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 |
|
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 |
|
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). |