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Modeling the total and polarized emission in evolving galaxies: "spotty" magnetic structures

Future radio observations with the SKA and its precursors will be sensitive to trace spiral galaxies and their magnetic field configurations up to redshift $z\approx3$. We suggest an evolutionary model for the magnetic configuration in star-forming disk galaxies and simulate the magnetic field distribution, the total and polarized synchrotron emission, and the Faraday rotation measures for disk galaxies at $z\la 3$. Since details of dynamo action in young galaxies are quite uncertain, we model the dynamo action heuristically relying only on well-established ideas of the form and evolution of magnetic fields produced by the mean-field dynamo in a thin disk. We assume a small-scale seed field which is then amplified by the small-scale turbulent dynamo up to energy equipartition with kinetic energy of turbulence. The large-scale galactic dynamo starts from seed fields of 100 pc and an averaged regular field strength of 0.02\,$μ$G, which then evolves to a "spotty" magnetic field configuration in about 0.8\,Gyr with scales of about one kpc and an averaged regular field strength of 0.6\,$μ$G. The evolution of these magnetic spots is simulated under the influence of star formation, dynamo action, stretching by differential rotation of the disk, and turbulent diffusion. The evolution of the regular magnetic field in a disk of a spiral galaxy, as well as the expected total intensity, linear polarization and Faraday rotation are simulated in the rest frame of a galaxy at 5\,GHz and 150\,MHz and in the rest frame of the observer at 150\,MHz. We present the corresponding maps for several epochs after disk formation. (abridged)