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The cosmic microwave background $B$-mode signal is potentially weaker thanthe diffuse Galactic foregrounds over most of the sky at any frequency. Acommon method of separating the CMB from these foregrounds is via pixel-basedparametric-model fitting. There are not currently enough all-sky maps to fitanything more than the most simple models of the sky. By simulating theemission in seven representative pixels, we demonstrate that the inclusion of a5 GHz data point allows for more complex models of low-frequency foregrounds tobe fitted than at present. It is shown that the inclusion of the CBASS datawill significantly reduce the uncertainties in a number of key parameters inthe modelling of both the galactic foregrounds and the CMB. The extra dataallow estimates of the synchrotron spectral index to be constrained much morestrongly than is presently possible, with corresponding improvements in theaccuracy of the recovery of the CMB amplitude. However, we show that to placegood limits on models of the synchrotron spectral curvature will requireadditional low-frequency data.

The C-Band All-Sky Survey (C-BASS): Simulated parametric fitting in single pixels in total intensity and polarization