Statistical properties of Galactic synchrotron temperature and polarization maps -- a multi-frequency comparison

Understanding the statistical properties of synchrotron emission from our Galaxy is valuable from the perspective of observations targeting signals of cosmological origin, as well as for understanding physical processes in our Galaxy. In this work, we extend the analysis of arXiv:2104.00419v2 to -- (a) all-sky observed maps of total foreground emissions at different frequencies provided by WMAP, Planck and Stockert-Villa, (b) component separated synchrotron temperature maps provided by WMAP, Planck and BeyondPlanck, and (c) component separated polarization maps provided by WMAP and Planck. The tools we use are Minkowski functionals and tensors. Our main goals are twofold. First, we determine the variation of morphological properties of the total foreground maps with observing frequency and compare with simulations. This elucidates how the morphology varies due to the relative dominance of different foreground components at different frequencies. Next, we analyze the nature of non-Gaussianity and statistical isotropy of synchrotron fluctuations on smaller scales using various component separated synchrotron temperature and polarization maps. We find that all maps exhibit kurtosis non-Gaussianity, in agreement with the Haslam map. This result can be an important input for the modelling of small-scale synchrotron fluctuations for component separation pipelines. This also suggests that residual synchrotron contamination in CMB will manifest as kurtosis. Studying different component separated maps, we find that BeyondPlanck and WMAP MCMC-e agree well with Haslam at all scales. The other maps show 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.