All Figures

$\begin{figure} \par\resizebox{4.2cm}{!}{\includegraphics[clip]{4535.f1a.ps}}\hsp... ...ce*{0.3mm} \resizebox{4.2cm}{!}{\includegraphics[clip]{4535.f1d.ps}}\end{figure}$ Figure 1: Realisations of patches; the squares represent the individual images. Nis the number of images per patch, R the patch radius. Each image has a size of 13 arcmin.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0172f2.eps}\end{figure}$ Figure 2: Number of galaxy pairs per angular bin $N_{\rm p}$ against the bin centre $\vartheta$ , for a single $13^{\prime} \times 13^{\prime}~$ -field. The points are the pair numbers obtained from the subrandom distribution, the dashed line is the approximation $N(\vartheta ) = 2 \pi A n^2 \vartheta \Delta \vartheta$ (Paper I), where A is the survey area and n the galaxy number density, which was taken to be 30 per square arcmin. The dotted curve is from King & Schneider (2003).
Open with DEXTER

In the text

$\begin{figure} \includegraphics[width=12.2cm,clip]{0172f3.eps}\end{figure}$ Figure 3: Contour plots of the covariance matrices of the correlation functions (11) and the aperture mass dispersions (12) $\left\langle M_{\rm ap}^2 \right\rangle$ ("E-mode'') and $\left\langle M_\perp^2 \right\rangle$ ("B-mode''), for a single $13^{\prime} \times 13^{\prime}~$ -image. Logarithmic contours are used, ranging from $2 \times 10^{-13}$ to 10^-8, with 4 spacings per decade. Negative values are plotted as dotted contours. The "boxiness'' of some contour lines is due to the coarse resolution; the matrices are calculated on a logarithmic $20 \times 20 ~$ -grid for $\vartheta _1$ and $\vartheta _2$ . The axes show $\vartheta _1$ and $\vartheta _2$ in arcmin. Note that the aperture mass covariances can only be calculated up to half the largest scale where the covariances of the correlation functions are known.
Open with DEXTER

In the text

$\begin{figure} \includegraphics[width=18cm,clip]{0172f4.eps}\end{figure}$ Figure 4: The diagonal elements of the covariance matrices (10), split up into the individual terms D, M and V (11). Upper row: 300 single uncorrelated images, where the largest scale is $\sqrt {2} \times 13^\prime$ (thick lines) and a patch geometry with N=60 and $R=80^\prime$ (thin lines). Lower row: N=10, $R=100^\prime$ (thick lines) and N=60, $R=100^\prime$ (thin lines). The left and middle panels are logarithmic plots, the y-axis of the right panel is linear. Note that the bin widths are different for the different geometries which affects D. Because logarithmic bins are used, the differences in the bin widths are small, however.
Open with DEXTER

In the text

$\begin{figure} \includegraphics[width=11.6cm,clip]{4535.f5.eps}\end{figure}$ Figure 5: 1- $\sigma$ , 2- $\sigma$ and 3- $\sigma$ confidence contours of the figure-of-merit (14). Solid lines correspond to $\chi ^2_{\rm tot}$ , dotted lines to $\chi ^2_+$ and dashed lines to $\chi ^2_-$ . The left panels show the results for the 300 uncorrelated images, the right panels are for a $(N=60, R=80^\prime )$ -patch geometry. The parameter $\Sigma _8 \propto \sigma _8$ is defined in (17).
Open with DEXTER

In the text

$\begin{figure} \includegraphics[width=11.3cm,clip]{4535.f6.eps}\end{figure}$ Figure 6: Confidence levels of the figure-of-merit (14). As in Fig. 5, 1- $\sigma$ , 2- $\sigma$ and 3- $\sigma$ contours are plotted; the solid lines display $\chi ^2_{\rm tot}$ , the dotted and dashed lines correspond to $\chi ^2_+$ and $\chi ^2_-$ , respectively. The left panels show the results for the 300 uncorrelated images, the right panels are for a $(N=60, R=80^\prime )$ -patch geometry.
Open with DEXTER

In the text

$\begin{figure} \includegraphics[width=8.8cm,clip]{0172f7.eps}\end{figure}$ Figure 7: The parameter q (19) for the $\Omega _{\rm m}$ - $\Sigma _8$ -contours. On the x-axes, the patch radius Rin arcmin is plotted, thus each point represents a patch geometry with N images in patches of radius R. The horizontal line in the upper panels indicates the value for the 300 uncorrelated images (omitted for q_- and $q_{\rm E}$ , see also Table 1).
Open with DEXTER

In the text

$\begin{figure} \includegraphics[width=8.8cm,clip]{0172f8.eps}\end{figure}$ Figure 8: 1- $\sigma$ -likelihood contours (solid lines) using $\chi ^2_{\rm tot}$ (14) compared with the 1- $\sigma$ -error ellipse from the Fisher matrix (22): the dashed ellipse is for a flat Universe (as it is the case for the likelihood contours), the dotted one is for $\Omega _\Lambda =0.7$ . a/b is the axis ratio of the ellipses (the case $\Omega _\Lambda =0.7$ is in parentheses). The configuration is a survey of 300 uncorrelated images.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{4535.f9.eps}}\end{figure}$ Figure 9: The minimum variance for the parameters $\Omega _{\rm m}, \Gamma$ and ${\sigma _8}$ using (21) and (22), for the $\left\langle M_{\rm ap}^2 \right\rangle$ -statistics. $\Omega _{\rm m}, \Gamma$ and ${\sigma _8}$ are assumed to be determined from the data, all other parameters are kept fixed and a flat Universe is assumed. Each point in the plot represents a patch geometry with N images in patches of radius R. The minimum variance bound for the uncorrelated images is given in Table 2.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{4535.f10.eps}}\end{figure}$ Figure 10: The minimum variance for the parameters $\Omega _{\rm m}, \Gamma , \sigma _8$ and $\Omega _\Lambda$ using the $\left\langle M_{\rm ap}^2 \right\rangle$ -statistics. See Fig. 9 for more details. The minimum variance bound for the uncorrelated images is given in Table 2.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{4535.f11.eps}}\end{figure}$ Figure 11: The minimum variance for the parameters $\Omega _{\rm m}, \Gamma , \sigma _8$ and $n_{\rm s}$ using the $\left\langle M_{\rm ap}^2 \right\rangle$ -statistics. See Fig. 9 for more details. The minimum variance bound for the uncorrelated images is given in Table 2.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{4.2cm}{!}{\includegraphics[clip]{4535.f1a.ps}}\hsp... ...ce*{0.3mm} \resizebox{4.2cm}{!}{\includegraphics[clip]{4535.f1d.ps}}\end{figure}$	Figure 1: Realisations of patches; the squares represent the individual images. Nis the number of images per patch, R the patch radius. Each image has a size of 13 arcmin.
Open with DEXTER

$\begin{figure} \includegraphics[width=8.8cm,clip]{0172f7.eps}\end{figure}$	Figure 7: The parameter q (19) for the $\Omega _{\rm m}$ - $\Sigma _8$ -contours. On the x-axes, the patch radius Rin arcmin is plotted, thus each point represents a patch geometry with N images in patches of radius R. The horizontal line in the upper panels indicates the value for the 300 uncorrelated images (omitted for q_- and $q_{\rm E}$ , see also Table 1).
Open with DEXTER

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{4535.f10.eps}}\end{figure}$	Figure 10: The minimum variance for the parameters $\Omega _{\rm m}, \Gamma , \sigma _8$ and $\Omega _\Lambda$ using the $\left\langle M_{\rm ap}^2 \right\rangle$ -statistics. See Fig. 9 for more details. The minimum variance bound for the uncorrelated images is given in Table 2.
Open with DEXTER

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{4535.f11.eps}}\end{figure}$	Figure 11: The minimum variance for the parameters $\Omega _{\rm m}, \Gamma , \sigma _8$ and $n_{\rm s}$ using the $\left\langle M_{\rm ap}^2 \right\rangle$ -statistics. See Fig. 9 for more details. The minimum variance bound for the uncorrelated images is given in Table 2.
Open with DEXTER