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.