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Accretion-powered X-ray pulsars are among the most luminous X-ray sources inthe Galaxy. However, despite decades of theoretical and observational worksince their discovery, no satisfactory model for the formation of the observedX-ray spectra has emerged. In particular, the previously available theories areunable to reproduce the power-law variation observed at high energies in manysources. In this paper, we present the first self-consistent calculation of thespectrum emerging from a pulsar accretion column that includes an explicittreatment of the energization occurring in the shock. Using a rigorouseigenfunction expansion method based on the exact dynamical solution for thevelocity profile in the column, we obtain a closed-form expression for theGreen's function describing the upscattering of radiation injected into thecolumn from a monochromatic source located at the top of the thermal mound,near the base of the flow. The Green's function is convolved with a Planckdistribution to calculate the radiation spectrum resulting from thereprocessing of blackbody photons emitted by the thermal mound. We demonstratethat the energization of the photons in the shock naturally produces an X-rayspectrum with a power-law shape at high energies and a blackbody shape at lowenergies, in agreement with many observations of accreting X-ray pulsars.Comment: Accepted for publication in Ap

Spectral Formation in X‐Ray Pulsars: Bulk Comptonization in the Accretion Shock