Studying the Effect of Shock Obliquity on the $γ$-ray and Diffuse Radio Emission in Galaxy Clusters

Observations of diffuse radio emission in galaxy clusters indicate that cosmic-ray electrons are accelerated on $\sim$Mpc scales. However, protons appear to be accelerated less efficiently since their associated hadronic $γ$-ray emission has not yet been detected. Inspired by recent particle-in-cell simulations, we study the cosmic-ray production and its signatures under the hypothesis that the efficiency of shock acceleration depends on the Mach number and on the shock obliquity. For this purpose, we combine ENZO cosmological magneto-hydrodynamical simulations with a Lagrangian tracer code to follow the properties of the cosmic rays. Our simulations suggest that the distribution of obliquities in galaxy clusters is random to first order. Quasi-perpendicular shocks are able to accelerate cosmic-ray electrons to the energies needed to produce observable radio emission. However, the $γ$-ray emission is lowered by a factor of a few, $\sim$3, if cosmic-ray protons are only accelerated by quasi-parallel shocks, reducing (yet not entirely solving) the tension with the non-detection of hadronic $γ$-ray emission by the \textit{Fermi}-satellite.

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