The X-shooter/ALMA Sample of Quasars in the Epoch of Reionization. II. Black Hole Masses, Eddington Ratios, and the Formation of the First Quasars

We present measurements of black hole masses and Eddington ratios for a sample of 38 bright (M$_{1450}$ < -24.4 mag) quasars at 5.8 < z < 7.5, derived from VLT/X-shooter near-IR spectroscopy of their broad CIV and MgII emission lines. The black hole masses (on average M$_{BH}$ ~ 4.6 x 10$^9$ M$_{\odot}$) and accretion rates (with Eddington ratios ranging between 0.1 and 1.0) are broadly consistent with that of similarly luminous 0.3 < z < 2.3 quasars, but there is evidence for a mild increase in the median Eddington ratio going towards z > 6. Combined with deep ALMA observations of the [CII] 158 $\mu$m line from the quasar host galaxies and VLT/MUSE investigations of the extended Ly$\alpha$ halos, this study provides fundamental clues to models of the formation and growth of the first massive galaxies and black holes. Compared to local scaling relations, z > 5.7 black holes appear to be over-massive with respect to their host galaxies, and their accretion properties do not change with host galaxy morphology. Under the assumption that the kinematics of the T ~ 10$^4$ K gas, traced by the extended Ly$\alpha$ halos, are dominated by the gravitational potential of the dark matter halo, we report a similar relation between the black hole mass and circular velocity to the one reported for z ~ 0 galaxies. These results paint a picture where the first supermassive black holes reside in massive halos at z > 6 and lead the first stages of galaxy formation by rapidly growing in mass with a duty cycle of order unity. However, this duty cycle needs to drastically drop towards lower redshifts, while the host galaxies continue forming stars at a rate of hundreds of solar masses per year, sustained by the large reservoirs of cool gas surrounding them.