Measures of Galaxy Environment - III. Difficulties in identifying
  proto-clusters at z ~ 2
  Galaxy environment is frequently discussed, but inconsistently defined. It is
especially difficult to measure at high redshift where only photometric
redshifts are available. With a focus on early forming proto-clusters, we use a
semi-analytical model of galaxy formation to show how the environment
measurement around high redshift galaxies is sensitive to both scale and
metric, as well as to cluster viewing angle, evolutionary state, and the
availability of either spectroscopic or photometric data. We use two types of
environment metrics (nearest neighbour and fixed aperture) at a range of scales
on simulated high-z clusters to see how "observed" overdensities compare to
"real" overdensities. We also "observationally" identify z = 2 proto-cluster
candidates in our model and track the growth histories of their parent halos
through time, considering in particular their final state at z = 0. Although
the measured environment of early forming clusters is critically dependent on
all of the above effects (and in particular the viewing angle), we show that
such clusters are very likely (< 90%) to remain overdense at z = 0, although
many will no longer be among the most massive. Object to object comparisons
using different methodologies and different data, however, require much more
caution.
