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Cosmological shocks are a critical part of large-scale structure formation,and are responsible for heating the intracluster medium in galaxy clusters. Inaddition, they are also capable of accelerating non-thermal electrons andprotons. In this work, we focus on the acceleration of electrons at shockfronts, which is thought to be responsible for radio relics - extended radiofeatures in the vicinity of merging galaxy clusters. By combining highresolution AMR/N-body cosmological simulations with an accurate shock findingalgorithm and a model for electron acceleration, we calculate the expectedsynchrotron emission resulting from cosmological structure formation. Weproduce synthetic radio maps of a large sample of galaxy clusters and presentluminosity functions and scaling relationships. With upcoming long wavelengthradio telescopes, we expect to see an abundance of radio emission associatedwith merger shocks in the intracluster medium. By producing observationallymotivated statistics, we provide predictions that can be compared withobservations to further improve our understanding of magnetic fields andelectron shock acceleration.

Galaxy Cluster Radio Relics in Adaptive Mesh Refinement Cosmological Simulations: Relic Properties and Scaling Relationships