How did clusters form? Part of the answer was mentioned above: if the conventional understanding of gravity physics is correct, we know that clusters, being massive and not isolated from the field, are growing by the gravitational accretion of surrounding material. But the central parts could form in some other way. In pancake theories (Shandarin and Zel'dovich 1989), such as those involving massive neutrinos or baryons with primeval adiabatic mass density fluctuations, the coherence length of the primeval mass distribution is large. This means the first generation would be protoclusters that fragment to form galaxies. The problem for this picture is field galaxies such as those in the Local Group (Peebles 1984). It is difficult to imagine that these galaxies ever were part of a cluster. The local relative galaxy velocity dispersion is less than ~ 100 km sec-1, and the local mean flow is directed more or less toward the nearest cluster, a situation difficult to imagine if we were ejected from the cluster. Could the local galaxies have been produced in an unusually low mass protocluster or pancake? Arguing against this is the indication, from the small local relative velocities, that the Local Group is only now collapsing for the first time. That is, the direct evidence is that the Local Group is considerably younger than our galaxy. It is also worth noting that galaxy masses (measured within a fixed radius, m ~ v2cr / G, where vc is the circular velocity in the disc, or the equivalent for ellipticals) and mass to infrared luminosities are quite similar in cluster members and the field. This suggests field and cluster galaxies formed under rather similar conditions, before clusters formed. If there were a sensible way to circumvent these simple points it would be good to know about it. Meanwhile, let us turn to hierarchical scenarios, where clusters form after the bulk of galaxy masses are assembled.
In the biased cold dark matter theory, the numerical solutions of Frenk et al. (1989) indicate that clusters formed soon after the assembly of the galaxies they contain. This has the great advantage that it is easy to think of ways of producing the systematic difference between the early type galaxies that tend to appear in clusters and the late types that prefer the field. At the same time, the model is tested by the predicted differences between cluster and field galaxies. In particular, White et al. (1987) conclude that in the biased cold dark matter theory galaxies with larger circular velocities prefer denser regions. This certainly is not true in our immediate neighborhood, within distances ~ 400 km sec-1, where, as Tully (1989) emphasizes, it is striking to see how strongly giant and dwarf galaxies alike avoid the local voids. White, Tully and Davis (1988) find evidence for a segregation of galaxies with large and small vc by local density in deeper samples of Tully's Nearby Galaxy Catalog. It will be interesting to follow the discussion of tests of this effect in clusters: is the prediction consistent with the high abundance of dwarf cluster members discussed by Haynes and Sandage?
In theories such as primeval baryon isocurvature (Peebles 1987) and massive cosmic strings (Turok 1985) protogalaxies form well before clusters, so one must find a way to develop the different abundance ratios of ellipticals to lenticulars in clusters and the field out of environmental effects. The one idea I know for how this might happen builds on the argument that discs have to be relatively late additions to galaxies even if the spheroids were assembled early: discs require a large collapse factor to spin up the material, which argues for late formation, and the fact that discs are fragile suggests that any that did manage to form early would tend to be destroyed by the high rate of accretion of debris onto galaxies at early epochs. If discs were added late, then it is easy to imagine that the character (or existence) of the disc would depend on the environment the galaxy finds itself in at low redshifts, for that determines the amount and state of the material available for accretion.