Abstract. The origin of extragalactic magnetic fields is still poorly understood. Based on a dedicated suite of cosmological magneto-hydrodynamical simulations with the ENZO code we have performed a survey of different models that may have caused present-day magnetic fields in galaxies and galaxy clusters. The outcomes of these models differ in cluster outskirts, filaments, sheets and voids and we use these simulations to find observational signatures of magnetogenesis. With these simulations, we predict the signal of extragalactic magnetic fields in radio observations of synchrotron emission from the cosmic web, in Faraday Rotation, in the propagation of Ultra High Energy Cosmic Rays, in the polarized signal from Fast Radio Bursts at cosmological distance and in spectra of distant blazars. In general, primordial scenarios in which present-day magnetic fields originate from the amplification of weak (≤ nG) uniform seed fields result more homogeneous and relatively easier to observe magnetic fields than than astrophysical scenarios, in which present-day fields are the product of feedback processes triggered by stars and active galaxies. In the near future the best evidence for the origin of cosmic magnetic fields will most likely come from a combination of synchrotron emission and Faraday Rotation observed at the periphery of large-scale structures.

Context. Radio relics are diffuse extended synchrotron sources that originate from shock fronts induced by galaxy cluster mergers. The actual particle acceleration mechanism at the shock fronts is still under debate. The galaxy cluster 1RXS J0603.3+4214 hosts one of the most intriguing examples of radio relics, known as the Toothbrush. Aims. To understand the mechanism(s) that accelerate relativistic particles in the intracluster medium (ICM), we investigate the spectral properties of large scale diffuse extended sources in the merging galaxy cluster 1RXS J0603.3+4214. Methods. We present new wideband radio continuum observations made with uGMRT and VLA. Our new observations in combination with previously published data, allowed us to carry out a detailed high spatial resolution spectral and curvature analysis of the known diffuse radio emission sources, over a broad range of frequencies.Results. The integrated spectrum of the Toothbrush follows closely a power law over close to 2 decades in frequency, with a spectral index of −1.16 ± 0.02. We do not find any evidence of spectral steepening below 8 GHz. The subregions of the main Toothbrush also exhibit near-perfect power laws, implying a very regular combination of shock properties across the shock front. Recent numerical simulations show an intriguing similar spectral index, suggesting that the radio spectrum is dominated by the average over the inhomogeneities within the shock, with most of the emission coming from the tail of the Mach number distribution. In contrast to the Toothbrush, the spectrum of the fainter relics show a high frequency steepening. Moreover, also the integrated spectrum of the halo follows a power law from 150 MHz to 3 GHz with a spectral index of −1.16 ± 0.04. We do not find any evidence for spectral curvature, not even in subareas of the halo. This suggest a homogeneous acceleration throughout the cluster volume. Between the "brush" region of the Toothbrush and the halo, the color-color analysis revealed emission that was consistent with an overlap between the two different spectral regions. Conclusions. None of the relic structures, the Toothbrush as a whole or its subregions or the other two fainter relics, show spectral shapes consistent with a single injection of relativistic electrons, such as at a shock, followed by synchrotron aging in a relatively homogeneous environment. Inhomogeneities in some combination of Mach number, magnetic field strengths and projection effects dominate the observed spectral shapes.

Weak shocks in the intracluster medium may accelerate cosmic-ray protons and cosmic-ray electrons differently depending on the angle between the upstream magnetic field and the shock normal. In this work, we investigate how shock obliquity affects the production of cosmic rays in high-resolution simulations of galaxy clusters. For this purpose, we performed a magneto-hydrodynamical simulation of a galaxy cluster using the mesh refinement code ENZO. We use Lagrangian tracers to follow the properties of the thermal gas, the cosmic rays and the magnetic fields over time. We tested a number of different acceleration scenarios by varying the obliquity-dependent acceleration efficiencies of protons and electrons, and by examining the resulting hadronic γ-ray and radio emission. We find that the radio emission does not change significantly if only quasi-perpendicular shocks are able to accelerate cosmic-ray electrons. Our analysis suggests that radio emitting electrons found in relics have been typically shocked many times before z = 0. On the other hand, the hadronic γ-ray emission from clusters is found to decrease significantly if only quasi-parallel shocks are allowed to accelerate cosmic-ray protons. This might reduce the tension with the low upper limits on γ-ray emission from clusters set by the Fermi-satellite.