Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectra

TL;DR

The paper reports the 5-year WMAP measurements of the CMB temperature and polarization power spectra, detailing improvements in calibration, beams, and foreground treatment that yield a TT spectrum cosmic-variance limited up to $\ell \approx 530$ and a clearly detected TE signal. A refined unresolved point-source correction with amplitude $A_{ps}=0.011\pm0.001\,\mu{\rm K}^2{\rm sr}$ is applied, and the data favor a six-parameter $\Lambda$CDM model with $\chi^2/\nu \approx 1.06$ over $\ell=33-1000$. The EE spectrum shows a robust reionization signature near $\tau=0.089$, while BB remains consistent with zero, placing a stringent upper limit on primordial B-modes. Overall, the 5-year results tighten cosmological constraints, validate the $\Lambda$CDM framework, and provide publicly accessible data and likelihood tools for the community.

Abstract

We present the temperature and polarization angular power spectra of the cosmic microwave background (CMB) derived from the first 5 years of WMAP data. The 5-year temperature (TT) spectrum is cosmic variance limited up to multipole l=530, and individual l-modes have S/N>1 for l<920. The best fitting six-parameter LambdaCDM model has a reduced chi^2 for l=33-1000 of chi^2/nu=1.06, with a probability to exceed of 9.3%. There is now significantly improved data near the third peak which leads to improved cosmological constraints. The temperature-polarization correlation (TE) is seen with high significance. After accounting for foreground emission, the low-l reionization feature in the EE power spectrum is preferred by Δχ^2=19.6 for optical depth tau=0.089 by the EE data alone, and is now largely cosmic variance limited for l=2-6. There is no evidence for cosmic signal in the BB, TB, or EB spectra after accounting for foreground emission. We find that, when averaged over l=2-6, l(l+1)C^{BB}_l/2π< 0.15 uK^2 (95% CL).

Figures (13)

• Figure 1: The WMAP 5-year temperature (TT) power spectrum. The red curve is the best-fit theory spectrum from the $\Lambda$CDM/WMAP chain dunkley/etal:prep based on WMAP alone, with parameters $( \Omega_bh^2, \Omega_mh^2, \Delta_{\cal R}^2, n_s, \tau, H_0 ) = ( 0.0227, 0.131, 2.41, 0.961, 0.089, 72.4 )$. The uncertainties include both cosmic variance, which dominates below $\ell=540$, and instrumental noise which dominates at higher multipoles. The uncertainties increase at large $\ell$ due to WMAP's finite resolution. The improved resolution of the third peak near $\ell=800$ in combination with the simultaneous measurement of the rest of the spectrum leads to the improved results reported in this release.
• Figure 2: The WMAP 5-year TT power spectrum along with recent results from the ACBAR reichardt/etal:prep, Boomerang jones/etal:2006, and CBI readhead/etal:2004 experiments. The other experiments calibrate with WMAP or WMAP's measurement of Jupiter (CBI). The red curve is the best-fit $\Lambda$CDM model to the WMAP data, which agrees well with all data sets when extrapolated to higher-$\ell$.
• Figure 3: The unresolved point source contamination $A_{ps}$, measured in bins of $\Delta\ell=100$ evaluated at 40.7 GHz (Q-band). For a source population whose fluxes are independent of frequency $A_{ps}$ scales roughly as $\sim\nu^{-2}$ in the WMAP data. The red data points are from the analysis of V and W bands alone and the blue points are from the analysis of Q, V, and W bands. The horizontal dashed green lines, at 0.010 and 0.012, show the $1\sigma$ bounds for our adopted value of $A_{ps}$. Note that the QVW amplitude is independent of $\ell$.
• Figure 4: The TT $\rm V-W$ null spectrum. After correcting for unresolved point source emission, the individual power spectra are subtracted in power spectrum space. The result is consistent with zero and thus there is no evidence of point source contamination. In these units, point source contamination would be evident as a horizontal offset from zero. At $\ell=500$, the TT power spectrum is $C^{\rm TT}_\ell\approx0.06$; thus the contamination is limited to roughly 3% in power.
• Figure 5: The WMAP 5-year TE power spectrum. The green curve is the best-fit theory spectrum from the $\Lambda$CDM/WMAP Markov chain dunkley/etal:prep. For the TE component of the fit, $\chi^2=415$, and there are 427 multipoles and 6 parameters; thus the number of degrees of freedom is $\nu=421$, leading to $\chi^2/\nu=0.99$. The particle horizon size at decoupling corresponds to $l\approx100$. The clear anticorrelation between the primordial plasma density (corresponding approximately to T) and velocity (corresponding approximately to E) in causally disconnected regions of the sky indicates that the primordial perturbations must have been on a superhorizon scale. Note that the vertical axis is $(\ell+1)C_\ell/(2\pi)$, and not $\ell(\ell+1)C_\ell/(2\pi)$.