Resonant cyclotron scattering and Comptonization in neutron star magnetospheres

Resonant cyclotron scattering of the surface radiation in the magnetospheres of neutron stars may considerably modify the emergent spectra and impede efforts to constrain neutron star properties. Resonant cyclotron scattering by a non-relativistic warm plasma in an inhomogeneous magnetic field has a number of unusual characteristics. (i) In the limit of high resonant optical depth, the cyclotron resonant layer is half opaque , in sharp contrast to the case of non-resonant scattering. (ii) The transmitted flux is on average Compton up-scattered by  ∼1 + 2β_T  , where  β_T  is the typical thermal velocity in units of the velocity of light; the reflected flux has on average the initial frequency. (iii) For both the transmitted and reflected fluxes, the dispersion of intensity decreases with increasing optical depth. (iv) The emergent spectrum is appreciably non-Planckian while narrow spectral features produced at the surface may be erased.
We derive semi-analytically modification of the surface Planckian emission due to multiple scattering between the resonant layers and apply the model to the anomalous X-ray pulsar 1E  1048.1 − 5937  . Our simple model fits just as well as the 'canonical' magnetar spectra model of a blackbody plus power law.