Discovery of a galaxy overdensity around a powerful, heavily obscured FRII radio-galaxy at z=1.7: star formation promoted by large scale AGN feedback?

We report the discovery of a galaxy overdensity around a Compton-thick Fanaroff-Riley type II (FRII) radio-galaxy at z=1.7 in the deep multi-band survey around the z=6.3 QSO SDSS J1030+0524. Based on a 6hr VLT/MUSE and on a 4hr LBT/LUCI observation, we identify at least 8 galaxy members in this structure with spectroscopic redshift z=1.687-1.699, including the FRII galaxy at z=1.699. Most of the identified overdensity members are blue, compact galaxies that are actively forming stars at rates of $\sim$8-60 $M_{\odot}$ yr$^{-1}$. Based on a 500ks Chandra ACIS-I observation we found that the FRII nucleus hosts a luminous QSO ($L_{2-10keV}=1.3\times10^{44}$ erg s$^{-1}$, intrinsic and rest-frame) that is obscured by Compton-thick absorption ($N_H=1.5\pm0.6\times 10^{24}$ cm$^{-2}$). Our Chandra observation, the deepest so far for a distant FRII within a galaxy overdensity, revealed significant diffuse X-ray emission within the region covered by the overdensity. In particular, X-ray emission extending for $\sim$240 kpc is found around the Eastern lobe of the FRII. Four out of the six MUSE star forming galaxies in the overdensity are distributed in an arc-like shape at the edge of this diffuse X-ray emission. The probability of observing by chance four out of the six $z=1.7$ sources at the edge of the diffuse emission is negligible. In addition, these four galaxies have the highest specific star formation rates among the MUSE galaxies in the overdensity and lie above the main sequence of field galaxies of equal stellar mass at z=1.7. We propose that the diffuse X-rays originate from an expanding bubble of gas shock-heated by the FRII jet, and that star formation is promoted by the compression of the cold interstellar medium of the galaxies around the bubble, which may be remarkable evidence of positive AGN feedback on cosmological scales. [shortened version]