Small‐Scale Clustering in the Isotropic Arrival Distribution of Ultra–High‐Energy Cosmic Rays and Implications for Their Source Candidates

Abstract

We present numerical simulations on the propagation of ultra-high-frequency protons with energies of 1019.5-1022 eV in extragalactic magnetic fields over 1 Gpc. We use the Optical Redshift Survey (ORS) galaxy sample, which allows us to accurately quantify the contribution of nearby sources to the energy spectrum and the arrival distribution, as a source model. The sample is corrected, taking the selection effect and absence of galaxies in the zone of avoidance (|b| < 20°) into account. We calculate three observable quantities - cosmic-ray spectrum, harmonic amplitude, and two-point correlation function-from our data of numerical simulations. With these quantities, we compare the results of our numerical calculations with the observation. We find that the arrival distribution of ultra-high-energy cosmic rays (UHECRs) becomes most isotropic as sources are restricted to to luminous galaxies (Mlim = -20.5). However, it is not isotropic enough to be consistent with the Akeno Giant Air Shower Array (AGASA) observation, even for Mlim = -20.5. In order to obtain a sufficiently isotropic arrival distribution, we randomly select sources more luminous than -20.5 mag from the ORS sample, which contribute to the observed cosmic-ray flux, and investigate the dependence of the results on their number. We show that three observable quantities, including the Greisen-Zatsepin-Kuz'min (GZK) cutoff of the energy spectrum, can be reproduced in the case that the number fraction ∼10-1.7 of the ORS galaxies more luminous than -20.5 mag is selected as UHECR sources. In terms of the source number density, this constraint corresponds to ∼10-6 Mpc-3. However, since the mean number of sources within the GZK sphere is only ∼0.5 in this case, the eight AGASA events above 1020.0 eV, which do not together constitute clustered events, cannot be reproduced. On the other hand, if the cosmic-ray flux measured by the High Resolution Fly's Eye EHE Cosmic-Ray Detector (HiRes), which is consistent with the GZK cutoff, is correct and observational features about the arrival distribution of UHECRs are same as the AGASA, our source model can explain both the arrival distribution and the flux at the same time. Thus, we conclude that a large fraction of the eight AGASA events above 1020 eV might originate in the top-down scenarios or that the cosmic-ray flux measured by the HiRes experiment might be better. We also discuss the origin of UHECRs below 1020.0 eV through comparisons between the number density of astrophysical source candidates and our result (∼10-6 Mpc-3).