The Radius-Luminosity Relationship Depends on Optical Spectra in Active Galactic Nuclei

The radius-luminosity (R-L) relationship of active galactic nuclei (AGNs) established by the reverberation mapping (RM) observations has been widely used as a single-epoch black hole mass estimator in the research of large AGN samples. However, the recent RM campaigns discovered that the AGNs with high accretion rates show shorter time lags by factors of a few comparing with the predictions from the R-L relationship. The explanation of the shortened time lags has not been finalized yet. We collect 8 different single-epoch spectral properties to investigate how the shortening of the time lags correlate with those properties and to understand what is the origin of the shortened lags. We find that the flux ratio between Fe II and H$\beta$ emission lines shows the most prominent correlation, thus confirm that accretion rate is the main driver for the shortened lags. In addition, we establish a new scaling relation including the relative strength of Fe II emission. This new scaling relation can provide less biased estimates of the black hole mass and accretion rate from the single-epoch spectra of AGNs.