The open circle (resp. plain squares, open squares) shows $\xi _{-}$ and regular pluses (resp crosses,dashed pluses) $\xi _{+}$ , measured in the max (resp medium, min) resolution datasets.

In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{4125f001.eps} \end{figure}$	Figure 1: Definition and convention of triangle variables.
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$\begin{figure} \par\includegraphics[width=8.1cm,clip]{4125f004.eps}\par\vspace*{2mm} \includegraphics[width=8.1cm,clip]{4125f005.eps} \end{figure}$	Figure 3: Same as Fig. 2 but for the real (positive-parity) and imaginary (negative parity) parts of $\Gamma _{i}$ . Line styles are as follows: $\Gamma _{0}$ (solid), $\Gamma _{1}$ (long-dashed), $\Gamma _{2}$ (dashed), $\Gamma _{3}$ (dotted).
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$\begin{figure} \par\includegraphics[width=8.1cm,clip]{4125f006.eps}\par\vspace*{2mm} \includegraphics[width=8.1cm,clip]{4125f007.eps} \end{figure}$	Figure 4: Same as Fig. 3 but only in the center of mass projection, for sides ratio $\ell _{2}/\ell _{3}=2$ ( top panel) and $\ell _{2}/\ell _{3}=3$ ( bottom panel).
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{4125f008.eps}\par\vspace{2mm} \hspace{1.3mm}\includegraphics[width=8.07cm,clip]{4125f009.eps} \end{figure}$	Figure 5: The real part of $\Gamma _{0}$ ( top) and the imaginary part of $\Gamma _{2}$ ( bottom) for different values of the profile index of the halo nand $\ell _{2}=\ell _{3}$ . Line styles are n=1.2 (long-dashed), n=2 (solid), n=2.1 (dotted), n=2.5 (dot-dashed).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{4125f010.eps} \end{figure}$	Figure 6: The real ( top) and imaginary part of $\daleth$ for the $\ell _{2}/\ell _{3}=2$ case as a function of $\psi _{1}$ . The non-zero imaginary part shows that there is no preferred projection convention where all negative-parity three-point functions vanish.
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$\begin{figure} \par\includegraphics[angle=270,width=7.8cm,clip]{4125f011.ps} \end{figure}$	Figure 7: Scaling test for $\ell _{0}=1.125'$ . The points with error bars represent $S=\bar{\ell\Gamma_{1}}(\ell)/(\ell_{0}\bar{\Gamma_{1}}(\ell_{0}))$ . The solid line is S=1 (n=2), whereas the dotted line denotes to which according to Eq. (32) correspond to $n\approx 2.3$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{4125f012.eps}\par\vspace*{2mm} \includegraphics[width=8cm,clip]{4125f013.eps} \end{figure}$	Figure 8: Predictions from our n=2 model compared against measurements in simulations for isosceles triangles with $\ell =2.25$ arcmin. The top ( bottom) panel shows the real (imaginary) part of $\Gamma _{1}$ , and the model arbitrary amplitude has been adjusted to match $\Gamma _{2}$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{4125f014.eps}\par\vspace{2mm} \hspace{1mm} \includegraphics[width=7.85cm,clip]{4125f015.eps} \end{figure}$	Figure 9: Same as previous figure, but modifying the model prediction to mimic the effect of binning in the simulations, approximately, as in Eq. (37).
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$\begin{figure} \par\includegraphics[angle=270,width=6.8cm,clip]{4125f023.eps}\pa... ...e*{2mm} \includegraphics[angle=270,width=6.8cm,clip]{4125f025.eps} \end{figure}$	Figure 10: $\Gamma _{i}$ measured for $\ell _{2}=0.42'$ . In each panel top ( bottom) part shows positive (negative) parity three-point functions. Panels correspond to isoceles triangles ( top), $\ell {}_{2}=2\ell _{3}$ ( middle) and $\ell _{2}=3\ell _{3}$ ( bottom). Symbols are as follows $\Gamma _{0}$ (plus), $\Gamma _{1}$ (cross), $\Gamma _{2}$ (star) and $\Gamma _{3}$ (box).
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$\begin{figure} \par\includegraphics[angle=270,width=6.8cm,clip]{4125f026.eps}\pa... ...e*{2mm} \includegraphics[angle=270,width=6.8cm,clip]{4125f028.eps} \end{figure}$	Figure 11: Same as previous figure for $\ell _{2}=2.8'$ .
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4125f019.eps} \end{figure}$	Figure 15: Same as Fig. 13 for our improved version of the BvWM estimator.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4125f020.eps} \end{figure}$	Figure 16: Signal to noise for $\mathcal{I}_{0}$ (solid line), $\mathcal{I}_{1}$ (dashed) and our improved version of the BvWM estimator (dotted). Only isoceles configurations have been taken into account. Data are projected on the n=2 model predictions. Only the medium resolution datasets are used.
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