  In this work, we report on a detailed simulation of the Bullet Cluster
(1E0657-56) merger, including magnetohydrodynamics, plasma cooling, and
adaptive mesh refinement. We constrain the simulation with data from
gravitational lensing reconstructions and 0.5 - 2 keV Chandra X-ray flux map,
then compare the resulting model to higher energy X-ray fluxes, the extracted
plasma temperature map, Sunyaev-Zel'dovich effect measurements, and cluster
halo radio emission. We constrain the initial conditions by minimizing the
chi-squared figure of merit between the full 2D observational data sets and the
simulation, rather than comparing only a few features such as the location of
subcluster centroids, as in previous studies. A simple initial configuration of
two triaxial clusters with NFW dark matter profiles and physically reasonable
plasma profiles gives a good fit to the current observational morphology and
X-ray emissions of the merging clusters. There is no need for unconventional
physics or extreme infall velocities. The study gives insight into the
astrophysical processes at play during a galaxy cluster merger, and constrains
the strength and coherence length of the magnetic fields. The techniques
developed here to create realistic, stable, triaxial clusters, and to utilize
the totality of the 2D image data, will be applicable to future simulation
studies of other merging clusters. This approach of constrained simulation,
when applied to well-measured systems, should be a powerful complement to
present tools for understanding X-ray clusters and their magnetic fields, and
the processes governing their formation.
