Testing cosmic-ray acceleration with radio relics: a high-resolution
  study using MHD and tracers
  Weak shocks in the intracluster medium may accelerate cosmic-ray protons and
cosmic-ray electrons differently depending on the angle between the upstream
magnetic field and the shock normal. In this work, we investigate how shock
obliquity affects the production of cosmic rays in high-resolution simulations
of galaxy clusters. For this purpose, we performed a magneto-hydrodynamical
simulation of a galaxy cluster using the mesh refinement code \enzo. We use
Lagrangian tracers to follow the properties of the thermal gas, the cosmic rays
and the magnetic fields over time. We tested a number of different acceleration
scenarios by varying the obliquity-dependent acceleration efficiencies of
protons and electrons, and by examining the resulting hadronic $\gamma$-ray and
radio emission. We find that the radio emission does not change significantly
if only quasi-perpendicular shocks are able to accelerate cosmic-ray electrons.
Our analysis suggests that radio emitting electrons found in relics have been
typically shocked many times before $z=0$. On the other hand, the hadronic
$\gamma$-ray emission from clusters is found to decrease significantly if only
quasi-parallel shocks are allowed to accelerate cosmic-ray protons. This might
reduce the tension with the low upper limits on $\gamma$-ray emission from
clusters set by the \textit{Fermi}-satellite.
