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 there is no small scale anisotropy in the arrival distribution of ultra-high energy cosmic rays (UHECRs) above $E>10^{19}$ eV contrary to the Akeno Giant Air Shower Array (AGASA) observation. In this paper, we discuss the statistical significance of this discrepancy between the two experiments. We calculate arrival distribution of UHECRs above $10^{19}$ eV predicted by the source models constructed using the Optical Redshift Survey galaxy sample. We apply the new method developed by us for calculating arrival distribution in the presence of the galactic magnetic field. The great advantage of this method is that it enables us to calculate UHECR arrival distribution with lower energy ($\sim 10^{19}$ eV) than previous studies within reasonable time by following only the trajectories of UHECRs actually reaching the earth. It has been realized that the small scale anisotropy observed by the AGASA can be explained with the source number density $\sim 10^{-5 \sim -6}$ Mpc$^{-3}$ assuming weak extragalactic magnetic field ($B \le 1$ nG). We find that the predicted small scale anisotropy for this source number density is also consistent with the current HiRes data. We thus conclude that the statement by the HiRes experiment that they do not find small scale anisotropy in UHECR arrival distribution is not statistically significant at present. We also show future prospect of determining the source number density with increasing amount of observed data. 
Hiroyuki Yoshiguchi, Shigehiro Nagataki, Katsuhiko Sato