SCUBA-2 observations of candidate starbursting protoclusters selected by
  Planck and Herschel-SPIRE
  We present SCUBA-2 850-$\mu$m observations of 13 candidate starbursting
protoclusters selected using Planck and Herschel data. The cumulative number
counts of the 850-$\mu$m sources in 9/13 of these candidate protoclusters show
significant overdensities compared to the field, with the probability
$<$10$^{-2}$ assuming the sources are randomly distributed in the sky. Using
the 250-, 350-, 500- and 850-$\mu$m flux densities, we estimate the photometric
redshifts of individual SCUBA-2 sources by fitting spectral energy distribution
(SED) templates with an MCMC method. The photometric redshift distribution,
peaking at $2<z<3$, is consistent with that of known $z>2$ protoclusters and
the peak of the cosmic star-formation rate density (SFRD). We find that the
850-$\mu$m sources in our candidate protoclusters have infrared luminosities of
$L_{\mathrm{IR}}\gtrsim$10$^{12}L_{\odot}$ and star-formation rates of
SFR=(500-1,500)$M_{\odot}$yr$^{-1}$. By comparing with results in the
literature considering only Herschel photometry, we conclude that our 13
candidate protoclusters can be categorised into four groups: six of them being
high-redshift starbursting protoclusters, one being a lower-redshift
cluster/protocluster, three being protoclusters that contain lensed DSFG(s) or
are rich in 850-$\mu$m sources, and three regions without significant Herschel
or SCUBA-2 source overdensities. The total SFRs of the candidate protoclusters
are found to be comparable or higher than those of known protoclusters,
suggesting our sample contains some of the most extreme protocluster
population. We infer that cross-matching Planck and Herschel data is a robust
method for selecting candidate protoclusters with overdensities of 850-$\mu$m
sources.
