Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components

Abstract

Separation of the B component of a cosmic microwave background (CMB) polarization map from the much larger E component is an essential step in CMB polarimetry. For a map with incomplete sky coverage, this separation is necessarily hampered by the presence of "ambiguous" modes which could be either E or B modes. I present an efficient pixel-space algorithm for removing the ambiguous modes and separating the map into "pure" E and B components. The method, which works for arbitrary geometries, does not involve generating a complete basis of such modes and scales the cube of the number of pixels on the boundary of the map.

Minor changes to previous version. Accepted for publication in Phys. Rev. D

References in corpus (36)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Efficient Computation of CMB anisotropies in closed FRW models
• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• An All-Sky Analysis of Polarization in the Microwave Background
• Statistics of Cosmic Microwave Background Polarization
• Signature of Gravity Waves in Polarization of the Microwave Background
• A Probe of Primordial Gravity Waves and Vorticity
• Improved measurements of the temperature and polarization of the CMB from QUaD
• Determining Neutrino Mass from the CMB Alone
• Polarization Observations with the Cosmic Background Imager
• Benchmark Parameters for CMB Polarization Experiments
• DASI Three-Year Cosmic Microwave Background Polarization Results
• Analysis of CMB polarization on an incomplete sky
• E/B decomposition of finite pixelized CMB maps
• Probing neutrino masses with CMB lensing extraction
• CMB Polarization Systematics Due to Beam Asymmetry: Impact on Inflationary Science
• Pseudo-$C_{\ell }$ estimators which do not mix E and B modes
• Systematic errors in cosmic microwave background polarization measurements
• Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach
• A general solution to the E-B mixing problem
• New Measurements of Fine-Scale CMB Polarization Power Spectra from CAPMAP at Both 40 and 90 GHz
• Error analysis of quadratic power spectrum estimates for CMB polarization: sampling covariance
• Harmonic E/B decomposition for CMB polarization maps
• Weak Lensing of the CMB: Sampling Errors on B-Modes
• Separating E and B types of polarization on an incomplete sky
• CMB E/B decomposition of incomplete sky: a pixel space approach
• Cosmic Microwave Background Anisotropy Observing Strategy Assessment
• Systematic Errors in Cosmic Microwave Background Interferometry
• Pure pseudo-C_l estimators for CMB B-modes
• A wavelet-Galerkin algorithm of the E/B decomposition of CMB polarization maps
• E/B Separation in CMB Interferometry
• Separating E from B
• Sensitivity of a Bolometric Interferometer to the CMB power spectrum
• Bandwidth in bolometric interferometry
• Measuring CMB polarisation with the Planck mission

Cited by in corpus (21)

• Planck 2013 results. XXIII. Isotropy and statistics of the CMB
• Planck 2018 results. VII. Isotropy and Statistics of the CMB
• A unified pseudo-$C_{\ell }$ framework
• Hyper Suprime-Cam Year 3 Results: Cosmology from Cosmic Shear Power Spectra
• A minimal power-spectrum-based moment expansion for CMB B-mode searches
• Lensing Simulation and Power Spectrum Estimation for High Resolution CMB Polarization Maps
• Methods for pixel domain correction of EB leakage
• How to make a clean separation between CMB E and B modes with proper foreground masking
• 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
• E and B families of the Stokes parameters in the polarized synchrotron and thermal dust foregrounds
• Detection of relic gravitational waves in the CMB: Prospects for CMBPol mission
• Optimal and fast E/B separation with a dual messenger field
• Relations between three-point configuration space shear and convergence statistics
• 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
• Pure-mode correlation functions for cosmic shear and application to KiDS-1000
• Statistics of CMB polarization angles
• Fisher Matrix Optimization of Cosmic Microwave Background Interferometers