We report new spectral modeling of the accreting X-ray pulsar Hercules X- 1. Our radiation-dominated radiative shock model is an implementation of the analytic work of Becker & Wolff on Comptonized accretion flows onto magnetic neutron stars. We obtain a good fit to the spin-phase averaged 4 to 78 keV X-ray spectrum observed by the Nuclear Spectroscopic Telescope Array during a main- on phase of the Her X-1 35-day accretion disk precession period. This model allows us to estimate the accretion rate, the Comptonizing temperature of the radiating plasma, the radius of the magnetic polar cap, and the average scattering opacity parameters in the accretion column. This is in contrast to previous phenomenological models that characterized the shape of the X-ray spectrum but could not determine the physical parameters of the accretion flow. We describe the spectral fitting details and discuss the interpretation of the accretion flow physical parameters.
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