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

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.