Numerical Study on the Propagation of Ultra–High‐Energy Cosmic Rays in the Galactic Magnetic Field

Abstract

We study the propagation of ultra-high-energy cosmic rays (UHECRs) with E > 1018 eV in the Galactic magnetic field (GMF). We present numerical simulations for the propagation of antiprotons from the Earth toward the outside of the Galaxy in the GMF and calculate the sky map of the position of antiprotons that have reached the boundary. This sky map is interpreted as the relative probability distribution for the ability of protons to reach the Earth for the case of isotropic source distribution, considering Liouville's theorem. Basically, we adopt a GMF model that is composed of the spiral and dipole magnetic fields. We also consider the propagation of UHECRs in both of these two components of the magnetic field. This enables us to see the effect of each component on the arrival distribution of UHECRs. The main effect of the dipole magnetic field is to deflect antiprotons toward high Galactic longitudes, because this field is directed toward the north Galactic pole in the Galactic plane. In particular, antiprotons injected in the direction ~300° are strongly deflected and then rotated by the strong magnetic field in the vicinity of the Galactic center. The ideal form of the dipole magnetic field causes the clear pattern of the sky map of the positions of antiprotons that have reached the boundary when they are plotted by color according to the rotation number of the orbits. On the other hand, the spiral field mainly deflects antiprotons injected at the Earth toward the north Galactic pole, i.e., toward the Virgo cluster. This is because the spiral field in the solar system is in the direction of l ~ 90°. Even if the dipole magnetic filed is also included, we find that almost all UHECRs come from the direction of the Virgo cluster, because the spiral magnetic field in the solar system is stronger than the dipole field. This result suggests the nuclei component of UHECRs from the Virgo cluster as an attractive possibility for the origin of UHECRs.