Does Galactic Magnetic Field Disturb the Correlation of the Highest
  Energy Cosmic Rays with their Sources?
  The propagation trajectories of the highest energy cosmic rays (HECRs) are
deflected by not only intergalactic magnetic field but also Galactic magnetic
field (GMF). These magnetic fields can weaken the positive correlation between
the arrival directions of HECRs and the positions of their sources. In order to
explore the effect of GMF on the expected correlation, we simulate the arrival
distribution of protons with the energy above $6 \times 10^{19}$ eV taking
several GMF models into account, and then test the correlation between the
protons and their sources assumed in the simulation. The dependence of the
correlation signals on GMF models are also investigated. The correlation can be
observed by accumulating $\sim 200$ protons in a half hemisphere. Typical
angular scale at which the positive signal of the correlation is maximized
depends on the spiral component of GMF models. That angular scale is $\sim 5^o$
for bisymmetric spiral (BS) GMF models and $\sim 7^o$ for axisymmetric spiral
(AS) GMF models if the number density of HECR sources, $n_s$, is $\sim 10^{-4}$
Mpc$^{-3}$. An additional vertical (dipole) component of GMF affects these
angular scale by $0.5^o$ - $1^o$. The difference between the correlation signal
for the BS models and that for the AS models is prominent in the northern sky.
Significance of the positive correlation depends on source distribution. The
probability that the number of simulated HECR events correlating with sources
is smaller than the number of random events correlating with the same sources
by chance is much less than $10^{-3}$ ($\sim 3\sigma$) in almost all the source
distributions with $n_s = 10^{-4}$ Mpc$^{-3}$ under 200 protons detection, but
$\sim 10\%$ of source distributions predicts the chance probability more than
$10^{-3}$ in the AS GMF model. In addition, we also briefly discuss the effect
of GMF for heavy-nuclei dominated composition.
