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$_{\rm BLR}$-L$_{\rm 5100}$ relation). To realize its full
potential, the intrinsic scatter in the R$_{\rm BLR}$-L$_{\rm 5100}$ relation
needs to be understood better. 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 FeII emission which has its origin from the BLR. This
paper aims to reveal the connection between theoretical entities, like, the
ionization parameter (U) and cloud mean density (n$_{\rm H}$) of the BLR, with
physical observables obtained directly from the spectra, such as optical FeII
strength (R$_{\rm FeII}$) that has immense potential to trace the accretion
rate. We utilize the photoionization code CLOUDY and perform a suite of models
to reveal the BLR in the U-n parameter space and estimate RFeII. We compare the
SEDs for a prototypical Population A and Population B source, I Zw 1 and NGC
5548, respectively, in this study. The results from the photoionization
modelling are combined with existing reverberation mapped sources with observed
R$_{\rm FeII}$ estimates, allowing us to provide an analytical formulation to
tie together the aforementioned quantities. We utilize the comparison of the
modelled equivalent widths for the low-ionization emission lines to their
observed values to identify the optimal (U,n$_{\rm H}$). The recovery of the
correct physical conditions in the BLR suggests that the BLR `sees' a
different, filtered ionizing continuum with only a very small fraction (~1-10%)
that leads to the line emission in the dustless, low-ionization BLR.
