Shocks and Tides Quantified in the "Sausage" Cluster, CIZA J2242.8+5301,
  using N-body/hydro-dynamical Simulations
  The colliding cluster, CIZA J2242.8+5301, displays a spectacular, almost 2
Mpc long shock front with a radio based Mach number M ~ 5, that is puzzlingly
large compared with the X-ray estimate of M ~ 2.5. The extent to which the
X-ray temperature jump is diluted by cooler unshocked gas projected through the
cluster currently lacks quantification. Thus, here we apply our self-consistent
N-body/hydro-dynamical code (based on FLASH) to model this binary cluster
encounter. We can account for the location of the shock front and also the
elongated X-ray emission by tidal stretching of the gas and dark matter between
the two cluster centers. The required total mass is $8.9 \times 10^{14}$ Msun
with a 1.3:1 mass ratio favoring the southern cluster component. The relative
velocity we derive is $\simeq 2500$ km/s initially between the two main cluster
components, with an impact parameter of 120 kpc. This solution implies that the
shock temperature jump derived from the low angular resolution X-ray satellite
SUZAKU is underestimated by a factor of two, due to cool gas in projection,
bringing the observed X-ray and radio estimates into agreement. We propose that
the complex southern relics in CIZA J2242.8+5301, have been broken up as the
southerly moving "back" shocked gas impacts the gas still falling in along the
collision axis. Finally, we use our model to generate Compton-y maps to
estimate the reduction in radio flux caused by the thermal Sunyaev-Zel'dovich
(SZ) effect. At 30 GHz, this amounts to $\Delta S_n = -0.072$ mJy/arcmin$^2$
and $\Delta S_s = -0.075$ mJy/arcmin$^2$ at the locations of the northern and
southern shock fronts respectively. Our model estimate agrees with previous
empirical estimates that have inferred the measured radio spectra can be
significantly affected by the SZ effect, with implications for charged particle
acceleration models of the radio relics.
