The sigma(HB)-based Dimensionless Accretion Rate and Its Connection with the Corona for AGNs

With respect to the H beta FWHM (FWHMH beta), the broad H beta line dispersion (sigma(H beta)) 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), sigma(H beta) and the optical Fe II relative strength (R-Fe) are measured from their optical spectra, which are used to calculate sigma(H beta)-based virial MBH and dimensionless accretion rate ((M)over dot). With respect to FWHMH beta, it is found that the mean value of sigma(H beta)-based M-BH is on average larger by 0.26 dex and the mean value of sigma(H beta)-based (M)over dot 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)over dot, i.e., L-Bol/E-dd proportional to (M)over dot(0.56 +/- 0.01). This nonlinear relationship comes from the accretion efficiency eta, which is smaller for AGNs with higher (M)over dot. We find a strong bivariate correlation of the fraction of energy released in the corona Fx with (M)over dot and M-BH, F-x proportional to (M)over dot(-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 Gamma with (M)over dot and F-x , Gamma proportional to (M)over dot(-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.