All Figures

$\begin{figure} \resizebox{9cm}{!}{\includegraphics[angle=-90]{1040fig1.eps}} \end{figure}$ Figure 1: True magnification, $\Delta m_{\rm true}$ , versus estimated magnification, $\Delta m_{\rm est}$ , for three different scenarios: no shift in halo masses (circles), underestimated halo masses (squares), and overestimated halo masses (triangles). The straight lines show the best fits to the no shift (solid line), underestimation (dashed line), and overestimation (dotted line) scenario.
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In the text

$\begin{figure} \resizebox{9cm}{!}{\includegraphics[angle=-90]{1040fig2.eps}} \end{figure}$ Figure 2: Bias (panel a)) and dispersion (panel b)) in $\epsilon$ as a function of redshift. The no shift scenario is represented by the thin solid curves. Dashed and dotted curves correspond to the under- and overestimation scenarios, respectively. Bias and dispersion of $\Delta m_{\rm true}$ , outlined by the thick solid curves, are also shown for comparison. The estimated magnifications, $\Delta m_{\rm est}$ , were used to correct for gravitational lensing.
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In the text

$\begin{figure} \resizebox{9cm}{!}{\includegraphics[angle=-90]{1040fig3.eps}} \end{figure}$ Figure 3: Scatter plot of $\langle \epsilon \rangle/\sigma_{\Delta m_{\rm true}}$ versus $\sigma _{\epsilon }/\sigma _{\Delta m_{\rm true}}$ for simulated SNLS-like data sets consisting of 250 SNe Ia each. Circles, squares, and triangles represent the no shift, under-, and overestimation scenarios, respectively. The different panels correspond to different intrinsic brightness dispersion and measurement errors: panel a) $\sigma _{\rm int}=0.13$ mag, $\sigma _{\rm err}$ given by Eq. (4); panel b) $\sigma _{\rm int}=0.09$ mag, $\sigma _{\rm err}$ given by Eq. (4); panel c) $\sigma _{\rm int}=0.09$ mag, $\sigma _{\rm err} = 0$ mag; panel d) $\sigma _{\rm int}=0.05$ mag, $\sigma _{\rm err} = 0$ mag.
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In the text

$\begin{figure} \resizebox{9cm}{!}{\includegraphics[angle=-90]{1040fig4.eps}} \end{figure}$ Figure 4: Probability distribution functions of $\sigma _{\epsilon }/\sigma _{\Delta m_{\rm true}}$ for different scenarios and errors. The distributions were obtained for simulated SNLS-like data sets consisting of 250 SNe Ia. Panels a), b), and c) correspond to the no shift, under-, and overestimation scenario. The curves show results for different assumed errors: solid curves correspond to $\sigma _{\rm err}$ given by Eq. (4) and $\sigma _{\rm int}=0.13$ mag; dashed curves correspond to $\sigma _{\rm err}$ given by Eq. (4) and $\sigma _{\rm int}=0.09$ mag; dotted curves correspond to $\sigma _{\rm err} = 0$ and $\sigma _{\rm int}=0.09$ mag; dash-dotted curves correspond to $\sigma _{\rm err} = 0$ and $\sigma _{\rm int}=0.05$ mag.
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In the text

$\begin{figure} \resizebox{9cm}{!}{\includegraphics[angle=-90]{1040fig5.eps}} \end{figure}$ Figure 5: Correction coefficient B as a function of redshift for three simulated scenarios. For the first scenario (solid curve) there is no systematic shift in halo masses. For the second (dashed curve) and third (dotted curve) scenario halo masses were systematically under- and overestimated by 50%.
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In the text

$\begin{figure} \resizebox{9cm}{!}{\includegraphics[angle=-90]{1040fig6.eps}} \end{figure}$ Figure 6: Bias (panel a)) and dispersion (panel b)) in $\epsilon$ as a function of redshift. The no shift scenario is represented by the thin solid curves. Dashed and dotted curves correspond to the under- and overestimation scenarios, respectively. Bias and dispersion of $\Delta m_{\rm true}$ , outlined by the thick solid curves, are also shown for comparison. To correct for gravitational lensing the formula $\Delta m_{\rm est}^{B}=B\Delta m_{\rm est}$ with B corresponding to the value outlined by the straight lines in Fig. 1 was used.
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In the text

$\begin{figure} \resizebox{9cm}{!}{\includegraphics[angle=-90]{1040fig7.eps}} \end{figure}$ Figure 7: Probability distribution functions of $\sigma _{\epsilon }/\sigma _{\Delta m_{\rm true}}$ for the no shift scenario and different errors. The distributions were obtained for simulated SNLS-like data sets consisting of 250 SNe Ia corrected for gravitational lensing using the formula $\Delta m_{\rm est}^{B}=B\Delta m_{\rm est}$ . The curves show results for different assumed errors: solid curves correspond to $\sigma _{\rm err}$ given by Eq. (4) and $\sigma _{\rm int}=0.13$ mag; dashed curves correspond to $\sigma _{\rm err}$ given by Eq. (4) and $\sigma _{\rm int}=0.09$ mag; dotted curves correspond to $\sigma _{\rm err} = 0$ and $\sigma _{\rm int}=0.09$ mag; dash-dotted curves correspond to $\sigma _{\rm err} = 0$ and $\sigma _{\rm int}=0.05$ mag.
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In the text

$\begin{figure} \resizebox{9cm}{!}{\includegraphics[angle=-90]{1040fig5.eps}} \end{figure}$	Figure 5: Correction coefficient B as a function of redshift for three simulated scenarios. For the first scenario (solid curve) there is no systematic shift in halo masses. For the second (dashed curve) and third (dotted curve) scenario halo masses were systematically under- and overestimated by 50%.
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