Quadratic estimator for CMB cross-correlation

TL;DR

This paper extends the quadratic maximum likelihood estimator to cross-correlation for CMB analysis, effectively removing noise bias and reducing systematic effects, especially in polarization measurements across various experiments.

Contribution

It introduces a novel cross-correlation quadratic estimator that mitigates noise bias and systematic effects in CMB polarization data analysis.

Findings

Estimator effectively removes noise bias in simulations.

Reduces variance increase from polarization leakage.

Performs better than pseudo-spectrum methods on large scales.

Abstract

The Quadratic Maximum Likelihood estimator can be used to reconstruct the Cosmic Microwave Background (CMB) power spectra with minimal error bars. Still, it requires an accurate estimate of the datasets noise covariance matrix in order to be corrected for spurious bias. We describe an extension of this method to cross-correlation, thus removing noise bias and mitigating the impact of systematic effects, providing they are uncorrelated. This estimator is tested on two simulation surveys at large and intermediate angular scales, respectively corresponding to satellite and ground-based CMB experiments. The analysis focuses on polarization maps, over a wide range of noise levels from 0.1 to 50 muK.arcmin. We show how this estimator minimizes the increase of variance due to polarization leakage between E and B modes. We compare this method with the pure pseudo-spectrum formalism which is computationally faster but less optimal, especially on large angular scales.