Mask Bias in Annulus Means: How Much a Galactic Cut Can Move an Azimuthal Average, Computed on Synthetic Skies

Every azimuthal-average analysis of the real microwave sky is performed through a galactic mask, and the mask is not innocent: in the rotated frame of a chosen axis the galactic band cuts each annulus unevenly, removing different azimuths at different latitudes. This paper measures what that does to annulus means, using six hundred synthetic Gaussian skies analysed with and without a Planck-like galactic band. The standard estimator, the mean of unmasked samples, is unbiased to within 0.39 microK at every annulus, but the mask adds scatter: the root-mean-square extra standard deviation across annuli is 3.43 microK, peaking at 6.0 microK where the band crosses an annulus most obliquely. At the cold-ring annulus the figures are -0.13 microK of bias and 5.27 microK of extra scatter. Mask effects are therefore a noise contribution to be budgeted, at the level of a few microK, not a bias capable of manufacturing or hiding a deep ring. The study is simulated, not measured.