Evolution and Distribution of Magnetic Fields from AGNs in Galaxy Clusters. I. The Effect of Injection Energy and Redshift

We present a series of cosmological magnetohydrodynamic (MHD) simulations that simultaneously follow the formation of a galaxy cluster and evolution of magnetic fields ejected by an Active Galactic Nucleus (AGN). Specifically, we investigate the influence of both the epoch of AGN (z $\sim$ 3-0.5) and the AGN energy ($\sim$ 3 $\times$ 10$^{57}$ - 2 $\times$ 10$^{60}$ ergs)on the final magnetic field distribution in a relatively massive cluster (M$_{vir}$ $\sim$10$^{15}$ M$_\odot$). We find that as long as the AGN magnetic fields are ejected before the major mergers in the cluster formation history, magnetic fields can be transported throughout the cluster and can be further amplified by the intra-cluster medium (ICM) turbulence cause by hierarchical mergers during the cluster formation process. The total magnetic energy in the cluster can reach $\sim$ $10^{61}$ ergs, with micro Gauss fields distributed over $\sim$ Mpc scale. The amplification of the total magnetic energy by the ICM turbulence can be significant, up to $\sim$1000 times in some cases. Therefore even weak magnetic fields from AGNs can be used to magnetize the cluster to the observed level. The final magnetic energy in the ICM is determined by the ICM turbulent energy, with a weak dependence on the AGN injection energy. We discuss the properties of magnetic fields throughout the cluster and the synthetic Faraday rotation measure maps they produce. We also show that high spatial resolution over most of the magnetic regions of the cluster is very important to capture the small scale dynamo process and maintain the magnetic field structure in our simulations.