TY - JOUR

T1 - Five-year wilkinson microwave anisotropy probe (WMAP) observations

T2 - Bayesian estimation of cosmic microwave background polarization maps

AU - Dunkley, J.

AU - Spergel, David N.

AU - Komatsu, E.

AU - Hinshaw, G.

AU - Larson, D.

AU - Nolta, M. R.

AU - Odegard, N.

AU - Page, L.

AU - Bennett, C. L.

AU - Gold, B.

AU - Hill, R. S.

AU - Jarosik, N.

AU - Weiland, J. L.

AU - Halpern, M.

AU - Kogut, A.

AU - Limon, M.

AU - Meyer, S. S.

AU - Tucker, G. S.

AU - Wollack, E.

AU - Wright, E. L.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Cosmic microwave background

KW - Cosmology: observations

KW - Methods: statistical

KW - Polarization

KW - Radio continuum: ISM

UR - http://www.scopus.com/inward/record.url?scp=70350486796&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350486796&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/701/2/1804

DO - 10.1088/0004-637X/701/2/1804

M3 - Article

AN - SCOPUS:70350486796

SN - 0004-637X

VL - 701

SP - 1804

EP - 1813

JO - Astrophysical Journal

JF - Astrophysical Journal

IS - 2

ER -