Ultrahigh energy cosmic rays in a structured and magnetized universe

We simulate propagation of cosmic ray nucleons above ${10}^{19}$ eV in scenarios where both the source distribution and magnetic fields within about 50 Mpc from us are obtained from an unconstrained large scale structure simulation. We find that a consistency of predicted sky distributions with current data above $4\times {10}^{19}$ eV requires magnetic fields of $\simeq 0.1\mu \mathrm{G}$ in our immediate environment, and a nearby source density of $\sim {10}^{-4}-{10}^{-3}{\mathrm{Mpc}}^{-3}.$ Radio galaxies could provide the required sources, but only if both high- and low-luminosity radio galaxies are very efficient cosmic ray accelerators. Moreover, at $\simeq {10}^{19}$ eV an additional isotropic flux component, presumably of cosmological origin, should dominate over the local flux component by about a factor of 3 in order to explain the observed isotropy. This argues against the scenario in which local astrophysical sources of cosmic rays above $\simeq {10}^{19}$ eV reside in a strongly magnetized $\left(B\simeq 0.1\mu \mathrm{G}\right)$ and structured intergalactic medium. Finally we discuss how future large scale full-sky detectors such as the Pierre Auger project will allow us to put much more stringent constraints on source and magnetic field distributions.