Increasing Evidence for Hemispherical Power Asymmetry in the Five-Year WMAP Data

Abstract

Motivated by the recent results of Hansen et al. concerning a noticeable hemispherical power asymmetry in the Wilkinson Microwave Anisotropy Probe (WMAP) data on small angular scales, we revisit the dipole-modulated signal model introduced by Gordon et al.. This model assumes that the true cosmic microwave background signal consists of a Gaussian isotropic random field modulated by a dipole, and is characterized by an overall modulation amplitude, A, and a preferred direction, ṕ. Previous analyses of this model have been restricted to very low resolution (i.e., 3°.6 pixels, a smoothing scale of 9° FWHM, and ℓ ≾40) due to computational cost. In this paper, we double the angular resolution (i.e., 1°.8 pixels and 4°.5 FWHM smoothing scale), and compute the full corresponding posterior distribution for the five-year WMAP data. The results from our analysis are the following: the best-fit modulation amplitude for ℓ ≤ 64 and the ILC data with the WMAP KQ85 sky cut is A = 0.072 ± 0.022, nonzero at 3.3σ, and the preferred direction points toward Galactic coordinates (l, b) = (224°, – 22°) ± 24°. The corresponding results for ℓ ≾ 40 from earlier analyses were A = 0.11 ± 0.04 and (l, b) = (225°, – 27°). The statistical significance of a nonzero amplitude thus increases from 2.8σ to 3.3σ when increasing ℓ_(max) from 40 to 64, and all results are consistent to within 1σ. Similarly, the Bayesian log-evidence difference with respect to the isotropic model increases from Δln E = 1.8 to Δln E = 2.6, ranking as "strong evidence" on the Jeffreys' scale. The raw best-fit log-likelihood difference increases from Δln L=6.1 to Δln L=7.3. Similar, and often slightly stronger, results are found for other data combinations. Thus, we find that the evidence for a dipole power distribution in the WMAP data increases with ℓ in the five-year WMAP data set, in agreement with the reports of Hansen et al.

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