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Detecting and characterizing the anisotropy pattern of the arrival directionsof the highest energy cosmic rays are crucial steps towards the identificationof their sources. We discuss a possible distortion of the cosmic ray fluxinduced by the anisotropic and inhomogeneous distribution of extragalacticmagnetic fields in cases where sources of ultrahigh energy cosmic rays are raretransient phenomena, such as gamma-ray bursts and/or newly born magnetars. Thisdistortion does not involve an angular deflection but the modulation of theflux related to the probability of seeing the source on an experiment lifetime.To quantify this distortion, we construct sky maps of the arrival directions ofthese highest energy cosmic rays for various magnetic field configurations andappeal to statistical tests proposed in the literature. We conclude that thisdistortion cannot affect present experiments but should be considered whenperforming anisotropy studies with future large-scale experiments that recordas many as hundreds of events above 6x10^19 eV.

Distortion of the ultrahigh energy cosmic ray flux from rare transient sources in inhomogeneous extragalactic magnetic fields