Propagation of Ultra–High‐Energy Cosmic Rays above 1019eV in a Structured Extragalactic Magnetic Field and Galactic Magnetic Field

We present numerical simulations on propagation of Ultra-High Energy CosmicRays (UHECRs) above $10^{19}$ eV in a structured extragalactic magnetic field(EGMF) and simulate their arrival distributions at the earth. We use the IRASPSCz catalogue in order to construct a model of the EGMF and source models ofUHECRs, both of which reproduce the local structures observed around the MilkyWay. We also consider modifications of UHECR arrival directions by the galacticmagnetic field. We follow an inverse process of their propagation from theearth and record the trajectories. This enables us to calculate onlytrajectories of UHECRs arriving at the earth, which saves the CPU time. Fromthese trajectories and our source models, we construct arrival distributions ofUHECRs and calculate the harmonic amplitudes and the two point correlationfunctions of them. We estimate number density of sources which reproduces theAkeno Ground Air Shower Array (AGASA) observation best. As a result, we findthat the most appropriate number density of the sources is $\sim 5 \times10^{-6}$ Mpc$^{-3}$. This constrains the source candidates of UHECRs. We alsodemonstrate skymaps of their arrival distribution with the event numberexpected by future experiments and examine how the EGMF affects their arrivaldistribution. A main result is diffusion of clustering events which areobtained from calculations in the absence of the EGMF. This tendency allows usto reproduce the observed two point correlation function better.Comment: 13 pages, 14 figures. Revised version, accepted for publication in the Astrophysical Journal. Higher resolution image of fig.5 will be in the published versio