Minkowski Functionals of CMB polarisation intensity with Pynkowski: theory and application to Planck and future data

TL;DR

This paper extends Minkowski Functional analysis to CMB polarisation intensity, develops a software tool, applies it to Planck data, and forecasts its potential for future experiments to detect subtle non-Gaussian signals.

Contribution

It introduces a novel extension of Minkowski Functionals to CMB polarisation intensity and provides a publicly available software tool for this analysis.

Findings

No significant non-Gaussianity detected in Planck polarisation data.

The methodology is validated with simulations and applied to real data.

Forecasts suggest improved sensitivity for future experiments like LiteBIRD and Simons Observatory.

Abstract

The angular power spectrum of the Cosmic Microwave Background (CMB) anisotropies is a key tool to study the Universe. However, it is blind to the presence of non--Gaussianities and deviations from statistical isotropy, which instead can be detected with other statistics such as Minkowski Functionals (MFs). These tools have been applied to CMB temperature and $E$-mode anisotropies with no detection of deviations from Gaussianity and isotropy. In this work, we extend the MFs formalism to the CMB polarisation intensity, $P^2=Q^2+U^2$. We use the Gaussian Kinematic Formula to derive the theoretical predictions of MFs for Gaussian isotropic fields. We develop a software that computes MFs on $P^2$ HEALPix maps and apply it to simulations to verify the robustness of both theory and methodology. We then estimate MFs of $P^2$ maps from Planck, both in pixel space and needlet domain, comparing them with realistic simulations which include CMB and instrumental noise residuals. We find no significant deviations from Gaussianity or isotropy in Planck CMB polarisation intensity. However, MFs could play an important role in the analysis of CMB polarisation measurements from upcoming experiments with improved sensitivity. Therefore we forecast the ability of MFs applied to $P^2$ maps to detect much fainter non-Gaussian anisotropic signals than with Planck data for two future complementary experiments: the LiteBIRD satellite and the ground-based Simons Observatory. We publicly release the software to compute MFs in arbitrary scalar HEALPix maps as a fully-documented Python package called $\texttt{Pynkowski}$ (https://github.com/javicarron/pynkowski).