  Local scaling properties of the co-added foreground-cleaned three-year
Wilkinson Microwave Anisotropy Probe (WMAP) data are estimated using weighted
scaling indices. The scaling index method (SIM) 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 fit $\Lambda$CDM power spectrum and WMAP-like beam and
noise properties. Statistical quantities based on the scaling indices, namely
the moments of the distribution and probability-based measures are determined.
We find for most of the test statistics significant deviations from the
Gaussian hypothesis. We find 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, which gives rise to highly significant signature for
non-Gaussianity in the spectrum of scaling indices. 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 asymmetries in the WMAP three-year data. More detailed bandand year-wise
analyses are needed to elucidate the origin of the detected anomalies. In
either case the scaling indices provide powerful nonlinear statistics to
analyse CMB maps.
