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 \textit{HST} and \textit{Spitzer} data with existing Gemini, \textit{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. However, when placed on the star formation efficiency plane, DRC components exhibit starburst-like characteristics with SFRs 10-100$\times$ greater than the expected field value at a given molecular gas mass. Assuming no future major influx of fresh gas, we estimate that these gas poor (f$_\mathrm{gas}<25\%$) yet bursty DSFGs will deplete their gas reservoirs in $<30$ Myr. 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 $z=0$.