Statistical Significance of Small‐Scale Anisotropy in Arrival Directions of Ultra–High‐Energy Cosmic Rays

Recently, the High Resolution Fly's Eye (HiRes) experiment claims that thereis no small scale anisotropy in the arrival distribution of ultra-high energycosmic rays (UHECRs) above $E>10^{19}$ eV contrary to the Akeno Giant AirShower Array (AGASA) observation. In this paper, we discuss the statisticalsignificance of this discrepancy between the two experiments. We calculatearrival distribution of UHECRs above $10^{19}$ eV predicted by the sourcemodels constructed using the Optical Redshift Survey galaxy sample. We applythe new method developed by us for calculating arrival distribution in thepresence of the galactic magnetic field. The great advantage of this method isthat it enables us to calculate UHECR arrival distribution with lower energy($\sim 10^{19}$ eV) than previous studies within reasonable time by followingonly the trajectories of UHECRs actually reaching the earth. It has beenrealized that the small scale anisotropy observed by the AGASA can be explainedwith the source number density $\sim 10^{-5 \sim -6}$ Mpc$^{-3}$ assuming weakextragalactic magnetic field ($B \le 1$ nG). We find that the predicted smallscale anisotropy for this source number density is also consistent with thecurrent HiRes data. We thus conclude that the statement by the HiRes experimentthat they do not find small scale anisotropy in UHECR arrival distribution isnot statistically significant at present. We also show future prospect ofdetermining the source number density with increasing amount of observed data.Comment: 8 pages, 7 figure