Protoclusters at z=5.7: A view from the MultiDark galaxies
  Protoclusters, which will yield galaxy clusters at lower redshift, can
provide valuable information on the formation of galaxy clusters. However,
identifying progenitors of galaxy clusters in observations is not an easy task,
especially at high redshift. Different priors have been used to estimate the
overdense regions that are thought to mark the locations of protoclusters. In
this paper, we use mimicked Ly$\alpha$-emitting galaxies at $z=5.7$ to identify
protoclusters in the MultiDark galaxies, which are populated by applying three
different semi-analytic models to the 1 $Gpc h^{-1}$ MultiDark Planck2
simulation. To compare with observational results, we extend the criterion 1 (a
Ly$\alpha$ luminosity limited sample), to criterion 2 (a match to the observed
mean galaxy number density). To further statistically study the finding
efficiency of this method, we enlarge the identified protocluster sample
(criterion 3) to about 3500 at $z=5.7$ and study their final mass distribution.
The number of overdense regions and their selection probability depends on the
semi-analytic models and strongly on the three selection criteria (partly by
design). The protoclusters identified with criterion 1 are associated with a
typical final cluster mass of $2.82\pm0.92 \times 10^{15} M_\odot$ which is in
agreement with the prediction (within $\pm 1 \sigma$) of an observed massive
protocluster at $z=5.7$. Identifying more protoclusters allows us to
investigate the efficiency of this method, which is more suitable for
identifying the most massive clusters: completeness ($\mathbb{C}$) drops
rapidly with decreasing halo mass. We further find that it is hard to have a
high purity ($\mathbb{P}$) and completeness simultaneously.
