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Parameterizing the AGN Radius–Luminosity Relation from the Eigenvector 1 Viewpoint

The study of the broad-line region (BLR) using reverberation mapping has allowed us to establish an empirical relation between the size of this line-emitting region and the continuum luminosity that drives the line emission (i.e., the R Hβ − L5100 relation). To realize its full potential, the intrinsic scatter in the R Hβ − L5100 relation needs to be understood better. The mass accretion rate (or equivalently the Eddington ratio) plays a key role in addressing this problem. On the other hand, the Eigenvector 1 schema has helped to reveal an almost clear connection between the Eddington ratio and the strength of the optical Fe II emission that originates from the BLR. This article aims to reveal the connection between theoretical entities, such as the ionization parameter (U) and cloud mean density (nH) of the BLR, with physical observables obtained directly from the spectra, such as optical Fe II strength (R FeII ) that has shown immense potential to trace the accretion rate. We utilize the photoionization code CLOUDY and perform a suite of models to reveal the physical conditions in the low-ionization, dust-free, line-emitting BLR. The key here is the focus on the recovery of the equivalent widths (EWs) for the two low-ionization emission lines—Hβ and the optical Fe II—in addition to the ratio of their EWs, i.e., R FeII . We compare the spectral energy distributions, I Zw 1 and NGC 5548, of prototypical Population A and Population B sources, respectively, in this study. The results from the photoionization modeling are then combined with the existing reverberation-mapped sources with observed R FeII estimates taken from the literature, thus allowing us to assess our analytical formulation to tie together the aforementioned quantities. The recovery of the correct physical conditions in the BLR then suggests that—the BLR “sees” only a very small fraction (∼1–10%) of the original ionizing continuum.