Arrival Distribution of Ultra-High Energy Cosmic Rays: Prospects for the Future
We predict the arrival distribution of UHECRs above $4 \times 10^{19}$ eV with the event number expected by future experiments in the next few years. We perform event simulations with the source model which is adopted in our recent study and can explain the current AGASA observation. At first, we calculate the harmonic amplitude and the two point correlation function for the simulated event sets. We find that significant anisotropy on large angle scale will be observed when $\sim 10^3$ cosmic rays above $4 \times 10^{19}$ eV are detected by future experiments. The statistics of the two point correlation function will also increase. The angle scale at which the events have strong correlation with each other corresponds to deflection angle of UHECR in propagating in the EGMF, which in turn can be determined by the future observations. We further investigate the relation between the number of events clustered at a direction and the distance of their sources. Despite the limited amount of data, we find that the C2 triplet events observed by the AGASA may originate from the source within 100 Mpc. Merger galaxy Arp 299 (NGC 3690 + IC 694) is the best candidate for their source. If data accumulate, the UHECR sources within $\sim 100$ Mpc can be identified from observed event clusterings significantly. This will provide some kinds of information about poorly known parameters which influence the propagation of UHECRs, such as extragalactic and galactic magnetic field, chemical composition of observed cosmic rays. Also, we will reveal their origin with our method to identify the sources of UHECR. Finally, we predict the arrival distribution of UHECRs above $10^{20}$ eV, which is expected to be observed if the current HiRes spectrum is correct, and discuss their statistical features and implications.