A general solution to the E-B mixing problem

Abstract

We derive a general ansatz for optimizing pseudo-C_l estimators used to measure CMB anisotropy power spectra, and apply it to the recently-proposed pure pseudo-C_l formalism, to obtain an estimator which achieves near-optimal B-mode power spectrum errors for any specified noise distribution while minimizing leakage from ambiguous modes. Our technique should be relevant for upcoming CMB polarization experiments searching for B-mode polarization. We compare our technique both to the theoretical limits based on a full Fisher matrix calculation and to the standard pseudo-C_l technique. We demonstrate it by applying it to a fiducial survey with realistic inhomogeneous noise, complex boundaries, point source masking, and noise level comparable to what is expected for next generation experiments (~5.75 uK-arcmin). For such an experiment our technique could improve the constraints on the amplitude of a gravity wave background by over a factor of ten compared to what could be obtained using ordinary pseudo-C_l, coming quite close to saturating the theoretical limit. Constraints on the amplitude of the lensing B-modes are improved by about a factor of 3.

25 pages, 10 figures, submitted to PRD

References in corpus (15)

• 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
• Power Spectrum Analysis of Three-Dimensional Redshift Surveys
• A Probe of Primordial Gravity Waves and Vorticity
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Gravitational Lensing Effect on Cosmic Microwave Background Polarization
• Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
• The Pseudo-$C_l$ method: Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
• E/B decomposition of finite pixelized CMB maps
• Pseudo-$C_{\ell }$ estimators which do not mix E and B modes
• Cosmological Information from Lensed CMB Power Spectra
• The EBEX Experiment
• Error analysis of quadratic power spectrum estimates for CMB polarization: sampling covariance
• Hybrid Estimation of CMB Polarization Power Spectra

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