We use new deep near-infrared (NIR) and mid-infrared (MIR) observations to analyze the 850$~mu$m image of the GOODS HDF-N region. We show that much of the submillimeter background at this wavelength is picked out by sources with $H(AB)$ or 3.6um (AB)<23.25 (1.8 uJy). These sources contribute an 850um background of 24pm2 Jy deg^-2. This is a much higher fraction of the measured background (31-45 Jy deg^-2) than is found with current 20cm or 24um samples. Roughly one-half of these NIR-selected sources have spectroscopic identifications, and we can assign robust photometric redshifts to nearly all of the remaining sources using their UV to MIR spectral energy distributions. We use the redshift and spectral type information to show that a large fraction of the 850um background light comes from sources with z=0-1.5 and that the sources responsible have intermediate spectral types. Neither the elliptical galaxies, which have no star formation, nor the bluest galaxies, which have little dust, contribute a significant amount of 850um light, despite the fact that together they comprise approximately half of the galaxies in the sample. The galaxies with intermediate spectral types have a mean flux of 0.40pm0.03 mJy at 850um and 9.1pm0.3 uJy at 20cm. The redshift distribution of the NIR-selected 850um light lies well below that of the much smaller amount of light traced by the more luminous, radio- selected submillimeter sources. We therefore require a revised star-formation history with a lower star-formation rate at high redshifts. We use a stacking analysis of the 20cm light in the NIR sample to show that the star-formation history of the total 850um sample is relatively flat down to z~1 and that half of the total star formation occurs at redshifts z<1.4.
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