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.
