Cosmological Magnetohydrodynamic Simulations of Galaxy Cluster Radio Relics: Insights and Warnings for Observations

Non-thermal radio emission from cosmic-ray electrons in the vicinity of merging galaxy clusters is an important tracer of cluster merger activity, and is the result of complex physical processes that involve magnetic fields, particle acceleration, gas dynamics, and radiation. In particular, objects known as radio relics are thought to be the result of shock-accelerated electrons that, when embedded in a magnetic field, emit synchrotron radiation in the radio wavelengths. In order to properly model this emission, we utilize the adaptive mesh refinement simulation of the magnetohydrodynamic evolution of a galaxy cluster from cosmological initial conditions. We locate shock fronts and apply models of cosmic-ray electron acceleration that are then input into radio emission models. We have determined the thermodynamic properties of this radio-emitting plasma and constructed synthetic radio observations to compare observed galaxy clusters. We find a significant dependence of the observed morphology and radio relic properties on the viewing angle of the cluster, raising concerns regarding the interpretation of observed radio features in clusters. We also find that a given shock should not be characterized by a single Mach number. We find that the bulk of the radio emission comes from gas with T > 5 × 10⁷ K, ρ ~ 10^-28-10^-27 g cm^-3, with magnetic field strengths of 0.1-1.0 μG, and shock Mach numbers of {M}∼ 3-6. We present an analysis of the radio spectral index which suggests that the spatial variation of the spectral index can mimic synchrotron aging. Finally, we examine the polarization fraction and position angle of the simulated radio features, and compare to observations.