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We present results from quantitative modeling and spectral analysis of thehigh mass X-ray binary Vela X-1 obtained with the Chandra HETGS. The spectraexhibit emission lines from H-like and He-like ions driven by photoionization,as well as fluorescent emission lines from several elements in lower chargestates. In order to interpret and make full use of the high-quality data, wehave developed a simulator, which calculates the ionization and thermalstructure of a stellar wind photoionized by an X-ray source, and performs MonteCarlo simulations of X-ray photons propagating through the wind. The emergentspectra are then computed as a function of the viewing angle accuratelyaccounting for photon transport in three dimensions including dynamics. Fromcomparisons of the observed spectra with the simulation results, we are able tofind the ionization structure and the geometrical distribution of material inVela X-1 that can reproduce the observed spectral line intensities andcontinuum shapes at different orbital phases remarkably well. It is found thata large fraction of X-ray emission lines from highly ionized ions are formed inthe region between the neutron star and the companion star. We also find thatthe fluorescent X-ray lines must be produced in at least three distinct regions--(1)the extended stellar wind, (2)reflection off the stellar photosphere, and(3)in a distribution of dense material partially covering and possibly trailingthe neutron star, which may be associated with an accretion wake. Finally, fromdetailed analysis of the emission lines, we demonstrate that the stellar windis affected by X-ray photoionization.Comment: 22 pages, 7 tables, 24 figures, accepted for publication in The  Astrophysical Journa

X‐Ray Spectral Study of the Photoionized Stellar Wind in Vela X‐1