Andrew Blain and I have been carrying out some computations of the expected source counts and background emission expected from star-forming galaxies at large redshifts in the submillimeter and millimeter wavebands (Blain and Longair 1993). Until recently, the prospects for making surveys of sources in the submillimeter waveband have not been very encouraging because of the lack of array detectors which would allow a significant region of sky to be surveyed. The situation will change dramatically in the near future with the introduction of submillimeter bolometer array detectors on telescopes such as the James Clerk Maxwell Telescope. Specifically, the Submillimeter Common User Bolometer Array (SCUBA) currently being completed for that telescope will enable the mapping of regions of the sky in these wavebands to be carried out about 10,000 times faster than is possible with the current generation of single element detectors.
It might be thought that the detection of star-forming galaxies at cosmologically interesting distances would be very difficult because nearby examples of these types of galaxy are only weak submillimeter emitters. This problem is, however, more than offset by the enormous far infrared luminosities of these galaxies which are redshifted into the submillimeter waveband at redshifts greater than about 1. Specifically, the far infrared spectra of IRAS galaxies peak about 100 µm and have very steep spectra, I where is about 3-4. As a consequence, the `K-corrections' are very large and negative at submillimeter wavelengths. The result is that, at redshifts greater than 1, the flux density of a standard IRAS galaxy is more or less independent of redshift until the far infrared maximum is redshifted through the submillimeter wavebands. This is illustrated in Fig. 4 which shows the expected flux density-redshift relations for a galaxy emitting 1013 L with a standard dust emission spectrum at temperatures of 30 and 60 K as observed at 450 and 1100 µm. Correspondingly, the counts of submillimeter sources show a remarkable behavior at those flux densities at which the `coasting phase' in the flux density-redshift relation is reached. The predicted differential number counts for a single luminosity class of source at different wavelengths and for different assumed temperatures of the dust grains are shown in Fig. 5. These differential counts have to be convolved with the luminosity function of the sources and this can be found from the IRAS luminosity function derived by Saunders et al. (1990). The differential source counts for a uniform population of sources is shown in Fig. 6 in which it can be seen that there is an enormous excess over the expectations of a `Euclidean' model. It must be emphasized that these computations are carried out for a uniform world model and that the apparent `excess' is entirely due to the large and negative K-corrections. If the effects of cosmological evolution are included, an even more remarkable excess of faint sources and extraordinarily steep source counts are predicted. Fig. 7 shows the results of incorporating the effects of luminosity evolution of the form L (1 + z)3 in the redshift interval 0 z 2 and a constant value at larger redshifts, L = 27 L0 where L0 is the luminosity of sources at zero redshift; according to Peacock (1993), this form of evolution can account not only for the radio and optical counts of quasars and radio sources but also for the counts of IRAS galaxies. In this case, there would be very large surface densities of submillimeter sources at flux densities which will be accessible to instruments such as SCUBA.
Figure 5. The flux density-redshift relations for a standard dust emission spectrum from a source of far infrared luminosity 1013 L evaluated for dust temperatures of 30 and 60 K and for wavelengths of 450 and 1100 µm (Blain and Longair 1993).
Figure 6. Differential source counts normalized to the expectations of a Euclidean world model for a uniform distribution of standard dust sources at temperatures of 30 and 60 K as observed at wavelengths of 450 and 1100 µm. The bolometric luminosity of the dust source is assumed to be 1013 L (Blain and Longair 1993).
Figure 7. 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 and luminosities of the sources are unchanged with cosmic epoch. (Blain and Longair 1993).