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Merging galaxy clusters have become one of the most important probes of darkmatter, providing evidence for dark matter over modified gravity and evenconstraints on the dark matter self-interaction cross-section. To properlyconstrain the dark matter cross-section it is necessary to understand thedynamics of the merger, as the inferred cross-section is a function of both thevelocity of the collision and the observed time since collision. While the bestunderstanding of merging system dynamics comes from N-body simulations, theseare computationally intensive and often explore only a limited volume of themerger phase space allowed by observed parameter uncertainty. Simple analyticmodels exist but the assumptions of these methods invalidate their results nearthe collision time, plus error propagation of the highly correlated mergerparameters is unfeasible. To address these weaknesses I develop a Monte Carlomethod to discern the properties of dissociative mergers and propagate theuncertainty of the measured cluster parameters in an accurate and Bayesianmanner. I introduce this method, verify it against an existing hydrodynamicN-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 thismethod surpasses existing analytic models - providing accurate (10% level)dynamic parameter and uncertainty estimates throughout the merger history. Thiscoupled with minimal required a priori information (subcluster mass, redshift,and projected separation) and relatively fast computation (~6 CPU hours) makesthis method ideal for large samples of dissociative merging clusters.

The Dynamics of Merging Clusters: A Monte Carlo Solution Applied to the Bullet and Musket Ball Clusters