The one-dimensional Fourier representation and large angular scale foregroundcontamination in the three-year Wilkinson Microwave Anisotropy Probe data

Abstract

We employ the one-dimensional Fourier representation (1DFR) to analyse the three-yearWMAP de-biased internal linear combination (DILC) map and its possible contaminationwith galactic foregrounds. The 1DFR is a representation of the spherical harmoniccoefficients for each ℓ mode using an inverse Fourier transform into one-dimensional curves. On the basis ofthe a priori assumption that the cosmic microwave background signal shouldbe statistically independent of, and consequently have no significant correlationwith, any foregrounds, we cross correlate the 1DFR curves of 2 ≤ ℓ ≤ 10 modes, which are claimed by the WMAP team to be free of contamination and suitablefor whole-sky analysis. We find that eight out of the nine modes are negatively crosscorrelated with the foreground maps, an event which has a probability of only 9/512 ≃ 0.0176 for uncorrelated signals. Furthermore, the local extrema of the 1DFR curves between theDILC and those of the foregrounds for ℓ = 2 and 6 are correlated with significance level below 0.04. We also discuss the minimumvariance optimization method and use the properties of the measured cross correlation toestimate the possible level of contamination present in the DILC map.