The nature of the E-B decomposition of CMB polarization

Abstract

We present a derivation of the transformation between the Q and U Stokes parameters and the E and B scalar and pseudo-scalar fields. We emphasize the geometrical properties that such transformation must satisfy. We present the E and B decomposition of some simple maps and of a model for a supernova remnant. We discuss the relative amplitudes of the E and B components and argue that for generic random maps E and B should have roughly the same amplitudes.

8 pages, 8 figures

References in corpus (1)

• How to measure CMB polarization power spectra without losing information

Cited by in corpus (60)

• Detection of Polarization in the Cosmic Microwave Background using DASI
• The Quest for B Modes from Inflationary Gravitational Waves
• Measurements of the E-Mode Polarization and Temperature-E-Mode Correlation of the CMB from SPT-3G 2018 Data
• Fast estimation of polarization power spectra using correlation functions
• Measurements of the Temperature and E-Mode Polarization of the CMB from 500 Square Degrees of SPTpol Data
• DASI Three-Year Cosmic Microwave Background Polarization Results
• Analysis of CMB polarization on an incomplete sky
• E/B decomposition of finite pixelized CMB maps
• Measurements of Sub-degree B-mode Polarization in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data
• Measurements of B-mode Polarization of the Cosmic Microwave Background from 500 Square Degrees of SPTpol Data
• Measurement of the Crab nebula polarization at 90 GHz as a calibrator for CMB experiments
• The Origin of Parity Violation in Polarized Dust Emission and Implications for Cosmic Birefringence
• Measurements of E-Mode Polarization and Temperature-E-Mode Correlation in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data
• Harmonic E/B decomposition for CMB polarization maps
• Dust polarization and ISM turbulence
• Dust Polarization Maps from TIGRESS: E/B power asymmetry and TE correlation
• The Power Spectra of Polarized, Dusty Filaments
• Extracting cosmic microwave background polarisation from satellite astrophysical maps
• Elliptical Beams in CMB Temperature and Polarization Anisotropy Experiments: An Analytic Approach
• Probing the Universe on Gigaparsec Scales with Remote Cosmic Microwave Background Quadrupole Measurements
• Detectability of Microwave Background Polarization
• Constraining the Stochastic Gravitational Wave Background with Photometric Surveys
• The Simons Observatory: Galactic Science Goals and Forecasts
• Extragalactic magnetism with SOFIA (Legacy Program) -- II: A magnetically-driven flow in the starburst ring of NGC 1097
• Planck intermediate results. XXXVIII. E- and B-modes of dust polarization from the magnetized filamentary structure of the interstellar medium
• Efficiency of pseudo-spectrum methods for estimation of Cosmic Microwave Background B-mode power spectrum
• Frequency dependence of the thermal dust $E/B$ ratio and $EB$ correlation: insights from the spin-moment expansion
• Magnetic Misalignment of Interstellar Dust Filaments
• Cosmic Microwave Background Polarisation: foreground contrast and component separation
• The large-scale polarization of the microwave background and foreground
• Is there a left-handed magnetic field in the solar neighborhood? Exploring helical magnetic fields in the interstellar medium through dust polarization power spectra
• Separating polarized cosmological and galactic emissions for CMB B-mode polarization experiments
• Single frequency CMB B-mode inference with realistic foregrounds from a single training image
• Signatures of Pseudoscalar Photon Mixing in CMB Radiation
• Wiener filtering and pure E/B decomposition of CMB maps with anisotropic correlated noise
• Foreground model recognition through Neural Networks for CMB B-mode observations
• First attempt at measuring the CMB cross-polarization
• Lyman-$\alpha$ Polarization Intensity Mapping
• A new perspective on turbulent Galactic magnetic fields through comparison of linear polarisation decomposition techniques
• Real-space computation of $E$/$B$-mode maps I: Formalism, Compact Kernels, and Polarized Filaments
• An angular power spectrum analysis of the DRAO 1.4 GHz polarization survey: implications for CMB observations
• The link between E-B polarization modes and gas column density from interstellar dust emission
• Filamentary Dust Polarization and the Morphology of Neutral Hydrogen Structures
• Morphology of CMB fields -- effect of weak gravitational lensing
• Optimal and fast E/B separation with a dual messenger field
• Generative Models of Multi-channel Data from a Single Example -- Application to Dust Emission
• Sensitivity of a Bolometric Interferometer to the CMB power spectrum
• Power Spectra of CMB Polarization by Scattering in Clusters
• CMB Polarization as complementary information to anisotropies
• Reassessing Dust's Role in Forming the CMB
• Polarization power spectra and dust cloud morphology
• A multifrequency angular power spectrum analysis of the Leiden polarization surveys
• Detecting the tensor-to-scalar ratio with the pure pseudospectrum reconstruction of $B$-mode
• Separation of foreground and background signals in single frequency measurements of the CMB Polarization
• The effect of cosmic variance on the characteristics of dust polarization power spectra
• Impact of intrinsic polarisation of Sgr A* historical flares on (polarisation) properties of their X-ray echoes
• A Pop III generated dust screen at z~16
• A New Upper Limit on the Polarization of the Cosmic Microwave Background Radiation
• Lyman-$\alpha$ polarization from cosmological ionization fronts: II. Implications for intensity mapping
• Weighting CMB and Galactic synchrotron polarisation