High-quality Far-Ultraviolet Spectroscopic Explorer (FUSE) observations at 20 km /s resolution of interstellar and intergalactic absorption from 910 to 1187 A are presented for the X-ray bright BL Lac object Mrk 421. In this study we consider the O VI absorption between -140 to 165 km /s and its relationship to the lower ionization absorption and to the strong absorption produced by O VII and O VIII at X-ray wavelengths. The O VI absorption extending from -140 to 60 km /s is associated with strong low ionization gas absorption and originates in the Galactic thick disk / halo. This O VI appears to be produced by a combination of processes, including conductive interfaces between warm and hot gas and possibly cooling Galactic Fountain gas and hot halo gas bubbles. The O VI absorption extending from 60 to 165 km /s has unusual ionization properties in that there is very little associated low ionization absorption, with the exception of C III. This absorption is not observed toward two foreground halo stars, implying that it occurs in gas more distant than 3.5 kpc from the Galactic disk. Over the 60 to 165 km/s velocity range, O VI and C III absorption have the same kinematic behavior. N(O VI)/N(C III) = 10+/-3 over the 60 to 120 km/s velocity range. Given the association of O VI with C III, it is unlikely that the high velocity O VI co-exists with the hotter gas responsible for the O VII and O VIII absorption. The O VI positive velocity absorption wing might be tracing cooler gas entrained in a hot Galactic Fountain outflow. The O VII and O VIII absorption observed by Chandra and XMM-Newton may trace the hot gas in a highly extended (~100 kpc) Galactic corona or hot gas in the Local Group.
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