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28 March 2024
 
  » arxiv » astro-ph/0010256

 Article overview


Fast CMB Analyses via Correlation Functions
Istvan Szapudi ; Simon Prunet ; Dmitry Pogosyan Alexander S. Szalay ; J. Richard Bond ;
Date 13 Oct 2000
Subject astro-ph
AffiliationCITA), Simon Prunet (CITA), Dmitry Pogosyan (CITA) Alexander S. Szalay (JHU), and J. Richard Bond (CITA
AbstractWe propose and implement a fast, universally applicable method for extracting the angular power spectrum C_l from CMB temperature maps by first estimating the correlation function xi( heta). Our procedure recovers the C_l’s using N^2 (but potentially N logN), operations, where N is the number of pixels. This is in contrast with standard maximum likelihood techniques which require N^3 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 xi( heta). The C_l 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 C_l’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.
Source arXiv, astro-ph/0010256
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