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.
