New estimates of the CMB angular power spectra from theWMAP5 year low-resolution data

A quadratic maximum likelihood (QML) estimator is applied to the <it>Wilkinson Microwave Anisotropy Probe</it> (<it>WMAP</it>) 5 year low-resolution maps to compute the cosmic microwave background angular power spectra (APS) at large scales for both temperature and polarization. Estimates and error bars for the six APS are provided up to ℓ= 32 and compared, when possible, to those obtained by the <it>WMAP</it> team, without finding any inconsistency. The conditional likelihood slices are also computed for the <it>C</it><inf>ℓ</inf> of all the six power spectra from ℓ= 2 to 10 through a pixel-based likelihood code. Both the codes treat the covariance for (<it>T</it>, <it>Q</it>, <it>U</it>) in a single matrix without employing any approximation. The inputs of both the codes (foreground-reduced maps, related covariances and masks) are provided by the <it>WMAP</it> 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 a fiducial power spectrum instead of the best-fitting theoretical power spectrum. By the full computation of the conditional likelihood on the estimated spectra, the value of the temperature quadrupole <it>C</it><it>TT</it><inf>ℓ=2</inf> is found to be less than 2σ away from the <it>WMAP</it> 5 year Λ cold dark matter best-fitting value. The <it>BB</it> spectrum is found to be well consistent with zero, and upper limits on the B modes are provided. The parity odd signals <it>TB</it> and <it>EB</it> are found to be consistent with zero.