A maximum likelihood analysis of the low cosmic microwave background multipoles from theWilkinson Microwave Anisotropy Probe

The amplitudes of the quadrupole and octopole measured from the Wilkinson Microwave Anisotropy Probe (WMAP) appear to be lower than expected according to the concordance cold dark matter ( CDM) cosmology. However, the pseudo-C estimator used by the WMAP team is non-optimal. In this paper, we discuss the effects of Galactic cuts on pseudo-C and quadratic maximum likelihood estimators. An application of a quadratic maximum likelihood estimator to Galaxy-subtracted maps produced by the WMAP team and Tegmark, de Oliveira-Costa & Hamilton shows that the amplitudes of the low multipoles are stable to different Galactic cuts. In particular, the quadrupole and octopole amplitudes are found to lie in the ranges T 2 2 = 176-250 (K) 2 and T 2 3 = 794-1183 (K) 2 (and more likely to be at the upper ends of these ranges) rather than the values T 2 2 = 123 (K) 2 and T 2 3 = 611 (K) 2 found by the WMAP team. These results indicate that the discrepancy with the concordance CDM model at low multipoles is not particularly significant and is in the region of a few per cent. This conclusion is consistent with an analysis of the low amplitude of the angular correlation function computed from quadratic maximum likelihood power spectrum estimates.