The Power Budget of the Highest-Energy Cosmic Rays: Required Emissivity Above 10 and 50 EeV and the Priced Candidate Sources

The flux of cosmic rays above the ankle, measured by the Pierre Auger Observatory, fixes the local energy density of ultra-high-energy cosmic rays and the power per unit volume their sources must supply. Integrating a stated parametrisation of the Auger spectrum gives energy densities of 1.41e-20 erg/cm3 above 10 EeV and 1.34e-21 erg/cm3 above 50 EeV; dividing by the pair-production and photopion loss times in each band gives required source emissivities of 2.54e44 erg/Mpc3/yr above 10 EeV and 3.45e44 erg/Mpc3/yr above 50 EeV. Pricing four candidate classes in the same units from stated published rates and energetics: long gamma-ray bursts clear both bands (margins 3.05 and 1.19); AGN jets clear the 10 EeV band and are marginal above 50 EeV (2.22 and 0.86); starburst galaxies and tidal disruption events fail both bands by more than an order of magnitude and are excluded as the dominant sources of the highest-energy cosmic rays.