The black hole and host galaxy growth in an isolated z ~ 6 QSO observed with ALMA

The outstanding mass growth of supermassive black holes (SMBHs) at the epoch of reionisation and its relation to the concurrent growth of their host galaxies poses challenges to theoretical models aimed at explaining how these systems formed on short timescales (<1 Gyr). To trace the average evolutionary paths of quasi-stellar objects (QSOs) and their host galaxies in the plane of BH mass to host mass (M-dyn), we compare the star formation rate (SFR), derived from the accurate estimate of the dust temperature and the dust mass (T-dust, M-dust) based on infrared and sub-millimeter (sub-mm) spectral energy distribution (SED), with the BH accretion rate, derived from L-bot based on X-ray and optical and ultraviolet SED. To this aim, we analysed a deep ALMA observation of the submm continuum, [CII], and H2O of the z similar to 6 QSO J2310+1855 with a resolution of 900 pc, which enabled a detailed study of dust properties and cold gas kinematics. We performed an accurate SED analysis obtaining a dust temperature of T-dust = 71 +/- 4 K, dust mass M-dust = (4.4 +/- 0.7) x 10(8) M-circle dot, and total far-infrared luminosity of L-TIR = 2.5(-0.5)(+0.6) x 10(13) L-circle dot. The implied active galactic nuclei (AGN) - corrected SFR = 1240(-260)(+360) M-circle dot yr(-1) is a factor of 2 lower than previously reported for this QSO. We measured a gas-to-dust ratio of GDR = 101 +/- 20. The dust continuum and [CII] surface brightness profiles are spatially extended out to r similar to 6.7 kpc and r similar to 5 kpc, respectively, with half-light radii of 0.9 and 1.1 kpc for the dust and gas, respectively. The derived gas surface density, Sigma(gas), and star formation rate density, Sigma(SFR), place the J2310+1855 host galaxy above the Kennicutt-Schmidt relation. We derived a best estimate of the dynamical mass M-dyn = 5.2x 10(10) M-circle dot within r = 1.7 kpc based on a dynamical model of the system with a rotating disk inclined at i = 25 deg. The Toomre parameter profile across the disk is Q(gas) similar to 3 and implies that the disk is unstable. We found that SFR /M-dyn > (M) over dot(BH)/M-BH, suggesting that AGN feedback might be efficiently acting to slow down the SMBH accretion, while stellar mass assembly is still vigorously taking place in the host galaxy. In addition, we were also able to detect high-velocity emission on the red and blue sides of the [CII] emission line that is not consistent with disk rotation and traces a gaseous outflow. We derived an outflow mass M-out = 3.5 x 10(8) M-circle dot, and a mass outflow rate in the range (M) over dot(out) = 1800-4500 M-circle dot yr(-1). The implied (E) over dot(out) similar to 0.0005-0.001 L-bol is in agreement with the values observed for ionised winds. For the first time, we mapped a spatially resolved water vapour disk through the H2O v = 0 3((2,2))-3((1,3)) emission line detected at v(obs) = 274.074 GHz, whose kinematic properties and size are broadly consistent with those of the [CII] disk. The luminosity ratio LH2O/LTIR = 1.4 x 10(-5) is consistent with line excitation by dust-reprocessed star formation in the interstellar medium of the host galaxy.