Real space tests of the statistical isotropy and Gaussianity of the WMAP CMB data

Abstract

ABRIDGED: We introduce and analyze a method for testing statistical isotropy and Gaussianity and apply it to the WMAP CMB foreground reduced, temperature maps, and cross-channel difference maps. We divide the sky into regions of varying size and shape and measure the first four moments of the one-point distribution within these regions, and using their simulated spatial distributions we test the statistical isotropy and Gaussianity hypotheses. By randomly varying orientations of these regions, we sample the underlying CMB field in a new manner, that offers a richer exploration of the data content, and avoids possible biasing due to a single choice of sky division. The statistical significance is assessed via comparison with realistic Monte-Carlo simulations. We find the three-year WMAP maps to agree well with the isotropic, Gaussian random field simulations as probed by regions corresponding to the angular scales ranging from 6 deg to 30 deg at 68% confidence level. 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-year data (99.3% CL). We notice the large scale hemispherical power asymmetry, and find that it is not highly statistically significant in the WMAP three-year data (<~ 97%) at scales l <= 40. The significance is even smaller if multipoles up to l=1024 are considered (~90% CL). We give constraints on the amplitude of the previously-proposed CMB dipole modulation field parameter. We easily detect the residual foregrounds in cross-band difference maps at rms level <~ 7 μK (at scales >~ 6 deg) and limit the systematical uncertainties to <~ 1.7 μK (at scales >~ 30 deg).

arXiv comment20 pages, 20 figures; more tests added; updated to match the version to be published in JCAP

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• A high-significance detection of non-Gaussianity in the WMAP 5-year data using directional spherical wavelets
• Long range correlation in cosmic microwave background radiation
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• Non-gaussianity in the foreground-reduced CMB maps
• Is the cold spot responsible for the CMB North-South asymmetry?
• Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator
• Hemispherical power asymmetry: parameter estimation from CMB WMAP5 data
• Hemispherical Variance Anomaly and Reionization Optical Depth
• Test for anisotropy in the mean of the CMB temperature fluctuation in spherical harmonic space