Optical and near-infrared observations of the SPT2349-56 proto-cluster
  core at z = 4.3
  We present Gemini-S and {\it Spitzer}-IRAC optical-through-near-IR
observations in the field of the SPT2349-56 proto-cluster at $z=4.3$. We detect
optical/IR counterparts for only nine of the 14 submillimetre galaxies (SMGs)
previously identified by ALMA in the core of SPT2349-56. In addition, we detect
four $z\sim4$ Lyman-break galaxies (LBGs) in the 30 arcsec diameter region
surrounding this proto-cluster core. Three of the four LBGs are new systems,
while one appears to be a counterpart of one of the nine observed SMGs. We
identify a candidate brightest cluster galaxy (BCG) with a stellar mass of
$(3.2^{+2.5}_{-1.4})\times10^{11}\,{\rm M}_{\odot}$. The stellar masses of the
eight other SMGs place them on, above, and below the main sequence of star
formation at $z\approx4.5$. The cumulative stellar mass for the SPT2349-56 core
is at least $(11.5\pm2.9)\times10^{11}\,{\rm M}_{\odot}$, a sizeable fraction
of the stellar mass in local BCGs, and close to the universal baryon fraction
(0.16) relative to the virial mass of the core ($10^{13}\,{\rm M}_{\odot}$). As
all 14 of these SMGs are destined to quickly merge, we conclude that the
proto-cluster core has already developed a significant stellar mass at this
early stage, comparable to $z=1$ BCGs. Importantly, we also find that the
SPT2349-56 core structure would be difficult to uncover in optical surveys,
with none of the ALMA sources being easily identifiable or constrained through
$g,r,$ and $i$ colour-selection in deep optical surveys and only a modest
overdensity of LBGs over the extended core structure. SPT2349-56 therefore
represents a truly dust-obscured phase of a massive cluster core under
formation.
