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

Abstract

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 $\rm H\beta$ line dispersion ($\sigma_{\rm H\beta}$) selected from the Sloan Digital Sky Survey (SDSS) and 120 compiled reverberation-mapped (RM) AGN, we use $\sigma_{\rm H\beta}$ and the extended $R_{\rm BLR}-L_{\rm 5100}$ relation to calculate supermassive black holes masses ($M_{\rm BH}$) from the single-epoch spectra for the SDSS subsample, and $\sigma_{\rm H\beta}$ from the mean spectra for the RM subsample. We find a strong correlation between the relative optical Fe II strength $R_{\rm Fe}$ and $\dot{\mathscr{M}}$ 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 $\dot{\mathscr{M}}$, 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 $M_{\rm BH}$ is due to the variable virial factor $f$ for adopting $ \rm FWHM_{H\beta}$ as the velocity tracer, we find that there is a relation between $f$ and $\rm FWHM_{H\beta}$, $\log f=-(0.41\pm 0.002) \rm \log FWHM_{\rm H\beta}+(1.719\pm 0.009)$ for the single-epoch spectrum. The relation between $\log f$ and $\sigma_{\rm H\beta}$ is not too strong, suggesting that $\sigma_{\rm H\beta}$ does not seem to depend much on the broad-line region inclination and a constant $\sigma$-based $f$ is suitable for $\sigma_{\rm H\beta}$ as the velocity tracer.