Determining foreground contamination in cosmic microwave background observations: Diffuse Galactic emission in the MAXIMA-I field

Observations of the cosmic microwave background (CMB) can be contaminated by diffuse foreground emission from sources such as Galactic dust and synchrotron radiation. In these cases, the morphology of the contaminating source is known from observations at different frequencies, but not its amplitude at the frequency of interest for the CMB. We develop a technique for accounting for the effects of such emission in this case, and for simultaneously estimating the foreground amplitude in the CMB observations. We apply the technique to CMB data from the MAXIMA-1 experiment, using maps of Galactic dust emission from combinations of IRAS and DIRBE observations, as well as compilations of Galactic synchrotron emission observations. The spectrum of the dust emission over the 150-450 GHz observed by MAXIMA is consistent with preferred models, but the effect on CMB power spectrum observations is negligible.