X-ray spectra from magnetar candidates. II Resonant cross sections for electron-photon scattering in the relativistic regime

Recent models of spectral formation in magnetars called renewed attention on electron-photon scattering in the presence of ultrastrong magnetic fields. Investigations presented so far mainly focused on mildly relativistic particles and magnetic scattering was treated in the non-relativistic (Thomson) limit. This allows for consistent spectral calculations up to a few tens of keV, but becomes inadequate in modelling the hard tails (<~200 keV) detected by INTEGRAL from magnetar sources. In this paper, the second in a series devoted to model the X-/soft γ-ray persistent spectrum of magnetar candidates, we present explicit, relatively simple expressions for the magnetic Compton cross-section at resonance which account for Landau-Raman scattering up to the second Landau level. No assumption is made on the magnetic field strength. We find that sensible departures from the Thomson regime can be already present at B ~ 5 × 1012 G. The form of the magnetic cross-section we derived can be easily implemented in Monte Carlo transfer codes and a direct application to magnetar spectral calculations will be presented in a forthcoming study.