A Redshift Survey of Herschel Far-Infrared Selected Starbursts and
  Implications for Obscured Star Formation
  We present Keck spectroscopic observations and redshifts for a sample of 767
Herschel-SPIRE selected galaxies (HSGs) at 250, 350, and 500um, taken with the
Keck I Low Resolution Imaging Spectrometer (LRIS) and the Keck II DEep Imaging
Multi-Object Spectrograph (DEIMOS). The redshift distribution of these SPIRE
sources from the Herschel Multitiered Extragalactic Survey (HerMES) peaks at
z=0.85, with 731 sources at z<2 and a tail of sources out to z~5. We measure
more significant disagreement between photometric and spectroscopic redshifts
(<delta_z>/(1+z)>=0.29) than is seen in non-infrared selected samples, likely
due to enhanced star formation rates and dust obscuration in infrared-selected
galaxies. We estimate that the vast majority (72-83%) of z<2 Herschel-selected
galaxies would drop out of traditional submillimeter surveys at 0.85-1mm. We
estimate the luminosity function and implied star-formation rate density
contribution of HSGs at z<1.6 and find overall agreement with work based on
24um extrapolations of the LIRG, ULIRG and total infrared contributions. This
work significantly increased the number of spectroscopically confirmed
infrared-luminous galaxies at z>>0 and demonstrates the growing importance of
dusty starbursts for galaxy evolution studies and the build-up of stellar mass
throughout cosmic time. [abridged]
