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

Weak lensing tomography with orthogonal polynomials

The topic of this paper is weak cosmic shear tomography where the line-of-sight weighting is carried out with a set of specifically constructed orthogonal polynomials, dubbed Tomography with Orthogonal Radial Distance Polynomial Systems (TaRDiS). We investigate the properties of these polynomials and employ weak convergence spectra, which have been obtained by weighting with these polynomials, for the estimation of cosmological parameters. We quantify their power in constraining parameters in a Fisher matrix technique and demonstrate how each polynomial projects out statistically independent information, and how the combination of multiple polynomials lifts degeneracies. The assumption of a reference cosmology is needed for the construction of the polynomials, and as a last point we investigate how errors in the construction with a wrong cosmological model propagate to misestimates in cosmological parameters. TaRDiS performs on a similar level as traditional tomographic methods and some key features of tomography are made easier to understan

Shear and vorticity in the spherical collapse of dark matter haloes

Traditionally the spherical collapse of objects is studied with respect to a uniform background density, yielding the critical over-density $\delta_\mathrm{c}$ as key ingredient to the mass function of virialized objects. Here we investigate the shear and rotation acting on a peak in a Gaussian random field. By assuming that collapsing objects mainly form at those peaks, we use this shear and rotation as external effects changing the dynamics of the spherical collapse, which is described by the Raychaudhuri equation. We therefore assume that the shear and rotation have no additional dynamics on top of their cosmological evolution and thus only appear as inhomogeneities in the differential equation.Comment: 8 pages, 5 figures, MNRAS accepte

A test of the Suyama-Yamaguchi inequality from weak lensing

We investigate the weak lensing signature of primordial non-Gaussianities of the local type by constraining the magnitude of the weak convergence bi- and trispectra expected for the EUCLID weak lensing survey. Starting from expressions for the weak convergence spectra, bispectra and trispectra, whose relative magnitudes we investigate as a function of scale, we compute their respective signal to noise ratios by relating the polyspectra's amplitude to their Gaussian covariance using a Monte-Carlo technique for carrying out the configuration space integrations. In computing the Fisher-matrix on the non-Gaussianity parameters f_nl, g_nl and tau_nl with a very similar technique, we can derive Bayesian evidences for a violation of the Suyama-Yamaguchi relation tau_nl>=(6 f_nl/5)^2 as a function of the true f_nl and tau_nl-values and show that the relation can be probed down to levels of f_nl~10^2 and tau_nl~10^5. In a related study, we derive analytical expressions for the probability density that the SY-relation is exactly fulfilled, as required by models in which any one field generates the perturbations. We conclude with an outlook on the levels of non-Gaussianity that can be probed with tomographic lensing surveys