Seeking and Mocking Non-thermal Emission in Galaxy Clusters

Diffuse synchrotron radio emission is observed in many clusters of galaxies probing the presence of high energy cosmic ray (CR) electrons. This emission can be explained by the hadronic model where the electron population originates from the interactions between CR protons and the cluster ambient gas. Additionally, a very high energy gamma-ray emission is also expected. I will briefly review the current knowledge on the non-thermal emission in galaxy clusters and report on our efforts in this field both observationally and theoretically.