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2.2. The luminosity function

The luminosity functions derived from the above surveys (see e.g., Lilly et al. 1995, Ellis et al. 1996, Cowie et al. 1996) are broadly similar. There is general agreement that the principal evolutionary change in the galaxy population back to z ~ 1 is manifested as a substantial increase with redshift in the number density of blue galaxies with luminosities close to present day L* (i.e., MAB(B) ~ -21 for H0 = 50 km s-1 Mpc-1). This phenomenon had been suggested by the first exploratory spectroscopy of faint galaxies almost a decade ago (see e.g., Colless et al. 1990, Lilly et al. 1991) but is now placed on a firm statistical footing.

The appearance of these galaxies at high redshift produces a substantial change in the luminosity function of galaxies selected to have blue colors, but little change in the luminosity function of redder (Lilly et al. 1995, Heyl et al. 1997). The same differential behavior is seen if selection is made by the equivalent width of [O II] 3727 (Ellis et al. 1996). Smail et al. (1997) have shown that this differential behavior is evident even at low redshifts, z < 0.5. The division of the luminosity function color classes is somewhat arbitrary and is likely masking a more complex behavior in which individual objects cross the color-divides, in either direction (see Section 3.3 below).

In particular, it is important to remember that the luminosity function is just a statistical description of the galaxy population and inferences about the evolution of individual galaxies based on the form of the changes in the luminosity function may be misleading. As a ready example, the changes in the CFRS B-band luminosity function (i.e., not split by color) appear as almost pure density evolution, yet splitting by color reveals one (red) unchanging component and one (blue) component behaving as if undergoing pure luminosity evolution! Similarly, computation of an ultraviolet luminosity function (e.g., at 2800 Å) reveals changes that are best represented as pure luminosity evolution (see also Cowie et al. 1997).

Determining the physical evolution of individual objects (as opposed to the statistical evolution of the population) thus requires additional data over and above the simple color-magnitude-redshift output of the redshift surveys. Ideally, an observable property of the galaxies could be found that would remain constant throughout the evolution of individual galaxies. Unfortunately no such invariant property has been identified. The (halo) mass is certainly attractive, but even this may be expected to increase with time in hierarchical models (Kauffmann et al. 1993, Baugh et al. 1996). There are several programs producing kinematic estimates of masses (see e.g., Rix et al. 1997, Vogt et al. 1996, 1997, Guzman et al. 1997), although the observational difficulties are still formidable.

Attempts have also been made to use the near-infrared luminosity as a measure of stellar mass, although the correspondence must be much weaker for blue galaxies dominated by young rapidly evolving stellar populations than it is for more mature systems in which the infrared light is dominated by old red giants. If luminosity is closely associated with mass, then the luminous blue galaxies at higher redshifts must be massive forming galaxies and galaxy formation is following the down-sizing picture described by Cowie et al. (1996).

Observations of the morphologies and sizes of distant galaxies that are possible with HST provide a useful new perspective on this problem though by no means do they provide a silver bullet! The "size" of a galaxy is a physical parameter that may or may not remain constant through its evolution and the "morphology" of the galaxy tells us about the nature of the star-formation activity in that galaxy as well as the occurrence of physically important processes such as merging. We describe below the results of our own program of HST observations of galaxies from the CFRS and LDSS redshift surveys.

Ultimately additional diagnostics such as metallicity measurements and estimates of the dust and gas content of the galaxies will also be brought to bear, and presumably a synthesis will emerge. The accounting methods for following the long-lived products of star-formation are sufficiently imprecise that it will be as important to focus as much on the presence or absence of passive galaxies as a function of redshift as on the properties of actively star-forming galaxies.

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