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.
