Separating E and B types of polarization on an incomplete sky

Abstract

Detection of magnetic-type ($B$-type) polarization in the Cosmic Microwave Background (CMB) radiation plays a crucial role in probing the relic gravitational wave (RGW) background. In this paper, we propose a new method to deconstruct a polarization map on an incomplete sky in real space into purely electric and magnetic polarization type maps, $\mathcal{E}(\hat{\gamma })$ and $\mathcal{B}(\hat{\gamma })$, respectively. The main properties of our approach are as follows: Firstly, the fields $\mathcal{E}(\hat{\gamma })$ and $\mathcal{B}(\hat{\gamma })$ are constructed in real space with a minimal loss of information. This loss of information arises due to the removal of a narrow edge of the constructed map in order to remove various numerical errors, including those arising from finite pixel size. Secondly, this method is fast and can be efficiently applied to high resolution maps due to the use of the fast spherical harmonics transformation. Thirdly, the constructed fields, $\mathcal{E}(\hat{\gamma })$ and $\mathcal{B}(\hat{\gamma })$, are scalar fields. For this reason various techniques developed to deal with temperature anisotropy maps can be directly applied to analyze these fields. As a concrete example, we construct and analyze an unbiased estimator for the power spectrum of the $B$-mode of polarization $C_{\ell }^{BB}$. Basing our results on the performance of this estimator, we discuss the RGW detection ability of two future ground-based CMB experiments, QUIET and POLARBEAR.

43 pages, 15 figures, 1 table. The finial version, will appear in PRD

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• Full-sky ray-tracing simulation of weak lensing using ELUCID simulations: exploring galaxy intrinsic alignment and cosmic shear correlations
• Methods for pixel domain correction of EB leakage
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• Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components
• Efficiency of pseudo-spectrum methods for estimation of Cosmic Microwave Background B-mode power spectrum
• CMB EB and TB cross-spectrum estimation via pseudo-spectrum techniques
• Probing the statistical properties of CMB $B$-mode polarization through Minkowski Functionals
• Wiener filtering and pure E/B decomposition of CMB maps with anisotropic correlated noise
• Pure E and B polarization maps via Wiener filtering
• Blind correction of the EB-leakage in the pixel domain
• Real space lensing reconstruction using cosmic microwave background polarization
• Analysis of NILC performance on B-modes data of sub-orbital experiments
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Scalar Perturbations in Synchronous Gauge
• Testing inflationary consistency relations by the potential CMB observations
• Detection of relic gravitational waves in the CMB: Prospects for CMBPol mission
• Fingerprint of Galactic Loop I on polarized microwave foregrounds
• Optimal and fast E/B separation with a dual messenger field
• Foreground removal with ILC methods for AliCPT-1
• Fast scalar quadratic maximum likelihood estimators for the CMB B-mode power spectrum
• Scalar quadratic maximum likelihood estimators for the CMB cross power spectrum
• Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis
• Forecast of CMB TB and EB correlations for AliCPT-1
• Detecting the tensor-to-scalar ratio with the pure pseudospectrum reconstruction of $B$-mode
• Smoothing methods comparison for CMB E- and B-mode separation
• Cosmic Bandits: Exploration versus Exploitation in CMB B-Mode Experiments
• Statistics of the CMB polarised anisotropies
• Forecasts of effects of beam systematics and deprojection on the third-generation ground-based cosmic microwave background experiment
• Reconstruction of full sky CMB $\mathbf{E}$ and $\mathbf{B}$ modes spectra removing $\mathbf{E}$-to-$\mathbf{B}$ leakage from partial sky using deep learning
• From top-hat masking to smooth transitions: P-filter and its application to polarized microwave sky maps
• Fisher Matrix Optimization of Cosmic Microwave Background Interferometers
• Forecasts of constraining isotropic cosmic birefringence on AliCPT-1