Scalar quadratic maximum likelihood estimators for the CMB cross power spectrum

TL;DR

This paper introduces a new scalar quadratic maximum likelihood estimator for the CMB cross power spectrum that significantly reduces computational costs while maintaining optimal estimation accuracy, aiding parity tests and systematics diagnosis.

Contribution

The paper presents the QML-SZ estimator, a novel unbiased method combining E-B separation with scalar QML for efficient cross power spectrum estimation.

Findings

Computational cost reduced by nearly an order of magnitude.

Estimation accuracy comparable to traditional QML methods.

Faster processing enables large-scale CMB data analysis.

Abstract

Estimating the cross-correlation power spectra of cosmic microwave background (CMB), in particular, the T B and EB spectra, is important for testing parity symmetry in cosmology and diagnosing insidious instruments systematics. The Quadratic Maximum Likelihood (QML) estimator provides the optimal estimates of power spectra, but it is computationally very expensive. The hybrid pseudo-Cl estimator is computationally fast but performs poorly on large scales. As a natural extension of previous work (Chen et al. 2021), in this article, we present a new unbiased estimator based on the Smith-Zaldarriaga (SZ) approach of E-B separation and scalar QML approach to reconstruct the cross-correlation power spectrum, called QML-SZ estimator. Our new estimator relies on the ability to construct scalar maps, which allows us to use a scalar QML estimator to obtain the cross-correlation power spectrum. By reducing the pixel number and algorithm complexity, the computational cost is nearly one order of magnitude smaller and the running time is nearly two orders of magnitude faster in the test situations.