Dynamical Modeling of the Broad-Line Region with High-Mass Active Galactic Nuclei and Constraints on the Virial Factor

TL;DR

This study models the broad-line regions of high-mass AGNs to refine black hole mass estimates and determine the virial factor, revealing BLR geometry, kinematics, and consistency with galaxy relations.

Contribution

It provides new dynamical modeling results for high-mass AGNs, refining the virial factor and extending the mass range for accurate black hole mass estimation.

Findings

BLRs are thick disks viewed at intermediate inclinations.

The virial factor derived is consistent with the $M_{\rm BH}$-$\sigma_{\ast}$ relation.

Updated $f$ values have an intrinsic dispersion of ~0.2 dex.

Abstract

We present the results of broad-line region (BLR) dynamical modeling for eight high-mass active galactic nuclei (AGNs) from the Seoul National University AGN Monitoring Project, by constraining BLR geometry and kinematics as well as black hole (BH) mass ($M_{\rm BH}$). We find that the H$\beta$-emitting BLRs are best described as thick disks viewed at intermediate inclinations, with emission preferentially originating from the far side of the BLR. BLR kinematics show a combination of rotational, inflowing and outflowing components. By comparing the $M_{\rm BH}$ from dynamical modeling with the virial products based on reverberation lags and line widths, we determine the virial factor $f$ for individual AGNs. Combining our sample with those $M_{\rm BH}$ consistently determined from BLR dynamical modeling, yielding a total of 38 objects, we derive a virial factor for future $M_{\rm BH}$ estimation of log$_{10}({f})_{\rm pred}=0.69\pm0.21$ based on $\sigma_{\rm line,rms}$ and $-0.08\pm0.23$ based on FWHM$_{\rm mean}$. The derived virial factor is consistent with that inferred by aligning the reverberation-mapped AGNs with quiescent galaxies in the $M_{\rm BH}$-$\sigma_{\ast}$relation, supporting the assumption that local active and inactive galaxies follow the same $M_{\rm BH}$-$\sigma_{\ast}$ relation. Our updated $f$ values exhibit an intrinsic dispersion of $\sim0.2$ dex, which allows for a more precise $M_{\rm BH}$ estimates than those based on the $M_{\rm BH}$-$\sigma_{\ast}$ relation. Our sample extends the dynamical modeling-based reverberation sample to $M_{\rm BH}$ $\sim$ [$10^8$, $10^{8.5}$] $M_{\odot}$ range, where the virial factor from the the AGN $M_{\rm BH}$-$\sigma_{\ast}$ relation remains poorly constrained, underscoring the unique value of dynamical modeling analysis in constraining the $M_{\rm BH}$ of the most massive BHs.