New estimates of the CMB angular power spectra from the WMAP 5 yrs low resolution data

TL;DR

This paper applies a quadratic maximum likelihood estimator to WMAP 5-year data to accurately estimate the CMB angular power spectra at large scales, providing new error estimates and confirming consistency with previous results.

Contribution

It introduces a novel application of QML to WMAP data for large-scale spectra, with a comprehensive likelihood analysis that treats covariances without approximation.

Findings

Estimated all six CMB power spectra with new error bars.

Found the temperature quadrupole close to the ΛCDM best-fit within 2 sigma.

Confirmed B-modes and parity odd signals are consistent with zero.

Abstract

A Quadratic Maximum Likelihood (QML) estimator is applied to the WMAP 5 year low resolution maps to compute the CMB angular power spectra at large scales for both temperature and polarization. Estimates and error bars for the six angular power spectra are provided and compared, when possible, to those obtained by the WMAP team, without finding any inconsistency. The conditional likelihood slices are also computed for the $C_{\ell}$ of all the six power spectra from $\ell =2$ to 10 through a pixel based likelihood code. Both the codes treat the covariance for $(T,Q,U)$ in a single matrix without employing any approximation. The inputs of both the codes (foreground reduced maps and related covariances) are provided by the WMAP team. The peaks of the likelihood slices are always consistent with the QML estimates within the error bars, however an excellent agreement occurs when the QML estimates are used as fiducial power spectrum instead of the best-fit theoretical power spectrum. By the full computation of the conditional likelihood on the estimated spectra, the value of the temperature quadrupole $C_{\ell=2}^{TT}$ is found to be less than $2 \sigma$ away from the WMAP 5 yrs $\Lambda$CDM best-fit value. The $BB$ spectrum is found well consistent with zero and upper limits on the B-modes are provided. The parity odd signals $TB$ and $EB$ are found consistent with zero.