CMB E/B decomposition of incomplete sky: a pixel space approach

Abstract

CMB polarization signal may be decomposed into gradient-like (E) and curl-like (B) mode. We have investigated E/B decomposition in pixel space. We find E/B mixing due to incomplete sky is localized in pixel-space, and negligible in the regions far away from the masked area. By estimating the expected local leakage power, we have diagnosed ambiguous pixels. Our criteria for ambiguous pixels (i.e. r_c) is associated with the tensor-to-scalar ratio of B mode power spectrum, which the leakage power is comparable to. By setting r_c to a lower value, we may reduce leakage level, but reduce sky fraction at the same time. Therefore, we have solved \partial ΔC_l/\partial r_c=0, and obtained the optimal r_c, which minimizes the estimation uncertainty, given a foreground mask and noise level. We have applied our method to a simulated map blocked by a foreground (diffuse + point source) mask. Our simulation shows leakage power is smaller than primordial (i.e. unlensed) B mode power spectrum of tensor-to-scalar ratio r\sim 10^{-3} at wide range of multipoles (50\lesssim l \lesssim 2000), while allowing us to retain sky fraction ~ 0.48.

v2: the point of the method strengthened, v3: criteria for ambiguous pixels rigorously derived, v4: matched with the accepted version in A&A (minor change), v5: typos corrected

References in corpus (31)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• An All-Sky Analysis of Polarization in the Microwave Background
• Statistics of Cosmic Microwave Background Polarization
• DASI First Results: A Measurement of the Cosmic Microwave Background Angular Power Spectrum
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Detection of Polarization in the Cosmic Microwave Background using DASI
• Estimating the Power Spectrum of the Cosmic Microwave Background
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectra
• Cosmological Parameter Extraction from the First Season of Observations with DASI
• Improved measurements of the temperature and polarization of the CMB from QUaD
• Gravitational lensing as a contaminant of the gravity wave signal in CMB
• DASI Three-Year Cosmic Microwave Background Polarization Results
• Analysis of CMB polarization on an incomplete sky
• The Pseudo-$C_l$ method: Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
• Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
• E/B decomposition of finite pixelized CMB maps
• Second and third season QUaD CMB temperature and polarization power spectra
• Measuring Polarization with DASI
• Pseudo-$C_{\ell }$ estimators which do not mix E and B modes
• Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach
• Limits on the detectability of the CMB B-mode polarization imposed by foregrounds
• CMB Polarization Experiments
• First season QUaD CMB temperature and polarization power spectra
• Hybrid Estimation of CMB Polarization Power Spectra
• Correlation Functions of CMB Anisotropy and Polarization
• QUaD: A High-Resolution Cosmic Microwave Background Polarimeter
• Experiment Design and First Season Observations with the Degree Angular Scale Interferometer
• Harmonic E/B decomposition for CMB polarization maps
• Efficient Power Spectrum Estimation for High Resolution CMB Maps
• Direct reconstruction of spherical harmonics from interferometer observations of the CMB polarization
• Optimizing interferometer experiments for CMB B mode measurement

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• Performance forecasts for the primordial gravitational wave detection pipelines for AliCPT-1
• Weak lensing statistics from the Coyote Universe
• Methods for pixel domain correction of EB leakage
• How to make a clean separation between CMB E and B modes with proper foreground masking
• 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
• Analysis of NILC performance on B-modes data of sub-orbital experiments
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• Testing inflationary consistency relations by the potential CMB observations
• Optimal and fast E/B separation with a dual messenger field
• Fingerprint of Galactic Loop I on polarized microwave foregrounds
• Detection of relic gravitational waves in the CMB: Prospects for CMBPol mission
• Scalar quadratic maximum likelihood estimators for the CMB cross power spectrum
• Isotropy-Violation Diagnostics for $B$-mode Polarization Foregrounds to the Cosmic Microwave Background
• A pseudo-spectrum analysis of galaxy-galaxy lensing
• Almanac: MCMC-based signal extraction of power spectra and maps on the sphere
• Fast scalar quadratic maximum likelihood estimators for the CMB B-mode power spectrum
• Detecting the tensor-to-scalar ratio with the pure pseudospectrum reconstruction of $B$-mode
• Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis
• Smoothing methods comparison for CMB E- and B-mode separation
• From top-hat masking to smooth transitions: P-filter and its application to polarized microwave sky maps
• CMB delensing with deep learning