An ALMA survey of the SCUBA-2 Cosmology Legacy Survey UKIDSS/UDS field:
  number counts of submillimeter galaxies
  We report the first results of AS2UDS: an 870 $\mu$m continuum survey with
the Atacama Large Millimeter/Submillimeter Array (ALMA) of a total area of
$\sim$ 50 arcmin$^2$ comprising a complete sample of 716 submillimeter sources
drawn from the SCUBA-2 Cosmology Legacy Survey (S2CLS) map of the UKIDSS/UDS
field. The S2CLS parent sample covers a 0.96 degree$^2$ field at
$\sigma_{850}=0.90\pm0.05$ mJy beam$^{-1}$. Our deep, high-resolution ALMA
observations with $\sigma_{\rm 870}\sim$ 0.25 mJy and a 0.15"--0.30" FWHM
synthesized beam, provide precise locations for 695 submillimetre galaxies
(SMGs) responsible for the submillimeter emission corresponding to 606 sources
in the low resolution, single-dish map. We measure the number counts of SMGs
brighter than $S_{\rm 870}\geq$ 4 mJy, free from the effects of blending and
show that the normalisation of the counts falls by 28 $\pm$ 2% in comparison to
the SCUBA-2 parent sample, but that the shape remains unchanged. We determine
that 44$^{+16}_{-14}$% of the brighter single-dish sources with $S_{850}\geq$ 9
mJy consist of a blend of two or more ALMA-detectable SMGs brighter than
$S_{870}\sim$ 1 mJy (corresponding to a galaxy with a total-infrared luminosity
of $L_{IR}\geq$ 10$^{12}$ L$_\odot$), in comparison to 28 $\pm$ 2% for the
single-dish sources at $S_{\rm 850}\geq$ 5 mJy. Using the 46 single-dish
submillimeter sources that contain two or more ALMA-detected SMGs with
photometric redshifts, we show that there is a significant statistical excess
of pairs of SMGs with similar redshifts ($<$1% probability of occurring by
chance), suggesting that at least 30% of these blends arise from physically
associated pairs of SMGs.
