Constraints on black hole spins with a general relativistic accretion
  disk corona model
  The peaks of the spectra of the accretion disks surrounding massive black
holes in quasars are in the far-UV or soft X-ray band, which are usually not
observed. However, in the disk corona model, the soft photons from the disk are
Comptonized to high energy in the hot corona, and the hard X-ray spectra
(luminosity and spectral shape) contain the information of the incident spectra
from the disk. The values of black hole spin parameter $a_{\ast}$ are inferred
from the spectral fitting, which spread over a large range, $\sim -0.94$ to
$0.998$. We find that the inclination angles and mass accretion rates are well
determined by the spectral fitting, while the results are sensitive to the
accuracy of black hole mass estimates. No tight constraints on the black hole
spins are achieved, if the uncertainties of black hole mass measurements are a
factor of four, which are typical for the single-epoch reverberation mapping
method. Recently, the accuracy of black hole mass measurement has been
significantly improved to $0.2-0.4$~dex with velocity resolved reverberation
mapping method (Pancoast et al., 2014). The black hole spin can be well
constrained if the mass measurement accuracy is $\la 50$\%. In the accretion
disk corona scenario, a fraction of power dissipated in the disk is transported
into the corona, and therefore the accretion disk is thinner than a bare disk
for the same mass accretion rate, because the radiation pressure in the disk is
reduced. We find that the thin disk approximation, $H/R\la 0.1$, is still valid
if $0.3<\dot{m}<0.5$, provided a half of the dissipated power is radiated in
the corona above the disk.
