The WISSH QSOs project IX. Cold gas content and environment of luminous QSOs at Cosmic noon.

Sources at the brightest end of QSO luminosity function during the peak epoch of star formation and black hole accretion (z~2-4, i.e. Cosmic noon) are privileged sites to study the feeding & feedback cycle of massive galaxies. We perform the first systematic study of cold gas properties in the most luminous QSOs, by characterising their host-galaxies and environment. We analyse ALMA, NOEMA and JVLA observations of FIR continuum, CO and [CII] emission lines in eight QSOs ($L_{\rm Bol}>3\times10^{47}$ erg/s) from the WISSH sample at z~2.4-4.7. We report a 100% emission line detection rate and a 80% detection rate in continuum emission, and we find CO emission to be consistent with the steepest CO ladders observed so far. Sub-mm data reveal widespread presence of (one or more) bright companion galaxies around 80% of WISSH QSOs, at projected distances of 6-130 kpc. We observe a variety of sizes for the molecular gas reservoirs (1.7-10 kpc), associated with rotating disks with disturbed kinematics. WISSH QSOs typically show lower CO luminosity and higher star formation efficiency than FIR matched, z~0-3 main-sequence galaxies, implying that, given the observed SFR ~170-1100 $M_\odot$/yr, molecular gas is converted into stars on <50 Myr. Most targets show extreme dynamical to black-hole mass ratios $M_{\rm dyn}/M_{\rm BH}\sim3-10$, two orders of magnitude smaller than local relations. The molecular gas fraction in WISSH hosts is lower by a factor of ~10-100 than in star forming galaxies with similar $M_*$. WISSH QSOs undergo an intense growth phase of both the central SMBH and host-galaxy. They pinpoint high-density sites where giant galaxies assemble and mergers play a major role in the build-up of the final host-galaxy mass. The observed low molecular gas fraction and short depletion timescale are likely due to AGN feedback, as traced by fast AGN-driven ionised outflows in all our targets.