Radiative Efficiency of Disk Accretion in Individual SDSS QSOs
  We estimate the radiative efficiency (epsilon) of individual type 1 SDSS QSOs
by using their bolometric luminosities (L_{bol}) and accretion rates
(\dot{M}_{\bullet,acc}), which may be related to the assembly histories and
spins of the central massive black holes (MBHs). We estimate L_{bol} by using
the empirical spectral energy distributions of QSOs and \dot{M}_{\bullet,acc}
by fitting the observed optical luminosity(/-ies) with the thin accretion disk
model, assuming the MBH masses given by the virial mass estimator(s)
(M_{\bullet,vir}). We find an apparent correlation between epsilon and
M_{\bullet,vir}, which is strong at redshift z \la 1.8, weak at z \ga 2, and
consistent with that found by Davis & Laor (2011) for 80 PG QSOs at z \leq 0.5.
To investigate whether this correlation is intrinsic or not, we construct a
mock sample of QSOs according to the true MBH mass and Eddington ratio
distributions given in Kelly & Shen (2013). By comparing the results obtained
from the mock sample with that from the SDSS sample, we demonstrate that the
apparent epsilon-M_{\bullet,vir} correlation can be produced by and mainly due
to the selection effects of the SDSS sample and the bias induced by the usage
of M_{\bullet,vir} as the true MBH mass. The mean values of epsilon of those
SDSS QSOs are consistent with being a constant \simeq 0.11-0.16 over the
redshift range of 0.3 \la z \la 4. We conclude that the current SDSS QSO data
is consistent with no strong intrinsic correlation between radiative efficiency
and true MBH mass and no significant redshift evolution of radiative
efficiencies.
