Magnetar Hard Spectral Tails

Pulsed non-thermal quiescent emission between 10 keV and around 150 keV has been observed in $\sim10$ magnetars. For inner magnetospheric models of such hard X-ray signals, resonant Compton upscattering of soft thermal photons from the neutron star surface is the most efficient radiative process. We present angle-dependent hard X-ray upscattering model spectra for uncooled monoenergetic relativistic electrons. The spectral cut-off energies are critically dependent on the observer viewing angles and electron Lorentz factor. We find that electrons with energies less than around 15 MeV will emit most of their radiation below 250 keV, consistent with the observed turnovers in magnetar hard X-ray tails. Moreover, electrons of higher energy still emit most of the radiation below around 1 MeV, except for quasi-equatorial emission locales for select pulses phases. Our spectral computations use new state-of-the-art, spin-dependent formalism for the QED Compton scattering cross section in strong magnetic fields.