Arrival Distribution of Ultra–High‐Energy Cosmic Rays: Prospects for the Future

We predict the arrival distribution of UHECRs above $4 \times 10^{19}$ eVwith the event number expected by future experiments in the next few years. Weperform event simulations with the source model which is adopted in our recentstudy and can explain the current AGASA observation. At first, we calculate theharmonic amplitude and the two point correlation function for the simulatedevent sets. We find that significant anisotropy on large angle scale will beobserved when $\sim 10^3$ cosmic rays above $4 \times 10^{19}$ eV are detectedby future experiments. The statistics of the two point correlation functionwill also increase. The angle scale at which the events have strong correlationwith each other corresponds to deflection angle of UHECR in propagating in theEGMF, which in turn can be determined by the future observations. We furtherinvestigate the relation between the number of events clustered at a directionand the distance of their sources. Despite the limited amount of data, we findthat the C2 triplet events observed by the AGASA may originate from the sourcewithin 100 Mpc. Merger galaxy Arp 299 (NGC 3690 + IC 694) is the best candidatefor their source. If data accumulate, the UHECR sources within $\sim 100$ Mpccan be identified from observed event clusterings significantly. This willprovide some kinds of information about poorly known parameters which influencethe propagation of UHECRs, such as extragalactic and galactic magnetic field,chemical composition of observed cosmic rays. Also, we will reveal their originwith our method to identify the sources of UHECR. Finally, we predict thearrival distribution of UHECRs above $10^{20}$ eV, which is expected to beobserved if the current HiRes spectrum is correct, and discuss theirstatistical features and implications.Comment: 11 pages, 9 figures. accepted version for publication in Ap