Annu. Rev. Astron. Astrophys. 2000. 38: 667-715
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The HDFs are exquisitely deep and sharp images, detecting thousands of objects distributed throughout the observable universe, but they are also very small fields of view, and each is only one sightline. Figure 2 illustrates some parameters relevant for studying galaxy evolution with a single HDF. The total co-moving volume out to redshift z has been scaled (top panel) by the present-day normalization of the galaxy luminosity function phi*. This gives a rough measure of the number of "L* volumes" out to z, i.e. approximately the number of L* galaxies expected in that volume, or at high redshift the number of L* galaxies that the "proto-galaxies" found there will someday become. At z < 1, this number is ~ 10 - 30 depending on the cosmology: very few high-luminosity galaxies are expected (or found, for that matter), and even purely Poissonian variations introduce large uncertainties in any statistical conclusions that can be derived from them. Given real galaxy clustering, these uncertainties are still greater. As an example, ~ 24% of the total rest-frame 6500Å luminosity summed over all HDF-N galaxies out to z = 1.1 comes from just four galaxies: two in a redshift "spike" at z = 0.96 and two in another spike at z = 1.02. The safest use (statistically) for the HDF at z < 1 is thus to study the vastly more numerous, low-luminosity galaxies. This caution similarly applies to clustering studies. The angular correlation functions derived from the z ltapprox 1 sample primarily refer to low-luminosity galaxies, whereas those at higher z refer to higher luminosities. Clustering variation with luminosity (or mass) can mimic evolution.

Figure 2

Figure 2. An illustration of volume and time in the Hubble deep fields (HDF). (Top) For the 5 arcmin2 WFPC2 field of view, the co-moving volume out to redshift z is plotted for several cosmologies, scaled by the present day normalization of the galaxy luminosity function [phi*, here taken to be 0.0166h3 Mpc-3 from Gardner (1997)]. This gives a rough measure of the number of "L*-volumes" out to that redshift. (Bottom) The fractional age of the universe versus redshift is shown. Most of cosmic time passes at low redshifts, where the HDF volume is very small.

At high redshift, the HDF volume is large (especially for the open and Lambda cosmologies), and thus is more likely to provide a fair sample of objects. 2 For (OmegaM, OmegaLambda) = (0.3, 0.7) there is ~ 20 × more volume at 2 < z < 10 than at 0 < z < 1, and the likelihood of finding even moderately rare objects becomes significant. There is, however, little time out at high redshift: Most of cosmic history takes place at z < 1 (Figure 2, bottom).

2 Even at high redshift, however, uncertainties due to clustering (cf. [Adelberger et al. 1998]) need to be kept in mind when analyzing one or two sightlines like the HDFs. Back.

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