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

With respect to the $\rm H\beta$ full width at half-maximum ($\rm FWHM_{H\beta}$), broad line dispersion ($\sigma_{\rm H\beta}$) was preferred as a velocity tracer calculate single-epoch supermassive black hole mass ($M_{\rm BH}$) suggested by \cite{Yu2020b}. For compiled sample of 311 broad-line active galactic nuclei (AGN) with measured hard X-ray photon index ($z<0.7$), $\sigma_{\rm H\beta}$ and optical Fe II relative strength ($R_{\rm Fe}$) are from their spectra, which used H\beta}$-based virial $M_{\rm BH}$ dimensionless accretion rate ($\dot{\mathscr{M}}$). FWHM_{\rm H\beta}$, it is found that mean value on average larger 0.26 dex, $\dot{\mathscr{M}}$ smaller 0.51 dex. It there exists non-linear relationship between Eddington ratio ($L_{\rm Bol}/L_{\rm Edd}$) $\dot{\mathscr{M}}$, i.e., $L_{\rm Edd} \propto \dot{\mathscr{M}}^{0.56\pm 0.01}$. This comes efficiency $\eta$, for AGN higher $\dot{\mathscr{M}}$. We find strong bivariate correlation fraction energy released in corona $F_{\rm X}$ \mbh, X} \dot{\mathscr{M}}^{-0.57\pm 0.05} M_{\rm BH}^{-0.54\pm 0.06}$. The flat slope $-0.57\pm 0.05$ favours shear stress tensor disk being proportional geometric gas pressure total pressure. relation $\Gamma$ X}$, $\Gamma \dot{\mathscr{M}}^{-0.21\pm 0.02}F_{\rm X}^{0.02\pm 0.04}$. spectrum becomes softer increasing although scatter large.