Letter to the Editor

Quasar main sequence unfolded by 2.5D FRADO

Natural expression of Eddington ratio, black hole mass, and inclination

¹ Institut d’Astrophysique et de Géophysique, Université de Liège, Allée du Six Août 19c, B-4000 Liège (Sart-Tilman), Belgium
² Astronomy Department, Universidad de Concepción, Barrio Universitario s/n, Concepción 4030000, Chile
³ Millennium Nucleus on Transversal Research and Technology to Explore Supermassive Black Holes (TITANs), Chile
⁴ Millennium Institute of Astrophysics (MAS), Nuncio Monseñor Sótero Sanz 100, Providencia, Santiago, Chile
⁵ National Institute for Astrophysics (INAF), Astronomical Observatory of Padua, Vicolo Osservatorio 5, IT35122 Padua, Italy
⁶ Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland

^⋆ Corresponding author: mh.naddaf@uliege.be

Received: 14 August 2025
Accepted: 28 September 2025

Abstract

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_•) 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_• 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_Fe), and vice versa. Our results suggest that ṁ can be the sole underlying physical tracer of R_Fe and should therefore scale directly with it. The M_• accounts for the virial mass–related scatter in the FWHM. The i then acts as a secondary driver modulating the R_Fe and FWHM for a given ṁ and M_•, respectively.