Properties of Merger Shocks in Merging Galaxy Clusters
  X-ray shocks and radio relics detected in the cluster outskirts are commonly
interpreted as shocks induced by mergers of sub-clumps. We study the properties
of merger shocks in merging galaxy clusters, using a set of cosmological
simulations for the large-scale structure formation of the universe. As a
representative case, we here focus on the simulated clusters that undergo
almost head-on collisions with mass ratio $\sim2$. Due to the turbulent nature
of the intracluster medium, shock surfaces are not smooth, but composed of
shocks with different Mach numbers. As the merger shocks expand outward from
the core to the outskirts, the average Mach number, $\left<M_s\right>$,
increases in time. We suggest that the shocks propagating along the merger axis
could be manifested as X-ray shocks and/or radio relics. The kinetic energy
through the shocks, $F_\phi$, peaks at $\sim1$ Gyr after their initial
launching, or at $\sim1-2$ Mpc from the core. Because of the Mach number
dependent model adopted here for the cosmic ray (CR) acceleration efficiency,
their CR-energy-weighted Mach number is higher with $\left< M_s \right>_{\rm
CR}\sim3-4$, compared to the kinetic-energy-weighted Mach number,
$\left<M_s\right>_{\phi}\sim2-3$. Most energetic shocks are to be found ahead
of the lighter dark matter (DM) clump, while the heavier DM clump is located in
the opposite side of clusters. Although our study is limited to the merger case
considered, the results such as the means and variations of shock properties
and their time evolution could be compared with the observed characteristics of
merger shocks, constraining interpretations of relevant observations.
