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Title:
Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Bayesian Estimation of Cosmic Microwave Background Polarization Maps
Authors:
Dunkley, J.; Spergel, D. N.; Komatsu, E.; Hinshaw, G.; Larson, D.; Nolta, M. R.; Odegard, N.; Page, L.; Bennett, C. L.; Gold, B.; Hill, R. S.; Jarosik, N.; Weiland, J. L.; Halpern, M.; Kogut, A.; Limon, M.; Meyer, S. S.; Tucker, G. S.; Wollack, E.; Wright, E. L.
Affiliation:
AA( Department of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544-0708, USA ; Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544-1001, USA ; Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK ; ), AB( Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544-1001, USA ; Princeton Center for Theoretical Physics, Princeton University, Princeton, NJ 08544, USA ), AC( University of Texas, Austin, Department of Astronomy, 2511 Speedway, RLM 15.306, Austin, TX 78712, USA ), AD( Code 665, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA ), AE( Department of Physics & Astronomy, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218-2686, USA ), AF( Canadian Institute for Theoretical Astrophysics, 60 St. George Street, University of Toronto, Toronto, ON M5S 3H8, Canada ), AG( Adnet Systems, Inc., 7515 Mission Dr., Suite A1C1 Lanham, MD 20706, USA ), AH( Department of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544-0708, USA ), AI( Department of Physics & Astronomy, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218-2686, USA ), AJ( Department of Physics & Astronomy, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218-2686, USA ), AK( Adnet Systems, Inc., 7515 Mission Dr., Suite A1C1 Lanham, MD 20706, USA ), AL( Department of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544-0708, USA ), AM( Adnet Systems, Inc., 7515 Mission Dr., Suite A1C1 Lanham, MD 20706, USA ), AN( Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada ), AO( Code 665, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA ), AP( Columbia Astrophysics Laboratory, 550 W. 120th Street, Mail Code 5247, New York, NY 10027-6902, USA ), AQ( Departments of Astrophysics and Physics, KICP and EFI, University of Chicago, Chicago, IL 60637, USA ), AR( Department of Physics, Brown University, 182 Hope St., Providence, RI 02912-1843, USA ), AS( Code 665, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA ), AT( PAB 3-909, UCLA Physics & Astronomy, P.O. Box 951547, Los Angeles, CA 90095-1547, USA)
Publication:
The Astrophysical Journal, Volume 701, Issue 2, pp. 1804-1813 (2009). (ApJ Homepage)
Publication Date:
08/2009
Origin:
IOP
ApJ Keywords:
cosmic microwave background, cosmology: observations, methods: statistical, polarization, radio continuum: ISM
DOI:
10.1088/0004-637X/701/2/1804
Bibliographic Code:
2009ApJ...701.1804D

Abstract

We describe a sampling method to estimate the polarized cosmic microwave background (CMB) signal from observed maps of the sky. We use a Metropolis-within-Gibbs algorithm to estimate the polarized CMB map, containing Q and U Stokes parameters at each pixel, and its covariance matrix. These can be used as inputs for cosmological analyses. The polarized sky signal is parameterized as the sum of three components: CMB, synchrotron emission, and thermal dust emission. The polarized Galactic components are modeled with spatially varying power-law spectral indices for the synchrotron, and a fixed power law for the dust, and their component maps are estimated as by-products. We apply the method to simulated low-resolution maps with pixels of side 7.2 deg, using diagonal and full noise realizations drawn from the WMAP noise matrices. The CMB maps are recovered with goodness of fit consistent with errors. Computing the likelihood of the E-mode power in the maps as a function of optical depth to reionization, τ, for fixed temperature anisotropy power, we recover τ = 0.091 ± 0.019 for a simulation with input τ = 0.1, and mean τ = 0.098 averaged over 10 simulations. A "null" simulation with no polarized CMB signal has maximum likelihood consistent with τ = 0. The method is applied to the five-year WMAP data, using the K, Ka, Q, and V channels. We find τ = 0.090 ± 0.019, compared to τ = 0.086 ± 0.016 from the template-cleaned maps used in the primary WMAP analysis. The synchrotron spectral index, β, averaged over high signal-to-noise pixels with standard deviation σ(β) < 0.25, but excluding ~6% of the sky masked in the Galactic plane, is -3.03 ± 0.04. This estimate does not vary significantly with Galactic latitude, although includes an informative prior.

WMAP is the result of a partnership between Princeton University and NASA's Goddard Space Flight Center. Scientific guidance is provided by the WMAP Science Team.

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