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

TL;DR

This paper introduces a method to analyze the shape and alignment of structures in Planck satellite data using Minkowski Tensors directly on the sphere, improving accuracy over previous stereographic projection methods.

Contribution

It extends Minkowski Tensors to curved spaces for direct sphere analysis, enabling more precise detection of alignments in CMB data without stereographic projection errors.

Findings

Good agreement between data and simulations within 1σ

No significant difference across most frequencies

Approximately 2σ discrepancy at 30 GHz, likely due to beam estimation issues

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 [29] to study the statistical isotropy of temperature and E mode data from the Planck satellite. The calculation in [29] 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 $\approx$ 1$\sigma$ . 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 Planck frequencies, except for the 30 GHz channel. For the 30 GHz channel we find $\approx$ 2$\sigma$ difference between the data and the simulations. This mild disagreement most likely originates from inaccurate estimation of the instrumental beam at 30 GHz.