A census of optically dark massive galaxies in the early Universe from
  magnification by lensing galaxy clusters
  We present ALMA 870um and JCMT SCUBA2 850um dust continuum observations of a
sample of optically dark and strongly lensed galaxies in the cluster fields.
The ALMA and SCUBA2 observations reach a median rms of about 0.11 mJy and 0.44
mJy, respectively, with the latter close to the confusion limit of the data at
850um. This represents one of the most sensitive searches for dust emission in
optically dark galaxies. We detect the dust emission in 12 out of 15 galaxies
at >3.8 sigma, corresponding to a detection rate of 80 per cent. Thanks to the
gravitational lensing, our observations reach a deeper limiting flux than
previous surveys in blank fields by a factor of 3. We estimate delensed
infrared luminosities in the range log(LIR)=11.5-12.7 Lsun, which correspond to
dust-obscured star formation rates (SFRs) of 30 to 520 Msun per year. Stellar
population fits to the optical-to-NIR photometric data yield a median redshift
z=4.26 and de-lensed stellar mass log(Mstar)=10.78 Msun. They contribute a
lensing-corrected star-formation rate density at least an order of magnitude
higher than that of equivalently massive UV-selected galaxies at z>3. The
results suggest that there is a missing population of massive star-forming
galaxies in the early Universe, which may dominate the SFR density at the
massive end. Five optically dark galaxies are located within r<50 arcsec in one
cluster field, representing a potential overdensity structure that has a
physical origin at a confidence level >99.974% from Poisson statistics.
Follow-up spectroscopic observations with ALMA and JWST are crucial to confirm
whether it is associated with a protocluster at similar redshifts.
