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Prompted by the H I Ly$\alpha$ absorption associated with the X-rayultra-fast outflow at -17,300 $\rm km~s^{-1}$ in the quasar PG~1211+143, wehave searched archival UV spectra at the expected locations of H I Ly$\alpha$absorption for a large sample of ultra-fast outflows identified in XMM-Newtonand Suzaku observations. Sixteen of the X-ray outflows have predicted H ILy$\alpha$ wavelengths falling within the bandpass of spectra from either theFar Ultraviolet Spectroscopic Explorer or the Hubble Space Telescope, althoughnone of the archival observations were simultaneous with the X-ray observationsin which UFOs were detected. In our spectra broad features with full-width athalf-maximum of 1000 $\rm km~s^{-1}$ have 2-$\sigma$ upper limits on the H Icolumn density of generally <$2\times10^{13}~\rm cm^{-2}$. Using grids ofphotoionization models covering a broad range of spectral energy distributions,we find that producing Fe XXVI Ly$\alpha$ X-ray absorption with equivalentwidths $>30$ eV and associated H I Ly$\alpha$ absorption with $\rmN_{HI}<2\times10^{13}~cm^{-2}$ requires total absorbing column densities $\rmN_{H}>5\times10^{22}~cm^{-2}$ and ionization parameters log $\xi$ > 3.7.Nevertheless, a wide range of SEDs would predict observable H I Ly$\alpha$absorption if ionization parameters are only slightly below peak ionizationfractions for Fe XXV and Fe XXVI. The lack of Ly$\alpha$ features in thearchival UV spectra indicates that either the UFOs have very high ionizationparameters, very hard UV-ionizing spectra, or that they were not present at thetime of the UV spectral observations due to variability.

A Search for H I Lyman $\alpha$ Counterparts to Ultra-Fast X-ray Outflows