Rest-frame Optical Spectra and Black Hole Masses of 3<z<6 Quasars

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 H$alpha$ emission line as far out as z~6. We extend the scaling relation between the rest-frame optical continuum and 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${rm AA}$ and H$alpha$ AGN luminosities over a wide range of luminosity (10$^{42}$<$L_{5100}$<10$^{47}$ergs/s) 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 H$beta$ black hole mass ($M_{rm BH}$) estimator of local AGNs, we derive the $M_{rm BH}$ estimators based on H$alpha$, MgII, and CIV lines, finding that the UV-line based masses are overall consistent with the Balmer-line based, but with a large intrinsic scatter of 0.40dex for the CIV estimates. Our 43 $M_{rm BH}$ estimates from H$alpha$ confirm the existence of BHs as massive as ~10$^{10}M_{odot}$ out to z~5, and provide a secure footing for previous MgII-line based studies that a rapid $M_{rm BH}$ growth has occurred in the early universe.