The Relation between the Optical \feii Emission and the Dimensionless Accretion Rate for Active Galactic Nuclei

It was suggested that the prominent feature of the optical Fe II emission has a connection with the accretion process in active galactic nuclei (AGN). For a large sample of 4037 quasars ($z<0.8$) with measured $\mathrm{H}\beta$ line dispersion (${\sigma }_{\mathrm{H}\beta }$) selected from the Sloan Digital Sky Survey (SDSS) and 120 compiled reverberation-mapped (RM) AGN, we use ${\sigma }_{\mathrm{H}\beta }$ and the extended $R_{\mathrm{B}\mathrm{L}\mathrm{R}}-L_{5100}$ relation to calculate supermassive black holes masses ($M_{\mathrm{B}\mathrm{H}}$) from the single-epoch spectra for the SDSS subsample, and ${\sigma }_{\mathrm{H}\beta }$ from the mean spectra for the RM subsample. We find a strong correlation between the relative optical Fe II strength $R_{\mathrm{F}\mathrm{e}}$ and $\dot{\mathcal{M}}$ for the SDSS subsample with the Spearman correlation coefficient $r_s$ of $0.727$, which is consistent with that derived from the mean spectra for the RM subsample. The magnitude of velocity shift of the optical Fe II emission has a strong anticorrelation with $\dot{\mathcal{M}}$, whenever there is inflow or outflow. These strong correlations show that the optical Fe II emission has an intimate connection with the accretion process. Assuming that the difference of $M_{\mathrm{B}\mathrm{H}}$ is due to the variable virial factor $f$ for adopting $\mathrm{F}\mathrm{W}\mathrm{H}{\mathrm{M}}_{\mathrm{H}\beta }$ as the velocity tracer, we find that there is a relation between $f$ and $\mathrm{F}\mathrm{W}\mathrm{H}{\mathrm{M}}_{\mathrm{H}\beta }$, $\log f=-(0.41\pm 0.002)\log \mathrm{F}\mathrm{W}\mathrm{H}{\mathrm{M}}_{\mathrm{H}\beta }+(1.719\pm 0.009)$ for the single-epoch spectrum. The relation between $\log f$ and ${\sigma }_{\mathrm{H}\beta }$ is not too strong, suggesting that ${\sigma }_{\mathrm{H}\beta }$ does not seem to depend much on the broad-line region inclination and a constant $\sigma$-based $f$ is suitable for ${\sigma }_{\mathrm{H}\beta }$ as the velocity tracer.