Astronomy & Astrophysics

All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig1.eps} \end{figure}$ Figure 1: The correlation coefficient between the original KSZ map and the series of 17 estimated KSZ maps as a function of the standard deviations of the estimated KSZ maps. Upper panel is for the best case and lower panel for the worst case. The triangles and the solid line stand for the interpolation with the biharmonic operator, the diamonds and the dashed line are for the interpolation with the Laplacian. The interpolation with the biharmonic operator gives better results, especially for the KSZ maps with low standard deviation. The vertical lines mark the standard deviation of the original KSZ maps ( $2.6\times 10^{-6}$ and $1.2\times 10^{-6}$ ). The standard deviation of the primary CMB is $1.9 \times 10^{-5}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig2.eps} \end{figure}$ Figure 2: For the best case (upper curve and triangles) and worst case (lower curve and diamonds), the correlation coefficient between the original and the 17 estimated KSZ maps as a function of the associated 17 TSZ threshold values. The highest threshold value is of the order of $y=3.5 \times 10^{-5}$ . The interpolation method uses the biharmonic operator.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig3.eps} \end{figure}$ Figure 3: Standard deviations of our set of 15 KSZ original simulated maps (triangles) as compared to the standard deviations of the 15 reconstructed KSZ maps (squares). The reconstruction is based on the minimisation of the statistical criterion (see text).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig4.eps} \end{figure}$ Figure 4: Top and middle panels: histogram and power spectrum of the original KSZ map (solid line), and of the reconstructed KSZ map (dashed line). The reconstruction is based on the minimisation of the statistical criterion (see text). The bottom panel exhibits the ratio of the two power spectra. Note the correlation coefficient between the original and reconstructed KSZ maps of $\sim$ 0.9 and the total power $P_{\rm real}$ and $P_{\rm est}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig5.eps} \end{figure}$ Figure 5: Same as Fig. 4. This is our worst case and corresponds to the original KSZ map with the lowest standard deviation. Note the low correlation coefficient 0.62.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig6.eps} \end{figure}$ Figure 6: Cuts across the best reconstructed KSZ map (dashed line) and its original counterpart (solid line). The cuts have the same position in both maps.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig7.eps} \end{figure}$ Figure 7: Same as Fig. 6 for the worst reconstructed KSZ map and its original counterpart.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig8.eps} \end{figure}$ Figure 8: Top and middle: histogram and power spectrum of the original KSZ map (solid line), and the reconstructed map (dashed line). Bottom panel exhibits the ratio of the two power spectra. The standard deviation of the original map is very low ( $\sigma _{0}=2.5\times 10^{-7}$ ). Note the excess of near zero values in the histogram of the estimated map (logarithmic scale). Note also the very low correlation coefficient 0.48. This is for the worst case.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig9.eps} \end{figure}$ Figure 9: Cuts across original (solid line) and reconstructed (dashed line) KSZ maps, at the same position, but with increasing (from top to bottom) original standard deviation (for $\sigma$ : 2.5 $\times$ 10^-7, 5.0 $\times$ 10^-7, 1.0 $\times$ 10^-6 and 2.0 $\times$ 10^-6). The important difference between original and reconstructed signals in the middle of the cuts illustrates the fact that large scale structures (this one is $\simeq$ 50 arc-min) are poorly resolved due to confusion with CMB fluctuations. Note that the largest fluctuation at the left is not reconstructed for the lowest $\sigma$ and that the quality of its reconstruction increases with increasing $\sigma$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig2.eps} \end{figure}$	Figure 2: For the best case (upper curve and triangles) and worst case (lower curve and diamonds), the correlation coefficient between the original and the 17 estimated KSZ maps as a function of the associated 17 TSZ threshold values. The highest threshold value is of the order of $y=3.5 \times 10^{-5}$ . The interpolation method uses the biharmonic operator.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig3.eps} \end{figure}$	Figure 3: Standard deviations of our set of 15 KSZ original simulated maps (triangles) as compared to the standard deviations of the 15 reconstructed KSZ maps (squares). The reconstruction is based on the minimisation of the statistical criterion (see text).
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig5.eps} \end{figure}$	Figure 5: Same as Fig. 4. This is our worst case and corresponds to the original KSZ map with the lowest standard deviation. Note the low correlation coefficient 0.62.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig6.eps} \end{figure}$	Figure 6: Cuts across the best reconstructed KSZ map (dashed line) and its original counterpart (solid line). The cuts have the same position in both maps.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0110fig7.eps} \end{figure}$	Figure 7: Same as Fig. 6 for the worst reconstructed KSZ map and its original counterpart.
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