How to measure CMB polarization power spectra without losing information

Abstract

We present a method for measuring CMB polarization power spectra given incomplete sky coverage and test it with simulated examples such as Boomerang 2001 and MAP. By augmenting the quadratic estimator method with an additional step, we find that the E and B power spectra can be effectively disentangled on angular scales substantially smaller than the width of the sky patch in the narrowest direction. We find that the basic quadratic and maximum-likelihood methods display a unneccesary sensitivity to systematic errors when T-E cross-correlation is involved, and show how this problem can be eliminated at negligible cost in increased error bars. We also test numerically the widely used approximation that sample variance scales inversely with sky coverage, and find it to be an excellent approximation on scales substantially smaller than the sky patch.