Annu. Rev. Astron. Astrophys. 1992. 30: 613-52
Copyright © 1992 by . All rights reserved

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By the mid-1930's, Milton Humason had determined a redshift of z = 0.131 for the Boötis I cluster and z = 0.137 for the Ursa Major II cluster (Humason 1936). The ability to measure light coming from such large distances inspired workers like Hubble and Tolman (1935) to consider whether such data could usefully constrain cosmological models (see Sandage 1988 for a review). The highest redshift in the Humason-Mayall-Sandage list (1956) was z = 0.201 for the Hydra cluster, a small gain for two decades of effort. In the 1950's, the question of how the intrinsic properties of galaxies might have evolved was linked to the rapidly developing field of post-main-sequence stellar evolution (Sandage 1961; Crampin and Hoyle 1961), with the conclusion that the overall change in luminosity of the galaxy was expected to be comparable in importance to cosmological effects. At higher redshifts, the distinction between world models should be more apparent, but so too should be the evolutionary changes in the galaxies. To probe cosmological distances, Hubble, Humason, and Minkowski were obliged to select for the highest luminosity galaxies, namely brightest cluster galaxies and radio sources. Surprisingly, the median redshift in the current faint-galaxy samples is not as high as the highest redshifts already reached in the early 1960's (Minkowski 1961; Baum 1962), despite orders-of-magnitude instrumental gain for faint field-galaxy spectroscopic surveys. The recent technological advances have instead given us the opportunity to study typical galaxies at large redshift.

In this review we focus on complete samples of faint field galaxies. By complete, we mean that the sample is defined by a quantifiable selection procedure, most commonly by magnitude, and by field galaxy we mean a galaxy that is selected without regard for its environment. By faint, we mean B > 19, limited at about B = 23 for spectroscopy and B = 28 for direct imaging. These depths are needed to reach redshifts beyond z = 0.1, or a look-back time of a tenth of the Hubble age of the universe. Such complete samples are necessary for tracking redshift-dependent selection effects; for estimating the volume element as a cosmological test; for determining the galaxy number density as a function of redshift; and for exploring the environment of each galaxy and clustering statistics in general.

In the past decade, several results from faint galaxy samples have received attention because comparisons to expectations yielded surprises. A few examples include counts of fainter galaxies in excess of calculations which do not include evolution; redshift distributions remarkably close to no-evolution predictions; shifts to very blue colors for fainter galaxies; and apparently enhanced fractions of galaxy spectra with strong emission lines. We first present the basic data in the form of counts, colors, and redshifts (Section 2), and we then critically comment on general difficulties in measuring faint or high-redshift objects. We also comment on the models in Section 3 that are needed to interpret such data. Finally, in Section 3.3, we present a relatively conventional yet simple model that appears to describe most of the observations.

Before discussing the data in detail, we emphasize the need to be careful in work that pushes photometry and spectroscopy to faint limits. Besides the possibility that the data are plagued by systematic errors, unrealized selection effects, and incompleteness, the interpretations are susceptible to a variety of other uncertainties. These include 1. our relatively poor knowledge of the basic properties of local galaxies; 2. inaccuracies in the comparison of models to the observations; 3. significant fluctuations due to large-scale structure; and 4. the unknown values of the parameters of the cosmological model.

Redshift-dependent selection effects,in particular, must be carefully evaluated. Lower-luminosity galaxies are favored at fainter apparent magnitudes unless luminosity evolution begins to compensate. In a non-expanding Euclidean universe, the distribution of galaxy luminosities seen in a flux-limited sample would be independent of the given flux limit. The apparent distribution is bell-shaped, peaking at the characteristic absolute magnitude M*. With expansion, however, a fixed optical band measures the generally lower flux in the rest frame, and lower-luminosity, nearer galaxies are favored. Thus, even though intrinsically faint galaxies are not expected to contribute much to the volume emissivity, they may appear in larger proportions in faint samples, and as a consequence, it is important to establish their local space density with precision before conclusions about evolution can be made.

Another effect is that distant galaxies suffer a strong decrease in surface brightness with increasing redshift, again assuming that evolutionary effects do not dominate. In a band with given lambdaobs and Deltalambda, the surface brightness (photon rate per angular resolution element) is proportional to (1 + z)-3. In the red spectral region, the rest-frame spectrum of a typical galaxy can be approximated as fnu ~ nu-2. Thus in the background-limited case, the signal-to-noise ratio is proportional to (1 + z)-5. The exposure time necessary to reach a fixed signal-to-noise ratio is then approximately proportional to (1 + z)10. (Detecting galaxies in a red spectral band gains little, since the sky background is brighter.)

The strong reduction in signal-to-noise ratio with increasing redshift is inevitably a major effect in the observability of distant galaxies and in the composition of actual faint samples. Galaxies selected optically at large redshift are likely to be those that have especially high intrinsic surface brightness and especially high luminosity at short wavelengths. We anticipate that a ``guillotine'' in redshift will apply (Pritchet and Kline 1981; Kron 1989; Phillipps, Davies, and Disney 1990; Yoshii and Fukugita 1991; Bohlin et al. 1991), such that the actual redshift distribution obtained for an incomplete galaxy sample will be deficient in high redshifts compared to what otherwise might be expected.

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