Re-analysis of the three-year wilkinson microwave anisotropy probe temperature power spectrum and likelihood

Abstract

We analyze the three-year 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 over-subtraction of unresolved point sources. As far as the low-ℓ bias is concerned, most parameters are affected by a few tenths of a sigma. The most important effect is seen in ns. For the combination of WMAP, Acbar and BOOMERanG, the significance of ns = 1 drops from ∼ 2.7σ to ∼ 2.3σ 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 regime. Finally, we make the products from the Gibbs sampling analysis publically available, thereby providing a fast and simple route to the exact likelihood without the need of expensive matrix inversions.