Minkowski functionals of CMB polarization intensity with pynkowski: theory and application to Planck and future data

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 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 MF formalism to the CMB polarization 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 P2healpix 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 that include CMB and instrumental noise residuals. We find no significant deviations from Gaussianity or isotropy in Planck CMB polarization intensity. However, MFs could play an important role in the analysis of CMB polarization 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 pynkowski.