Ultrahigh energy cosmic rays from a nearby extragalactic source in the diffusive regime

We study the effects that the diffusion of the cosmic rays in the magnetic field of the Local Supercluster can have on the spectrum of a nearby extragalactic source at ultrahigh energies. We find that the strong enhancement of the flux below the energy at which the transition between the diffusive and quasirectilinear regimes takes place, as well as the suppression at lower energies associated with a finite source age, can help to explain the observed features of the cosmic-ray spectrum and the composition. Scenarios are discussed in which a nearby extragalactic source with mixed composition and rigidity-dependent spectrum accounts for most of the observed cosmic rays at energies above a few EeV while the rest of the extragalactic sources lead to a diffuse flux that dominates at lower energies and down to $\sim 0.1$~EeV. The nearby source can also naturally account for the dipolar anisotropy measurements above 4~EeV, and these measurements can also help to constrain its evolution with redshift.