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Using the 5 year WMAP data, we re-investigate claims of non-Gaussianities andasymmetries detected in local curvature statistics of the 1 year WMAP data. InHansen et al 2004, it was found that the northern ecliptic hemisphere wasnon-Gaussian at the ~1% level testing the densities of hill-, lake and saddlepoints based on the second derivatives of the CMB temperature map. The 5 yearWMAP data has a much lower noise level and better control of systematics. Usingthese, we find that the anomalies are still present at a consistent level. Alsothe direction of maximum non-Gaussianity remains. Due to limited availabilityof computer resources, Hansen et al. 2004 were unable to calculate the fullcovariance matrix for the chi^2 test used. Here we apply the full covariancematrix instead of the diagonal approximation and find that thenon-Gaussianities disappear and there is no preferred non-Gaussian direction.We compare with simulations of weak lensing to see if this may cause theobserved non-Gaussianity when using diagonal covariance matrix. We concludethat weak lensing does not produce non-Gaussianity in the local curvaturestatistics at the scales investigated in this paper. The cause of thenon-Gaussian detection in the case of a diagonal matrix remains unclear.

Non-Gaussianities in the local curvature of the 5-year WMAP data