BICEP2 / Keck Array VII: Matrix based E/B Separation applied to BICEP2 and the Keck Array

Abstract

A linear polarization field on the sphere can be uniquely decomposed into an E-mode and a B-mode component. These two components are analytically defined in terms of spin-2 spherical harmonics. Maps that contain filtered modes on a partial sky can also be decomposed into E-mode and B-mode components. However, the lack of full sky information prevents orthogonally separating these components using spherical harmonics. In this paper, we present a technique for decomposing an incomplete map into E and B-mode components using E and B eigenmodes of the pixel covariance in the observed map. This method is found to orthogonally define E and B in the presence of both partial sky coverage and spatial filtering. This method has been applied to the BICEP2 and the Keck Array maps and results in reducing E to B leakage from LCDM E-modes to a level corresponding to a tensor-to-scalar ratio of $r<1\times 10^{-4}$.

21 pages, 23 figures, minor updates to reflect accepted version

References in corpus (9)

• BICEP2 / Keck Array VI: Improved Constraints On Cosmology and Foregrounds When Adding 95 GHz Data From Keck Array
• Polarization Observations with the Cosmic Background Imager
• CMB Polarization Systematics Due to Beam Asymmetry: Impact on Inflationary Science
• BICEP2 / Keck Array V: Measurements of B-mode Polarization at Degree Angular Scales and 150 GHz by the Keck Array
• Antenna-coupled TES bolometers used in BICEP2, Keck array, and SPIDER
• Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach
• A general solution to the E-B mixing problem
• Testable polarization predictions for models of CMB isotropy anomalies
• BICEP2 III: Instrumental Systematics

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• BICEP2 / Keck Array x: Constraints on Primordial Gravitational Waves using Planck, WMAP, and New BICEP2/Keck Observations through the 2015 Season
• CMB-S4: Forecasting Constraints on Primordial Gravitational Waves
• BICEP2 / Keck Array VIII: Measurement of gravitational lensing from large-scale B-mode polarization
• A Measurement of the Degree Scale CMB B-mode Angular Power Spectrum with POLARBEAR
• BICEP2 / Keck Array IX: New Bounds on Anisotropies of CMB Polarization Rotation and Implications for Axion-Like Particles and Primordial Magnetic Fields
• A minimal power-spectrum-based moment expansion for CMB B-mode searches
• BICEP / Keck XVII: Line of Sight Distortion Analysis: Estimates of Gravitational Lensing, Anisotropic Cosmic Birefringence, Patchy Reionization, and Systematic Errors
• BICEP2 / Keck Array XI: Beam Characterization and Temperature-to-Polarization Leakage in the BK15 Dataset
• Full-sky Models of Galactic Microwave Emission and Polarization at Sub-arcminute Scales for the Python Sky Model
• BICEP / Keck XVI: Characterizing Dust Polarization through Correlations with Neutral Hydrogen
• Making maps of Cosmic Microwave Background polarization for B-mode studies: the POLARBEAR example
• Impact of nonlinear growth of the large-scale structure on CMB B-mode delensing
• A Simulation-Based Method for Correcting Mode Coupling in CMB Angular Power Spectra
• Controlling systematics in ground-based CMB surveys with partial boresight rotation
• On the regularity of the covariance matrix of a discretized scalar field on the sphere
• The Simons Observatory: Validation of reconstructed power spectra from simulated filtered maps for the Small Aperture Telescope survey
• Deprojecting beam systematics for next-generation CMB B-mode searches
• The Simons Observatory: laboratory beam characterization for the first small aperture telescope
• BICEP/Keck XXI: Constraints on Early-Universe Parity Violation from Multipole-Dependent Birefringence