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Astron. Astrophys. 334, 409-419 (1998)

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Study case

We filter the large scales of a map of CMB+moving lens fluctuations (no SZ kinetic contribution) in order to test the robustness and efficiency of the wavelet transform filtering. In this case, the noise due to the CMB is efficiently cleaned. In fact, Fig. 6 lower left panel shows a residual signal (symbolised by the dots) associated with the moving lens fluctuations, which are simulated in the upper right panel of the same figure. We have confirmed that the positions of the residual signal agree with the positions of the input structures. Moreover, we were able to successfully extract the secondary fluctuations due to the moving lenses, as well as estimate their average peak to peak [FORMULA] values. Fig. 8 shows the average peak to peak amplitudes of the input simulated fluctuations (solid line) and the extracted values (dashed line). The main features are well-recovered, although the amplitudes suffer from the smoothing of the filtering procedure. In this study case, with no SZ kinetic contribution, we find a correlation coefficient between input and recovered values of about 0.95.

[FIGURE] Fig. 6. The two upper panels show simulated maps: on the left, total map of the fluctuations (CMB+SZ+lens) linear scale between [FORMULA] (white) and [FORMULA] (black). On the right is shown the map of the moving lenses fluctuations (linear scale between [FORMULA] (white) and [FORMULA] (black)). The two lower panels are the result of the wavelet filtering process. The left panel is for a CMB+lens configuration, in which we notice that the secondary anisotropies are rather well extracted. The right panel represents the case of all contributors and shows that the moving lenses are completely dominated by the SZ kinetic noise.

[FIGURE] Fig. 8. Average peak to peak amplitude of the secondary anisotropies due to the moving lenses (cut-off mass [FORMULA]) for lenses with decreasing y parameter. Solid line represents the amplitudes in the original simulated lens map. The dashed line represents the extracted amplitudes without sorting the wavelet coefficients and after filtering the CBM+lenses contributions (no SZ kinetic). The dotted-dashed line represents the extracted amplitudes after sorting the wavelet coefficients and filtering all contributions (CBM+lenses+SZ kinetic).

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© European Southern Observatory (ESO) 1998

Online publication: May 15, 1998