A general relativistic model of accretion disks with coronae surrounding Kerr black holes

We calculate the structure of a standard accretion disk with corona surrounding a massive Kerr black hole in general relativistic frame, in which the corona is assumed to be heated by the reconnection of the strongly buoyant magnetic fields generated in the cold accretion disk. The emergent spectra of the accretion disk-corona systems are calculated by using the relativistic ray-tracing method. We propose a new method to calculate the emergent Comptonized spectra from the coronae. The spectra of the disk-corona systems with a modified $\alpha$-magnetic stress show that both the hard X-ray spectral index and the hard X-ray bolometric correction factor $L_{\rm bol}/L_{\rm X,2-10keV}$ increase with the dimensionless mass accretion rate, which are qualitatively consistent with the observations of active galactic nuclei (AGNs). The fraction of the power dissipated in the corona decreases with increasing black hole spin parameter $a$, which leads to lower electron temperatures of the coronas for rapidly spinning black holes. The X-ray emission from the coronas surrounding rapidly spinning black holes becomes weak and soft. The ratio of the X-ray luminosity to the optical/UV luminosity increases with the viewing angle, while the spectral shape in the X-ray band is insensitive with the viewing angle. We find that the spectral index in the infrared waveband depends on the mass accretion rate and the black hole spin $a$, which deviates from $f_\nu\propto\nu^{1/3}$ expected by the standard thin disk model.