Intergalactic Magnetic Field and Arrival Direction of Ultra-High-Energy
  Protons
  We studied how the intergalactic magnetic field (IGMF) affects the
propagation of super-GZK protons that originate from extragalactic sources
within the local GZK sphere. Toward this end, we set up hypothetical sources of
ultra-high-energy cosmic-rays (UHECRs), virtual observers, and the magnetized
cosmic web in a model universe constructed from cosmological structure
formation simulations. We then arranged a set of reference objects mimicking
active galactic nuclei (AGNs) in the local universe, with which correlations of
simulated UHECR events are analyzed. With our model IGMF, the deflection angle
between the arrival direction of super-GZK protons and the sky position of
their actual sources is quite large with the mean value of $<\theta > \sim
15^{\circ}$ and the median value of $\tilde \theta \sim 7 - 10^{\circ}$. On the
other hand, the separation angle between the arrival direction and the sky
position of nearest reference objects is substantially smaller with $<S > \sim
3.5 - 4^{\circ}$, which is similar to the mean angular distance in the sky to
nearest neighbors among the reference objects. This is a direct consequence of
our model that the sources, observers, reference objects, and the IGMF all
trace the matter distribution of the universe. The result implies that
extragalactic objects lying closest to the arrival direction of UHECRs are not
necessary their actual sources. With our model for the distribution of
reference objects, the fraction of super-GZK proton events, whose closest AGNs
are true sources, is less than 1/3. We discussed implications of our findings
for correlation studies of real UHECR events.
