Analysis of CMB polarization on an incomplete sky

Abstract

The full sky cosmic microwave background polarization field can be decomposed into 'electric' and 'magnetic' components. Working in harmonic space we construct window functions that allow clean separation of the electric and magnetic modes from observations over only a portion of the sky. Our construction is exact for azimuthally symmetric patches, but should continue to perform well for arbitrary patches. From the window functions we obtain variables that allow for robust estimation of the magnetic component without risk of contamination from the probably much larger electric signal. For isotropic, uncorrelated noise the variables have a very simple diagonal noise correlation, and further analysis using them should be no harder than analysing the temperature field. For an azimuthally-symmetric patch, such as that obtained from survey missions when the galactic region is removed, the exactly-separated variables are fast to compute allowing us to estimate the magnetic signal that could be detected by the Planck satellite in the absence of non-galactic foregrounds. We also discuss the sensitivity of future experiments to tensor modes in the presence of a magnetic signal generated by weak lensing, and give lossless methods for analysing the electric polarization field in the case that the magnetic component is negligible.

27 pages, 8 figures. New appendix on weak signal detection and revised plots using a better statistic. Other changes to match version accepted by PRD. Sample source code now available at http://cosmologist.info/polar

References in corpus (1)

• The nature of the E-B decomposition of CMB polarization

Cited by in corpus (140)

• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• Weak Gravitational Lensing of the CMB
• Cosmology and Fundamental Physics with the Euclid Satellite
• Cosmology and fundamental physics with the Euclid satellite
• Cosmic Microwave Background Anisotropies
• A Cyclic Model of the Universe
• 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
• The Quest for B Modes from Inflationary Gravitational Waves
• Galaxy Clusters Selected with the Sunyaev-Zel'dovich Effect from 2008 South Pole Telescope Observations
• Relativistic cosmology and large-scale structure
• Likelihood Analysis of CMB Temperature and Polarization Power Spectra
• Gravitational lensing as a contaminant of the gravity wave signal in CMB
• Fast estimation of polarization power spectra using correlation functions
• Separation of Gravitational-Wave and Cosmic-Shear Contributions to Cosmic Microwave Background Polarization
• Hyper Suprime-Cam Year 3 Results: Cosmology from Cosmic Shear Power Spectra
• Benchmark Parameters for CMB Polarization Experiments
• Cosmic Microwave Background Fluctuations from Gravitational Waves: An Analytic Approach
• E/B decomposition of finite pixelized CMB maps
• Lensed CMB power spectra from all-sky correlation functions
• Weak lensing analysis in three dimensions
• Lensed CMB simulation and parameter estimation
• CMB temperature lensing power reconstruction
• Robust forecasts on fundamental physics from the foreground-obscured, gravitationally-lensed CMB polarization
• CMB Polarization Systematics Due to Beam Asymmetry: Impact on Inflationary Science
• Implications of the Cosmic Background Imager Polarization Data
• Planck pre-launch status: High Frequency Instrument polarization calibration
• CMB temperature and polarisation pseudo-Cl estimators and covariances
• Considerations in optimizing CMB polarization experiments to constrain inflationary physics
• Pseudo-$C_{\ell }$ estimators which do not mix E and B modes
• Maximum a posteriori CMB lensing reconstruction
• Systematic errors in cosmic microwave background polarization measurements
• Inflation versus Cyclic Predictions for Spectral Tilt
• Full-sky lensing shear at second order
• Forecasts for detecting the gravitational-wave memory effect with Advanced LIGO and Virgo
• Limits on the detectability of the CMB B-mode polarization imposed by foregrounds
• Bianchi Model CMB Polarization and its Implications for CMB Anomalies
• Error analysis of quadratic power spectrum estimates for CMB polarization: sampling covariance
• Dark Energy Survey Year 3 results: cosmological constraints from the analysis of cosmic shear in harmonic space
• The Lyth Bound Revisited
• Hybrid Estimation of CMB Polarization Power Spectra
• Demonstration of cosmic microwave background delensing using the cosmic infrared background
• B polarization of cosmic microwave background as a tracer of strings
• Disconnected pseudo-$C_{\ell }$ covariances for projected large-scale structure data
• Lensing of 21-cm Fluctuations by Primordial Gravitational Waves
• Observable primordial vector modes
• Measuring our peculiar velocity on the CMB with high-multipole off-diagonal correlations
• Geometry of weak lensing of CMB polarization
• QUIJOTE scientific results -- IV. A northern sky survey in intensity and polarization at 10-20GHz with the Multi-Frequency Instrument
• SPT-GMOS: A Gemini/GMOS-South Spectroscopic Survey of Galaxy Clusters in the SPT-SZ Survey
• Harmonic E/B decomposition for CMB polarization maps
• Cosmic 21-cm Delensing of Microwave Background Polarization and the Minimum Detectable Energy Scale of Inflation
• Cosmological parameters after WMAP5: forecasts for Planck and future galaxy surveys
• Scientific optimization of a ground-based CMB polarization experiment
• Separating E and B types of polarization on an incomplete sky
• Higher-order moments of the lensing shear and other spin two fields
• Detectability of tensor modes in the presence of foregrounds
• Relativistic wide-angle galaxy bispectrum on the light-cone
• A minimal power-spectrum-based moment expansion for CMB B-mode searches
• CMB-S4: Iterative Internal Delensing and $r$ Constraints
• Improved cosmic microwave background (de-)lensing using general spherical harmonic transforms
• Fast CMB Power Spectrum Estimation of Temperature and Polarisation with Gabor Transforms
• Statistical Isotropy of CMB Polarization Maps
• Probing the Universe on Gigaparsec Scales with Remote Cosmic Microwave Background Quadrupole Measurements
• CMB E/B decomposition of incomplete sky: a pixel space approach
• Detectability of Microwave Background Polarization
• Spider Optimization: Probing the Systematics of a Large Scale B-Mode Experiment
• Lensing Simulation and Power Spectrum Estimation for High Resolution CMB Polarization Maps
• On the road to discovery of relic gravitational waves: The TE and BB Correlations in the cosmic microwave background radiation
• The intrinsic B-mode polarisation of the Cosmic Microwave Background
• Likelihood methods for CMB experiments
• Weak lensing statistics from the Coyote Universe
• Methods for pixel domain correction of EB leakage
• Weak lensing generated by vector perturbations and detectability of cosmic strings
• How to make a clean separation between CMB E and B modes with proper foreground masking
• Small Aperture Telescopes for the Simons Observatory
• Full-sky formulae for weak lensing power spectra from total angular momentum method
• Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components
• Systematic Errors in Cosmic Microwave Background Interferometry
• Impact of modulation on CMB B-mode polarization experiments
• A 3D model for CO molecular line emission as a potential CMB polarization contaminant
• The large-scale polarization of the microwave background and foreground
• Optimal constraints on primordial gravitational waves from the lensed CMB
• Minkowski Functionals of CMB polarisation intensity with Pynkowski: theory and application to Planck and future data
• Separating polarized cosmological and galactic emissions for CMB B-mode polarization experiments
• Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses
• Detecting relic gravitational waves in the CMB: Comparison of different methods
• Wiener filtering and pure E/B decomposition of CMB maps with anisotropic correlated noise
• Reconstructing Patchy Reionization with Deep Learning
• Delensing the CMB with the cosmic infrared background: the impact of foregrounds
• Pure E and B polarization maps via Wiener filtering
• Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys
• The impact of extragalactic foregrounds on internal delensing of CMB B-mode polarization
• Spin-SILC: CMB polarisation component separation with spin wavelets
• Blind correction of the EB-leakage in the pixel domain
• Stable indications of relic gravitational waves in Wilkinson Microwave Anisotropy Probe data and forecasts for the Planck mission
• Robust and efficient CMB lensing power spectrum from polarization surveys
• Lyman-$\alpha$ Polarization Intensity Mapping
• Trade-off between angular resolution and straylight contamination in CMB anisotropy experiments. II. Straylight evaluation
• First attempt at measuring the CMB cross-polarization
• Cosmic microwave background polarization analysis
• E/B Separation in CMB Interferometry
• Real space lensing reconstruction using cosmic microwave background polarization
• Separating E from B
• CMB lensing reconstruction using cut sky polarization maps and pure-$B$ modes
• Low Scale Inflation at High Energy Colliders and Meson Factories
• CMB lensing with shear-only reconstruction on the full sky
• Model independent approaches to reionization in the analysis of upcoming CMB data
• Reconstructing Cosmic Polarization Rotation with ResUNet-CMB
• Analysis of NILC performance on B-modes data of sub-orbital experiments
• Exact joint likelihood of pseudo-$C_{\ell }$ estimates from correlated Gaussian cosmological fields
• Spider Optimization II: Optical, Magnetic and Foreground Effects
• Testing inflationary consistency relations by the potential CMB observations
• Delensing of Cosmic Microwave Background Polarization with machine learning
• Detection of relic gravitational waves in the CMB: Prospects for CMBPol mission
• CMB Optical Depth Measurements: Past, Present, Future
• Cosmological Constraints on the Very Low Frequency Gravitational-Wave Background
• Optimal and fast E/B separation with a dual messenger field
• Iterative map-making with two-level preconditioning for polarized Cosmic Microwave Background data sets
• Almanac: MCMC-based signal extraction of power spectra and maps on the sphere
• General solutions of the leakage in integral transforms and applications to the EB-leakage and detection of the cosmological gravitational wave background
• Testing Quadratic Maximum Likelihood estimators for forthcoming Stage-IV weak lensing surveys
• Lensing reconstruction from the cosmic microwave background polarization with machine learning
• A Constrained NILC method for CMB B mode observations
• The Large-Scale Polarization of the Microwave Foreground
• The Simons Observatory: Assessing the Impact of Dust Complexity on the Recovery of Primordial $B$-modes
• Smoothing methods comparison for CMB E- and B-mode separation
• An Accurate Reconstruction of CMB E Mode Signal over Large Angular Scales using Prior Information of CMB Covariance Matrix in ILC Algorithm
• Foreground removal from WMAP 7yr polarization maps using an MLP neural network
• Measuring CMB polarisation with the Planck mission
• Red Density Perturbations and Inflationary Gravitational Waves
• A comprehensive study of Modulation effects on CMB Polarization
• 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
• Cosmic Microwave Background anisotropies: the power spectrum and beyond
• Fisher Matrix Optimization of Cosmic Microwave Background Interferometers
• Pixel domain multi-resolution minimum variance painting of CMB maps
• Requirements on bandpass resolution and measurement precision for LiteBIRD
• Local bandpower diagnostics for the hemispherical power asymmetry in CMB E-mode polarization
• Euclid: Optimising tomographic redshift binning for 3$\times$2pt power spectrum constraints on dark energy