We report the first counts of faint submillimetre galaxies (SMGs) in the
870-μm band derived from arcsecond-resolution observations with the
Atacama Large Millimeter Array (ALMA). We have used ALMA to map a sample
of 122 870-μm-selected submillimetre sources drawn from the
0.5°×0.5° the Large Apex BOlometer CAmera (LABOCA)
Extended Chandra Deep Field South submillimetre survey (LESS). These
ALMA maps have an average depth of σ870 μm ˜
0.4 mJy, some approximately three times deeper than the original LABOCA
survey and critically the angular resolution is more than an order of
magnitude higher, FWHM of ˜1.5 arcsec compared to ˜19 arcsec
for the LABOCA discovery map. This combination of sensitivity and
resolution allows us to precisely pinpoint the SMGs contributing to the
submillimetre sources from the LABOCA map, free from the effects of
confusion. We show that our ALMA-derived SMG counts broadly agree with
the submillimetre source counts from previous, lower resolution
single-dish surveys, demonstrating that the bulk of the submillimetre
sources are not caused by blending of unresolved SMGs. The difficulty
which well-constrained theoretical models have in reproducing the high
surface densities of SMGs, thus remains. However, our observations do
show that all of the very brightest sources in the LESS sample,
S870 μm ≳ 12 mJy, comprise emission from multiple,
fainter SMGs, each with 870-μm fluxes of ≲9 mJy. This implies a
natural limit to the star formation rate in SMGs of ≲103
M⊙ yr-1, which in turn suggests that the space
densities of z > 1 galaxies with gas masses in excess of ˜5
× 1010 M⊙ is
