Application of Contour Minkowski Tensor and $\mathcal{D}$ Statistic to
  the Planck $E$-mode data
  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 $\alpha$ estimator that is derived from the
contour Minkowski Tensor (CMT), and the Directional statistic ($\mathcal{D}$
statistic). The $\alpha$ estimator obtained from the CMT provides information
about 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. We compute $\alpha$ and $\mathcal{D}$ statistic for the
low resolution component separated SMICA $E$-mode map of CMB polarization, and
compare with the values calculated using FFP10 SMICA simulations. We find good
agreement between the Planck data and SMICA simulations for both $\alpha$
estimator and $\mathcal{D}$ statistic.
