Comparing and combining cosmic microwave background data sets

One of the best ways of spotting previously undetected systematic errors in cosmic microwave background (CMB) experiments is to compare two independen t observations of the same region. We derive a set of tools for comparing a nd combining CMB data sets, applicable also in the common case where the tw o have different resolution or beam shape and therefore do not measure the same signal. We present a consistency test that is better than a chi(2) tes t at detecting systematic errors. We show how two maps of different angular resolution can be combined without smoothing the higher resolution down to the lower one, and we generalize this to arbitrary beam configurations. We also show how lossless foreground removal can be performed even for foregr ound models involving scale dependence, latitude dependence, and spectral i ndex variations in combination.