2022A&A...665A.107T

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_bol based on X-ray and optical and ultraviolet SED. To this aim, we analysed a deep ALMA observation of the sub-mm continuum, [CII], and H₂O of the z ∼ 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)x10⁸ M_☉, and total far-infrared luminosity of L_TIR = 2.5_–0.5^+0.6 x 10¹³ L_☉. The implied active galactic nuclei (AGN) - corrected SFR = 1240_–260⁺³¹⁰ M_☉ 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 ∼ 6.7 kpc and r ∼ 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, Σ_gas, and star formation rate density, Σ_SFR, place the J2310+1855 host galaxy above the Kennicutt-Schmidt relation. We derived a best estimate of the dynamical mass M_dyn = 5.2 x 10¹⁰ M_☉ 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 ∼ 3 and implies that the disk is unstable. We found that SFR/M_dyn > M_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 10⁸ M_☉, and a mass outflow rate in the range M_out = 1800 - 4500 M_☉ yr^–1. The implied E_out ∼ 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 ν_obs = 274.074 GHz, whose kinematic properties and size are broadly consistent with those of the [CII] disk. The luminosity ratio L_H2_O/L_TIR = 1.4 x 10^–5 is consistent with line excitation by dust-reprocessed star formation in the interstellar medium of the host galaxy.