Testing the Gaussian Random Hypothesis with the Cosmic Microwave Background Temperature Anisotropies in the 3-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 de-biased internal linear combination (DILC) map produced from the 3-year WMAP data. We test the phases for spherical harmonic modes with l ≤ 10 (which should be the cleanest) for their uniformity, randomness, and correlation with those of the foreground templates. The phases themselves are consistent with a uniform distribution, but not for l ≤ 5, and the differences between phases are not consistent with uniformity. For l = 3 and l = 6, the phases of the CMB maps cross-correlate with the foregrounds, suggestion the presence of residual contamination in the DILC map even on these large scales. We also use a one-dimensional Fourier representation to assemble alm into the ∆Tl(φ) 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 being concentrated around the origin φ = 0. This strongly significant alignment with the Galactic meridian, together with the crosscorrelation 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. Subject headings: cosmology: cosmic microwave background — cosmology: observations — methods: data analysis