The Occurrence of Compact Groups of Galaxies Through Cosmic Time
  We use the outputs of a semi-analytical model of galaxy formation run on the
Millennium Simulation to investigate the prevalence of 3D compact groups (CGs)
of galaxies from $z = 11$ to 0. Our publicly available code identifies CGs
using the 3D galaxy number density, the mass ratio of secondary+tertiary to the
primary member, mass density in a surrounding shell, the relative velocities of
candidate CG members, and a minimum CG membership of three. We adopt "default"
values for the first three criteria, representing the observed population of
Hickson CGs at $z = 0$. The percentage of non-dwarf galaxies ($M > 5 \times
10^{8}h^{-1}\ M_{\odot}$) in CGs peaks near $z \sim 2$ for the default set, and
between $z \sim 1 - 3$ for other parameter sets. This percentage declines
rapidly at higher redshifts ($z \gtrsim 4$), consistent with the galaxy
population as a whole being dominated by low-mass galaxies excluded from this
analysis. According to the most liberal criteria, $\lesssim 3\%$ of non-dwarf
galaxies are members of CGs at the redshift where the CG population peaks. Our
default criteria result in a population of CGs at $z < 0.03$ with number
densities and sizes consistent with Hickson CGs. Tracking identified CG
galaxies and merger products to $z = 0$, we find that $\lesssim 16\%$ of
non-dwarf galaxies have been CG members at some point in their history.
Intriguingly, the great majority ($96\%$) of $z = 2$ CGs have merged to a
single galaxy by $z= 0$. There is a discrepancy in the velocity dispersions of
Millennium Simulation CGs compared to those in observed CGs, which remains
unresolved.
