Real space tests of the statistical isotropy and Gaussianity of the Wilkinson MicrowaveAnisotropy Probe cosmic microwave background data

Abstract

We introduce and analyze a method for testing statistical isotropy and Gaussianity andapply it to the Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwavebackground (CMB) foreground reduced temperature maps. We also test cross-channeldifference maps to constrain levels of residual foreground contamination and systematicuncertainties. We divide the sky into regions of varying size and shape and measure thefirst four moments of the one-point distribution within these regions, and using theirsimulated spatial distributions we test the statistical isotropy and Gaussianity hypotheses.By randomly varying orientations of these regions, we sample the underlying CMBfield in a new manner, that offers a richer exploration of the data content, andavoids possible biasing due to a single choice of sky division. In our analysis weaccount for all two-point correlations between different regions and also showthe impact on the results when these correlations are neglected. The statisticalsignificance is assessed via comparison with realistic Monte Carlo simulations.We find the three-year WMAP maps to agree well with the isotropic, Gaussian randomfield simulations as probed by regions corresponding to the angular scales ranging from6° to30° at68% confidence level (CL).We report a strong, anomalous(99.8% CL)dipole ‘excess’ in the V band of the three-year WMAP data and also in the V band of the WMAP five-yeardata (99.3% CL).Using our statistics, we notice large scale hemispherical power asymmetry, and find that itis not highly statistically significant in the WMAP three-year data () at scales . The significance is even smaller if multipoles up to are considered (∼90% CL). We give constraints on the amplitude of the previously proposed CMB dipolemodulation field parameter.We find some hints of foreground contamination in the form of a locally strong, anomalous kurtosis excessin the Q+V +W co-added map, which however is not significant globally.We easily detect the residual foregrounds in cross-band difference maps at rms level (at scales ) and limit the systematical uncertainties to (at scales ).