Small Scale Anisotropy Predictions for the Auger Observatory

We study the small scale anisotropy signal expected at the Pierre Auger Observatory in the next 1, 5, 10, and 15 years of operation, from sources of ultra-high energy (UHE) protons. We numerically propagate UHE protons over cosmological distances using an injection spectrum and normalization that fits current data up to $\sim 10^{20}\eV$. We characterize possible sources of ultra-high energy cosmic rays (UHECRs) by their mean density in the local Universe, $\bar{\rho} = 10^{-r}$ Mpc$^{-3}$, with $r$ between 3 and 6. These densities span a wide range of extragalactic sites for UHECR sources, from common to rare galaxies or even clusters of galaxies. We simulate 100 realizations for each model and calculate the two point correlation function for events with energies above $4 \times 10^{19}\eV$ and above $10^{20}\eV$, as specialized to the case of the Auger telescope. We find that for $r\ga 4$, Auger should be able to detect small scale anisotropies in the near future. Distinguishing between different source densities based on cosmic ray data alone will be more challenging than detecting a departure from isotropy and is likely to require larger statistics of events. Combining the angular distribution studies with the spectral shape around the GZK feature will also help distinguish between different source scenarios.