High-resolution SMA imaging of bright submillimetre sources from the
  SCUBA-2 Cosmology Legacy Survey
  We have used the Submillimeter Array at 860$\,\mu$m to observe the brightest
SCUBA-2 sources in 4$\,$deg$^{2}$ of the Cosmology Legacy Survey. We have
targeted 75 of the brightest single-dish SCUBA-2 850$\,\mu$m sources down to
$S_{850}\,{\approx}\,8\,$mJy, achieving an average synthesized beam of
2.4$^{\prime\prime}$ and an average rms of $\sigma_{860}\,{=}\,1.5\,$mJy in our
primary beam-corrected maps. We searched our maps for $4\sigma$ peaks,
corresponding to $S_{860}\,{\gtrsim}\,6\,$mJy sources, and detected 59 single
galaxies and three pairs of galaxies. We include in our study 28 archival
observations, bringing our sample size to 103 bright single-dish submillimetre
sources with interferometric follow-up. We compute the cumulative and
differential number counts of our sample, finding them to overlap with previous
single-dish survey number counts within the uncertainties, although our
cumulative number count is systematically lower than the parent SCUBA-2
cumulative number count by $24\,{\pm}\,6$ per cent between 11 and 15$\,$mJy. We
estimate the probability that a ${\gtrsim}\,10\,$mJy single-dish submillimetre
source resolves into two or more galaxies with similar flux densities, causing
a significant change in the number counts, to be about 15 per cent. Assuming
the remaining 85 per cent of the targets are ultra-luminous starburst galaxies
between $z\,{=}\,2$-3, we find a likely volume density of
${\gtrsim}\,400\,$M$_{\odot}\,$yr$^{-1}$ sources to be
${\sim}\,3^{+0.7}_{-0.6}\,{\times}\,10^{-7}\,$Mpc$^{-3}$. We show that the
descendants of these galaxies could be
${\gtrsim}\,4\,{\times}\,10^{11}\,$M$_{\odot}$ local quiescent galaxies, and
that about 10 per cent of their total stellar mass would have formed during
these short bursts of star-formation.
