Chandra reveals a luminous Compton-thick QSO powering a $Ly\alpha$ blob
  in a $z=4$ starbursting protocluster
  Galaxy clusters in the local universe descend from high-redshift overdense
regions known as protoclusters. The large gas reservoirs and high rate of
galaxy interaction in protoclusters are expected to trigger star-formation
activity and luminous SMBH accretion in the host galaxies. We investigated the
AGN content of a gas-rich and starbursting protocluster at $z=4$, known as the
Distant Red Core (DRC). We observed with Chandra (139 ks) the 13 identified
members of the structure, and searched for luminous and possibly obscured AGN
among them. We also tested whether a hidden AGN can power the $Ly\alpha$ blob
(LAB) detected with VLT/MUSE in the DRC. We detected obscured X-ray emission
from the two most gas-rich members of the DRC, named DRC-1 and DRC-2. Both of
them are resolved into multiple interacting clumps in high-resolution ALMA and
HST observations. In particular, DRC-2 is found to host a luminous
($L_{2-10\,\mathrm{keV}}\approx3\times10^{45}\,\mathrm{erg\,s^{-1}}$)
Compton-thick ($N_H\gtrsim10^{24}\,\mathrm{cm^{-2}}$) QSO, comparable to the
most luminous QSOs known at all cosmic times. The AGN fraction among DRC
members is consistent with results found for lower redshift protoclusters.
However, X-ray stacking analysis reveals that SMBH accretion is likely also
taking place in other DRC galaxies that are not detected individually by
Chandra. Our results point toward the presence of a strong link between large
gas reservoirs, galaxy interactions, and luminous and obscured nuclear activity
in protocluster members. The powerful and obscured QSO detected in DRC-2 is
likely powering the nearby LAB detected with VLT/MUSE, possibly through
photoionization; however, we propose that the diffuse $Ly\alpha$ emission may
be due to gas shocked by a massive outflow launched by DRC-2 over a $\approx10$
kpc scale.
