A Population of z>2 Far-Infrared Herschel-SPIRE selected Starbursts
  We present spectroscopic observations for a sample of 36 Herschel-SPIRE
250-500um selected galaxies (HSGs) at 2<z<5 from the Herschel Multi-tiered
Extragalactic Survey (HerMES). Redshifts are confirmed as part of a large
redshift survey of Herschel-SPIRE-selected sources covering ~0.93deg^2 in six
extragalactic legacy fields. Observations were taken with the Keck I Low
Resolution Imaging Spectrometer (LRIS) and the Keck II DEep Imaging
Multi-Object Spectrograph (DEIMOS). Precise astrometry, needed for
spectroscopic follow-up, is determined by identification of counterparts at
24um or 1.4GHz using a cross-identification likelihood matching method.
Individual source luminosities range from log(L_IR/Lsun)=12.5-13.6
(corresponding to star formation rates 500-9000Msun/yr, assuming a Salpeter
IMF), constituting some of the most intrinsically luminous, distant infrared
galaxies yet discovered. We present both individual and composite rest-frame
ultraviolet spectra and infrared spectral energy distributions (SEDs). The
selection of these HSGs is reproducible and well characterized across large
areas of sky in contrast to most z>2 HyLIRGs in the literature which are
detected serendipitously or via tailored surveys searching only for high-z
HyLIRGs; therefore, we can place lower limits on the contribution of HSGs to
the cosmic star formation rate density at (7+-2)x10^(-3)Msun/yr h^3Mpc^(-3) at
z~2.5, which is >10% of the estimated total star formation rate density (SFRD)
of the Universe from optical surveys. The contribution at z~4 has a lower limit
of 3x10^(-3)Msun/yr h^3 Mpc^(-3), ~>20% of the estimated total SFRD. This
highlights the importance of extremely infrared-luminous galaxies with high
star formation rates to the build-up of stellar mass, even at the earliest
epochs.
