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We performed a systematic spectroscopic observation of a protocluster at$z=6.01$ in the Subaru Deep Field. We took spectroscopy for all 53 $i'$-dropoutgalaxies down to $z'=27.09\,\mathrm{mag}$ in/around the protocluster region.From these observations, we confirmed that 28 galaxies are at $z\sim6$, ofwhich ten are clustered in a narrow redshift range of $\Delta z<0.06$. To tracethe evolution of this primordial structure, we applied the same $i'$-dropoutselection and the same overdensity measurements used in the observations to asemi-analytic model built upon the Millennium Simulation. We obtain a relationbetween the significance of overdensities observed at $z\sim6$ and thepredicted dark matter halo mass at $z=0$. This protocluster with $6\sigma$overdensity is expected to grow into a galaxy cluster with a mass of$\sim5\times10^{14}\,\mathrm{M_\odot}$ 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 significantdifferences appeared in UV and Ly$\alpha$ luminosities between the protoclusterand field galaxies, suggesting that this protocluster is still in the earlyphase of cluster formation before the onset of any obvious environmentaleffects. However, further observations are required to study other properties,such as stellar mass, dust, and age. We do find that galaxies tend to be inclose pairs in this protocluster. These pair-like subgroups will coalesce intoa single halo and grow into a more massive structure. We may witness an onsetof cluster formation at $z\sim6$ toward a cluster as seen in local universe.

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