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.