Constrained Simulations of the Magnetic Field in the Local Universe and   the Propagation of UHECRs
  We use simulations of LSS formation to study the build-up of magnetic fields (MFs) in the ICM. Our basic assumption is that cosmological MFs grow in a MHD amplification process driven by structure formation out of a seed MF present at high z. Our LCDM initial conditions for the density fluctuations have been statistically constrained by the observed galaxies, based on the IRAS 1.2-Jy all-sky redshift survey. As a result, prominent galaxy clusters in our simulation coincide closely with their real counterparts. We find excellent agreement between RMs of our simulated clusters and observational data. The improved resolution compared to previous work also allows us to study the MF in large-scale filaments, sheets and voids. By tracing the propagation of UHE protons in the simulated MF we construct full-sky maps of expected deflection angles of protons with arrival energies E=1e20eV and 4e19eV, respectively. Strong deflections are only produced if UHE protons cross clusters, however covering only a small area on the sky. Multiple crossings of sheets and filaments over larger distances may give rise to noticeable deflections, depending on the model adopted for the magnetic seed field. Based on our results we argue that over a large fraction of the sky the deflections are likely to remain smaller than the present experimental angular sensitivity. Therefore, we conclude that forthcoming air shower experiments should be able to locate sources of UHE protons and shed more light on the nature of cosmological MFs. 
Klaus Dolag, Dario Grasso, Volker Springel and Igor Tkachev