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

The three Minkowski functionals and the recently defined length of theskeleton are estimated for the co-added first-year Wilkinson MicrowaveAnisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations,based on Gaussian fluctuations with the a-priori best-fit running-index powerspectrum and WMAP-like beam and noise properties. Several powerspectrum-dependent quantities, such as the number of stationary points, thetotal length of the skeleton, and a spectral parameter, gamma, are alsoestimated. While the area and length Minkowski functionals and the length ofthe skeleton show no evidence for departures from the Gaussian hypothesis, thenorthern hemisphere genus has a chi^2 that is large at the 95% level for allscales. For the particular smoothing scale of 3.40 degrees FWHM it is largerthan that found in 99.5% of the simulations. In addition, the WMAP genus fornegative thresholds in the northern hemisphere has an amplitude that is largerthan in the simulations with a significance of more than 3 sigma. On thesmallest angular scales considered, the number of extrema in the WMAP data ishigh at the 3 sigma level. However, this can probably be attributed to theeffect of point sources. Finally, the spectral parameter gamma is high at the99% level in the northern Galactic hemisphere, while perfectly acceptable inthe southern hemisphere. The results provide strong evidence for the presenceof both non-Gaussian behavior and an unexpected power asymmetry between thenorthern and southern hemispheres in the WMAP data.Comment: 17 pages, 10 figures, accepted for publication in Ap