Comparing and Combining Cosmic Microwave Background Data Sets

One of the best ways of spotting previously undetected systematic errors inCMB experiments is to compare two independent observations of the same region.We derive a set of tools for comparing and combining CMB data sets, applicablealso in the common case where the two have different resolution or beam shapeand therefore do not measure the same signal. We present a consistency testthat is better than a chi-squared test at detecting systematic errors. We showhow two maps of different angular resolution can be combined without smoothingthe higher resolution down to the lower one, and generalize this to arbitrarybeam configurations. We also show how lossless foreground removal can beperformed even for foreground models involving scale dependence, latitudedependence and spectral index variations in combination.