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

TL;DR

This study provides a physically grounded interpretation of the quasar main sequence (QMS) by using a 2.5D FRADO model to connect EV1 trends to the central engine. It identifies the Eddington ratio $\dot{m}$ as the primary driver of QMS structure, with black hole mass $M_{\bullet}$ and inclination $i$ contributing secondary effects through the H$\beta$ line width $\mathrm{FWHM}_{\mathrm{H}\beta}$ and Fe II strength $R_{\rm{Fe}}$. A dense FRADO grid at $Z=5Z_{\odot}$ shows that $\mathrm{FWHM}_{\mathrm{H}\beta}$ tracks $M_{\bullet}$ while $R_{\rm{Fe}}$ tracks $\dot{m}$, reproducing the observed $\mathrm{FWHM}$–$\dot{m}$ locus and the PA/PB/NLS1 distributions, and highlighting orientation as a secondary modulator. The work also discusses metallicity as a secondary factor and outlines future work to model Fe II emission and explore $Z$-related effects, aiming to provide a unified BLR-based explanation for EV1. Overall, the FRADO framework ties QMS trends to BLR physics driven by the central engine, offering a path toward a more predictive, physically grounded understanding of quasar spectral diversity.

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$β$ 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 $M_{\rm BH}$.

Figures (3)

• Figure 1: EV1 expressed with $\dot{m}$ as the proxy for $R_{\rm{Fe}}$. Points show $\mathrm{FWHM}_{\rm H\beta}$ vs. $\dot{m}$ from FRADO-driven BLR models at different inclinations, color-coded by (left) $\log M_{\bullet}$ and (right) $D_{\rm{H}\beta}$. The upper and lower horizontal axes correspond to FRADO and observational data (gray-shaded area), respectively, with no scaling relation applied between them. Green and yellow circles ($\oplus$) mark the $R_{\rm{Fe}}$-based locations of I Zw 1 Marziani2021 and NGC 5548 Dupu2019. The horizontal green dashed line marks the PA/PB boundary, and the region below the red dashed line indicates the location of NLS1 objects.
• Figure 2: Contour representation of the $\log \lambda_{\rm Edd}$--$\log R_{\rm Fe}$ plane, showing the density distribution of sources for each of the three samples. Black, blue, and red dashed lines are our best-fit linear regressions to datasets from Hu2008, Wu2022, and N+25, respectively. Slopes and intercepts are shown with their 95% confidence intervals ($\sim 2\sigma$); numbers in brackets are the RMS scatters of each sample about the respective best-fit lines. Note that $\lambda_{\rm Edd}$ and $\dot{m}$ are used interchangeably; see Appendix \ref{['sec:accretion_definition']}.
• Figure 3: Relations between $\log R_{\rm Fe}$ and $\log \lambda_{\rm Edd}$ for three different samples. Green circles show our N+25 reproduced data . Black, blue, and red dashed lines are our best-fit linear regressions to datasets from Hu2008, Wu2022, and N+25, respectively. The purple solid curve is the nonlinear prescription from dupu2016L found based on a sample of 63 RM super-Eddington quasars. Slopes and intercepts are shown with their 95% confidence intervals ($\sim 2\sigma$); numbers in brackets are the RMS scatters of each sample about the respective best-fit lines. Note that $\lambda_{\rm Edd}$ and $\dot{m}$ are used interchangeably; see Appendix \ref{['sec:accretion_definition']}.