Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets

TL;DR

This paper detects a localized non-Gaussian signature in the WMAP 1-year CMB data using the Spherical Mexican Hat Wavelet (SMHW), observing excess kurtosis at scales around $R oughly 4^ ext{°}$ (≈$10^ ext{°}$ on the sky) with a right-tail probability near $0.4 ext{%.}$ The analysis shows the effect is confined mainly to the southern hemisphere and is not attributable to systematics, Galactic foregrounds, or uncertainties in the cosmological power spectrum; a whitening test and frequency-insensitive results further support robustness. The authors identify a southern cold spot as a potential localized source, yet they cannot rule out intrinsic fluctuations (secondary anisotropies or primordial features) as the origin. The work underscores the SMHW’s ability to localize non-Gaussian signals on the sphere and motivates confirmation with forthcoming data, such as the WMAP 2-year release.

Abstract

A non-Gaussian detection in the WMAP 1-year data is reported. The detection has been found in the combined Q-V-W map proposed by the WMAP team (Komatsu et al. 2003) after applying a wavelet technique based on the Spherical Mexican Hat Wavelet (SMHW). The skewness and the kurtosis of the SMHW coefficients are calculated at different scales. A non-Gaussian signal is detected at scales of the SMHW around 4 deg (size in the sky of around 10 deg). The right tail probability of the detection is approx. 0.4%. In addition, a study of Gaussianity is performed in each hemisphere. The northern hemisphere is compatible with Gaussianity, whereas the southern one deviates from Gaussianity with a right tail probability of approx. 0.1%. Systematics, foregrounds and uncertainties in the estimation of the cosmological parameters are carefully studied in order to identify the possible source of non-Gaussianity. The detected deviation from Gaussianity is not found to be caused by systematic effects: 1) each one of the Q, V and W receivers shows the same non-Gaussianity pattern, and 2) several combinations of the different receivers at each frequency band do not show this non-Gaussian pattern. Similarly, galactic foregrounds show a negligible contribution to the non-Gaussian detection: non-Gaussianity is detected in all the WMAP maps and no frequency dependence is observed. Moreover, the expected foreground contribution to the combined WMAP map was added to CMB Gaussian simulations showing a behaviour compatible with the Gaussian model. Influence of uncertainties in the CMB power spectrum estimation are also quantified. Hence, possible intrinsic temperature fluctuations (like secondary anisotropies and primordial features) can not be rejected as the source of this non-Gaussian detection.

Figures (14)

• Figure 1: Analysed WMAP map at $N_{side} = 256$ (in $mK$ units). It is a combination of all the receivers in Q-Band, V-Band and W-Band after the foreground correction described in Bennett et al. (2003b). The Kp0 mask has been applied and the residual monopole and dipole have been subtracted.
• Figure 2: Set of exclusion masks ($M(R)$) used in our analysis. This set is defined in order to discard in the SMHW analysis those pixels with a strong kp0 mask contamination. Since the number of excluded pixels grows with the SMHW scale, there is one exclusion mask per scale $R$. The exclusion masks (from left to right and top to bottom) correspond to the following scales: $R_1 = 13.7$, $R_2 = 25$, $R_3 = 50$, $R_4 = 75$, $R_5 = 100$, $R_6 = 150$, $R_7 = 200$, $R_8 = 250$, $R_9 = 300$, $R_{10} = 400$, $R_{11} = 500$, $R_{12} = 600$, $R_{13} = 750$, $R_{14} = 900$ and $R_{15} = 1050$ arcmin
• Figure 3: The skewness ($S(R)$, left panel) and kurtosis ($K(R)$, right panel) values obtained from the application of the SMHW analysis to the combined WMAP map ($\hat{T}({\mathbf{x}})$) are shown as blue starts. Acceptance intervals for the 32% (red, inner), 5% (green, middle) and 1% (magenta, outer) significance levels are also plotted, as well as the mean value given by the 10000 simulations performed in this work (yellow solid line). Only those pixels allowed by the exclusion masks set ($M(R)$) have been used in the analysis (see text).
• Figure 4: The dispersion ($\sigma(R)$, top) skewness ($S(R)$, middle) and kurtosis ($K(R)$, bottom) values obtained from the application of the SMHW analysis to the combined WMAP map ($\hat{T}({\mathbf{x}})$) are shown (blue starts). The left column corresponds to the analysis performed only in the northern hemisphere, whereas the analysis of the southern one is in the right column. Acceptance intervals for the 32% (red, inner), 5% (green, middle) and 1% (magenta, outer) significance levels are also plotted, as well as the mean value given by the 10000 simulations (yellow solid line). The exclusion masks set ($M(R)$) have been used in the analysis (see text).
• Figure 5: Kurtosis values ($K(R)$) obtained from the application of the analysis described in this work to each WMAP maps observed at channels: $Q_1$ and $Q_2$ (top panel), $V_1$ and $V_2$ (middle panel) and $W_1$, $W_2$, $W_3$ and $W_4$ (bottom panel). For a better comparison, the kurtosis obtained for the combined WMAP map has also been included (blue starts) in all the panels.