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.