Annu. Rev. Astron. Astrophys. 2000. 38: 667-715
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5.5. Global star-formation history and chemical evolution

Interest in the integrated background light from galaxy formation is long-standing (e.g. [Bondi et al. 1955]), and has motivated a large number of experiments aimed at measuring the diffuse extragalactic background (e.g. [Spinrad & Stone 1978, Dube et al. 1979, Matsumoto et al. 1988, Bernstein 1997, Hauser et al. 1998]). Although the integrated background records the light from all galaxies, whether or not they are individually detected, the task of separating out galactic foregrounds and instrumental backgrounds is formidable, and many of the measurements are only upper limits. An alternative approach is to add up the UV emission from galaxies that are individually detected. This approach formally produces only a lower limit for the true UV luminosity density, but it provides a basis for exploring connections of the high- and low-redshift universe and for deciding which of the various selection effects are plausible and important.

The UV emission from galaxies is directly connected to their metal production [Cowie et al. 1988] because the UV photons come from the same massive stars that produce most of the metals through type II SNe. The relation between UV emissivity and metal production is not strongly dependent on the initial mass function, varying by a factor of only 3.3 between the [Salpeter 1955] and [Scalo 1986] forms. In contrast, the relation of UV emission to the total star-formation rate is much more tenuous because the low-mass end of the IMF contains most of the mass whereas the high-mass end produces most of the UV emission. As a result, it is easier to constrain the history of metal production in the universe than it is to constrain the overall star-formation history. Prior to the HDF, estimates of the metal-production vs. redshift, dot{rho}Z(z) had been made from ground-based galaxy redshift surveys [Lilly et al. 1996] and from QSO absorption line statistics (e.g. [Lanzetta et al. 1995, Pei & Fall 1995, Fall et al. 1996]), and the observations at the time suggested an order-of-magnitude increase in dot{rho}Z(z) from z = 0 to z = 1.

[Madau et al. 1996] made the first attempt to connect the luminosity density in HDF high-redshift galaxy samples to lower-redshift surveys. The plot of the metal-formation rate vs. redshift has provided a focal point for discussion of the HDF and for comparisons to theoretical models. In the [Madau et al. 1996] paper, galaxies in redshift slices 2 < z < 3.5 and 3.5 < z < 4.5 were identified by strict color-selection criteria that were shown via simulations to provide strong rejection of objects outside of the desired redshift intervals. The luminosity of the galaxies within these redshift intervals was estimated by simply summing the observed fluxes of the galaxies, and no dust or surface-brightness corrections were applied. The results were presented as lower limits because nearly all of the corrections will drive the derived metal-formation rates up. The initial [Madau et al. 1996] diagram showed a metal-production rate at z ~ 4 that was roughly a factor of 10 lower than the rate at z ~ 1. [Madau 1997] subsequently modified the color-selection criteria and integrated down an assumed luminosity function, revising the z > 2 rates upward by about a factor of 3. There was remarkable agreement between dot{rho}Z(z) derived from the galaxy luminosities, the results of [Pei & Fall 1995], and the predictions of hierarchical models (e.g. [White & Frenk 1991, Cole et al. 1994, Baugh et al. 1998]), all of which show a peak in the metal production rate at z ~ 1 - 2. Subsequent work in this area has focused on (a) galaxy selection (b) effects of dust, and (c) the connection of the Madau diagram to general issues of galaxy evolution and cosmic chemical evolution, which we discuss in turn.

5.5.1. Galaxy Selection

The color-selection criteria of [Madau et al. 1996] are extremely conservative, and spectroscopic surveys [Steidel et al. 1996, Lowenthal et al. 1997] have identified at least a dozen 2 < z < 3.5 galaxies with U300 - B450 > 1.3 but with B450 - I814 redder than the [Madau et al. 1996] selection boundary. Alternative color-selection criteria (particularly in the 2 < z < 3.5 range) have been explored in a number of studies [Clements & Couch1996, Lowenthal et al. 1997, Madau et al. 1998, Meurer et al. 1999], with the result that the luminosity-density goes up as the area in color space is enlarged. The number of low- z interlopers also may go up, although spectroscopic surveys suggest that the [Meurer et al. 1999] selection boundary is not prone to this problem. Similar techniques have been applied to ground-based images covering much wider areas but sensitive only to brighter objects (see, e.g. [Steidel et al. 1999] and [Giallongo et al. 1998] for recent examples). Substantial progress has been made both in refining the estimates of the volume sampled by the color selection and in estimates of the high- z galaxy luminosity functions [Dickinson 1998, Steidel et al. 1999]. These allow more precise (but more model-dependent) estimates of the luminosity density at z > 3. In Fig. 5 we provide an updated plot of star-formation vs. redshift from the color-selected samples of [Steidel et al. 1999] and [Casertano et al. 2000], now including integration down the luminosity function and a correction for mean dust attenuation.

Figure 5

Figure 5. (Left) Star-formation rate density vs. redshift derived from ultraviolet luminosity density. The z > 2 points are from Lyman-break objects in the Hubble deep field (HDF) north (open triangles), in the HDF-south (filled triangles) and in the Steidel et al. (1999) ground-based survey (X's). The luminosity density has been determined by integrating over the luminosity function and correcting for extinction following the prescription of Steidel et al. (1999). Distances and volumes are computed using the cosmological parameters h, Omegam, OmegaLambda, Omegatot = 0.65, 0.3, 0.7, 1.0. Possible contributions from far-IR and sub-millimeter sources are not included. Also not included are the upward revisions of the z < 1 star-formation densities suggested by Tresse & Maddox (1998) and Cowie et al. (1999). For the lower-redshift points, the open squares are from HDF photometric redshifts by Connolly et al (1997), the open circles are from Lilly et al. (1996), and the solid square is from the Halpha survey of Gallego et al. (1995).

Photometric redshifts computed via template fitting can also be used to identify samples of high-z objects, and several such samples have been presented and discussed [Lanzetta et al. 1996, Sawicki et al. 1997, Sawicki & Yee 1998, Miralles & Pello 1998, Rowan-Robinson 1999, Fontana et al. 1999]. Luminosity densities at z > 2 from these studies are generally higher than those of [Madau et al. 1996], and the apparent drop in dot{rho}Z(z) at z gtapprox 2 is not universally evident. A striking example of the difference between color-selected samples and photometric-redshift selected samples is the fact that HDF-S comes out with a higher UV luminosity-density than HDF-N in the color-selected sample shown in Fig. 5, but a lower luminosity density in the photometric-redshift selected sample of [Fontana et al. 1999]. One general concern about object selection is that galaxies at lower redshift are typically brighter than the high-z objects. Interlopers that make it into photometric samples can dominate the UV luminosity-density estimates.

It does appear evident that the original criteria of [Madau et al. 1996] were too conservative, and the directly measured UV luminosity density in bins at z ~ 3 and z ~ 4 is not demonstrably lower than it is at z ~ 1. At still higher redshifts, from the very small number of candidate objects with z > 5, [Lanzetta et al. 1998] computes an upper limit on the star-formation density at z ~ 5 - 12. For the cosmology adopted here, the limit on star formation in galaxies with dot{M} gtapprox 100h Modot yr-2 is lower than the inferred rate from Lyman-break galaxies at z = 4. With NICMOS observations it has become possible to identify z > 5 candidates to much fainter limits, detecting objects with UV luminosities more like those of typical Lyman break galaxies at 2 < z < 5. [Dickinson 2000] derives number counts for color-selected candidates at 4.5 < z < 8.5 in the HDF-N/NICMOS survey, and finds that they fall well below non-evolving predictions based on the well-characterized z = 3 Lyman break luminosity function. It appears that the space density, the luminosities, or the surface brightnesses (and hence, the detectability) of UV bright galaxies fall off at z > 5, at least in the HDF-N.

5.5.2. Dust and selection effects

Many of the discussions of the Madau diagram have centered around selection effects and whether the data actually support a decrease in dot{rho}Z(z) for z gtapprox 2. Star-formation in dusty or low-surface-brightness galaxies may be unaccounted for in the HDF source counts. Meurer and collaborators [Meurer et al. 1997, Meurer et al. 1999] use local starburst galaxy samples to calibrate a relation between UV spectral slope and far-IR (60 - 100 µm) emission, and hence compute bolometric corrections for dust attenuation. They apply these corrections to a sample of color-selected Lyman-break galaxies in the HDF and derive an absorption-corrected luminosity density at z ~ 3 that is a factor of 9 higher than that derived by [Madau et al. 1996]. Not all of this comes from the dust correction; the luminosity-weighted mean dust-absorption factor for the [Meurer et al. 1999] sample is 5.4 at 1600Å. [Sawicki & Yee 1998] analyzed the optical/near-IR spectral energy distributions of spectroscopically confirmed Lyman-break galaxies in the HDF and found the best fit synthetic spectra involved corrections of more than a factor of 10. Smaller corrections were derived by [Steidel et al. 1999] for a sample of galaxies of similar luminosity. In general, the danger of interpreting UV spectral slopes as a measure of extinction is that the inferred luminosity corrections are very sensitive to the form of the reddening law at UV wavelengths. For the [Calzetti et al. 1994] effective attenuation law, used in all of the aforementioned studies, a small change in the UV color requires a large change in the total extinction. Photometric errors also tend to increase the dust correction, because objects that scatter to the red are assigned larger corrections that are not offset by smaller corrections for the blue objects. The corrections for dust must thus be regarded as tentative, and must be confirmed with more extensive Halpha studies such as that of [Pettini et al. 1998], and further studies in the mid-IR, radio, and sub-millimeter.

The NICMOS HDF observations provide some additional insight into possible reddening corrections. Figure 6 shows the spectral-energy distributions of HDF galaxies with spectroscopic 2.5 < z < 3.5, superimposed on models with a constant star-formation rate and an age of 109 years. The galaxies are typically best fitted with ages 107-9 years and reddening 0.1 < E(B - V) < 0.4 with the [Calzetti et al. 1994] attenuation law. Very young galaxies with little extinction appear to be rare, and older or more reddened galaxies would possibly escape the Lyman-break selection. However, [Ferguson 1999] identified only 12 galaxies with V606 < 27 in the HDF-N that fail the [Dickinson 1998] color criteria but nevertheless have 2.5 < zphot < 3.5 from spectral-template fitting. In general these galaxies fall just outside the color selection boundaries, and the non-dropout sample contributes only 12% of the luminosity-density of the dropout sample. It thus appears unlikely that there is a population that dominates the metal-enrichment rate at z ~ 3 that is just missing from the Lyman-break samples. If the optically unidentified sub-millimeter sources (see Section 4.7) are really at z gtapprox 3, they are probably a disjoint population, rather than simply the red tail of the Lyman-break population.

Figure 6

Figure 6. Spectral energy distributions of 28 spectroscopically confirmed Lyman-break galaxies with 2.5 < z < 3.5, superimposed on stellar population models. The models assume solar metallicity and a Salpeter IMF and include attenuation due to the IGM for z = 3. The models reflect constant star formation for 109, with different amounts of interstellar dust attenuation. The reddening values are E(B - V) = 0, 0.2, and 0.4, with the curve that is highest at long wavelengths having the highest value. The Calzetti et al. (1994) attenuation law was used.

If sources akin to ultra-luminous IRAS galaxies were present at z ~ 3 in the HDF, it is likely that they would be detected, but unlikely that they would be identified as Lyman-break galaxies. [Trentham et al. 1999] use HST observations to extend the spectral energy distributions for three nearby ultra-luminous IR galaxies down to rest-frame 1400 Å. Although this is not far enough into the UV to predict HDF B450 colors at z = 3 with confidence, it at least gives some indication of whether such galaxies are detectable. All three galaxies would likely be detected in the F814W band if shifted out to z = 3, although VII Zw 031 would be very near the detection limit. None of the galaxies would meet the [Madau et al. 1996] Lyman-break galaxy selection criteria, but might plausibly show up as high-z objects from their photometric redshifts.

In addition to dust, cosmological surface-brightness can bias the samples of high-redshift galaxies. For fixed luminosity and physical size, i.e. no evolution, surface-brightness will drop by about 1 mag between z = 3 and z = 4. This lower surface brightness will result in a decrease in the number density of objects and the inferred luminosity density, even if there is no intrinsic evolution. Using simulated images for one particular galaxy evolution model [Ferguson & Babul 1998], [Ferguson 1998b] arrived at corrections to dot{rho}Z(z) of a factor of 1.5 at z ~ 3 and 4.7 at z ~ 4. [Lanzetta et al. 1999] have looked at surface-brightness selection in a less model-dependent way, computing the star-formation "intensity" (in solar masses per year per square kiloparsec) from the UV flux in each pixel of the galaxy images. The comoving volume density of the regions of highest star-formation intensity appears to increase monotonically with increasing redshift, whereas a strong selection cutoff for star-formation intensities less than 1.5 Modot yr-1 kpc-2 affects samples beyond z > 2. The results suggest that surface-brightness effects produce a substantial underestimate of dot{rho}Z(z) at high redshift.

The undetected low-surface-brightness UV-emitting regions should contribute to the total diffuse background in the image. [Bernstein 1997] has attempted to measure the mean level of the extragalactic background light (EBL) in the HDF images, while [Vogeley 1997] has analyzed the autocorrelation function of the residual fluctuations after masking the galaxies. [Vogeley 1997] concludes that diffuse light clustered similarly to faint galaxies can contribute no more than ~ 20 % of the mean EBL. In contrast [Bernstein 1997], concludes that the total optical EBL is two to three times the integrated flux in published galaxy counts. The two results can be made marginally compatible if the fluxes of detected galaxies are corrected for light lost outside the photometric apertures and for oversubtraction of background due to the overlapping wings of galaxy profiles. If this interpretation is correct, there is not much room for the UV luminosity density to increase significantly at high redshift.

5.5.3. Connection to galaxy evolution

An important use of the metal-enrichment rate derived from the HDF and other surveys is the attempt to "close the loop": to show that the emission history of the universe produces the metal abundances and stellar population colors we see at z ~ 0. [Madau et al. 1996] made a first attempt at this, concluding that the metals we observe being formed [integrating dot{rho}Z(z) over time] are a substantial fraction of the entire metal content of galaxies.

[Madau et al. 1998] compared the integrated color of galaxy populations in the local universe to that expected from the UV-emission history, exploring a variety of options for IMF and dust obscuration. With a Salpeter IMF and modest amounts of dust attenuation, they find that a star-formation history that rises by about an order of magnitude from z = 0 to a peak at z ~ 1.5 is compatible with the present-day colors of galaxies, with the FIR background, and with the metallicities of damped Lyalpha absorbers. [Fall et al. 1996], [Calzetti & Heckman 1999] and [Pei et al. 1999] have attempted to incorporate dust and chemical evolution in a more self-consistent way. The models include a substantial amount of obscured star-formation; more than 50% of the UV radiation is reprocessed by dust. The obscuration corrections increase the value of dot{rho}Z(z) from samples already detected in optical surveys, but do not introduce whole classes of completely dust-obscured objects. Although there are significant differences in the inputs and assumptions of the models, in all cases a model with a peak in dot{rho}Z(z) at z ~ 1 - 1.5 is found consistent with a wide variety of observations. In particular the models can simultaneously fit the COBE DMR and FIRAS measurements of the cosmic IR background [Puget et al. 1996, Hauser et al. 1998, Fixsen et al. 1998] and the integrated light from galaxy counts. The total mass in metals at z = 0 is higher in these new models than in those of [Madau et al. 1996], but the local census now includes metals in cluster X-ray gas, which were ignored by [Madau et al. 1996].

Overall, the success of these consistency checks is quite remarkable. Various imagined populations of galaxies (dwarfs, low-surface-brightness galaxies, highly dust obscured objects, etc.) now seem unlikely to be cosmologically dominant. The fact that the UV emission, gas metallicities, and IR backgrounds all appear capable of producing a universe like the one we see today leaves little room for huge repositories of gas and stars missing from either our census at z = 0 or our census at high redshift.

Nonetheless, there is room for caution in this conclusion. In clusters of galaxies, the mass of metals ejected from galaxies into the X-ray emitting gas exceeds that locked inside stars by a factor of 2-5 [Mushotzky & Loewenstein 1997]. If the same factor applies to galaxies outside clusters [Renzini 1997], then the local mass-density of metals greatly exceeds the integral of metal-enrichment rate, implying that most star-formation is hidden from the UV census (although the differences in galaxy morphology in clusters and the field suggests that clusters might not be typical regions of the universe). Various lines of evidence cited in Section 5.3 point to old ages for elliptical galaxies (both inside and outside of clusters) and the bulges of luminous early-type spirals [Renzini 1999, Goudfrooij et al. 1999]. The requirements for the early formation of metals in these systems look to be at odds with the inferences from the models described above. [Renzini 1999] estimates that 30% of the current density of metals must be formed by z ~ 3, whereas the best-fit models to the evolution of the luminosity density have only 10% formed by then. The discrepancy is interesting but is not outside of the range of error of the estimates of both dot{rho}Z(z) and the ages of stellar populations in present-day spheroidal systems.

It also remains a challenge to ascertain how the metals got from where they are at high redshift to where they are today. The bulk of the metals locked up in stars at z = 0 are in luminous, normal, elliptical and spiral galaxies. If elliptical galaxies (and spheroids in general) formed early and rapidly, they probably account for the lion's share of dot{rho}Z(z) above z = 2. Thus the metals formed in the z = 1 peak of dot{rho}Z(z) must end up for the most part in luminous spiral galaxies today. This is difficult to reconcile with the lack of evolution observed in number-density or luminosity of luminous spirals out to z = 1. An order-of-magnitude decline in star-formation rate in galaxy disks since z = 1 also seems inconsistent with present-day colors of spiral galaxy disks, or with star-formation histories derived from chemical-evolution models (e.g. [Tosi 1996, Prantzos & Silk 1998]). Furthermore, at z ~ 1 it appears that compact-narrow-emission-line galaxies [Guzman et al. 1997] and irregular galaxies account for a significant fraction of the UV luminosity density. If these galaxies fade into obscurity today, then they have not been accounted for in the census of metals in the local universe, and the z = 0 metallicity should be revised upwards in the global chemical-evolution models. On the other hand if these galaxies are merging into luminous spirals and ellipticals, it is hard to understand how luminous spiral and elliptical galaxy properties can remain consistent with PLE models out z = 1.

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