Statistical properties of thermal Sunyaev-Zel'dovich maps

On small angular scales, i.e. at high angular frequencies, beyond the damping tail of the primary power spectrum, the dominant contribution to the power spectrum of cosmic microwave background temperature fluctuations is the thermal Sunyaev-Zel'dovich (tSZ) effect. We investigate various important statistical properties of the Sunyaev-Zel'dovich maps, using well-motivated models for dark matter clustering to construct statistical descriptions of the tSZ effect to all orders enabling us to determine the entire probability distribution function (PDF). Any generic deterministic biasing scheme can be incorporated in our analysis and the effects of projection, biasing and the underlying density distribution can be analysed separately and transparently in this approach. We introduce the cumulant correlators as tools to analyse tSZ catalogues and relate them to corresponding statistical descriptors of the underlying density distribution. The statistics of hot spots in frequency-cleaned tSZ maps are also developed in a self-consistent way to an arbitrary order, to obtain results complementary to those found using the halo model. We also consider different beam sizes to check the extent to which the PDF can be extracted from various observational configurations. The formalism is presented with two specific models for underlying matter clustering, the hierarchical ansatz and the lognormal distribution. We find both models to be in very good agreement with the simulation results, though the extension of the hierarchical model has an edge over the lognormal model. In addition to testing against simulations made using semi-analytical techniques, we have also used the maps made using Millennium Gas Simulations to prove that the PDF and bias can indeed be predicted with very high accuracy using these models. The presence of significant non-gravitational effects such as preheating, however, cannot be modelled using an analytical approach which is based on the modelling of gravitational clustering alone. Our results indicate that the PDFs we construct are insensitive to the underlying cosmology and can thus provide a useful probe of non-gravitational processes, e.g. preheating or feedback.