A Multiwavelength Study of ELAN Environments (AMUSE$^2$): Ubiquitous
  dusty star-forming galaxies associated with enormous Ly$\alpha$ nebulae on
  megaparsec scales
  We have been undertaking a systematic survey at 850 $\mu$m based on a sample
of four prototypical $z\sim2-3$ enormous Ly$\alpha$ nebulae (ELANe) as well as
their megaparsec-scale (Mpc-scale) environments to study the physical
connections between ELANe and their coeval dusty submillimeter galaxies (SMGs).
By analysing the SCUBA-2 data with self-consistent Monte Carlo simulations to
construct the number counts, here, we report on the overabundance of 850
$\mu$m-selected submillimeter sources around all the four ELANe, by a factor of
3.6$\pm$0.6 (weighted average) compared to the blank fields. This suggests that
the excessive number of submillimeter sources are likely to be part of the
Mpc-scale environment around the ELANe, corroborating the co-evolution scenario
for SMGs and quasars; this is a process which may be more commonly observed in
the ELAN fields. If the current form of the underlying count models continues
toward the fainter end, our results would suggest an excess of the 850 $\mu$m
extragalactic background light by a factor of between 2-10, an indication of
significant background light fluctuations on the survey scales. Finally, by
assuming that all the excessive submillimeter sources are associated with their
corresponding ELAN environments, we estimate the SFR densities of each ELAN
field, as well as a weighted average of $\Sigma$SFR=1200$\pm$300 $M_\odot$
yr$^{-1}$ Mpc$^{-3}$, consistent with that found in the vicinity of other
quasar systems or proto-clusters at similar redshifts; in addition, it is a
factor of about 300 greater than the cosmic mean.
