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Submillimetre galaxies in a hierarchical universe: number counts, redshift distribution, and implications for the IMF

High-redshift submillimetre galaxies (SMGs) are some of the most rapidly star-forming galaxies in the Universe. Historically, galaxy formation models have had difficulty explaining the observed number counts of SMGs. We combine a semi-empirical model with 3-D hydrodynamical simulations and 3-D dust radiative transfer to predict the number counts of unlensed SMGs. Because the stellar mass functions, gas and dust masses, and sizes of our galaxies are constrained to match observations, we can isolate uncertainties related to the dynamical evolution of galaxy mergers and the dust radiative transfer. The number counts and redshift distributions predicted by our model agree well with observations. Isolated disc galaxies dominate the faint (S_1.1 < ~1 mJy, or S_850 < ~2 mJy) population. The brighter sources are a mix of merger-induced starbursts and galaxy-pair SMGs; the latter subpopulation accounts for ~30 - 50 per cent of all SMGs at all S_1.1 > ~0.5 mJy (S_850 > ~1 mJy). The mean redshifts are ~3.0 - 3.5, depending on the flux cut, and the brightest sources tend to be at higher redshifts. Because the galaxy-pair SMGs will be resolved into multiple fainter sources by ALMA, the bright ALMA counts should be as much as 2 times less than those observed using single-dish telescopes. The agreement between our model, which uses a Kroupa IMF, and observations suggests that the IMF in high-redshifts starbursts need not be top-heavy; if the IMF were top-heavy, our model would over-predict the number counts. We conclude that the difficulty some models have reproducing the observed SMG counts is likely indicative of more general problems -- such as an under-prediction of the abundance of massive galaxies or a star formation rate--stellar mass relation normalisation lower than that observed -- rather than a problem specific to the SMG population.