Merging galaxy clusters may provide a unique window into the behavior of dark
matter and the evolution of member galaxies. To interpret these natural
collider experiments we must account for how much time has passed since
pericenter passage (TSP), the maximum relative speed of the merging
subclusters, merger phase (outbound after first pericenter or returning for
second pericenter), and other dynamical parameters that are not directly
observable. These quantities are often inferred from staged simulations or
analytical timing arguments that include neither substructure, large-scale
structure, nor a cosmologically motivated range of impact parameters. We
include all these effects by extracting dynamical parameters from analog
systems in a cosmological n-body simulation, and we present constraints for 11
observed systems. The TSP and viewing angles we derive are consistent with
those of staged hydrodynamical simulations, but we find lower maximum speeds.
Compared to the analytical MCMAC method we find lower TSP, and viewing angles
that put the separation vector closer to the plane of the sky; we attribute
this to the MCMAC assumption of zero pericenter distance. We discuss potential
extensions to the basic analog method as well as complementarities between
methods.Comment: 17 pages, 15 figures. This version accepted to ApJ improves on v0 by
demonstrating recovery of correct parameters in cases where the correct
answer is know
