Comparisons of Cosmological MHD Galaxy Cluster Simulations to Radio
  Observations
  Radio observations of galaxy clusters show that there are $\mu$G magnetic
fields permeating the intra-cluster medium (ICM), but it is hard to accurately
constrain the strength and structure of the magnetic fields without the help of
advanced computer simulations. We present qualitative comparisons of synthetic
VLA observations of simulated galaxy clusters to radio observations of Faraday
Rotation Measure (RM) and radio halos. The cluster formation is modeled using
adaptive mesh refinement (AMR) magneto-hydrodynamic (MHD) simulations with the
assumption that the initial magnetic fields are injected into the ICM by active
galactic nuclei (AGNs) at high redshift. In addition to simulated clusters in
Xu et al. (2010, 2011), we present a new simulation with magnetic field
injections from multiple AGNs. We find that the cluster with multiple injection
sources is magnetized to a similar level as in previous simulations with a
single AGN. The RM profiles from simulated clusters, both $|RM|$ and the
dispersion of RM ($\sigma_{RM}$), are consistent at a first-order with the
radial distribution from observations. The correlations between the
$\sigma_{RM}$ and X-ray surface brightness from simulations are in a broad
agreement with the observations, although there is an indication that the
simulated clusters could be slightly over-dense and less magnetized with
respect to those in the observed sample. In addition, the simulated radio halos
agree with the observed correlations between the radio power versus the cluster
X-ray luminosity and between the radio power versus the radio halo size. These
studies show that the cluster wide magnetic fields that originate from AGNs and
are then amplified by the ICM turbulence (Xu et al. 2010) match observations of
magnetic fields in galaxy clusters.
