Methods for detecting and characterising clusters of galaxies

The main theme of this PhD-thesis is the observation of clusters of galaxies at submillimetric wavelengths. The Sunyaev-Zel'dovich (SZ) effect due to interaction of cosmic microwave background (CMB) photons with electrons of the hot intra-cluster medium causes a distinct modulation in the spectrum of the CMB and is a very promising tool for detecting clusters out to very large distances. Especially the European PLANCK-mission, a satellite dedicated to the mapping of CMB anisotropies, will be the first experiment to routinely detect clusters of galaxies by their SZ-signature. This thesis presents an extensive simulation of PLANCK's SZ-capabilities, that combines all-sky maps of the SZ-effect with a realisation of the fluctuating CMB and submillimetric emission components of the Milky Way and of the Solar system, and takes instrumental issues such as the satellite's point-spread function, the frequency response, scan paths and detector noise of the receivers into account. For isolating the weak SZ-signal in the presence of overwhelming spurious components with complicated correlation properties across PLANCK's channels, multifrequency filters based on matched and scale-adaptive filtering have been extended to spherical topologies and applied to simulated data. These filters were shown to efficiently amplify and extract the SZ-signal by combining spatial band-filtering and linear combination of observations at different frequencies, where the filter shapes and the linear combination coefficients follow from the cross- and autocorrelation properties of the sky maps, the anticipated profile of SZ clusters and the known SZ spectral dependence. The characterisation of the resulting SZ-sample yielded a total number of 6000 detections above a statistical significance of 3 sigma and the distribution of detected clusters in mass, redshift, and position on the sky. In a related project, a method of constructing morphological distance estimators for resolved SZ cluster images is proposed. This method measures a cluster's SZ-morphology by wavelet decomposition. It was shown that the spectrum of wavelet moments can be modeled by elementary functions and has characteristic properties that are non-degenerate and indicative of cluster distance. Distance accuracies following from a maximum likelihood approach yielded values as good as 5% for the relative deviation, and deteriorate only slightly when noise components such as instrumental noise or CMB fluctuations were added. Other complications like cool cores of clusters and finite instrumental resolution were shown not to affect the wavelet distance estimation method significantly. Another line of research is the Rees-Sciama (RS) effect, which is due to gravitational interaction of CMB photons with non-stationary potential wells. This effect was shown to be a second order gravitational lensing effect arising in the post-Newtonian expansion of general relativity and measures the divergence of gravitomagnetic potentials integrated along the line-of-sight. The spatial autocorrelation function of the Rees-Sciama effect was derived in perturbation theory and projected to yield the angular autocorrelation function while taking care of the differing time evolution of the various terms emerging in the perturbation expansion. The RS-effect was shown to be detectable by PLANCK as a correction to the primordial CMB power spectrum at low multipoles. Within the same perturbative formalism, the gravitomagnetic corrections to the autocorrelation function of weak gravitational lensing observables such as cosmic shear could be determined. It was shown that those corrections are most important on the largest scales beyond 1~Gpc, which are difficult to access observationally. For contemporary weak lensing surveys, gravitomagnetic corrections were confirmed not play a significant role. A byproduct of the simulation of CMB fluctuations on the basis of Gaussian random fields was a new way of generating coded mask patterns for X-ray and gamma-ray imaging. Coded mask cameras observe a source by recording the shadow cast by a mask onto a position-sensitive detector. The distribution of sources can be reconstructed from this shadowgram by correlation techniques. By using Gaussian random fields, coded mask patterns can be specifically tailored for a predefined point-spread function which yields significant advantages with respect to sensitivity in the observation of extended sources while providing a moderate performance compared to traditional mask generation schemes in the observation of point sources. Coded mask patterns encoding Gaussian point-spread functions have been subjected to extensive ray-tracing studies where their performance has been evaluated