The Ubiquity of Coeval Starbursts in Massive Galaxy Cluster Progenitors
  The Universe's largest galaxy clusters likely built the majority of their
massive $>10^{11} M_\odot$ galaxies in simultaneous, short-lived bursts of
activity well before virialization. This conclusion is reached from emerging
datasets on $z>2$ proto-clusters and the characteristics of their member
galaxies, in particular, rare starbursts and ultraluminous active galactic
nuclei (AGN). The most challenging observational hurdle in identifying such
structures is their very large volumes, $\sim10^{4}$ comoving Mpc$^3$ at $z>2$,
subtending areas $\sim$half a degree on the sky. Thus the contrast afforded by
an overabundance of very rare galaxies in comparison to the background can more
easily distinguish overdense structures from the surrounding, normal density
field. Five $2<z<3$ proto-clusters from the literature are discussed in detail
and are found to contain up to 12 dusty starbursts or luminous AGN galaxies
each, a phenomenon that is unlikely to occur by chance even in overdense
environments. Measurements of gas depletion times suggest that they are indeed
short-lived on $\sim$100 Myr timescales, and the probability of finding a
structure containing more than 8 such systems is $\sim$0.2\%, unless their
`triggering' is correlated on very large spatial scales, $\sim$10 Mpc across.
The volume density of starburst-rich proto-clusters is found to be comparable
to all $>10^{15} M_\odot$ galaxy clusters in the nearby Universe, a factor of
five larger than expected in some simulations. Some tension yet exists between
measurements of their volume density of starburst-rich proto-clusters and the
expectation that they are generated via short-lived episodes. However, improved
observations of proto-clusters over large regions of sky will certainly shed
more light on the assembly of galaxy clusters, and whether or not they build
their galaxies through episodic bursts as suggested here. [abridged]
