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Description
Current observations of arrival directions of ultra-high energy cosmic rays (UHECR) whose energies are above 100 EeV do not show significant anisotropy.
A heavier nucleus (ex. uranium) is known to have a longer propagation length than that of protons or irons. With a convolution of the longer propagation length and homogenous distribution of galaxies in longer distances, we can explain the current absence of UHECR anisotropy above 100 EeV.
Based on this idea, we conduct a mock observation of UHECR above 100 EeV for single-proton, iron, and uranium cases.
We predict the UHECR distribution from the Millenium Run semi-analytic galaxy catalog (Springel et al. 2005) and turbulent extra-galactic magnetic fields. Changing the parameters of UHECR source density and magnetic fields ${\rm \alpha} = \left( \frac{\lambda}{1\:\rm Mpc} \right)^{1/2} \left(\frac{B}{1\:\rm nG} \right)$, we evaluate the anisotropy for each case.
With no magnetic fields, current observation excludes single-proton and iron cases.
The single-uranium case can explain the current observation even without turbulent magnetic fields when the source density is high ($\rho=10^{-3} {\rm Mpc}^{-3}$). When the turbulent field is strong, the single-iron and uranium cases are consistent with the observation. Any parameter sets $(\rho,\alpha)$ rejects the single-proton case.
In this study, we set the limit of UHECR source density $\rho$ and the strength of magnetic fields $\alpha$ for each nucleus case and discuss the scenario of future UHECR observation.