Resonant Compton Upscattering in High Field Neutron Stars
  The extremely efficient process of resonant Compton upscattering by relativistic electrons in high magnetic fields is believed to be a leading emission mechanism of high field pulsars and magnetars in the production of intense X-ray radiation. New analytic developments for the Compton scattering cross section using Sokolov & Ternov (S&T) states with spin-dependent resonant widths are presented. These new results display significant numerical departures from both the traditional cross section using spin-averaged widths, and also from the spin-dependent cross section that employs the Johnson & Lippmann (J&L) basis states, thereby motivating the astrophysical deployment of this updated resonant Compton formulation. Useful approximate analytic forms for the cross section in the cyclotron resonance are developed for S&T basis states. These calculations are applied to an inner magnetospheric model of the hard X-ray spectral tails in magnetars, recently detected by RXTE and INTEGRAL. Relativistic electrons cool rapidly near the stellar surface in the presence of intense baths of thermal X-ray photons. We present resonant Compton cooling rates for electrons, and the resulting photon spectra at various magnetospheric locales, for magnetic fields above the quantum critical value. These demonstrate how this scattering mechanism has the potential to produce the characteristically flat spectral tails observed in magnetars. 
Peter L. Gonthier, Matthew T. Eiles, Zorawar Wadiasingh, and Matthew   G. Baring
astro-ph.HE