Small Scale Clustering in Isotropic Arrival Distribution of Ultra-High Energy Cosmic Rays

We present numerical simulations on the propagation of ultra-high energy (UHE) protons with energies of (1019.5 - 1022 ) eV in extragalactic magnetic fields (EGMF) over 1 Gp c. We use the Optical Redshit Survey (ORS) galaxy sample, which is corrected taking the selection effect and absence of galaxies in the zone of avoidance (|b| < 20° ) into account. We calculate the cosmic ray spectrum, harmonic amplitude, and two point correlation function, and compare the results of our numerical calculations with the observation. One of our conclusions is that a large fraction of cosmic rays above 1020 eV observed by the AGASA experiment might originate in the top-down scenarios, or that the energy spectrum measured by the HiRes experiment might be better. As for the UHECR arrival distribution, we can explain the AGASA observation when ∼ 1/50 of the ORS galaxies more luminous than Mlim = -20.5 is selected as UHECR sources, and in the case of weak EGMF (BRMS ≤ 1nG). In terms of the source number density, this constraint corresp onds to ∼ 10-6 Mp c-3 .