tokens: and the lack of a large additional population of variable sources beyond those identified with the CRATES catalogue. 4.4 Differential source counts Differential source counts have been intensively studied (e.g. de Zotti et al. 2005 ; de Zotti et al. 2010 ; AMI Consortium et al. 2011 ), having important implications for models of cosmic evolution (e.g. Condon 1984 ; Massardi et al. 2010 ) and provided the first clear evidence against the Steady State Theory (Pooley Ryle 1968 ). However, for the purposes of C-BASS analysis, we calculate the differential source counts to provide an additional cross-check on the statistical properties of our bright-source population. Given that we are concerned with the statistical properties of our catalogue at flux-densities , where the C-BASS catalogue is largely complete, we do not consider correction factors to the differential source counts necessary at lower flux densities to account for catalogue incompleteness and varying flux-density sensitivities across the sky. Sources are put into flux-density bins of width . For each bin, source counts are determined against a central flux density, S c , taken to be the geometric mean of flux densities in that bin. The differential source counts for a given flux-density bin are then given by where N c is the number of sources in the flux-density bin, A is the sky area to which the catalogue corresponds, and Δ S is the bin width. Errors are estimated for the source counts by assuming Poisson statistics. We only consider bins with N c ≥ 9 so as to maintain a SNR ≥ 3 for each bin. The differential source counts for C-BASS North in total intensity, applying the CG30 mask, are plotted in Fig. 12 , alongside the differential source counts for the GB6 catalogue. We can see that at low flux densities the C-BASS source counts are significantly lower. This is to be expected from the increasing catalogue incompleteness at these lower flux densities. From the differential source counts, we can again see the catalogue completeness level from the point at which the source count turn-off ends and we have good agreement between the C-BASS and GB6 counts, i.e. over flux densities . It is worth noting here that the errors obtained from assuming Poisson statistics are likely to be somewhat optimistic. These do not account for false positives in the source catalogues, or errors arising from incorrect binning due to uncertain flux-density estimates. These effects become significant at lower flux densities, where the proportion of false positives in the catalogue is greater, and our photometry methods become less reliable. Figure 12. Differential source counts calculated using the C-BASS northern sky total intensity catalogue, plotted alongside the differential source counts for the GB6 catalogue. Source counts were calculated applying the CG30 mask. We also plot as grey-scale the fitted model source counts corresponding to 100 posterior samples for the C-BASS and GB6 models. At low-flux
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