All Figures

$\begin{figure} \par\includegraphics[width=5.95cm,clip]{Figures/3762f1a.ps}\hspac... ...space*{1mm} \includegraphics[width=5.95cm,clip]{Figures/3762f1d.ps}\end{figure}$ Figure 1: Lensing cross sections for long and thin arcs with a length-to-width ratio exceeding d as a function of the distance between the centres of two dark matter haloes, for two (lens and source) redshifts. The haloes are modelled as NFW density profiles with elliptically distorted lensing potential with ellipticity e=0.3 (see Sect. 4). Green lines show the results of ray-tracing simulations for five different realisations of the source distribution. Black lines are the results obtained with our semi-analytic method.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{Figures/3762f2.ps}\end{figure}$ Figure 2: Mass of the lowest-mass halo producing large arcs in the sample of 46 haloes used here to compute the lensing optical depth. The source redshift is $z_{\rm s}=2$ . The overall trend in the curve reflects the geometrical lensing sensitivity, while the fluctuations and the depth of the minimum reflect how mergers can lift low-mass haloes above the strong-lensing threshold that would otherwise not be capable of strong lensing.
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In the text

$\begin{figure} \par\includegraphics[width=3.8cm,clip]{Figures/3762f3a.ps}\hspace... ...hspace*{2mm} \includegraphics[width=3.8cm,clip]{Figures/3762f3h.ps}\end{figure}$ Figure 3: Evolution of the lensing cross section for gravitational arcs with a length-to-width ratio equal to or greater than d=7.5 ( top panels) and d=10 ( bottom panels) for four of the most massive haloes in the sample. Sources are at redshift $z_{\rm s}=2$ . Red-dashed lines show cross sections calculated without taking account of merger processes. Black lines show cross sections enhanced by cluster interactions. Filled blue dots are the counterparts of the black lines obtained from fully numerical ray-tracing simulations.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{Figures/3762f4a.ps}\vspace*{3mm} \par\includegraphics[width=8.2cm,clip]{Figures/3762f4b.ps}\end{figure}$ Figure 4: The evolution with redshift of the optical depth per unit redshift for gravitational arcs with a length-to-width ratios equal to or larger than d. Solid lines include the effect of cluster mergers, while dashed lines do not. Upper curves refer to sources with $z_{\rm s}=2$ and lower curves to sources with $z_{\rm s} = 1$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{Figures/3762f5.ps}\end{figure}$ Figure 5: Cross section for gravitational arcs with a length-to-width ratio exceeding d=10 for a dark-matter halo of $10^{15}~M_\odot~ h^{-1}$ as a function of the source size in arc sec. Black and green lines show the results of the semi-analytic and of ray-tracing simulations, respectively, which are repeated with different random-number seeds for the ellipticities and the position angles of the sources, as in Fig. 1. The source redshift is $z_{\rm s} = 1$ , and the lens redshift is $z_{\rm l}=0.3$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{Figures/3762f6.ps}\end{figure}$ Figure 6: Cross section for gravitational arcs with a length-to-width ratio exceeding d=10 for several haloes of increasing mass. Black and red lines refer to point-like or extended sources with area equal to that of a circle of radius 0.5'', respectively. Short dashed lines indicate circular sources, long dashed lines refer to sources with random ellipticity drawn from the interval [0,0.5] $\left ( q_{\rm s} \in [0.5,1] \right )$ , and solid lines refer to sources with ellipticity 0.5. Sources are at redshift $z_{\rm s} = 1$ and the lens redshift is $z_{\rm l}=0.3$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{Figures/3762f7.ps}\end{figure}$ Figure 7: Cross section for arcs with a length-to-width ratio exceeding d=10 for a dark matter halo of $10^{15}~M_\odot~ h^{-1}$ as a function of the source redshift. Three different lens redshifts are considered, as labeled in the plot.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{Figures/3762f4a.ps}\vspace*{3mm} \par\includegraphics[width=8.2cm,clip]{Figures/3762f4b.ps}\end{figure}$	Figure 4: The evolution with redshift of the optical depth per unit redshift for gravitational arcs with a length-to-width ratios equal to or larger than d. Solid lines include the effect of cluster mergers, while dashed lines do not. Upper curves refer to sources with $z_{\rm s}=2$ and lower curves to sources with $z_{\rm s} = 1$ .
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{Figures/3762f7.ps}\end{figure}$	Figure 7: Cross section for arcs with a length-to-width ratio exceeding d=10 for a dark matter halo of $10^{15}~M_\odot~ h^{-1}$ as a function of the source redshift. Three different lens redshifts are considered, as labeled in the plot.
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