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Radio observations have revealed magnetic fields in the intracluster medium (ICM) of galaxy clusters nearly in equipartition with turbulence. This suggests magnetic field amplification by dynamo processes. However, observations are limited to redshifts z <~ 0.7, and the weakly collisional nature of the ICM complicates studying magnetic field evolution at higher redshifts through theoretical models and simulations. Using a model of the weakly collisional dynamo, we modelled the evolution of the Faraday rotation measure (RM) in clusters of different masses, up to z <~ 1.5, and investigated its properties. We compared our results with radio observations of various galaxy clusters. We used merger trees generated by the modified GALFORM algorithm to track the evolution of plasma quantities during galaxy cluster formation. Assuming the magnetic field remains in equipartition with the turbulent velocity field, we generated RM maps to study their properties. We find that both the standard deviation of RM, sigma_RM, and the absolute average |mu_RM| increase with cluster mass. Due to redshift dilution, RM values for a fixed cluster mass remain nearly constant between z=0 and z=1.5. For r/r200 >~ 0.4, sigma_RM does not vary significantly with L/r200, with L being the size of the observed RM patch. Below this limit, sigma_RM increases as L decreases. We find that radial RM profiles have a consistent shape, proportional to 10^{-1.2(r/r200)}, and are nearly independent of redshift. Our z~0 profiles for M_clust = 10^15 Msol match RM observations in the Coma cluster but show discrepancies with Perseus, possibly due to high gas mixing. Models for clusters with M_clust = 10^13 and M_clust = 10^15 Msol at z=0 and z = 0.174 align well with Fornax and A2345 data for r/r200 <~ 0.4. Our model can be useful for generating mock polarization observations for radio telescopes., Comment: 14 pages, 11 figures

We analyse observational signatures of magnetic fields for simulations of a Milky-Way like disc with supernova-driven interstellar turbulence and self-consistent chemical processes. In particular, we post-process two simulations data sets of the SILCC Project for two initial amplitudes of the magnetic field, $B_0 = $ 3 and 6 $\mu$G, to study the evolution of Faraday rotation measures (RM) and synchrotron luminosity. For calculating the RM, three different models of the electron density $n_e$ are considered. A constant electron density, and two estimations based on the density of ionized species and the fraction of the total gas, respectively. Our results show that the RM profiles are extremely sensitive to the $n_e$ models, which assesses the importance of accurate electron distribution observations/estimations for the magnetic fields to be probed using Faraday RMs. As a second observable of the magnetic field, we estimate the synchrotron luminosity in the simulations using a semi-analytical cosmic ray model. We find that the synchrotron luminosity decreases over time, which is connected to the decay of magnetic energy in the simulations. The ratios between the magnetic, the cosmic ray, and the thermal energy density indicate that the assumption of equipartition does not hold for most regions of the ISM. In particular, for the ratio of the cosmic ray to the magnetic energy the assumption of equipatition could lead to a wrong interpretation of the observed synchrotron emission., Comment: 21 pages, 15 figures, published in MNRAS