As part of our analysis, we have investigated the feasibility of distinguishing different models of galaxy formation by submillimeter observations. The expectations of Hot Dark Matter or "pancake" models in which large scale structures form first at relatively late epochs can be well approximated by the evolution models described at the end of the last section and result in very steep number counts of submillimeter sources. In fact, it is a quite general result that any model in which the bulk of the star and galaxy formation takes place at redshifts of the order 2-5 results in large number densities of sources at accessible submillimeter flux densities. The background radiation from such populations are strongly constrained by the fact that the spectrum of the Cosmic Microwave Background Radiation is known to be very precisely of black-body form in the wavelength interval 2500 to 500 µm. The problem can be alleviated if it is assumed that the dust grains in the large redshift star-forming galaxies are at a higher temperature, say, 60-80 K.
The currently favored picture of galaxy formation involving Cold Dark Matter and hierarchical clustering of galaxies can be modeled using the Press-Schechter formulation for the mass function of galaxies as a function of cosmic epoch (Press and Schechter 1974). We have converted this function into a rate of coalescence of small galaxies into larger ones and assumed that each time this occurs a fixed fraction of the mass involved in the collision results in star formation with the standard dust emission spectrum. As expected, the number counts in these models are not nearly as remarkable at those expected in the strong evolution models because the galaxies are built up gradually over a long time period and become more rather than less luminous at later epochs. The number densities of submillimeter sources are expected to be much smaller in these models at the same flux density.
The millimeter background radiation from these models is, however, of considerable interest. The results of computations of the background intensity expected from these models is shown in Fig. 8 and compared with the current upper limits to the deviations of the spectrum of the Cosmic Microwave Background Radiation from a pure black-body spectrum. It can be seen that the upper limits are precisely parallel to the upper limits to the contribution which such sources could make to the background radiation. It can be seen that these models are already constrained by the remarkable precision with which the spectrum of the Cosmic Microwave Background Radiation is known to be of black body form. The point of special interest is the fact that the predicted background radiation spectrum extends well into the millimeter waveband. This background is associated with star formation in coalescing galaxies at redshifts of the order of 10 or more. The intriguing point is that these galaxies must be far infrared emitters due to the star formation which must occur as the small galaxies collide to form larger ones. It is apparent that the precise spectrum is sensitive to the exact assumptions made about the amount of star formation associated with each coalescence but, quite independent of these predictions, the millimeter and submillimeter background radiation provide a direct measure of the rates of star formation as a function of cosmic epoch.
Figure 8. The normalized differential source counts of all IRAS galaxies at wavelengths of 450 and 1100 µm for assumed dust temperatures of 30 and 60 K. It is assumed that the comoving number densities are unchanged with cosmic epoch but that the luminosities of the sources evolve as (1 + z)3 in the redshift interval 0 < z < 2 and remain constant at 27 times the local luminosity at all redshifts greater than 2. (Blain and Longair 1993).
The prediction of this analysis is that, at some sensitivity level, it must be possible to detect the integrated emission from star formation in young galaxies and that by measuring precisely the spectrum of the background due to these galaxies in the millimeter and submillimeter wavebands, the rate of star formation at very large redshifts can be read off directly. These observations would be of the utmost cosmological importance. The magnificent COBE spectrum of the background is already constraining these models but with further increase in sensitivity, the young galaxies must make their presence known.
Figure 9. Comparison of the integrated background emission expected from dusty merging galaxies with the intensity of the Cosmic Microwave Background Radiation and upper limits to the far infrared background radiation from the IRAS survey. The assumed temperatures of the dust grains are 30 K (solid lines) and 60 K (dashed lines). In each case, the upper curve has been normalized to the maximum allowable density of metals at the present epoch. The lower curve corresponds to about one tenth that density of metals. The dotted lines correspond to 1%, 0.25% and 0.1% of the maximum intensity of the Cosmic Microwave Background Radiation. (Blain and Longair 1993).