Statistical Isotropy of the CMB E-mode signal
  We test the statistical isotropy (SI) of the $E$-mode polarization of the
cosmic microwave background (CMB) radiation observed by the Planck satellite
using two statistics, namely, the contour Minkowski Tensor (CMT) and the
Directional statistic ($\mathcal{D}$ statistic). The parameter $\alpha$
obtained from the CMT provides information of the alignment of structures and
can be used to infer statistical properties such as Gaussianity and SI of
random fields. The $\mathcal{D}$ statistic is based on detecting preferred
directionality shown by vectors defined by the field. These two tests are
complementary to each other in terms of sensitivity at different angular
scales. The CMT is sensitive towards small-scale information present in the CMB
map while $\mathcal{D}$ statistic is more sensitive at large-scales. We compute
$\alpha$ and $\mathcal{D}$ statistic for the observed $E$-mode of CMB
polarization, focusing on the SMICA maps, and compare with the values
calculated using FFP10 SMICA simulations which contain both CMB and noise. We
find good agreement between the observed data and simulations. Further, in
order to specifically analyze the CMB signal in the data, we compare the values
of the two statistics obtained from the observed Planck data with the values
obtained from isotropic simulations having the same power spectrum, and from
SMICA noise simulations. We find no statistically significant deviation from SI
using the $\alpha$ parameter. From $\mathcal{D}$ statistic we find that the
data shows slight deviation from SI at large angular scales.
