Three-year Wilkinsonmicrowave Anisotropy Probe (WMAP) observations: Polarization analysis

L. Page, G. Hinshaw, E. Komatsu, M. R. Nolta, D. N. Spergel, C. L. Bennett, C. Barnes, R. Bean, O. Doré, J. Dunkley, M. Halpern, R. S. Hill, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, H. V. Peiris, G. S. Tucker, L. VerdeJ. L. Weiland, E. Wollack, E. L. Wright

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The Wilkinson Microwave Anisotropy Probe (WMAP) has mapped the entire sky in five frequency bands between 23 and 94 GHz with polarization-sensitive radiometers. We present 3 year full-sky maps of the polarization and analyze them for foreground emission and cosmological implications. These observations open up a new window for understanding how the universe began and help set a foundation for future observations. WMAP observes significant levels of polarized foreground emission due to both Galactic synchrotron radiation and thermal dust emission. Synchrotron radiation is the dominant signal at l < 50 and ν ≲ 40 GHz, while thermal dust emission is evident at 94 GHz. The least contaminated channel is at 61 GHz. We present a model of polarized foreground emission that captures the large angular scale characteristics of the microwave sky. After applying a Galactic mask that cuts 25.7% of the sky, we show that the high Galactic latitude rms polarized foreground emission, averaged over l = 4-6, ranges from ≈ 5 μK at 22 GHz to ≲0.6 μK at 61 GHz. By comparison, the levels of intrinsic CMB polarization for a ACDM model with an optical depth of τ = 0.09 and assumed tensor-to-scalar ratio r = 0.3 are ≈0.3 μK for E-mode polarization and ≈0.1 μK for B-mode polarization. To analyze the maps for CMB polarization at l < 16, we subtract a model of the foreground emission that is based primarily on a scaling WMAP's 23 GHz map. In the foreground-corrected maps, we detect l(l + 1)C l=〈2-6〉EE/2π = 0.086 ± 0.029 (μK)2. This is interpreted as the result of rescattering of the CMB by free electrons released during reionization at zr = 10.9 -2.3+2.7 for a model with instantaneous reionization. By computing the likelihood of just the EE data as a function of τ we find τ = 0.10 ± 0.03. When the same EE data are used in the full six-parameter fit to all WMAP data (TT, TE, EE), we find τ = 0.09 ± 0.03. Marginalization over the foreground subtraction affects this value by δτ < 0.01. We see no evidence for B modes, limiting them to l(l + 1)Cl=〈2-6〉BB/2π = -0.04 ± 0.03 (μK)2. We perform a template fit to the E-mode and B-mode data with an approximate model for the tensor scalar ratio. We find that the limit from the polarization signals alone is r < 2.2 (95% CL), where r is evaluated at k = 0.002 Mpc-1. This corresponds to a limit on the cosmic density of gravitational waves of ΩGWh2 < 5 × 10-12. From the full WMAP analysis, we find r < 0.55 (95% CL) corresponding to a limit of ΩGWh2 < 1 × 10-12 (95% CL). The limit on r is approaching the upper bound of predictions for some of the simplest models of inflation, r ∼ 0.3.

Original languageEnglish (US)
Pages (from-to)335-376
Number of pages42
JournalAstrophysical Journal, Supplement Series
Issue number2
StatePublished - Jun 1 2007

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmic microwave background
  • Cosmology: observations
  • Polarization

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    Page, L., Hinshaw, G., Komatsu, E., Nolta, M. R., Spergel, D. N., Bennett, C. L., Barnes, C., Bean, R., Doré, O., Dunkley, J., Halpern, M., Hill, R. S., Jarosik, N., Kogut, A., Limon, M., Meyer, S. S., Odegard, N., Peiris, H. V., Tucker, G. S., ... Wright, E. L. (2007). Three-year Wilkinsonmicrowave Anisotropy Probe (WMAP) observations: Polarization analysis. Astrophysical Journal, Supplement Series, 170(2), 335-376.