The WISSH quasars project. IX. Cold gas content and environment of luminous QSOs at z {ensuremath{sim}} 2.4-4.7

Context. Sources at the brightest end of the quasi-stellar object (QSO) luminosity function, during the peak epoch in the history of star formation and black hole accretion (z ∼ 2-4, often referred to as "Cosmic noon") are privileged sites to study the cycle of feeding & feedback processes in massive galaxies. Aims: We aim to perform the first systematic study of cold gas properties in the most luminous QSOs, by characterising their host-galaxies and environment. These targets exhibit indeed widespread evidence of outflows at nuclear and galactic scales. Methods: We analyse ALMA, NOEMA and JVLA observations of the far-infrared continuum, CO and [CII] emission lines in eight QSOs (bolometric luminosity LBol ≳ 3 × 1047 erg s-1) from the WISE-SDSS selected hyper-luminous (WISSH) QSOs sample at z ∼ 2.4-4.7. Results: 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-millimetre data reveal 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), mostly associated with rotating disks with disturbed kinematics. WISSH QSOs typically show lower CO luminosity and higher star formation efficiency than infrared matched, z ∼ 0-3 main-sequence galaxies, implying that, given the observed SFR ∼170-1100 M⊙ yr-1, molecular gas is converted into stars in ≲50 Myr. Most targets show extreme dynamical to black-hole mass ratios Mdyn/MBH ∼ 3-10, two orders of magnitude smaller than local relations. The molecular gas fraction in the host-galaxies of WISSH is lower by a factor of ∼10-100 than in star forming galaxies with similar M*. Conclusions: Our analysis reveals that hyper-luminous QSOs at Cosmic noon undergo an intense growth phase of both the central super-massive black hole and of the host-galaxy. These systems pinpoint the high-density sites where giant galaxies assemble, where we show that mergers play a major role in the build-up of the final host-galaxy mass. We suggest that the observed low molecular gas fraction and short depletion timescale are due to AGN feedback, whose presence is indicated by fast AGN-driven ionised outflows in all our targets