Departure from Gaussianity of the Cosmic Microwave Background Temperature Anisotropies in the Three-Year WMAP Data

We test the hypothesis that the temperature of the cosmic microwave background is consistent with a Gaussian random field defined on the celestial sphere, using the full sky debiased internal linear combination (DILC) map produced from the three-year WMAP data. We test the phases for spherical harmonic modes with [unk] [unk] 10 (which should be the cleanest) for uniformity, randomness, and correlation with phases of the foreground maps. The phases themselves are consistent with a uniform distribution, but the differences between phases (randomness) are not consistent with uniformity. For l = 3 and l = 6, the phases of the CMB maps cross-correlate with the foregrounds, suggesting the presence of residual contamination in the DILC map even on these large scales. We also use a one-dimensional Fourier representation to assemble [unk] into the Delta T [unk]( [unk]) for each l mode and test the positions of the resulting maxima and minima for consistency with uniformity randomness on the unit circle. The results show significant departures at the 0.5% level, with the one-dimensional peaks concentrated around [unk] = 180 [unk]. This strongly significant alignment with the Galactic meridian, together with the cross-correlation of DILC phases with the foreground maps, strongly suggests that even the lowest spherical harmonic modes in the map are significantly contaminated with foreground radiation.