Submillimetre-luminous galaxies at high-redshift are the most luminous, heavily star-forming galaxies in the Universe, and are characterised by prodigious emission in the far-infrared at 850 microns (S850 > 5 mJy). They reside in halos ~ 10^13Msun, have low gas fractions compared to main sequence disks at a comparable redshift, trace complex environments, and are not easily observable at optical wavelengths. Their physical origin remains unclear. Simulations have been able to form galaxies with the requisite luminosities, but have otherwise been unable to simultaneously match the stellar masses, star formation rates, gas fractions and environments. Here we report a cosmological hydrodynamic galaxy formation simulation that is able to form a submillimetre galaxy which simultaneously satisfies the broad range of observed physical constraints. We find that groups of galaxies residing in massive dark matter halos have rising star formation histories that peak at collective rates ~ 500-1000 Msun/yr at z=2-3, by which time the interstellar medium is sufficiently enriched with metals that the region may be observed as a submillimetre-selected system. The intense star formation rates are fueled in part by a reservoir gas supply enabled by stellar feedback at earlier times, not through major mergers. With a duty cycle of nearly a gigayear, our simulations show that the submillimetre-luminous phase of high-z galaxies is a drawn out one that is associated with significant mass buildup in early Universe proto-clusters, and that many submillimetre-luminous galaxies are actually composed of numerous unresolved components (for which there is some observational evidence).
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