Application of the contour Minkowski tensor and D statistic to the Planck E -mode data

Abstract

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 α estimator that is derived from the contour Minkowski tensor (CMT), and the directional statistic ( D statistic). The α estimator provides information about the alignment of structures and can be used to infer statistical properties such as Gaussianity and SI of random fields. The D statistic is based on detecting preferred directionality shown by vectors defined by the field. We compute α and 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 α estimator and D statistic.