Dependence of the Spin of Supermassive Black Holes on the Eddington Factor for Accretion Disks in Active Galactic Nuclei

An equation relating the spin of supermassive black holes (SMBH) to the Eddington factor, i.e., the ratio of the bolometric and Eddington luminosities for accretion disks in active galactic nuclei (AGN), is presented. This equation also depends on the relationship between the magnetic field pressure and the flux of accreted matter at the radius of the event horizon for a black hole. When the pressures of the magnetic field and of the accreted matter are equal, there is a direct relationship between the spin of the black hole and the Eddington factor. Based on available data on the bolometric luminosity and mass of black holes, it is possible to determine the spin of a black hole. The spins of the central SMBH are given for a number of AGN. The proposed method can also be used to determine the ratio of the magnetic field pressure and the pressure of the accreted gas at the event horizon of SMBH for AGN for which the spin of the black hole has been determined reliably.