Abstract:
Minkowski Tensors are tensorial generalizations of the scalar Minkowski Functionals. Due to their tensorial nature they contain additional morphological information of structures, in particular about shape and alignment, in comparison to the scalar Minkowski functionals. They have recently been used [1] to study the statistical isotropy of temperature and E mode data from the Planck satellite. The calculation in [2] relied on stereographic projection of the fields to extract the shape and alignment information. In this work, we calculate Minkowski Tensors directly on the sphere and compute the net alignment in the data, based on a recent work that extends the definition of Minkowski Tensors to random fields on curved spaces. This method circumvents numerical errors that can be introduced by the stereographic projection. We compare the resulting net alignment parameter values obtained from the frequency coadded CMB temperature data cleaned by the SMICA pipeline, to those obtained from simulations that include instrumental beam effects and residual foreground and noise. We find very good agreement between the two within ≈ 1σ. We further compare the alignments obtained from the beam-convolved CMB maps at individual Planck frequencies to those in the corresponding simulations. We find no significant difference between observed data and simulations across all {\rm Planck} frequencies, except for the 30 GHz channel. For the 30 GHz channel we find ≈ 2 σ difference between the data and the simulations. This mild disagreement could originate from an inaccurate estimation of the instrumental beam at 30 GHz.
