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Chluba, Jens (2005): Spectral Distortions of the Cosmic Microwave Background. Dissertation, LMU München: Faculty of Physics
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Abstract

Studying the cosmic microwave background (CMB) has proven to be an immensely rich source of information about the Universe we live in. Many groups were and are intensely working on the interpretation of the large amount of CMB data, which has become available during the last decades and will be obtained with many new projects already observing at present or planned for the near future. The observations by COBE in the 90's have shown that the CMB is extremely uniform, with angular fluctuations of the temperature on the level of one part in 10^5 on angular scales larger than 7 degree. On the other hand on these scales no deviations of the CMB energy spectrum from a perfect blackbody were found. But today we do know that there exist spectral distortions of the CMB on arcminute scales due to the scattering of CMB photons off the hot electrons residing inside the deep potential well of clusters of galaxies, which leads to the so called thermal-SZ effect (th-SZ). The th-SZ effect has already been measured for several big cluster and within the next 5 years, many CMB experiments like ACBAR, SZA, PLANCK, SPT, ACT, APEX, AMI and QUIET will perform deep searches for clusters with very high sensitivity. Many tens of thousands of clusters will be detected allowing us to carry out detailed studies of cluster physics and to place constraints on parameters of the Universe. Due to this great advance in technology one can expect that small deviations from the main SZ cluster signal, e.g. related to relativistic corrections to Compton scattering for high electron temperature, will become observable. Motivated by this promising perspective here we studied the influence of the motion of the Solar System with respect to the CMB rest frame on the SZ cluster signature. This kind of contribution to the SZ signal has been neglected in the literature so far, but as we show here it is of the same order as other corrections under discussion. We found that this motion-induced SZ signal has a very strong spectral and spatial dependence and due to the great knowledge about the motion-induced CMB dipole it can be predicted with high precision, which makes it easy to account for it in the analysis of future SZ studies. Here one big problem naturally arises: any experiment trying to observe tiny frequency-dependent signals needs a cross calibration of the different frequency channels. Several different standard methods for calibration issues are known, e.g. based on the annual modulation of the CMB dipole, the microwave flux from planets like Jupiter or the comparison with CMB sky maps obtained by well calibrated experiments like WMAP, each with their own problems and drawbacks. However the achieved level of cross calibration is limited by the knowledge of the calibrator. Today scientists are already speaking about extremely small frequency-dependent features in the CMB temperature power spectrum resulting from the scattering of CMB photons in the fine structure lines of different atomic species during the dark ages. Obtaining these signals can in principle be used to answer some of the interesting questions about the history of chemical enrichment and reionization, but it is likely that the necessary level of cross calibration cannot be reached with the standard methods. In this context we considered the fact that the superposition of blackbodies with different temperatures is not again a blackbody. We show that in the limit of small temperature difference the superposition leads to a y-type spectral distortion. This kind of distortion arises whenever one in observing the CMB sky with finite angular resolution. We discuss the spectral distortions due to the primordial CMB temperature fluctuations and the motion-induced CMB dipole. Furthermore we considered possible applications for calibration issues. We show that within this context also clusters of galaxies, especially for experiments observing only small parts of the sky, in the future may become standard sources for calibration issues. Although the observations with COBE/FIRAS have proven that the CMB energy spectrum on large angular scales is extremely close to a pure blackbody one may still expect some deviations due to processes like the damping of acoustic waves, turbulent motion of the matter, the decay of unstable particles or annihilation of matter in the early Universe. Especially possible distortions from very early epochs (redshifts z> few x 10^5) lead to deviations of the CMB brightness temperature at frequencies (1-few x 10 GHz) well below the range of COBE/FIRAS. Currently people in the USA and especially at the NASA Goddard Space Flight Center are intensely working on experiments to measure the CMB temperature at these frequencies, where the largest distortions could be expected. One can therefore hope that in the near future also new constraints on the CMB energy spectrum will become available. Therefore in this thesis we also reexamined the thermalization of spectral distortions of the CMB in the early Universe. Due to the large entropy here one of the most important processes is the production of low frequency photons by double Compton scattering. Until now people were only using a description of this emission in the limit of cold electrons and soft initial photons, but especially for the thermalization of large distortions at very high redshifts (z > 10^6) the inclusion of relativistic corrections to the main processes at work may become necessary. Here we provide two steps towards a solution of this problem. First we discuss in detail the full kinetic equation for the time evolution of the photon field under double Compton scattering in a hot, isotropic thermal plasma, both numerically and analytically. We obtained accurate approximations for the effective double Compton Gaunt factor, which are applicable in a very broad range of physical situations. We then provide a reformulation of the thermalization problem with respect to relativistic corrections and discuss its solution in the limit of small chemical potential distortions at high redshifts. Our results indicate that due to relativistic corrections the thermalization at high redshifts slows down notably and therefore makes the CMB more vulnerable for distortions at epochs z > 10^6. Here we also report some of our attempts to solve the full problem numerically.