Non-Gaussian signatures in the temperature fluctuation observed by the Wilkinson Microwave Anisotropy Probe

Abstract

We present results from a test for the Gaussianity of the whole sky subdegree‐scale cosmic microwave background (CMB) temperature anisotropy measured by the Wilkinson Microwave Anisotropy Probe (WMAP). We calculate the genus from the foreground‐subtracted and Kp0‐masked WMAP maps and measure the genus shift parameters defined at negative and positive threshold levels (Δν− and Δν+) and the asymmetry parameter (Δg) to quantify the deviation from the Gaussian relation. At WMAP Q, V and W bands, the genus and genus‐related statistics imply that the observed CMB sky is consistent with a Gaussian random phase field. However, from the genus measurement on the Galactic northern and southern hemispheres, we have found two non‐Gaussian signatures at the W‐band resolution ( scale), i.e. the large difference of genus amplitudes between the north and the south and the positive genus asymmetry in the south, which are statistically significant at 2.6σ and 2.4σ levels, respectively. The large genus amplitude difference also appears in the WMAP Q‐ and V‐band maps, deviating from the Gaussian prediction with a significance level of about 2σ. The probability that the genus curves show such a large genus amplitude difference exceeding the observed values at all Q, V and W bands in a Gaussian sky is only 1.4 per cent. Such non‐Gaussian features are reduced as the higher Galactic cut is applied, but their dependence on the Galactic cut is weak. We discuss possible sources that can induce non‐Gaussian features, such as the Galactic foregrounds, the integrated Sachs–Wolfe and the Sunyaev–Zel'dovich effects, and the reionization‐induced low ℓ‐mode non‐Gaussianity that are aligned along the Galactic plane. We conclude that CMB data with higher signal‐to‐noise ratio and an accurate foreground model are needed to understand the non‐Gaussian signatures.

Testing for Non‐Gaussianity in theWilkinson Microwave Anisotropy ProbeData: Minkowski Functionals and the Length of the Skeleton

“…Each statistic is evaluated independently on the northern and southern Galactic hemispheres. Interesting hemisphere effects have been reported by several authors (Eriksen et al 2004;Park 2004), and we focus our tests accordingly.…”

“…In total, the narrowest of the beams (0N53 FWHM) is sensitive to multipoles up to about l % 600; therefore, both noise and point sources are expected to play a major role at this and smaller scales. Here it is worth noticing that Park (2004) considered even smaller scales, since the maps were not explicitly smoothed at all, except for a small effect introduced by a stereographical projection. However, in the subsequent analysis, the 700 point sources resolved by WMAP were masked out, and it was therefore possible to produce results on smaller scales than presented in this paper.…”

“…While the skeleton length has not been measured for the WMAP first-year data set to this date, at least three other groups have computed the genus Minkowski functional for this data set, namely, Komatsu et al (2003), Colley & Gott (2003), and Park (2004). While the former group does not describe their algorithms in great depth, the latter two use pixel-by-pixel methods for computing the genus.…”

“…It is possible that other statistics could be more sensitive to particular features. To study the behavior of the genus in more detail, we therefore fit the parametric function given by equation (24) to each realization (Park 2004), allowing for nonzero shifts and arbitrary amplitudes. The results from these computations are shown in Tables 5 ( Kp0 base mask) and 6 (larger base mask).…”

“…Tests for nonGaussianity afford possible methods for detecting, characterizing, and subsequently removing such effects. Further impetus for the study of such signatures has arisen in recent months from putative detections of non-Gaussian features in the Wilkinson Microwave Anisotropy Probe (WMAP; Bennett et al 2003a) first-year sky maps (Coles et al 2004;Naselsky et al 2003;Vielva et al 2004;Copi et al 2004;Park 2004;Eriksen et al 2004).…”