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We test the statistical isotropy (SI) of the $E$-mode polarization of theCosmic Microwave Background (CMB) radiation observed by the Planck satelliteusing two statistics, namely, the $\alpha$ estimator that is derived from thecontour Minkowski Tensor (CMT), and the Directional statistic ($\mathcal{D}$statistic). The $\alpha$ estimator obtained from the CMT provides informationabout the alignment of structures and can be used to infer statisticalproperties such as Gaussianity and SI of random fields. The $\mathcal{D}$statistic is based on detecting preferred directionality shown by vectorsdefined by the field. We compute $\alpha$ and $\mathcal{D}$ statistic for thelow resolution component separated SMICA $E$-mode map of CMB polarization, andcompare with the values calculated using FFP10 SMICA simulations. We find goodagreement between the Planck data and SMICA simulations for both $\alpha$estimator and $\mathcal{D}$ statistic.

Application of Contour Minkowski Tensor and $\mathcal{D}$ Statistic to the Planck $E$-mode data