I will now change tack completely and look at some aspects of galaxy evolution and in particular at the very beautiful analysis by Lilly and Cowie (1987) of the constraints on metal production in large redshift galaxies. Let me first repeat their argument.
The analysis begins with the observation that a prolonged burst of star
formation
in a galaxy has a remarkably flat emission spectrum out to the Lyman
limit at 91.2 nm.
This is nicely illustrated by the model star-bursts synthesized by
Bruzual and presented
by White (1989)
(Fig. 4). These spectra show the integrated
spectra of the starburst
galaxy at different ages assuming that the star formation rate is a
constant and that the
stars are formed with the same Salpeter mass function. The flatness of
the spectrum
is due to the fact that, although the most luminous blue stars have
short lifetimes,
they are constantly being replenished by new stars. Furthermore, the
intensity of the
flat part of the spectrum is directly proportional to the rate of
formation of heavy
elements since their energy is primarily derived from the conversion of
hydrogen into
helium which is the first stage in the formation of the heavy elements -
these are only
formed in stars with mass greater than about 4
M
. From the
model starbursts and
from simple physical arguments, it can be shown that the intensity of
the flat spectrum
region of the spectrum is related to the mass of heavy elements produced
by the simple relation
|
at all wavelengths longer than the Lyman continuum edge at 91.2
nm. 
Z is the rate
of formation of heavy elements. It is a simple calculation to work out
the background
intensity due to such sources and, provided the Lyman limit is not
redshifted into
the observing waveband, Lilly and Cowie show that the intensity expected
for a given
amount of element formation is independent of the cosmological
model. Specifically,
the background intensity due to the formation of a density of the heavy
elements 
m is
|
Notice that the density used in this relation is the density of heavy
elements observed
at the present epoch and that a density of 10-31 kg
m-3 of heavy elements would
correspond roughly to Z = 0.01 in an
= 0.01 Universe. The beautiful
thing about
this relation is that, by inserting the intensity of the background
radiation originating in a particular redshift interval
z, we can immediately
read off the density of metals synthesized in that interval.
|
Figure 4. Synthetic spectra for a region
with constant star formation rate at the ages
indicated. A Salpeter initial mass function has been assumed with
cut-offs at 75 and
0.08 M |
Cowie and Lilly have observed a class of flat spectrum objects in their very deep optical surveys. Originally, it was though that these objects lay at large redshifts but it is now believed that they have redshifts roughly one. The background intensity due to such objects amounted to about 6.6 x 10-25 W m-2 Hz-1 sr-1. Lilly and Cowie interpret this result as meaning that a significant fraction of the heavy elements must have been produced about a redshift of one. In fact, this heavy element abundance is significantly less than the maximum permissible. If we were to assume that H0 = 50 km s-1 Mpc-1, the upper limit to the baryon density in the Universe as determined by the need to produce at least the observed abundance of deuterium is about 0.1. If a maximum metal abundance of Z = 0.03 is adopted, the total background intensity due to metal formation could be up to about 30 or 40 times the intensity already detected by Lilly and Cowie. In fact such an intensity would exceed the upper limit to the background intensity reported by Toller (1990).
Now, it is well known that galaxies undergoing bursts of star formation are not only sources of ultraviolet continuum radiation but also are strong emitters in the far infrared waveband because of the presence of dust in the star forming regions. According to Weedman (1993), in a sample of star forming galaxies studied by the IUE, most of the galaxies emit much more of their luminosities in the far infrared rather than in the ultraviolet region of the spectrum. As a result, it is quite possible that most of the radiation associated with the formation of the heavy elements is not radiated in the ultraviolet-optical region of the spectrum but in the far infrared region and would permit a higher abundance of the elements as compared with the existing optical and ultraviolet limits.
This was one of the motivations for undertaking a study of the feasibility of detecting the far-infrared emission from star-forming galaxies at large redshifts in the submillimeter waveband.