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In the fallback disk model for the persistent emission of Anomalous X-raypulsars (AXPs) and soft gamma-ray repeaters (SGRs), the hard X-ray emissionarises from bulk- and thermal Comptonization of bremsstrahlung photons, whichare generated in the accretion column. The relatively low X-ray luminosity ofthese sources implies a moderate transverse optical depth to electronscattering, with photons executing a small number of shock crossings beforeescaping sideways. We explore the range of spectral shapes that can be obtainedwith this model and characterize the most important parameter dependencies. Weuse a Monte Carlo code to study the crisscrossing of photons in a radiativeshock in an accretion column and compute the resulting spectrum. As expected,high-energy power-law X-ray spectra are produced in radiative shocks withphoton-number spectral index larger than or about 0.5. We find that therequired transverse optical depth is between 1 and 7. Such spectra are observedin low-luminosity X-ray pulsars. We demonstrate here with a simple model thatCompton upscattering in the radiative shock in the accretion column can producehard X-ray spectra similar to those seen in the persistent and transientemission of AXPs and SGRs. In particular, one can obtain a high-energypower-law spectrum, with photon-number spectral index ~ 1 and a cutoff at 100 -200 keV, with a transverse Thomson optical depth of ~ 5, which is shown to betypical in AXPs/SGRs.

Spectral formation in a radiative shock: application to anomalous X-ray pulsars and soft gamma-ray repeaters