HOW TO MEASURE CMB POWER SPECTRA WITHOUT LOSING INFORMATION

A new method for estimating the angular power spectrum C-l from cosmic microwave background (CM) maps is presented, which has the following desirable properties. (1) It is unbeatable in the sense that no other method can measure C-l with smaller error bars. (2) It is quadratic, w hich makes the statistical properties of the measurements easy to comp ute and use for estimation of cosmological parameters. (3) It is compu tationally faster than rival high-precision methods such as the nonlin ear maximum-likelihood technique, with the crucial steps scaling as n( 2) rather than n(3), where n is the number of map pixels. (4) It is ap plicable to any survey geometry whatsoever, with arbitrary regions mas ked out and arbitrary noise behavior. (5) It is not a ''black-box'' me thod, but quite simple to understand intuitively: it corresponds to a high-pass filtering and edge softening of the original map followed by a straight expansion in truncated spherical harmonics. It is argued t hat this method is computationally feasible even for future high-resol ution CMB experiments with n similar to 10(6)-10(7). It is shown that C-l computed with this method is useful not merely for graphical prese ntation purposes, but also as an intermediate (and arguably necessary) step in the data analysis pipeline, reducing the data set to a more m anageable size before the final step of constraining Gaussian cosmolog ical models and parameters - while retaining all the cosmological info rmation that was present in the original map.