Wavelets andWilkinson Microwave Anisotropy ProbeNon‐Gaussianity

We study the statistical properties of the 1st year WMAP data on differentscales using the spherical mexican hat wavelet transform. Consistent with theresults of Vielva et al. (2003) we find a deviation from Gaussianity in theform of kurtosis of wavelet coefficients on $3-4^\circ$ scales in the southernGalactic hemisphere. This paper extends the work of Vielva et al. as follows.We find that the non-Gaussian signal shows up more strongly in the form of alarger than expected number of cold pixels and also in the form of scale-scalecorrelations amongst wavelet coefficients. We establish the robustness of thenon-Gaussian signal under more wide-ranging assumptions regarding the Galacticmask applied to the data and the noise statistics. This signal is unlikely tobe due to the usual quadratic term parametrized by the non-linearity parameter$f_{NL}$. We use the skewness of the spherical mexican hat wavelet coefficientsto constrain $f_{NL}$ with the 1st year WMAP data. Our results constrain$f_{NL}$ to be $50\pm 80$ at 68% confidence, and less than 280 at 99%confidence.Comment: 22 pages, 10 figures, ApJ accepte