2.3. The luminosity density

Averaging over the luminosity function to compute a comoving emissivity of the galaxy population (i.e., the luminosity density of the Universe) as a function of redshift in a particular waveband has proved to be a powerful tool (Cowie et al. 1995, Pei and Fall 1995, Lilly et al. 1996). This approach sidesteps many of the present uncertainties regarding the evolution of single objects and unresolved issues such as whether star-formation occurs in bursts or as a steady process, and the degree of merging between galaxies, have no effect on the derived luminosity density of the Universe. Even the effects of the cosmological model are weak, (1 + z)^0.5. In effect, the Universe is considered as a single stellar system and the identity of individual galaxies is submerged. This is both the strength and weakness of this approach. The luminosity density approach is particularly powerful when combined with other global measures of the Universe, such as changes in the quantity and metallicity of neutral Hydrogen in the Universe (e.g., Pei and Fall 1995, Fall and Pei 1996).

Using the CFRS redshift sample and attempting to correct for sources below the survey limits, Lilly et al. (1996) found that the luminosity densities in the ultraviolet, optical and far-red wavebands increase strongly with redshift out to z = 1. We estimated L₂₈₀₀ (1 + z)^3.9±0.7, L_B (1 + z)^2.7±0.5 and L₁₀₀₀₀ (1 + z)^2.2±0.5 for ₀ = 1 (the exponents are reduced by 0.5 for ₀ = 0). The increase in [O II] 3727 luminosity density (Hammer et al. 1997, Cowie et al. 1995) is comparable to that seen in at 2800 Å.

For a constant initial mass function (i.m.f.) and constant extinction by dust, the ultraviolet luminosity density should reflect the instantaneous star-formation rate, suggesting that the Universe was forming stars of order 10 times faster, per comoving volume, than it is now. An interesting question was whether a self-consistent model for the stellar content of the Universe as a whole can be found. A self-consistent model with a Salpeter initial mass and a turn-down in the ^-2 increase in star-formation rate at around z ~ 2 was found to work (Lilly et al. 1996). Models with i.m.f.s that are more deficient in high mass stars or with ever increasing star-formation rates at early epochs overproduced the near-infrared light from long-lived stars (see also Piero Madau's contribution to these proceedings).

The luminosity density approach has been used and extended to higher redshifts by Madau et al. (1996) and Connolly et al. (1997) using photometrically estimated redshifts of galaxies in the HDF. Both studies suggest that the rise seen in the CFRS does indeed not continue indefinitely and that a peak in the ultraviolet luminosity density exists in the region 1.0 < z < 2.5.

A major uncertainty in interpreting the changes in ultraviolet luminosity density is the role of dust. The v_Lv luminosity density at 60 µm at the present epoch (Saunders et al. 1990) is about 2/3 as large as that at 4400 Å and 2.5 times larger that at 2800 Å. It also probably increases as roughly (1 + z)³ towards z ~ 1 (Pearson & Rowan-Robinson 1996). Further information on the role of dust will come from ISO (see Rowan-Robinsons contribution to these proceedings) and particularly from sub-millimeter measurements at high redshifts that will come from a new generation of sensitive array bolometers such as SCUBA on JCMT (see Smail et al. 1997). Early indications from both of these are that dust continues to play a significant role in absorbing and re-radiating ultraviolet light from high redshift galaxies.