The nature of non-Gaussianity and statistical isotropy of the 408 MHz Haslam synchrotron map

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. Using scalar Minkowski functionals and their tensorial generalization known as Minkowski tensors, we analyze the statistical properties of one of the major foreground components, namely the Galactic synchrotron given by the full sky 408 MHz Haslam map. We focus on understanding the nature of non-Gaussianity and statistical isotropy of the cooler regions of the map as a function of angular scale. 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. However, they remain significantly high, of order 3.3$\sigma$, at the smallest angular scales relevant for the Haslam map. We carry out a detailed examination of the non-Gaussian nature using the generalized skewness and kurtosis cumulants that arise in the perturbative expansion of Minkowski functionals for weakly non-Gaussian fields. We find that the leading sources of non-Gaussianity are the kurtosis terms which are considerably larger than the skewness terms at all angular scales. Further, for the cooler regions of the Haslam map, we find that the non-Gaussian deviations of the Minkowski functionals can be well explained by the perturbative expansion up to second-order (up to kurtosis terms), with first-order terms being sub-dominant. Lastly, we test the statistical isotropy of the Haslam map and find that it becomes increasingly more isotropic at smaller scales.