HYPERION. Coevolution of supermassive black holes and galaxies at $z>6$ and the build-up of massive galaxies

We used low- to high-frequency ALMA observations to investigate the cold gas and dust in ten QSOs at $z\gtrsim 6$. Our analysis of the CO(6-5) and CO(7-6) emission lines in the selected QSOs provided insights into their molecular gas masses, which average around $10^{10}\ \rm M_\odot$, consistent with typical values for high-redshift QSOs. Proprietary and archival ALMA observations in bands 8 and 9 enabled precise constraints on the dust properties and star formation rate (SFR) of four QSOs in our sample for the first time. The examination of the redshift distribution of dust temperatures revealed a general trend of increasing $T_{\rm dust}$ with redshift, which agrees with theoretical expectations. We computed a mean cold dust spectral energy distribution considering all ten QSOs. This offers a comprehensive view of the dust properties of high-$z$ QSOs. The QSOs marked by a more intense growth of the supermassive black hole (HYPERION QSOs) showed lower dust masses and higher gas-to-dust ratios on average, but their $\rm H_2$ gas reservoirs are consistent with those of other QSOs at the same redshift. The observed high SFR in our sample yields high SF efficiencies and thus very short gas depletion timescales ($\tau_{\rm dep}\sim 10^{-2}$ Gyr). Beyond supporting the paradigm that high-$z$ QSOs reside in highly star-forming galaxies, our findings portrayed an interesting evolutionary path at $z>6$. Our study suggests that they are undergoing rapid galaxy growth that might be regulated by strong outflows. Their inferred evolutionary path shows a convergence toward the massive end of the local relation, which supports the idea that they are candidate progenitors of local massive galaxies. The observed pathway involves intense BH growth followed by substantial galaxy growth, in contrast with a symbiotic growth scenario. The abstract has been shortened (full version in the article).