Asymmetry and non-random orientation of the inflight effective beam pattern in the WMAP Data

The anomaly against the Gaussianity in the WMAP data was alleged to be due to insufficient handling of beam asymmetries. In this paper we investigate this issue and develop a method to estimate the shape of the inflight effective beam, particularly the asymmetry and azimuthal orientation. We divide the whole map into square patches and exploit the information in the Fourier space. For patches containing bright extra-galactic point sources, we can directly estimate their shapes, from which the inflight effective beam manifests itself. For those without, we estimate the pattern via perturbing the phases and directly from the Fourier amplitudes. We show that the inflight effective beam convolving the signal is indeed non-symmetric for most part of the sky, and it's not randomly oriented. Around the ecliptic poles, however, the asymmetry is smaller due to the averaging effect from different orientations of the beam from the scan strategy. The effective beam with significant asymmetry is combing with almost parallel fashion along the lines of Ecliptic longitude. In the foreground-cleaned ILC map, however, the systematics caused by beam effect is significantly lessened.