Using double radio relics to constrain galaxy cluster mergers: A model
  of double radio relics in CIZA J2242.8+5301
  Galaxy clusters grow by mergers with other clusters and galaxy groups. These
mergers create shock waves within the intracluster medium (ICM) that can
accelerate particles to extreme energies. In the presence of magnetic fields,
relativistic electrons form large regions emitting synchrotron radiation,
so-called radio relics. Behind the shock front, synchrotron and inverse Compton
(IC) losses cause the radio spectral index to steepen away from the shock
front. An example of such a cluster is CIZA J2242.8+5301, where very clear
spectral steepening in the downstream region is observed. Here we present
hydrodynamical simulations of idealized binary cluster mergers with the aim of
constraining the merger scenario for this cluster. From our simulations, we
find that CIZA J2242.8+5301 is probably undergoing a merger in the plane of the
sky (less then 10 deg from edge-on) with a mass ratio of about 2:1, and an
impact parameter < 400 kpc. We find that the core passage of the clusters
happened about 1 Gyr ago. We conclude that double relics relics can set
constraints on the mass ratios, impact parameters, timescales, and viewing
geometry of binary cluster mergers, which is particularly useful when detailed
X-ray observations are not available. In addition, the presence of large radio
relics can be used to constrain the degree of clumping in the outskirts of the
ICM, which is important to constrain the baryon fraction, density and entropy
profiles, around the virial radius and beyond. We find that the amplitude of
density fluctuations, with sizes of < 200 kpc, in the relic in CIZA
J2242.8+5301 is not larger than 30%. [abridged]
