The N-point correlation functions of the first-year Wilkinson Microwave Anisotropy Probe sky maps

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Abstract
We compute the two-, three- and four-point correlation functions from the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data, and compare these to a Monte Carlo ensemble of 5000 realizations, based on the best-fit WMAP running-index spectrum of Gaussian fluctuations. The analysis is carried out in three steps, covering small (< 72'), intermediate (< 5 degrees) and large scales (up to 180 degrees). On the largest scales our results are consistent with the previously reported hemisphere power asymmetries: the northern ecliptic hemisphere is practically devoid of large scale fluctuations, while the southern hemisphere show relatively strong fluctuations. We also detect excess correlations in W-band difference maps as compared to the detailed noise simulations produced by the WMAP team, possibly indicative of unknown systematics. While unlikely to affect any temperature based results, this effect could potentially be important for the upcoming polarization data. On intermediate angular scales we find hints of a similar anisotropic distribution of power as seen on the very largest scales, but not to the same extent. In general the model is accepted on these scales. Finally, the same is also true on the smallest scales probed in this paper.

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