This paper provides an analytical description of the transport of ultrahigh energy cosmic rays in an inhomogeneously magnetized intergalactic medium. The latter is modeled as a collection of magnetized scattering centers, such as radio cocoons, magnetized galactic winds, clusters or magnetized filaments of large scale structure, with negligible magnetic fields in between. Magnetic deflection is no longer a continuous process, it is rather dominated by scattering events. We study the interaction between high-energy cosmic rays and the scattering agents. We then compute the optical depth of the Universe to cosmic ray scattering and discuss the phenomenological consequences for various source scenarios. For typical parameters of the scattering centers, the optical depth is greater than unity at $5\times {10}^{19}\mathrm{eV}$, but the total angular deflection is smaller than unity. One important consequence of this scenario is the possibility that the last scattering center encountered by a cosmic ray be mistaken with the source of this cosmic ray. In particular, we suggest that part of the correlation recently reported by the Pierre Auger Observatory may be affected by such delusion: this experiment may be observing in part the last scattering surface of ultrahigh energy cosmic rays rather than their source population. Since the optical depth falls rapidly with increasing energy, one should probe the arrival directions of the highest energy events beyond ${10}^{20}\mathrm{eV}$ on an event by event basis to circumvent this effect.

• Received 17 January 2008

DOI:https://doi.org/10.1103/PhysRevD.77.123003