Component separation for all-sky CMB temperature maps

The work described in this Thesis is related to the Planck mission, scheduled for launch in 2008, which will observe the microwave sky with unprecedent resolution and sensitivity. The Planck collaboration involves hundreds of scientists and prots from the contributions of research groups in many countries. Among them, an Italian collaboration has a key role on component separation. This is a crucial step of the data reduction process, aimed at disentangling the Cosmic Microwave Background (CMB) and all the astrophysical components which are mixed in the nine observational channels of Planck. The most important diuse components are, besides the CMB, synchrotron, free-free and thermal dust emissions due to our own Galaxy. Moreover, the Planck maps will contain radio and infrared extragalactic sources as well as the Sunyaev-Zel'dovich eects from clusters of galaxies. All the components which mix with the CMB are referred to as foregrounds, as they are placed between the CMB and the observer. The main goal of component separation is to provide a map of the CMB, from which the relevant cosmological information will be derived, clean from foreground contamination. On the other hand, maps of astrophysical components are of great interest per se. The accuracy of the component separation process will ultimately set that of the nal results Planck will provide. Our work was mainly focused on the development and testing of a new method for the separation of diuse foregrounds, the Correlated Component Analysis (CCA), proposed by Bedini et al. (2005). This technique exploits second-order statistics to estimate the mixing matrix, which contains the frequency behavior of the components mixed in the data. It is necessary to adopt a model for such components, i.e. to parametrize their frequency scaling in a suitable way. Our approach is to estimate the mixing matrix separately in dierent regions of the sky, where the spectral dependencies of foregrounds can be assumed to be constant. Once the mixing matrix is known, several methods are available to perform component separation, such as Wiener Filtering (WF), Maximum Entropy Method (MEM) or other Bayesian inversion techniques. After having suitably implemented the CCA method, we tested its performances on simulated Planck data. In Bonaldi et al. (2006) we applied the method to dierent sets of simulated Planck channels and estimated the errors on the mixing matrix with a Monte Carlo approach. The simulations included realistic diuse foregrounds, with spatially varying spectral properties, and Gaussian noise at the nominal level for the Planck satellite. This test showed that the method is ecient and that the errors on the mixing matrix estimation produce a minor contribution to the errors on the CMB power spectrum. We then partecipated in a blind comparative test of component separation methods coordinated by the Planck working group on component separation. The test used a more sophisticated simulation of Planck data, which included, besides diuse foreground emissions, also point sources and extragalactic background and a more realistic treatment of the noise. On these data, we tested CCA combined with harmonic Wiener Filtering. We focused on the reconstruction of the CMB map and on the power spectrum estimation, and obtained in both cases very good results, highly competitive with those provided with the best methods developed so far. We also got satisfactory reconstructions of Galactic dust emission, which is the dominant foreground in the highest resolution (high frequency) Planck channels. In Bonaldi et al. (2007b) we tested the same strategy on real data i.e. the rst three years of WMAP data. Our results are generally compatible with the result published by the WMAP team. We investigated the presence in the data of the so-called "microwave anomalous emission", an additional foreground component which could dominate in the lowest frequency WMAP channel (23 GHz). This component, revealed by cross correlations of microwave data with IR maps, appears to be correlated with thermal dust emission and has been interpreted as emission due to spinning dust grains (Draine & Lazarian 1998) or, alternatively, as synchrotron emission from dusty active star-forming regions (Hinshaw et al. 2006). We adopted various models for the frequency scaling of such component, whose properties are still poorly known. We then applied several quality tests to the maps reconstructed for each model and selected a subset of models having a good compatibility with the data. We also managed to get the rst, albeit preliminary, template of the anomalous emission over about 90% of the sky. We then estimated how our imperfect knowledge of the foreground components aects the CMB power spectrum. To this end we compared the CMB power spectra obtained adopting dierent foreground models that passed our quality tests. A signicant spread has been found for the largest scales, where anomalies of the WMAP power spectrum compared to the expectations from the best t cosmological model have been reported. Taking into account modelization errors, we nd no large scale power spectrum anomalies signicant at ¸ 1.5¾, except for the excess power at ` ' 40, which is signicant at around the 4¾ level. A minor part of this Thesis was devoted to the study of the Sunyaev-Zel'dovich (SZ) eect, due to inverse Compton scattering of CMB photons by hot electrons in the astrophysical plasmas bound to the cosmic structures. Planck is expected to provide a big sample of galaxy clusters observed through the SZ eect. One exploitation of the Planck cluster sample is related to the study of the physics of the intra-cluster (IC) gas. In Bonaldi et al. (2007a) we investigated the observable eects of dierent modeling of the physics of the IC gas. Another research eld related to the SZ eect concerns the study of the Large Scale Structure of the Universe. In Dolag et al. (2006) we analysed the SZ emission due to the so-called cosmic web, the network of lamentary structures which is now believed to connect galaxy clusters. The signal is too weak to be detected but its presence may bias the observed properties of galaxy clusters both in the X-ray band and in the microwaves. The outline of the Thesis is the following: Chapter 1 summarizes the theory of the CMB uctuations and their information content. In Chapter 2 we discuss the foreground components. In Chapter 3 we state the component separation problem and we review the main component separation techniques, from the most traditional ones to those recently developed for the Planck mission. In Chapter 4 and Chapter 5 we report on the work on the CCA method we performed respectively on simulated Planck data and on the WMAP data. Finally, in Chapter 6 we present our conclusions, together with the most recent developments of our work.