Spectroscopic Confirmation of a Massive Protocluster with Two Substructures at $z\simeq 3.1$

We present the results of a Keck and NOEMA spectroscopic survey of 507 galaxies, where we confirm the presence of two massive overdensities at $z=3.090-3.110$ and $z=3.133-3.155$ in the neighborhood of the GOODS-N, each with over a dozen spectroscopically confirmed members. We find that both of these have galaxy overdensities of NIR-detected galaxies of ${\delta }_{\mathrm{g}\mathrm{a}\mathrm{l},\mathrm{o}\mathrm{b}\mathrm{s}}=6-9$ within corrected volumes of $(6-7)\times {10}^3{\mathrm{c}\mathrm{M}\mathrm{p}\mathrm{c}}^3$. We estimate the properties of the $z=0$ descendants of these overdensities using a spherical collapse model and find that both should virialize by $z\simeq 0.5-0.8$, with total masses of $M_{\mathrm{t}\mathrm{o}\mathrm{t}}\simeq (6-7)\times {10}^{14}{\mathrm{M}}_{\odot }$. The same spherical collapse calculations, as well as a clustering-of-clusters statistical analysis, suggest a >80% likelihood that the two overdensities will collapse into a single cluster with $M_{\mathrm{t}\mathrm{o}\mathrm{t}}=(1.0-1.5)\times {10}^{15}{\mathrm{M}}_{\odot }$ by $z\sim 0.1-0.4$. The $z=3.14$ substructure contains a core of four bright dusty star-forming galaxies with $\mathrm{\Sigma }\mathrm{S}\mathrm{F}\mathrm{R}=2700\pm 700{\mathrm{M}}_{\odot }{\mathrm{y}\mathrm{r}}^{-1}$ in a volume of only 280 ${\mathrm{c}\mathrm{M}\mathrm{p}\mathrm{c}}^3$.