In our work, we investigate the secondary fluctuations induced by moving lenses with masses ranging from those of groups of galaxies to those of clusters of galaxies in a simple way, based on predicted structure counts and simulated maps. This method allows us to explore a rather wide range of scales ( arcseconds) in various cosmological models. The analysis, in terms of angular power spectra, show the scales for which the primary fluctuations are dominant (Fig. 3). In the standard and lambda CDM models, the primary anisotropies are dominant respectively for scales and whereas in the Open CDM model they are dominant for . In practice, it is thus impossible to detect the secondary anisotropies due to moving lenses in the open model. The standard CDM model shows the smallest cut-off scale with an intermediate SZ kinetic pollution, compared to the other two models. It is therefore the "best case" framework for making an analysis and predicting the detection of fluctuations and the contributions that they induce. One must keep in mind that the results quoted in this particular case represent the "best" results we get from the analysis.
The results of our analysis are obtained under the assumption of a universe that never re-ionises, which is of course not the case. The re-ionisation, if it is homogeneous, is supposed to somewhat ease the task of extraction of the pattern. In fact, its main effect is to damp the angular power spectrum of the primary anisotropies on small scales, shifting the cut-off towards larger scales. In this case, the effect of moving lenses dominates over the CMB fluctuations, and the SZ kinetic is not as high as it is on very small scales. However, if the re-ionisation is late and inhomogeneous, it generates additional SZ kinetic-type secondary fluctuations (Aghanim et al. 1996) without damping the power spectrum by more than a few percent. Here, the re-ionisation might worsen the analysis at small scales. In any case, there could be some other additional secondary fluctuations principally due to the Vishniac effect, that arise in a re-ionised universe. Our work thus gives a "best case" configuration of the problem, with all other effects tending to worsen the situation.
We found that the secondary fluctuations induced by the moving gravitational lenses can be as high as ; with rms contributions of about 5 to in the three cosmological models. Even if the moving lens fluctuations have a particular dipolar pattern and even if they are "perfectly" located through their SZ thermal effect, the detection of the moving lens effect and its separation from the SZ kinetic and primary fluctuations are very difficult because of the very high level of confusion, on the scales of interest, with the point-like SZ kinetic anisotropies and because of spectral confusion.
We nevertheless analysed the simulated maps using an adapted wavelet technique in order to extract the moving lens fluctuations. We conclude that the contribution of the secondary anisotropies due to the moving lenses is thus negligible whatever the cosmological model. Therefore it will not affect the future CMB measurements except as a background contribution. We have highlighted the fact that the moving lens fluctuations have a very significant spatial signature but we did not succeed in separating this contribution from the other signals.
© European Southern Observatory (ESO) 1998
Online publication: May 15, 1998