The Infrared Medium-deep Survey. IV. Low Eddington Ratio of A Faint
  Quasar at $z\sim6$: Not Every Supermassive Black Hole is Growing Fast in the
  Early Universe
  To date, most of the luminous quasars known at $z\sim6$ have been found to be
in maximal accretion with the Eddington ratios, $\lambda_{\rm{Edd}}\sim1$,
suggesting enhanced nuclear activities in the early universe. However, this may
not be the whole picture of supermassive black hole (SMBH) growth since
previous studies have not reached on faint quasars that are more likely to
harbor SMBHs with low $\lambda_{\rm{Edd}}$. To gain a better understanding on
the accretion activities in quasars in the early universe, we obtained a deep
near-infrared (NIR) spectrum of a quasar, IMS J220417.92+011144.8 (hereafter
IMS J2204+0112), one of the faintest quasars that have been identified at
$z\sim6$. From the redshifted C IV $\lambda 1549$ emission line in the NIR
spectrum, we find that IMS J2204+0112 harbors a SMBH with about a billion solar
mass and $\lambda_{\rm{Edd}} \sim 0.1$, but with a large uncertainty in both
quantities (0.41 dex). IMS J2204+0112 has one of the lowest Eddington ratios
among quasars at $z\sim6$, but a common value among quasars at $z\sim2$. Its
low $\lambda_{\rm{Edd}}$ can be explained with two scenarios; the SMBH growth
from a stellar mass black hole through short-duration super-Eddington accretion
events or from a massive black hole seed ($\sim10^{5}\,M_{\odot}$) with
Eddington-limited accretion. NIR spectra of more faint quasars are needed to
better understand the accretion activities of SMBHs at $z \sim 6$.
