A Pair of Early- and Late-Forming Galaxy Cluster Samples: Implications
  for Detection of Halo Assembly Bias
  The halo assembly bias, a phenomenon referring to dependencies of the
large-scale bias of a dark matter halo other than its mass, is a fundamental
property of our standard cosmological model. First discovered in 2005 via
high-resolution numerical simulations, it has been proven very difficult to be
detected observationally, with only a few convincing claims of detection thus
far. The main obstacle lies in finding an accurate proxy of the halo formation
time. In this study, by utilizing a constrained simulation that can faithfully
reproduce the observed structures larger than $\sim 2\,$Mpc in the local
universe, for a sample of about 630 massive clusters at $z\le 0.12$, we find
their counterpart halos in the simulation and use the mass growth history of
the matched halos to estimate the formation time of the observed clusters. This
allows us to construct a pair of early- and late-forming clusters, with similar
mass as measured via weak gravitational lensing, and large-scale bias differing
at $\gtrsim 4\sigma$ level, clearly showing the signature of assembly bias.
