Bayesian analysis of the low-resolution polarized 3 year WMAP sky maps

We apply a previously developed Gibbs sampling framework to the foreground-corrected 3 yr WMAP polarization data and compute the power spectrum and residual foreground template amplitude posterior distributions. We first analyze the co-added Q- and V-band data, and compare our results to the likelihood code published by the WMAP team. We find good agreement, and thus verify the numerics and data-processing steps of both approaches. However, we also analyze the Q- and V-band data separately, allowing for nonzero EB cross-correlations and including two individual foreground template amplitudes tracing synchrotron and dust emission. In these analyses, we find tentative evidence of systematics: The foreground tracers correlate with each of the Q- and V-band sky maps individually, although not with the co-added QV map; there is a noticeable negative EB cross-correlation at l ≾ 16 in the V-band map; and finally, when relaxing the constraints on EB and BB, noticeable differences are observed between the marginalized band powers in the Q and V bands. Further studies of these features are imperative, given the importance of the low-l EE spectrum on the optical depth of reionization τ and the spectral index of scalar perturbations ns.