Two sub-millimetre bright protoclusters bounding the epoch of peak
  star-formation activity
  We present James Clerk Maxwell Telescope Submillimetre Common-User Bolometer
Array 2 (SCUBA-2) 850 & 450 $\mu$m observations ($\sigma_{850}\sim0.5$ mJy,
$\sigma_{450}\sim5$ mJy) of the HS1549+19 and HS1700+64 survey fields
containing two of the largest known galaxy over-densities at $z=2.85$ and
$2.30$, respectively. We detect 56 sub-millimetre galaxies (SMGs) with SNR $>
4$ over $\sim 50$ arcmin$^2$ at 850 $\mu$m with flux densities of 3 - 17 mJy.
The number counts indicate over-densities in the $3$-arcmin diameter core
region ($\sim 1.5$ Mpc at $z=2.5$) of $6^{+4}_{-2}\times$ (HS1549) and
$4^{+6}_{-2}\times$ (HS1700) compared to blank field surveys. Within these core
regions, we spectroscopically confirm that approximately one third of the SMGs
lie at the protocluster redshifts for both HS1549 and HS1700. We use
statistical identifications of other SMGs in the wider fields to constrain an
additional four candidate protocluster members in each system. We combine multi
wavelength estimates of the star-formation rates (SFRs) from Lyman-break
dropout- and narrowband-selected galaxies, and the SCUBA-2 SMGs, to estimate
total SFRs of 12,$500\pm2800$ M$_\odot$ yr$^{-1}$ ($4900\pm1200$ M$_\odot$
yr$^{-1}$) in HS1549 (HS1700), and SFR densities (SFRDs) within the central
1.5-Mpc diameter of each protocluster to be $3000\pm900$ M$_\odot$ yr$^{-1}$
Mpc$^{-3}$ ($1300\pm400$ M$_\odot$ yr$^{-1}$ Mpc$^{-3}$) in the HS1549 (HS1700)
protocluster, $\sim10^4\times$ larger than the global SFRDs found at their
respective epochs, due to the concentration of star-forming galaxies in the
small volume of the dense cluster cores. Our results suggest centrally
concentrated starbursts within protoclusters may be a relatively common
scenario for the build up of mass in rich clusters assembling at $z\gtrsim2$.
