CMB Power Spectrum Estimation via Hierarchical Decomposition

Abstract

We have developed a fast, accurate and generally applicable method for inferring the power spectrum and its uncertainties from maps of the cosmic microwave background (CMB) in the presence of inhomogeneous and correlated noise. For maps with 10 to 100 thousand pixels, we apply an exact power spectrum estimation algorithm to submaps of the data at various resolutions, and then combine the results in an optimal manner. To analyze larger maps efficiently one must resort to sub-optimal combinations in which cross-map power spectrum error correlations are only calculated approximately. We expect such approximations to work well in general, and in particular for the megapixel maps to come from the next generation of satellite missions.