A New Method for Calculating Arrival Distribution of Ultra–High‐Energy Cosmic Rays above 1019eV with Modifications by the Galactic Magnetic Field

We present a new method for calculating arrival distribution of UHECRsincluding modifications by the galactic magnetic field. We perform numericalsimulations of UHE anti-protons, which are injected isotropically at the earth,in the Galaxy and record the directions of velocities at the earth and outsidethe Galaxy for all of the trajectories. We then select some of them so that theresultant mapping of the velocity directions outside the Galaxy of the selectedtrajectories corresponds to a given source location scenario, applyingLiouville's theorem. We also consider energy loss processes of UHE protons inthe intergalactic space. Applying this method to our source location scenariowhich is adopted in our recent study and can explain the AGASA observationabove 4 \times 10^{19} eV, we calculate the arrival distribution of UHECRsincluding lower energy (E>10^19 eV) ones. We find that our source model canreproduce the large-scale isotropy and the small-scale anisotropy on UHECRarrival distribution above 10^19 eV observed by the AGASA. We also demonstratethe UHECR arrival distribution above 10^19 eV with the event number expected byfuture experiments in the next few years. The interesting feature of theresultant arrival distribution is the arrangement of the clustered events inthe order of their energies, reflecting the directions of the galactic magneticfield. This is also pointed out by Alvarez-Muniz et al.(2002). This featurewill allow us to obtain some kind of information about the composition ofUHECRs and the magnetic field with increasing amount of data.Comment: 10 pages, 8 figures, to appear in the Astrophysical Journa