GA-NIFS: The core of an extremely massive proto-cluster at the Epoch of Reionization probed with JWST/NIRSpec

The SPT0311-58 system resides in a massive dark matter halo at z   6.9. It hosts two dusty galaxies (E and W) with a combined star formation rate of  3500 Msun/yr. Its surrounding field exhibits an overdensity of sub-mm sources, making it a candidate proto-cluster. We use spatially-resolved spectroscopy provided by the JWST/NIRSpec Integral Field Unit (IFU) to probe a field of view (FoV)   17 x 17 kpc^2 around this object. These observations have revealed ten new galaxies at z   6.9, characterised by dynamical masses spanning from  10^9 to 10^10 Msun and a range in radial velocities of   1500 km/s, in addition to the already known E and W galaxies. The implied large number density, and the wide spread in velocities, indicate that SPT0311-58 is at the core of a proto-cluster, immersed in a very massive dark matter halo of   6 x 10^12 Msun. Hence, it represents the most massive proto-cluster ever found at the EoR. We also study the dynamical stage of the system and find that it likely is not fully virialised. The galaxies exhibit a great diversity of properties showing a range of evolutionary stages. We derive their ongoing Ha-based unobscured SFR, and find that its contribution to the total SF varies significantly across the galaxies in the system. Their ionization conditions range from those typical of field galaxies at similar redshift recently studied with JWST to those found in more evolved objects at lower z. The metallicity spans more than 0.8 dex across the FoV, reaching nearly solar values in some cases. The detailed IFU spectroscopy of the E galaxy reveals that it is actively assembling its stellar mass, showing sub-kpc inhomogeneities, and a metallicity gradient that can be explained by accretion of low metallicity gas from the IGM. The kinematic maps indicate departures from regular rotation, high turbulence, and a possible pre-collision minor merger. (Abridged)