Seven-year wilkinson microwave anisotropy probe (WMAP*) observations: Power spectra and WMAP-derived parameters

D. Larson, J. Dunkley, G. Hinshaw, E. Komatsu, M. R. Nolta, C. L. Bennett, B. Gold, M. Halpern, R. S. Hill, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, L. Page, K. M. Smith, D. N. Spergel, G. S. Tucker, J. L. Weiland, E. WollackE. L. Wright

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The WMAP mission has produced sky maps from seven years of observations at L2. We present the angular power spectra derived from the seven-year maps and discuss the cosmological conclusions that can be inferred from WMAP data alone. With the seven-year data, the temperature (TT) spectrum measurement has a signal-to-noise ratio per multipole that exceeds unity for l < 919; and in band powers of width Δl = 10, the signal-to-noise ratio exceeds unity up to l = 1060. The third acoustic peak in the TT spectrum is now well measured by WMAP. In the context of a flat ACDM model, this improvement allows us to place tighter constraints on the matter density from WMAP data alone, Ωmh2 = 0.1334+0.0056-0.0055, and on the epoch of matter-radiation equality, zeq = 3196 +134-133. The temperature-polarization (TE) spectrum is detected in the seven-year data with a significance of 20σ, compared to 13s with the five-year data. We now detect the second dip in the TE spectrum near l ∼ 450 with high confidence. The TB and EB spectra remain consistent with zero, thus demonstrating low systematic errors and foreground residuals in the data. The low-lEE spectrum, a measure of the optical depth due to reionization, is detected at 5.5σ significance when averaged over l = 2-7: l(l+1)Cl EE/(2π) = 0.074+0.034 -0.025μK2 (68% CL). We now detect the high-l, 24 ≤ l ≤ 800, EE spectrum at over 8σ. The BB spectrum, an important probe of gravitational waves from inflation, remains consistent with zero; when averaged over l = 2-7, l(l + 1)ClBB/(2π) < 0.055 μK 2 (95% CL). The upper limit on tensor modes from polarization data alone is a factor of two lower with the seven-year data than it was using the five-year data. The data remain consistent with the simple ACDM model: the best-fit TT spectrum has an effective χ2 of 1227 for 1170 degrees of freedom, with a probability to exceed of 9.6%. The allowable volume in the six-dimensional space of ACDM parameters has been reduced by a factor of 1.5 relative to the five-year volume, while the ACDM model that allows for tensor modes and a running scalar spectral index has a factor of three lower volume when fit to the seven-year data. We test the parameter recovery process for bias and find that the scalar spectral index, ns, is biased high, but only by 0.09σ, while the remaining parameters are biased by <0.15σ. The improvement in the third peak measurement leads to tighter lower limits from WMAP on the number of relativistic degrees of freedom (e.g., neutrinos) in the early universe: Neff > 2.7 (95% CL). Also, using WMAP data alone, the primordial helium mass fraction is found to be Y He = 0.28+0.14-0.15, and with data from higher-resolution cosmic microwave background experiments included, we now establish the existence of pre-stellar helium at >3σ. These new WMAP measurements provide important tests of big bang cosmology.

Original languageEnglish (US)
JournalAstrophysical Journal, Supplement Series
Issue number2
StatePublished - Feb 1 2011

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmic background radiation
  • Cosmological parameters
  • Cosmology: observations
  • Dark matter
  • Early universe
  • Space vehicles: instruments

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    Larson, D., Dunkley, J., Hinshaw, G., Komatsu, E., Nolta, M. R., Bennett, C. L., Gold, B., Halpern, M., Hill, R. S., Jarosik, N., Kogut, A., Limon, M., Meyer, S. S., Odegard, N., Page, L., Smith, K. M., Spergel, D. N., Tucker, G. S., Weiland, J. L., ... Wright, E. L. (2011). Seven-year wilkinson microwave anisotropy probe (WMAP*) observations: Power spectra and WMAP-derived parameters. Astrophysical Journal, Supplement Series, 192(2).