Emergence of an Ultra-Red Ultra-Massive Galaxy Cluster Core at $z=4$
  Recent simulations and observations of massive galaxy cluster evolution
predict that the majority of stellar mass build up happens within cluster
members by $z=2$, before cluster virialization. Protoclusters rich with dusty,
star-forming galaxies (DSFGs) at $z>3$ are the favored candidate progenitors
for these massive galaxy clusters at $z\sim0$. We present here the first study
analyzing stellar emission along with cold dust and gas continuum emission in a
spectroscopically confirmed $z=4.002$ protocluster core rich with DSFGs, the
Distant Red Core (DRC). We combine new HST and Spitzer data with existing
Gemini, Herschel, and ALMA observations to derive individual galaxy-level
properties, and compare them to coeval field and other protocluster galaxies.
All of the protocluster members are massive ($>10^{10}$ M$_\odot$), but not
significantly more so than their coeval field counterparts. Within uncertainty,
all are nearly indistinguishable from galaxies on the star-forming vs. stellar
mass main-sequence relationship, and on the star formation efficiency plane.
Assuming no future major influx of fresh gas, we estimate that these gaseous
DSFGs will deplete their gas reservoirs in $\sim300$ Myr, becoming the massive
quiescent ellipticals dominating cluster cores by $z\sim3$. Using various
methodologies, we derive a total $z=4$ halo mass of $\sim10^{14}$ M$_\odot$,
and estimate that the DRC will evolve to become an ultra-massive cluster core
of mass $\gtrsim10^{15}$ M$_\odot$ by $z=0$.
