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Resonant Cyclotron Scattering in Three Dimensions and the Quiescent Non-thermal X-ray Emission of Magnetars

Although the surface of a magnetar is a source of bright thermal X-rays, its spectrum contains substantial non-thermal components. The X-ray emission is pulsed, with pulsed fractions that can be as high as ~ 70%. Several properties of magnetars indicate the presence of persistent, static currents flowing across the stellar surface and closing within the magnetosphere. The charges supporting these currents supply a significant optical depth to resonant cyclotron scattering in the 1-100 keV band. Here we describe a Monte Carlo approach to calculating the redistribution of thermal seed photons in frequency and angle by multiple resonant scattering in the magnetosphere. The calculation includes the full angular dependence of the cyclotron scattering cross section, the relativistic Doppler effect due to the motion of the charges, and allows for an arbitrary particle velocity distribution and magnetic field geometry. We construct synthetic spectra and pulse profiles for arbitrary orientations of the spin axis, magnetic axis, and line of sight, using a self-similar, twisted dipole field geometry, and assuming that the seed photons are supplied by single-temperature black body emission from the stellar surface. Pulse profiles and 1-10 keV spectra typical of AXPs are easily produced by this model, with pulsed fractions of ~ 50%. However, this model cannot reproduce the hard, rising energy spectra that are observed from SGRs during periods of activity, without overproducing the thermal emission peak. This suggests that the 1-100 keV emission of SGRs has a common origin with the hard X-ray emission detected from some AXPs above ~20 keV.