Exploring the magnetized cosmic web through low frequency radio emission

Recent improvements in the capabilities of low frequency radio telescopes provide a unique opportunity to study thermal and non-thermal properties of the cosmic web. We argue that the diffuse, polarized emission from giant radio relics traces structure formation shock waves and illuminates the large-scale magnetic field. To show this, we model the population of shockaccelerated relativistic electrons in high-resolution cosmological simulations of galaxy clusters and calculate the resulting radio synchrotron emission. We find that the sensitive observations possible with upcoming telescopes should find more low-luminosity relics, and that the luminosities and number counts of the relics strongly depend on the cluster mass and dynamical state. By suitably combining different cluster data, including Faraday rotation measures, we are able to measure the underlying properties of the plasma at the structure formation shocks, including properties that are degenerate in current measurements. We also predict properties of the warm-hot intergalactic medium, such as its temperature and density. The luminosity function of cluster relics depends strongly on the magnetic field properties, cluster mass and dynamical state. We find that individual shock waves correspond to localized peaks in the radio surface brightness map. In the best cases, the associated radio observables enable us to extract unique physical properties of the formation shocks, such as Mach numbers, the turbulent spectra of the magnetic field, and the energy densities of shock-accelerated electrons. We predict that the current generation of radio telescopes (LOFAR, GMRT, MWA, LWA) have the potential to discover a substantially larger sample of radio relics, with multiple relics expected for each violently merging cluster. Future experiments (SKA) should enable us to probe fundamental parameters of plasma physics in clusters.