Determining cosmic microwave background anisotropies in the presence of foregrounds

Separating foregrounds from the signal is one of the major challenges in cosmic microwave background (CMB) experiments. A simple way to estimate the CMB temperature in a given pixel is to fit for the amplitudes of the CMB and the various foreground components. The variance squared of this estimator is shown to be equal to (FDF)(2) sigma(theta)((0)2) + sigma(shape)(2)s where sigma(theta)((0)) is the variance in the absence of foregrounds, sigma(shape) is the variance due to the uncertainty in the shapes of the foreground components, and FDF is the foreground degradation factor. This one number, the FDF, gives a good indication of the ability of a given experiment to disentangle the CMB from foreground sources. A variety of applications relating to the planning and analyzing of experiments is presented. This approach, viz., analyzing the variance, can be used to assess the usefulness of any estimator.