A method for subtracting foregrounds from multifrequency CMB sky maps**

An improved method for subtracting contaminants from cosmic microwave background (CMB) sky maps is presented, and used to estimate how well future experiments will be able to recover the primordial CMB fluctuations. We find that the naive method of subtracting foregrounds (such as dust emission, synchrotron radiation, free-free emission, unresolved point sources, etc.) on a pixel-by-pixel basis can be improved by more than an order of magnitude by taking advantage of the correlation of the emission in neighbouring pixels. The optimal multifrequency subtraction method improves on simple pixel-by-pixel subtraction, both by taking noise levels into account and by exploiting the fact that most contaminants have angular power spectra that differ substantially from that of the CMB. The results are natural to visualize in the two-dimensional plane with axes defined by multipole L and frequency v. We present a brief overview of the geography of this plane, showing the regions probed by various experiments and where we expect contaminants to dominate. We illustrate the method by estimating how well the proposed ESA COBRAS/SAMBA mission will be able to recover the CMB fluctuations against contaminating foregrounds.