Astron. Astrophys. 347, 409-418 (1999)

7. Discussion and conclusion

The secondary anisotropies, due to CMB photon interactions, are superimposed on the primary anisotropies which are directly related to the seeds of the cosmic structures. The primary anisotropies can be Gaussian distributed (inflationary models) or can exhibit an intrinsic non-Gaussian signature (topological defect models). In the context of future CMB observations (high sensitivity, high resolution and large sky coverage), we will use the full information related to the CMB temperature anisotropies, in particular the statistical information, to distinguish between the two main cosmological models. Similarly, studies aiming at predicting and quantifying the foreground contributions to the temperature anisotropies have to characterise the non-Gaussian foreground signals in order to subtract them before detailed CMB analysis.

In the present study, we investigate the tests for non-gaussianity when this is induced by secondary anisotropies, the primary anisotropies being Gaussian distributed. We study the effects arising from the interactions of the CMB photons and the ionised matter. More specifically, we focus on two effects which dominate all the other secondary effects of a scattering nature: the spatially inhomogeneous re-ionisation which peaks at scales of a few tens of arcminutes to one degree and the SZ effect which dominates at the few arcminutes scale. In order to search for non-gaussianity, we use discriminators based on the study of the statistical properties of the coefficients in a four level wavelet decomposition (Forni & Aghanim 1999).

The primary anisotropies are Gaussian at all scales. Nonetheless, we find a non-zero value of the multi-scale gradient excess of kurtosis, and hence first derivatives, at the second decomposition scale which could be misinterpreted as a non-Gaussian signature. This can be understood in the following way: the window function of the wavelet at this scale (centred around ) encompasses the cut off in the angular power spectrum. As a result the corresponding sample variance induces a non-zero kurtosis for the multi-scale gradient coefficients. The presence of this non-zero value depends on the cosmological model as well as on the window filter that is the wavelet function. A similar non-zero value could exist at any decomposition scale where the CMB power spectrum has a sharp cut off. For the standard CDM model we use here, the cut off occurs at the second scale. In the case where the cosmological model has more power at small angular scales, or undergoes an overall shift of the spectrum towards large multipoles, the sample variance effects decrease. In the same way, we can use a wider wavelet which in turn decreases the sample effects. However, this attenuates the non-Gaussian signature we search for. We apply a detection strategy proposed in Forni & Aghanim (1999), which allows the quantification of the detectability regardless of the power spectrum of the studied signal.

We have studied the case of secondary anisotropies induced by a spatially inhomogeneous re-ionisation of the Universe. Assuming that this was the only source of secondary anisotropies, we succeed in demonstrating its non-Gaussian signature at the first and second decomposition scales. However, inhomogeneous re-ionisation is far from being the only source of anisotropies. The SZ effect due to galaxy clusters is known to be the most common source which is related to the CMB photon scattering off free electrons. In this study, we also take into account the SZ effect of a predicted cluster population which we add to the primary CMB fluctuations and to the re-ionisation anisotropies. The non-Gaussian foreground model is a worst case example because we do not remove any foregrounds. Owing to its peculiar spectral signature the thermal SZ effect is expected to be removed from the cosmological signal (temperature anisotropies). However, the subtraction is not complete because almost 1/5 of the SZ effect contribution is due to the kinetic SZ effect, which is spectrally indistinguishable from the primary anisotropies, and there remains a significant non-Gaussian foreground contribution. In our study, we find that the dominant non-Gaussian signal is due to the SZ effect of clusters. The non-Gaussian signature is found to be orders of magnitude larger than in the case without the SZ contribution and we clearly detect the non-gaussianity. The strong non-Gaussian signature, associated with the SZ effect, comes from the gas profile of individual clusters. We have analysed temperature anisotropy maps with different profiles (Gaussian, profiles or even so point-like sources) to which we add the primary Gaussian anisotropies. As it is very peaked at the centre, the cluster induces a sharp variation in the signal from the center to the outskirts of the structure. In addition, an important fraction of the cluster population is composed of unresolved point-like clusters. We thus find that clusters represent the dominant non-Gaussian foreground.

We apply our statistical tests to Planck-like and MAP-like instrumental configurations in order to compare the capabilities of the two planned satellites for detecting the non-Gaussian signature induced by the secondary anisotropies (mainly the SZ effect). For both configurations the fourth, and largest scale, shows no significant non-gaussianity due to the SZ contribution. In the MAP-like configuration, the beam convolution affects the first two decomposition scales. Therefore, we are only left with the third scale to search for non-gaussianity. At the same time, the convolution rather sharply reduces the contribution at angular scale associated with the third decomposition level. This induces a non-zero excess of kurtosis. We apply our detection strategy to overcome the problem and avoid a possible misinterpretation on non-gaussianity. We find no significant detection of the non-Gaussian signature at the third scale for the MAP-like configuration. By contrast, for the Planck-like configuration, we detect the non-Gaussian signature at the third decomposition scale, the first and, second being affected by the beam convolution.

We have shown that our statistical tests combined with a detection strategy based on the characterisation of Gaussian test maps, with same power spectrum as the non-Gaussian studied process, are appropriate tools for demonstrating a non-Gaussian signature. In a forthcoming paper, we will search for other discriminatory methods that allow two (or more) non-Gaussian signals to be distinguished, in order to subtract the non-Gaussian signature of the secondary anisotropies from the non-Gaussian signature of the primary fluctuations.

© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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