We present observations of the UV absorption lines in the luminous Seyfert 1 galaxy Mrk 509, obtained with the medium resolution (lambda/Delta-lambda ~ 40,000) echelle gratings of the Space Telescope Imaging Spectrograph on the Hubble Space Telescope. The spectra reveal the presence of eight kinematic components of absorption in Ly-alpha, C IV, and N V, at radial velocities of -422, -328, -259, -62, -22, +34, +124, and +210 km s^-1 with respect to an emission-line redshift of z = 0.03440, seven of which were detected in an earlier Far Ultraviolet Spectrographic Explorer (FUSE) spectrum. The component at -22 km s^-1 also shows absorption by Si IV. The covering factor and velocity width of the Si IV lines were lower than those of the higher ionization lines for this component, which is evidence for two separate absorbers at this velocity. We have calculated photoionization models to match the UV column densities in each of these components. Using the predicted O VI column densities, we were able to match the O VI profiles observed in the FUSE spectrum. Based on our results, none of the UV absorbers can produce the X-ray absorption seen in simultaneous Chandra observations; therefore, there must be more highly ionized gas in the radial velocity ranges covered by the UV absorbers.
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