A scaling index analysis of the Wilkinson Microwave Anisotropy Probe three-year data: signatures of non-Gaussianities and asymmetries in the cosmic microwave background

Local scaling properties of the co-added foreground-cleaned three-year Wilkinson Microwave Anisotropy Probe (WMAP) data are estimated using weighted scaling indices a. The scaling index method is - for the first time - adapted and applied to the case of spherical symmetric spatial data. The results are compared with 1000 Monte Carlo simulations based on Gaussian fluctuations with a best-fitting A cold dark matter power spectrum and WMAP-like beam and noise properties. Statistical quantities based on the scaling indices, namely the mean and standard deviation, a combination of both and probability-based measures are determined. We find for most of the test statistics highly significant deviations from the Gaussian hypothesis. Using a very conservative X 2 statistics, which averages over all scales, we detect non-Gaussianity for the full sky at a level of 97.3 per cent regarding the mean, 97.3 per cent for the standard deviation and 97.7 per cent for a combination of mean and standard deviation. For the Northern hemisphere, the signatures of non-Gaussianities are more pronounced and we obtain 97.7 per cent (mean), 99.8 per cent (standard deviation) and 99.0 per cent (combination), whereas the Southern hemisphere is more consistent with Gaussianity [94.8 per cent (mean), 71.0 per cent (standard deviation) and 91.5 per cent (combination)]. These differences between Northern and Southern hemispheres induce pronounced asymmetries, which can be interpreted as a global lack of structure in the Northern hemisphere, which is consistent with previous findings. Furthermore, we detect a localized anomaly in the Southern hemisphere giving rise to highly significant signature for non-Gaussianity in the spectrum of scaling indices P(a). We identify this signature as the cold spot, which was also already detected in the first-year WMAP data. Our results provide further evidence for both the presence of non-Gaussianities and the presence of asymmetries in the WMAP three-year data. More detailed band- and year-wise analyses are needed to elucidate the origin of the detected anomalies. In either case the scaling indices provide powerful non-linear statistics to analyse cosmic microwave background maps.