| Summary: | This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society. © 2014 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. Motivated by the current controversy over the redshift distribution and physical properties of luminous (sub-)mm sources, we have undertaken a new study of the brightest sample of unlensed (sub-)mm sources with pre-ALMA interferometric follow-up in the COSMOS field. Exploiting the very latest multi-frequency supporting data, we find that this sample displays a redshift distribution indistinguishable from that of the lensed sources uncovered with the South Pole Telescope (SPT), with z_median ~ 3.5. We also find that, over the redshift range z ~ 2-6 the median stellar mass of the most luminous (sub-)mm sources is M_* ~ 3 * 10^11 M_odot, yielding a typical specific star-formation rate sSFR ~ 3 Gyr^-1. Consistent with recent ALMA and SMA studies, we confirm that source blending is not a serious issue in the study of luminous (sub-)mm sources uncovered by ground-based, single-dish surveys; only ~ 10-15% of bright (S_850 ~ 5 - 10 mJy) (sub-)mm sources arise from significant (i.e. >20%) blends, and so our conclusions are largely unaffected by whether we adopt the original single-dish mm/sub-mm flux-densities/positions, or the interferometric data. Our results suggest that apparent disagreements over the redshift distribution of (sub-)mm sources are a result of "down-sizing" in dust-enshrouded star-formation, consistent with existing knowledge of the star-formation histories of massive galaxies. They also indicate that extreme star-forming galaxies at high redshift are, on average, subject to the same star-formation rate-limiting processes as less luminous objects, and lie on the "main sequence" of star-forming galaxies at z>3. Peer reviewed
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