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.