Scatter Analysis Along the Multidimensional Radius-Luminosity Relations
  for Reverberation-Mapped Mg II Sources
  The usage of the radius-luminosity (R-L) relation for the determination of
black hole masses across the cosmic history as well as its application for
cosmological studies motivates us to analyze its scatter, which has recently
increased significantly both for the optical (H$\beta$) and UV (Mg II) lines.
To this purpose, we determined the scatter along the R-L relation for an
up-to-date reverberation-mapped Mg II sample. Studying linear combinations of
the luminosity at 3000 A with independent parameters such as the Full Width at
Half Maximum (FWHM), Fe II strength (R$_\mathrm{FeII}$), and the fractional
variability ($F\mathrm{_{var}}$) for the whole sample, we get only a small
decrease in the scatter ($\sigma{_{\rm rms}}=0.29-0.30$ dex). Linear
combinations with the dimensionless accretion rate ($\dot{\mathcal{M}}$) and
the Eddington ratio ($\alpha_\mathrm{Edd}$) lead to significant reductions of
the scatter ($\sigma_{\rm rms}\sim 0.1$ dex), albeit both suffering from the
inter-dependency on the observed time-delay. After the division into two
sub-samples considering the median value of the $\dot{\mathcal{M}}$ in the full
sample, we find that the scatter decreases significantly for the highly
accreting sub-sample. In particular, the smallest scatter of $\sigma{_{\rm
rms}}=0.17$ dex is associated with the independent parameter R$_\mathrm{FeII}$,
followed by the combination with $F\mathrm{_{var}}$, with $\sigma{_{\rm
rms}}=0.19$ dex. Both of these independent observationally-inferred parameters
are in turn correlated with $\dot{\mathcal{M}}$ and $\alpha_\mathrm{Edd}$.
These results suggest that the large scatter along the R-L relation is driven
$\textit{mainly}$ by the accretion rate intensity.
