Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis

TL;DR

This paper presents the three-year WMAP temperature analysis, delivering full-sky maps across five frequency bands with improved calibration, beam models, and polarization handling. The authors implement a hybrid angular power-spectrum estimator combining a low-$l$ maximum-likelihood approach with a high-$l$ pseudo-$C_\ell$ method, achieving cosmic-variance limited precision up to $l\approx400$ and robust peak detection with cross-year cross-spectra. Foreground separation is advanced through updated ILC, MEM, and template-subtraction methods, while extragalactic contaminants are characterized via a larger point-source catalog and SZ analysis. The results strengthen the standard cosmological model, provide tighter constraints on parameters, and deliver a comprehensive data release (maps, spectra, and likelihoods) for community use across cosmology and CMB foreground studies.

Abstract

We present new full-sky temperature maps in five frequency bands from 23 to 94 GHz, based on the first three years of the WMAP sky survey. The new maps, which are consistent with the first-year maps and more sensitive, incorporate improvements in data processing made possible by the additional years of data and by a more complete analysis of the polarization signal. These include refinements in the gain calibration and beam response models. We employ two forms of multi-frequency analysis to separate astrophysical foreground signals from the CMB, each of which improves on our first-year analyses. First, we form an improved 'Internal Linear Combination' map, based solely on WMAP data, by adding a bias correction step and by quantifying residual uncertainties in the resulting map. Second, we fit and subtract new spatial templates that trace Galactic emission; in particular, we now use low-frequency WMAP data to trace synchrotron emission. The WMAP point source catalog is updated to include 115 new sources. We derive the angular power spectrum of the temperature anisotropy using a hybrid approach that combines a maximum likelihood estimate at low l (large angular scales) with a quadratic cross-power estimate for l>30. Our best estimate of the CMB power spectrum is derived by averaging cross-power spectra from 153 statistically independent channel pairs. The combined spectrum is cosmic variance limited to l=400, and the signal-to-noise ratio per l-mode exceeds unity up to l=850. The first two acoustic peaks are seen at l=220.8 +- 0.7 and l=530.9 +- 3.8, respectively, while the first two troughs are seen at l=412.4 +- 1.9 and l=675.1 +- 11.1, respectively. The rise to the third peak is unambiguous; when the WMAP data are combined with higher resolution CMB measurements, the existence of a third acoustic peak is well established.

Figures (23)

• Figure 1: Full-sky maps in Galactic coordinates smoothed with a $0\hbox{${\hbox{.}}^\circ$}2$ Gaussian beam, shown in Mollweide projection. top left: K-band (23 GHz), middle left: Ka-band (33 GHz), bottom left: Q-band (41 GHz), top right: V-band (61 GHz), bottom right: W-band (94 GHz).
• Figure 2: The number of independent W-band observations per pixel in Galactic coordinates, top: year-1, middle: year-2, and bottom: year-3. The number of observations is greatest near the ecliptic poles and in rings approximately 141$^{\circ}$ from each pole (determined by the angular separation between the two bore-sight directions). The number of observations is least in the ecliptic plane. The small circular cuts in the ecliptic are where Mars, Saturn, Jupiter, Uranus, and Neptune are masked so as not to contaminate the CMB signal. The coverage is quite consistent from year to year, with the planet cuts being responsible for the largest fractional variation.
• Figure 3: Comparison of the three-year maps with the previously released one-year maps. The data are smoothed to $1^{\circ}$ resolution and are shown in Galactic coordinates. The frequency bands K through W are shown top to bottom. The first-year maps ( left) and the three-year maps ( middle) are shown scaled to $\pm$200 $\mu$K. The difference maps ( right) are degraded to pixel resolution 4 and scaled to $\pm$20 $\mu$K. The small difference in low-$l$ power is mostly due to improvements in the gain model of the instrument as a function of time jarosik/etal:prep. See §\ref{['sec:maps']} and Table \ref{['tab:3yr_1yr_diff']}.
• Figure 4: Results from the MEM foreground degeneracy analysis. (a) The spectrum of total foreground emission (diamonds) compared to the sum of the MEM components (lines connecting the diamonds), averaged over the full sky. The three component spectra of the model are also shown, as indicated. (b-f) The contour plots illustrate the degeneracy between selected components. The panels show the change in the MEM functional (in units of $\Delta \chi^2$) as a function of two global model parameters. For example, panel (b) shows the change in the MEM functional that results from adding a constant value to the synchrotron and/or free-free solutions, while panel (f) shows the dependence of the functional on a global steepening of the synchrotron spectrum, modeled as $\beta_{\rm s} = \beta_0 + d\beta_{\rm s}/d\log\nu \cdot (\log\nu - \log\nu_K)$. The only strong degeneracy is between the synchrotron and free-free amplitudes in (b). This effect is mitigated by the prior distributions assumed for each component (see text). The dust spectral index, $\beta_d$, was found to be essentially unconstrained, so contour plots for that quantity are not shown.
• Figure 5: Galactic signal component maps from the Maximum Entropy Method (MEM) analysis (§\ref{['sec:gal_mem']}). top-bottom: synchrotron, free-free, and dust emission with logarithmic temperature scales, as indicated. left: Input prior maps for each component. right: Output maps based on three-year WMAP data for each component. See text for discussion.