5.2. Observational tests of models
The key observational test of models of submm-wave galaxy formation is the redshift distribution, which is know in outline from radio-submm observations (Smail et al., 2000). Determining the redshift distribution is a key goal of extensive ongoing follow-up observations, but the process has proved to be difficult and time-consuming, as documented extensively by Smail et al. (2002). The crucial problems are the faintness of the counterparts, combined with the relatively poor positional accuracy of the centroids of the submm galaxies, which are unresolved due to the coarse spatial resolution of existing submm images.
Detailed measurements of the counts of galaxies at both brighter and fainter flux densities than those shown in Fig. 9 would also constrain models. However, determining the bright counts requires a large-area survey, which is likely to be relatively inefficient (Fig. 23), while determining the faint counts requires greater angular resolution than can be provided by the telescopes used to make existing surveys, to avoid source confusion. The very bright counts will certainly be probed directly towards the end of the decade by the Planck Surveyor all-sky survey at a resolution of 5 arcmin, and sooner by large-area surveys using forthcoming large-format mm/submm-wave bolometer arrays on ground-based telescopes, including BOLOCAM (Glenn et al., 1998) and SCUBA-II. Limits on the bright submm-wave counts can be imposed from the number of candidate point sources that can be found in large-area submm maps of Galactic fields (Pierce-Price et al., 2001; Barnard et al., 2002). The faint counts will ultimately be determined directly using the SMA, CARMA and ALMA interferometers.
The results of deep ISO surveys have been regularly cited as a useful constraint on galaxy evolution (Rowan-Robinson et al., 1997; Xu, 2000; Chary and Elbaz, 2001). This is certainly true out to z 1. However, when estimating a total luminosity density from 15-µm data, it is vital that the correct SED is used to extrapolate to longer wavelengths, as it is easy to overestimate the amount of luminosity associated with a 15-µm source by assuming a mid-IR SED that is too steep. For example, compare the inferred luminosity density results at redshifts z 0.7 quoted by Rowan-Robinson et al. (1997) and Flores et al. (1999). The results differ by a factor of 5; Flores et al. (1999) obtain the lower result by using radio observations to constrain the total luminosity of the galaxies detected at 15 µm. Extrapolating mid-IR data towards the peak of the SED at longer wavelengths is more difficult than extrapolating submm observations to fix the position of the peak of the SED that lies at shorter wavelengths. This is both because the form of the SED is intrinsically simpler on the long-wavelength side of the peak, and because the well-determined spectrum of the far-IR background radiation can be used to constrain the luminosity-averaged dust temperature of the submm galaxies. Mid-IR observations with SIRTF after 2002 will provide much more information about the SEDs and evolution of dusty galaxies to redshifts z 2.
In Fig. 22 we show the deep 15-µm counts predicted by models designed to account for the submm data (Blain et al., 1999b, c), updated to the current data and cosmology. If the mid-IR SED is chosen appropriately, then the fit is quite acceptable. Including PAH emission features or varying the mid-IR SED index has relatively little effect on the result. The same approach can be used to estimate the deep cm-wave radio counts. If we assume just the form of the radio-far-IR correlation (Condon, 1992), without any fine tuning, and a radio SED of the form f -0.6, then the predicted 8.4-GHz counts brighter than 10 µJy, based on the submm-based models are 1.05 and 0.98 arcmin-2 respectively; the corresponding power-law indices of the count function N( > S) S are = - 1.4 and -1.3 respectively. The results in both models match the observed 8.4-GHz 10-µJy count of 1.01 ± 0.14 arcmin-2 with = - 1.25 ± 0.2 (Partridge et al., 1997). The reasonable agreement between the predictions of the models, which are constrained only by observations in the submm and far-IR, and the observed deep mid-IR and radio counts confirms that the models are reliable. The source confusion estimates shown in Fig. 13, which are based on the same models, should thus be reliable over a wide wavelength range from about 10 cm to 10 µm.
Figure 22. A summary of observed (Elbaz et al., 1999) and predicted (Blain et al., 1999b, c) differential counts of galaxies in the 15-µm ISO band. The model predictions assume only a power-law SED in the mid-IR, with f -1.95: no fine-tuning with PAH features in the SED is included. The hierarchical model (Blain et al., 1999c) provides a better fit to the data, but both agree reasonably well with the observations. Both models asymptote to the same count at greater flux densities. Note that the relative form of the model counts reflects that seen in Fig. 9, with the hierarchical model having the steepest rise.