Redshift distribution of the faint submillimeter galaxy population

We present a Keck II Low Resolution Imaging Spectrometer follow-up study of the possible optical counterparts to a flux-limited sample of galaxies selected from an 850 mu m survey of massive lensing clusters using the Submillimeter Common User Bolometer Array on the James Clerk Maxwell Telescope. These sources represent a population of luminous dusty galaxies responsible for the bulk of the 850 mu m background detected by COBE and thus for a substantial fraction of the total far-infrared emission in the universe. We present reliable redshifts for 20 galaxies and redshift limits for a further four galaxies selected from the error boxes of 14 submillimeter sources. Two other submillimeter detections in the sample have no obvious optical counterparts, and the final submillimeter source was only identified from imaging data after the completion of our spectroscopic observations. The optical identifications for four of the submillimeter sources have been confirmed through either their detection in CO at millimeter wavelengths (two pairs of galaxies at z = 2.55 and z = 2.80) or from the characteristics of their spectral energy distributions (two of the central cD galaxies in the lensing clusters). Plausible arguments based on the optical spectral properties (starburst or active galactic nucleus [AGN] signatures) of the counterparts allow us to identify a further two likely counterparts at z = 1.06 and 1.16. For the remaining eight cases, it is not always clear which, if any, of the optical sources identified are the true counterparts. Possible counterparts for these have redshifts ranging from z = 0.18 to z = 2.11. The application of a range of techniques, including near- and mid-infrared imaging and radio mapping, will assist in the identification of the true sources of the submillimeter emission, while CO line mapping with current millimeter interferometers and hard X-ray observations should aid in the determination of the nature of their emission. Working with the current identifications, we suggest that the majority of the extragalactic background light in the submillimeter is emitted by sources at z<3 and hence that the peak activity in highly obscured sources (both AGNs and starbursts) lies at relatively modest redshifts. We find that a lower limit of 20% of the submillimeter sources in our sample show some sign of AGN activity; however, we caution that this does not necessarily translate into a 20% AGN contribution to the measured submillimeter emission from these sources.