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 its 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.

Direct measurement of the angular power spectrum of cosmic microwave background temperature anisotropies in the WMAP Data

Angular power spectrum of the cosmic microwave background (CMB) temperature anisotropies is one of the most important on characteristics of the Universe such as its geometry and total density. Using flat sky approximation and Fourier analysis, we estimate the angular power spectrum from an ensemble of least foreground-contaminated square patches from WMAP W and V frequency band map. This method circumvents the issue of foreground cleaning and that of breaking orthogonality in spherical harmonic analysis due to masking out the bright Galactic plane region, thereby rendering a direct measurement of the angular power spectrum. We test and confirm Gaussian statistical characteristic of the selected patches, from which the first and second acoustic peak of the power spectrum are reproduced, and the third peak is clearly visible albeit with some noise residual at the tail.

Cross-Power Spectrum and Its Application on Window Functions in the WMAP data

Cross-power spectrum is a quadratic estimator between two maps that can provide unbiased estimate of the underlying power spectrum of the correlated signals, which is therefore used for extracting the power spectrum in the WMAP data. In this paper we discuss the limit of cross-power spectrum and derive the residual from uncorrelated signal, which is the source of error in power spectrum extraction. We employ the estimator to extract window functions by crossing pairs of extragalactic point sources. We desmonstrate its usefulness in WMAP Difference Assembly maps where the window functions are measured via Jupiter and then extract the window functions of the 5 WMAP frequency band maps.

Cosmic Covariance and the Low Quadrupole Anisotropy of the Wilkinson Microwave Anisotropy Probe (WMAP) Data

The quadrupole power of cosmic microwave background (CMB) temperature anisotropies seen in the WMAP data is puzzlingly low. In this paper we demonstrate that Minimum Variance Optimization (MVO), a technique used by many authors (including the WMAP science team) to separate the CMB from contaminating foregrounds, has the effect of forcing the extracted CMB map to have zero statistical correlation with the foreground emission. Over an ensemble of universes the true CMB and foreground are indeed expected to be uncorrelated, but any particular sky pattern (such as the one we happen to observe) will generate non-zero measured correlations simply by chance. We call this effect cosmic covariance and it is a possible source of bias in the CMB maps cleaned using the MVO technique. We show that the presence of cosmic covariance is expected to artificially suppress the variance of the Internal Linear Combination (ILC) map obtained via MVO. It also propagates into the multipole expansion of the ILC map, generating a quadrupole deficit with more than 90% confidence. Since we do not know the CMB and the foregrounds a priori, there is therefore an unknown contribution to the uncertainty in the measured quadrupole power, over and above the usual cosmic variance contribution. Using the MVO on a series of Monte Carlo simulations that assume Gaussian CMB fluctuations, we estimate that the real quadrupole power of the CMB lies in the range [305.16,400.40] microKelvin^2 (at the 1-sigma level).

Phase analysis of the cosmic microwave background from an incomplete sky coverage

Phases of the spherical harmonic analysis of full-sky cosmic microwave background (CMB) temperature data contain useful information complementary to the ubiquitous angular power spectrum. In this letter we present a new method of phase analysis on incomplete sky maps. It is based on Fourier phases of equal-latitude pixel rings of the map, which are related to the mean angle of the trigonometric moments from the full-sky phases. They have an advantage for probing regions of interest without tapping polluted Galactic plane area, and can localize non-Gaussian features and departure from statistical isotropy in the CMB.