Radio synchrotron emission by protons and electrons in pulsars and the nuclei of quasars

Relations enabling estimation of the limiting brightness temperature of synchrotron radiation subject to self-absorption and inverse Compton scattering are presented for the case of relativistic electrons (positrons) and protons. Analogous expressions are presented for relativistic particles moving along curved magnetic lines of force (curvature radiation) and coherent radiation by relativistic particles. These relations can be used to determine the brightness temperatures expected for the central regions of active galactic nuclei, neutron stars, and other objects that produce relativistic particles. Radiation by relativistic protons yields higher intensities, and could be a source of the highest-energy cosmic rays.