Does Galactic Magnetic Field Disturb the Correlation of the Highest Energy Cosmic Rays with their Sources?

Abstract

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.