  We present new Hubble Space Telescope Cosmic Origins Spectrograph
far-ultraviolet (far-UV) spectroscopy and Keck Echellete optical spectroscopy
of 11 ultraluminous infrared galaxies (ULIRGs), a rare population of local
galaxies experiencing massive gas inflows, extreme starbursts, and prominent
outflows. We detect H Lyman alpha emission from 8 ULIRGs and the companion to
IRAS09583+4714. In contrast to the P Cygni profiles often seen in galaxy
spectra, the H Lyman alpha profiles exhibit prominent, blueshifted emission out
to Doppler shifts exceeding -1000 km/s in three HII-dominated and two
AGN-dominated ULIRGs. To better understand the role of resonance scattering in
shaping the H Lyman alpha line profiles, we directly compare them to
non-resonant emission lines in optical spectra. We find that the line wings are
already present in the intrinsic nebular spectra, and scattering merely
enhances the wings relative to the line core. The H Lyman alpha attenuation (as
measured in the COS aperture) ranges from that of the far-UV continuum to over
100 times more. A simple radiative transfer model suggests the H Lyman alpha
photons escape through cavities which have low column densities of neutral
hydrogen and become optically thin to the Lyman continuum in the most advanced
mergers. We show that the properties of the highly blueshifted line wings on
the H Lyman alpha and optical emission-line profiles are consistent with
emission from clumps of gas condensing out of a fast, hot wind. The luminosity
of the H Lyman alpha emission increases non-linearly with the ULIRG bolometric
luminosity and represents about 0.1 to 1% of the radiative cooling from the hot
winds in the HII-dominated ULIRGs.
