CMB EB and TB cross-spectrum estimation via pseudo-spectrum techniques

TL;DR

This paper develops and compares pseudo-spectrum techniques for estimating the EB and TB cross-spectra of CMB maps, aiming to improve detection of parity violations or systematics in limited sky observations.

Contribution

Introduces three unbiased estimators for CMB polarization spectra using pseudo-spectrum methods and assesses their performance through extensive simulations.

Findings

Hybrid estimator yields smallest error bars for EB and TB spectra.

Pure estimation of both E and B modes increases EB error by no more than 30%.

Uncertainties are within a factor of 1.4 to 2 of Fisher estimates for various spectra.

Abstract

We discuss methods for estimating EB and TB spectra of the Cosmic Microwave Background anisotropy maps covering limited sky area. Such odd-parity correlations are expected to vanish whenever parity is not broken. As this is indeed the case in the standard cosmologies, any evidence to the contrary would have a profound impact on our theories of the early Universe. Such correlations could also become a sensitive diagnostic of some particularly insidious instrumental systematics. In this work we introduce three different unbiased estimators based on the so-called standard and pure pseudo-spectrum techniques and later assess their performance by means of extensive Monte Carlo simulations performed for different experimental configurations. We find that a hybrid approach combining a pure estimate of B-mode multipoles with a standard one for E-mode (or T) multipoles, leads to the smallest error bars for both EB (or TB respectively) spectra as well as for the three other polarization-related angular power spectra i.e. EE, BB and TE$. However, if both E and B multipoles are estimated using the pure technique the loss of precision for the EB spectrum is not larger than ~30%. Moreover, for the experimental configurations considered here, the statistical uncertainties -- due to sampling variance and instrumental noise -- of the pseudo-spectrum estimates is at most a factor ~1.4 for TT, EE and TE spectra and a factor ~2 for BB, TB and EB spectra, higher than the most optimistic Fisher estimate of the variance.