Removing real-world foregrounds from cosmic microwave background maps

Most work on foreground removal has treated the case where the frequency dependence of all components is perfectly known and independent of position. In contrast, real-world foregrounds are generally not perfectly correlated between frequencies, with the spectral index varying slightly with position and (in the case of some radio sources) with time. A method incorporating this complication is presented and illustrated with an application to the upcoming satellite missions MAP and Planck. We find that even spectral index variations as small as Delta alpha similar to 0.1 can have a substantial impact on how channels should be combined and on attainable accuracy.