A First Site of Galaxy Cluster Formation: Complete Spectroscopy of a Protocluster at $z=6.01$

We performed a systematic spectroscopic observation of a protocluster at $z=6.01$ in the Subaru Deep Field. We took spectroscopy for all 53 $i$-dropout galaxies down to $z=27.09,mathrm{mag}$ in/around the protocluster region. From these observations, we confirmed that 28 galaxies are at $zsim6$, of which ten are clustered in a narrow redshift range of $Delta z<0.06$. To trace the evolution of this primordial structure, we applied the same $i$-dropout selection and the same overdensity measurements used in the observations to a semi-analytic model built upon the Millennium Simulation. We obtain a relation between the significance of overdensities observed at $zsim6$ and the predicted dark matter halo mass at $z=0$. This protocluster with $6sigma$ overdensity is expected to grow into a galaxy cluster with a mass of $sim5times10^{14},mathrm{M_odot}$ at $z=0$. Ten galaxies within $10,mathrm{comoving>Mpc}$ of the overdense region can, with more than an 80% probability, merge into a single dark matter halo by $z=0$. No significant differences appeared in UV and Ly$alpha$ luminosities between the protocluster and field galaxies, suggesting that this protocluster is still in the early phase of cluster formation before the onset of any obvious environmental effects. However, further observations are required to study other properties, such as stellar mass, dust, and age. We do find that galaxies tend to be in close pairs in this protocluster. These pair-like subgroups will coalesce into a single halo and grow into a more massive structure. We may witness an onset of cluster formation at $zsim6$ toward a cluster as seen in local universe.