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 n t, where n is the number density of galaxies in a cluster, is the cross section for interactions, is the encounter velocity, and t is the age of the cluster. If = rp2, where rp is the impact parameter, and = 2 , 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 -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 E / 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
m =1,
log(M /
M) =
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
m = 1
cosmologies, the
encounter rates in clusters stays relatively constant with time as the
cluster slowly accretes, while under open or
-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
(rel <
500 km s-1). Clearly, not all interactions are of the
high-speed variety!
Figure 1. Top: Number of close encounters
per galaxy per Gyr in a simulated log(M /
M) =
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
=
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.