Determining cosmic microwave background anisotropies in the presence of foregrounds

Separating foregrounds from the signal is one of the big 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 $[(FDF)^2\ \sigzt + \sigsh^2]$, where $\sigz$ is the variance in the absence of foregrounds; $\sigsh$ is the variance due to the uncertainty in the shapes of the foreground components; and FDF is the {\it 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.