A SCUBA-2 850$\mu$m Survey of Heavily Reddened Quasars at z~2
  We present new 850$\mu$m SCUBA-2 observations for a sample of 19 heavily
reddened Type-I quasars at redshifts $z\sim$2 with dust extinctions of
A$_{\rm{V}} \simeq 2-6$ mag. Three of the 19 quasars are detected at
$>$3$\sigma$ significance corresponding to an 850$\mu$m flux-limit of
$\gtrsim$4.8 mJy. Assuming the 850$\mu$m flux is dominated by dust heating due
to star formation, very high star formation rates (SFR) of $\sim$2500-4500
M$_\odot$ yr$^{-1}$ in the quasar host galaxies are inferred. Even when
considering a large contribution to the 850$\mu$m flux from dust heated by the
quasar itself, significant SFRs of $\sim$600-1500 M$_\odot$ yr$^{-1}$ are
nevertheless inferred for two of the three detected quasars. We stack the
remaining 16 heavily reddened quasars and derive an average 3$\sigma$ upper
limit on the SFRs in these quasar host galaxies of $<$880 M$_\odot$ yr$^{-1}$.
The number counts of sub-mm galaxies in the total survey area (134.3arcmin$^2$)
are consistent with predictions from blank-field surveys. There are, however,
individual quasars where we find evidence for an excess of associated sub-mm
galaxies. For two quasars, higher spatial resolution and spectroscopic ALMA
observations confirm the presence of an excess of sub-mm sources. We compare
the 850$\mu$m detection rate of our quasars to both unobscured, ultraviolet
luminous quasars as well as the much more obscured population of mid-infrared
luminous Hot Dust Obscured Galaxies (HotDOGs). When matched by luminosity and
redshift, we find no significant differences in the 850$\mu$m flux densities of
these various quasar populations given the current small sample sizes.
