Quasar main sequence unfolded by 2.5D FRADO: Natural expression of Eddington ratio, black hole mass, and inclination

Aims. 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 it has long eluded a fully self-consistent physical interpretation, our physically motivated 2.5D failed radiatively accelerated dusty outflow (FRADO) model now naturally predicts that the Eddington ratio (ṁ) is the underlying physical primary driver of QMS, with the black hole mass (M<SUB>•</SUB>) and inclination (i) acting as secondary contributors. Methods. We recruited a dense grid of FRADO simulations of the geometry and dynamics of the broad-line region covering a representative range of M<SUB>•</SUB> and ṁ. For each simulation, we computed the full width at half maximum (FWHM) of the Hβ line under different i. Results. The resulting FWHM–ṁ diagram strikingly resembles the characteristic trend observed in the EV1 parameter space. Therefore, it establishes the role of ṁ as the true proxy for the Fe II strength parameter (R<SUB>Fe</SUB>), and vice versa. Our results suggest that ṁ can be the sole underlying physical tracer of R<SUB>Fe</SUB> and should therefore scale directly with it. The M<SUB>•</SUB> accounts for the virial mass–related scatter in the FWHM. The i then acts as a secondary driver modulating the R<SUB>Fe</SUB> and FWHM for a given ṁ and M<SUB>•</SUB>, respectively.