Investigations of Statistical Properties of Galactic Foreground Components and the CMB

Abstract

Accurate component separation of full-sky maps in the radio and microwave frequencies, such as the cosmic microwave background (CMB), relies on a thorough understanding of the statistical properties of the Galactic foreground emissions. These Galactic emissions include Galactic synchrotron, free-free, Anomalous Microwave Emission (AME), thermal dust emissions, etc. This thesis aims to characterize these foreground components with the goal of improving the component separation methods in experiments looking for cosmological signals. For this, we utilize a set of geometric and topological tools such as Minkowski functionals (MFs) and Minkowski tensors (MTs), along with conventional tools like power spectrum, skewness, kurtosis, etc. We begin our analysis by studying the MFs for composite random fields, which are the sum of two fields. Using analytic expressions for MFs, we examine and quantify how the presence of a secondary field, such as noise or any residual contamination, affects the morphology of the field of interest, say the CMB field. We find that the secondary field can alter the amplitude and nature of non-Gaussianity of the signal field, depending on the signal-to-noise ratio (SNR) and the relative size of structures of the two fields. Next, we focus on the statistical properties, namely non-Gaussianity and statistical isotropy (SI), of the all-sky Haslam 408 MHz temperature map, which is widely used as a proxy for synchrotron emission. Our goal is to investigate how the non-Gaussian properties vary at different spatial regions as well as angular scales of the Haslam map. We find that the overall level of the non-Gaussian deviations does decrease as more high-emission regions are masked and as we go down to smaller scales, in agreement with the results obtained in earlier works. Our results show that the leading sources of non-Gaussianity are the kurtosis terms, with skewness terms being subdominant at all angular scales. We test the SI of the Haslam map and find that it becomes increasingly more isotropic towards smaller scales. Next, we examine the Galactic emission maps at high-frequency bands provided by WMAP and Planck CMB experiments. Here, our goals are two-fold. First, we determine the variation of morphological properties of the total foreground with observing frequency and compare them with simulations. This study elucidates how the morphology varies with frequency due to the relative dominance of different foreground components at different frequencies. This is an example of a composite field composed of different foreground signals. Secondly, we use various component-separated synchrotron temperature and polarization maps to determine the nature of non-Gaussianity and SI of synchrotron fluctuations towards smaller scales. We find that all maps exhibit kurtosis-type non-Gaussianity, in agreement with the Haslam map. This result can be an important input for modelling small-scale synchrotron fluctuations for component separation pipelines. From a comparison of the different component-separated maps, we find that these synchrotron maps show morphological differences of varying statistical significance. Our analysis suggests a combination of residual AME and/or free-free emissions and point sources as contributing to these differences and underscores the need for further improvement of the pipelines. As a next step, we study the statistical properties of other major Galactic emissions, namely free-free, AME and thermal dust. In this work, we investigate whether the observed kurtosis nature of non-Gaussianity in synchrotron maps is a generic feature of foreground emissions or any random field with positively skewed probability distribution. Our study using different toy models of random fields reveals that the nature of non-Gaussianity is dependent on the underlying distribution of the field and is not a generic feature. We find that, at small scales, the non-Gaussianity of all the foreground fields is of kurtosis origin, with different levels of non-Gaussianity for different fields. These findings provide valuable insights into preparing realistic nonGaussian models of foreground components. In the last part of the thesis, we introduce a new morphological tool known as total absolute curvature (K), which can complement MFs in extracting the properties of different random fields, including foreground fields. Our results open up new avenues in the statistical modelling of foreground components, thereby enhancing the efficiency of foreground removal techniques for CMB and other cosmological experiments.