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 500 mu m, taken with the Keck I Low Resolution Imaging Spectrometer and the Keck II DEep Imaging Multi-Object Spectrograph. The redshift distribution of these SPIRE sources from the Herschel Multitiered Extragalactic Survey peaks at z = 0.85, with 731 sources at z < 2 and a tail of sources out to z similar to 5. We measure more significant disagreement between photometric and spectroscopic redshifts (<Delta z/(1 + z(spec))> = 0.29) than is seen in non-infrared selected samples, likely due to enhanced star formation rates and dust obscuration in infrared-selected galaxies. The infrared data are used to directly measure integrated infrared luminosities and dust temperatures independent of radio or 24 mu m flux densities. By probing the dust spectral energy distribution (SED) at its peak, we estimate that the vast majority (72%-83%) of z < 2 Herschel-selected galaxies would drop out of traditional submillimeter surveys at 0.85-1 mm. We find that dust temperature traces infrared luminosity, due in part to the SPIRE wavelength selection biases, and partially from physical effects. As a result, we measure no significant trend in SPIRE color with redshift; if dust temperature were independent of luminosity or redshift, a trend in SPIRE color would be expected. Composite infrared SEDs are constructed as a function of infrared luminosity, showing the increase in dust temperature with luminosity, and subtle change in near-infrared and mid-infrared spectral properties. Moderate evolution in the far-infrared (FIR)/radio correlation is measured for this partially radio-selected sample, with q(IR) proportional to (1 + z)(-0.30 +/- 0.02) at z < 2. 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 24 mu m 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.