Simulations of the Galaxy Cluster CIZA J2242.8+5301 I: Thermal Model and
  Shock Properties
  The giant radio relic in CIZA J2242.8+5301 is likely evidence of a Mpc sized
shock in a massive merging galaxy cluster. However, the exact shock properties
are still not clearly determined. In particular, the Mach number derived from
the integrated radio spectrum exceeds the Mach number derived from the X-ray
temperature jump by a factor of two. We present here a numerical study, aiming
for a model that is consistent with the majority of observations of this galaxy
cluster. We first show that in the northern shock upstream X-ray temperature
and radio data are consistent with each other. We then derive progenitor masses
for the system using standard density profiles, X-ray properties and the
assumption of hydrostatic equilibrium. We find a class of models that is
roughly consistent with weak lensing data, radio data and some of the X-ray
data. Assuming a cool-core versus non-cool-core merger, we find a fiducial
model with a total mass of $1.6 \times 10^{15}\,M_\odot$, a mass ratio of 1.76
and a Mach number that is consistent with estimates from the radio spectrum. We
are not able to match X-ray derived Mach numbers, because even low mass models
over-predict the X-ray derived shock speeds. We argue that deep X-ray
observations of CIZA J2242.8+5301 will be able to test our model and
potentially reconcile X-ray and radio derived Mach numbers in relics.
