An Efficient Technique to Determine the Power Spectrum from Cosmic Microwave Background Sky Maps

There is enormous potential to advance cosmology from statisticalcharacterizations of cosmic microwave background sky maps. The angular powerspectrum of the microwave anisotropy is a particularly important statistic.Existing algorithms for computing the angular power spectrum of a pixelized maptypically require O(N^3) operations and O(N^2) storage, where N is the numberof independent pixels in the map. The MAP and Planck satellites will producemegapixel maps of the cosmic microwave background temperature at multiplefrequencies; thus, existing algorithms are not computationally feasible. Inthis article, we introduce an algorithm that requires O(N^2) operations andO(N^1.5) storage that can find the minimum variance power spectrum from sky mapdata roughly one million times faster than was previously possible. This makesfeasible an analysis that was hitherto intractable.Comment: 35 pages, 8 figures, LaTex, aaspp4. Accepted by ApJ. Minor changes to match accepted versio