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.