Redshift Distribution of the Faint Submillimeter Galaxy Population

We present a Keck II LRIS spectroscopic follow-up study of the possibleoptical counterparts to a flux-limited sample of galaxies selected from an850-micron survey of massive lensing clusters using the SCUBA bolometer arrayon the JCMT. These sources represent a population of luminous dusty galaxiesresponsible for the bulk of the 850-micron background detected by COBE and thusfor a substantial fraction of the total far-infrared emission in the Universe.We present reliable redshifts for 20 galaxies and redshift limits for a further4 galaxies selected from the error-boxes of 14 submm sources. Two other submmdetections in the sample have no obvious optical counterparts, and the finalsubmm source was only identified from imaging data after the completion of ourspectroscopic observations. The optical identifications for 4 of the submmsources have been confirmed through either their detection in CO atmm-wavelengths (two pairs of galaxies at z=2.55 and z=2.80) or from thecharacteristics of their spectral energy distributions (two of the central cDgalaxies in the lensing clusters). Plausible arguments based on the opticalspectral properties (starburst or AGN signatures) of the counterparts allow usto identify a further two likely counterparts at z=1.06 and 1.16. For theremaining 8 cases, it is not always clear which, if any, of the optical sourcesidentified are the true counterparts. Possible counterparts for these haveredshifts ranging from z=0.18 to z=2.11. Working with the currentidentifications, we suggest that the majority of the extragalactic backgroundlight in the submm is emitted by sources at z<3 and hence that the peakactivity in highly-obscured sources (both AGN and starbursts) lies atrelatively modest redshifts. (Abridged)Comment: 10 pages, accepted by The Astronomical Journal for the June 1999 issu