A Reanalysis of the 3 Year Wilkinson Microwave Anisotropy Probe Temperature Power Spectrum and Likelihood

We analyze the 3 yr Wilkinson Microwave Anisotropy Probe (WMAP) temperature anisotropy data seeking to confirm the power spectrum and likelihoods published by the WMAP team. We apply five independent implementations of four algorithms to the power spectrum estimation and two implementations to the parameter estimation. Our single most important result is that we broadly confirm the WMAP power spectrum and analysis. Still, we do find two small but potentially important discrepancies. On large angular scales there is a small power excess in the WMAP spectrum (5%-10% at ℓ ≲ 30) primarily due to likelihood approximation issues between 13 ≤ ℓ ≲ 30. On small angular scales there is a systematic difference between the V- and W-band spectra (few percent at ℓ ≳ 300). Recently, the latter discrepancy was explained by Huffenberger et al. (2006) in terms of oversubtraction of unresolved point sources. As far as the low-ℓ bias is concerned, most parameters are affected by a few tenths of a σ. The most important effect is seen in n_s. For the combination of WMAP, ACBAR, and BOOMERANG, the significance of n_s ≠ 1 drops from ~2.7 σ to ~2.3 σ when correcting for this bias. We propose a few simple improvements to the low-ℓ WMAP likelihood code, and introduce two important extensions to the Gibbs sampling method that allows for proper sampling of the low signal-to-noise ratio regime. Finally, we make the products from the Gibbs sampling analysis publicly available, thereby providing a fast and simple route to the exact likelihood without the need of expensive matrix inversions.