Minkowski Functionals of CMB polarisation intensity with Pynkowski: theory and application to Planck and future data
arxiv(2022)
摘要
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 (https://github.com/javicarron/pynkowski).
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