AUTO- AND CROSS-CORRELATION OF PHASES OF THE WHOLE-SKY CMB AND FOREGROUND MAPS FROM THE 1-YEAR WMAP DATA

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Abstract
The issue of non-Gaussianity is not only related to distinguishing the theories of the origin of primordial fluctuations, but also crucial for the determination of cosmological parameters in the framework of inflation paradigm. We present a method for testing non-Gaussianity on the whole-sky cosmic microwave background (CMB) anisotropies. This method is based on the Kuiper's statistic to probe the two-dimensional uniformity on a periodic mapping square associating phases: return mapping of phases of the derived CMB (similar to auto-correlation) and cross-correlations between phases of the derived CMB and foregrounds. Since phases reflect morphology, detection of cross-correlation of phases signifies the contamination of foreground signals in the derived CMB map. The advantage of this method is that one can cross-check the auto- and cross-correlation of phases of the derived maps and foregrounds, and mark off those multipoles in which the non-Gaussianity results from the foreground contaminations. We apply this statistic on the derived signals from the 1-year WMAP data. The auto-correlations of phases from the internal linear combination map show the significance above 95% C.L. against the random phase hypothesis on 17 spherical harmonic multipoles, among which some have pronounced cross-correlations with the foreground maps. We find that most of the non-Gaussianity found in the derived maps are from foreground contaminations. With this method we are better equipped to approach the issue of non-Gaussianity of primordial origin for the upcoming Planck mission.