The Nature of 500 Micron Risers II: Sub-mm Faint Dusty Star Forming
  Galaxies
  We present SCUBA-2 and SMA follow-up observations of four candidate high
redshift Dusty Star-Forming Galaxies, selected as sources with rising SEDs in
the 250, 350 and 500$\mu$m Herschel SPIRE bands. Previous SMA observations
showed no counterparts to these sources, but in our deeper sub-mm observations
we detect counterparts to all four 500$\mu$m risers, with three resolving into
multiple systems. For these three multiple systems, the SMA 345GHz ($\approx
870\mu$m) observations recover $123 \pm 73\%$, $60 \pm 15\%$ and $19 \pm 4\%$
respectively of the integrated 850$\mu$m flux density from SCUBA-2, indicating
that there may be additional sources below our SMA detection limit making up a
dense, protocluster core. The fourth 500$\mu$m riser was observed at a lower
frequency and so we cannot make a similar comparison. We estimate photometric
redshifts based on FIR/sub-mm colours, finding that 3/4 likely lie at $z \geq
2$. This fits with the interpretation that the 500$\mu$m riser selection
criterion selects both intrinsically red, individual galaxies at $z > 4$, and
multiple systems at more moderate redshifts, artificially reddened by the
effects of blending. We use the SCUBA-2 850$\mu$m maps to investigate the
environments of these 500$\mu$m risers. By constructing cumulative number
counts and estimating photometric redshifts for surrounding SCUBA-2 detections,
we find that one of our 500$\mu$m risers could plausibly reside in a $z \geq 2$
protocluster. We infer that bright 500$\mu$m risers with faint 850$\mu$m flux
densities are typically multiple systems at $z \geq 2$ that may reside in
overdensities of bright sub-mm galaxies.
