2000/10/12 by István Szapudi, Istvan Szapudi, Simon Prunet +9
Engineering · Physics and Astronomy · #Reservoir Engineering and Simulation Methods #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0010256
4 pages with 2 figures included, submitted to ApJ Letters, version of epsfig.sty used is included
arxiv created 2000/10/12 · arxiv updated 2009/12/01
We propose and implement a fast, universally applicable method for extracting the angular power spectrum Cl from CMB temperature maps by first estimating the correlation function ξ(θ). Our procedure recovers the Cl's using N2 (but potentially N logN), operations, where N is the number of pixels. This is in contrast with standard maximum likelihood techniques which require N3 operations. Our method makes no special assumptions about the map, unlike present fast techniques which rely on symmetries of the underlying noise matrix, sky coverage, scanning strategy, and geometry. This enables for the first time the analysis of megapixel maps without symmetries. The key element of our technique is the accurate multipole decomposition of ξ(θ). The Cl error bars and cross-correlations are found by a Monte-Carlo approach. We applied our technique to a large number of simulated maps with Boomerang sky coverage in 81000 pixels. We used a diagonal noise matrix, with approximately the same amplitude as Boomerang. These studies demonstrate that our technique provides an unbiased estimator of the Cl's. Even though our method is approximate, the error bars obtained are nearly optimal, and converged only after few tens of Monte-Carlo realizations. Our method is directly applicable for the non-diagonal noise matrix. This, and other generalizations, such as minimum variance weighting schemes, polarization, and higher order statistics are also discussed.