5.1. An array of possible treatments

A variety of approaches have been taken to making predictions for and interpreting the results of submm surveys. This work began after the deep 60-µm counts of IRAS galaxies were derived, and it was clear that strong evolution was being observed out to z ~ 0.1 (Hacking and Houck, 1987; Saunders et al., 1990; Bertin et al., 1997). Observations of more distant galaxies at longer wavelengths could probe the extrapolated form of evolution, and disentangle the degenerate signatures of density and luminosity evolution (Franceschini et al., 1988; Oliver et al. 1992).

Before the first deep submm survey observations in 1997, Franceschini et al. (1991), Blain and Longair (1993a, b, 1996) and Pearson and Rowan-Robinson (1996) made a variety of predictions of what might be detected in submm surveys. Guiderdoni et al. (1998) and Toffolatti et al. (1998) did similarly as the first observational results become available. Generally, the observed surface density of submm galaxies was underpredicted. Prior to the recognition that an isotropic signal in the far-IR COBE-FIRAS data was an extragalactic background (Puget et al., 1996) and not Zodiacal emission (Mather et al., 1994), this could be accounted for by the use of this unduly restrictive limit on the intensity of the submm background spectrum. Once submm count data became available after SCUBA was commissioned, it was possible to take either a more empirical or a more theoretical view of the consequences for dusty galaxy evolution.

On the empirical side, forms of evolution of the low-redshift luminosity function of dusty galaxies (Saunders et al., 1990; Soifer and Neugebauer, 1991) that were required to fit the count and background data could be determined (Malkan and Stecker, 1998, 2001; Blain et al., 1999b; Tan et al., 1999; Pearson, 2001; Rowan-Robinson, 2001). At redshifts less than about unity, this is done by requiring that the predicted counts of low-redshift IRAS and moderate-redshift ISO galaxies are in reasonable agreement with observations. At greater redshifts, where the form of evolution is constrained by submm count and background data, there is significant degeneracy in the models: strong evolution could proceed all the way out to a relatively low cutoff redshift (z ~ 2-3), or the strong evolution could terminate at a lower redshift z ~ 1, followed by a tail of either non-evolving or declining luminosity density out to greater redshifts (z 5) (see Fig. 9 of Blain et al., 1999b). This degeneracy occurs because the far-IR background radiation (like almost all backgrounds) is generated predominantly at z ~ 1, while submm galaxies can contribute to the counts equally at almost any redshift 1 < z < 10. It can be broken by determining a redshift distribution of submm galaxies, which would be very different in the two cases. The form of evolution that is consistent with the latest observational constraints and radio-derived redshift information for submm-selected galaxies (Smail et al., 2002) is shown by the thick solid and dashed lines in Fig. 21.

Figure 21. The history of energy generation in the Universe, parameterized as a star-formation rate per unit comoving volume. The absolute normalization of the curves depends on the assumed stellar IMF and the fraction of the dust-enshrouded luminosity of galaxies that is generated by AGN. The points show results derived from a large number of optical and near-IR studies, for which detailed references can be found in Blain et al. (1999b) and Smail et al. (2002). The most important results are from Lilly et al. (1996; filled stars) and Steidel et al. (1999; high-redshift diagonal crosses). The up-pointing arrow comes from the submm-based estimate of Hughes et al. (1998). An important new measurement of the extinction-free low-redshift star-formation rate from radio data, that is not plotted, has been obtained by Yun et al. (2001): 0.015 ± 0.005 M yr-1. The thick solid and dashed lines represent the current best fits to far-IR and submm data in a simple luminosity evolution model and a hierarchical model of luminous merging galaxies respectively, as updated to reflect additional data and a currently favored non-zero- cosmology. The thinner solid lines show the approximate envelope of 68% uncertainty in the results of the luminosity evolution model. The thin and thick dotted lines represent the best-fitting results obtained in the original derivations (Blain et al., 1999b, c).

Note that the assumptions that underlie these derivations are not yet all verified by observations. It is unclear whether all high-redshift dusty galaxies detected in submm surveys have similar SEDs. It is possible that the properties of the dust grains in galaxies evolve with redshift, leading to a systematic modification to the temperature or emissivity index. It is reasonable to expect the dust-to-gas ratio in the highest redshift galaxies to be lower than in low-redshift galaxies, as less enrichment has taken place. However, note that enrichment proceeds very rapidly once intense star formation activity is underway. Even the very first regions of intense star formation could thus be readily visible in the submm, despite the global metallicity being extremely low. While it seems unlikely, based on a handful of observations (Fig. 2), it is certainly possible that a population of dusty galaxies with a significantly different SED is missing from current calculations (Blain and Phillips, 2002).

A more theoretically-motivated approach, based on making assumptions about the astrophysical processes at work in galaxy evolution and then predicting the observational consequences, has rightly become popular in recent years. These `semi-analytic' models, which were generally developed to explain optical and near-IR observations, take a representative set of dark-matter halos that evolve and merge over cosmic time, from the results of N-body simulations, and determine their star-formation histories and appearance using a set of recipes for star-formation and feedback (White and Frenk, 1991; Kauffmann and White, 1993; Cole et al., 1994, 2000; Guiderdoni et al., 1998; Granato et al., 2000, 2001; Baugh et al., 2001; Benson et al., 2001; Somerville et al., 2001). Unfortunately, at present there is insufficient information from submm observations to justify a model that contains more than a handful of uncertain parameters, and so it is difficult to exploit the full machinery of semi-analytic models to explain the submm observations. Despite the free parameters available, semi-analytic models have had limited success in accounting for the observed population of high-redshift submm galaxies, without adding in an extra population of more luminous galaxies to the standard prescription (Guiderdoni et al., 1998), or breaking away from their traditional reliance on a universal initial mass function (IMF). As more information becomes available, then the full capabilities of the semi-analytic models can hopefully be applied to address dusty galaxy evolution.

In a blend of these approaches, assuming that the SCUBA galaxies are all associated with merging galaxies (Ivison et al., 1998a, 2001; Figs. 14 and 18), and yet not being sure of the physical processes by which the mergers generate the luminosity we observe, Blain et al. (1999c) used a minimally-parametrized semi-analytic model to investigate the change in the properties of merging galaxies required to reproduce the submm and far-IR counts and backgrounds: see also Jameson (2000) and Longair (2000). The observed background spectrum can only be reproduced for strong evolution of the total luminosity density out to redshift z 1, by a factor of about 20 (see Fig. 21). In addition, the lifetime of the luminous phase associated with mergers, and thus the mass-to-light ratio also had to be reduced by a large factor at high redshift in order to reproduce the observed submm counts. The physical reason for this change must be an increased efficiency of star formation during starburst activity or of AGN fueling at increasing redshifts; both make sense in light of the greater gas densities expected at high redshifts. The model has the advantage of being able to reproduce the faint optical counts, if blue LBGs are also associated with merging galaxies. The submm galaxies release about four times more energy in total than the LBGs, and do so over a period of time during a merger that is about ten times shorter. It is likely that the total baryonic mass and geometry of the merging galaxies also play important roles in determining the details of star-formation activity or AGN fueling during a merger.

When reviewing the predictions and results of any model, note that it is easy to produce a model that can account for the far-IR-submm background radiation intensity; more difficult to account for the submm counts; and more difficult again to reproduce a plausible redshift distribution.