ESTIMATING THE FLUX OF THE BRIGHTEST COSMIC-RAY SOURCE ABOVE 57 x 1018 eV

The sources of ultrahigh energy cosmic rays (CRs) are not yet known. However, the discovery of anisotropic CRs above 57 x 10(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 57 x 10(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 CR 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 57 x 10(18) eV per year. Therefore, it is plausible that, over the course of several years, tens of CRs from a single source will be detected.