SCUBA-2 overdensities associated with candidate protoclusters selected
  from Planck data
  We measure the 850-$\mu$m source densities of 46 candidate protoclusters
selected from the Planck High-z catalogue (PHz) and the Planck Catalogue of
Compact Sources (PCCS) that were followed up with Herschel-SPIRE and SCUBA-2.
This paper aims to search for overdensities of 850-$\mu$m sources in order to
select the fields that are most likely to be genuine protoclusters. Of the 46
candidate protoclusters, 25 have significant overdensities ($>$5 times the
field counts), 11 have intermediate overdensities (3--5 times the field counts)
and 10 have no overdensity ($<$3 times the field counts) of 850-$\mu$m sources.
We find that the enhanced number densities are unlikely to be the result of
sample variance. Compared with the number counts of another sample selected
from Planck's compact source catalogues, this [PHz+PCCS]-selected sample has a
higher fraction of candidate protoclusters with significant overdensities,
though both samples show overdensities of 850-$\mu$m sources above intermediate
level. Based on the estimated star-formation rate densities (SFRDs), we suggest
that both samples can efficiently select protoclusters with starbursting
galaxies near the redshift at which the global field SFRD peaks ($2 < z < 3$).
Based on the confirmation of overdensities found here, future follow-up
observations on other PHz targets may greatly increase the number of genuine
DSFG-rich clusters/protoclusters.
