Abstract
We present the rest-frame optical spectral properties of 155 luminous quasars at 3.3 < z < 6.4 taken with the AKARI space telescope, including the first detection of the Hα emission line as far out as z ∼ 6. We extend the scaling relation between the rest-frame optical continuum and the line luminosity of active galactic nuclei (AGNs) to the high-luminosity, high-redshift regime that has rarely been probed before. Remarkably, we find that a single log-linear relation can be applied to the 5100 and Hα AGN luminosities over a wide range of luminosity (10 <sup>42</sup> < < 10 <sup>47</sup> ergs s <sup>-1</sup> ) or redshift (0 < z < 6), suggesting that the physical mechanism governing this relation is unchanged from z = 0 to 6, over five decades in luminosity. Similar scaling relations are found between the optical and the UV continuum luminosities or line widths. Applying the scaling relations to the Hβ black hole (BH) mass () estimator of local AGNs, we derive the estimators based on the Hα, Mg ii, and C iv lines, finding that the UV-line-based masses are overall consistent with the Balmer-line-based, but with a large intrinsic scatter of 0.40 dex for the C iv estimates. Our 43 estimates from Hα confirm the existence of BHs as massive as ∼ out to z ∼ 5 and provide a secure footing for previous results from Mg ii-line-based studies that a rapid growth has occurred in the early universe.