Deep counts of submillimeter galaxies

We present the counts of luminous submillimeter (sub-mm) galaxies from an a nalysis of our completed survey of the distant universe seen through lensin g clusters. This survey uses massive cluster lenses with well-constrained m ass models to obtain a magnified view of the background sky. This both incr eases the sensitivity of our sub-mm maps and reduces the effects of source confusion. Accurate lens models are used to correct the observed sub-mm sou rce counts for the lens amplification. We show that the uncertainties assoc iated with this correction do not dominate the final errors. We present sub -Him counts derived from two independent methods: a direct inversion of the observed sources, which are corrected individually for lens amplification, and a Monte Carlo simulation of our observations using a parametric model for the background counts, which is folded through the lens models and inco mpleteness estimates to determine best-fitting values of the count paramete rs. Both methods agree well and confirm the robustness of our analysis. Det ections that are identified with galaxies in the lensing clusters in deep o ptical images are removed prior to our analysis, and the results are insens itive both to the details of the correction and to the redshift distributio n of the detections. We present the 850 mu m counts at flux densities betwe en 0.5 and 8 mJy. The count of galaxies brighter than 4 mJy is 1500 +/- 700 deg(-2), in agreement with the value of 2500 +/- 1400 deg(-2) reported by Small, Ivison, & Blain in 1997. The most accurate 850 mu m count is determi ned at 1 mJy: 7900 +/- 3000 deg(-2). All quoted errors include both Poisson and systematic terms. These are the deepest sub-mm counts published, and t hey are not subject to source confusion because the detected galaxies are s eparated and magnified by the lens. Down to the 0.5 mJy limit of our counts , the resolved 850 mu m background radiation intensity is (5 +/- 2) x 10(-1 0) W m(-2) sr(-1), comparable to the current COBE estimate of the backgroun d. This indicates that the bulk of the 850 mu m background radiation origin ated in distant ultraluminous galaxies.