The large-scale properties of simulated cosmological magnetic fields
  We perform uniformly sampled large-scale cosmological simulations including
magnetic fields with the moving mesh code AREPO. We run two sets of MHD
simulations: one including adiabatic gas physics only; the other featuring the
fiducial feedback model of the Illustris simulation. In the adiabatic case, the
magnetic field amplification follows the $B \propto \rho^{2/3}$ scaling derived
from `flux-freezing' arguments, with the seed field strength providing an
overall normalization factor. At high baryon overdensities the amplification is
enhanced by shear flows and turbulence. Feedback physics and the inclusion of
radiative cooling change this picture dramatically. In haloes, gas collapses to
much larger densities and the magnetic field is amplified strongly and to the
same maximum intensity irrespective of the initial seed field of which any
memory is lost. At lower densities a dependence on the seed field strength and
orientation, which in principle can be used to constrain models of cosmic
magnetogenesis, is still present. Inside the most massive haloes magnetic
fields reach values of $\sim 10-100\,\,{\rm \mu G}$, in agreement with galaxy
cluster observations. The topology of the field is tangled and gives rise to
rotation measure signals in reasonable agreement with the observations.
However, the rotation measure signal declines too rapidly towards larger radii
as compared to observational data.
