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

Abstract

We present a new method for calculating arrival distribution of ultra-high-energy cosmic rays (UHECRs), including modifications by the Galactic magnetic field. We perform numerical simulations of UHE antiprotons, which are injected isotropically at the Earth, in the Galaxy and record the directions of velocities at the Earth and outside the Galaxy for all of the trajectories. We then select some of them so that the resultant mapping of the velocity directions outside the Galaxy of the selected trajectories corresponds to a given source location scenario, applying Liouville's theorem. We also consider energy-loss processes of UHE protons in the intergalactic space. Applying this method to the source location scenario that is adopted in our recent study and can explain the Akeno Giant Air Shower Array (AGASA) observation above 4 × 1019 eV, we calculate the arrival distribution of UHECRs, including lower energy (E > 1019 eV) ones. We find that our source model can reproduce the large-scale isotropy and the small-scale anisotropy on UHECR arrival distribution above 1019 eV observed by the AGASA. We also demonstrate the UHECR arrival distribution above 1019 eV, with the event number expected by future experiments in the next few years. The interesting feature of the resultant arrival distribution is the arrangement of the clustered events in the order of their energies, reflecting the directions of the Galactic magnetic field. This is also pointed out by Alvarez-Muniz, Engel, & Stanev. This feature will allow us to obtain some kind of information about the composition of UHECRs and the magnetic field with increasing amount of data.