Cosmological shocks are a critical part of large-scale structure formation, and are responsible for heating the intracluster medium in galaxy clusters. In addition, they are also capable of accelerating non-thermal electrons and protons. In this work, we focus on the acceleration of electrons at shock fronts, which is thought to be responsible for radio relics - extended radio features in the vicinity of merging galaxy clusters. By combining high resolution AMR/N-body cosmological simulations with an accurate shock finding algorithm and a model for electron acceleration, we calculate the expected synchrotron emission resulting from cosmological structure formation. We produce synthetic radio maps of a large sample of galaxy clusters and present luminosity functions and scaling relationships. With upcoming long wavelength radio telescopes, we expect to see an abundance of radio emission associated with merger shocks in the intracluster medium. By producing observationally motivated statistics, we provide predictions that can be compared with observations to further improve our understanding of magnetic fields and electron shock acceleration.
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