Faint submillimeter counts from deep 850 micron observations of the lensing clusters A370, A851, and A2390

We present deep 850 mum maps of three massive lensing clusters, A370, A851, and A2390, with well-constrained mass models. Our cluster exposure times are more than 2-5 times longer than any other published cluster field observations. We catalog the sources and determine the submillimeter number counts. The counts are best determined in the 0.3-2 mJy range, where the areas are large enough to provide a significant sample. At 0.3 mJy the cumulative counts are 3.3(-1.3)(+6.3) x 10(4) deg(-2), where the upper and lower bounds are the 90% confidence range. The surface density at these faint count limits enters the realm of significant overlap with other galaxy populations. The corresponding percentage of the extragalactic background light (EBL) residing in this flux range is about 45%-65%, depending on the EBL measurement used. Given that 20%-30% of the EBL is resolved at flux densities between 2 and 10 mJy, most of the submillimeter EBL is arising in sources above 0.3 mJy. We also performed a noise analysis to obtain an independent estimate of the counts. The upper bounds on the counts determined from the noise analysis closely match the upper limits obtained from the direct counts. The differential counts from this and other surveys can reasonably be described by the parameterization n(S) = 3 x 10(4) deg(-2) mJy(-1)/(0.7 + S-3.0) with S in mJy, which also integrates to match the EBL.