The energetics, spectrum, and composition of cosmic rays with energies below ~1015 eV are fairly well explained by models involving supernova shocks. In contrast, no widely accepted theory exists for the origin of ultra-high-energy cosmic rays (UHECRs), which have energies above 1015 eV. Instead of proposing a specific model, here we place strong constraints on any model of UHECRs involving isolated neutron stars (no companions). We consider the total power requirements and show that the only viable power source associated with isolated neutron stars is rotation. Mechanisms based on accretion from the interstellar medium fall short of the necessary power despite the most optimistic assumptions. Power considerations also demonstrate that not enough rotational energy is tapped by a "propeller"-like acceleration of interstellar matter. The most promising source of energy is rotational spindown via magnetic braking. We examine microphysical energy loss processes near magnetized neutron stars and conclude that the most likely site for yielding UHECRs from isolated neutron stars is near or beyond the light cylinder.
Aparna Venkatesan, M. Coleman Miller and Angela V. Olinto. Constraints on the Production of Ultra–High-Energy Cosmic Rays by Isolated Neutron Stars. The Astrophysical Journal, 484:323–328, 1997 July 20 http://dx.doi.org/10.1086/304304