Heyl, J. S.Hernquist, L.2019-09-202005Heyl, J. S., and L. Hernquist. 2005. “A Quantum Electrodynamics Model for Non-Thermal Emission from Soft Gamma Repeaters and Anomalous X-Ray Pulsars.” Monthly Notices of the Royal Astronomical Society 362 (3): 777–83. https://doi.org/10.1111/j.1365-2966.2005.09338.x.0035-87111365-2966http://nrs.harvard.edu/urn-3:HUL.InstRepos:41381847Previously, we showed that, owing to effects arising from quantum electrodynamics (QED), magnetohydrodynamic fast modes of sufficient strength will break down to form electron-positron pairs while traversing the magnetospheres of strongly magnetized neutron stars. The bulk of the energy of the fast mode fuels the development of an electron-positron fireball. However, a small, but potentially observable, fraction of the energy (similar to 10(33) erg) can generate a non-thermal distribution of electrons and positrons far from the star. In this paper, we examine the cooling and radiative output of these particles. We also investigate the properties of non-thermal emission in the absence of a fireball to understand the breakdown of fast modes that do not yield an optically thick pair plasma. This quiescent, non-thermal radiation associated with fast-mode breakdown may account for the recently observed non-thermal emission from several anomalous X-ray pulsars and soft gamma repeaters.en-USJournal Article2019-09-2010.1111/j.1365-2966.2005.09338.x