Estimation Prospects of the Source Number Density of Ultra-high-energy Cosmic Rays

Abstract

We discuss the possibility of accurately estimating the source number density of ultra-high-energy cosmic rays (UHECRs) using small-scale anisotropy in their arrival distribution. The arrival distribution has information on their source and source distribution. We calculate the propagation of UHE protons in a structured extragalactic magnetic field (EGMF) and simulate their arrival distribution at the Earth using our previously developed method. The source number density that can best reproduce observational results by Akeno Giant Air Shower Array is estimated at about $10^{-5} {\rm Mpc}^{-3}$ in a simple source model. Despite having large uncertainties of about one order of magnitude, due to small number of observed events in current status, we find that more detection of UHECRs in the Auger era can sufficiently decrease this so that the source number density can be more robustly estimated. 200 event observation above $4 \times 10^{19} {\rm eV}$ in a hemisphere can discriminate between $10^{-5}$ and $10^{-6} {\rm Mpc}^{-3}$. Number of events to discriminate between $10^{-4}$ and $10^{-5} {\rm Mpc}^{-3}$ is dependent on EGMF strength. We also discuss the same in another source model in this paper.