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The morphological analysis reported above reinforces the view that emerged from the original luminosity function analyses - that field galaxy evolution is differential. Galaxies with different sizes and present-day luminosities evolve differently. Kinematic studies (Vogt et al. 1997, Guzman et al. 1997, Illingworth in these proceedings) also point in this direction. The largest changes in a multi-dimensional phi(L, color, size, morphology, sigmav) distribution function are occurring, out to z = 0.8, for moderately sized, moderate luminosity galaxies rather than for the largest most luminous galaxies. These latter appear to be in place by z ~ 0.8 and to then evolve only moderately through to the present.

That evolution should be differential is not at all surprising since even a cursory examination of the galaxy population reveals that the average properties of present-day galaxies vary with luminosity and/or size and mass. As has been noted for several years, the sense of the differential behavior is interesting: at least superficially it is the opposite to what might have been expected in hierarchical models for galaxy formation, in that it is the larger galaxies that appear to be in place first.

4.1. How important is merging in the evolution of the galaxy population?

An important unanswered and highly relevant question is to what extent the merging of galaxies drives the evolution of the galaxy population. One direct approach is to study the fraction of galaxies observed at any epoch to be undergoing a merger, and we look at this below.

A complementary approach is to study whether the number density of massive elliptical galaxies has increased with epoch (cf. Kauffmann et al. 1996). The present samples are too small and too limited to answer this latter question definitively. Two analyses of the V / Vmax statistic based on color-selection in the CFRS sample (Lilly et al. 1995, Kaufmann et al. 1996) give different values which appear to be largely due to different philosophies concerning the redshift range that should be used. In our original analysis (Lilly et al. 1995), with an unevolving cut in rest-frame color, (U - V)0,AB > 2.05, with photometrically estimated redshifts for the spectroscopic failures and limiting the redshift range to 0.3 < z < 1.0, we found V / Vmax = 0.50 * 0.04. In contrast, Kauffmann et al., with no redshift cutoff, with evolving color selection criteria (from Bruzual and Charlot models) and including the effects of passive luminosity evolution, found V / Vmax = 0.41 ± 0.03. In the new sample with morphological information from HST we find, for 0.3 < z < 1.0, V / Vmax = 0.53 ± 0.04 for galaxies with r0.25 profiles, decreasing to 0.49 ± 0.05 when an additional color and morphological cut is applied. The effects of adding luminosity evolution decreases this to 0.46 ± 0.05, which is still insignificantly different from a value of 0.5. Im et al. (1995) have sought to use a larger sample using color estimated redshifts for a morphologically selected sample of ellipticals found evidence for luminosity evolution at constant comoving density.

Returning to the direct approach, the primary difficulty is in translating any observationally defined "merger fraction" (e.g., the fraction of galaxies in close pairs) to a merger rate. This requires an indication of the length of time for which the particular phenomenon will be observed during a particular merger event. Our own analysis of the HST images of the CFRS-LDSS sample is not yet completed (Le Fevre et al., in preparation, Paper 4). However, there are already many indications in the literature that the fraction of galaxies undergoing mergers or major interactions increases with redshift (Zepf & Koo 1989, Carlberg et al. 1994, Patton et al. 1997). The recent study of the CNOC-1 sample by Patton et al. (1997) yielded a merging pair fraction as a function of redshift as fm ~ 0.02(1 + z)3.

Is this merger activity consistent with the above observations of a roughly constant comoving number densities of large disk galaxies (cf. Toth & Ostriker 1992)? The probability that a given galaxy undergoes a merger in the redshift interval dz is given by:


where fm is the fraction of galaxies exhibiting some merger signature and tm is the (uncertain) time for which that phenomenon will be observable. The resulting survival probability Ps(z) for fm = 0.02(1 + z)3, H0 = 70 km s-1 Mpc-1 and tM = 5 x 108 years is shown in Fig. 6.

Figure 6

Figure 6. The probability for galaxies to survive to the present epoch without having undergone a major merger since a redshift z, based on the parameters describe in the text.

This suggests that it is plausible that most disks have survived since an epoch corresponding to z ~ 0.8, consistent with the roughly constant size function discussed above, and also with the survival of the Milky Way disk. However, if the trend continues with redshift to z >> 1 (a regime of particular relevance to the HDF) we would expect merging to be increasingly important. Relatively few galaxies will have survived from this epoch without having undergone a major merger.

Indeed, it is tempting to associate the peak in the L(2800 Å) luminosity density at 1 < z < 2 with the point at which the merging of galaxies becomes a dominant evolutionary driver. This is would be consistent with the often highly disturbed morphologies of HDF galaxies. In this picture, the rise in the global star-formation rate with epoch at z > 2 could be associated with the production of stars which ended up in spheroidal components through extensive merging whereas the subsequent decline at z < 1 would involve primarily the consumption of gas in disks more or less isolated systems.

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