Resonant Inverse Compton Scattering Spectra from Highly-magnetized Neutron Stars

Hard, non-thermal, persistent pulsed X-ray emission extending between 10 keV and $\sim 150$ keV has been observed in nearly ten magnetars. For inner-magnetospheric models of such emission, resonant inverse Compton scattering of soft thermal photons by ultra-relativistic charges is the most efficient production mechanism. We present angle-dependent upscattering spectra and pulsed intensity maps for uncooled, relativistic electrons injected in inner regions of magnetar magnetospheres, calculated using collisional integrals over field loops. Our computations employ a new formulation of the QED Compton scattering cross section in strong magnetic fields that is physically correct for treating important spin-dependent effects in the cyclotron resonance, thereby producing correct photon spectra. The spectral cut-off energies are sensitive to the choices of observer viewing geometry, electron Lorentz factor, and scattering kinematics. We find that electrons with energies $\lesssim 15$ MeV will emit most of their radiation below 250 keV, consistent with inferred turnovers for magnetar hard X-ray tails. More energetic electrons still emit mostly below 1 MeV, except for viewing perspectives sampling field line tangents. Pulse profiles may be singly- or doubly-peaked dependent upon viewing geometry, emission locale, and observed energy band. Magnetic pair production and photon splitting will attenuate spectra to hard X-ray energies, suppressing signals in the Fermi-LAT band. The resonant Compton spectra are strongly polarized, suggesting that hard X-ray polarimetry instruments such as X-Calibur, or a future Compton telescope, can prove central to constraining model geometry and physics.