Quasar Main Sequence unfolded by 2.5D FRADO (Natural expression of Eddington ratio, black hole mass, and inclination)

Abstract: The quasar main sequence (QMS), characterized by the Eigenvector 1 (EV1), serves as a unifying framework for classifying type-1 active galactic nuclei (AGNs) based on their diverse spectral properties. Although a fully self-consistent physical interpretation has long been lacking, our physically motivated 2.5D FRADO (Failed Radiatively Accelerated Dusty Outflow) model naturally predicts that the Eddington ratio ($\dot{m}$) is the primary physical driver of the QMS, with black hole mass ($M_{\rm BH}$) and inclination ($i$) acting as secondary contributors. We employed a dense grid of FRADO simulations of the geometry and dynamics of the broad-line region (BLR), covering a representative range of $M_{\rm BH}$ and $\dot{m}$. For each simulation, we computed the full width at half maximum (FWHM) of the H$\beta$ line under different $i$. The resulting FWHM--$\dot{m}$ diagram closely resembles the characteristic trend observed in the EV1 parameter space. This establishes the role of $\dot{m}$ as the true proxy for the Fe II strength parameter ($R_{\rm Fe}$), and vice versa. Our results suggest that $\dot{m}$ can be regarded as the sole underlying physical tracer of $R_{\rm Fe}$ and should therefore scale directly with it. The $M_{\rm BH}$ accounts for the virial mass-related scatter in FWHM, while $i$ acts as a secondary driver modulating $R_{\rm Fe}$ and FWHM for a given $\dot{m}$ and $M_{\rm BH}$.