4.2. IRAS Flux Densities - Completeness
With the exception of 19 sources which were not detected at 12 µm, the objects in the RBGS were detected in all four IRAS bands. Therefore, despite the fact that the RBGS was selected only on the basis of 60 µm, the flux distributions and infrared colors involving all four of the IRAS bands (see Table 1) are a fair representation of the true distributions of the IRAS properties of galaxies selected at 60 µm.
The distribution of fluxes in Table 1 can be compared with the distribution N(S) S-1.5 expected for a complete sample of objects in a non-evolving Euclidean universe that should be a reasonable approximation for the relatively small redshift range covered by the objects in the RBGS. Figure 4 shows the integral and differential logN - logS plots for each IRAS band. The apparent turn over in the fainest bin of the differential source counts suggests a possible incompleteness near the 60 µm sample flux limit. However, this interpretation is based on the assumption that the volume shell containing the bulk of these objects is as uniformly filled with galaxies as the shells containing the brighter galaxies; studies of large-scale structure indicate that such uniformity is not actually present. In addition, the error bars plotted in Figure 4 are merely statistical uncertainties, N1/2; they do not account for other possible errors. The relatively constant slope of the number of sources versus flux density at 60 µm down to the selection limit, with a power law fit of -1.48 ± 0.13 in the integral counts, shows that at 60 µm the RBGS is reasonably complete to the selection limit of 5.24 Jy.
Figure 4. Integral and differential number counts vs. flux density (logN - logS) for objects in the RBGS. Nineteen objects with upper limits are not included in the 12 µm. The bins have width d(log S) = 0.1, and the thin vertical bars represent statistical uncertainties (i.e., N1/2).
At 12 µm, 25 µm, and 100 µm, there is a portion of the logN - logS plot that follows the -1.5 power-law relation, suggesting that the RBGS sample contains a complete flux-density-limited sample at those wavelengths to the turnover point in the plots (i.e. near log S = -0.1, 0.0, and 1.1 at 12 µm, 25 µm, and 100 µm respectively). The turnover point represents the flux-density value beyond which a significant population of sources is being lost as a result of the 60 µm selection criterion. At 100 µm the turnover is at a value S ~ 16 Jy, nearly 10 times the completeness limit of the PSC at 100 µm (IRAS Explanatory Supplement 1988), and is consistent with the rare occurrence of "extremely cold" galaxies with S100 / S60 > 3.5. At 25 µm the turnover point at 0.8Jy is only a factor of ~ 2.2 above the PSC completeness limit at 25 µm, and the turnover reflects a true loss of "warm" IRAS galaxies with S25 / S60 > 0.15 from the RBGS. Similarly at 12 µm where the turnover at ~ 0.75Jy is again approximately twice the PSC completeness limit at 12 µm, there is a true loss of objects with S12 / S60 > 0.1 from the RBGS.