6.2. The global cosmic star-formation history

The rest-frame UV luminosity of galaxies traces nicely their metal production rate, because both are produced primarily by massive stars. On the other hand, the conversion from a UV luminosity density to an actual cosmic star formation rate is somewhat less straightforward, since it involves a knowledge of the Initial Mass Function (IMF).

Early estimates of the metal production rate as a function of redshift, _Z(z), relied on ground-based redshift surveys (Lilly et al. 1996, Gallego et al. 1995) and data from QSO absorption line systems (e.g., Lanzetta et al. 1995, Pei and Fall 1995). These estimates indicated a monotonic increase in the metal production rate from z = 0 to z 1 (with the rate at z 1 being about an order of magnitude higher than at the present).

One of the seminal results to have come out of the HDF-N was the attempt to estimate the metal production rate at high redshifts and thereby to generate a continuous plot of the star formation rate as a function of redshift (Madau et al. 1996). In the original diagram, no corrections were made, for either dust extinction or for surface brightness effects. Consequently, the results were presented as lower limits. Both in the original work and in some of the subsequent work that followed (some of which included the effects of dust extinction), it was found that the star formation rate peaks at a redshift of z ~ 1-2 and decreases or stays nearly constant at higher redshifts (e.g., Fig. 26, Steidel et al. 1999, Hopkins, Connolly and Szalay 2000, Calzetti and Heckman 1999, Pei, Fall and Hauser 1999). The question of whether there truly is a decrease in the star formation rate for z 2 has become a focal point of the discussion of the cosmic star formation history. Some doubts were raised on the basis of dust extinction and selection effects on one hand, and cosmological surface brightness dimming effects on the other. Broadly speaking, the UV luminosity density could be underestimated if a significant fraction of the star formation occurred in environments obscured by dust or in very low-surface-brightness galaxies. Several attemps were made to correct for dust attenuation (using the empirical attenuation law of Calzetti, Kinney and Storchi-Bergmann 1994), by calibrating the relation between the UV spectral slope and the far IR emission (e.g., Meurer, Heckman and Calzetti 1999, Steidel et al. 1999). Others used constraints obtained from extragalactic background radiation and neutral gas (e.g., Pei, Fall and Hauser 1999, Calzetti and Heckman 1999). Most of these investigations concluded that the star formation rate rises from the present to z ~ 1-2 and then stays approximately flat to z ~ 5.

Figure 26. The star formation rate density versus redshift derived from the UV luminosity density. Adapted from Ferguson, Dickinson and Williams (2000).

Another way to address the question of the history of mass assembly in galaxies is to try to measure the actual stellar masses of galaxies (as opposed to the rates of star formation; ideally one would want to do both). To this goal, observations in the near-infrared are typically used, since the near-infrared luminosity traces the stellar mass reasonably well. Dickinson et al. (2003) used an infrared-selected sample of galaxies from the HDF-N to determine the global stellar mass density, _*(z), for 0 < z < 3. They found that _*(z) increases with time from z = 3 to the present (Fig. 27). Dickinson et al. concluded that by z ~ 1, about 50-75% of the present-day stellar mass density had already formed, but that the stellar mass density at z ~ 2.7 was about 17 times lower than today. These observations appear to be in clear contradiction with scenarios in which most stars in today's spheroids formed at z >> 2, but the observations are in general agreement with a global star formation rate that rises from the present to z ~ 1 and then stays fairly flat.

Figure 27. The redshift evolution of the co-moving stellar mass density. The vertical extent of the boxes shows the range of systematic uncertainty. The bottom two solid lines (on the right-hand scale) show the result of integrating the star-formation-rate histories traced by the rest-frame UV light, with and without corrections for dust extinction. The top two solid lines and the dashed line show theoretical predictions from semi-analytical galaxy evolution models (Cole et al. 2000, Somerville, Primak, and Faber 2001). Adapted from Dickinson et al. (2003).

A different spin on the cosmic star formation rate has been put by Lanzetta et al. (2002). These authors claimed that by neglecting cosmological surface brightness dimming effects, previous works have missed a significant fraction of the ultraviolet luminosity density at high redshifts. Specifically, since the surface brightness decreases with redshift as (1 + z)^-3 (because of the cosmic expansion), intrinsically faint regions of high-redshift galaxies become undetectable.

Lanzetta et al. designated the unobscured star formation rate intensity (i.e., the intensity inferred from the observed rest-frame UV light) by x, and used a distribution function h(x) (defined so that h(x)dx is the projected proper area per comoving volume of star formation rate intensity in the interval x to x + dx), to estimate the ultraviolet luminosity density at high redshifts (including the surface brightness dimming effects). They found that the star formation rate density, _s, increases monotonically with redshift to the highest redshifts observed (z ~ 8; although in one of the possible corrections for incompleteness _s remains fairly flat above z ~ 2).

The low fraction of stellar mass formed by z = 3 according to the Dickinson et al. results appears to contradict evidence for significant star formation occurring at still higher redshifts. One possible way out of this conundrum is that the initial mass function (IMF) at high redshifts is very top-heavy (tilted towards massive stars; Ferguson et al. 2002). Massive stars dominate the UV luminosity in star forming galaxies, but their contribution to the total surviving (at lower redshifts) stellar mass is relatively low.

Most recently, Stanway, Bunker and McMahon (2003) used HST's Advanced Camera for Surveys, the ground-based Sloan Digital Sky Survey and the Very Large Telescope (VLT) to determine the space density of UV-luminous starburst galaxies at z ~ 6. They found a lower bound to the integrated, volume-averaged, global star formation rate at z ~ 6, that was about six times less than that at z ~ 3-4. The question of the true behavior of _s above z ~ 2 remains, therefore, presently somewhat unresolved.

Fortunately, a more definitive answer may come in the near future, through a combination of planned observations with HST and with the Space Infrared Telescope Facility (SIRTF; currently scheduled to be launched in April 2003). The Great Observatories Origins Deep Survey (GOODS; Principal Investigator M. Dickinson) will produce a very deep image of two fields (the HDF-N and the southern deep field observed with the Chandra Observatory) with SIRTF at 3.6-24 µm, and will thereby produce a much more complete census of stellar mass at high redshifts. At the same time, observations (of the same fields) with Hubble's Advanced Camera for Surveys (Principal Investigator M. Giavalisco; the observations are being carried out as these lines are being written) will determine the star formation rates, sizes, and morphologies of galaxies. The combined observations will allow for the first time for a determination of the evolving mass assembly distribution f (M, , t) (where M denotes the stellar mass and the star formation rate). Given the fact that under pure luminosity evolution, M = dt, a comparison between the observed evolution of the (M, ) phase space with time and the evolution obtained from direct integration (of , to produce M), will allow, in principle, for an identification of the role of mergers and interactions. Even when the expected observational uncertainties are taken into account, there is no doubt that the planned GOODS observations will yield a huge step forward in the understanding of the assembly of present-day galaxies, and their morphological evolution (the emergence of the "Hubble Sequence"). Furthermore, the planned Hubble Ultra Deep Field with the Advanced Camera for Surveys (currently scheduled for July-August 2003) could extend the redshift coverage unambiguously to z ~ 6, close to the tail of the tentative second reionization epoch (Fan et al. 2001, Becker et al. 2001) of the universe (the first reionization having tentatively occurred at z ~ 20⁺¹⁰_-9; Bennett et al. 2003). Such a study could therefore produce results that are not merely incremental in our understanding of the cosmic star formation history, galaxy evolution, and the ionization history of the universe, and that can be used to place meaningful constraints on theoretical models (e.g., Somerville and Livio 2003).