| Summary: | We present spectroscopic observations for a sample of 36 Herschel-SPIRE 250-500 μm selected galaxies (HSGs) at 2 < z < 5 from the Herschel Multi-tiered Extragalactic Survey. Redshifts are confirmed as part of a large redshift survey of Herschel-SPIRE-selected sources covering ~0.93 deg2 in six extragalactic legacy fields. Observations were taken with the Keck I Low Resolution Imaging Spectrometer and the Keck II DEep Imaging Multi-Object Spectrograph. Precise astrometry, needed for spectroscopic follow-up, is determined by identification of counterparts at 24 μm or 1.4 GHz using a cross-identification likelihood matching method. Individual source luminosities range from log (L IR/L ☉) = 12.5-13.6 (corresponding to star formation rates (SFRs) 500-9000 M ☉ yr–1, assuming a Salpeter initial mass function), constituting some of the most intrinsically luminous, distant infrared galaxies discovered thus far. We present both individual and composite rest-frame ultraviolet spectra and infrared spectral energy distributions. The selection of these HSGs is reproducible and well characterized across large areas of the 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 (SFRD) at (7 ± 2) × 10–3 M ☉ yr–1 h 3 Mpc–3 at z ~ 2.5, which is >10% of the estimated total SFRD of the universe from optical surveys. The contribution at z ~ 4 has a lower limit of 3 × 10–3 M ☉ yr–1 h 3 Mpc–3, 20% of the estimated total SFRD. This highlights the importance of extremely infrared-luminous galaxies with high SFRs to the buildup of stellar mass, even at the earliest epochs.
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