On Estimating the Flux of the Brightest Cosmic Ray Source above 57x10^18 eV

The sources of ultra-high energy cosmic rays are not yet known. However, the discovery of anisotropic cosmic rays above 57x10^18 eV by the Pierre Auger Observatory suggests that a direct source detection may soon be possible. The near-future prospects for such a measurement are heavily dependent on the flux of the brightest source. In this work, we show that the flux of the brightest source above 57x10^18 eV is expected to comprise 10% or more of the total flux if two general conditions are true. The conditions are: 1.) the source objects are associated with galaxies other than the Milky Way and its closest neighbors, and 2.) the cosmic ray particles are protons or heavy nuclei such as iron and the Greisen-Zatsepin-Kuz'min effect is occurring. The Pierre Auger Observatory collects approximately 23 events above 57x10^18 eV per year. Therefore, it is plausible that, over the course of several years, tens of cosmic rays from a single source will be detected.Comment: 10 pages, 2 figures, submitted to Astrophysical Journal Letter