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The importance of collisions in the life of cluster galaxies can be seen through a simple rate argument. A characteristic number of interactions per galaxy can be written as N approx nsigma upsilon t, where n is the number density of galaxies in a cluster, sigma is the cross section for interactions, upsilon is the encounter velocity, and t is the age of the cluster. If sigma = pi rp2, where rp is the impact parameter, and upsilon = sqrt2 sigmaupsilon, then for a cluster like Coma we have


While very crude, this calculation shows that it is reasonable to expect that over the course of its lifetime in the cluster, a typical galaxy should experience several close interactions with other cluster members.

While interactions should be common in clusters, they will also be fast. Because the characteristic encounter velocity is much higher than the typical circular velocities of galaxies, these perturbations will be impulsive in nature. Simple analytic arguments suggest that both the energy input and dynamical friction should scale as upsilon-2 (Binney & Tremaine 1987), so that a fast encounter does less damage and is much less likely to lead to a merger than are the slow encounters experienced by galaxies in the field. A common view has arisen, therefore, that slow interactions and mergers of galaxies are a rarity in massive clusters (e.g., Ostriker 1980), and that much of the dynamical evolution in cluster galaxy populations is driven by the effects of the global tidal field (e.g., Byrd & Valtonen 1990; Henriksen & Byrd 1996). Combined with the possible effects of ram pressure stripping of the dense interstellar mediuum (ISM) (Gunn & Gott 1972) or hot gas in galaxy halos ("strangulation"; Larson, Tinsley, & Caldwell 1980), a myriad of processes, aside from galaxy interactions themselves, seemed available to transform cluster galaxies.

However, the abandonment of individual collisions as a mechanism to drive cluster galaxy evolution has proved premature. More recent work on the dynamical evolution of cluster galaxies has emphasized the importance of fast collisions. Moore et al. (1996) and Moore, Lake, & Katz (1998) have shown that repeated fast encounters, coupled with the effects of the global tidal field, can drive a very strong response in cluster galaxies. For galaxy-like potentials, the amount of heating during an impulsive encounter scales like DeltaE / E ~ rp-2, such that distant encounters impart less energy. However, this effect is balanced by the fact that under simple geometric weighting the number of encounters scales as rp2, so that the total heating, summed over all interactions, can be significant. While this simple argument breaks down when one considers more realistic galaxy potentials and the finite time scales involved, in hindsight it is not surprising that repeated high-speed encounters - "galaxy harassment" - should drive strong evolution. However, the efficacy of harassment is largely limited to low-luminosity hosts, due to their slowly rising rotation curves and low-density cores. In luminous spirals, the effects of harassment are much more limited (Moore et al. 1999). This effect leads to a situation where harassment can effectively describe processes such as the formation of dwarf ellipticals (Moore et al. 1998), the fueling of low-luminosity AGNs (Lake, Katz, & Moore 1998), and the destruction of low-surface brightness galaxies in clusters (Moore et al. 1999), but is less able to explain the evolution of luminous cluster galaxies.

Even as the effects of high-speed collisions are being demonstrated, a new attention is focusing on slow encounters and mergers in clusters. The crucial element that is often overlooked in a classical discussion of cluster interactions is the fact that structure forms hierarchically. Galaxy clusters form not by accreting individual galaxies randomly from the field environment, but rather through the infall of less massive groups falling in along the filaments that make up the "cosmic web." Observationally, evidence for this accretion of smaller galaxy groups is well established. Clusters show ample evidence for substructure in X-rays, galaxy populations, and velocity structure (see, e.g., reviews by Buote 2002; Girardi & Biviano 2002). These infalling groups have velocity dispersions that are much smaller than that of the cluster as a whole, permitting the slow, strong interactions normally associated with field galaxies. Imaging of distant clusters show populations of strongly interacting and possibly merging galaxies (e.g., Dressler et al. 1997; van Dokkum et al. 1999), which may contribute to the Butcher-Oemler effect (e.g., Lavery & Henry 1988). Even in nearby (presumably dynamically older) clusters, several notable examples of strongly interacting systems exist (e.g., Schweizer 1998; Dressler, this volume), including the classic Toomre-sequence pair "The Mice" (NGC 4676) located at a projected distance of ~ 5 Mpc from the center of the . Interactions in the infalling group environment may in effect represent a "preprocessing" step in the evolution of cluster galaxies.

While the observational record contains many examples of group accretion and slow encounters, numerical simulations are also beginning to reveal this evolutionary path for cluster galaxies. Modern N-body calculations can follow the evolution of individual galaxy-mass dark matter halos in large-scale cosmological simulations, allowing the interaction and merger history of cluster galaxies to be probed. Ghigna et al. (1998) tracked galaxy halos in an Omegam =1, log(M / Modot) = 14.7 cluster and showed at late times (z < 0.5) that, while no mergers occurred within the inner virialized 1.5 Mpc of the cluster, in the outskirts the merger rate was ~ 5%-10%. Similar models by Dubinski (1998) confirmed these results, and showed more intense activity between z = 1 and z = 0.4. Gnedin (2003) expanded on these works by studying the interaction and merger rates in clusters under different cosmological models (Fig. 1). In Omegam = 1 cosmologies, the encounter rates in clusters stays relatively constant with time as the cluster slowly accretes, while under open or Lmabda-dominated cosmologies, the interaction rate increases significantly once the cluster virializes, as the galaxies experience many high-speed encounters in the cluster core. The distribution of velocities in these encounters shows a large tail to high encounter velocities, but a significant fraction of encounters, largely those in the cluster periphery or those occurring at higher redshift, before the cluster has fully collapsed, occur at low relative velocities (upsilonrel < 500 km s-1). Clearly, not all interactions are of the high-speed variety!

Figure 1a
Figure 1b

Figure 1. Top: Number of close encounters per galaxy per Gyr in a simulated log(M / Modot) = 14.6 cluster under different cosmologies. Bottom: The distribution of galaxy encounter velocities in the simulated clusters. (From Gnedin 2003.)

In summary, clusters are an active dynamical environment, with a multitude of processes available to drive evolution in the galaxy population. Disentangling these different processes continues to prove difficult, in large part because nearly all of them correlate with cluster richness and clustercentric distance. Indeed, seeking to isolate the "dominant" mechanism driving evolution may be ill motivated, as these processes likely work in concert, such as the connection between high-speed collisions and tidal field that describes galaxy harassment. What is clear from both observational and computational studies is that slow encounters and mergers of galaxies can be important over the life of a cluster - at early times when the cluster is first collapsing, and at later times in the outskirts as the cluster accretes groups from the field.

Finally, it is also particularly important to remember two points. First, clusters come in a range of mass and richness: not every cluster is as massive as the archetypal , with its extraordinarily high velocity dispersion of sigmaupsilon = 1000 km s-1. In smaller clusters and groups, the lower velocity dispersion will slow the encounter velocities and make them behave more like field encounters. Second, as we push observations out to higher and higher redshift, we begin to probe the regime of cluster formation, where unvirialized dense environments can host strong encounters.

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