Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach

TL;DR

This paper extends a formalism for estimating polarized CMB power spectra by incorporating cross-spectra from multiple maps, improving efficiency and accuracy on small angular scales, and demonstrating its effectiveness with realistic sky scans.

Contribution

It introduces an extended pure pseudo-power-spectrum formalism that includes cross-spectra, with detailed implementation and analysis of optimization and residual leakage effects.

Findings

The method is faster and more efficient than traditional optimal estimators.

It can reduce the variance of B-mode spectrum estimates to within a factor of 2 of the noise limit.

Effective on angular scales smaller than ~10 degrees, suitable for balloon-borne experiments.

Abstract

We extend the pure pseudo-power-spectrum formalism proposed recently in the context of the Cosmic Microwave Background polarized power spectra estimation by Smith (2006) to incorporate cross-spectra computed for multiple maps of the same sky area. We present an implementation of such a technique, paying particular attention to a calculation of the relevant window functions and mixing (mode-coupling) matrices. We discuss the relevance and treatment of the residual $E/B$ leakage for a number of considered sky apodizations as well as compromises and assumptions involved in an optimization of the resulting power spectrum uncertainty. In particular, we investigate the importance of a pixelization scheme, patch geometry, and sky signal priors used in apodization optimization procedures. In addition, we also present results derived for more realistic sky scans as motivated by the proposed balloon borne experiment EBEX. We conclude that the presented formalism thanks to its speed and efficiency can provide an interesting alternative to the CMB polarized power spectra estimators based on the optimal methods at least on angular scales smaller than ~10 degrees. In this regime, we find that it is capable of suppressing the total variance of the estimated $B$-mode spectrum to within a factor of ~2 of the variance due to only the sampling and noise uncertainty of the B-modes alone, as derived from the Fisher matrix approach.