The Dynamics of Merging Clusters: A Monte Carlo Solution Applied to the
  Bullet and Musket Ball Clusters
  Merging galaxy clusters have become one of the most important probes of dark
matter, providing evidence for dark matter over modified gravity and even
constraints on the dark matter self-interaction cross-section. To properly
constrain the dark matter cross-section it is necessary to understand the
dynamics of the merger, as the inferred cross-section is a function of both the
velocity of the collision and the observed time since collision. While the best
understanding of merging system dynamics comes from N-body simulations, these
are computationally intensive and often explore only a limited volume of the
merger phase space allowed by observed parameter uncertainty. Simple analytic
models exist but the assumptions of these methods invalidate their results near
the collision time, plus error propagation of the highly correlated merger
parameters is unfeasible. To address these weaknesses I develop a Monte Carlo
method to discern the properties of dissociative mergers and propagate the
uncertainty of the measured cluster parameters in an accurate and Bayesian
manner. I introduce this method, verify it against an existing hydrodynamic
N-body simulation, and apply it to two known dissociative mergers: 1ES 0657-558
(Bullet Cluster) and DLSCL J0916.2+2951 (Musket Ball Cluster). I find that this
method surpasses existing analytic models - providing accurate (10% level)
dynamic parameter and uncertainty estimates throughout the merger history. This
coupled with minimal required a priori information (subcluster mass, redshift,
and projected separation) and relatively fast computation (~6 CPU hours) makes
this method ideal for large samples of dissociative merging clusters.
