The σHβ -based Dimensionless Accretion Rate and Its Connection with the Corona for AGNs

With respect to the H β FWHM (FWHM H β ), the broad H β line dispersion ( σ H β ) was preferred as a velocity tracer to calculate the single-epoch supermassive black hole mass ( M BH ) suggested by Yu et al. For a compiled sample of 311 broad-line active galactic nuclei (AGNs) with measured hard X-ray photon index ( z < 0.7), σ H β and the optical Fe ii relative strength ( R Fe ) are measured from their optical spectra, which are used to calculate σ H β -based virial M BH and dimensionless accretion rate ( M ̇ ). With respect to FWHM H β , it is found that the mean value of σ H β -based M BH is on average larger by 0.26 dex and the mean value of σ H β -based M ̇ is on average smaller by 0.51 dex. It is found that there exists a nonlinear relationship between the Eddington ratio ( L Bol / L Edd ) and M ̇ , i.e., L Bol / L Edd ∝ M ̇ 0.56 ± 0.01 . This nonlinear relationship comes from the accretion efficiency η , which is smaller for AGNs with higher M ̇ . We find a strong bivariate correlation of the fraction of energy released in the corona F X with M ̇ and M BH , F X ∝ M ̇ − 0.57 ± 0.05 M BH − 0.54 ± 0.06 . The flat slope of −0.57 ± 0.05 favors the shear stress tensor of the accretion disk being proportional to the geometric mean of gas pressure and total pressure. We find a strong bivariate relation of Γ with M ̇ and F X , Γ ∝ M ̇ − 0.21 ± 0.02 F X 0.02 ± 0.04 . The hard X-ray spectrum becomes softer with increasing F X , although the scatter is large.