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Minkowski Tensors are tensorial generalizations of the scalar MinkowskiFunctionals. Due to their tensorial nature they contain additionalmorphological information of structures, in particular about shape andalignment, in comparison to the scalar Minkowski functionals. They haverecently been used [29] to study the statistical isotropy of temperature and Emode data from the Planck satellite. The calculation in [29] relied onstereographic projection of the fields to extract the shape and alignmentinformation. In this work, we calculate Minkowski Tensors directly on thesphere and compute the net alignment in the data, based on a recent work thatextends the definition of Minkowski Tensors to random fields on curved spaces.This method circumvents numerical errors that can be introduced by thestereographic projection. We compare the resulting net alignment parametervalues obtained from the frequency coadded CMB temperature data cleaned by theSMICA pipeline, to those obtained from simulations that include instrumentalbeam effects and residual foreground and noise. We find very good agreementbetween the two within $\approx$ 1$\sigma$ . We further compare the alignmentsobtained from the beam-convolved CMB maps at individual Planck frequencies tothose in the corresponding simulations. We find no significant differencebetween observed data and simulations across all Planck frequencies, except forthe 30 GHz channel. For the 30 GHz channel we find $\approx$ 2$\sigma$difference between the data and the simulations. This mild disagreement mostlikely originates from inaccurate estimation of the instrumental beam at 30GHz.

Search for anomalous alignments of structures in Planck data using Minkowski Tensors